Finite Group Databasebeta

← #35196913

Subgroups — #35196913

Order 20224.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777694C214yesmaximal, complemented
2#23777687C214yesmaximal, complemented
3#23777646C214yesmaximal, complemented
4#23777623C214yesmaximal, complemented
5#23777607C218yesmaximal, complemented
6#23777446C214yesmaximal, complemented
7#23777440C214yesmaximal, complemented
8#23777229C214yesmaximal, complemented
9#23777197C214yesmaximal, complemented
10#23777155C212yesmaximal, complemented
11#23777153C212yesmaximal, complemented
12#23777109C211yesmaximal, characteristic, complemented
13#23777106C214yesmaximal, complemented
14#23777083C214yesmaximal, complemented
15#23777081C212yesmaximal, complemented
16#23777075C212yesmaximal, complemented
17#23777047C212yesmaximal, complemented
18#525×D79C212yesmaximal, complemented
19C22×#14579141C211yesmaximal, characteristic, complemented
20C79×#3492C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yescomplemented
22C2×#41×D79C2212yescomplemented
23C23×Dic158C2211yescharacteristic, complemented
24C23×C4×D79C2211yescharacteristic
25#19099317C2218yescomplemented
26#19099315C2218yescomplemented
27#19099310C2218yescomplemented
28#19099309C2218yescomplemented
29#19099287C2214yescomplemented
30#19099281C2214yescomplemented
31#19099274C2214yescomplemented
32#19099271C2218yescomplemented
33#19099271C2218yescomplemented
34#19099270C2218yescomplemented
35#19099269C2218yescomplemented
36#19099268C2214yescomplemented
37#19099268C2214yescomplemented
38#19099265C2218yescomplemented
39#19099261C2214yescomplemented
40#19099259C2218yescomplemented
41#19099255C2218yescomplemented
42#19099253C2218yescomplemented
43#19099252C2214yescomplemented
44#19099251C2214yescomplemented
45#19099251C2214yescomplemented
46#19099248C2214yescomplemented
47#19099248C2214yescomplemented
48#19099242C2218yescomplemented
49#19099240C2218yescomplemented
50#19099238C2218yescomplemented
51#19099237C2218yescomplemented
52#19099236C2218yescomplemented
53#19099236C2218yescomplemented
54Q8×D316C2214yescomplemented
55D4×Dic158C2214yescomplemented
56D4×Dic158C2214yescomplemented
57#19099226C2214yescomplemented
58#19099226C2214yescomplemented
59#19099226C2214yescomplemented
60#19099225C2214yescomplemented
61#19099222C2214yescomplemented
62#19099222C2214yescomplemented
63#19099219C2214yescomplemented
64#19099219C2214yescomplemented
65#19099219C2214yescomplemented
66#19099217C2218yescomplemented
67#19099217C2214yescomplemented
68#19099215C2214yescomplemented
69#19099214C2214yescomplemented
70#19099213C2218yescomplemented
71#19099210C2214yescomplemented
72#19099208C2218yescomplemented
73#19099208C2214yescomplemented
74#19099205C2218yescomplemented
75#19099202C2218yescomplemented
76#19099201C2218yescomplemented
77#19099194C2211yescharacteristic, complemented
78#19099193C2218yescomplemented
79#19099191C2214yescomplemented
80#19099188C2214yes—
81#19099188C2218yescomplemented
82#19099187C2214yescomplemented
83#19099186C2218yescomplemented
84#19099179C2218yescomplemented
85#19099178C2214yescomplemented
86#19099176C2214yescomplemented
87#19099171C2214yescomplemented
88#19099161C2218yescomplemented
89#19099160C2214yescomplemented
90#19099157C2218yescomplemented
91#19099157C2218yescomplemented
92#19099157C2218yescomplemented
93#19099154C2218yescomplemented
94#19099153C2214yescomplemented
95#19099150C2214yescomplemented
96#19099149C2218yescomplemented
97#19099146C2218yescomplemented
98#19099144C2211yescharacteristic, complemented
99#19099144C2214yescomplemented
100#19099142C2214yescomplemented
101#19099141C2214yescomplemented
102#19099139C2212yescomplemented
103#19099139C2214yescomplemented
104#19099136C2214yescomplemented
105#19099135C2218yescomplemented
106#19099134C2212yescomplemented
107#19099121C2214yes—
108#19099118C2214yescomplemented
109#19099117C2214yescomplemented
110#19099098C2214yescomplemented
111#19099095C2214yescomplemented
112#19099076C2212yes—
113#19099076C2212yescomplemented
114#19099075C2212yes—
115#19099075C2214yescomplemented
116#19099074C2212yescomplemented
117#19099074C2214yescomplemented
118#19099073C2212yes—
119#19099073C2212yescomplemented
120#19099073C2214yescomplemented
121#19099072C2214yes—
122#19099072C2214yescomplemented
123#19099071C2214yes—
124#19099070C2212yes—
125#19099069C2218yescomplemented
126#19099069C2214yescomplemented
127#123×D79C2214yescomplemented
128C2×#14579141C2214yes—
129C2×#14579141C2212yescomplemented
130C2×#14579141C2212yescomplemented
131C2×#14579141C2214yescomplemented
132C2×#14579141C2214yescomplemented
133C2×#14579141C2214yescomplemented
134C2×#14579141C2214yescomplemented
135C2×#14579141C2214yescomplemented
136C22⋊Q8×D79C2212yes—
137C22⋊Q8×D79C2212yescomplemented
138C22⋊Q8×D79C2214yescomplemented
139#121×D79C2212yes—
140#121×D79C2212yescomplemented
141#120×D79C2214yes—
142#19099046C2214yescomplemented
143#19099044C2212yescomplemented
144#19099043C2214yescomplemented
145#19099040C2212yescomplemented
146#19099035C2218yes—
147C4×D4×D79C2214yes—
148C4×D4×D79C2214yescomplemented
149#117×D79C2212yescomplemented
150C22×C4⋊Dic79C2212yescomplemented
151C22×(C2×D79)⋊C4C2212yes—
152#554×C79C2214yescomplemented
153#553×C79C2214yescomplemented
154#552×C79C2214yescomplemented
155#547×C79C2214yescomplemented
156#544×C79C2211yescharacteristic, complemented
157#539×C79C2214yescomplemented
158#537×C79C2211yescharacteristic, complemented
159#525×C79C2212yescomplemented
160#525×C79C2214yescomplemented
161#520×C79C2212yescomplemented
162C22×C4⋊C4×C79C2211yescharacteristic, complemented
163C24×D79C2311yescharacteristic
164#14579208—48no—
165C2×#11929625C2312yes—
166C2×#11929624C2312yes—
167C2×#11929624C2314yes—
168C2×#11929624C2314yes—
169C2×#11929624C2314yescomplemented
170C2×#11929623C2318yes—
171C2×#11929623C2314yes—
172C2×#11929623C2312yes—
173C2×#11929623C2314yescomplemented
174#41×D79—48no—
175C22×Dic158—44no—
176C22×Dic158C2312yes—
177C22×Dic158C2314yes—
178C22×Dic158C2314yes—
179C22×Dic158C2312yes—
180C22×Dic158C2314yescomplemented
181C2×Q8×D79C2312yes—
182C2×Q8×D79C2314yescomplemented
183C2×D4×D79C2314yes—
184C2×D4×D79C2314yes—
185C2×D4×D79C2314yes—
186C2×D4×D79C2312yes—
187C23×Dic79C2312yes—
188C23×Dic79C2311yescharacteristic
189C22×C4×D79—44no—
190C22×C4×D79C2312yes—
191C22×C4×D79C2312yes—
192C22×C4×D79C2314yes—
193C22×C4×D79C2312yes—
194C22×C4×D79C2312yes—
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197#14579161C2314yescomplemented
198#14579161C2318yescomplemented
199#14579160C2318yescomplemented
200#14579160C2314yescomplemented
201#14579160C2318yescomplemented
202#14579160C2318yescomplemented
203#14579159C2314yescomplemented
204#14579156C2318yes—
205#14579156C2318yes—
206#14579156C2318yes—
207#14579156C2318yescomplemented
208#14579156C2318yescomplemented
209#14579156C2318yescomplemented
210#14579155C2318yes—
211#14579154C2318yescomplemented
212#14579154C2318yescomplemented
213#14579153C2318yescomplemented
214#14579152C2318yescomplemented
215#14579152C2318yescomplemented
216#14579152C2318yescomplemented
217#14579152C2314yescomplemented
218#14579151C2318yescomplemented
219#14579151C2318yescomplemented
220#14579151C2318yescomplemented
221#14579150C2318yes—
222#14579149C2318yes—
223#14579149C2314yescomplemented
224#14579148C2314yescomplemented
225#14579147C2318yes—
226#14579147C2318yes—
227#14579147C2318yescomplemented
228#14579147C2318yescomplemented
229#14579146C2318yes—
230#14579146C2318yes—
231#14579146C2318yes—
232#14579146C2314yes—
233#14579146C2314yes—
234#14579146C2318yescomplemented
235#14579145C2318yes—
236#14579145C2318yes—
237#14579145C2314yes—
238#14579145C2318yescomplemented
239#14579145C2318yescomplemented
240#14579144C2318yes—
241#14579144C2318yes—
242#14579144C2314yes—
243#14579143C2318yes—
244#14579143C2314yes—
245#14579143C2314yes—
246#14579143C2318yescomplemented
247#14579143C2318yescomplemented
248#14579142C2318yes—
249#14579142C2314yes—
250#14579141C2314yes—
251#14579141C2312yes—
252#14579141C2314yes—
253#14579141C2318yes—
254#14579141C2318yes—
255#14579141C2318yes—
256#14579141C2314yes—
257#14579141C2314yes—
258#14579141C2314yes—
259#14579141C2314yes—
260#14579141C2318yes—
261#14579141C2318yes—
262#14579141C2312yes—
263#14579141C2314yes—
264#14579141C2314yes—
265#14579141C2314yescomplemented
266#14579141C2314yescomplemented
267#14579141C2314yescomplemented
268#14579141C2318yescomplemented
269#14579141C2318yescomplemented
270#14579140C2314yes—
271#14579140C2314yes—
272#14579140C2312yes—
273#14579140C2312yes—
274#14579140C2314yescomplemented
275#14579140C2318yescomplemented
276#14579140C2314yescomplemented
277#14579139C2318yes—
278#14579139C2318yes—
279#14579139C2314yes—
280#14579139C2314yes—
281#14579139C2318yescomplemented
282#14579139C2318yescomplemented
283#14579139C2318yescomplemented
284#14579138C2318yes—
285#14579138C2314yes—
286#14579138C2318yes—
287#14579138C2314yes—
288#14579138C2318yescomplemented
289#14579138C2318yescomplemented
290#14579138C2318yescomplemented
291#14579138C2318yescomplemented
292#14579137C2312yes—
293#14579137C2318yes—
294#14579137C2312yes—
295#14579137C2318yescomplemented
296#14579136C2312yes—
297#14579136C2318yes—
298#14579136C2312yes—
299#14579136C2314yescomplemented
300#14579135C2318yes—
301#14579135C2314yes—
302#14579135C2314yes—
303#14579135C2312yes—
304#14579135C2312yes—
305#14579135C2318yescomplemented
306#14579134C2318yes—
307#14579134C2314yes—
308#14579134C2314yes—
309#14579133C2314yes—
310#14579133C2318yes—
311#14579133C2318yes—
312#14579133C2318yes—
313#14579133C2314yes—
314#14579132C2312yes—
315#14579132C2312yes—
316#14579132C2318yescomplemented
317#14579131C2314yes—
318#14579131C2318yes—
319#14579131C2314yes—
320#14579131C2314yes—
321#14579130C2314yes—
322#14579129C2314yes—
323#14579129C2318yes—
324#14579129C2314yes—
325#14579129C2314yes—
326Q8×Dic79C2318yescomplemented
327C4×Dic158C2314yescomplemented
328C4×Dic158C2314yescomplemented
329C4×Dic158C2318yescomplemented
330#14579126C2314yescomplemented
331#14579126C2314yescomplemented
332#14579126C2314yescomplemented
333C4×D316C2318yes—
334C4×D316C2314yes—
335C4×D316C2314yes—
336C4×D316C2318yescomplemented
337D4×Dic79C2318yes—
338D4×Dic79C2314yes—
339D4×Dic79C2318yes—
340D4×Dic79C2314yes—
341D4×Dic79C2318yescomplemented
342#14579123C2318yes—
343#14579123C2314yes—
344#14579123C2314yes—
345#14579123C2314yescomplemented
346C4×C22⋊D79C2318yes—
347C4×C22⋊D79C2318yes—
348C4×C22⋊D79C2318yes—
349C4×C22⋊D79C2314yes—
350C4×C22⋊D79C2314yes—
351C4×C22⋊D79C2314yes—
352C4×C22⋊D79C2314yes—
353(C22⋊D79)⋊C4C2318yes—
354(C22⋊D79)⋊C4C2318yes—
355(C22⋊D79)⋊C4C2314yes—
356(C22⋊D79)⋊C4C2314yes—
357(C22⋊D79)⋊C4C2318yes—
358(C22⋊D79)⋊C4C2314yes—
359(C22⋊D79)⋊C4C2314yes—
360#14579120C2314yes—
361#14579120C2312yes—
362#14579120C2318yescomplemented
363#14579119C2318yes—
364#14579119C2312yes—
365#14579119C2312yes—
366#14579119C2314yescomplemented
367#14579119C2318yescomplemented
368#14579118C2314yes—
369#14579118C2318yes—
370#14579117C2318yes—
371#14579117C2314yes—
372C2×C4⋊Dic79C2314yes—
373C2×C4⋊Dic79C2314yes—
374C2×C4⋊Dic79C2314yes—
375C2×C4⋊Dic79C2314yes—
376C2×C4⋊Dic79C2318yes—
377C2×C4⋊Dic79C2318yescomplemented
378C4⋊C4×D79C2314yes—
379C4⋊C4×D79C2312yes—
380C4⋊C4×D79C2312yes—
381C4⋊C4×D79C2314yes—
382C4⋊C4×D79C2314yescomplemented
383C4⋊C4×D79C2318yescomplemented
384C2×(C2×D79)⋊C4C2314yes—
385C2×(C2×D79)⋊C4C2314yes—
386C2×(C2×D79)⋊C4C2318yes—
387C2×(C2×D79)⋊C4C2318yes—
388C2×(C2×D79)⋊C4C2314yes—
389C2×(C2×D79)⋊C4C2314yes—
390C22⋊C4×D79C2314yes—
391C22⋊C4×D79C2314yes—
392C22⋊C4×D79C2318yes—
393C22⋊C4×D79C2314yes—
394C22⋊C4×D79C2314yes—
395C22⋊C4×D79C2314yes—
396C42×D79C2314yes—
397C2×#41×C79C2312yes—
398C2×#41×C79C2314yes—
399C23×C4×C79C2311yescharacteristic
400C23×C4×C79C2312yes—
401C4⋊Q8×C79C2314yescomplemented
402#126×C79C2318yescomplemented
403#125×C79C2318yescomplemented
404#125×C79C2314yescomplemented
405#123×C79C2318yes—
406#123×C79C2314yes—
407#123×C79C2318yescomplemented
408C22⋊Q8×C79C2314yes—
409C22⋊Q8×C79C2312yes—
410C22⋊Q8×C79C2312yes—
411C22⋊Q8×C79C2314yes—
412C22⋊Q8×C79C2314yescomplemented
413C22⋊Q8×C79C2318yescomplemented
414#121×C79C2314yes—
415#121×C79C2314yes—
416#121×C79C2312yes—
417#121×C79C2312yes—
418#121×C79C2314yescomplemented
419#120×C79C2314yes—
420C4×Q8×C79C2314yescomplemented
421C4×D4×C79C2318yes—
422C4×D4×C79C2318yes—
423C4×D4×C79C2314yes—
424C4×D4×C79C2314yes—
425C4×D4×C79C2314yescomplemented
426#117×C79C2312yes—
427#117×C79C2314yes—
428#117×C79C2314yescomplemented
429C2×C4⋊C4×C79C2311yescharacteristic
430C2×C4⋊C4×C79C2312yes—
431C2×C4⋊C4×C79C2314yes—
432C2×C4⋊C4×C79C2311yescharacteristic
433C2×C4⋊C4×C79C2314yes—
434C2×C4⋊C4×C79C2314yescomplemented
435C23×D79—24no—
436C23×D79—42no—
437C23×D79—42no—
438C23×D79C2412yes—
439C23×D79C2412yes—
440C23×D79C2411yescharacteristic
441C23×D79C2414yes—
442C23×D79C2411yescharacteristic
443#11929625—44no—
444#11929624—28no—
445#11929624—48no—
446#11929624—48no—
447#11929624—48no—
448#11929623—48no—
449#11929623—416no—
450#11929623—44no—
451#11929623—48no—
452C2×Dic158—28no—
453C2×Dic158—48no—
454C2×Dic158—48no—
455C2×Dic158—48no—
456C2×Dic158—44no—
457C2×Dic158C2412yes—
458C2×Dic158C2414yes—
459C2×Dic158C2414yes—
460C2×Dic158C2414yes—
461C2×Dic158C2418yes—
462C2×Dic158C2418yes—
463C2×Dic158C2414yes—
464Q8×D79—44no—
465Q8×D79—48no—
466C2×D316C2412yes—
467C2×D316C2414yes—
468C2×D316C2414yes—
469C2×D316C2414yes—
470C2×D316C2414yes—
471C2×C22⋊D79C2414yes—
472C2×C22⋊D79C2414yes—
473C2×C22⋊D79C2414yes—
474C2×C22⋊D79C2414yes—
475C2×C22⋊D79C2418yes—
476C2×C22⋊D79C2414yes—
477C2×C22⋊D79C2414yes—
478C2×C22⋊D79C2414yes—
479D4×D79—216no—
480D4×D79—48no—
481D4×D79—48no—
482D4×D79—44no—
483C22×Dic79—44no—
484C22×Dic79—42no—
485C22×Dic79C2414yes—
486C22×Dic79C2412yes—
487C22×Dic79C2414yes—
488C22×Dic79C2414yes—
489C22×Dic79C2418yes—
490C22×Dic79C2414yes—
491C22×Dic79C2411yescharacteristic
492C22×Dic79C2412yes—
493C22×Dic79C2411yescharacteristic
494C2×C4×D79—28no—
495C2×C4×D79—44no—
496C2×C4×D79—48no—
497C2×C4×D79—44no—
498C2×C4×D79—44no—
499C2×C4×D79—44no—
500C2×C4×D79—44no—
501C2×C4×D79C2412yes—
502C2×C4×D79C2414yes—
503C2×C4×D79C2412yes—
504C2×C4×D79C2412yes—
505C2×C4×D79C2412yes—
506C2×C4×D79C2414yes—
507C2×C4×D79C2414yes—
508C2×C4×D79C2418yes—
509C2×C4×D79C2414yes—
510C2×C4×D79C2418yes—
511C2×C4×D79C2414yes—
512C2×C4×D79C2412yes—
513C2×C4×D79C2412yes—
514C2×C4×D79C2412yes—
515C2×C4×D79C2412yes—
516C4⋊Dic79C2412yes—
517C4⋊Dic79C2414yes—
518C4⋊Dic79C2412yes—
519C4⋊Dic79C2414yes—
520C4⋊Dic79C2418yes—
521C4⋊Dic79C2418yes—
522C4⋊Dic79C2418yes—
523C4⋊Dic79C2418yes—
524C4⋊Dic79C2414yes—
525C4⋊Dic79C2418yes—
526C4⋊Dic79C2418yes—
527C4⋊Dic79C2414yes—
528Dic79⋊C4C2414yes—
529Dic79⋊C4C2414yes—
530Dic79⋊C4C2414yes—
531Dic79⋊C4C2414yes—
532Dic79⋊C4C2414yes—
533Dic79⋊C4C2414yes—
534Dic79⋊C4C2418yes—
535Dic79⋊C4C2418yes—
536Dic79⋊C4C2418yes—
537Dic79⋊C4C2418yes—
538Dic79⋊C4C2418yes—
539Dic79⋊C4C2418yes—
540C22⋊Dic79C2414yes—
541C22⋊Dic79C2414yes—
542C22⋊Dic79C2414yes—
543C22⋊Dic79C2414yes—
544C22⋊Dic79C2414yes—
545C22⋊Dic79C2418yes—
546C22⋊Dic79C2418yes—
547(C2×D79)⋊C4C2414yes—
548(C2×D79)⋊C4C2418yes—
549(C2×D79)⋊C4C2414yes—
550(C2×D79)⋊C4C2414yes—
551(C2×D79)⋊C4C2414yes—
552(C2×D79)⋊C4C2414yes—
553(C2×D79)⋊C4C2414yes—
554(C2×D79)⋊C4C2414yes—
555(C2×D79)⋊C4C2414yes—
556(C2×D79)⋊C4C2414yes—
557(C2×D79)⋊C4C2414yes—
558(C2×D79)⋊C4C2418yes—
559(C2×D79)⋊C4C2418yes—
560(C2×D79)⋊C4C2418yes—
561(C2×D79)⋊C4C2418yes—
562(C2×D79)⋊C4C2418yes—
563(C2×D79)⋊C4C2418yes—
564(C2×D79)⋊C4C2418yes—
565C4×Dic79C2414yes—
566C4×Dic79C2414yes—
567C4×Dic79C2414yes—
568C4×Dic79C2418yes—
569C4×Dic79C2418yes—
570C4×Dic79C2418yes—
571C24×C79C2411yescharacteristic
572#41×C79—28no—
573#41×C79—48no—
574C2×Q8×C79C2412yes—
575C2×Q8×C79C2414yes—
576C2×D4×C79C2414yes—
577C2×D4×C79C2412yes—
578C2×D4×C79C2414yes—
579C2×D4×C79C2414yes—
580C2×D4×C79C2414yes—
581C22×C4×C79—24no—
582C22×C4×C79—44no—
583C22×C4×C79C2412yes—
584C22×C4×C79C2412yes—
585C22×C4×C79C2411yescharacteristic
586C22×C4×C79C2414yes—
587C22×C4×C79C2414yes—
588C22×C4×C79C2412yes—
589C22×C4×C79C2414yes—
590C22×C4×C79C2412yes—
591C22×C4×C79C2418yes—
592C22×C4×C79C2411yescharacteristic
593C4⋊C4×C79C2414yes—
594C4⋊C4×C79C2414yes—
595C4⋊C4×C79C2418yes—
596C4⋊C4×C79C2412yes—
597C4⋊C4×C79C2418yes—
598C4⋊C4×C79C2412yes—
599C4⋊C4×C79C2414yes—
600C4⋊C4×C79C2414yes—
601C4⋊C4×C79C2414yes—
602C4⋊C4×C79C2418yes—
603C4⋊C4×C79C2414yes—
604C22⋊C4×C79C2414yes—
605C22⋊C4×C79C2414yes—
606C22⋊C4×C79C2418yes—
607C22⋊C4×C79C2414yes—
608C22⋊C4×C79C2418yes—
609C22⋊C4×C79C2414yes—
610C22⋊C4×C79C2414yes—
611C42×C79C2418yes—
612C42×C79C2414yes—
613C23×C79—22no—
614C23×C79—22no—
615C23×C79—22no—
616C23×C79C2514yes—
617C23×C79C2511yescharacteristic
618C23×C79C2511yescharacteristic
619C23×C79C2511yescharacteristic
620C22×D79—24no—
621C22×D79—22no—
622C22×D79—24no—
623C22×D79—24no—
624C22×D79—24no—
625C22×D79—28no—
626C22×D79—41no—
627C22×D79—42no—
628C22×D79—41no—
629C22×D79—41no—
630C22×D79—42no—
631C22×D79—41no—
632C22×D79—44no—
633C22×D79—44no—
634C22×D79—416no—
635C22×D792−1+414yescomplemented
636C22×D79C2512yes—
637C22×D79C2514yes—
638C22×D79C2512yes—
639Q8×C79—24no—
640Q8×C79—44no—
641D4×C79—28no—
642D4×C79—28no—
643D4×C79—28no—
644D4×C79—24no—
645D4×C79—44no—
646C2×C4×C79—22no—
647C2×C4×C79—28no—
648C2×C4×C79—24no—
649C2×C4×C79—24no—
650C2×C4×C79—28no—
651C2×C4×C79—42no—
652C2×C4×C79—44no—
653C2×C4×C79—42no—
654C2×C4×C79—48no—
655C2×C4×C79H(5,𝔽2)14yes—
656C2×C4×C79C2514yes—
657C2×C4×C79C2514yes—
658C2×C4×C79C2514yes—
659C2×C4×C79C2514yes—
660C2×C4×C79C2512yes—
661C2×C4×C79C2514yes—
662C2×C4×C79C2512yes—
663C22⋊D79—28no—
664C22⋊D79—28no—
665C22⋊D79—28no—
666C22⋊D79—28no—
667C22⋊D79—44no—
668C22⋊D79—44no—
669C22⋊D79—44no—
670C22⋊D79—48no—
671C2×Dic79—24no—
672C2×Dic79—28no—
673C2×Dic79—41no—
674C2×Dic79—42no—
675C2×Dic79—41no—
676C2×Dic79—44no—
677C2×Dic79—44no—
678C2×Dic79—44no—
679C2×Dic79—48no—
680C2×Dic79C2514yes—
681C2×Dic79C2514yes—
682C2×Dic79C2512yes—
683C2×Dic79C2518yes—
684C2×Dic79C2514yes—
685C2×Dic79C2512yes—
686D316—28no—
687D316—24no—
688D316—44no—
689D316—44no—
690D316—44no—
691C4×D79—28no—
692C4×D79—24no—
693C4×D79—24no—
694C4×D79—24no—
695C4×D79—24no—
696C4×D79—28no—
697C4×D79—42no—
698C4×D79—42no—
699C4×D79—42no—
700C4×D79—42no—
701C4×D79—44no—
702C4×D79—44no—
703C4×D79—44no—
704C4×D79—48no—
705C4×D79—48no—
706Dic158—28no—
707Dic158—24no—
708Dic158—28no—
709Dic158—48no—
710Dic158—44no—
711Dic158—48no—
712Dic158—44no—
713C22×C79—28no—
714C22×C79—21no—
715C22×C79—21no—
716C22×C79—21no—
717C22×C79—21no—
718C22×C79—21no—
719C22×C79—21no—
720C22×C79—24no—
721C22×C79—24no—
722C22×C79—24no—
723C22×C79C2×H(5,𝔽2)12yes—
724C22×C79C2×2−1+412yes—
725C22×C79#58512yes—
726C22×C79C2611yescharacteristic
727C2×D79—22no—
728C2×D79—22no—
729C2×D79—24no—
730C2×D79—22no—
731C2×D79—24no—
732C2×D79—22no—
733C2×D79—24no—
734C2×D79—22no—
735C2×D79—44no—
736C2×D79—48no—
737C2×D79—48no—
738C2×D79—44no—
739C2×D79—88no—
740C2×D79C2×2−1+414yes—
741C4×C79—22no—
742C4×C79—24no—
743C4×C79—24no—
744C4×C79—24no—
745C4×C79—24no—
746C4×C79—24no—
747C4×C79C2×H(5,𝔽2)14yes—
748Dic79—24no—
749Dic79—22no—
750Dic79—28no—
751Dic79—22no—
752Dic79—24no—
753Dic79—24no—
754#62819—791nomaximal, Sylow
755C2×C79—22no—
756C2×C79—22no—
757C2×C79—22no—
758C2×C79—44no—
759C2×C79C22×H(5,𝔽2)11yescharacteristic
760C2×C79C22×2−1+411yescharacteristic
761C2×C79C2×#58511yescharacteristic
762D79—24no—
763D79—42no—
764D79—44no—
765#3541—794no—
766#3541—794no—
767#3538—794no—
768#3536—794no—
769#3535—798no—
770#3520—794no—
771#3520—794no—
772#3505—794no—
773#3501—794no—
774#3495—792no—
775#3495—792no—
776#3492—794no—
777#3492—791no—
778#3492D7911yescharacteristic, complemented
779#3490—794no—
780#3489—792no—
781#3489—792no—
782#3486—792no—
783C2×#525—792no—
784C22×C22⋊Q8—791no—
785C79#6281911yescharacteristic, complemented, Sylow
786C2×2−1+4—792no—
787C22×#41—792no—
788C23×Q8—791no—
789C24×C4—791no—
790#563—798no—
791#563—798no—
792#562—798no—
793#562—798no—
794#556—794no—
795#556—794no—
796#554—794no—
797#554—798no—
798#554—798no—
799#554—798no—
800#554—798no—
801#554—794no—
802#554—794no—
803#554C2×D7914yescomplemented
804#553—798no—
805#553—798no—
806#553—794no—
807#553C2×D7914yescomplemented
808#552—794no—
809#552—794no—
810#552—798no—
811#552—798no—
812#552—794no—
813#552—794no—
814#552—794no—
815#552C2×D7914yescomplemented
816#551—798no—
817#551—798no—
818#551—798no—
819#551—798no—
820#551—798no—
821#551—798no—
822D4×Q8—794no—
823D4×Q8—794no—
824D4×Q8—794no—
825D4×Q8—794no—
826D4×Q8—794no—
827D4×Q8—794no—
828#548—794no—
829#548—794no—
830#548—794no—
831#548—794no—
832#548—794no—
833#548—794no—
834#547—794no—
835#547—798no—
836#547—798no—
837#547—794no—
838#547—794no—
839#547C2×D7914yescomplemented
840#546—798no—
841#546—798no—
842#546—798no—
843#546—794no—
844#546—798no—
845#546—794no—
846#544—798no—
847#544—794no—
848#544—791no—
849#544C2×D7911yescharacteristic, complemented
850#543—794no—
851#543—798no—
852#542—794no—
853#542—798no—
854#542—798no—
855#542—794no—
856#541—794no—
857#541—794no—
858#539—798no—
859#539—798no—
860#539—798no—
861#539—798no—
862#539—798no—
863#539—794no—
864#539C2×D7914yescomplemented
865#538—798no—
866#538—794no—
867#538—794no—
868#538—798no—
869#537—794no—
870#537—794no—
871#537—791no—
872#537—794no—
873#537C2×D7911yescharacteristic, complemented
874#536—792no—
875#536—798no—
876#536—794no—
877#536—792no—
878#536—794no—
879#534—794no—
880#533—794no—
881#533—794no—
882#529—794no—
883#529—794no—
884#525—792no—
885#525—792no—
886#525—794no—
887#525—794no—
888#525—792no—
889#525—792no—
890#525—792no—
891#525—792no—
892#525—794no—
893#525—794no—
894#525—798no—
895#525—794no—
896#525—794no—
897#525—792no—
898#525—794no—
899#525C2×D7912yescomplemented
900#525C2×D7914yescomplemented
901C2×#123—794no—
902C2×C22⋊Q8—792no—
903C2×C22⋊Q8—792no—
904C2×C22⋊Q8—794no—
905C2×C22⋊Q8—792no—
906C2×C22⋊Q8—792no—
907C2×C22⋊Q8—794no—
908C2×C22⋊Q8—794no—
909C2×C22⋊Q8—794no—
910C2×C22⋊Q8—794no—
911C2×C22⋊Q8—794no—
912C2×C22⋊Q8—794no—
913C2×#121—792no—
914C2×#121—792no—
915C2×#120—794no—
916#520—794no—
917#520—794no—
918#520—792no—
919#520C2×D7912yescomplemented
920#519—792no—
921#518—798no—
922C2×C4×D4—794no—
923C2×C4×D4—794no—
924C2×#117—792no—
925C22×C4⋊C4—792no—
926C22×C4⋊C4C2×D7911yescharacteristic, complemented
927C22×C22⋊C4—792no—
928C25—791no—
9292−1+4—3168no—
930C2×#41—3168no—
931C2×#41—792no—
932C2×#41—794no—
933C2×#41—792no—
934C2×#41—798no—
935C2×#41—794no—
936C2×#41—794no—
937C2×#41—794no—
938C2×#41—794no—
939C2×#41—792no—
940C2×#41C22×D7912yes—
941C2×#41C22×D7914yes—
942C22×Q8—3164no—
943C22×Q8—792no—
944C22×Q8—794no—
945C22×Q8—792no—
946C22×Q8—794no—
947C22×Q8—794no—
948C22×Q8—794no—
949C22×Q8—792no—
950C22×D4—794no—
951C22×D4—794no—
952C22×D4—792no—
953C22×D4—794no—
954C23×C4—3164no—
955C23×C4—792no—
956C23×C4—791no—
957C23×C4—792no—
958C23×C4—792no—
959C23×C4—794no—
960C23×C4—792no—
961C23×C4—792no—
962C23×C4—792no—
963C23×C4—792no—
964C23×C4C22×D7911yescharacteristic
965C23×C4C22×D7912yes—
966C4⋊Q8—794no—
967C4⋊Q8—794no—
968C4⋊Q8—798no—
969C4⋊Q8—798no—
970C4⋊Q8—798no—
971C4⋊Q8—794no—
972C4⋊Q8—798no—
973C4⋊Q8C22×D7914yescomplemented
974#126—798no—
975#126—798no—
976#126—798no—
977#126—798no—
978#126—798no—
979#126—798no—
980#126—798no—
981#126—798no—
982#126—798no—
983#126C22×D7918yescomplemented
984#125—794no—
985#125—798no—
986#125—798no—
987#125—798no—
988#125—798no—
989#125—798no—
990#125—798no—
991#125—798no—
992#125C22×D7914yescomplemented
993#125C22×D7918yescomplemented
994#124—798no—
995#124—794no—
996#124—798no—
997#124—798no—
998#124—798no—
999#124—798no—
1000#124—794no—
1001#124—798no—
1002#123—794no—
1003#123—798no—
1004#123—794no—
1005#123—798no—
1006#123—798no—
1007#123—794no—
1008#123—794no—
1009#123—798no—
1010#123—798no—
1011#123—798no—
1012#123—798no—
1013#123—794no—
1014#123—794no—
1015#123—794no—
1016#123—798no—
1017#123—798no—
1018#123—798no—
1019#123—798no—
1020#123—798no—
1021#123—798no—
1022#123—798no—
1023#123C22×D7914yes—
1024#123C22×D7918yes—
1025#123C22×D7918yescomplemented
1026C22⋊Q8—792no—
1027C22⋊Q8—792no—
1028C22⋊Q8—798no—
1029C22⋊Q8—798no—
1030C22⋊Q8—792no—
1031C22⋊Q8—792no—
1032C22⋊Q8—794no—
1033C22⋊Q8—794no—
1034C22⋊Q8—794no—
1035C22⋊Q8—794no—
1036C22⋊Q8—798no—
1037C22⋊Q8—794no—
1038C22⋊Q8—794no—
1039C22⋊Q8—792no—
1040C22⋊Q8—794no—
1041C22⋊Q8—794no—
1042C22⋊Q8—798no—
1043C22⋊Q8—798no—
1044C22⋊Q8—794no—
1045C22⋊Q8—794no—
1046C22⋊Q8—794no—
1047C22⋊Q8—794no—
1048C22⋊Q8—798no—
1049C22⋊Q8—798no—
1050C22⋊Q8—792no—
1051C22⋊Q8—794no—
1052C22⋊Q8—794no—
1053C22⋊Q8—794no—
1054C22⋊Q8—794no—
1055C22⋊Q8—798no—
1056C22⋊Q8—798no—
1057C22⋊Q8—798no—
1058C22⋊Q8—794no—
1059C22⋊Q8—798no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8—798no—
1063C22⋊Q8—798no—
1064C22⋊Q8—794no—
1065C22⋊Q8—794no—
1066C22⋊Q8—798no—
1067C22⋊Q8—798no—
1068C22⋊Q8—798no—
1069C22⋊Q8—798no—
1070C22⋊Q8—798no—
1071C22⋊Q8—798no—
1072C22⋊Q8C22×D7912yes—
1073C22⋊Q8C22×D7912yes—
1074C22⋊Q8C22×D7914yes—
1075C22⋊Q8C22×D7914yes—
1076C22⋊Q8C22×D7914yescomplemented
1077C22⋊Q8C22×D7918yescomplemented
1078#121—792no—
1079#121—794no—
1080#121—792no—
1081#121—794no—
1082#121—798no—
1083#121—798no—
1084#121—798no—
1085#121—798no—
1086#121—792no—
1087#121—792no—
1088#121—794no—
1089#121—794no—
1090#121—798no—
1091#121—798no—
1092#121—792no—
1093#121—792no—
1094#121—794no—
1095#121—798no—
1096#121—794no—
1097#121—794no—
1098#121—798no—
1099#121C22×D7912yes—
1100#121C22×D7912yes—
1101#121C22×D7914yes—
1102#121C22×D7914yes—
1103#121C22×D7914yescomplemented
1104#120—794no—
1105#120—794no—
1106#120—794no—
1107#120—794no—
1108#120—798no—
1109#120—794no—
1110#120—794no—
1111#120—794no—
1112#120—798no—
1113#120C22×D7914yes—
1114C4×Q8—798no—
1115C4×Q8—794no—
1116C4×Q8—794no—
1117C4×Q8—794no—
1118C4×Q8—794no—
1119C4×Q8—794no—
1120C4×Q8—798no—
1121C4×Q8C22×D7914yescomplemented
1122C4×D4—794no—
1123C4×D4—794no—
1124C4×D4—798no—
1125C4×D4—798no—
1126C4×D4—798no—
1127C4×D4—794no—
1128C4×D4—794no—
1129C4×D4—794no—
1130C4×D4—794no—
1131C4×D4—798no—
1132C4×D4—798no—
1133C4×D4—798no—
1134C4×D4—794no—
1135C4×D4—794no—
1136C4×D4—798no—
1137C4×D4—794no—
1138C4×D4—794no—
1139C4×D4—794no—
1140C4×D4—794no—
1141C4×D4—794no—
1142C4×D4—798no—
1143C4×D4—798no—
1144C4×D4—798no—
1145C4×D4—794no—
1146C4×D4—794no—
1147C4×D4—798no—
1148C4×D4—798no—
1149C4×D4C22×D7914yes—
1150C4×D4C22×D7914yes—
1151C4×D4C22×D7918yes—
1152C4×D4C22×D7918yes—
1153C4×D4C22×D7914yescomplemented
1154#117—792no—
1155#117—794no—
1156#117—798no—
1157#117—792no—
1158#117—792no—
1159#117—798no—
1160#117—794no—
1161#117—798no—
1162#117—794no—
1163#117—798no—
1164#117—794no—
1165#117—798no—
1166#117C22×D7912yes—
1167#117C22×D7914yes—
1168#117C22×D7914yescomplemented
1169C2×C4⋊C4—794no—
1170C2×C4⋊C4—794no—
1171C2×C4⋊C4—794no—
1172C2×C4⋊C4—794no—
1173C2×C4⋊C4—798no—
1174C2×C4⋊C4—798no—
1175C2×C4⋊C4—792no—
1176C2×C4⋊C4—792no—
1177C2×C4⋊C4—794no—
1178C2×C4⋊C4—794no—
1179C2×C4⋊C4—794no—
1180C2×C4⋊C4—798no—
1181C2×C4⋊C4C22×D7911yescharacteristic
1182C2×C4⋊C4C22×D7911yescharacteristic
1183C2×C4⋊C4C22×D7912yes—
1184C2×C4⋊C4C22×D7914yes—
1185C2×C4⋊C4C22×D7914yes—
1186C2×C4⋊C4C22×D7914yescomplemented
1187C2×C22⋊C4—794no—
1188C2×C22⋊C4—794no—
1189C2×C22⋊C4—798no—
1190C2×C22⋊C4—794no—
1191C2×C22⋊C4—794no—
1192C2×C22⋊C4—798no—
1193C2×C22⋊C4—794no—
1194C2×C22⋊C4—794no—
1195C2×C22⋊C4—794no—
1196C2×C22⋊C4—794no—
1197C2×C22⋊C4—794no—
1198C2×C22⋊C4—798no—
1199C2×C42—794no—
1200C24—3162no—
1201C24—3162no—
1202C24—791no—
1203C24—794no—
1204C24—791no—
1205C24—792no—
1206C24—792no—
1207C24—1584no—
1208C24C23×D7911yescharacteristic
1209#41—28no—
1210#41—48no—
1211#41—3168no—
1212#41—3168no—
1213#41—3168no—
1214#41—3164no—
1215#41—3168no—
1216#41—3168no—
1217#41—31616no—
1218#41—3164no—
1219#41—1588no—
1220C2×Q8—3168no—
1221C2×Q8—3168no—
1222C2×Q8—3168no—
1223C2×Q8—3164no—
1224C2×Q8—3164no—
1225C2×Q8—3168no—
1226C2×Q8—794no—
1227C2×Q8—798no—
1228C2×Q8—794no—
1229C2×Q8—798no—
1230C2×Q8—794no—
1231C2×Q8—794no—
1232C2×Q8—792no—
1233C2×Q8—1588no—
1234C2×Q8C23×D7912yes—
1235C2×Q8C23×D7914yes—
1236C2×D4—3168no—
1237C2×D4—3168no—
1238C2×D4—3164no—
1239C2×D4—794no—
1240C2×D4—798no—
1241C2×D4—794no—
1242C2×D4—794no—
1243C2×D4—794no—
1244C2×D4—794no—
1245C2×D4—794no—
1246C2×D4—794no—
1247C2×D4—794no—
1248C2×D4—794no—
1249C2×D4—794no—
1250C2×D4—794no—
1251C2×D4—792no—
1252C2×D4—15816no—
1253C2×D4C23×D7914yes—
1254C2×D4C23×D7914yes—
1255C2×D4C23×D7914yes—
1256C2×D4C23×D7912yes—
1257C2×D4C23×D7914yes—
1258C22×C4—24no—
1259C22×C4—44no—
1260C22×C4—3164no—
1261C22×C4—3164no—
1262C22×C4—3164no—
1263C22×C4—3164no—
1264C22×C4—3164no—
1265C22×C4—3168no—
1266C22×C4—3162no—
1267C22×C4—3164no—
1268C22×C4—794no—
1269C22×C4—794no—
1270C22×C4—798no—
1271C22×C4—791no—
1272C22×C4—792no—
1273C22×C4—791no—
1274C22×C4—794no—
1275C22×C4—794no—
1276C22×C4—792no—
1277C22×C4—794no—
1278C22×C4—792no—
1279C22×C4—798no—
1280C22×C4—798no—
1281C22×C4—794no—
1282C22×C4—792no—
1283C22×C4—792no—
1284C22×C4—794no—
1285C22×C4—792no—
1286C22×C4—792no—
1287C22×C4—794no—
1288C22×C4—792no—
1289C22×C4—794no—
1290C22×C4—792no—
1291C22×C4—792no—
1292C22×C4—1588no—
1293C22×C4C23×D7914yes—
1294C22×C4C23×D7912yes—
1295C22×C4C23×D7912yes—
1296C22×C4C23×D7911yescharacteristic
1297C22×C4C23×D7914yes—
1298C22×C4C23×D7912yes—
1299C22×C4C23×D7914yes—
1300C22×C4C23×D7912yes—
1301C22×C4C23×D7918yes—
1302C22×C4C23×D7911yescharacteristic
1303C4⋊C4—794no—
1304C4⋊C4—794no—
1305C4⋊C4—794no—
1306C4⋊C4—794no—
1307C4⋊C4—794no—
1308C4⋊C4—794no—
1309C4⋊C4—798no—
1310C4⋊C4—798no—
1311C4⋊C4—798no—
1312C4⋊C4—798no—
1313C4⋊C4—798no—
1314C4⋊C4—798no—
1315C4⋊C4—798no—
1316C4⋊C4—798no—
1317C4⋊C4—792no—
1318C4⋊C4—794no—
1319C4⋊C4—798no—
1320C4⋊C4—798no—
1321C4⋊C4—794no—
1322C4⋊C4—792no—
1323C4⋊C4—794no—
1324C4⋊C4—798no—
1325C4⋊C4—794no—
1326C4⋊C4—798no—
1327C4⋊C4C23×D7914yes—
1328C4⋊C4C23×D7914yes—
1329C4⋊C4C23×D7912yes—
1330C4⋊C4C23×D7912yes—
1331C4⋊C4C23×D7914yes—
1332C4⋊C4C23×D7914yes—
1333C4⋊C4C23×D7914yes—
1334C4⋊C4C23×D7918yes—
1335C4⋊C4C23×D7918yes—
1336C4⋊C4C23×D7914yes—
1337C4⋊C4C23×D7918yes—
1338C22⋊C4—794no—
1339C22⋊C4—794no—
1340C22⋊C4—794no—
1341C22⋊C4—794no—
1342C22⋊C4—794no—
1343C22⋊C4—798no—
1344C22⋊C4—798no—
1345C22⋊C4—798no—
1346C22⋊C4—798no—
1347C22⋊C4—794no—
1348C22⋊C4—794no—
1349C22⋊C4—798no—
1350C22⋊C4—798no—
1351C22⋊C4—794no—
1352C22⋊C4—794no—
1353C22⋊C4—794no—
1354C22⋊C4—794no—
1355C22⋊C4—794no—
1356C22⋊C4—794no—
1357C22⋊C4—798no—
1358C22⋊C4—798no—
1359C22⋊C4—794no—
1360C22⋊C4—794no—
1361C22⋊C4—798no—
1362C22⋊C4—798no—
1363C22⋊C4C23×D7914yes—
1364C22⋊C4C23×D7914yes—
1365C22⋊C4C23×D7914yes—
1366C22⋊C4C23×D7918yes—
1367C22⋊C4C23×D7914yes—
1368C22⋊C4C23×D7914yes—
1369C22⋊C4C23×D7918yes—
1370C42—794no—
1371C42—794no—
1372C42—794no—
1373C42—798no—
1374C42—798no—
1375C42—798no—
1376C42C23×D7914yes—
1377C42C23×D7918yes—
1378C23—22no—
1379C23—22no—
1380C23—22no—
1381C23—31616no—
1382C23—3161no—
1383C23—3162no—
1384C23—3161no—
1385C23—3161no—
1386C23—3162no—
1387C23—3161no—
1388C23—3164no—
1389C23—3164no—
1390C23—794no—
1391C23—792no—
1392C23—792no—
1393C23—794no—
1394C23—1584no—
1395C23—1584no—
1396C23—1588no—
1397C23—1584no—
1398C23—1582no—
1399C23—1584no—
1400C23C24×D7914yes—
1401C23C24×D7911yescharacteristic
1402C23C24×D7911yescharacteristic
1403C23C24×D7911yescharacteristic
1404Q8—24no—
1405Q8—44no—
1406Q8—3168no—
1407Q8—3168no—
1408Q8—3164no—
1409Q8—3164no—
1410Q8—1588no—
1411Q8—1588no—
1412Q8—1584no—
1413D4—28no—
1414D4—28no—
1415D4—28no—
1416D4—24no—
1417D4—44no—
1418D4—3164no—
1419D4—3164no—
1420D4—3164no—
1421D4—3164no—
1422D4—3164no—
1423D4—3164no—
1424D4—3168no—
1425D4—1588no—
1426D4—1588no—
1427D4—1588no—
1428D4—1588no—
1429D4—1588no—
1430D4—1584no—
1431C2×C4—22no—
1432C2×C4—28no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—28no—
1436C2×C4—42no—
1437C2×C4—44no—
1438C2×C4—42no—
1439C2×C4—48no—
1440C2×C4—3162no—
1441C2×C4—3162no—
1442C2×C4—3162no—
1443C2×C4—3162no—
1444C2×C4—3164no—
1445C2×C4—3164no—
1446C2×C4—3164no—
1447C2×C4—3168no—
1448C2×C4—3168no—
1449C2×C4—3161no—
1450C2×C4—3162no—
1451C2×C4—3161no—
1452C2×C4—3164no—
1453C2×C4—3164no—
1454C2×C4—3164no—
1455C2×C4—3168no—
1456C2×C4—794no—
1457C2×C4—794no—
1458C2×C4—792no—
1459C2×C4—798no—
1460C2×C4—794no—
1461C2×C4—792no—
1462C2×C4—1588no—
1463C2×C4—1584no—
1464C2×C4—1588no—
1465C2×C4—1584no—
1466C2×C4—1584no—
1467C2×C4—1584no—
1468C2×C4—1584no—
1469C2×C4—1588no—
1470C2×C4#1457920714yes—
1471C2×C4C24×D7914yes—
1472C2×C4C24×D7914yes—
1473C2×C4C24×D7914yes—
1474C2×C4C24×D7914yes—
1475C2×C4C24×D7914yes—
1476C2×C4C24×D7912yes—
1477C2×C4C24×D7912yes—
1478C22—28no—
1479C22—21no—
1480C22—21no—
1481C22—21no—
1482C22—21no—
1483C22—21no—
1484C22—21no—
1485C22—24no—
1486C22—24no—
1487C22—24no—
1488C22—3164no—
1489C22—3168no—
1490C22—3168no—
1491C22—3164no—
1492C22—794no—
1493C22—6328no—
1494C22—1584no—
1495C22—1582no—
1496C22—1584no—
1497C22—1582no—
1498C22—1584no—
1499C22—1582no—
1500C22—1582no—
1501C22—1582no—
1502C22C2×#1457920712yes—
1503C222−1+4×D7912yes—
1504C22#1909939812yes—
1505C22C25×D7911yescharacteristic
1506C4—22no—
1507C4—24no—
1508C4—24no—
1509C4—24no—
1510C4—24no—
1511C4—24no—
1512C4—1582no—
1513C4—1582no—
1514C4—1584no—
1515C4—1588no—
1516C4—1584no—
1517C4—1584no—
1518C4C2×#1457920714yes—
1519C2—22no—
1520C2—22no—
1521C2—22no—
1522C2—44no—
1523C2—3162no—
1524C2—3164no—
1525C2—1584no—
1526C2C22×#1457920711yescharacteristic
1527C2C2×2−1+4×D7911yescharacteristic
1528C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3492C2
hypercenter#3492D79
hypocenterC79#62819
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #23777694C2semidirect
2. #23777687C2semidirect
3. #23777646C2semidirect
4. #23777623C2semidirect
5. #23777607C2semidirect
6. #23777446C2semidirect
7. #23777440C2semidirect
8. #23777229C2semidirect
9. #23777197C2semidirect
10. #23777155C2semidirect
11. #23777153C2semidirect
12. #23777109C2semidirect
13. #23777106C2semidirect
14. #23777083C2semidirect
15. #23777081C2semidirect
16. #23777075C2semidirect
17. #23777047C2semidirect
18. #525×D79C2semidirect
19. C22×#14579141C2semidirect
20. C79×#3492C2semidirect
21. C2×#14579208C22semidirect
22. C2×#41×D79C22semidirect
23. C23×Dic158C22semidirect
25. #19099317C22semidirect
26. #19099315C22semidirect
27. #19099310C22semidirect
28. #19099309C22semidirect
29. #19099287C22semidirect
30. #19099281C22semidirect
31. #19099274C22semidirect
32. #19099271C22semidirect
33. #19099271C22semidirect
34. #19099270C22semidirect
35. #19099269C22semidirect
36. #19099268C22semidirect
37. #19099268C22semidirect
38. #19099265C22semidirect
39. #19099261C22semidirect
40. #19099259C22semidirect
41. #19099255C22semidirect
42. #19099253C22semidirect
43. #19099252C22semidirect
44. #19099251C22semidirect
45. #19099251C22semidirect
46. #19099248C22semidirect
47. #19099248C22semidirect
48. #19099242C22semidirect
49. #19099240C22semidirect
50. #19099238C22semidirect
51. #19099237C22semidirect
52. #19099236C22semidirect
53. #19099236C22semidirect
54. Q8×D316C22semidirect
55. D4×Dic158C22semidirect
56. D4×Dic158C22semidirect
57. #19099226C22semidirect
58. #19099226C22semidirect
59. #19099226C22semidirect
60. #19099225C22semidirect
61. #19099222C22semidirect
62. #19099222C22semidirect
63. #19099219C22semidirect
64. #19099219C22semidirect
65. #19099219C22semidirect
66. #19099217C22semidirect
67. #19099217C22semidirect
68. #19099215C22semidirect
69. #19099214C22semidirect
70. #19099213C22semidirect
71. #19099210C22semidirect
72. #19099208C22semidirect
73. #19099208C22semidirect
74. #19099205C22semidirect
75. #19099202C22semidirect
76. #19099201C22semidirect
77. #19099194C22semidirect
78. #19099193C22semidirect
79. #19099191C22semidirect
81. #19099188C22semidirect
82. #19099187C22semidirect
83. #19099186C22semidirect
84. #19099179C22semidirect
85. #19099178C22semidirect
86. #19099176C22semidirect
87. #19099171C22semidirect
88. #19099161C22semidirect
89. #19099160C22semidirect
90. #19099157C22semidirect
91. #19099157C22semidirect
92. #19099157C22semidirect
93. #19099154C22semidirect
94. #19099153C22semidirect
95. #19099150C22semidirect
96. #19099149C22semidirect
97. #19099146C22semidirect
98. #19099144C22semidirect
99. #19099144C22semidirect
100. #19099142C22semidirect
101. #19099141C22semidirect
102. #19099139C22semidirect
103. #19099139C22semidirect
104. #19099136C22semidirect
105. #19099135C22semidirect
106. #19099134C22semidirect
108. #19099118C22semidirect
109. #19099117C22semidirect
110. #19099098C22semidirect
111. #19099095C22semidirect
113. #19099076C22semidirect
115. #19099075C22semidirect
116. #19099074C22semidirect
117. #19099074C22semidirect
119. #19099073C22semidirect
120. #19099073C22semidirect
122. #19099072C22semidirect
125. #19099069C22semidirect
126. #19099069C22semidirect
127. #123×D79C22semidirect
129. C2×#14579141C22semidirect
130. C2×#14579141C22semidirect
131. C2×#14579141C22semidirect
132. C2×#14579141C22semidirect
133. C2×#14579141C22semidirect
134. C2×#14579141C22semidirect
135. C2×#14579141C22semidirect
137. C22⋊Q8×D79C22semidirect
138. C22⋊Q8×D79C22semidirect
140. #121×D79C22semidirect
142. #19099046C22semidirect
143. #19099044C22semidirect
144. #19099043C22semidirect
145. #19099040C22semidirect
148. C4×D4×D79C22semidirect
149. #117×D79C22semidirect
150. C22×C4⋊Dic79C22semidirect
152. #554×C79C22semidirect
153. #553×C79C22semidirect
154. #552×C79C22semidirect
155. #547×C79C22semidirect
156. #544×C79C22semidirect
157. #539×C79C22semidirect
158. #537×C79C22semidirect
159. #525×C79C22semidirect
160. #525×C79C22semidirect
161. #520×C79C22semidirect
162. C22×C4⋊C4×C79C22semidirect
169. C2×#11929624C23semidirect
173. C2×#11929623C23semidirect
180. C22×Dic158C23semidirect
182. C2×Q8×D79C23semidirect
197. #14579161C23semidirect
198. #14579161C23semidirect
199. #14579160C23semidirect
200. #14579160C23semidirect
201. #14579160C23semidirect
202. #14579160C23semidirect
203. #14579159C23semidirect
207. #14579156C23semidirect
208. #14579156C23semidirect
209. #14579156C23semidirect
211. #14579154C23semidirect
212. #14579154C23semidirect
213. #14579153C23semidirect
214. #14579152C23semidirect
215. #14579152C23semidirect
216. #14579152C23semidirect
217. #14579152C23semidirect
218. #14579151C23semidirect
219. #14579151C23semidirect
220. #14579151C23semidirect
223. #14579149C23semidirect
224. #14579148C23semidirect
227. #14579147C23semidirect
228. #14579147C23semidirect
234. #14579146C23semidirect
238. #14579145C23semidirect
239. #14579145C23semidirect
246. #14579143C23semidirect
247. #14579143C23semidirect
265. #14579141C23semidirect
266. #14579141C23semidirect
267. #14579141C23semidirect
268. #14579141C23semidirect
269. #14579141C23semidirect
274. #14579140C23semidirect
275. #14579140C23semidirect
276. #14579140C23semidirect
281. #14579139C23semidirect
282. #14579139C23semidirect
283. #14579139C23semidirect
288. #14579138C23semidirect
289. #14579138C23semidirect
290. #14579138C23semidirect
291. #14579138C23semidirect
295. #14579137C23semidirect
299. #14579136C23semidirect
305. #14579135C23semidirect
316. #14579132C23semidirect
326. Q8×Dic79C23semidirect
327. C4×Dic158C23semidirect
328. C4×Dic158C23semidirect
329. C4×Dic158C23semidirect
330. #14579126C23semidirect
331. #14579126C23semidirect
332. #14579126C23semidirect
336. C4×D316C23semidirect
341. D4×Dic79C23semidirect
345. #14579123C23semidirect
362. #14579120C23semidirect
366. #14579119C23semidirect
367. #14579119C23semidirect
377. C2×C4⋊Dic79C23semidirect
382. C4⋊C4×D79C23semidirect
383. C4⋊C4×D79C23semidirect
401. C4⋊Q8×C79C23semidirect
402. #126×C79C23semidirect
403. #125×C79C23semidirect
404. #125×C79C23semidirect
407. #123×C79C23semidirect
412. C22⋊Q8×C79C23semidirect
413. C22⋊Q8×C79C23semidirect
418. #121×C79C23semidirect
420. C4×Q8×C79C23semidirect
425. C4×D4×C79C23semidirect
428. #117×C79C23semidirect
434. C2×C4⋊C4×C79C23semidirect
635. C22×D792−1+4semidirect
778. #3492D79semidirect
785. C79#62819semidirect
803. #554C2×D79semidirect
807. #553C2×D79semidirect
815. #552C2×D79semidirect
839. #547C2×D79semidirect
849. #544C2×D79semidirect
864. #539C2×D79semidirect
873. #537C2×D79semidirect
899. #525C2×D79semidirect
900. #525C2×D79semidirect
919. #520C2×D79semidirect
926. C22×C4⋊C4C2×D79semidirect
973. C4⋊Q8C22×D79semidirect
983. #126C22×D79semidirect
992. #125C22×D79semidirect
993. #125C22×D79semidirect
1025. #123C22×D79semidirect
1076. C22⋊Q8C22×D79semidirect
1077. C22⋊Q8C22×D79semidirect
1103. #121C22×D79semidirect
1121. C4×Q8C22×D79semidirect
1153. C4×D4C22×D79semidirect
1168. #117C22×D79semidirect
1186. C2×C4⋊C4C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237776942
#237776872
#237776462
#237776232
#237776072
#237774462
#237774402
#237772292
#237771972
#237771552
#237771532
#237771092
#237771062
#237770832
#237770812
#237770752
#237770472
#525×D792
C22×#145791412
C79×#34922
#6281979