Finite Group Databasebeta

← #35196569

Subgroups — #35196569

Order 20224.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777510C212yesmaximal, complemented
2#23777506C216yesmaximal, complemented
3#23777414C213yesmaximal, complemented
4#23777412C211yesmaximal, characteristic, complemented
5#23777407C211yesmaximal, characteristic, complemented
6#23777405C213yesmaximal, complemented
7#23777253C213yesmaximal, complemented
8#23777250C213yesmaximal, complemented
9#23777204C211yesmaximal, characteristic, complemented
10#23777170C211yesmaximal, characteristic, complemented
11#23777118C216yesmaximal, complemented
12#23777057C212yesmaximal, complemented
13#23777026C211yesmaximal, characteristic, complemented
14#23777026C213yesmaximal, complemented
15#23777018C213yesmaximal, complemented
16#23776995C212yesmaximal, complemented
17#23776991C216yesmaximal, complemented
18#23776821C216yesmaximal, complemented
19#23776697C213yesmaximal, complemented
20#23776693C213yesmaximal, complemented
21C4×#14579209C212yesmaximal, complemented
22C4×#41×D79C211yesmaximal, characteristic, complemented
23C79×#3482C211yesmaximal, characteristic, complemented
24C2×#14579209C2212yes—
25C2×#41×D79C2211yescharacteristic
26#19099298C2216yescomplemented
27#19099297C22112yescomplemented
28#19099295C2216yescomplemented
29Q8×Dic158C2211yescharacteristic, complemented
30Q8×Dic158C2213yescomplemented
31#19099292C2212yescomplemented
32#19099290C2216yescomplemented
33#19099288C2213yescomplemented
34#19099287C2213yescomplemented
35#19099286C2216yescomplemented
36#19099284C2216yescomplemented
37#19099284C2216yescomplemented
38#19099280C22112yescomplemented
39#19099278C2216yescomplemented
40#19099278C2213yescomplemented
41#19099278C2213yescomplemented
42#19099276C2216yescomplemented
43#19099276C22112yescomplemented
44#19099276C2216yescomplemented
45#19099266C2216yescomplemented
46#19099264C22112yescomplemented
47#19099261C2216yescomplemented
48#19099261C2216yescomplemented
49#19099260C2216yescomplemented
50#19099258C22112yescomplemented
51#19099247C2216yescomplemented
52#19099245C22112yescomplemented
53#19099235C2212yes—
54#19099235C2211yescharacteristic, complemented
55#19099235C2213yescomplemented
56#19099234C2216yes—
57#19099234C2213yescomplemented
58#19099234C2213yescomplemented
59#19099232C2212yes—
60#19099232C2216yescomplemented
61#19099231C2216yes—
62#19099228C2213yescomplemented
63#19099224C2212yes—
64#19099224C2212yescomplemented
65#19099223C2216yes—
66#19099223C2216yescomplemented
67#19099221C2216yes—
68#19099216C2213yescomplemented
69#19099215C2216yescomplemented
70#19099193C2216yes—
71#19099186C2216yescomplemented
72#19099182C2216yescomplemented
73#19099179C22112yescomplemented
74#19099169C2216yescomplemented
75#19099166C2216yescomplemented
76#19099165C22112yescomplemented
77#19099152C22112yes—
78#19099149C22112yes—
79#19099143C2216yes—
80#19099131C2216yes—
81#19099129C2216yes—
82#19099118C2213yes—
83#19099118C2213yescomplemented
84#19099117C2213yes—
85#19099117C2213yescomplemented
86#19099116C2213yescomplemented
87#19099114C2213yes—
88#19099114C2213yescomplemented
89#19099113C2213yescomplemented
90#19099113C2216yescomplemented
91#19099110C2213yes—
92#19099110C2213yescomplemented
93#19099110C2216yescomplemented
94#19099110C22112yescomplemented
95#19099109C2213yescomplemented
96#19099100C2213yes—
97#19099100C2216yescomplemented
98#19099100C2213yescomplemented
99#19099100C2216yescomplemented
100#19099099C2216yescomplemented
101#19099099C2216yescomplemented
102#19099098C2216yes—
103#19099098C2216yescomplemented
104#19099095C2211yescharacteristic
105#19099095C2213yescomplemented
106#19099093C2216yescomplemented
107#19099093C2216yescomplemented
108#19099091C2216yes—
109#19099091C22112yescomplemented
110#19099091C2216yescomplemented
111#19099076C2216yes—
112#19099076C2216yes—
113#19099075C2216yes—
114#19099075C2213yes—
115#19099072C2216yes—
116#19099072C2216yes—
117#19099070C2213yes—
118#19099045C2216yes—
119#19099045C2212yescomplemented
120#19099044C2216yes—
121#19099044C2216yescomplemented
122#19099041C2212yescomplemented
123#19099039C2212yes—
124#19099039C2216yescomplemented
125#41×Dic79C2211yescharacteristic
126C4×#11929625C2216yes—
127C4×#11929625C2211yescharacteristic
128C4×#11929625C2211yescharacteristic
129C4×#11929625C2212yescomplemented
130C4×#11929625C2216yescomplemented
131C4×#11929624C2213yes—
132C4×#11929624C2216yes—
133C4×#11929624C2216yescomplemented
134C4×#11929624C2213yescomplemented
135C4×#11929624C2216yescomplemented
136#19099031C2213yes—
137#19099031C2216yescomplemented
138C4×#11929623C2213yes—
139C4×#11929623C2213yes—
140C4×Q8×D79C2211yescharacteristic
141C4×Q8×D79C2211yescharacteristic
142C4×Q8×D79C2216yescomplemented
143C4×D4×D79C2213yes—
144C4×D4×D79C2213yes—
145#117×D79C2213yes—
146C2×C42×D79C2213yes—
147#557×C79C2211yescharacteristic, complemented
148#556×C79C2213yescomplemented
149#552×C79C2216yescomplemented
150D4×Q8×C79C2211yescharacteristic, complemented
151#548×C79C2212yes—
152#547×C79C2213yescomplemented
153#533×C79C2213yescomplemented
154#529×C79C2216yescomplemented
155C4×#41×C79C2211yescharacteristic
156C4×#41×C79C2213yescomplemented
157C2×C4×Q8×C79C2212yescomplemented
158#14579209—216no—
159C2×#11929625C2316yes—
160C2×#11929625C2312yes—
161C2×#11929625C2311yescharacteristic
162C2×#11929625C2316yes—
163C2×#11929624C2316yes—
164C2×#11929624C2316yes—
165C2×#11929624C2313yes—
166C2×#11929624C2313yes—
167C2×#11929624C2316yes—
168C2×#11929624C2316yes—
169C2×#11929623C2313yes—
170#41×D79—28no—
171C2×Q8×D79C2316yes—
172C2×Q8×D79C2311yescharacteristic
173C2×D4×D79C2313yes—
174C22×C4×D79C2313yes—
175C22×C4×D79C2313yes—
176C22×C4×D79C2313yes—
177#14579161C2316yes—
178#14579161C2313yes—
179#14579160C23112yes—
180#14579160C2316yes—
181#14579160C2313yes—
182#14579160C2313yes—
183#14579159C2313yes—
184#14579158C2316yes—
185#14579158C2313yes—
186#14579157C23112yes—
187#14579157C2316yes—
188#14579157C2313yes—
189#14579156C23112yes—
190#14579156C23112yes—
191#14579156C23112yes—
192#14579156C2316yes—
193#14579156C2316yes—
194#14579154C23112yes—
195#14579154C2316yes—
196#14579154C2312yes—
197#14579152C2316yes—
198#14579152C2316yes—
199#14579152C2311yescharacteristic
200#14579152C2313yes—
201#14579151C23112yes—
202#14579151C2316yes—
203#14579151C2316yes—
204#14579150C2316yes—
205#14579150C2316yes—
206#14579150C2313yes—
207#14579149C23112yes—
208#14579149C2316yes—
209#14579148C2311yescharacteristic
210#14579147C23112yes—
211#14579147C23112yes—
212#14579147C23112yes—
213#14579147C23112yes—
214#14579147C2316yes—
215#14579147C2316yes—
216#14579146C23112yes—
217#14579146C23112yes—
218#14579146C2316yes—
219#14579146C23112yes—
220#14579146C2316yes—
221#14579145C23112yes—
222#14579145C2316yes—
223#14579143C23112yes—
224#14579143C2316yes—
225#14579143C2312yes—
226#14579142C2316yes—
227#14579141C2316yes—
228#14579141C2316yes—
229#14579141C2313yes—
230#14579141C2311yescharacteristic
231#14579139C23112yes—
232#14579139C2316yes—
233#14579139C2316yes—
234#14579138C2316yes—
235#14579138C2316yes—
236#14579137C2316yes—
237#14579137C2313yes—
238#14579137C2316yes—
239#14579137C2313yes—
240#14579136C2316yes—
241#14579136C2316yes—
242#14579136C23112yes—
243#14579136C2316yes—
244#14579136C2316yes—
245#14579136C2316yes—
246#14579136C2313yes—
247#14579136C2313yes—
248#14579135C2316yes—
249#14579135C23112yes—
250#14579135C2316yes—
251#14579135C2316yes—
252#14579135C2316yes—
253#14579134C2316yes—
254#14579134C23112yes—
255#14579134C23112yes—
256#14579134C23112yes—
257#14579134C23112yes—
258#14579134C2316yes—
259#14579133C2316yes—
260#14579133C2316yes—
261#14579132C23112yes—
262#14579132C2316yes—
263#14579132C2313yes—
264#14579132C2311yescharacteristic
265#14579131C23112yes—
266#14579131C2316yes—
267#14579129C2316yes—
268Q8×Dic79C2316yes—
269Q8×Dic79C2312yes—
270Q8×Dic79C2311yescharacteristic
271Q8×Dic79C2316yes—
272Q8×Dic79C2316yes—
273Q8×Dic79C2311yescharacteristic
274C4×Dic158C2316yes—
275C4×Dic158C2316yes—
276C4×Dic158C2313yes—
277C4×Dic158C2313yes—
278C4×Dic158C2316yes—
279C4×Dic158C2313yes—
280C4×Dic158C2316yes—
281C4×Dic158C2311yescharacteristic
282C4×Dic158C2316yes—
283#14579126C2316yes—
284#14579126C2313yes—
285#14579126C23112yes—
286#14579126C2316yes—
287#14579126C2313yes—
288#14579126C2316yes—
289C4×D316C2316yes—
290C4×D316C2313yes—
291C4×D316C2313yes—
292C4×D316C2316yes—
293C4×D316C2316yes—
294C4×D316C2316yes—
295C4×D316C2313yes—
296C4×D316C2316yes—
297C4×D316C2316yes—
298C4×D316C2313yes—
299C4×D316C23112yes—
300D4×Dic79C2313yes—
301D4×Dic79C2313yes—
302#14579123C23112yes—
303#14579123C2316yes—
304#14579123C2313yes—
305#14579123C2316yes—
306#14579123C23112yes—
307#14579123C2316yes—
308#14579123C2316yes—
309#14579123C2316yes—
310#14579123C2313yes—
311C4×C22⋊D79C2316yes—
312C4×C22⋊D79C2316yes—
313C4×C22⋊D79C2316yes—
314C4×C22⋊D79C2316yes—
315C4×C22⋊D79C2316yes—
316C4×C22⋊D79C2316yes—
317C4×C22⋊D79C23112yes—
318C4×C22⋊D79C2316yes—
319C4×C22⋊D79C2316yes—
320C4×C22⋊D79C2316yes—
321C4×C22⋊D79C2312yes—
322C4×C22⋊D79C2316yes—
323C4×C22⋊D79C2316yes—
324(C22⋊D79)⋊C4C2316yes—
325(C22⋊D79)⋊C4C23112yes—
326(C22⋊D79)⋊C4C23112yes—
327(C22⋊D79)⋊C4C2316yes—
328#14579120C2316yes—
329#14579120C2313yes—
330#14579120C2316yes—
331#14579120C2313yes—
332#14579120C2312yes—
333#14579119C23112yes—
334#14579119C2316yes—
335#14579119C23112yes—
336#14579119C2313yes—
337#14579119C2316yes—
338#14579119C2313yes—
339#14579119C2316yes—
340#14579118C2316yes—
341#14579118C2316yes—
342#14579118C2316yes—
343#14579118C2316yes—
344#14579118C23112yes—
345#14579118C2316yes—
346#14579118C2316yes—
347#14579117C2316yes—
348C4⋊C4×D79C2313yes—
349C4⋊C4×D79C23112yes—
350C4⋊C4×D79C2316yes—
351C4⋊C4×D79C2313yes—
352C22⋊C4×D79C2316yes—
353C2×C4×Dic79C2313yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2313yes—
356C42×D79C2311yescharacteristic
357C42×D79C2313yes—
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C23112yes—
365C42×D79C2316yes—
366C2×#41×C79C2311yescharacteristic
367C2×#41×C79C2313yes—
368C22×Q8×C79C2312yes—
369C4⋊Q8×C79C2313yes—
370C4⋊Q8×C79C2313yes—
371#126×C79C23112yes—
372#125×C79C2316yes—
373#125×C79C2316yes—
374#124×C79C2316yes—
375#123×C79C23112yes—
376C22⋊Q8×C79C2316yes—
377C22⋊Q8×C79C2316yes—
378C22⋊Q8×C79C2316yes—
379#121×C79C2316yes—
380C4×Q8×C79C2311yescharacteristic
381C4×Q8×C79C2312yes—
382C4×Q8×C79C2316yes—
383C4×Q8×C79C2316yes—
384C4×Q8×C79C2311yescharacteristic
385C4×Q8×C79C2313yes—
386C4×Q8×C79C2313yes—
387C4×D4×C79C2316yes—
388C4×D4×C79C2313yes—
389C4×D4×C79C2313yes—
390C4×D4×C79C2313yes—
391C4×D4×C79C2311yescharacteristic
392C4×D4×C79C2316yes—
393#117×C79C2313yes—
394#117×C79C2316yes—
395#117×C79C2313yes—
396#117×C79C2316yes—
397C2×C4⋊C4×C79C2316yes—
398C2×C42×C79C2316yes—
399C2×C42×C79C2313yes—
400C23×D79C2413yes—
401#11929625—224no—
402#11929625—24no—
403#11929625—28no—
404#11929625—412no—
405#11929624—224no—
406#11929624—212no—
407#11929624—224no—
408#11929624—46no—
409#11929624—412no—
410#11929624—412no—
411#11929623—212no—
412C2×Dic158C2416yes—
413C2×Dic158C2411yescharacteristic
414C2×Dic158C2416yes—
415C2×Dic158C2416yes—
416C2×Dic158C2413yes—
417Q8×D79—224no—
418Q8×D79#4118yescomplemented
419C2×D316C2416yes—
420C2×D316C2416yes—
421C2×D316C2413yes—
422C2×D316C2413yes—
423C2×D316C2416yes—
424C2×D316C2416yes—
425C2×D316C24112yes—
426C2×C22⋊D79C2416yes—
427C2×C22⋊D79C2412yes—
428C2×C22⋊D79C2416yes—
429C2×C22⋊D79C24112yes—
430C2×C22⋊D79C2416yes—
431C2×C22⋊D79C2416yes—
432C2×C22⋊D79C2416yes—
433D4×D79—212no—
434C22×Dic79C2413yes—
435C22×Dic79C2413yes—
436C22×Dic79C2413yes—
437C2×C4×D79—212no—
438C2×C4×D79—46no—
439C2×C4×D79—46no—
440C2×C4×D79C24112yes—
441C2×C4×D79C2416yes—
442C2×C4×D79C2413yes—
443C2×C4×D79C2416yes—
444C2×C4×D79C2413yes—
445C2×C4×D79C2413yes—
446C2×C4×D79C2413yes—
447C2×C4×D79C2411yescharacteristic
448C2×C4×D79C2411yescharacteristic
449C2×C4×D79C2411yescharacteristic
450C2×C4×D79C2416yes—
451C2×C4×D79C24112yes—
452C2×C4×D79C2413yes—
453C2×C4×D79C2413yes—
454C2×C4×D79C2413yes—
455C2×C4×D79C2413yes—
456C2×C4×D79C2413yes—
457C4⋊Dic79C2413yes—
458C4⋊Dic79C2416yes—
459C4⋊Dic79C2413yes—
460C4⋊Dic79C2416yes—
461C4⋊Dic79C2413yes—
462C4⋊Dic79C2416yes—
463C4⋊Dic79C24112yes—
464C4⋊Dic79C2411yescharacteristic
465C4⋊Dic79C2412yes—
466C4⋊Dic79C2412yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C2416yes—
470Dic79⋊C4C2416yes—
471Dic79⋊C4C2412yes—
472Dic79⋊C4C2416yes—
473Dic79⋊C4C2412yes—
474Dic79⋊C4C2416yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2416yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2416yes—
479C22⋊Dic79C2416yes—
480C22⋊Dic79C2416yes—
481C22⋊Dic79C2412yes—
482C22⋊Dic79C2412yes—
483C22⋊Dic79C2412yes—
484C22⋊Dic79C2416yes—
485(C2×D79)⋊C4C2416yes—
486(C2×D79)⋊C4C2416yes—
487(C2×D79)⋊C4C2412yes—
488(C2×D79)⋊C4C2416yes—
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C2416yes—
491(C2×D79)⋊C4C2416yes—
492(C2×D79)⋊C4C24112yes—
493(C2×D79)⋊C4C2416yes—
494(C2×D79)⋊C4C2416yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498(C2×D79)⋊C4C24112yes—
499(C2×D79)⋊C4C24112yes—
500C4×Dic79C2413yes—
501C4×Dic79C2411yescharacteristic
502C4×Dic79C2411yescharacteristic
503C4×Dic79C2411yescharacteristic
504C4×Dic79C2412yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2413yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C2413yes—
513C4×Dic79C24112yes—
514C4×Dic79C2416yes—
515C4×Dic79C2416yes—
516C4×Dic79C24112yes—
517#41×C79—24no—
518#41×C79—46no—
519C2×Q8×C79—28no—
520C2×Q8×C79C2416yes—
521C2×Q8×C79C2413yes—
522C2×Q8×C79C2411yescharacteristic
523C2×D4×C79C2413yes—
524C2×D4×C79C2411yescharacteristic
525C2×D4×C79C2416yes—
526C22×C4×C79C2412yes—
527C22×C4×C79C2416yes—
528C22×C4×C79C2413yes—
529C22×C4×C79C2413yes—
530C22×C4×C79C2413yes—
531C22×C4×C79C2416yes—
532C4⋊C4×C79C2413yes—
533C4⋊C4×C79C2416yes—
534C4⋊C4×C79C24112yes—
535C4⋊C4×C79C2411yescharacteristic
536C4⋊C4×C79C2413yes—
537C4⋊C4×C79C2416yes—
538C4⋊C4×C79C2413yes—
539C4⋊C4×C79C2416yes—
540C4⋊C4×C79C2416yes—
541C4⋊C4×C79C2416yes—
542C22⋊C4×C79C2412yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2416yes—
545C22⋊C4×C79C2416yes—
546C22⋊C4×C79C24112yes—
547C42×C79C2413yes—
548C42×C79C2411yescharacteristic
549C42×C79C2413yes—
550C42×C79C2416yes—
551C42×C79C2416yes—
552C42×C79C2413yes—
553C42×C79C2416yes—
554C23×C79C2512yes—
555C23×C79C2513yes—
556C22×D79—26no—
557C22×D79—43no—
558C22×D79—43no—
559C22×D79C2513yes—
560C22×D79C2516yes—
561C22×D79C2511yescharacteristic
562Q8×C79—212no—
563Q8×C79—26no—
564Q8×C79C2×#4114yes—
565D4×C79—26no—
566D4×C79—22no—
567D4×C79—46no—
568C2×C4×C79—26no—
569C2×C4×C79—212no—
570C2×C4×C79—26no—
571C2×C4×C79—26no—
572C2×C4×C79—24no—
573C2×C4×C79—46no—
574C2×C4×C79C2511yescharacteristic
575C2×C4×C79C2513yes—
576C2×C4×C79C2516yes—
577C2×C4×C79C2516yes—
578C2×C4×C79C2513yes—
579C2×C4×C79C2512yes—
580C2×C4×C79C2513yes—
581C2×C4×C79C2511yescharacteristic
582C2×C4×C79C2511yescharacteristic
583C22⋊D79—24no—
584C22⋊D79—212no—
585C22⋊D79—212no—
586C22⋊D79—46no—
587C22⋊D79—412no—
588C22⋊D79—46no—
589C22⋊D79—46no—
590C2×Dic79—26no—
591C2×Dic79—43no—
592C2×Dic79—43no—
593C2×Dic79C2511yescharacteristic
594C2×Dic79C2511yescharacteristic
595C2×Dic79C2511yescharacteristic
596C2×Dic79C2513yes—
597C2×Dic79C2516yes—
598C2×Dic79C2512yes—
599C2×Dic79C2513yes—
600C2×Dic79C2512yes—
601C2×Dic79C2513yes—
602D316—212no—
603D316—26no—
604D316—212no—
605D316—26no—
606D316—46no—
607D316—46no—
608D316—412no—
609C4×D79—22no—
610C4×D79—26no—
611C4×D79—212no—
612C4×D79—22no—
613C4×D79—22no—
614C4×D79—26no—
615C4×D79—26no—
616C4×D79—212no—
617C4×D79—26no—
618C4×D79—224no—
619C4×D79—43no—
620C4×D79—43no—
621C4×D79—43no—
622C4×D79—43no—
623C4×D79—46no—
624C4×D79—412no—
625C4×D79C2×#41112yes—
626Dic158—22no—
627Dic158—212no—
628Dic158—46no—
629Dic158—46no—
630Dic158C2×#41112yes—
631C22×C79—22no—
632C22×C79—23no—
633C22×C79—22no—
634C22×C79—23no—
635C22×C79—23no—
636C22×C79—22no—
637C22×C79C2611yescharacteristic
638C2×D79—21no—
639C2×D79—21no—
640C2×D79—23no—
641C2×D79—26no—
642C2×D79—26no—
643C2×D79—23no—
644C2×D79—26no—
645C2×D79—23no—
646C2×D79—412no—
647C2×D79C22×#4112yes—
648C4×C79—21no—
649C4×C79—26no—
650C4×C79—23no—
651C4×C79—22no—
652C4×C79—23no—
653C4×C79—26no—
654C4×C79C22×#4116yes—
655C4×C79#58512yes—
656C4×C79#58512yes—
657Dic79—22no—
658Dic79—21no—
659Dic79—22no—
660Dic79—26no—
661Dic79—23no—
662Dic79—23no—
663Dic79—21no—
664Dic79—21no—
665Dic79C22×#4116yes—
666#62793—791nomaximal, Sylow
667C2×C79—43no—
668C2×C79—42no—
669C2×C79C23×#4111yescharacteristic
670C2×C79C2×#58511yescharacteristic
671C2×C79C2×#58511yescharacteristic
672D79—22no—
673D79—46no—
674D79—43no—
675#3524—796no—
676#3524—792no—
677#3518—793no—
678#3518—791no—
679#3517—791no—
680#3517—793no—
681#3506—793no—
682#3506—793no—
683#3502—791no—
684#3497—791no—
685#3493—796no—
686#3487—792no—
687#3483—791no—
688#3483—793no—
689#3482—793no—
690#3482D7911yescharacteristic, complemented
691#3480—796no—
692#3480—792no—
693#3460—796no—
694#3444—793no—
695#3444—793no—
696C4×2−1+4—792no—
697C2×C4×#41—791no—
698C79#6279311yescharacteristic, complemented, Sylow
699C2×2−1+4—792no—
700C22×#41—791no—
701#559—796no—
702#559—7912no—
703#559—796no—
704Q82—791no—
705Q82—793no—
706#557—793no—
707#557—796no—
708#557—792no—
709#557C2×D7911yescharacteristic, complemented
710#556—793no—
711#556—7912no—
712#556—796no—
713#556—796no—
714#556—796no—
715#556C2×D7913yescomplemented
716#555—796no—
717#555—793no—
718#555—793no—
719#555—796no—
720#555—7912no—
721#555—796no—
722#553—7912no—
723#553—796no—
724#553—7912no—
725#553—796no—
726#553—796no—
727#553—796no—
728#552—7912no—
729#552—796no—
730#552C2×D7916yescomplemented
731#550—792no—
732#550—796no—
733#550—796no—
734#550—792no—
735#550—791no—
736#550—793no—
737#550—796no—
738#550—793no—
739#550—793no—
740D4×Q8—793no—
741D4×Q8C2×D7911yescharacteristic, complemented
742#548—792no—
743#548—792no—
744#548—796no—
745#548—796no—
746#548—796no—
747#548C2×D7912yes—
748#547—793no—
749#547—796no—
750#547C2×D7913yescomplemented
751#544—796no—
752#542—7912no—
753#542—796no—
754#542—796no—
755#540—796no—
756#540—7912no—
757#540—796no—
758#538—7912no—
759#538—7912no—
760#537—796no—
761#535—796no—
762#535—796no—
763#533—793no—
764#533—793no—
765#533—793no—
766#533—793no—
767#533—793no—
768#533C2×D7913yescomplemented
769#532—793no—
770#532—793no—
771#532—793no—
772#532—793no—
773#532—793no—
774#532—7912no—
775#532—796no—
776#532—793no—
777#532—796no—
778#529—796no—
779#529—796no—
780#529—796no—
781#529—796no—
782#529—793no—
783#529—796no—
784#529—793no—
785#529—796no—
786#529—791no—
787#529—796no—
788#529—793no—
789#529—796no—
790#529—796no—
791#529—796no—
792#529—7912no—
793#529C2×D7916yescomplemented
794#525—793no—
795#525—796no—
796#525—796no—
797#525—796no—
798#525—796no—
799#525—796no—
800#525—793no—
801#520—796no—
802#520—792no—
803#520—796no—
804#520—796no—
805#519—792no—
806#519—792no—
807#519—796no—
808C4×#41—791no—
809C4×#41—791no—
810C4×#41—791no—
811C4×#41—796no—
812C4×#41—792no—
813C4×#41—796no—
814C4×#41—793no—
815C4×#41—793no—
816C4×#41—793no—
817C4×#41—796no—
818C4×#41—793no—
819C4×#41—796no—
820C4×#41—796no—
821C4×#41—796no—
822C4×#41—793no—
823C4×#41C2×D7911yescharacteristic
824C4×#41C2×D7913yescomplemented
825C2×C4×Q8—791no—
826C2×C4×Q8—791no—
827C2×C4×Q8—796no—
828C2×C4×Q8C2×D7912yescomplemented
829C2×C4×D4—793no—
830C2×C4×D4—793no—
831C2×#117—793no—
832C22×C42—793no—
8332−1+4—15816no—
834C2×#41—796no—
835C2×#41—791no—
836C2×#41—796no—
837C2×#41—792no—
838C2×#41—793no—
839C2×#41—796no—
840C2×#41—796no—
841C2×#41—793no—
842C2×#41—793no—
843C2×#41—796no—
844C2×#41—796no—
845C2×#41—1588no—
846C2×#41C22×D7911yescharacteristic
847C2×#41C22×D7913yes—
848C22×Q8—791no—
849C22×Q8—796no—
850C22×Q8C22×D7912yes—
851C22×D4—793no—
852C23×C4—793no—
853C23×C4—793no—
854C23×C4—793no—
855C4⋊Q8—793no—
856C4⋊Q8—793no—
857C4⋊Q8—793no—
858C4⋊Q8—7912no—
859C4⋊Q8—796no—
860C4⋊Q8—793no—
861C4⋊Q8—796no—
862C4⋊Q8C22×D7913yes—
863C4⋊Q8C22×D7913yes—
864#127—793no—
865#127—796no—
866#127—7912no—
867#127—793no—
868#127—796no—
869#126—796no—
870#126—796no—
871#126—7912no—
872#126—7912no—
873#126—7912no—
874#126—792no—
875#126—796no—
876#126—7912no—
877#126C22×D79112yes—
878#125—791no—
879#125—793no—
880#125—796no—
881#125—796no—
882#125—796no—
883#125—7912no—
884#125—796no—
885#125C22×D7916yes—
886#125C22×D7916yes—
887#124—793no—
888#124—796no—
889#124—796no—
890#124—791no—
891#124—796no—
892#124—796no—
893#124—7912no—
894#124—7912no—
895#124—7912no—
896#124—7912no—
897#124—796no—
898#124—7912no—
899#124C22×D7916yes—
900#123—796no—
901#123—796no—
902#123—796no—
903#123—7912no—
904#123—7912no—
905#123—7912no—
906#123—792no—
907#123—796no—
908#123—7912no—
909#123—796no—
910#123—7912no—
911#123C22×D79112yes—
912C22⋊Q8—793no—
913C22⋊Q8—793no—
914C22⋊Q8—796no—
915C22⋊Q8—796no—
916C22⋊Q8—791no—
917C22⋊Q8—796no—
918C22⋊Q8—796no—
919C22⋊Q8—796no—
920C22⋊Q8—793no—
921C22⋊Q8—796no—
922C22⋊Q8—7912no—
923C22⋊Q8—796no—
924C22⋊Q8—796no—
925C22⋊Q8C22×D7916yes—
926C22⋊Q8C22×D7916yes—
927C22⋊Q8C22×D7916yes—
928#121—791no—
929#121—796no—
930#121—796no—
931#121—793no—
932#121—796no—
933#121—7912no—
934#121—796no—
935#121—796no—
936#121—796no—
937#121—796no—
938#121—7912no—
939#121—793no—
940#121—796no—
941#121—796no—
942#121—796no—
943#121—793no—
944#121—796no—
945#121—796no—
946#121—7912no—
947#121—796no—
948#121—796no—
949#121—7912no—
950#121—7912no—
951#121—7912no—
952#121—7912no—
953#121C22×D7916yes—
954#120—796no—
955#120—796no—
956#120—7912no—
957C4×Q8—791no—
958C4×Q8—791no—
959C4×Q8—796no—
960C4×Q8—796no—
961C4×Q8—792no—
962C4×Q8—796no—
963C4×Q8—793no—
964C4×Q8—793no—
965C4×Q8—796no—
966C4×Q8—7912no—
967C4×Q8—796no—
968C4×Q8—796no—
969C4×Q8—793no—
970C4×Q8—796no—
971C4×Q8—793no—
972C4×Q8—791no—
973C4×Q8—796no—
974C4×Q8—796no—
975C4×Q8—793no—
976C4×Q8—796no—
977C4×Q8—796no—
978C4×Q8C22×D7911yescharacteristic
979C4×Q8C22×D7916yes—
980C4×Q8C22×D7911yescharacteristic
981C4×Q8C22×D7912yes—
982C4×Q8C22×D7916yes—
983C4×Q8C22×D7913yes—
984C4×Q8C22×D7913yes—
985C4×D4—793no—
986C4×D4—793no—
987C4×D4—796no—
988C4×D4—796no—
989C4×D4—792no—
990C4×D4—796no—
991C4×D4—796no—
992C4×D4—796no—
993C4×D4—7912no—
994C4×D4—796no—
995C4×D4—796no—
996C4×D4—796no—
997C4×D4—796no—
998C4×D4—796no—
999C4×D4—796no—
1000C4×D4—793no—
1001C4×D4—793no—
1002C4×D4—7912no—
1003C4×D4—796no—
1004C4×D4—796no—
1005C4×D4—7912no—
1006C4×D4—796no—
1007C4×D4—796no—
1008C4×D4—796no—
1009C4×D4—796no—
1010C4×D4—796no—
1011C4×D4—7912no—
1012C4×D4—7912no—
1013C4×D4—793no—
1014C4×D4—793no—
1015C4×D4—796no—
1016C4×D4—796no—
1017C4×D4—793no—
1018C4×D4—796no—
1019C4×D4—796no—
1020C4×D4—7912no—
1021C4×D4—796no—
1022C4×D4—796no—
1023C4×D4—793no—
1024C4×D4C22×D7913yes—
1025C4×D4C22×D7913yes—
1026C4×D4C22×D7911yescharacteristic
1027C4×D4C22×D7916yes—
1028C4×D4C22×D7916yes—
1029C4×D4C22×D7913yes—
1030#117—793no—
1031#117—792no—
1032#117—796no—
1033#117—796no—
1034#117—793no—
1035#117—793no—
1036#117—793no—
1037#117—796no—
1038#117—7912no—
1039#117—796no—
1040#117—796no—
1041#117—7912no—
1042#117—796no—
1043#117—796no—
1044#117—796no—
1045#117—796no—
1046#117—796no—
1047#117—7912no—
1048#117—796no—
1049#117—796no—
1050#117C22×D7913yes—
1051#117C22×D7916yes—
1052#117C22×D7913yes—
1053#117C22×D7916yes—
1054C2×C4⋊C4—793no—
1055C2×C4⋊C4—793no—
1056C2×C4⋊C4—7912no—
1057C2×C4⋊C4—796no—
1058C2×C4⋊C4C22×D7916yes—
1059C2×C22⋊C4—796no—
1060C2×C42—793no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—793no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—7912no—
1067C2×C42—796no—
1068C2×C42—793no—
1069C2×C42—793no—
1070C2×C42—793no—
1071C2×C42—793no—
1072C2×C42—791no—
1073C2×C42C22×D7916yes—
1074C2×C42C22×D7913yes—
1075C24—793no—
1076#41—24no—
1077#41—46no—
1078#41—3166no—
1079#41—31612no—
1080#41—31612no—
1081#41—31612no—
1082#41—15824no—
1083#41—15812no—
1084#41—15824no—
1085#41—15824no—
1086#41—15812no—
1087#41—1584no—
1088#41—1588no—
1089C2×Q8—28no—
1090C2×Q8—798no—
1091C2×Q8—796no—
1092C2×Q8—796no—
1093C2×Q8—793no—
1094C2×Q8—796no—
1095C2×Q8—791no—
1096C2×Q8—15824no—
1097C2×Q8C23×D7916yes—
1098C2×Q8C23×D7913yes—
1099C2×Q8C23×D7911yescharacteristic
1100C2×D4—796no—
1101C2×D4—796no—
1102C2×D4—7912no—
1103C2×D4—796no—
1104C2×D4—792no—
1105C2×D4—796no—
1106C2×D4—796no—
1107C2×D4—7912no—
1108C2×D4—796no—
1109C2×D4—796no—
1110C2×D4—796no—
1111C2×D4—793no—
1112C2×D4—793no—
1113C2×D4—796no—
1114C2×D4—15812no—
1115C2×D4C23×D7913yes—
1116C2×D4C23×D7911yescharacteristic
1117C2×D4C23×D7916yes—
1118C22×C4—3166no—
1119C22×C4—3166no—
1120C22×C4—793no—
1121C22×C4—793no—
1122C22×C4—793no—
1123C22×C4—793no—
1124C22×C4—793no—
1125C22×C4—793no—
1126C22×C4—7912no—
1127C22×C4—796no—
1128C22×C4—793no—
1129C22×C4—793no—
1130C22×C4—791no—
1131C22×C4—791no—
1132C22×C4—793no—
1133C22×C4—793no—
1134C22×C4—793no—
1135C22×C4—7912no—
1136C22×C4—796no—
1137C22×C4—791no—
1138C22×C4—796no—
1139C22×C4—793no—
1140C22×C4—15812no—
1141C22×C4C23×D7913yes—
1142C22×C4C23×D7913yes—
1143C22×C4C23×D7916yes—
1144C22×C4C23×D7913yes—
1145C22×C4C23×D7912yes—
1146C22×C4C23×D7916yes—
1147C4⋊C4—796no—
1148C4⋊C4—796no—
1149C4⋊C4—796no—
1150C4⋊C4—796no—
1151C4⋊C4—792no—
1152C4⋊C4—796no—
1153C4⋊C4—792no—
1154C4⋊C4—796no—
1155C4⋊C4—796no—
1156C4⋊C4—796no—
1157C4⋊C4—796no—
1158C4⋊C4—796no—
1159C4⋊C4—793no—
1160C4⋊C4—796no—
1161C4⋊C4—793no—
1162C4⋊C4—791no—
1163C4⋊C4—793no—
1164C4⋊C4—796no—
1165C4⋊C4—796no—
1166C4⋊C4—792no—
1167C4⋊C4—792no—
1168C4⋊C4—7912no—
1169C4⋊C4C23×D7913yes—
1170C4⋊C4C23×D7916yes—
1171C4⋊C4C23×D79112yes—
1172C4⋊C4C23×D7913yes—
1173C4⋊C4C23×D7913yes—
1174C4⋊C4C23×D7916yes—
1175C4⋊C4C23×D7911yescharacteristic
1176C4⋊C4C23×D7916yes—
1177C4⋊C4C23×D7916yes—
1178C4⋊C4C23×D7916yes—
1179C22⋊C4—796no—
1180C22⋊C4—792no—
1181C22⋊C4—796no—
1182C22⋊C4—792no—
1183C22⋊C4—792no—
1184C22⋊C4—796no—
1185C22⋊C4—796no—
1186C22⋊C4—796no—
1187C22⋊C4—796no—
1188C22⋊C4—792no—
1189C22⋊C4—796no—
1190C22⋊C4—796no—
1191C22⋊C4—7912no—
1192C22⋊C4—796no—
1193C22⋊C4—796no—
1194C22⋊C4—796no—
1195C22⋊C4—796no—
1196C22⋊C4—796no—
1197C22⋊C4—7912no—
1198C22⋊C4—796no—
1199C22⋊C4—7912no—
1200C22⋊C4C23×D7916yes—
1201C22⋊C4C23×D7912yes—
1202C22⋊C4C23×D79112yes—
1203C22⋊C4C23×D7916yes—
1204C22⋊C4C23×D7916yes—
1205C42—791no—
1206C42—791no—
1207C42—793no—
1208C42—793no—
1209C42—793no—
1210C42—793no—
1211C42—793no—
1212C42—793no—
1213C42—793no—
1214C42—793no—
1215C42—7912no—
1216C42—796no—
1217C42—7912no—
1218C42—796no—
1219C42—791no—
1220C42—793no—
1221C42—792no—
1222C42C23×D7913yes—
1223C42C23×D7913yes—
1224C42C23×D7916yes—
1225C42C23×D7916yes—
1226C42C23×D7911yescharacteristic
1227C42C23×D7913yes—
1228C42C23×D7916yes—
1229C23—3163no—
1230C23—3163no—
1231C23—791no—
1232C23—793no—
1233C23—796no—
1234C23—1586no—
1235C23C24×D7912yes—
1236C23C24×D7913yes—
1237Q8—26no—
1238Q8—212no—
1239Q8—3166no—
1240Q8—3166no—
1241Q8—7912no—
1242Q8—15812no—
1243Q8—1582no—
1244Q8#41×D7914yes—
1245D4—22no—
1246D4—26no—
1247D4—46no—
1248D4—31612no—
1249D4—3166no—
1250D4—3166no—
1251D4—3166no—
1252D4—3166no—
1253D4—31612no—
1254D4—3166no—
1255D4—15812no—
1256D4—15812no—
1257D4—15812no—
1258D4—1584no—
1259D4—1586no—
1260D4—1586no—
1261D4—15812no—
1262C2×C4—26no—
1263C2×C4—26no—
1264C2×C4—24no—
1265C2×C4—26no—
1266C2×C4—212no—
1267C2×C4—46no—
1268C2×C4—3163no—
1269C2×C4—3163no—
1270C2×C4—3163no—
1271C2×C4—3163no—
1272C2×C4—3166no—
1273C2×C4—31612no—
1274C2×C4—3163no—
1275C2×C4—3163no—
1276C2×C4—793no—
1277C2×C4—7912no—
1278C2×C4—791no—
1279C2×C4—791no—
1280C2×C4—793no—
1281C2×C4—791no—
1282C2×C4—796no—
1283C2×C4—792no—
1284C2×C4—793no—
1285C2×C4—792no—
1286C2×C4—1586no—
1287C2×C4—15824no—
1288C2×C4—1582no—
1289C2×C4—1586no—
1290C2×C4—1582no—
1291C2×C4—1586no—
1292C2×C4—1582no—
1293C2×C4—1586no—
1294C2×C4—15812no—
1295C2×C4—1586no—
1296C2×C4—15812no—
1297C2×C4C24×D7911yescharacteristic
1298C2×C4C24×D7913yes—
1299C2×C4C24×D7916yes—
1300C2×C4C24×D7913yes—
1301C2×C4C24×D7916yes—
1302C2×C4C24×D7912yes—
1303C2×C4C24×D7911yescharacteristic
1304C2×C4C24×D7913yes—
1305C2×C4C24×D7911yescharacteristic
1306C22—22no—
1307C22—23no—
1308C22—23no—
1309C22—22no—
1310C22—23no—
1311C22—22no—
1312C22—31612no—
1313C22—792no—
1314C22—1586no—
1315C22—1583no—
1316C22—1586no—
1317C22—1583no—
1318C22—1583no—
1319C22—1586no—
1320C22—1581no—
1321C22—1581no—
1322C22C25×D7911yescharacteristic
1323C4—21no—
1324C4—26no—
1325C4—23no—
1326C4—26no—
1327C4—23no—
1328C4—22no—
1329C4—796no—
1330C4—1581no—
1331C4—1582no—
1332C4—1581no—
1333C4—1583no—
1334C4—1582no—
1335C4—1581no—
1336C4—1583no—
1337C4—1586no—
1338C4C2×#41×D7916yes—
1339C4#1909939912yes—
1340C4#1909940012yes—
1341C2—43no—
1342C2—42no—
1343C2—3163no—
1344C2—3166no—
1345C2—1582no—
1346C2C22×#41×D7911yescharacteristic
1347C2C2×#1909939911yescharacteristic
1348C2C2×#1909940011yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC79×#3482C2
hypercenter#3482D79
hypocenterC79#62793
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #23777510C2semidirect
2. #23777506C2semidirect
3. #23777414C2semidirect
4. #23777412C2semidirect
5. #23777407C2semidirect
6. #23777405C2semidirect
7. #23777253C2semidirect
8. #23777250C2semidirect
9. #23777204C2semidirect
10. #23777170C2semidirect
11. #23777118C2semidirect
12. #23777057C2semidirect
13. #23777026C2semidirect
14. #23777026C2semidirect
15. #23777018C2semidirect
16. #23776995C2semidirect
17. #23776991C2semidirect
18. #23776821C2semidirect
19. #23776697C2semidirect
20. #23776693C2semidirect
21. C4×#14579209C2semidirect
22. C4×#41×D79C2semidirect
23. C79×#3482C2semidirect
26. #19099298C22semidirect
27. #19099297C22semidirect
28. #19099295C22semidirect
29. Q8×Dic158C22semidirect
30. Q8×Dic158C22semidirect
31. #19099292C22semidirect
32. #19099290C22semidirect
33. #19099288C22semidirect
34. #19099287C22semidirect
35. #19099286C22semidirect
36. #19099284C22semidirect
37. #19099284C22semidirect
38. #19099280C22semidirect
39. #19099278C22semidirect
40. #19099278C22semidirect
41. #19099278C22semidirect
42. #19099276C22semidirect
43. #19099276C22semidirect
44. #19099276C22semidirect
45. #19099266C22semidirect
46. #19099264C22semidirect
47. #19099261C22semidirect
48. #19099261C22semidirect
49. #19099260C22semidirect
50. #19099258C22semidirect
51. #19099247C22semidirect
52. #19099245C22semidirect
54. #19099235C22semidirect
55. #19099235C22semidirect
57. #19099234C22semidirect
58. #19099234C22semidirect
60. #19099232C22semidirect
62. #19099228C22semidirect
64. #19099224C22semidirect
66. #19099223C22semidirect
68. #19099216C22semidirect
69. #19099215C22semidirect
71. #19099186C22semidirect
72. #19099182C22semidirect
73. #19099179C22semidirect
74. #19099169C22semidirect
75. #19099166C22semidirect
76. #19099165C22semidirect
83. #19099118C22semidirect
85. #19099117C22semidirect
86. #19099116C22semidirect
88. #19099114C22semidirect
89. #19099113C22semidirect
90. #19099113C22semidirect
92. #19099110C22semidirect
93. #19099110C22semidirect
94. #19099110C22semidirect
95. #19099109C22semidirect
97. #19099100C22semidirect
98. #19099100C22semidirect
99. #19099100C22semidirect
100. #19099099C22semidirect
101. #19099099C22semidirect
103. #19099098C22semidirect
105. #19099095C22semidirect
106. #19099093C22semidirect
107. #19099093C22semidirect
109. #19099091C22semidirect
110. #19099091C22semidirect
119. #19099045C22semidirect
121. #19099044C22semidirect
122. #19099041C22semidirect
124. #19099039C22semidirect
129. C4×#11929625C22semidirect
130. C4×#11929625C22semidirect
133. C4×#11929624C22semidirect
134. C4×#11929624C22semidirect
135. C4×#11929624C22semidirect
137. #19099031C22semidirect
142. C4×Q8×D79C22semidirect
147. #557×C79C22semidirect
148. #556×C79C22semidirect
149. #552×C79C22semidirect
150. D4×Q8×C79C22semidirect
152. #547×C79C22semidirect
153. #533×C79C22semidirect
154. #529×C79C22semidirect
156. C4×#41×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
418. Q8×D79#41semidirect
690. #3482D79semidirect
698. C79#62793semidirect
709. #557C2×D79semidirect
715. #556C2×D79semidirect
730. #552C2×D79semidirect
741. D4×Q8C2×D79semidirect
750. #547C2×D79semidirect
768. #533C2×D79semidirect
793. #529C2×D79semidirect
824. C4×#41C2×D79semidirect
828. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237775102
#237775062
#237774142
#237774122
#237774072
#237774052
#237772532
#237772502
#237772042
#237771702
#237771182
#237770572
#237770262
#237770182
#237769952
#237769912
#237768212
#237766972
#237766932
C4×#145792092
C4×#41×D792
C79×#34822
#6279379