Finite Group Databasebeta

← #35196995

Subgroups — #35196995

Order 20224.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778004C214yesmaximal, complemented
2#23778001C214yesmaximal, complemented
3#23777932C214yesmaximal, complemented
4#23777929C214yesmaximal, complemented
5#23777850C218yesmaximal, complemented
6#23777379C214yesmaximal, complemented
7#23777375C214yesmaximal, complemented
8#23777371C214yesmaximal, complemented
9#23777369C214yesmaximal, complemented
10#23777321C212yesmaximal, complemented
11#23777317C212yesmaximal, complemented
12#23777223C212yesmaximal, complemented
13#23777222C212yesmaximal, complemented
14#23777109C211yesmaximal, characteristic, complemented
15#23777106C212yesmaximal, complemented
16#23777106C214yesmaximal, complemented
17#23777101C214yesmaximal, complemented
18#23776692C212yesmaximal, complemented
19C22×#14579152C211yesmaximal, characteristic, complemented
20C79×#3492C211yesmaximal, characteristic, complemented
21C79⋊#564C2218yescomplemented
22#19099315C2218yescomplemented
23#19099314C2218yescomplemented
24#19099310C2218yescomplemented
25#19099292C2214yescomplemented
26#19099290C2214yescomplemented
27#19099289C2214yescomplemented
28#19099288C2214yescomplemented
29#19099274C2214yescomplemented
30#19099272C2218yes—
31#19099272C2214yescomplemented
32#19099271C2218yes—
33#19099271C2214yes—
34#19099270C2218yes—
35#19099270C2214yes—
36#19099270C2214yescomplemented
37#19099269C2214yescomplemented
38#19099268C2214yes—
39#19099267C2218yes—
40#19099265C2218yes—
41#19099265C2214yes—
42#19099265C2214yescomplemented
43#19099262C2218yes—
44#19099261C2214yes—
45#19099261C2214yescomplemented
46#19099260C2214yescomplemented
47#19099259C2218yes—
48#19099259C2214yes—
49#19099257C2214yescomplemented
50#19099256C2218yes—
51#19099255C2218yes—
52#19099255C2214yes—
53#19099255C2214yescomplemented
54#19099255C2218yescomplemented
55#19099253C2218yes—
56#19099253C2214yes—
57#19099252C2214yescomplemented
58#19099251C2218yescomplemented
59#19099250C2218yes—
60#19099250C2218yescomplemented
61#19099249C2218yescomplemented
62#19099248C2214yes—
63#19099248C2214yescomplemented
64#19099247C2214yescomplemented
65#19099246C2218yes—
66#19099217C2214yes—
67#19099217C2218yes—
68#19099214C2214yes—
69#19099213C2214yes—
70#19099213C2218yes—
71#19099212C2218yes—
72#19099211C2218yes—
73#19099194C2211yescharacteristic
74#19099194C2214yescomplemented
75#19099193C2214yescomplemented
76#19099192C2214yes—
77#19099191C2212yes—
78#19099191C2214yes—
79#19099191C2214yescomplemented
80#19099190C2214yescomplemented
81#19099176C2218yescomplemented
82#19099173C2214yescomplemented
83#19099173C2218yescomplemented
84#19099172C2218yescomplemented
85#19099171C2214yescomplemented
86#19099170C2218yescomplemented
87#19099166C2214yescomplemented
88#19099164C2214yescomplemented
89#19099162C2214yes—
90#19099162C2218yescomplemented
91#19099160C2214yes—
92#19099158C2214yes—
93#19099157C2218yes—
94#19099157C2218yes—
95#19099157C2218yes—
96#19099157C2218yescomplemented
97#19099156C2218yescomplemented
98#19099155C2218yes—
99#19099154C2218yescomplemented
100#19099144C2211yescharacteristic
101#19099141C2212yes—
102#19099141C2214yes—
103#19099140C2214yes—
104#19099118C2214yescomplemented
105#19099116C2212yes—
106#19099116C2214yescomplemented
107#19099115C2212yes—
108#19099115C2212yes—
109#19099109C2212yes—
110#19099108C2212yes—
111#19099108C2212yes—
112#19099100C2214yescomplemented
113#19099099C2212yes—
114#19099099C2212yes—
115#19099099C2214yescomplemented
116#19099095C2214yescomplemented
117#19099094C2212yes—
118#19099094C2212yes—
119#19099094C2214yescomplemented
120#19099093C2214yes—
121#19099093C2214yes—
122#19099090C2214yes—
123#19099090C2214yes—
124C2×#14579152C2212yes—
125C2×#14579152C2212yes—
126C2×#14579152C2214yes—
127C2×#14579152C2214yes—
128C2×#14579152C2214yes—
129C2×#14579152C2214yes—
130C2×#14579152C2214yes—
131C2×#14579152C2214yescomplemented
132#125×D79C2214yescomplemented
133#19099074C2214yes—
134#19099074C2212yes—
135#19099069C2214yes—
136#19099069C2218yes—
137#19099069C2214yes—
138#19099046C2212yes—
139#19099046C2214yes—
140#19099044C2212yes—
141#19099043C2212yes—
142#19099043C2214yes—
143#19099042C2218yes—
144#41×Dic79C2212yes—
145#19099031C2212yes—
146C4×#11929623C2214yes—
147C4×#11929623C2214yes—
148C22×C4⋊Dic79C2211yescharacteristic
149C22×C4⋊Dic79C2212yes—
150C22×Dic79⋊C4C2212yes—
151C22×C4×Dic79C2211yescharacteristic
152#554×C79C2214yes—
153#553×C79C2214yes—
154#552×C79C2214yes—
155#547×C79C2214yes—
156#544×C79C2211yescharacteristic
157#539×C79C2214yes—
158#537×C79C2211yescharacteristic
159#525×C79C2214yes—
160#525×C79C2212yes—
161#520×C79C2212yes—
162C22×C4⋊C4×C79C2211yescharacteristic
163C2×#11929624C2312yes—
164C2×#11929624C2314yes—
165C2×#11929623C2318yes—
166C2×#11929623C2314yes—
167C2×#11929623C2314yes—
168C23×Dic79C2311yescharacteristic
169C23×Dic79C2311yescharacteristic
170C23×Dic79C2312yes—
171#14579161C2318yes—
172#14579161C2314yes—
173#14579160C2318yes—
174#14579160C2318yes—
175#14579160C2312yes—
176#14579160C2314yes—
177#14579160C2312yes—
178#14579160C2314yes—
179#14579159C2312yes—
180#14579159C2318yes—
181#14579157C2312yes—
182#14579156C2314yes—
183#14579156C2318yes—
184#14579156C2318yes—
185#14579156C2318yes—
186#14579156C2318yes—
187#14579156C2318yes—
188#14579156C2314yes—
189#14579155C2318yes—
190#14579154C2318yes—
191#14579154C2314yes—
192#14579154C2318yes—
193#14579154C2318yes—
194#14579154C2318yes—
195#14579154C2314yes—
196#14579154C2318yes—
197#14579153C2318yes—
198#14579153C2318yes—
199#14579153C2314yes—
200#14579152C2318yes—
201#14579152C2318yes—
202#14579152C2318yes—
203#14579152C2318yes—
204#14579152C2318yes—
205#14579152C2318yes—
206#14579152C2314yes—
207#14579152C2314yes—
208#14579152C2318yes—
209#14579152C2314yes—
210#14579152C2314yes—
211#14579152C2314yes—
212#14579152C2314yes—
213#14579152C2318yes—
214#14579152C2314yes—
215#14579152C2314yes—
216#14579152C2318yes—
217#14579152C2312yes—
218#14579152C2314yes—
219#14579152C2314yes—
220#14579152C2312yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579151C2318yes—
227#14579151C2318yes—
228#14579151C2318yes—
229#14579151C2314yes—
230#14579151C2314yes—
231#14579150C2312yes—
232#14579148C2312yes—
233#14579147C2314yes—
234#14579147C2314yes—
235#14579146C2318yes—
236#14579146C2318yes—
237#14579145C2318yes—
238#14579145C2318yes—
239#14579145C2318yes—
240#14579145C2318yes—
241#14579145C2314yes—
242#14579145C2314yes—
243#14579144C2318yes—
244#14579144C2314yes—
245#14579144C2318yes—
246#14579143C2318yes—
247#14579143C2318yes—
248#14579143C2318yes—
249#14579143C2318yes—
250#14579142C2318yes—
251#14579142C2318yes—
252#14579142C2314yes—
253#14579142C2314yes—
254#14579141C2314yes—
255#14579141C2318yes—
256#14579141C2318yes—
257#14579141C2318yes—
258#14579140C2318yes—
259#14579140C2314yes—
260#14579140C2318yes—
261#14579140C2314yes—
262#14579140C2314yes—
263#14579140C2312yes—
264#14579140C2312yes—
265#14579139C2318yes—
266#14579139C2318yes—
267#14579139C2318yes—
268#14579138C2318yes—
269#14579138C2318yes—
270#14579138C2314yes—
271#14579138C2318yes—
272#14579138C2314yes—
273#14579138C2318yes—
274#14579138C2318yes—
275#14579138C2318yes—
276#14579138C2318yes—
277#14579138C2314yes—
278#14579138C2314yes—
279#14579137C2318yes—
280#14579137C2314yes—
281#14579137C2318yes—
282#14579136C2314yes—
283#14579135C2314yes—
284#14579135C2318yes—
285#14579135C2314yes—
286#14579135C2314yes—
287#14579135C2312yes—
288#14579135C2312yes—
289#14579134C2318yes—
290#14579133C2314yes—
291#14579133C2318yes—
292#14579133C2314yes—
293#14579133C2318yes—
294#14579133C2318yes—
295#14579133C2314yes—
296#14579133C2314yes—
297#14579132C2318yes—
298#14579132C2314yes—
299#14579130C2314yes—
300Q8×Dic79C2318yes—
301Q8×Dic79C2314yes—
302Q8×Dic79C2312yes—
303Q8×Dic79C2312yes—
304C4×Dic158C2318yes—
305C4×Dic158C2314yes—
306C4×Dic158C2318yes—
307C4×Dic158C2314yes—
308C4×Dic158C2314yes—
309#14579126C2314yes—
310#14579126C2314yes—
311#14579126C2314yes—
312#14579126C2318yes—
313#14579126C2312yes—
314#14579126C2312yes—
315C4×D316C2318yes—
316C4×D316C2314yes—
317D4×Dic79C2314yes—
318D4×Dic79C2318yes—
319D4×Dic79C2318yes—
320D4×Dic79C2318yes—
321D4×Dic79C2314yes—
322D4×Dic79C2314yes—
323D4×Dic79C2314yes—
324D4×Dic79C2312yes—
325D4×Dic79C2314yes—
326D4×Dic79C2312yes—
327#14579123C2314yes—
328#14579123C2312yes—
329#14579123C2312yes—
330C4×C22⋊D79C2318yes—
331C4×C22⋊D79C2318yes—
332C4×C22⋊D79C2318yes—
333C4×C22⋊D79C2314yes—
334C4×C22⋊D79C2314yes—
335C4×C22⋊D79C2314yes—
336C4×C22⋊D79C2314yes—
337(C22⋊D79)⋊C4C2314yes—
338(C22⋊D79)⋊C4C2314yes—
339(C22⋊D79)⋊C4C2314yes—
340(C22⋊D79)⋊C4C2318yes—
341(C22⋊D79)⋊C4C2318yes—
342(C22⋊D79)⋊C4C2314yes—
343(C22⋊D79)⋊C4C2318yes—
344(C22⋊D79)⋊C4C2314yes—
345(C22⋊D79)⋊C4C2314yes—
346#14579120C2314yes—
347#14579120C2318yes—
348#14579120C2312yes—
349#14579120C2314yes—
350#14579120C2314yes—
351#14579119C2318yes—
352#14579119C2314yes—
353#14579119C2314yes—
354#14579119C2314yes—
355#14579119C2314yes—
356#14579118C2314yes—
357#14579118C2318yes—
358#14579117C2318yes—
359#14579117C2318yes—
360#14579117C2314yes—
361#14579117C2314yes—
362#14579117C2314yes—
363#14579117C2314yes—
364C2×C4⋊Dic79C2314yes—
365C2×C4⋊Dic79C2312yes—
366C2×C4⋊Dic79C2312yes—
367C2×C4⋊Dic79C2314yes—
368C2×C4⋊Dic79C2318yes—
369C2×C4⋊Dic79C2314yes—
370C2×C4⋊Dic79C2314yes—
371C2×C4⋊Dic79C2318yes—
372C2×C4⋊Dic79C2314yes—
373C2×C4⋊Dic79C2314yes—
374C2×C4⋊Dic79C2314yes—
375C2×Dic79⋊C4C2314yes—
376C2×Dic79⋊C4C2314yes—
377C2×Dic79⋊C4C2318yes—
378C2×Dic79⋊C4C2318yes—
379C2×Dic79⋊C4C2314yes—
380C2×Dic79⋊C4C2314yes—
381C4⋊C4×D79C2318yes—
382C4⋊C4×D79C2318yes—
383C4⋊C4×D79C2314yes—
384C4⋊C4×D79C2314yes—
385C2×C4×Dic79C2312yes—
386C2×C4×Dic79C2312yes—
387C2×C4×Dic79C2312yes—
388C2×C4×Dic79C2312yes—
389C2×C4×Dic79C2312yes—
390C2×C4×Dic79C2312yes—
391C2×C4×Dic79C2314yes—
392C42×D79C2314yes—
393C2×#41×C79C2312yes—
394C2×#41×C79C2314yes—
395C23×C4×C79C2311yescharacteristic
396C23×C4×C79C2312yes—
397C4⋊Q8×C79C2314yes—
398#126×C79C2318yes—
399#125×C79C2318yes—
400#125×C79C2314yes—
401#123×C79C2318yes—
402#123×C79C2318yes—
403#123×C79C2314yes—
404C22⋊Q8×C79C2314yes—
405C22⋊Q8×C79C2318yes—
406C22⋊Q8×C79C2314yes—
407C22⋊Q8×C79C2312yes—
408C22⋊Q8×C79C2314yes—
409C22⋊Q8×C79C2312yes—
410#121×C79C2314yes—
411#121×C79C2314yes—
412#121×C79C2312yes—
413#121×C79C2314yes—
414#121×C79C2312yes—
415#120×C79C2314yes—
416C4×Q8×C79C2314yes—
417C4×D4×C79C2318yes—
418C4×D4×C79C2314yes—
419C4×D4×C79C2314yes—
420C4×D4×C79C2318yes—
421C4×D4×C79C2314yes—
422#117×C79C2312yes—
423#117×C79C2314yes—
424#117×C79C2314yes—
425C2×C4⋊C4×C79C2311yescharacteristic
426C2×C4⋊C4×C79C2312yes—
427C2×C4⋊C4×C79C2314yes—
428C2×C4⋊C4×C79C2314yes—
429C2×C4⋊C4×C79C2311yescharacteristic
430C2×C4⋊C4×C79C2314yes—
431#11929624—28no—
432#11929624—48no—
433#11929623—416no—
434#11929623—48no—
435#11929623—48no—
436C2×Dic158C2412yes—
437C2×Dic158C2418yes—
438C2×Dic158C2414yes—
439C2×Dic158C2414yes—
440C2×Dic158C2414yes—
441C2×D316C2412yes—
442C2×D316C2414yes—
443C2×C22⋊D79C2414yes—
444C2×C22⋊D79C2414yes—
445C2×C22⋊D79C2414yes—
446C2×C22⋊D79C2418yes—
447C2×C22⋊D79C2414yes—
448C2×C22⋊D79C2414yes—
449C22×Dic79—42no—
450C22×Dic79—44no—
451C22×Dic79—42no—
452C22×Dic79C2412yes—
453C22×Dic79C2412yes—
454C22×Dic79C2414yes—
455C22×Dic79C2414yes—
456C22×Dic79C2414yes—
457C22×Dic79C2418yes—
458C22×Dic79C2411yescharacteristic
459C22×Dic79C2412yes—
460C22×Dic79C2411yescharacteristic
461C22×Dic79C2411yescharacteristic
462C22×Dic79C2412yes—
463C22×Dic79C2411yescharacteristic
464C22×Dic79C2414yes—
465C22×Dic79C2414yes—
466C2×C4×D79C2414yes—
467C2×C4×D79C2414yes—
468C2×C4×D79C2414yes—
469C2×C4×D79C2418yes—
470C2×C4×D79C2418yes—
471C4⋊Dic79C2414yes—
472C4⋊Dic79C2412yes—
473C4⋊Dic79C2414yes—
474C4⋊Dic79C2418yes—
475C4⋊Dic79C2414yes—
476C4⋊Dic79C2418yes—
477C4⋊Dic79C2418yes—
478C4⋊Dic79C2418yes—
479C4⋊Dic79C2418yes—
480C4⋊Dic79C2412yes—
481C4⋊Dic79C2414yes—
482C4⋊Dic79C2414yes—
483C4⋊Dic79C2418yes—
484C4⋊Dic79C2418yes—
485C4⋊Dic79C2414yes—
486C4⋊Dic79C2414yes—
487C4⋊Dic79C2414yes—
488Dic79⋊C4C2414yes—
489Dic79⋊C4C2418yes—
490Dic79⋊C4C2418yes—
491Dic79⋊C4C2418yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2418yes—
495Dic79⋊C4C2418yes—
496Dic79⋊C4C2418yes—
497Dic79⋊C4C2414yes—
498Dic79⋊C4C2418yes—
499Dic79⋊C4C2418yes—
500Dic79⋊C4C2414yes—
501Dic79⋊C4C2414yes—
502Dic79⋊C4C2414yes—
503Dic79⋊C4C2414yes—
504Dic79⋊C4C2414yes—
505Dic79⋊C4C2414yes—
506Dic79⋊C4C2414yes—
507Dic79⋊C4C2414yes—
508C22⋊Dic79C2414yes—
509C22⋊Dic79C2414yes—
510C22⋊Dic79C2414yes—
511C22⋊Dic79C2414yes—
512C22⋊Dic79C2414yes—
513C22⋊Dic79C2414yes—
514C22⋊Dic79C2418yes—
515C22⋊Dic79C2418yes—
516C22⋊Dic79C2414yes—
517(C2×D79)⋊C4C2414yes—
518(C2×D79)⋊C4C2414yes—
519(C2×D79)⋊C4C2414yes—
520(C2×D79)⋊C4C2418yes—
521(C2×D79)⋊C4C2414yes—
522(C2×D79)⋊C4C2414yes—
523(C2×D79)⋊C4C2414yes—
524(C2×D79)⋊C4C2418yes—
525(C2×D79)⋊C4C2418yes—
526(C2×D79)⋊C4C2418yes—
527C4×Dic79C2412yes—
528C4×Dic79C2414yes—
529C4×Dic79C2414yes—
530C4×Dic79C2412yes—
531C4×Dic79C2412yes—
532C4×Dic79C2412yes—
533C4×Dic79C2412yes—
534C4×Dic79C2412yes—
535C4×Dic79C2412yes—
536C4×Dic79C2412yes—
537C4×Dic79C2414yes—
538C4×Dic79C2414yes—
539C4×Dic79C2414yes—
540C4×Dic79C2418yes—
541C4×Dic79C2418yes—
542C4×Dic79C2418yes—
543C24×C79C2411yescharacteristic
544#41×C79—28no—
545#41×C79—48no—
546C2×Q8×C79C2412yes—
547C2×Q8×C79C2414yes—
548C2×D4×C79C2414yes—
549C2×D4×C79C2414yes—
550C2×D4×C79C2414yes—
551C2×D4×C79C2412yes—
552C2×D4×C79C2414yes—
553C22×C4×C79—24no—
554C22×C4×C79—44no—
555C22×C4×C79C2414yes—
556C22×C4×C79C2412yes—
557C22×C4×C79C2412yes—
558C22×C4×C79C2411yescharacteristic
559C22×C4×C79C2414yes—
560C22×C4×C79C2412yes—
561C22×C4×C79C2414yes—
562C22×C4×C79C2412yes—
563C22×C4×C79C2418yes—
564C22×C4×C79C2411yescharacteristic
565C4⋊C4×C79C2414yes—
566C4⋊C4×C79C2414yes—
567C4⋊C4×C79C2418yes—
568C4⋊C4×C79C2412yes—
569C4⋊C4×C79C2418yes—
570C4⋊C4×C79C2412yes—
571C4⋊C4×C79C2414yes—
572C4⋊C4×C79C2414yes—
573C4⋊C4×C79C2414yes—
574C4⋊C4×C79C2418yes—
575C4⋊C4×C79C2414yes—
576C22⋊C4×C79C2414yes—
577C22⋊C4×C79C2414yes—
578C22⋊C4×C79C2418yes—
579C22⋊C4×C79C2414yes—
580C22⋊C4×C79C2418yes—
581C22⋊C4×C79C2414yes—
582C22⋊C4×C79C2414yes—
583C42×C79C2418yes—
584C42×C79C2414yes—
585C23×C79—22no—
586C23×C79—22no—
587C23×C79—22no—
588C23×C79C2514yes—
589C23×C79C2511yescharacteristic
590C23×C79C2511yescharacteristic
591C23×C79C2511yescharacteristic
592C22×D79C2514yes—
593Q8×C79—24no—
594Q8×C79—44no—
595D4×C79—28no—
596D4×C79—28no—
597D4×C79—28no—
598D4×C79—24no—
599D4×C79—44no—
600C2×C4×C79—22no—
601C2×C4×C79—28no—
602C2×C4×C79—24no—
603C2×C4×C79—24no—
604C2×C4×C79—28no—
605C2×C4×C79—42no—
606C2×C4×C79—44no—
607C2×C4×C79—42no—
608C2×C4×C79—48no—
609C2×C4×C792−1+414yes—
610C2×C4×C79C2514yes—
611C2×C4×C79C2512yes—
612C2×C4×C79C2514yes—
613C2×C4×C79C2514yes—
614C2×C4×C79C2514yes—
615C2×C4×C79C2514yes—
616C2×C4×C79C2512yes—
617C22⋊D79—28no—
618C22⋊D79—28no—
619C22⋊D79—28no—
620C22⋊D79—44no—
621C22⋊D79—44no—
622C22⋊D79—48no—
623C2×Dic79—24no—
624C2×Dic79—24no—
625C2×Dic79—28no—
626C2×Dic79—41no—
627C2×Dic79—41no—
628C2×Dic79—42no—
629C2×Dic79—42no—
630C2×Dic79—44no—
631C2×Dic79—44no—
632C2×Dic79—41no—
633C2×Dic79—41no—
634C2×Dic79—44no—
635C2×Dic79—48no—
636C2×Dic79—44no—
637C2×Dic79C2512yes—
638C2×Dic79C2512yes—
639C2×Dic79C2514yes—
640C2×Dic79C2514yes—
641C2×Dic79C2512yes—
642C2×Dic79C2512yes—
643C2×Dic79C2514yes—
644C2×Dic79C2518yes—
645D316—24no—
646D316—44no—
647C4×D79—28no—
648C4×D79—48no—
649C4×D79—44no—
650C4×D79—44no—
651C4×D79—48no—
652Dic158—24no—
653Dic158—44no—
654Dic158—44no—
655Dic158—48no—
656Dic158—44no—
657C22×C79—28no—
658C22×C79—21no—
659C22×C79—21no—
660C22×C79—21no—
661C22×C79—21no—
662C22×C79—21no—
663C22×C79—21no—
664C22×C79—24no—
665C22×C79—24no—
666C22×C79—24no—
667C22×C79C2×2−1+412yes—
668C22×C79#58512yes—
669C22×C79#58512yes—
670C22×C79C2611yescharacteristic
671C2×D79—24no—
672C2×D79—24no—
673C2×D79—24no—
674C4×C79—22no—
675C4×C79—24no—
676C4×C79—24no—
677C4×C79—24no—
678C4×C79—24no—
679C4×C79—24no—
680C4×C79C2×2−1+414yes—
681Dic79—24no—
682Dic79—24no—
683Dic79—24no—
684Dic79—22no—
685Dic79—22no—
686Dic79—28no—
687Dic79—22no—
688Dic79—22no—
689#62825—791nomaximal, Sylow
690C2×C79—22no—
691C2×C79—22no—
692C2×C79—22no—
693C2×C79—44no—
694C2×C79C22×2−1+411yescharacteristic
695C2×C79C2×#58511yescharacteristic
696C2×C79C2×#58511yescharacteristic
697D79—44no—
698#3563—794no—
699#3563—794no—
700#3559—794no—
701#3559—794no—
702#3553—798no—
703#3515—794no—
704#3515—794no—
705#3515—794no—
706#3515—794no—
707#3512—792no—
708#3512—792no—
709#3504—792no—
710#3504—792no—
711#3492—794no—
712#3492—792no—
713#3492—794no—
714#3492—791no—
715#3492D7911yescharacteristic, complemented
716#3444—792no—
717C22×#125—791no—
718C79#6282511yescharacteristic, complemented, Sylow
719#564—798no—
720#563—798no—
721#563—798no—
722#562—798no—
723#557—794no—
724#557—794no—
725#557—794no—
726#557—794no—
727#554—794no—
728#554—794no—
729#554—798no—
730#554—798no—
731#554—794no—
732#554—798no—
733#554—794no—
734#554—794no—
735#554—798no—
736#554—794no—
737#554—794no—
738#554C2×D7914yes—
739#553—798no—
740#553—794no—
741#553—798no—
742#553—794no—
743#553—794no—
744#553—798no—
745#553—794no—
746#553—798no—
747#553—794no—
748#553—794no—
749#553—794no—
750#553C2×D7914yes—
751#552—798no—
752#552—798no—
753#552—798no—
754#552—798no—
755#552—794no—
756#552—798no—
757#552—794no—
758#552—794no—
759#552—798no—
760#552—798no—
761#552—794no—
762#552—798no—
763#552—794no—
764#552—794no—
765#552—794no—
766#552C2×D7914yes—
767#547—798no—
768#547—798no—
769#547—798no—
770#547—794no—
771#547—798no—
772#547—794no—
773#547—794no—
774#547C2×D7914yes—
775#544—794no—
776#544—794no—
777#544—794no—
778#544—792no—
779#544—794no—
780#544—794no—
781#544—791no—
782#544—794no—
783#544C2×D7911yescharacteristic
784#541—798no—
785#541—798no—
786#541—798no—
787#541—794no—
788#541—798no—
789#541—794no—
790#540—794no—
791#540—794no—
792#539—798no—
793#539—798no—
794#539—798no—
795#539—798no—
796#539—798no—
797#539—798no—
798#539—794no—
799#539—798no—
800#539—794no—
801#539—798no—
802#539—794no—
803#539C2×D7914yes—
804#537—792no—
805#537—794no—
806#537—794no—
807#537—791no—
808#537C2×D7911yescharacteristic
809#533—794no—
810#533—792no—
811#533—792no—
812#533—792no—
813#533—794no—
814#532—792no—
815#532—792no—
816#532—792no—
817#529—794no—
818#529—794no—
819#529—792no—
820#529—792no—
821#529—794no—
822#529—792no—
823#529—792no—
824#529—794no—
825#529—794no—
826#529—794no—
827#529—794no—
828#529—794no—
829C2×#125—794no—
830C2×#125—792no—
831C2×#125—792no—
832C2×#125—794no—
833C2×#125—794no—
834C2×#125—794no—
835C2×#125—794no—
836C2×#125—794no—
837C2×#125—794no—
838#525—792no—
839#525—794no—
840#525—794no—
841#525—794no—
842#525—798no—
843#525C2×D7912yes—
844#525C2×D7914yes—
845#520—792no—
846#520—794no—
847#520—798no—
848#520—792no—
849#520—794no—
850#520—792no—
851#520C2×D7912yes—
852C4×#41—792no—
853C4×#41—794no—
854C4×#41—794no—
855C4×#41—792no—
856C22×C4⋊C4—792no—
857C22×C4⋊C4—791no—
858C22×C4⋊C4—792no—
859C22×C4⋊C4C2×D7911yescharacteristic
860C22×C42—791no—
861C2×#41—794no—
862C2×#41—794no—
863C2×#41—798no—
864C2×#41—794no—
865C2×#41—792no—
866C2×#41C22×D7912yes—
867C2×#41C22×D7914yes—
868C23×C4—792no—
869C23×C4—791no—
870C23×C4—791no—
871C23×C4C22×D7911yescharacteristic
872C23×C4C22×D7912yes—
873C4⋊Q8—792no—
874C4⋊Q8—798no—
875C4⋊Q8—792no—
876C4⋊Q8—792no—
877C4⋊Q8—794no—
878C4⋊Q8—794no—
879C4⋊Q8—798no—
880C4⋊Q8—798no—
881C4⋊Q8—794no—
882C4⋊Q8—798no—
883C4⋊Q8C22×D7914yes—
884#127—792no—
885#126—794no—
886#126—794no—
887#126—798no—
888#126—798no—
889#126—798no—
890#126—798no—
891#126—798no—
892#126—794no—
893#126—794no—
894#126—798no—
895#126—798no—
896#126—798no—
897#126—798no—
898#126—798no—
899#126—798no—
900#126C22×D7918yes—
901#125—794no—
902#125—794no—
903#125—798no—
904#125—798no—
905#125—794no—
906#125—794no—
907#125—798no—
908#125—794no—
909#125—794no—
910#125—794no—
911#125—794no—
912#125—798no—
913#125—792no—
914#125—792no—
915#125—798no—
916#125—798no—
917#125—798no—
918#125—798no—
919#125—794no—
920#125—794no—
921#125—794no—
922#125—794no—
923#125—798no—
924#125—798no—
925#125—798no—
926#125—798no—
927#125—798no—
928#125—798no—
929#125—798no—
930#125—798no—
931#125—798no—
932#125—794no—
933#125—798no—
934#125—798no—
935#125C22×D7914yes—
936#125C22×D7918yes—
937#124—792no—
938#124—792no—
939#124—794no—
940#124—794no—
941#123—794no—
942#123—794no—
943#123—798no—
944#123—798no—
945#123—794no—
946#123—798no—
947#123—798no—
948#123—798no—
949#123—798no—
950#123—794no—
951#123—794no—
952#123—798no—
953#123—798no—
954#123—798no—
955#123—798no—
956#123—798no—
957#123—798no—
958#123—798no—
959#123—798no—
960#123C22×D7914yes—
961#123C22×D7918yes—
962#123C22×D7918yes—
963C22⋊Q8—794no—
964C22⋊Q8—798no—
965C22⋊Q8—798no—
966C22⋊Q8—792no—
967C22⋊Q8—792no—
968C22⋊Q8—794no—
969C22⋊Q8—794no—
970C22⋊Q8—794no—
971C22⋊Q8—798no—
972C22⋊Q8—798no—
973C22⋊Q8—794no—
974C22⋊Q8—798no—
975C22⋊Q8—798no—
976C22⋊Q8—798no—
977C22⋊Q8—798no—
978C22⋊Q8—798no—
979C22⋊Q8—798no—
980C22⋊Q8—794no—
981C22⋊Q8—794no—
982C22⋊Q8—794no—
983C22⋊Q8—794no—
984C22⋊Q8—798no—
985C22⋊Q8—798no—
986C22⋊Q8—798no—
987C22⋊Q8—798no—
988C22⋊Q8—798no—
989C22⋊Q8—798no—
990C22⋊Q8—798no—
991C22⋊Q8C22×D7912yes—
992C22⋊Q8C22×D7912yes—
993C22⋊Q8C22×D7914yes—
994C22⋊Q8C22×D7914yes—
995C22⋊Q8C22×D7914yes—
996C22⋊Q8C22×D7918yes—
997#121—794no—
998#121—794no—
999#121—794no—
1000#121—794no—
1001#121—798no—
1002#121—798no—
1003#121—794no—
1004#121—798no—
1005#121—798no—
1006#121—792no—
1007#121—792no—
1008#121—794no—
1009#121—794no—
1010#121—794no—
1011#121—798no—
1012#121—794no—
1013#121—798no—
1014#121C22×D7912yes—
1015#121C22×D7912yes—
1016#121C22×D7914yes—
1017#121C22×D7914yes—
1018#121C22×D7914yes—
1019#120—794no—
1020#120C22×D7914yes—
1021C4×Q8—792no—
1022C4×Q8—792no—
1023C4×Q8—794no—
1024C4×Q8—798no—
1025C4×Q8—794no—
1026C4×Q8—794no—
1027C4×Q8—792no—
1028C4×Q8—792no—
1029C4×Q8—794no—
1030C4×Q8—798no—
1031C4×Q8—794no—
1032C4×Q8—794no—
1033C4×Q8—794no—
1034C4×Q8—798no—
1035C4×Q8—798no—
1036C4×Q8C22×D7914yes—
1037C4×D4—794no—
1038C4×D4—794no—
1039C4×D4—794no—
1040C4×D4—794no—
1041C4×D4—792no—
1042C4×D4—792no—
1043C4×D4—798no—
1044C4×D4—798no—
1045C4×D4—798no—
1046C4×D4—794no—
1047C4×D4—794no—
1048C4×D4—794no—
1049C4×D4—794no—
1050C4×D4—794no—
1051C4×D4—798no—
1052C4×D4—798no—
1053C4×D4—798no—
1054C4×D4—792no—
1055C4×D4—792no—
1056C4×D4—794no—
1057C4×D4—794no—
1058C4×D4—794no—
1059C4×D4—794no—
1060C4×D4—794no—
1061C4×D4—794no—
1062C4×D4—794no—
1063C4×D4—798no—
1064C4×D4—798no—
1065C4×D4—798no—
1066C4×D4—798no—
1067C4×D4—794no—
1068C4×D4C22×D7914yes—
1069C4×D4C22×D7914yes—
1070C4×D4C22×D7918yes—
1071C4×D4C22×D7918yes—
1072C4×D4C22×D7914yes—
1073#117—792no—
1074#117—794no—
1075#117—794no—
1076#117—798no—
1077#117—794no—
1078#117—794no—
1079#117—794no—
1080#117—798no—
1081#117—794no—
1082#117—794no—
1083#117—794no—
1084#117—794no—
1085#117—794no—
1086#117—794no—
1087#117—798no—
1088#117—798no—
1089#117—794no—
1090#117—798no—
1091#117C22×D7912yes—
1092#117C22×D7914yes—
1093#117C22×D7914yes—
1094C2×C4⋊C4—792no—
1095C2×C4⋊C4—794no—
1096C2×C4⋊C4—794no—
1097C2×C4⋊C4—794no—
1098C2×C4⋊C4—794no—
1099C2×C4⋊C4—792no—
1100C2×C4⋊C4—798no—
1101C2×C4⋊C4—794no—
1102C2×C4⋊C4—798no—
1103C2×C4⋊C4—794no—
1104C2×C4⋊C4—794no—
1105C2×C4⋊C4—794no—
1106C2×C4⋊C4—794no—
1107C2×C4⋊C4—794no—
1108C2×C4⋊C4—798no—
1109C2×C4⋊C4—798no—
1110C2×C4⋊C4—794no—
1111C2×C4⋊C4—798no—
1112C2×C4⋊C4—798no—
1113C2×C4⋊C4—794no—
1114C2×C4⋊C4—794no—
1115C2×C4⋊C4C22×D7911yescharacteristic
1116C2×C4⋊C4C22×D7911yescharacteristic
1117C2×C4⋊C4C22×D7912yes—
1118C2×C4⋊C4C22×D7914yes—
1119C2×C4⋊C4C22×D7914yes—
1120C2×C4⋊C4C22×D7914yes—
1121C2×C42—794no—
1122C2×C42—792no—
1123C2×C42—792no—
1124C2×C42—792no—
1125C2×C42—792no—
1126C2×C42—792no—
1127C2×C42—792no—
1128C2×C42—794no—
1129C24C23×D7911yescharacteristic
1130#41—28no—
1131#41—48no—
1132#41—3168no—
1133#41—3168no—
1134#41—3168no—
1135#41—31616no—
1136#41—1588no—
1137C2×Q8—794no—
1138C2×Q8—798no—
1139C2×Q8—794no—
1140C2×Q8—794no—
1141C2×Q8—792no—
1142C2×Q8C23×D7912yes—
1143C2×Q8C23×D7914yes—
1144C2×D4—798no—
1145C2×D4—794no—
1146C2×D4—794no—
1147C2×D4—794no—
1148C2×D4—794no—
1149C2×D4—794no—
1150C2×D4—794no—
1151C2×D4—792no—
1152C2×D4C23×D7914yes—
1153C2×D4C23×D7912yes—
1154C2×D4C23×D7914yes—
1155C2×D4C23×D7914yes—
1156C2×D4C23×D7914yes—
1157C22×C4—24no—
1158C22×C4—44no—
1159C22×C4—3162no—
1160C22×C4—3164no—
1161C22×C4—3162no—
1162C22×C4—791no—
1163C22×C4—791no—
1164C22×C4—792no—
1165C22×C4—792no—
1166C22×C4—791no—
1167C22×C4—791no—
1168C22×C4—794no—
1169C22×C4—794no—
1170C22×C4—794no—
1171C22×C4—794no—
1172C22×C4—798no—
1173C22×C4—794no—
1174C22×C4—794no—
1175C22×C4—798no—
1176C22×C4—798no—
1177C22×C4—792no—
1178C22×C4—792no—
1179C22×C4—794no—
1180C22×C4—794no—
1181C22×C4C23×D7912yes—
1182C22×C4C23×D7912yes—
1183C22×C4C23×D7911yescharacteristic
1184C22×C4C23×D7914yes—
1185C22×C4C23×D7914yes—
1186C22×C4C23×D7912yes—
1187C22×C4C23×D7914yes—
1188C22×C4C23×D7912yes—
1189C22×C4C23×D7918yes—
1190C22×C4C23×D7911yescharacteristic
1191C4⋊C4—798no—
1192C4⋊C4—798no—
1193C4⋊C4—798no—
1194C4⋊C4—798no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—798no—
1198C4⋊C4—798no—
1199C4⋊C4—798no—
1200C4⋊C4—798no—
1201C4⋊C4—798no—
1202C4⋊C4—798no—
1203C4⋊C4—794no—
1204C4⋊C4—794no—
1205C4⋊C4—794no—
1206C4⋊C4—794no—
1207C4⋊C4—794no—
1208C4⋊C4—794no—
1209C4⋊C4—794no—
1210C4⋊C4—794no—
1211C4⋊C4—794no—
1212C4⋊C4—794no—
1213C4⋊C4—798no—
1214C4⋊C4—798no—
1215C4⋊C4—798no—
1216C4⋊C4—798no—
1217C4⋊C4—798no—
1218C4⋊C4—792no—
1219C4⋊C4—792no—
1220C4⋊C4—794no—
1221C4⋊C4—794no—
1222C4⋊C4—794no—
1223C4⋊C4—798no—
1224C4⋊C4—798no—
1225C4⋊C4—794no—
1226C4⋊C4—794no—
1227C4⋊C4—794no—
1228C4⋊C4C23×D7912yes—
1229C4⋊C4C23×D7914yes—
1230C4⋊C4C23×D7914yes—
1231C4⋊C4C23×D7918yes—
1232C4⋊C4C23×D7914yes—
1233C4⋊C4C23×D7918yes—
1234C4⋊C4C23×D7912yes—
1235C4⋊C4C23×D7918yes—
1236C4⋊C4C23×D7914yes—
1237C4⋊C4C23×D7914yes—
1238C4⋊C4C23×D7914yes—
1239C22⋊C4—794no—
1240C22⋊C4—794no—
1241C22⋊C4—794no—
1242C22⋊C4—794no—
1243C22⋊C4—794no—
1244C22⋊C4—794no—
1245C22⋊C4—794no—
1246C22⋊C4—798no—
1247C22⋊C4—798no—
1248C22⋊C4—794no—
1249C22⋊C4—794no—
1250C22⋊C4—794no—
1251C22⋊C4—794no—
1252C22⋊C4—798no—
1253C22⋊C4—798no—
1254C22⋊C4—798no—
1255C22⋊C4—798no—
1256C22⋊C4—794no—
1257C22⋊C4—794no—
1258C22⋊C4C23×D7914yes—
1259C22⋊C4C23×D7914yes—
1260C22⋊C4C23×D7918yes—
1261C22⋊C4C23×D7914yes—
1262C22⋊C4C23×D7914yes—
1263C22⋊C4C23×D7914yes—
1264C22⋊C4C23×D7918yes—
1265C42—792no—
1266C42—792no—
1267C42—792no—
1268C42—792no—
1269C42—792no—
1270C42—792no—
1271C42—792no—
1272C42—792no—
1273C42—794no—
1274C42—794no—
1275C42—794no—
1276C42—794no—
1277C42—794no—
1278C42—798no—
1279C42—798no—
1280C42—798no—
1281C42C23×D7914yes—
1282C42C23×D7918yes—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—794no—
1287C23C24×D7914yes—
1288C23C24×D7911yescharacteristic
1289C23C24×D7911yescharacteristic
1290C23C24×D7911yescharacteristic
1291Q8—24no—
1292Q8—44no—
1293Q8—3164no—
1294Q8—3164no—
1295Q8—3168no—
1296Q8—3164no—
1297Q8—1584no—
1298D4—28no—
1299D4—28no—
1300D4—28no—
1301D4—24no—
1302D4—44no—
1303D4—3164no—
1304D4—3164no—
1305D4—3168no—
1306D4—3164no—
1307D4—1588no—
1308D4—1588no—
1309D4—1588no—
1310D4—1584no—
1311C2×C4—22no—
1312C2×C4—28no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—28no—
1316C2×C4—42no—
1317C2×C4—44no—
1318C2×C4—42no—
1319C2×C4—48no—
1320C2×C4—3168no—
1321C2×C4—3164no—
1322C2×C4—3164no—
1323C2×C4—3168no—
1324C2×C4—3161no—
1325C2×C4—3162no—
1326C2×C4—3161no—
1327C2×C4—3161no—
1328C2×C4—3162no—
1329C2×C4—3164no—
1330C2×C4—3164no—
1331C2×C4—3161no—
1332C2×C4—3164no—
1333C2×C4—3164no—
1334C2×C4—3168no—
1335C2×C4—792no—
1336C2×C4—792no—
1337C2×C4—794no—
1338C2×C4—794no—
1339C2×C4—794no—
1340C2×C4—792no—
1341C2×C4—792no—
1342C2×C4—798no—
1343C2×C4—1584no—
1344C2×C4—1584no—
1345C2×C4—1588no—
1346C2×C4—1588no—
1347C2×C4#1457920814yes—
1348C2×C4C24×D7914yes—
1349C2×C4C24×D7912yes—
1350C2×C4C24×D7914yes—
1351C2×C4C24×D7914yes—
1352C2×C4C24×D7914yes—
1353C2×C4C24×D7914yes—
1354C2×C4C24×D7912yes—
1355C22—28no—
1356C22—21no—
1357C22—21no—
1358C22—21no—
1359C22—21no—
1360C22—21no—
1361C22—21no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—1584no—
1366C22—1584no—
1367C22—1584no—
1368C22C2×#1457920812yes—
1369C22#1909939812yes—
1370C22#1909940012yes—
1371C22C25×D7911yescharacteristic
1372C4—22no—
1373C4—24no—
1374C4—24no—
1375C4—24no—
1376C4—24no—
1377C4—24no—
1378C4—1584no—
1379C4—1582no—
1380C4—1584no—
1381C4—1582no—
1382C4—1582no—
1383C4—1588no—
1384C4—1584no—
1385C4—1582no—
1386C4C2×#1457920814yes—
1387C2—22no—
1388C2—22no—
1389C2—22no—
1390C2—44no—
1391C2—3164no—
1392C2C22×#1457920811yescharacteristic
1393C2C2×#1909939811yescharacteristic
1394C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3492C2
hypercenter#3492D79
hypocenterC79#62825
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #23778004C2semidirect
2. #23778001C2semidirect
3. #23777932C2semidirect
4. #23777929C2semidirect
5. #23777850C2semidirect
6. #23777379C2semidirect
7. #23777375C2semidirect
8. #23777371C2semidirect
9. #23777369C2semidirect
10. #23777321C2semidirect
11. #23777317C2semidirect
12. #23777223C2semidirect
13. #23777222C2semidirect
14. #23777109C2semidirect
15. #23777106C2semidirect
16. #23777106C2semidirect
17. #23777101C2semidirect
18. #23776692C2semidirect
19. C22×#14579152C2semidirect
20. C79×#3492C2semidirect
21. C79⋊#564C22semidirect
22. #19099315C22semidirect
23. #19099314C22semidirect
24. #19099310C22semidirect
25. #19099292C22semidirect
26. #19099290C22semidirect
27. #19099289C22semidirect
28. #19099288C22semidirect
29. #19099274C22semidirect
31. #19099272C22semidirect
36. #19099270C22semidirect
37. #19099269C22semidirect
42. #19099265C22semidirect
45. #19099261C22semidirect
46. #19099260C22semidirect
49. #19099257C22semidirect
53. #19099255C22semidirect
54. #19099255C22semidirect
57. #19099252C22semidirect
58. #19099251C22semidirect
60. #19099250C22semidirect
61. #19099249C22semidirect
63. #19099248C22semidirect
64. #19099247C22semidirect
74. #19099194C22semidirect
75. #19099193C22semidirect
79. #19099191C22semidirect
80. #19099190C22semidirect
81. #19099176C22semidirect
82. #19099173C22semidirect
83. #19099173C22semidirect
84. #19099172C22semidirect
85. #19099171C22semidirect
86. #19099170C22semidirect
87. #19099166C22semidirect
88. #19099164C22semidirect
90. #19099162C22semidirect
96. #19099157C22semidirect
97. #19099156C22semidirect
99. #19099154C22semidirect
104. #19099118C22semidirect
106. #19099116C22semidirect
112. #19099100C22semidirect
115. #19099099C22semidirect
116. #19099095C22semidirect
119. #19099094C22semidirect
131. C2×#14579152C22semidirect
132. #125×D79C22semidirect
715. #3492D79semidirect
718. C79#62825semidirect

Maximal subgroups

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

subgroupindex
#237780042
#237780012
#237779322
#237779292
#237778502
#237773792
#237773752
#237773712
#237773692
#237773212
#237773172
#237772232
#237772222
#237771092
#237771062
#237771012
#237766922
C22×#145791522
C79×#34922
#6282579