Finite Group Databasebeta

← #35197298

Subgroups — #35197298

Order 20224.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777259C214yesmaximal, complemented
2#23777256C214yesmaximal, complemented
3#23777255C214yesmaximal, complemented
4#23777247C214yesmaximal, complemented
5#23777246C214yesmaximal, complemented
6#23777242C214yesmaximal, complemented
7#23777121C211yesmaximal, characteristic, complemented
8#23777120C211yesmaximal, characteristic, complemented
9#23777119C211yesmaximal, characteristic, complemented
10#23777114C214yesmaximal, complemented
11#23777111C214yesmaximal, complemented
12#23777106C212yesmaximal, complemented
13#23777104C214yesmaximal, complemented
14#23777103C212yesmaximal, complemented
15#23777100C214yesmaximal, complemented
16#23776811C214yesmaximal, complemented
17#23776810C214yesmaximal, complemented
18#23776804C211yesmaximal, characteristic, complemented
19#23776730C212yesmaximal, complemented
20#23776728C211yesmaximal, characteristic, complemented
21C2×#19099043C211yesmaximal, characteristic, complemented
22#520×D79C212yesmaximal, complemented
23C79×#3493C211yesmaximal, characteristic, complemented
24C22×#11929624C2211yescharacteristic
25C2×#41×D79C2212yes—
26#19099297C2218yescomplemented
27#19099296C2214yescomplemented
28#19099295C2214yescomplemented
29#19099295C2218yescomplemented
30#19099290C2214yescomplemented
31#19099289C2214yescomplemented
32#19099287C2214yescomplemented
33#19099285C2214yescomplemented
34#19099284C2214yescomplemented
35#19099282C2214yescomplemented
36#19099281C2214yescomplemented
37#19099281C2218yescomplemented
38#19099280C2218yescomplemented
39#19099280C2218yescomplemented
40#19099279C2214yescomplemented
41#19099277C2214yescomplemented
42#19099276C2214yescomplemented
43#19099275C2218yescomplemented
44#19099273C2214yescomplemented
45#19099272C2214yescomplemented
46#19099271C2214yescomplemented
47#19099270C2214yescomplemented
48#19099269C2214yescomplemented
49#19099268C2214yescomplemented
50#19099266C2214yescomplemented
51#19099265C2214yescomplemented
52#19099265C2214yescomplemented
53#19099264C2218yescomplemented
54#19099263C2214yescomplemented
55#19099259C2214yescomplemented
56#19099257C2214yescomplemented
57#19099257C2214yescomplemented
58#19099256C2218yescomplemented
59#19099255C2214yescomplemented
60#19099255C2214yescomplemented
61#19099254C2214yescomplemented
62#19099253C2214yescomplemented
63#19099252C2214yescomplemented
64#19099252C2214yescomplemented
65#19099251C2214yescomplemented
66#19099249C2218yescomplemented
67#19099246C2218yescomplemented
68#19099231C2218yescomplemented
69#19099218C2214yescomplemented
70#19099217C2214yescomplemented
71#19099214C2214yescomplemented
72#19099213C2214yescomplemented
73#19099211C2218yescomplemented
74#19099194C2211yescharacteristic, complemented
75#19099193C2214yescomplemented
76#19099191C2212yescomplemented
77#19099190C2214yescomplemented
78#19099188C2214yes—
79#19099161C2218yescomplemented
80#19099157C2218yescomplemented
81#19099156C2218yescomplemented
82#19099155C2218yescomplemented
83#19099154C2218yescomplemented
84#19099154C2218yescomplemented
85#19099153C2214yescomplemented
86#19099152C2218yescomplemented
87#19099151C2214yescomplemented
88#19099150C2214yescomplemented
89#19099147C2218yescomplemented
90#19099147C2218yescomplemented
91#19099145C2218yescomplemented
92#19099144C2211yescharacteristic
93#19099143C2212yes—
94#19099143C2212yes—
95#19099142C2212yes—
96#19099142C2212yes—
97#19099141C2212yes—
98#19099136C2214yescomplemented
99#19099136C2212yescomplemented
100#19099136C2212yescomplemented
101#19099135C2214yescomplemented
102#19099129C2214yescomplemented
103#19099129C2212yescomplemented
104#19099129C2212yescomplemented
105#19099128C2214yescomplemented
106#19099124C2214yes—
107#19099123C2214yes—
108#19099121C2214yes—
109#19099119C2214yescomplemented
110#19099118C2214yescomplemented
111#19099115C2214yescomplemented
112#19099110C2214yes—
113#19099110C2214yes—
114#19099108C2214yes—
115#19099100C2218yescomplemented
116#19099099C2214yescomplemented
117#19099097C2214yescomplemented
118#19099096C2218yescomplemented
119#19099094C2214yescomplemented
120#19099092C2218yescomplemented
121#19099091C2218yescomplemented
122#19099076C2214yescomplemented
123#19099075C2218yescomplemented
124#19099075C2212yescomplemented
125#19099074C2212yescomplemented
126#19099073C2218yescomplemented
127#19099073C2214yescomplemented
128#19099072C2218yescomplemented
129#19099072C2218yescomplemented
130#19099072C2214yescomplemented
131#19099072C2214yescomplemented
132#19099071C2218yescomplemented
133#19099070C2212yescomplemented
134#19099069C2218yescomplemented
135#19099046C2212yescomplemented
136#19099045C2214yescomplemented
137#19099044C2212yescomplemented
138#19099044C2214yescomplemented
139#19099043C2214yescomplemented
140#19099043C2212yescomplemented
141#19099043C2214yescomplemented
142#19099043C2214yescomplemented
143#19099043C2214yescomplemented
144#19099043C2214yescomplemented
145#19099042C2214yescomplemented
146#19099042C2218yescomplemented
147C2×C4×Dic158C2212yescomplemented
148C4×Q8×D79C2214yescomplemented
149C2×C4×D316C2212yes—
150C2×(C22⋊D79)⋊C4C2212yes—
151C2×(C22⋊D79)⋊C4C2212yescomplemented
152C4×D4×D79C2218yes—
153C4×D4×D79C2214yescomplemented
154C2×#14579119C2211yescharacteristic
155C2×#14579119C2211yescharacteristic, complemented
156#117×D79C2212yes—
157#117×D79C2214yescomplemented
158C22×C4⋊Dic79C2211yescharacteristic, complemented
159C2×C4⋊C4×D79C2211yescharacteristic
160C2×C4⋊C4×D79C2214yescomplemented
161C2×C4⋊C4×D79C2211yescharacteristic, complemented
162#556×C79C2214yescomplemented
163#555×C79C2214yescomplemented
164#553×C79C2214yescomplemented
165#552×C79C2214yescomplemented
166#544×C79C2211yescharacteristic, complemented
167#538×C79C2214yescomplemented
168#537×C79C2211yescharacteristic
169#529×C79C2214yescomplemented
170#525×C79C2212yescomplemented
171#520×C79C2212yescomplemented
172C2×#117×C79C2211yescharacteristic, complemented
173C2×#11929625C2312yes—
174C2×#11929624—28no—
175C2×#11929624C2312yes—
176C2×#11929624C2312yes—
177C2×#11929624C2314yes—
178C2×#11929624C2312yes—
179C2×#11929624C2312yes—
180C2×#11929624C2312yes—
181C2×#11929624C2318yes—
182C2×#11929623C2312yes—
183C2×#11929623C2314yes—
184C2×#11929623C2318yes—
185#41×D79—216no—
186C22×Dic158C2311yescharacteristic
187C2×Q8×D79C2312yes—
188C22×D316C2311yescharacteristic
189C22×C22⋊D79C2311yescharacteristic
190C22×C22⋊D79C2311yescharacteristic
191C2×D4×D79C2314yes—
192C2×D4×D79C2312yes—
193C23×Dic79C2312yes—
194C22×C4×D79C2314yes—
195C22×C4×D79C2311yescharacteristic
196C22×C4×D79C2312yes—
197C22×C4×D79C2318yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2311yescharacteristic
200#14579161C2314yes—
201#14579160C2314yes—
202#14579160C2314yes—
203#14579160C2314yes—
204#14579160C2314yes—
205#14579160C2314yes—
206#14579160C2314yes—
207#14579159C2314yes—
208#14579157C2314yes—
209#14579157C2314yes—
210#14579157C2314yes—
211#14579156C2318yes—
212#14579156C2318yes—
213#14579156C2318yes—
214#14579156C2318yes—
215#14579155C2318yes—
216#14579155C2318yes—
217#14579154C2318yes—
218#14579154C2318yes—
219#14579154C2318yes—
220#14579154C2318yes—
221#14579153C2314yes—
222#14579153C2318yes—
223#14579153C2314yes—
224#14579152C2314yes—
225#14579152C2318yes—
226#14579152C2314yes—
227#14579152C2314yes—
228#14579152C2314yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2318yes—
232#14579150C2314yes—
233#14579150C2318yes—
234#14579149C2314yes—
235#14579148C2314yes—
236#14579147C2314yes—
237#14579147C2314yes—
238#14579147C2318yes—
239#14579147C2318yes—
240#14579147C2318yes—
241#14579147C2314yes—
242#14579147C2314yes—
243#14579146C2314yes—
244#14579146C2318yes—
245#14579146C2314yes—
246#14579146C2318yes—
247#14579146C2318yes—
248#14579145C2318yes—
249#14579145C2318yes—
250#14579145C2318yes—
251#14579145C2314yes—
252#14579144C2318yes—
253#14579144C2314yes—
254#14579143C2314yes—
255#14579143C2318yes—
256#14579143C2314yes—
257#14579143C2318yes—
258#14579143C2318yes—
259#14579143C2318yes—
260#14579143C2318yes—
261#14579142C2318yes—
262#14579142C2314yes—
263#14579141C2312yes—
264#14579141C2312yes—
265#14579141C2314yes—
266#14579141C2318yes—
267#14579141C2318yes—
268#14579140C2314yes—
269#14579140C2312yes—
270#14579140C2312yes—
271#14579140C2314yes—
272#14579140C2318yes—
273#14579139C2314yes—
274#14579139C2314yes—
275#14579139C2318yes—
276#14579139C2318yes—
277#14579139C2318yes—
278#14579139C2318yes—
279#14579138C2314yes—
280#14579138C2314yes—
281#14579138C2318yes—
282#14579138C2318yes—
283#14579138C2318yes—
284#14579137C2314yes—
285#14579137C2312yes—
286#14579137C2312yes—
287#14579137C2318yes—
288#14579136C2314yes—
289#14579136C2314yes—
290#14579136C2312yes—
291#14579136C2312yes—
292#14579136C2314yes—
293#14579136C2318yes—
294#14579135C2314yes—
295#14579135C2312yes—
296#14579135C2312yes—
297#14579135C2314yes—
298#14579134C2314yes—
299#14579134C2314yes—
300#14579134C2314yes—
301#14579134C2314yes—
302#14579134C2314yes—
303#14579134C2314yes—
304#14579134C2318yes—
305#14579134C2318yes—
306#14579133C2318yes—
307#14579133C2314yes—
308#14579133C2314yes—
309#14579133C2318yes—
310#14579133C2318yes—
311#14579132C2314yes—
312#14579132C2314yes—
313#14579132C2314yes—
314#14579132C2312yes—
315#14579132C2312yes—
316#14579131C2314yes—
317#14579131C2318yes—
318#14579131C2314yes—
319#14579131C2314yes—
320#14579130C2314yes—
321#14579129C2314yes—
322#14579129C2318yes—
323#14579129C2314yes—
324#14579129C2314yes—
325Q8×Dic79C2314yes—
326Q8×Dic79C2314yes—
327Q8×Dic79C2314yes—
328C4×Dic158C2314yes—
329C4×Dic158C2314yes—
330C4×Dic158C2314yes—
331C4×Dic158C2314yes—
332C4×Dic158C2318yes—
333C4×Dic158C2314yes—
334C4×Dic158C2314yes—
335#14579126C2318yes—
336#14579126C2314yes—
337#14579126C2318yes—
338#14579126C2314yes—
339#14579126C2314yes—
340C4×D316C2318yes—
341C4×D316C2318yes—
342C4×D316C2318yes—
343C4×D316C2314yes—
344C4×D316C2314yes—
345C4×D316C2314yes—
346C4×D316C2318yes—
347C4×D316C2314yes—
348D4×Dic79C2318yes—
349D4×Dic79C2314yes—
350D4×Dic79C2314yes—
351D4×Dic79C2318yes—
352D4×Dic79C2314yes—
353#14579123C2318yes—
354#14579123C2314yes—
355#14579123C2314yes—
356#14579123C2314yes—
357C4×C22⋊D79C2318yes—
358C4×C22⋊D79C2318yes—
359C4×C22⋊D79C2314yes—
360C4×C22⋊D79C2314yes—
361C4×C22⋊D79C2318yes—
362C4×C22⋊D79C2318yes—
363C4×C22⋊D79C2314yes—
364C4×C22⋊D79C2314yes—
365(C22⋊D79)⋊C4C2318yes—
366(C22⋊D79)⋊C4C2318yes—
367(C22⋊D79)⋊C4C2318yes—
368(C22⋊D79)⋊C4C2318yes—
369(C22⋊D79)⋊C4C2318yes—
370(C22⋊D79)⋊C4C2318yes—
371(C22⋊D79)⋊C4C2318yes—
372(C22⋊D79)⋊C4C2318yes—
373(C22⋊D79)⋊C4C2318yes—
374#14579120C2312yes—
375#14579120C2314yes—
376#14579119C2312yes—
377#14579119C2312yes—
378#14579119C2314yes—
379#14579119C2314yes—
380#14579119C2318yes—
381#14579119C2314yes—
382#14579119C2314yes—
383#14579119C2314yes—
384#14579119C2314yes—
385#14579118C2314yes—
386#14579118C2318yes—
387#14579118C2318yes—
388#14579118C2318yes—
389#14579117C2318yes—
390#14579117C2318yes—
391#14579117C2318yes—
392#14579117C2314yes—
393C2×C4⋊Dic79C2311yescharacteristic
394C2×C4⋊Dic79C2312yes—
395C2×C4⋊Dic79C2314yes—
396C2×C4⋊Dic79C2314yes—
397C2×C4⋊Dic79C2314yes—
398C2×C4⋊Dic79C2311yescharacteristic
399C2×Dic79⋊C4C2312yes—
400C2×Dic79⋊C4C2318yes—
401C2×Dic79⋊C4C2312yes—
402C4⋊C4×D79C2312yes—
403C4⋊C4×D79C2312yes—
404C4⋊C4×D79C2318yes—
405C4⋊C4×D79C2318yes—
406C4⋊C4×D79C2314yes—
407C4⋊C4×D79C2314yes—
408C4⋊C4×D79C2314yes—
409C4⋊C4×D79C2314yes—
410C4⋊C4×D79C2314yes—
411C4⋊C4×D79C2314yes—
412C2×(C2×D79)⋊C4C2312yes—
413C2×(C2×D79)⋊C4C2312yes—
414C22⋊C4×D79C2318yes—
415C22⋊C4×D79C2314yes—
416C2×C4×Dic79C2312yes—
417C2×C4×Dic79C2312yes—
418C42×D79C2314yes—
419C42×D79C2318yes—
420C2×#41×C79C2312yes—
421C23×C4×C79C2311yescharacteristic
422C4⋊Q8×C79C2314yes—
423#126×C79C2318yes—
424#126×C79C2318yes—
425#125×C79C2314yes—
426#125×C79C2314yes—
427#124×C79C2314yes—
428#124×C79C2318yes—
429#123×C79C2318yes—
430#123×C79C2314yes—
431C22⋊Q8×C79C2312yes—
432C22⋊Q8×C79C2312yes—
433C22⋊Q8×C79C2314yes—
434C22⋊Q8×C79C2314yes—
435#121×C79C2312yes—
436#121×C79C2312yes—
437#121×C79C2318yes—
438#121×C79C2314yes—
439#121×C79C2314yes—
440#120×C79C2314yes—
441C4×Q8×C79C2314yes—
442C4×Q8×C79C2314yes—
443C4×D4×C79C2318yes—
444C4×D4×C79C2314yes—
445C4×D4×C79C2314yes—
446C4×D4×C79C2314yes—
447C4×D4×C79C2314yes—
448#117×C79C2312yes—
449#117×C79C2314yes—
450#117×C79C2314yes—
451#117×C79C2314yes—
452#117×C79C2318yes—
453C2×C4⋊C4×C79C2311yescharacteristic
454C2×C4⋊C4×C79C2314yes—
455C2×C4⋊C4×C79C2311yescharacteristic
456C2×C22⋊C4×C79C2312yes—
457C2×C42×C79C2312yes—
458C23×D79C2414yes—
459C23×D79C2411yescharacteristic
460C23×D79C2411yescharacteristic
461#11929625—28no—
462#11929624—216no—
463#11929624—28no—
464#11929624—28no—
465#11929624—28no—
466#11929624—28no—
467#11929624—28no—
468#11929624—88no—
469#11929623—216no—
470#11929623—28no—
471#11929623—88no—
472C2×Dic158—24no—
473C2×Dic158C2412yes—
474C2×Dic158C2414yes—
475C2×Dic158C2411yescharacteristic
476C2×Dic158C2411yescharacteristic
477C2×Dic158C2411yescharacteristic
478C2×Dic158C2411yescharacteristic
479C2×Dic158C2418yes—
480C2×Dic158C2414yes—
481Q8×D79—28no—
482C2×D316—24no—
483C2×D316C2412yes—
484C2×D316C2412yes—
485C2×D316C2414yes—
486C2×D316C2412yes—
487C2×D316C2414yes—
488C2×D316C2414yes—
489C2×D316C2414yes—
490C2×C22⋊D79—24no—
491C2×C22⋊D79—24no—
492C2×C22⋊D79C2414yes—
493C2×C22⋊D79C2414yes—
494C2×C22⋊D79C2414yes—
495C2×C22⋊D79C2412yes—
496C2×C22⋊D79C2412yes—
497C2×C22⋊D79C2412yes—
498C2×C22⋊D79C2412yes—
499C2×C22⋊D79C2414yes—
500C2×C22⋊D79C2418yes—
501C2×C22⋊D79C2414yes—
502C2×C22⋊D79C2414yes—
503C2×C22⋊D79C2414yes—
504D4×D79—28no—
505D4×D79—216no—
506C22×Dic79—82no—
507C22×Dic79C2411yescharacteristic
508C22×Dic79C2414yes—
509C22×Dic79C2418yes—
510C22×Dic79C2418yes—
511C22×Dic79C2412yes—
512C22×Dic79C2412yes—
513C22×Dic79C2411yescharacteristic
514C2×C4×D79—216no—
515C2×C4×D79—24no—
516C2×C4×D79—82no—
517C2×C4×D79—82no—
518C2×C4×D79—88no—
519C2×C4×D79#4118yescomplemented
520C2×C4×D79C2414yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2412yes—
523C2×C4×D79C2412yes—
524C2×C4×D79C2414yes—
525C2×C4×D79C2418yes—
526C2×C4×D79C2418yes—
527C2×C4×D79C2418yes—
528C2×C4×D79C2414yes—
529C2×C4×D79C2418yes—
530C2×C4×D79C2414yes—
531C2×C4×D79C2412yes—
532C2×C4×D79C2412yes—
533C4⋊Dic79C2414yes—
534C4⋊Dic79C2412yes—
535C4⋊Dic79C2414yes—
536C4⋊Dic79C2418yes—
537C4⋊Dic79C2412yes—
538C4⋊Dic79C2414yes—
539C4⋊Dic79C2414yes—
540C4⋊Dic79C2414yes—
541C4⋊Dic79C2418yes—
542C4⋊Dic79C2414yes—
543C4⋊Dic79C2414yes—
544C4⋊Dic79C2414yes—
545Dic79⋊C4C2414yes—
546Dic79⋊C4C2414yes—
547Dic79⋊C4C2414yes—
548Dic79⋊C4C2414yes—
549Dic79⋊C4C2414yes—
550Dic79⋊C4C2418yes—
551Dic79⋊C4C2418yes—
552Dic79⋊C4C2414yes—
553Dic79⋊C4C2414yes—
554Dic79⋊C4C2418yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2418yes—
557Dic79⋊C4C2414yes—
558Dic79⋊C4C2418yes—
559Dic79⋊C4C2414yes—
560Dic79⋊C4C2414yes—
561C22⋊Dic79C2414yes—
562C22⋊Dic79C2418yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2414yes—
565C22⋊Dic79C2414yes—
566C22⋊Dic79C2418yes—
567C22⋊Dic79C2414yes—
568(C2×D79)⋊C4C2414yes—
569(C2×D79)⋊C4C2418yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2418yes—
572(C2×D79)⋊C4C2418yes—
573(C2×D79)⋊C4C2418yes—
574(C2×D79)⋊C4C2414yes—
575(C2×D79)⋊C4C2414yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2418yes—
578(C2×D79)⋊C4C2414yes—
579(C2×D79)⋊C4C2418yes—
580(C2×D79)⋊C4C2414yes—
581(C2×D79)⋊C4C2414yes—
582(C2×D79)⋊C4C2414yes—
583(C2×D79)⋊C4C2414yes—
584C4×Dic79C2418yes—
585C4×Dic79C2418yes—
586C4×Dic79C2418yes—
587C4×Dic79C2414yes—
588C4×Dic79C2414yes—
589C4×Dic79C2414yes—
590C4×Dic79C2414yes—
591C4×Dic79C2414yes—
592C4×Dic79C2414yes—
593C4×Dic79C2414yes—
594C24×C79C2411yescharacteristic
595#41×C79—28no—
596C2×Q8×C79C2412yes—
597C2×Q8×C79C2414yes—
598C2×D4×C79C2414yes—
599C2×D4×C79C2412yes—
600C2×D4×C79C2414yes—
601C2×D4×C79C2414yes—
602C2×D4×C79C2414yes—
603C22×C4×C79—24no—
604C22×C4×C79C2411yescharacteristic
605C22×C4×C79C2412yes—
606C22×C4×C79C2412yes—
607C22×C4×C79C2414yes—
608C22×C4×C79C2418yes—
609C22×C4×C79C2412yes—
610C22×C4×C79C2412yes—
611C22×C4×C79C2411yescharacteristic
612C4⋊C4×C79C2414yes—
613C4⋊C4×C79C2412yes—
614C4⋊C4×C79C2414yes—
615C4⋊C4×C79C2418yes—
616C4⋊C4×C79C2412yes—
617C4⋊C4×C79C2414yes—
618C4⋊C4×C79C2418yes—
619C4⋊C4×C79C2414yes—
620C4⋊C4×C79C2414yes—
621C4⋊C4×C79C2414yes—
622C22⋊C4×C79C2418yes—
623C22⋊C4×C79C2414yes—
624C22⋊C4×C79C2414yes—
625C22⋊C4×C79C2418yes—
626C22⋊C4×C79C2418yes—
627C22⋊C4×C79C2414yes—
628C22⋊C4×C79C2414yes—
629C22⋊C4×C79C2414yes—
630C42×C79C2414yes—
631C42×C79C2414yes—
632C42×C79C2418yes—
633C42×C79C2414yes—
634C23×C79—22no—
635C23×C79—41no—
636C23×C79—41no—
637C23×C79C2514yes—
638C23×C79C2512yes—
639C23×C79C2511yescharacteristic
640C22×D79—22no—
641C22×D79—28no—
642C22×D79—41no—
643C22×D79—44no—
644C22×D79—41no—
645C22×D79—41no—
646C22×D79—44no—
647C22×D79—41no—
648C22×D79C2×#4114yes—
649C22×D79C2514yes—
650C22×D79C2512yes—
651C22×D79C2512yes—
652Q8×C79—24no—
653Q8×C79—44no—
654D4×C79—28no—
655D4×C79—24no—
656D4×C79—44no—
657D4×C79—44no—
658D4×C79—44no—
659C2×C4×C79—22no—
660C2×C4×C79—28no—
661C2×C4×C79—24no—
662C2×C4×C79—24no—
663C2×C4×C79—42no—
664C2×C4×C79—48no—
665C2×C4×C79—42no—
666C2×C4×C79C2×#4114yes—
667C2×C4×C79C2514yes—
668C2×C4×C79C2514yes—
669C2×C4×C79C2514yes—
670C2×C4×C79C2514yes—
671C2×C4×C79C2514yes—
672C2×C4×C79C2511yescharacteristic
673C2×C4×C79C2511yescharacteristic
674C2×C4×C79C2512yes—
675C22⋊D79—28no—
676C22⋊D79—28no—
677C22⋊D79—24no—
678C22⋊D79—24no—
679C22⋊D79—28no—
680C22⋊D79—24no—
681C22⋊D79—24no—
682C22⋊D79—44no—
683C22⋊D79—44no—
684C22⋊D79—44no—
685C22⋊D79—48no—
686C22⋊D79—44no—
687C2×Dic79—22no—
688C2×Dic79—28no—
689C2×Dic79—42no—
690C2×Dic79—42no—
691C2×Dic79—48no—
692C2×Dic79—48no—
693C2×Dic79C2×#4114yes—
694C2×Dic79C2514yes—
695C2×Dic79C2514yes—
696C2×Dic79C2514yes—
697C2×Dic79C2511yescharacteristic
698C2×Dic79C2511yescharacteristic
699C2×Dic79C2514yes—
700C2×Dic79C2514yes—
701C2×Dic79C2511yescharacteristic
702C2×Dic79C2511yescharacteristic
703D316—28no—
704D316—24no—
705D316—24no—
706D316—24no—
707D316—44no—
708D316—44no—
709D316—44no—
710C4×D79—28no—
711C4×D79—28no—
712C4×D79—24no—
713C4×D79—24no—
714C4×D79—28no—
715C4×D79—44no—
716C4×D79—48no—
717C4×D79—48no—
718C4×D79—48no—
719C4×D79—48no—
720C4×D79—44no—
721C4×D79C2×#4118yes—
722C4×D79C2×#4118yes—
723Dic158—24no—
724Dic158—28no—
725Dic158—22no—
726Dic158—22no—
727Dic158—22no—
728Dic158—22no—
729Dic158—44no—
730Dic158—48no—
731C22×C79—21no—
732C22×C79—21no—
733C22×C79—22no—
734C22×C79—24no—
735C22×C79—24no—
736C22×C79—22no—
737C22×C79—22no—
738C22×C79—24no—
739C22×C79—44no—
740C22×C79C22×#4112yes—
741C22×C79C2611yescharacteristic
742C2×D79—22no—
743C2×D79—22no—
744C2×D79—24no—
745C2×D79—22no—
746C2×D79—24no—
747C2×D79—22no—
748C2×D79—22no—
749C2×D79—24no—
750C2×D79—44no—
751C2×D79—416no—
752C2×D79—44no—
753C2×D79C22×#4114yes—
754C4×C79—21no—
755C4×C79—21no—
756C4×C79—24no—
757C4×C79—24no—
758C4×C79—24no—
759C4×C79—24no—
760C4×C79—24no—
761C4×C79C22×#4114yes—
762Dic79—24no—
763Dic79—21no—
764Dic79—21no—
765Dic79—24no—
766Dic79—24no—
767Dic79—24no—
768Dic79—24no—
769Dic79C22×#4112yes—
770Dic79C22×#4112yes—
771#62845—791nomaximal, Sylow
772C2×C79—22no—
773C2×C79—44no—
774C2×C79—42no—
775C2×C79C23×#4111yescharacteristic
776C2×C79H(7,𝔽2)11yescharacteristic
777C2×C792−1+611yescharacteristic
778D79—24no—
779D79—44no—
780D79—42no—
781#3507—794no—
782#3507—794no—
783#3507—794no—
784#3506—794no—
785#3506—794no—
786#3506—794no—
787#3493—794no—
788#3493—794no—
789#3493—791no—
790#3493—791no—
791#3493—791no—
792#3493D7911yescharacteristic, complemented
793#3492—794no—
794#3492—794no—
795#3492—792no—
796#3492—792no—
797#3459—794no—
798#3459—794no—
799#3458—791no—
800#3449—791no—
801#3449—792no—
802C2×#520—792no—
803C2×#520—791no—
804C79#6284511yescharacteristic, complemented, Sylow
805C22×#41—792no—
806C22×#41—791no—
807#559—798no—
808#559—794no—
809#559—798no—
810#559—794no—
811#557—794no—
812#557—794no—
813#556—794no—
814#556—798no—
815#556—798no—
816#556—794no—
817#556—794no—
818#556—794no—
819#556—794no—
820#556—798no—
821#556C2×D7914yescomplemented
822#555—794no—
823#555—798no—
824#555—794no—
825#555—794no—
826#555C2×D7914yescomplemented
827#554—794no—
828#554—794no—
829#554—794no—
830#554—794no—
831#554—794no—
832#554—794no—
833#553—798no—
834#553—794no—
835#553—798no—
836#553—794no—
837#553—794no—
838#553—794no—
839#553—794no—
840#553—794no—
841#553—794no—
842#553C2×D7914yescomplemented
843#552—798no—
844#552—794no—
845#552—794no—
846#552—794no—
847#552—794no—
848#552—794no—
849#552—798no—
850#552—794no—
851#552—794no—
852#552C2×D7914yescomplemented
853#550—798no—
854#547—798no—
855#547—794no—
856#547—794no—
857#547—794no—
858#547—794no—
859#544—794no—
860#544—794no—
861#544—792no—
862#544—791no—
863#544C2×D7911yescharacteristic, complemented
864#543—794no—
865#539—798no—
866#539—798no—
867#539—798no—
868#539—798no—
869#539—798no—
870#539—798no—
871#538—798no—
872#538—798no—
873#538—798no—
874#538—794no—
875#538—798no—
876#538—794no—
877#538—794no—
878#538C2×D7914yescomplemented
879#537—792no—
880#537—792no—
881#537—792no—
882#537—792no—
883#537—792no—
884#537—791no—
885#537C2×D7911yescharacteristic
886#536—794no—
887#536—794no—
888#536—792no—
889#536—792no—
890#535—794no—
891#535—792no—
892#535—792no—
893#535—794no—
894#534—794no—
895#534—794no—
896#534—794no—
897#533—794no—
898#533—794no—
899#533—794no—
900#532—794no—
901#532—794no—
902#532—794no—
903#529—798no—
904#529—798no—
905#529—794no—
906#529—794no—
907#529—798no—
908#529—798no—
909#529—794no—
910#529C2×D7914yescomplemented
911#525—792no—
912#525—792no—
913#525—798no—
914#525—794no—
915#525—794no—
916#525—798no—
917#525—798no—
918#525—794no—
919#525—794no—
920#525—798no—
921#525—798no—
922#525—792no—
923#525—798no—
924#525C2×D7912yescomplemented
925#520—792no—
926#520—794no—
927#520—794no—
928#520—798no—
929#520—792no—
930#520—794no—
931#520—794no—
932#520—794no—
933#520—794no—
934#520—794no—
935#520—792no—
936#520—794no—
937#520C2×D7912yescomplemented
938C2×C4×Q8—794no—
939C2×C4×Q8—792no—
940C2×C4×D4—798no—
941C2×C4×D4—794no—
942C2×C4×D4—792no—
943C2×C4×D4—792no—
944C2×C4×D4—792no—
945C2×#117—792no—
946C2×#117—794no—
947C2×#117—791no—
948C2×#117—791no—
949C2×#117C2×D7911yescharacteristic, complemented
950C22×C4⋊C4—791no—
951C22×C4⋊C4—791no—
952C22×C4⋊C4—791no—
953C22×C4⋊C4—794no—
954C2×#41—792no—
955C2×#41—798no—
956C2×#41—792no—
957C2×#41—794no—
958C2×#41—798no—
959C2×#41—792no—
960C2×#41—792no—
961C2×#41—792no—
962C2×#41—792no—
963C2×#41—792no—
964C2×#41—794no—
965C2×#41—1588no—
966C2×#41—15816no—
967C2×#41C22×D7912yes—
968C22×Q8—792no—
969C22×Q8—791no—
970C22×D4—791no—
971C22×D4—791no—
972C22×D4—794no—
973C22×D4—792no—
974C22×D4—791no—
975C23×C4—791no—
976C23×C4—792no—
977C23×C4—792no—
978C23×C4—792no—
979C23×C4—798no—
980C23×C4—794no—
981C23×C4—791no—
982C23×C4C22×D7911yescharacteristic
983C4⋊Q8—794no—
984C4⋊Q8—794no—
985C4⋊Q8—794no—
986C4⋊Q8—794no—
987C4⋊Q8—794no—
988C4⋊Q8—794no—
989C4⋊Q8—794no—
990C4⋊Q8—794no—
991C4⋊Q8C22×D7914yes—
992#127—794no—
993#127—794no—
994#127—794no—
995#126—798no—
996#126—798no—
997#126—798no—
998#126—798no—
999#126—798no—
1000#126—798no—
1001#126—798no—
1002#126—798no—
1003#126—798no—
1004#126—798no—
1005#126C22×D7918yes—
1006#126C22×D7918yes—
1007#125—798no—
1008#125—798no—
1009#125—794no—
1010#125—794no—
1011#125—798no—
1012#125—798no—
1013#125—794no—
1014#125—794no—
1015#125—798no—
1016#125—794no—
1017#125—794no—
1018#125C22×D7914yes—
1019#125C22×D7914yes—
1020#124—794no—
1021#124—798no—
1022#124—794no—
1023#124—798no—
1024#124—798no—
1025#124—794no—
1026#124—794no—
1027#124—794no—
1028#124—798no—
1029#124—794no—
1030#124—794no—
1031#124C22×D7918yes—
1032#124C22×D7914yes—
1033#123—794no—
1034#123—798no—
1035#123—794no—
1036#123—798no—
1037#123—798no—
1038#123—794no—
1039#123—794no—
1040#123—798no—
1041#123—798no—
1042#123—794no—
1043#123—794no—
1044#123—798no—
1045#123—794no—
1046#123—798no—
1047#123—798no—
1048#123—798no—
1049#123—798no—
1050#123—798no—
1051#123—798no—
1052#123—798no—
1053#123C22×D7918yes—
1054#123C22×D7914yes—
1055C22⋊Q8—792no—
1056C22⋊Q8—794no—
1057C22⋊Q8—792no—
1058C22⋊Q8—798no—
1059C22⋊Q8—792no—
1060C22⋊Q8—794no—
1061C22⋊Q8—792no—
1062C22⋊Q8—798no—
1063C22⋊Q8—794no—
1064C22⋊Q8—798no—
1065C22⋊Q8—798no—
1066C22⋊Q8—794no—
1067C22⋊Q8—792no—
1068C22⋊Q8—794no—
1069C22⋊Q8—792no—
1070C22⋊Q8—794no—
1071C22⋊Q8—798no—
1072C22⋊Q8—798no—
1073C22⋊Q8—798no—
1074C22⋊Q8—798no—
1075C22⋊Q8—798no—
1076C22⋊Q8—794no—
1077C22⋊Q8—794no—
1078C22⋊Q8—798no—
1079C22⋊Q8—798no—
1080C22⋊Q8C22×D7914yes—
1081C22⋊Q8C22×D7912yes—
1082C22⋊Q8C22×D7912yes—
1083C22⋊Q8C22×D7914yes—
1084#121—794no—
1085#121—798no—
1086#121—792no—
1087#121—794no—
1088#121—794no—
1089#121—792no—
1090#121—794no—
1091#121—798no—
1092#121—798no—
1093#121—794no—
1094#121—792no—
1095#121—794no—
1096#121—792no—
1097#121—794no—
1098#121—794no—
1099#121—792no—
1100#121—792no—
1101#121—794no—
1102#121—798no—
1103#121—794no—
1104#121—794no—
1105#121—794no—
1106#121—794no—
1107#121—794no—
1108#121—798no—
1109#121—798no—
1110#121—794no—
1111#121—794no—
1112#121C22×D7914yes—
1113#121C22×D7918yes—
1114#121C22×D7912yes—
1115#121C22×D7912yes—
1116#121C22×D7914yes—
1117#120—794no—
1118#120—794no—
1119#120—794no—
1120#120—798no—
1121#120—794no—
1122#120—794no—
1123#120—798no—
1124#120—794no—
1125#120—794no—
1126#120C22×D7914yes—
1127C4×Q8—794no—
1128C4×Q8—794no—
1129C4×Q8—794no—
1130C4×Q8—794no—
1131C4×Q8—798no—
1132C4×Q8—794no—
1133C4×Q8—798no—
1134C4×Q8—794no—
1135C4×Q8—794no—
1136C4×Q8—794no—
1137C4×Q8—794no—
1138C4×Q8—798no—
1139C4×Q8—794no—
1140C4×Q8—794no—
1141C4×Q8—794no—
1142C4×Q8C22×D7914yes—
1143C4×Q8C22×D7914yes—
1144C4×D4—798no—
1145C4×D4—794no—
1146C4×D4—794no—
1147C4×D4—798no—
1148C4×D4—794no—
1149C4×D4—798no—
1150C4×D4—798no—
1151C4×D4—798no—
1152C4×D4—798no—
1153C4×D4—794no—
1154C4×D4—794no—
1155C4×D4—794no—
1156C4×D4—794no—
1157C4×D4—798no—
1158C4×D4—794no—
1159C4×D4—794no—
1160C4×D4—794no—
1161C4×D4—798no—
1162C4×D4—798no—
1163C4×D4—798no—
1164C4×D4—798no—
1165C4×D4—798no—
1166C4×D4—798no—
1167C4×D4—798no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—798no—
1171C4×D4—798no—
1172C4×D4—798no—
1173C4×D4—794no—
1174C4×D4—798no—
1175C4×D4—794no—
1176C4×D4—794no—
1177C4×D4—794no—
1178C4×D4C22×D7918yes—
1179C4×D4C22×D7914yes—
1180C4×D4C22×D7914yes—
1181C4×D4C22×D7914yes—
1182C4×D4C22×D7914yes—
1183#117—792no—
1184#117—794no—
1185#117—794no—
1186#117—792no—
1187#117—794no—
1188#117—792no—
1189#117—794no—
1190#117—794no—
1191#117—794no—
1192#117—794no—
1193#117—798no—
1194#117—794no—
1195#117—798no—
1196#117—798no—
1197#117—798no—
1198#117—794no—
1199#117—798no—
1200#117—798no—
1201#117—798no—
1202#117C22×D7912yes—
1203#117C22×D7914yes—
1204#117C22×D7914yes—
1205#117C22×D7914yes—
1206#117C22×D7918yes—
1207C2×C4⋊C4—791no—
1208C2×C4⋊C4—791no—
1209C2×C4⋊C4—792no—
1210C2×C4⋊C4—792no—
1211C2×C4⋊C4—792no—
1212C2×C4⋊C4—798no—
1213C2×C4⋊C4—794no—
1214C2×C4⋊C4—794no—
1215C2×C4⋊C4—794no—
1216C2×C4⋊C4—794no—
1217C2×C4⋊C4—792no—
1218C2×C4⋊C4—794no—
1219C2×C4⋊C4—798no—
1220C2×C4⋊C4—798no—
1221C2×C4⋊C4—794no—
1222C2×C4⋊C4—794no—
1223C2×C4⋊C4—794no—
1224C2×C4⋊C4—794no—
1225C2×C4⋊C4—792no—
1226C2×C4⋊C4C22×D7911yescharacteristic
1227C2×C4⋊C4C22×D7914yes—
1228C2×C4⋊C4C22×D7911yescharacteristic
1229C2×C22⋊C4—792no—
1230C2×C22⋊C4—792no—
1231C2×C22⋊C4—794no—
1232C2×C22⋊C4—798no—
1233C2×C22⋊C4C22×D7912yes—
1234C2×C42—792no—
1235C2×C42—792no—
1236C2×C42—798no—
1237C2×C42—794no—
1238C2×C42C22×D7912yes—
1239C24—791no—
1240C24—794no—
1241C24—791no—
1242C24C23×D7911yescharacteristic
1243#41—28no—
1244#41—6328no—
1245#41—6328no—
1246#41—1588no—
1247#41—1588no—
1248#41—1588no—
1249#41—1588no—
1250#41—15816no—
1251#41—15816no—
1252#41—1588no—
1253#41—1588no—
1254#41—1588no—
1255C2×Q8—794no—
1256C2×Q8—798no—
1257C2×Q8—791no—
1258C2×Q8—791no—
1259C2×Q8—792no—
1260C2×Q8—794no—
1261C2×Q8—791no—
1262C2×Q8—791no—
1263C2×Q8—1584no—
1264C2×Q8—1588no—
1265C2×Q8C23×D7912yes—
1266C2×Q8C23×D7914yes—
1267C2×D4—794no—
1268C2×D4—794no—
1269C2×D4—798no—
1270C2×D4—794no—
1271C2×D4—794no—
1272C2×D4—794no—
1273C2×D4—792no—
1274C2×D4—792no—
1275C2×D4—794no—
1276C2×D4—792no—
1277C2×D4—794no—
1278C2×D4—792no—
1279C2×D4—794no—
1280C2×D4—794no—
1281C2×D4—794no—
1282C2×D4—794no—
1283C2×D4—792no—
1284C2×D4—792no—
1285C2×D4—792no—
1286C2×D4—1584no—
1287C2×D4—1588no—
1288C2×D4—1584no—
1289C2×D4—15816no—
1290C2×D4—1584no—
1291C2×D4C23×D7914yes—
1292C2×D4C23×D7912yes—
1293C2×D4C23×D7914yes—
1294C2×D4C23×D7914yes—
1295C2×D4C23×D7914yes—
1296C22×C4—24no—
1297C22×C4—792no—
1298C22×C4—792no—
1299C22×C4—798no—
1300C22×C4—798no—
1301C22×C4—794no—
1302C22×C4—798no—
1303C22×C4—794no—
1304C22×C4—798no—
1305C22×C4—798no—
1306C22×C4—798no—
1307C22×C4—791no—
1308C22×C4—798no—
1309C22×C4—792no—
1310C22×C4—792no—
1311C22×C4—791no—
1312C22×C4—794no—
1313C22×C4—794no—
1314C22×C4—794no—
1315C22×C4—792no—
1316C22×C4—794no—
1317C22×C4—792no—
1318C22×C4—6322no—
1319C22×C4—6322no—
1320C22×C4—6328no—
1321C22×C4—6322no—
1322C22×C4—15816no—
1323C22×C4—1584no—
1324C22×C4C23×D7911yescharacteristic
1325C22×C4C23×D7912yes—
1326C22×C4C23×D7912yes—
1327C22×C4C23×D7914yes—
1328C22×C4C23×D7912yes—
1329C22×C4C23×D7912yes—
1330C22×C4C23×D7918yes—
1331C22×C4C23×D7911yescharacteristic
1332C4⋊C4—794no—
1333C4⋊C4—794no—
1334C4⋊C4—794no—
1335C4⋊C4—798no—
1336C4⋊C4—794no—
1337C4⋊C4—794no—
1338C4⋊C4—798no—
1339C4⋊C4—794no—
1340C4⋊C4—794no—
1341C4⋊C4—798no—
1342C4⋊C4—794no—
1343C4⋊C4—798no—
1344C4⋊C4—798no—
1345C4⋊C4—798no—
1346C4⋊C4—794no—
1347C4⋊C4—794no—
1348C4⋊C4—794no—
1349C4⋊C4—792no—
1350C4⋊C4—794no—
1351C4⋊C4—798no—
1352C4⋊C4—794no—
1353C4⋊C4—794no—
1354C4⋊C4—792no—
1355C4⋊C4—794no—
1356C4⋊C4—794no—
1357C4⋊C4—798no—
1358C4⋊C4—794no—
1359C4⋊C4—794no—
1360C4⋊C4C23×D7914yes—
1361C4⋊C4C23×D7912yes—
1362C4⋊C4C23×D7918yes—
1363C4⋊C4C23×D7912yes—
1364C4⋊C4C23×D7914yes—
1365C4⋊C4C23×D7918yes—
1366C4⋊C4C23×D7914yes—
1367C4⋊C4C23×D7914yes—
1368C4⋊C4C23×D7914yes—
1369C4⋊C4C23×D7914yes—
1370C22⋊C4—794no—
1371C22⋊C4—798no—
1372C22⋊C4—794no—
1373C22⋊C4—794no—
1374C22⋊C4—794no—
1375C22⋊C4—798no—
1376C22⋊C4—794no—
1377C22⋊C4—794no—
1378C22⋊C4—798no—
1379C22⋊C4—794no—
1380C22⋊C4—798no—
1381C22⋊C4—798no—
1382C22⋊C4—798no—
1383C22⋊C4—794no—
1384C22⋊C4—794no—
1385C22⋊C4—798no—
1386C22⋊C4—794no—
1387C22⋊C4—794no—
1388C22⋊C4—794no—
1389C22⋊C4—794no—
1390C22⋊C4—798no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4C23×D7914yes—
1394C22⋊C4C23×D7918yes—
1395C22⋊C4C23×D7918yes—
1396C22⋊C4C23×D7914yes—
1397C22⋊C4C23×D7918yes—
1398C22⋊C4C23×D7914yes—
1399C22⋊C4C23×D7914yes—
1400C22⋊C4C23×D7914yes—
1401C42—798no—
1402C42—798no—
1403C42—794no—
1404C42—794no—
1405C42—798no—
1406C42—794no—
1407C42—794no—
1408C42—794no—
1409C42—794no—
1410C42—794no—
1411C42C23×D7918yes—
1412C42C23×D7914yes—
1413C42C23×D7914yes—
1414C42C23×D7914yes—
1415C23—22no—
1416C23—41no—
1417C23—41no—
1418C23—3161no—
1419C23—3161no—
1420C23—3164no—
1421C23—3161no—
1422C23—3161no—
1423C23—3164no—
1424C23—794no—
1425C23—792no—
1426C23—792no—
1427C23—794no—
1428C23—1588no—
1429C23—1582no—
1430C23C24×D7914yes—
1431C23C24×D7912yes—
1432C23C24×D7911yescharacteristic
1433Q8—24no—
1434Q8—44no—
1435Q8—3168no—
1436Q8—3164no—
1437Q8—1582no—
1438Q8—1582no—
1439Q8—1582no—
1440Q8—1582no—
1441Q8—1588no—
1442Q8—1584no—
1443D4—28no—
1444D4—24no—
1445D4—44no—
1446D4—44no—
1447D4—44no—
1448D4—3164no—
1449D4—3164no—
1450D4—3164no—
1451D4—3164no—
1452D4—3164no—
1453D4—3168no—
1454D4—3164no—
1455D4—3164no—
1456D4—1584no—
1457D4—1584no—
1458D4—1588no—
1459D4—1584no—
1460D4—1584no—
1461D4—1588no—
1462D4—1584no—
1463D4—1584no—
1464D4—1588no—
1465D4—1588no—
1466D4—1584no—
1467C2×C4—22no—
1468C2×C4—24no—
1469C2×C4—24no—
1470C2×C4—28no—
1471C2×C4—42no—
1472C2×C4—48no—
1473C2×C4—42no—
1474C2×C4—3168no—
1475C2×C4—3164no—
1476C2×C4—3168no—
1477C2×C4—3168no—
1478C2×C4—3168no—
1479C2×C4—3164no—
1480C2×C4—3162no—
1481C2×C4—3162no—
1482C2×C4—3168no—
1483C2×C4—3168no—
1484C2×C4—791no—
1485C2×C4—791no—
1486C2×C4—794no—
1487C2×C4—798no—
1488C2×C4—798no—
1489C2×C4—794no—
1490C2×C4—794no—
1491C2×C4—791no—
1492C2×C4—794no—
1493C2×C4—791no—
1494C2×C4—794no—
1495C2×C4—794no—
1496C2×C4—1588no—
1497C2×C4—1588no—
1498C2×C4—1588no—
1499C2×C4—1582no—
1500C2×C4—1588no—
1501C2×C4—1584no—
1502C2×C4—1584no—
1503C2×C4#41×D7914yes—
1504C2×C4C24×D7914yes—
1505C2×C4C24×D7914yes—
1506C2×C4C24×D7914yes—
1507C2×C4C24×D7914yes—
1508C2×C4C24×D7914yes—
1509C2×C4C24×D7911yescharacteristic
1510C2×C4C24×D7911yescharacteristic
1511C2×C4C24×D7912yes—
1512C22—21no—
1513C22—21no—
1514C22—22no—
1515C22—24no—
1516C22—24no—
1517C22—22no—
1518C22—24no—
1519C22—22no—
1520C22—44no—
1521C22—3164no—
1522C22—3164no—
1523C22—31616no—
1524C22—794no—
1525C22—1584no—
1526C22—1582no—
1527C22—1582no—
1528C22—1584no—
1529C22—1584no—
1530C22—1582no—
1531C22—1582no—
1532C22—1582no—
1533C22C2×#41×D7912yes—
1534C22C25×D7911yescharacteristic
1535C4—21no—
1536C4—21no—
1537C4—24no—
1538C4—24no—
1539C4—24no—
1540C4—24no—
1541C4—24no—
1542C4—792no—
1543C4—792no—
1544C4—1584no—
1545C4—1581no—
1546C4—1581no—
1547C4—1584no—
1548C4—1584no—
1549C4—1584no—
1550C4—1584no—
1551C4C2×#41×D7914yes—
1552C2—22no—
1553C2—42no—
1554C2—44no—
1555C2—3162no—
1556C2—3164no—
1557C2—1584no—
1558C2C22×#41×D7911yescharacteristic
1559C2#2377821111yescharacteristic
1560C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3493C2
hypercenter#3493D79
hypocenterC79#62845
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #23777259C2semidirect
2. #23777256C2semidirect
3. #23777255C2semidirect
4. #23777247C2semidirect
5. #23777246C2semidirect
6. #23777242C2semidirect
7. #23777121C2semidirect
8. #23777120C2semidirect
9. #23777119C2semidirect
10. #23777114C2semidirect
11. #23777111C2semidirect
12. #23777106C2semidirect
13. #23777104C2semidirect
14. #23777103C2semidirect
15. #23777100C2semidirect
16. #23776811C2semidirect
17. #23776810C2semidirect
18. #23776804C2semidirect
19. #23776730C2semidirect
20. #23776728C2semidirect
21. C2×#19099043C2semidirect
22. #520×D79C2semidirect
23. C79×#3493C2semidirect
26. #19099297C22semidirect
27. #19099296C22semidirect
28. #19099295C22semidirect
29. #19099295C22semidirect
30. #19099290C22semidirect
31. #19099289C22semidirect
32. #19099287C22semidirect
33. #19099285C22semidirect
34. #19099284C22semidirect
35. #19099282C22semidirect
36. #19099281C22semidirect
37. #19099281C22semidirect
38. #19099280C22semidirect
39. #19099280C22semidirect
40. #19099279C22semidirect
41. #19099277C22semidirect
42. #19099276C22semidirect
43. #19099275C22semidirect
44. #19099273C22semidirect
45. #19099272C22semidirect
46. #19099271C22semidirect
47. #19099270C22semidirect
48. #19099269C22semidirect
49. #19099268C22semidirect
50. #19099266C22semidirect
51. #19099265C22semidirect
52. #19099265C22semidirect
53. #19099264C22semidirect
54. #19099263C22semidirect
55. #19099259C22semidirect
56. #19099257C22semidirect
57. #19099257C22semidirect
58. #19099256C22semidirect
59. #19099255C22semidirect
60. #19099255C22semidirect
61. #19099254C22semidirect
62. #19099253C22semidirect
63. #19099252C22semidirect
64. #19099252C22semidirect
65. #19099251C22semidirect
66. #19099249C22semidirect
67. #19099246C22semidirect
68. #19099231C22semidirect
69. #19099218C22semidirect
70. #19099217C22semidirect
71. #19099214C22semidirect
72. #19099213C22semidirect
73. #19099211C22semidirect
74. #19099194C22semidirect
75. #19099193C22semidirect
76. #19099191C22semidirect
77. #19099190C22semidirect
79. #19099161C22semidirect
80. #19099157C22semidirect
81. #19099156C22semidirect
82. #19099155C22semidirect
83. #19099154C22semidirect
84. #19099154C22semidirect
85. #19099153C22semidirect
86. #19099152C22semidirect
87. #19099151C22semidirect
88. #19099150C22semidirect
89. #19099147C22semidirect
90. #19099147C22semidirect
91. #19099145C22semidirect
98. #19099136C22semidirect
99. #19099136C22semidirect
100. #19099136C22semidirect
101. #19099135C22semidirect
102. #19099129C22semidirect
103. #19099129C22semidirect
104. #19099129C22semidirect
105. #19099128C22semidirect
109. #19099119C22semidirect
110. #19099118C22semidirect
111. #19099115C22semidirect
115. #19099100C22semidirect
116. #19099099C22semidirect
117. #19099097C22semidirect
118. #19099096C22semidirect
119. #19099094C22semidirect
120. #19099092C22semidirect
121. #19099091C22semidirect
122. #19099076C22semidirect
123. #19099075C22semidirect
124. #19099075C22semidirect
125. #19099074C22semidirect
126. #19099073C22semidirect
127. #19099073C22semidirect
128. #19099072C22semidirect
129. #19099072C22semidirect
130. #19099072C22semidirect
131. #19099072C22semidirect
132. #19099071C22semidirect
133. #19099070C22semidirect
134. #19099069C22semidirect
135. #19099046C22semidirect
136. #19099045C22semidirect
137. #19099044C22semidirect
138. #19099044C22semidirect
139. #19099043C22semidirect
140. #19099043C22semidirect
141. #19099043C22semidirect
142. #19099043C22semidirect
143. #19099043C22semidirect
144. #19099043C22semidirect
145. #19099042C22semidirect
146. #19099042C22semidirect
147. C2×C4×Dic158C22semidirect
148. C4×Q8×D79C22semidirect
151. C2×(C22⋊D79)⋊C4C22semidirect
153. C4×D4×D79C22semidirect
155. C2×#14579119C22semidirect
157. #117×D79C22semidirect
158. C22×C4⋊Dic79C22semidirect
160. C2×C4⋊C4×D79C22semidirect
161. C2×C4⋊C4×D79C22semidirect
162. #556×C79C22semidirect
163. #555×C79C22semidirect
164. #553×C79C22semidirect
165. #552×C79C22semidirect
166. #544×C79C22semidirect
167. #538×C79C22semidirect
169. #529×C79C22semidirect
170. #525×C79C22semidirect
171. #520×C79C22semidirect
172. C2×#117×C79C22semidirect
519. C2×C4×D79#41semidirect
792. #3493D79semidirect
804. C79#62845semidirect
821. #556C2×D79semidirect
826. #555C2×D79semidirect
842. #553C2×D79semidirect
852. #552C2×D79semidirect
863. #544C2×D79semidirect
878. #538C2×D79semidirect
910. #529C2×D79semidirect
924. #525C2×D79semidirect
937. #520C2×D79semidirect
949. C2×#117C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237772592
#237772562
#237772552
#237772472
#237772462
#237772422
#237771212
#237771202
#237771192
#237771142
#237771112
#237771062
#237771042
#237771032
#237771002
#237768112
#237768102
#237768042
#237767302
#237767282
C2×#190990432
#520×D792
C79×#34932
#6284579