Finite Group Databasebeta

← #35197310

Subgroups — #35197310

Order 20224.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777474C214yesmaximal, complemented
2#23777472C214yesmaximal, complemented
3#23777434C214yesmaximal, complemented
4#23777430C214yesmaximal, complemented
5#23777363C214yesmaximal, complemented
6#23777359C214yesmaximal, complemented
7#23777346C214yesmaximal, complemented
8#23777344C214yesmaximal, complemented
9#23777254C211yesmaximal, characteristic, complemented
10#23777249C211yesmaximal, characteristic, complemented
11#23777232C214yesmaximal, complemented
12#23777201C211yesmaximal, characteristic, complemented
13#23777162C211yesmaximal, characteristic, complemented
14#23777117C212yesmaximal, complemented
15#23777086C214yesmaximal, complemented
16#23777033C212yesmaximal, complemented
17#23776816C212yesmaximal, complemented
18#23776808C214yesmaximal, complemented
19#23776790C211yesmaximal, characteristic, complemented
20#538×D79C214yesmaximal, complemented
21C4×#14579207C212yesmaximal, complemented
22C2×#19099037C211yesmaximal, characteristic, complemented
23C79×#3455C211yesmaximal, characteristic, complemented
24C2×#14579207C2212yes—
25C23×D316C2211yescharacteristic
26#19099298C2214yescomplemented
27#19099295C2214yescomplemented
28#19099287C2212yescomplemented
29#19099286C2212yescomplemented
30#19099284C2214yescomplemented
31#19099283C2214yescomplemented
32#19099279C2212yescomplemented
33#19099278C2214yescomplemented
34#19099278C2212yescomplemented
35#19099277C2214yescomplemented
36#19099274C2212yescomplemented
37#19099273C2212yescomplemented
38#19099273C2214yescomplemented
39#19099269C2214yescomplemented
40#19099266C2218yescomplemented
41#19099266C2214yescomplemented
42#19099264C2218yescomplemented
43#19099260C2214yescomplemented
44#19099259C2214yescomplemented
45#19099259C2214yescomplemented
46#19099258C2218yescomplemented
47#19099253C2214yescomplemented
48#19099247C2214yescomplemented
49#19099245C2218yescomplemented
50#19099243C2218yescomplemented
51#19099241C2218yescomplemented
52#19099240C2218yescomplemented
53#19099238C2218yescomplemented
54#19099238C2218yescomplemented
55#19099238C2218yescomplemented
56#19099235C2212yescomplemented
57#19099233C2212yescomplemented
58Q8×D316C2212yescomplemented
59#19099228C2212yescomplemented
60#19099223C2218yescomplemented
61#19099218C2212yescomplemented
62#19099217C2212yescomplemented
63#19099216C2212yescomplemented
64#19099216C2212yescomplemented
65#19099210C2218yescomplemented
66#19099209C2214yescomplemented
67#19099209C2214yescomplemented
68#19099209C2214yescomplemented
69#19099206C2214yescomplemented
70#19099206C2218yescomplemented
71#19099205C2218yescomplemented
72#19099205C2218yescomplemented
73#19099204C2214yescomplemented
74#19099204C2214yescomplemented
75#19099202C2218yescomplemented
76D4×D316C2214yescomplemented
77D4×D316C2214yescomplemented
78D4×D316C2212yescomplemented
79#19099198C2212yescomplemented
80#19099197C2214yescomplemented
81#19099197C2214yescomplemented
82#19099191C2212yescomplemented
83#19099188C2214yescomplemented
84#19099185C2214yescomplemented
85#19099184C2212yescomplemented
86#19099184C2212yescomplemented
87#19099184C2214yescomplemented
88#19099175C2212yescomplemented
89#19099168C2212yescomplemented
90#19099168C2214yescomplemented
91#19099164C2214yescomplemented
92#19099161C2218yescomplemented
93#19099160C2212yescomplemented
94#19099160C2212yescomplemented
95#19099159C2218yescomplemented
96#19099153C2214yescomplemented
97#19099152C2218yescomplemented
98#19099152C2218yescomplemented
99#19099151C2212yescomplemented
100#19099151C2212yescomplemented
101#19099150C2214yescomplemented
102#19099149C2218yescomplemented
103#19099149C2218yescomplemented
104#19099148C2218yescomplemented
105#19099147C2218yescomplemented
106#19099146C2218yescomplemented
107#19099145C2218yescomplemented
108#19099141C2212yescomplemented
109#19099132C2212yescomplemented
110#19099127C2212yescomplemented
111#19099124C2218yescomplemented
112#19099121C2214yescomplemented
113#19099120C2211yescharacteristic, complemented
114#19099113C2211yescharacteristic, complemented
115#19099113C2214yescomplemented
116#19099110C2214yescomplemented
117#19099100C2214yescomplemented
118#19099098C2218yescomplemented
119#19099097C2214yescomplemented
120#19099096C2218yescomplemented
121#19099091C2214yescomplemented
122#19099091C2214yescomplemented
123#19099090C2218yescomplemented
124#126×D79C2218yescomplemented
125#124×D79C2218yescomplemented
126#19099076C2214yescomplemented
127#19099076C2218yescomplemented
128#19099074C2212yescomplemented
129#19099073C2214yescomplemented
130#19099072C2218yescomplemented
131#19099071C2218yescomplemented
132#123×D79C2218yescomplemented
133C22⋊Q8×D79C2214yescomplemented
134#121×D79C2218yescomplemented
135#121×D79C2214yescomplemented
136#120×D79C2218yescomplemented
137#19099046C2212yescomplemented
138#19099045C2214yescomplemented
139#19099043C2212yescomplemented
140#19099043C2214yescomplemented
141#19099037C2212yes—
142#19099037C2214yescomplemented
143#19099037C2214yescomplemented
144#19099037C2214yescomplemented
145#19099037C2214yescomplemented
146#19099037C2214yescomplemented
147#19099035C2218yescomplemented
148#19099035C2214yescomplemented
149C4×#11929625C2214yescomplemented
150C4×#11929624C2212yescomplemented
151C4×#11929624C2214yescomplemented
152C2×C4×D316C2211yescharacteristic
153C2×C4×D316C2211yescharacteristic
154C2×C4×D316C2211yescharacteristic, complemented
155C2×C4×D316C2211yescharacteristic, complemented
156C2×C4×D316C2214yescomplemented
157C2×#14579123C2212yescomplemented
158C2×#14579123C2212yescomplemented
159C4×D4×D79C2218yescomplemented
160C4×D4×D79C2214yescomplemented
161C2×#14579120C2211yescharacteristic, complemented
162C2×C22⋊C4×D79C2212yescomplemented
163C2×C22⋊C4×D79C2212yescomplemented
164#542×C79C2212yescomplemented
165#542×C79C2212yescomplemented
166#541×C79C2212yescomplemented
167#540×C79C2212yescomplemented
168#539×C79C2212yescomplemented
169#539×C79C2212yescomplemented
170#538×C79C2212yescomplemented
171#538×C79C2212yescomplemented
172#533×C79C2211yescharacteristic, complemented
173#532×C79C2211yescharacteristic, complemented
174#529×C79C2214yescomplemented
175#529×C79C2214yescomplemented
176#525×C79C2212yescomplemented
177C4×#41×C79C2212yescomplemented
178C2×#117×C79C2211yescharacteristic, complemented
179C24×D79C2312yes—
180#14579207—216no—
181C2×#11929625C2314yes—
182C2×#11929625C2314yescomplemented
183C2×#11929624C2312yes—
184C2×#11929624C2314yes—
185C2×#11929624C2318yescomplemented
186C2×#11929623C2314yescomplemented
187C2×Q8×D79C2314yescomplemented
188C22×D316—28no—
189C22×D316C2314yes—
190C22×D316C2314yes—
191C22×D316C2314yes—
192C22×D316C2312yes—
193C22×D316C2311yescharacteristic
194C22×D316C2311yescharacteristic
195C2×D4×D79C2314yes—
196C2×D4×D79C2318yes—
197C2×D4×D79C2318yes—
198C2×D4×D79C2318yes—
199C2×D4×D79C2314yescomplemented
200C22×C4×D79C2312yes—
201C22×C4×D79C2312yes—
202C22×C4×D79C2312yes—
203C22×C4×D79C2312yes—
204C22×C4×D79C2318yescomplemented
205#14579161C2311yescharacteristic, complemented
206#14579161C2311yescharacteristic, complemented
207#14579161C2311yescharacteristic, complemented
208#14579161C2314yescomplemented
209#14579160C2314yescomplemented
210#14579158C2314yes—
211#14579158C2311yescharacteristic, complemented
212#14579157C2314yes—
213#14579156C2318yescomplemented
214#14579156C2318yescomplemented
215#14579156C2314yescomplemented
216#14579156C2318yescomplemented
217#14579156C2318yescomplemented
218#14579156C2314yescomplemented
219#14579155C2318yescomplemented
220#14579154C2314yes—
221#14579154C2318yes—
222#14579154C2318yes—
223#14579154C2314yes—
224#14579154C2318yescomplemented
225#14579153C2312yescomplemented
226#14579153C2314yescomplemented
227#14579152C2314yescomplemented
228#14579151C2314yescomplemented
229#14579151C2318yescomplemented
230#14579151C2314yescomplemented
231#14579150C2314yes—
232#14579150C2318yescomplemented
233#14579149C2314yes—
234#14579149C2318yescomplemented
235#14579149C2312yescomplemented
236#14579148C2318yes—
237#14579147C2318yes—
238#14579147C2314yes—
239#14579147C2314yes—
240#14579147C2318yescomplemented
241#14579147C2318yescomplemented
242#14579147C2318yescomplemented
243#14579146C2318yes—
244#14579146C2318yes—
245#14579146C2318yescomplemented
246#14579146C2318yescomplemented
247#14579146C2318yescomplemented
248#14579146C2314yescomplemented
249#14579146C2314yescomplemented
250#14579146C2318yescomplemented
251#14579146C2318yescomplemented
252#14579145C2318yescomplemented
253#14579144C2314yes—
254#14579144C2318yescomplemented
255#14579143C2314yes—
256#14579143C2318yes—
257#14579143C2314yes—
258#14579143C2318yescomplemented
259#14579143C2318yescomplemented
260#14579143C2318yescomplemented
261#14579142C2318yes—
262#14579141C2314yescomplemented
263#14579141C2318yescomplemented
264#14579141C2314yescomplemented
265#14579140C2312yes—
266#14579140C2312yes—
267#14579140C2312yes—
268#14579140C2312yes—
269#14579140C2314yescomplemented
270#14579139C2318yescomplemented
271#14579139C2318yescomplemented
272#14579139C2314yescomplemented
273#14579139C2314yescomplemented
274#14579139C2318yescomplemented
275#14579139C2318yescomplemented
276#14579138C2318yes—
277#14579137C2314yescomplemented
278#14579137C2314yescomplemented
279#14579137C2314yescomplemented
280#14579137C2318yescomplemented
281#14579136C2318yes—
282#14579136C2318yes—
283#14579136C2314yes—
284#14579136C2314yes—
285#14579136C2314yescomplemented
286#14579136C2314yescomplemented
287#14579136C2318yescomplemented
288#14579135C2312yes—
289#14579135C2312yes—
290#14579135C2312yes—
291#14579135C2312yes—
292#14579135C2314yes—
293#14579135C2314yes—
294#14579135C2314yescomplemented
295#14579135C2318yescomplemented
296#14579134C2318yes—
297#14579134C2314yes—
298#14579134C2314yes—
299#14579134C2318yes—
300#14579134C2318yescomplemented
301#14579134C2318yescomplemented
302#14579134C2318yescomplemented
303#14579133C2318yes—
304#14579133C2318yes—
305#14579133C2318yescomplemented
306#14579132C2318yes—
307#14579132C2314yescomplemented
308#14579132C2314yescomplemented
309#14579132C2314yescomplemented
310#14579131C2318yes—
311#14579131C2318yes—
312#14579131C2318yes—
313#14579131C2318yes—
314#14579131C2318yes—
315#14579131C2318yescomplemented
316#14579130C2314yes—
317#14579129C2318yes—
318#14579129C2318yes—
319#14579129C2318yes—
320#14579129C2318yescomplemented
321Q8×Dic79C2314yescomplemented
322C4×Dic158C2312yescomplemented
323C4×Dic158C2312yescomplemented
324C4×Dic158C2312yescomplemented
325C4×Dic158C2312yescomplemented
326C4×Dic158C2314yescomplemented
327#14579126C2318yescomplemented
328C4×D316C2314yes—
329C4×D316C2314yes—
330C4×D316C2312yes—
331C4×D316C2314yes—
332C4×D316C2314yes—
333C4×D316C2312yes—
334C4×D316C2312yes—
335C4×D316C2312yes—
336C4×D316C2312yes—
337C4×D316C2312yes—
338C4×D316C2312yes—
339C4×D316C2312yes—
340C4×D316C2314yes—
341C4×D316C2314yes—
342C4×D316C2318yescomplemented
343C4×D316C2312yescomplemented
344C4×D316C2312yescomplemented
345C4×D316C2312yescomplemented
346C4×D316C2312yescomplemented
347C4×D316C2318yescomplemented
348C4×D316C2318yescomplemented
349C4×D316C2314yescomplemented
350D4×Dic79C2318yes—
351D4×Dic79C2314yescomplemented
352#14579123C2318yes—
353#14579123C2318yes—
354#14579123C2314yes—
355#14579123C2314yes—
356#14579123C2318yes—
357#14579123C2318yes—
358#14579123C2318yescomplemented
359#14579123C2318yescomplemented
360#14579123C2318yescomplemented
361C4×C22⋊D79C2314yes—
362C4×C22⋊D79C2314yes—
363C4×C22⋊D79C2314yes—
364C4×C22⋊D79C2314yes—
365C4×C22⋊D79C2318yescomplemented
366C4×C22⋊D79C2318yescomplemented
367C4×C22⋊D79C2318yescomplemented
368(C22⋊D79)⋊C4C2318yes—
369(C22⋊D79)⋊C4C2318yescomplemented
370(C22⋊D79)⋊C4C2318yescomplemented
371(C22⋊D79)⋊C4C2318yescomplemented
372(C22⋊D79)⋊C4C2318yescomplemented
373#14579120C2312yes—
374#14579120C2314yes—
375#14579120C2314yes—
376#14579120C2314yescomplemented
377#14579119C2314yescomplemented
378#14579119C2318yescomplemented
379#14579119C2318yescomplemented
380#14579119C2314yescomplemented
381#14579119C2314yescomplemented
382#14579118C2314yescomplemented
383#14579118C2318yescomplemented
384#14579118C2318yescomplemented
385#14579117C2318yescomplemented
386C2×C4⋊Dic79C2311yescharacteristic
387C2×C4⋊Dic79C2311yescharacteristic
388C2×C4⋊Dic79C2314yescomplemented
389C4⋊C4×D79C2318yescomplemented
390C4⋊C4×D79C2314yescomplemented
391C4⋊C4×D79C2314yescomplemented
392C4⋊C4×D79C2318yescomplemented
393C4⋊C4×D79C2314yescomplemented
394C2×C22⋊Dic79C2312yes—
395C2×(C2×D79)⋊C4C2312yes—
396C2×(C2×D79)⋊C4C2312yes—
397C2×(C2×D79)⋊C4C2312yes—
398C2×(C2×D79)⋊C4C2312yes—
399C2×(C2×D79)⋊C4C2318yescomplemented
400C22⋊C4×D79C2318yes—
401C22⋊C4×D79C2318yes—
402C22⋊C4×D79C2318yes—
403C22⋊C4×D79C2318yes—
404C22⋊C4×D79C2318yes—
405C22⋊C4×D79C2318yes—
406C22⋊C4×D79C2318yes—
407C22⋊C4×D79C2318yescomplemented
408C22⋊C4×D79C2318yescomplemented
409C22⋊C4×D79C2318yescomplemented
410C2×C4×Dic79C2312yes—
411C42×D79C2318yescomplemented
412C42×D79C2314yescomplemented
413C2×#41×C79C2312yes—
414C23×C4×C79C2311yescharacteristic
415C4⋊Q8×C79C2311yescharacteristic, complemented
416C4⋊Q8×C79C2311yescharacteristic, complemented
417C4⋊Q8×C79C2311yescharacteristic, complemented
418#127×C79C2311yescharacteristic, complemented
419#126×C79C2314yes—
420#126×C79C2314yes—
421#126×C79C2314yescomplemented
422#126×C79C2314yescomplemented
423#125×C79C2314yescomplemented
424#125×C79C2314yescomplemented
425#125×C79C2312yescomplemented
426#124×C79C2314yes—
427#124×C79C2314yes—
428#124×C79C2312yescomplemented
429#123×C79C2314yes—
430#123×C79C2314yes—
431#123×C79C2314yes—
432#123×C79C2314yescomplemented
433#123×C79C2314yescomplemented
434C22⋊Q8×C79C2312yes—
435C22⋊Q8×C79C2312yes—
436C22⋊Q8×C79C2312yes—
437C22⋊Q8×C79C2312yes—
438C22⋊Q8×C79C2314yescomplemented
439C22⋊Q8×C79C2314yescomplemented
440#121×C79C2314yes—
441#121×C79C2312yes—
442#121×C79C2312yes—
443#121×C79C2312yes—
444#121×C79C2314yes—
445#121×C79C2312yes—
446#120×C79C2314yes—
447C4×Q8×C79C2312yescomplemented
448C4×Q8×C79C2312yescomplemented
449C4×Q8×C79C2312yescomplemented
450C4×Q8×C79C2312yescomplemented
451C4×D4×C79C2314yes—
452C4×D4×C79C2314yes—
453C4×D4×C79C2314yes—
454C4×D4×C79C2314yes—
455C4×D4×C79C2312yescomplemented
456C4×D4×C79C2312yescomplemented
457C4×D4×C79C2312yescomplemented
458C4×D4×C79C2312yescomplemented
459#117×C79C2312yes—
460#117×C79C2312yes—
461#117×C79C2312yes—
462#117×C79C2312yes—
463#117×C79C2312yes—
464#117×C79C2314yescomplemented
465C2×C4⋊C4×C79C2311yescharacteristic
466C2×C4⋊C4×C79C2311yescharacteristic
467C2×C22⋊C4×C79C2311yescharacteristic
468C2×C22⋊C4×C79C2311yescharacteristic
469C2×C42×C79C2311yescharacteristic
470C2×C42×C79C2311yescharacteristic
471C2×C42×C79C2314yescomplemented
472C23×D79—28no—
473C23×D79—82no—
474C23×D79—82no—
475C23×D79C2418yes—
476C23×D79C2412yes—
477C23×D79C2418yes—
478C23×D79C2412yes—
479#11929625—216no—
480#11929625—84no—
481#11929624—216no—
482#11929624—28no—
483#11929624—88no—
484#11929623—84no—
485C2×Dic158C2412yes—
486C2×Dic158C2412yes—
487C2×Dic158C2418yes—
488C2×Dic158C2412yes—
489Q8×D79—84no—
490C2×D316—216no—
491C2×D316—216no—
492C2×D316—216no—
493C2×D316—28no—
494C2×D316—24no—
495C2×D316#4118yescomplemented
496C2×D316C2412yes—
497C2×D316C2418yes—
498C2×D316C2418yes—
499C2×D316C2412yes—
500C2×D316C2412yes—
501C2×D316C2418yes—
502C2×D316C2412yes—
503C2×D316C2418yes—
504C2×D316C2412yes—
505C2×D316C2412yes—
506C2×D316C2412yes—
507C2×C22⋊D79C2414yes—
508C2×C22⋊D79C2418yes—
509C2×C22⋊D79C2418yes—
510C2×C22⋊D79C2418yes—
511C2×C22⋊D79C2418yes—
512C2×C22⋊D79C2414yes—
513C2×C22⋊D79C2414yes—
514D4×D79—216no—
515D4×D79—232no—
516D4×D79—88no—
517D4×D79—88no—
518D4×D79—84no—
519C22×Dic79C2418yes—
520C22×Dic79C2412yes—
521C22×Dic79C2412yes—
522C2×C4×D79—82no—
523C2×C4×D79—82no—
524C2×C4×D79—82no—
525C2×C4×D79—82no—
526C2×C4×D79—88no—
527C2×C4×D79C2418yes—
528C2×C4×D79C2414yes—
529C2×C4×D79C2418yes—
530C2×C4×D79C2414yes—
531C2×C4×D79C2414yes—
532C2×C4×D79C2414yes—
533C2×C4×D79C2418yes—
534C2×C4×D79C2414yes—
535C2×C4×D79C2418yes—
536C2×C4×D79C2418yes—
537C2×C4×D79C2414yes—
538C2×C4×D79C2418yes—
539C2×C4×D79C2414yes—
540C4⋊Dic79C2412yes—
541C4⋊Dic79C2412yes—
542C4⋊Dic79C2412yes—
543C4⋊Dic79C2418yes—
544C4⋊Dic79C2418yes—
545C4⋊Dic79C2412yes—
546C4⋊Dic79C2412yes—
547C4⋊Dic79C2412yes—
548C4⋊Dic79C2412yes—
549C4⋊Dic79C2412yes—
550C4⋊Dic79C2412yes—
551C4⋊Dic79C2412yes—
552Dic79⋊C4C2418yes—
553Dic79⋊C4C2414yes—
554Dic79⋊C4C2414yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2418yes—
557Dic79⋊C4C2418yes—
558Dic79⋊C4C2414yes—
559Dic79⋊C4C2414yes—
560Dic79⋊C4C2414yes—
561Dic79⋊C4C2414yes—
562C22⋊Dic79C2418yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2414yes—
565C22⋊Dic79C2414yes—
566C22⋊Dic79C2418yes—
567C22⋊Dic79C2418yes—
568(C2×D79)⋊C4C2418yes—
569(C2×D79)⋊C4C2414yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2414yes—
572(C2×D79)⋊C4C2418yes—
573(C2×D79)⋊C4C2414yes—
574(C2×D79)⋊C4C2418yes—
575(C2×D79)⋊C4C2418yes—
576(C2×D79)⋊C4C2418yes—
577(C2×D79)⋊C4C2418yes—
578(C2×D79)⋊C4C2418yes—
579(C2×D79)⋊C4C2418yes—
580(C2×D79)⋊C4C2414yes—
581(C2×D79)⋊C4C2414yes—
582(C2×D79)⋊C4C2418yes—
583(C2×D79)⋊C4C2418yes—
584(C2×D79)⋊C4C2414yes—
585(C2×D79)⋊C4C2414yes—
586(C2×D79)⋊C4C2414yes—
587(C2×D79)⋊C4C2414yes—
588C4×Dic79C2414yes—
589C4×Dic79C2418yes—
590C4×Dic79C2414yes—
591C4×Dic79C2418yes—
592C4×Dic79C2414yes—
593C4×Dic79C2418yes—
594C24×C79C2411yescharacteristic
595#41×C79—28no—
596C2×Q8×C79C2412yes—
597C2×Q8×C79C2412yes—
598C2×Q8×C79C2412yes—
599C2×D4×C79C2414yes—
600C2×D4×C79C2412yes—
601C2×D4×C79C2412yes—
602C2×D4×C79C2414yes—
603C2×D4×C79C2414yes—
604C2×D4×C79C2412yes—
605C22×C4×C79—24no—
606C22×C4×C79C2414yes—
607C22×C4×C79C2411yescharacteristic
608C22×C4×C79C2412yes—
609C22×C4×C79C2412yes—
610C22×C4×C79C2414yes—
611C22×C4×C79C2411yescharacteristic
612C22×C4×C79C2411yescharacteristic
613C22×C4×C79C2411yescharacteristic
614C22×C4×C79C2411yescharacteristic
615C22×C4×C79C2414yes—
616C22×C4×C79C2411yescharacteristic
617C4⋊C4×C79C2412yes—
618C4⋊C4×C79C2412yes—
619C4⋊C4×C79C2412yes—
620C4⋊C4×C79C2412yes—
621C4⋊C4×C79C2412yes—
622C4⋊C4×C79C2412yes—
623C4⋊C4×C79C2414yes—
624C4⋊C4×C79C2414yes—
625C4⋊C4×C79C2414yes—
626C4⋊C4×C79C2414yes—
627C4⋊C4×C79C2412yes—
628C4⋊C4×C79C2412yes—
629C4⋊C4×C79C2414yes—
630C4⋊C4×C79C2414yes—
631C4⋊C4×C79C2412yes—
632C4⋊C4×C79C2412yes—
633C22⋊C4×C79C2412yes—
634C22⋊C4×C79C2412yes—
635C22⋊C4×C79C2412yes—
636C22⋊C4×C79C2412yes—
637C22⋊C4×C79C2414yes—
638C22⋊C4×C79C2414yes—
639C22⋊C4×C79C2414yes—
640C22⋊C4×C79C2414yes—
641C22⋊C4×C79C2414yes—
642C22⋊C4×C79C2414yes—
643C22⋊C4×C79C2414yes—
644C22⋊C4×C79C2414yes—
645C22⋊C4×C79C2414yes—
646C42×C79C2412yes—
647C42×C79C2412yes—
648C42×C79C2411yescharacteristic
649C42×C79C2411yescharacteristic
650C42×C79C2411yescharacteristic
651C42×C79C2411yescharacteristic
652C42×C79C2414yes—
653C42×C79C2414yes—
654C42×C79C2414yes—
655C23×C79—22no—
656C23×C79—41no—
657C23×C79—41no—
658C23×C79C2512yes—
659C23×C79C2514yes—
660C23×C79C2511yescharacteristic
661C22×D79—24no—
662C22×D79—216no—
663C22×D79—216no—
664C22×D79—42no—
665C22×D79—42no—
666C22×D79—42no—
667C22×D79—42no—
668C22×D79—48no—
669C22×D79—48no—
670C22×D79—48no—
671C22×D79—48no—
672C22×D79—816no—
673C22×D79C2×#4118yes—
674C22×D79C2514yes—
675C22×D79C2514yes—
676C22×D79C2514yes—
677Q8×C79—24no—
678Q8×C79—42no—
679Q8×C79—42no—
680D4×C79—28no—
681D4×C79—24no—
682D4×C79—42no—
683D4×C79—44no—
684D4×C79—44no—
685D4×C79—42no—
686C2×C4×C79—22no—
687C2×C4×C79—24no—
688C2×C4×C79—24no—
689C2×C4×C79—28no—
690C2×C4×C79—41no—
691C2×C4×C79—41no—
692C2×C4×C79—44no—
693C2×C4×C79—41no—
694C2×C4×C79—41no—
695C2×C4×C79—44no—
696C2×C4×C79C2×#4114yes—
697C2×C4×C79C2512yes—
698C2×C4×C79C2514yes—
699C2×C4×C79C2512yes—
700C2×C4×C79C2512yes—
701C2×C4×C79C2514yes—
702C2×C4×C79C2511yescharacteristic
703C2×C4×C79C2511yescharacteristic
704C2×C4×C79C2511yescharacteristic
705C2×C4×C79C2514yes—
706C2×C4×C79C2511yescharacteristic
707C2×C4×C79C2511yescharacteristic
708C2×C4×C79C2511yescharacteristic
709C22⋊D79—28no—
710C22⋊D79—216no—
711C22⋊D79—44no—
712C22⋊D79—44no—
713C22⋊D79—48no—
714C22⋊D79—48no—
715C22⋊D79—48no—
716C2×Dic79—42no—
717C2×Dic79—42no—
718C2×Dic79—48no—
719C2×Dic79C2514yes—
720C2×Dic79C2514yes—
721C2×Dic79C2514yes—
722C2×Dic79C2514yes—
723C2×Dic79C2514yes—
724D316—216no—
725D316—216no—
726D316—24no—
727D316—24no—
728D316—24no—
729D316—42no—
730D316—48no—
731D316—48no—
732D316—42no—
733D316C2×#4118yes—
734D316C2×#4118yes—
735C4×D79—216no—
736C4×D79—28no—
737C4×D79—44no—
738C4×D79—48no—
739C4×D79—48no—
740C4×D79—44no—
741C4×D79—44no—
742C4×D79—44no—
743C4×D79—48no—
744C4×D79—48no—
745C4×D79—44no—
746C4×D79—48no—
747C4×D79—44no—
748Dic158—24no—
749Dic158—42no—
750Dic158—48no—
751Dic158—42no—
752C22×C79—21no—
753C22×C79—21no—
754C22×C79—24no—
755C22×C79—22no—
756C22×C79—24no—
757C22×C79—24no—
758C22×C79—22no—
759C22×C79—22no—
760C22×C79—44no—
761C22×C79C22×#4112yes—
762C22×C79C2611yescharacteristic
763C2×D79—24no—
764C2×D79—24no—
765C2×D79—24no—
766C2×D79—24no—
767C2×D79—24no—
768C2×D79—24no—
769C2×D79—24no—
770C2×D79—24no—
771C2×D79—48no—
772C2×D79—48no—
773C2×D79—816no—
774C2×D79—816no—
775C2×D79C22×#4118yes—
776C4×C79—22no—
777C4×C79—24no—
778C4×C79—22no—
779C4×C79—22no—
780C4×C79—21no—
781C4×C79—21no—
782C4×C79—24no—
783C4×C79—24no—
784C4×C79—21no—
785C4×C79—21no—
786C4×C79C22×#4112yes—
787C4×C79C22×#4112yes—
788Dic79—24no—
789Dic79—24no—
790Dic79—24no—
791Dic79—24no—
792Dic79—24no—
793#62846—791nomaximal, Sylow
794C2×C79—22no—
795C2×C79—42no—
796C2×C79—44no—
797C2×C79C23×#4111yescharacteristic
798C2×C79H(7,𝔽2)11yescharacteristic
799C2×C79H(7,𝔽2)11yescharacteristic
800D79—28no—
801D79—44no—
802D79—44no—
803#3521—794no—
804#3521—794no—
805#3519—794no—
806#3519—794no—
807#3514—794no—
808#3514—794no—
809#3513—794no—
810#3513—794no—
811#3506—791no—
812#3506—791no—
813#3505—794no—
814#3501—791no—
815#3496—791no—
816#3493—792no—
817#3490—794no—
818#3484—792no—
819#3460—792no—
820#3459—794no—
821#3455—791no—
822#3455D7911yescharacteristic, complemented
823C2×#538—794no—
824C4×H(5,𝔽2)—792no—
825C2×#518—791no—
826C79#6284611yescharacteristic, complemented, Sylow
827C2×H(5,𝔽2)—792no—
828C23×D4—791no—
829#559—794no—
830#559—794no—
831#556—792no—
832#556—794no—
833#556—792no—
834#556—794no—
835#555—792no—
836#555—794no—
837#555—794no—
838#555—792no—
839#554—792no—
840#554—794no—
841#554—792no—
842#554—794no—
843#553—798no—
844#553—798no—
845#553—794no—
846#553—798no—
847#553—794no—
848#553—794no—
849#553—794no—
850#552—798no—
851#552—794no—
852#552—794no—
853#551—798no—
854#551—798no—
855#551—798no—
856#551—798no—
857#551—798no—
858#551—798no—
859#550—792no—
860#550—792no—
861D4×Q8—792no—
862D4×Q8—792no—
863#548—798no—
864#547—792no—
865#547—792no—
866#547—792no—
867#547—792no—
868#546—798no—
869#546—794no—
870#546—798no—
871#546—798no—
872#546—794no—
873#546—794no—
874#546—798no—
875#546—798no—
876#546—794no—
877#546—794no—
878#546—794no—
879D42—792no—
880D42—794no—
881D42—794no—
882D42—794no—
883D42—794no—
884D42—792no—
885#544—792no—
886#543—794no—
887#542—794no—
888#542—792no—
889#542—792no—
890#542—794no—
891#542C2×D7912yescomplemented
892#542C2×D7912yescomplemented
893#541—792no—
894#541C2×D7912yescomplemented
895#540—794no—
896#540—792no—
897#540—794no—
898#540C2×D7912yescomplemented
899#539—798no—
900#539—798no—
901#539—792no—
902#539—792no—
903#539C2×D7912yescomplemented
904#539C2×D7912yescomplemented
905#538—798no—
906#538—798no—
907#538—798no—
908#538—798no—
909#538—798no—
910#538—794no—
911#538—798no—
912#538—794no—
913#538—798no—
914#538—798no—
915#538—792no—
916#538—792no—
917#538C2×D7912yescomplemented
918#538C2×D7912yescomplemented
919#537—792no—
920#535—792no—
921#535—792no—
922#534—798no—
923#534—794no—
924#533—791no—
925#533C2×D7911yescharacteristic, complemented
926#532—794no—
927#532—791no—
928#532—794no—
929#532C2×D7911yescharacteristic, complemented
930#529—798no—
931#529—798no—
932#529—798no—
933#529—794no—
934#529—794no—
935#529—794no—
936#529—794no—
937#529C2×D7914yescomplemented
938#529C2×D7914yescomplemented
939C2×#126—798no—
940C2×#124—798no—
941#525—792no—
942#525—798no—
943#525—794no—
944#525—798no—
945#525—794no—
946#525—798no—
947#525C2×D7912yescomplemented
948C2×#123—798no—
949C2×C22⋊Q8—794no—
950C2×#121—794no—
951C2×#121—798no—
952C2×#120—798no—
953#520—792no—
954#520—794no—
955#520—792no—
956#520—794no—
957#518—798no—
958#518—794no—
959#518—794no—
960#518—794no—
961#518—794no—
962#518—794no—
963#518—792no—
964#518—794no—
965C4×#41—794no—
966C4×#41—792no—
967C4×#41—794no—
968C4×#41C2×D7912yescomplemented
969C2×C4×D4—798no—
970C2×C4×D4—794no—
971C2×C4×D4—792no—
972C2×C4×D4—792no—
973C2×C4×D4—791no—
974C2×C4×D4—791no—
975C2×C4×D4—791no—
976C2×C4×D4—791no—
977C2×C4×D4—794no—
978C2×#117—791no—
979C2×#117C2×D7911yescharacteristic, complemented
980C22×C22⋊C4—792no—
981C22×C22⋊C4—792no—
982C25—792no—
983H(5,𝔽2)—15816no—
984C2×#41—794no—
985C2×#41—794no—
986C2×#41—794no—
987C2×#41—798no—
988C2×#41—792no—
989C2×#41—794no—
990C2×#41C22×D7912yes—
991C22×Q8—794no—
992C22×D4—798no—
993C22×D4—798no—
994C22×D4—794no—
995C22×D4—798no—
996C22×D4—794no—
997C22×D4—791no—
998C22×D4—792no—
999C22×D4—791no—
1000C22×D4—794no—
1001C22×D4—794no—
1002C22×D4—794no—
1003C22×D4—1588no—
1004C23×C4—792no—
1005C23×C4—792no—
1006C23×C4—792no—
1007C23×C4—792no—
1008C23×C4—798no—
1009C23×C4C22×D7911yescharacteristic
1010C4⋊Q8—794no—
1011C4⋊Q8—791no—
1012C4⋊Q8—794no—
1013C4⋊Q8—791no—
1014C4⋊Q8—791no—
1015C4⋊Q8C22×D7911yescharacteristic, complemented
1016C4⋊Q8C22×D7911yescharacteristic, complemented
1017C4⋊Q8C22×D7911yescharacteristic, complemented
1018#127—794no—
1019#127—794no—
1020#127—791no—
1021#127C22×D7911yescharacteristic, complemented
1022#126—798no—
1023#126—798no—
1024#126—798no—
1025#126—794no—
1026#126—798no—
1027#126—794no—
1028#126—794no—
1029#126—798no—
1030#126—798no—
1031#126—798no—
1032#126—794no—
1033#126—798no—
1034#126C22×D7914yes—
1035#126C22×D7914yes—
1036#126C22×D7914yescomplemented
1037#126C22×D7914yescomplemented
1038#125—794no—
1039#125—798no—
1040#125—794no—
1041#125—794no—
1042#125—794no—
1043#125—792no—
1044#125C22×D7914yescomplemented
1045#125C22×D7914yescomplemented
1046#125C22×D7912yescomplemented
1047#124—798no—
1048#124—794no—
1049#124—798no—
1050#124—794no—
1051#124—798no—
1052#124—798no—
1053#124—798no—
1054#124—798no—
1055#124—794no—
1056#124—798no—
1057#124—794no—
1058#124—792no—
1059#124C22×D7914yes—
1060#124C22×D7914yes—
1061#124C22×D7912yescomplemented
1062#123—798no—
1063#123—798no—
1064#123—794no—
1065#123—798no—
1066#123—798no—
1067#123—794no—
1068#123—798no—
1069#123—798no—
1070#123—798no—
1071#123—798no—
1072#123—798no—
1073#123—794no—
1074#123—794no—
1075#123—798no—
1076#123—798no—
1077#123—798no—
1078#123—798no—
1079#123—798no—
1080#123—794no—
1081#123C22×D7914yes—
1082#123C22×D7914yes—
1083#123C22×D7914yes—
1084#123C22×D7914yescomplemented
1085#123C22×D7914yescomplemented
1086C22⋊Q8—794no—
1087C22⋊Q8—794no—
1088C22⋊Q8—798no—
1089C22⋊Q8—794no—
1090C22⋊Q8—792no—
1091C22⋊Q8—792no—
1092C22⋊Q8—792no—
1093C22⋊Q8—792no—
1094C22⋊Q8—794no—
1095C22⋊Q8—798no—
1096C22⋊Q8—794no—
1097C22⋊Q8—794no—
1098C22⋊Q8—794no—
1099C22⋊Q8—798no—
1100C22⋊Q8—798no—
1101C22⋊Q8—798no—
1102C22⋊Q8—798no—
1103C22⋊Q8—794no—
1104C22⋊Q8—798no—
1105C22⋊Q8C22×D7912yes—
1106C22⋊Q8C22×D7912yes—
1107C22⋊Q8C22×D7912yes—
1108C22⋊Q8C22×D7912yes—
1109C22⋊Q8C22×D7914yescomplemented
1110C22⋊Q8C22×D7914yescomplemented
1111#121—798no—
1112#121—794no—
1113#121—798no—
1114#121—798no—
1115#121—798no—
1116#121—794no—
1117#121—794no—
1118#121—792no—
1119#121—798no—
1120#121—792no—
1121#121—792no—
1122#121—792no—
1123#121—794no—
1124#121—794no—
1125#121—794no—
1126#121—794no—
1127#121—798no—
1128#121—798no—
1129#121—794no—
1130#121—798no—
1131#121—794no—
1132#121—794no—
1133#121—794no—
1134#121—798no—
1135#121—798no—
1136#121—798no—
1137#121—798no—
1138#121—798no—
1139#121—794no—
1140#121C22×D7914yes—
1141#121C22×D7912yes—
1142#121C22×D7912yes—
1143#121C22×D7912yes—
1144#121C22×D7912yes—
1145#121C22×D7914yes—
1146#120—794no—
1147#120—798no—
1148#120—798no—
1149#120—798no—
1150#120—798no—
1151#120—798no—
1152#120—798no—
1153#120—798no—
1154#120—798no—
1155#120—798no—
1156#120—798no—
1157#120C22×D7914yes—
1158C4×Q8—794no—
1159C4×Q8—798no—
1160C4×Q8—792no—
1161C4×Q8—792no—
1162C4×Q8—794no—
1163C4×Q8—792no—
1164C4×Q8—792no—
1165C4×Q8C22×D7912yescomplemented
1166C4×Q8C22×D7912yescomplemented
1167C4×Q8C22×D7912yescomplemented
1168C4×Q8C22×D7912yescomplemented
1169C4×D4—798no—
1170C4×D4—794no—
1171C4×D4—794no—
1172C4×D4—798no—
1173C4×D4—794no—
1174C4×D4—798no—
1175C4×D4—794no—
1176C4×D4—794no—
1177C4×D4—798no—
1178C4×D4—798no—
1179C4×D4—798no—
1180C4×D4—798no—
1181C4×D4—798no—
1182C4×D4—798no—
1183C4×D4—794no—
1184C4×D4—794no—
1185C4×D4—798no—
1186C4×D4—798no—
1187C4×D4—798no—
1188C4×D4—798no—
1189C4×D4—798no—
1190C4×D4—798no—
1191C4×D4—798no—
1192C4×D4—794no—
1193C4×D4—794no—
1194C4×D4—798no—
1195C4×D4—792no—
1196C4×D4—794no—
1197C4×D4—794no—
1198C4×D4—792no—
1199C4×D4—792no—
1200C4×D4—792no—
1201C4×D4—792no—
1202C4×D4—792no—
1203C4×D4—792no—
1204C4×D4—792no—
1205C4×D4—792no—
1206C4×D4—794no—
1207C4×D4—798no—
1208C4×D4—794no—
1209C4×D4—792no—
1210C4×D4—794no—
1211C4×D4—798no—
1212C4×D4—792no—
1213C4×D4—792no—
1214C4×D4C22×D7914yes—
1215C4×D4C22×D7914yes—
1216C4×D4C22×D7914yes—
1217C4×D4C22×D7914yes—
1218C4×D4C22×D7912yescomplemented
1219C4×D4C22×D7912yescomplemented
1220C4×D4C22×D7912yescomplemented
1221C4×D4C22×D7912yescomplemented
1222#117—794no—
1223#117—794no—
1224#117—792no—
1225#117—794no—
1226#117—798no—
1227#117—794no—
1228#117—794no—
1229#117—794no—
1230#117—798no—
1231#117—798no—
1232#117—794no—
1233#117—798no—
1234#117—798no—
1235#117C22×D7912yes—
1236#117C22×D7912yes—
1237#117C22×D7912yes—
1238#117C22×D7912yes—
1239#117C22×D7912yes—
1240#117C22×D7914yescomplemented
1241C2×C4⋊C4—791no—
1242C2×C4⋊C4—791no—
1243C2×C4⋊C4—794no—
1244C2×C4⋊C4—798no—
1245C2×C4⋊C4—794no—
1246C2×C4⋊C4—798no—
1247C2×C4⋊C4—794no—
1248C2×C4⋊C4—794no—
1249C2×C4⋊C4C22×D7911yescharacteristic
1250C2×C4⋊C4C22×D7911yescharacteristic
1251C2×C22⋊C4—792no—
1252C2×C22⋊C4—792no—
1253C2×C22⋊C4—792no—
1254C2×C22⋊C4—792no—
1255C2×C22⋊C4—792no—
1256C2×C22⋊C4—798no—
1257C2×C22⋊C4—798no—
1258C2×C22⋊C4—798no—
1259C2×C22⋊C4—798no—
1260C2×C22⋊C4—798no—
1261C2×C22⋊C4—798no—
1262C2×C22⋊C4—798no—
1263C2×C22⋊C4—798no—
1264C2×C22⋊C4—798no—
1265C2×C22⋊C4—798no—
1266C2×C22⋊C4—798no—
1267C2×C22⋊C4C22×D7911yescharacteristic
1268C2×C22⋊C4C22×D7911yescharacteristic
1269C2×C42—792no—
1270C2×C42—798no—
1271C2×C42—794no—
1272C2×C42C22×D7911yescharacteristic
1273C2×C42C22×D7911yescharacteristic
1274C2×C42C22×D7914yescomplemented
1275C24—792no—
1276C24—798no—
1277C24—798no—
1278C24—792no—
1279C24—6322no—
1280C24—6322no—
1281C24—1588no—
1282C24C23×D7911yescharacteristic
1283#41—28no—
1284#41—6328no—
1285#41—6324no—
1286#41—6324no—
1287#41—15816no—
1288#41—15816no—
1289#41—1588no—
1290C2×Q8—792no—
1291C2×Q8—792no—
1292C2×Q8—798no—
1293C2×Q8—792no—
1294C2×Q8—6324no—
1295C2×Q8C23×D7912yes—
1296C2×Q8C23×D7912yes—
1297C2×Q8C23×D7912yes—
1298C2×D4—794no—
1299C2×D4—798no—
1300C2×D4—794no—
1301C2×D4—798no—
1302C2×D4—798no—
1303C2×D4—798no—
1304C2×D4—794no—
1305C2×D4—798no—
1306C2×D4—792no—
1307C2×D4—798no—
1308C2×D4—798no—
1309C2×D4—792no—
1310C2×D4—792no—
1311C2×D4—792no—
1312C2×D4—798no—
1313C2×D4—798no—
1314C2×D4—792no—
1315C2×D4—792no—
1316C2×D4—792no—
1317C2×D4—6324no—
1318C2×D4—6328no—
1319C2×D4—6328no—
1320C2×D4—15816no—
1321C2×D4—15816no—
1322C2×D4—15816no—
1323C2×D4—1588no—
1324C2×D4—15816no—
1325C2×D4—15832no—
1326C2×D4—1584no—
1327C2×D4C23×D7914yes—
1328C2×D4C23×D7912yes—
1329C2×D4C23×D7914yes—
1330C2×D4C23×D7914yes—
1331C2×D4C23×D7912yes—
1332C2×D4C23×D7912yes—
1333C22×C4—24no—
1334C22×C4—792no—
1335C22×C4—792no—
1336C22×C4—798no—
1337C22×C4—798no—
1338C22×C4—798no—
1339C22×C4—794no—
1340C22×C4—794no—
1341C22×C4—794no—
1342C22×C4—794no—
1343C22×C4—798no—
1344C22×C4—794no—
1345C22×C4—794no—
1346C22×C4—798no—
1347C22×C4—798no—
1348C22×C4—798no—
1349C22×C4—794no—
1350C22×C4—6322no—
1351C22×C4—6328no—
1352C22×C4—6322no—
1353C22×C4—6322no—
1354C22×C4—6322no—
1355C22×C4C23×D7911yescharacteristic
1356C22×C4C23×D7914yes—
1357C22×C4C23×D7912yes—
1358C22×C4C23×D7912yes—
1359C22×C4C23×D7911yescharacteristic
1360C22×C4C23×D7911yescharacteristic
1361C22×C4C23×D7911yescharacteristic
1362C22×C4C23×D7911yescharacteristic
1363C22×C4C23×D7914yes—
1364C22×C4C23×D7914yes—
1365C22×C4C23×D7911yescharacteristic
1366C4⋊C4—798no—
1367C4⋊C4—794no—
1368C4⋊C4—794no—
1369C4⋊C4—798no—
1370C4⋊C4—798no—
1371C4⋊C4—798no—
1372C4⋊C4—794no—
1373C4⋊C4—794no—
1374C4⋊C4—794no—
1375C4⋊C4—794no—
1376C4⋊C4—792no—
1377C4⋊C4—792no—
1378C4⋊C4—792no—
1379C4⋊C4—798no—
1380C4⋊C4—792no—
1381C4⋊C4—792no—
1382C4⋊C4—792no—
1383C4⋊C4—792no—
1384C4⋊C4—798no—
1385C4⋊C4—792no—
1386C4⋊C4—792no—
1387C4⋊C4—792no—
1388C4⋊C4C23×D7912yes—
1389C4⋊C4C23×D7914yes—
1390C4⋊C4C23×D7912yes—
1391C4⋊C4C23×D7914yes—
1392C4⋊C4C23×D7912yes—
1393C4⋊C4C23×D7912yes—
1394C4⋊C4C23×D7912yes—
1395C4⋊C4C23×D7912yes—
1396C4⋊C4C23×D7912yes—
1397C4⋊C4C23×D7912yes—
1398C4⋊C4C23×D7914yes—
1399C4⋊C4C23×D7914yes—
1400C4⋊C4C23×D7912yes—
1401C4⋊C4C23×D7912yes—
1402C4⋊C4C23×D7914yes—
1403C4⋊C4C23×D7914yes—
1404C22⋊C4—798no—
1405C22⋊C4—794no—
1406C22⋊C4—798no—
1407C22⋊C4—794no—
1408C22⋊C4—794no—
1409C22⋊C4—798no—
1410C22⋊C4—798no—
1411C22⋊C4—794no—
1412C22⋊C4—794no—
1413C22⋊C4—794no—
1414C22⋊C4—798no—
1415C22⋊C4—794no—
1416C22⋊C4—798no—
1417C22⋊C4—798no—
1418C22⋊C4—794no—
1419C22⋊C4—798no—
1420C22⋊C4—794no—
1421C22⋊C4—794no—
1422C22⋊C4—798no—
1423C22⋊C4—798no—
1424C22⋊C4—798no—
1425C22⋊C4—798no—
1426C22⋊C4—798no—
1427C22⋊C4—794no—
1428C22⋊C4—794no—
1429C22⋊C4—794no—
1430C22⋊C4C23×D7912yes—
1431C22⋊C4C23×D7912yes—
1432C22⋊C4C23×D7912yes—
1433C22⋊C4C23×D7912yes—
1434C22⋊C4C23×D7914yes—
1435C22⋊C4C23×D7914yes—
1436C22⋊C4C23×D7914yes—
1437C22⋊C4C23×D7914yes—
1438C22⋊C4C23×D7914yes—
1439C22⋊C4C23×D7914yes—
1440C22⋊C4C23×D7914yes—
1441C22⋊C4C23×D7914yes—
1442C22⋊C4C23×D7914yes—
1443C42—794no—
1444C42—798no—
1445C42—794no—
1446C42—798no—
1447C42—798no—
1448C42—794no—
1449C42C23×D7912yes—
1450C42C23×D7914yes—
1451C42C23×D7912yes—
1452C42C23×D7911yescharacteristic
1453C42C23×D7911yescharacteristic
1454C42C23×D7911yescharacteristic
1455C42C23×D7911yescharacteristic
1456C42C23×D7914yes—
1457C42C23×D7914yes—
1458C23—22no—
1459C23—41no—
1460C23—41no—
1461C23—3162no—
1462C23—3162no—
1463C23—3162no—
1464C23—3162no—
1465C23—3168no—
1466C23—3168no—
1467C23—3168no—
1468C23—3168no—
1469C23—798no—
1470C23—794no—
1471C23—794no—
1472C23—794no—
1473C23—63216no—
1474C23—15816no—
1475C23—15816no—
1476C23—1584no—
1477C23C24×D7912yes—
1478C23C24×D7914yes—
1479C23C24×D7911yescharacteristic
1480Q8—24no—
1481Q8—42no—
1482Q8—42no—
1483Q8—3162no—
1484Q8—3168no—
1485Q8—3162no—
1486Q8—1584no—
1487D4—28no—
1488D4—24no—
1489D4—42no—
1490D4—44no—
1491D4—44no—
1492D4—42no—
1493D4—3162no—
1494D4—3168no—
1495D4—3168no—
1496D4—3162no—
1497D4—3164no—
1498D4—3164no—
1499D4—3168no—
1500D4—3168no—
1501D4—3168no—
1502D4—798no—
1503D4—798no—
1504D4—15816no—
1505D4—15816no—
1506D4—15816no—
1507D4—1588no—
1508D4—1584no—
1509D4—1584no—
1510D4—1584no—
1511C2×C4—22no—
1512C2×C4—24no—
1513C2×C4—24no—
1514C2×C4—28no—
1515C2×C4—41no—
1516C2×C4—41no—
1517C2×C4—44no—
1518C2×C4—41no—
1519C2×C4—41no—
1520C2×C4—44no—
1521C2×C4—3168no—
1522C2×C4—3164no—
1523C2×C4—3164no—
1524C2×C4—3168no—
1525C2×C4—3164no—
1526C2×C4—3168no—
1527C2×C4—3164no—
1528C2×C4—3168no—
1529C2×C4—3164no—
1530C2×C4—3168no—
1531C2×C4—3164no—
1532C2×C4—3162no—
1533C2×C4—3162no—
1534C2×C4—3168no—
1535C2×C4—794no—
1536C2×C4—794no—
1537C2×C4—794no—
1538C2×C4—794no—
1539C2×C4—794no—
1540C2×C4—15816no—
1541C2×C4—1588no—
1542C2×C4#41×D7914yes—
1543C2×C4C24×D7912yes—
1544C2×C4C24×D7912yes—
1545C2×C4C24×D7912yes—
1546C2×C4C24×D7914yes—
1547C2×C4C24×D7914yes—
1548C2×C4C24×D7911yescharacteristic
1549C2×C4C24×D7911yescharacteristic
1550C2×C4C24×D7911yescharacteristic
1551C2×C4C24×D7914yes—
1552C2×C4C24×D7911yescharacteristic
1553C2×C4C24×D7911yescharacteristic
1554C2×C4C24×D7911yescharacteristic
1555C22—21no—
1556C22—21no—
1557C22—22no—
1558C22—24no—
1559C22—24no—
1560C22—24no—
1561C22—22no—
1562C22—22no—
1563C22—44no—
1564C22—3168no—
1565C22—3168no—
1566C22—798no—
1567C22—63216no—
1568C22—63216no—
1569C22—1584no—
1570C22—1584no—
1571C22—1584no—
1572C22—1584no—
1573C22—1584no—
1574C22—1584no—
1575C22—1584no—
1576C22—1584no—
1577C22C2×#41×D7912yes—
1578C22C25×D7911yescharacteristic
1579C4—22no—
1580C4—24no—
1581C4—22no—
1582C4—22no—
1583C4—21no—
1584C4—21no—
1585C4—24no—
1586C4—21no—
1587C4—21no—
1588C4—24no—
1589C4—1584no—
1590C4—1584no—
1591C4—1584no—
1592C4—1584no—
1593C4—1584no—
1594C4C2×#41×D7912yes—
1595C4C2×#41×D7912yes—
1596C2—22no—
1597C2—42no—
1598C2—44no—
1599C2—3164no—
1600C2—3164no—
1601C2—1588no—
1602C2C22×#41×D7911yescharacteristic
1603C2#2377821111yescharacteristic
1604C2#2377821111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3455C2
hypercenter#3455D79
hypocenterC79#62846
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3455

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777474C2semidirect
2. #23777472C2semidirect
3. #23777434C2semidirect
4. #23777430C2semidirect
5. #23777363C2semidirect
6. #23777359C2semidirect
7. #23777346C2semidirect
8. #23777344C2semidirect
9. #23777254C2semidirect
10. #23777249C2semidirect
11. #23777232C2semidirect
12. #23777201C2semidirect
13. #23777162C2semidirect
14. #23777117C2semidirect
15. #23777086C2semidirect
16. #23777033C2semidirect
17. #23776816C2semidirect
18. #23776808C2semidirect
19. #23776790C2semidirect
20. #538×D79C2semidirect
21. C4×#14579207C2semidirect
22. C2×#19099037C2semidirect
23. C79×#3455C2semidirect
26. #19099298C22semidirect
27. #19099295C22semidirect
28. #19099287C22semidirect
29. #19099286C22semidirect
30. #19099284C22semidirect
31. #19099283C22semidirect
32. #19099279C22semidirect
33. #19099278C22semidirect
34. #19099278C22semidirect
35. #19099277C22semidirect
36. #19099274C22semidirect
37. #19099273C22semidirect
38. #19099273C22semidirect
39. #19099269C22semidirect
40. #19099266C22semidirect
41. #19099266C22semidirect
42. #19099264C22semidirect
43. #19099260C22semidirect
44. #19099259C22semidirect
45. #19099259C22semidirect
46. #19099258C22semidirect
47. #19099253C22semidirect
48. #19099247C22semidirect
49. #19099245C22semidirect
50. #19099243C22semidirect
51. #19099241C22semidirect
52. #19099240C22semidirect
53. #19099238C22semidirect
54. #19099238C22semidirect
55. #19099238C22semidirect
56. #19099235C22semidirect
57. #19099233C22semidirect
58. Q8×D316C22semidirect
59. #19099228C22semidirect
60. #19099223C22semidirect
61. #19099218C22semidirect
62. #19099217C22semidirect
63. #19099216C22semidirect
64. #19099216C22semidirect
65. #19099210C22semidirect
66. #19099209C22semidirect
67. #19099209C22semidirect
68. #19099209C22semidirect
69. #19099206C22semidirect
70. #19099206C22semidirect
71. #19099205C22semidirect
72. #19099205C22semidirect
73. #19099204C22semidirect
74. #19099204C22semidirect
75. #19099202C22semidirect
76. D4×D316C22semidirect
77. D4×D316C22semidirect
78. D4×D316C22semidirect
79. #19099198C22semidirect
80. #19099197C22semidirect
81. #19099197C22semidirect
82. #19099191C22semidirect
83. #19099188C22semidirect
84. #19099185C22semidirect
85. #19099184C22semidirect
86. #19099184C22semidirect
87. #19099184C22semidirect
88. #19099175C22semidirect
89. #19099168C22semidirect
90. #19099168C22semidirect
91. #19099164C22semidirect
92. #19099161C22semidirect
93. #19099160C22semidirect
94. #19099160C22semidirect
95. #19099159C22semidirect
96. #19099153C22semidirect
97. #19099152C22semidirect
98. #19099152C22semidirect
99. #19099151C22semidirect
100. #19099151C22semidirect
101. #19099150C22semidirect
102. #19099149C22semidirect
103. #19099149C22semidirect
104. #19099148C22semidirect
105. #19099147C22semidirect
106. #19099146C22semidirect
107. #19099145C22semidirect
108. #19099141C22semidirect
109. #19099132C22semidirect
110. #19099127C22semidirect
111. #19099124C22semidirect
112. #19099121C22semidirect
113. #19099120C22semidirect
114. #19099113C22semidirect
115. #19099113C22semidirect
116. #19099110C22semidirect
117. #19099100C22semidirect
118. #19099098C22semidirect
119. #19099097C22semidirect
120. #19099096C22semidirect
121. #19099091C22semidirect
122. #19099091C22semidirect
123. #19099090C22semidirect
124. #126×D79C22semidirect
125. #124×D79C22semidirect
126. #19099076C22semidirect
127. #19099076C22semidirect
128. #19099074C22semidirect
129. #19099073C22semidirect
130. #19099072C22semidirect
131. #19099071C22semidirect
132. #123×D79C22semidirect
133. C22⋊Q8×D79C22semidirect
134. #121×D79C22semidirect
135. #121×D79C22semidirect
136. #120×D79C22semidirect
137. #19099046C22semidirect
138. #19099045C22semidirect
139. #19099043C22semidirect
140. #19099043C22semidirect
142. #19099037C22semidirect
143. #19099037C22semidirect
144. #19099037C22semidirect
145. #19099037C22semidirect
146. #19099037C22semidirect
147. #19099035C22semidirect
148. #19099035C22semidirect
149. C4×#11929625C22semidirect
150. C4×#11929624C22semidirect
151. C4×#11929624C22semidirect
154. C2×C4×D316C22semidirect
155. C2×C4×D316C22semidirect
156. C2×C4×D316C22semidirect
157. C2×#14579123C22semidirect
158. C2×#14579123C22semidirect
159. C4×D4×D79C22semidirect
160. C4×D4×D79C22semidirect
161. C2×#14579120C22semidirect
162. C2×C22⋊C4×D79C22semidirect
163. C2×C22⋊C4×D79C22semidirect
164. #542×C79C22semidirect
165. #542×C79C22semidirect
166. #541×C79C22semidirect
167. #540×C79C22semidirect
168. #539×C79C22semidirect
169. #539×C79C22semidirect
170. #538×C79C22semidirect
171. #538×C79C22semidirect
172. #533×C79C22semidirect
173. #532×C79C22semidirect
174. #529×C79C22semidirect
175. #529×C79C22semidirect
176. #525×C79C22semidirect
177. C4×#41×C79C22semidirect
178. C2×#117×C79C22semidirect
182. C2×#11929625C23semidirect
185. C2×#11929624C23semidirect
186. C2×#11929623C23semidirect
187. C2×Q8×D79C23semidirect
199. C2×D4×D79C23semidirect
204. C22×C4×D79C23semidirect
205. #14579161C23semidirect
206. #14579161C23semidirect
207. #14579161C23semidirect
208. #14579161C23semidirect
209. #14579160C23semidirect
211. #14579158C23semidirect
213. #14579156C23semidirect
214. #14579156C23semidirect
215. #14579156C23semidirect
216. #14579156C23semidirect
217. #14579156C23semidirect
218. #14579156C23semidirect
219. #14579155C23semidirect
224. #14579154C23semidirect
225. #14579153C23semidirect
226. #14579153C23semidirect
227. #14579152C23semidirect
228. #14579151C23semidirect
229. #14579151C23semidirect
230. #14579151C23semidirect
232. #14579150C23semidirect
234. #14579149C23semidirect
235. #14579149C23semidirect
240. #14579147C23semidirect
241. #14579147C23semidirect
242. #14579147C23semidirect
245. #14579146C23semidirect
246. #14579146C23semidirect
247. #14579146C23semidirect
248. #14579146C23semidirect
249. #14579146C23semidirect
250. #14579146C23semidirect
251. #14579146C23semidirect
252. #14579145C23semidirect
254. #14579144C23semidirect
258. #14579143C23semidirect
259. #14579143C23semidirect
260. #14579143C23semidirect
262. #14579141C23semidirect
263. #14579141C23semidirect
264. #14579141C23semidirect
269. #14579140C23semidirect
270. #14579139C23semidirect
271. #14579139C23semidirect
272. #14579139C23semidirect
273. #14579139C23semidirect
274. #14579139C23semidirect
275. #14579139C23semidirect
277. #14579137C23semidirect
278. #14579137C23semidirect
279. #14579137C23semidirect
280. #14579137C23semidirect
285. #14579136C23semidirect
286. #14579136C23semidirect
287. #14579136C23semidirect
294. #14579135C23semidirect
295. #14579135C23semidirect
300. #14579134C23semidirect
301. #14579134C23semidirect
302. #14579134C23semidirect
305. #14579133C23semidirect
307. #14579132C23semidirect
308. #14579132C23semidirect
309. #14579132C23semidirect
315. #14579131C23semidirect
320. #14579129C23semidirect
321. Q8×Dic79C23semidirect
322. C4×Dic158C23semidirect
323. C4×Dic158C23semidirect
324. C4×Dic158C23semidirect
325. C4×Dic158C23semidirect
326. C4×Dic158C23semidirect
327. #14579126C23semidirect
342. C4×D316C23semidirect
343. C4×D316C23semidirect
344. C4×D316C23semidirect
345. C4×D316C23semidirect
346. C4×D316C23semidirect
347. C4×D316C23semidirect
348. C4×D316C23semidirect
349. C4×D316C23semidirect
351. D4×Dic79C23semidirect
358. #14579123C23semidirect
359. #14579123C23semidirect
360. #14579123C23semidirect
365. C4×C22⋊D79C23semidirect
366. C4×C22⋊D79C23semidirect
367. C4×C22⋊D79C23semidirect
369. (C22⋊D79)⋊C4C23semidirect
370. (C22⋊D79)⋊C4C23semidirect
371. (C22⋊D79)⋊C4C23semidirect
372. (C22⋊D79)⋊C4C23semidirect
376. #14579120C23semidirect
377. #14579119C23semidirect
378. #14579119C23semidirect
379. #14579119C23semidirect
380. #14579119C23semidirect
381. #14579119C23semidirect
382. #14579118C23semidirect
383. #14579118C23semidirect
384. #14579118C23semidirect
385. #14579117C23semidirect
388. C2×C4⋊Dic79C23semidirect
389. C4⋊C4×D79C23semidirect
390. C4⋊C4×D79C23semidirect
391. C4⋊C4×D79C23semidirect
392. C4⋊C4×D79C23semidirect
393. C4⋊C4×D79C23semidirect
399. C2×(C2×D79)⋊C4C23semidirect
407. C22⋊C4×D79C23semidirect
408. C22⋊C4×D79C23semidirect
409. C22⋊C4×D79C23semidirect
411. C42×D79C23semidirect
412. C42×D79C23semidirect
415. C4⋊Q8×C79C23semidirect
416. C4⋊Q8×C79C23semidirect
417. C4⋊Q8×C79C23semidirect
418. #127×C79C23semidirect
421. #126×C79C23semidirect
422. #126×C79C23semidirect
423. #125×C79C23semidirect
424. #125×C79C23semidirect
425. #125×C79C23semidirect
428. #124×C79C23semidirect
432. #123×C79C23semidirect
433. #123×C79C23semidirect
438. C22⋊Q8×C79C23semidirect
439. C22⋊Q8×C79C23semidirect
447. C4×Q8×C79C23semidirect
448. C4×Q8×C79C23semidirect
449. C4×Q8×C79C23semidirect
450. C4×Q8×C79C23semidirect
455. C4×D4×C79C23semidirect
456. C4×D4×C79C23semidirect
457. C4×D4×C79C23semidirect
458. C4×D4×C79C23semidirect
464. #117×C79C23semidirect
471. C2×C42×C79C23semidirect
495. C2×D316#41semidirect
822. #3455D79semidirect
826. C79#62846semidirect
891. #542C2×D79semidirect
892. #542C2×D79semidirect
894. #541C2×D79semidirect
898. #540C2×D79semidirect
903. #539C2×D79semidirect
904. #539C2×D79semidirect
917. #538C2×D79semidirect
918. #538C2×D79semidirect
925. #533C2×D79semidirect
929. #532C2×D79semidirect
937. #529C2×D79semidirect
938. #529C2×D79semidirect
947. #525C2×D79semidirect
968. C4×#41C2×D79semidirect
979. C2×#117C2×D79semidirect
1015. C4⋊Q8C22×D79semidirect
1016. C4⋊Q8C22×D79semidirect
1017. C4⋊Q8C22×D79semidirect
1021. #127C22×D79semidirect
1036. #126C22×D79semidirect
1037. #126C22×D79semidirect
1044. #125C22×D79semidirect
1045. #125C22×D79semidirect
1046. #125C22×D79semidirect
1061. #124C22×D79semidirect
1084. #123C22×D79semidirect
1085. #123C22×D79semidirect
1109. C22⋊Q8C22×D79semidirect
1110. C22⋊Q8C22×D79semidirect
1165. C4×Q8C22×D79semidirect
1166. C4×Q8C22×D79semidirect
1167. C4×Q8C22×D79semidirect
1168. C4×Q8C22×D79semidirect
1218. C4×D4C22×D79semidirect
1219. C4×D4C22×D79semidirect
1220. C4×D4C22×D79semidirect
1221. C4×D4C22×D79semidirect
1240. #117C22×D79semidirect
1274. C2×C42C22×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237774742
#237774722
#237774342
#237774302
#237773632
#237773592
#237773462
#237773442
#237772542
#237772492
#237772322
#237772012
#237771622
#237771172
#237770862
#237770332
#237768162
#237768082
#237767902
#538×D792
C4×#145792072
C2×#190990372
C79×#34552
#6284679