Finite Group Databasebeta

← #35196499

Subgroups — #35196499

Order 20224.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777493C213yesmaximal, complemented
2#23777491C211yesmaximal, characteristic, complemented
3#23777486C211yesmaximal, characteristic, complemented
4#23777484C213yesmaximal, complemented
5#23777394C212yesmaximal, complemented
6#23777390C216yesmaximal, complemented
7#23777266C213yesmaximal, complemented
8#23777263C213yesmaximal, complemented
9#23777209C211yesmaximal, characteristic, complemented
10#23777170C211yesmaximal, characteristic, complemented
11#23777108C216yesmaximal, complemented
12#23777050C212yesmaximal, complemented
13#23777018C216yesmaximal, complemented
14#23777017C212yesmaximal, complemented
15#23776995C211yesmaximal, characteristic, complemented
16#23776993C213yesmaximal, complemented
17#23776978C213yesmaximal, complemented
18#23776831C216yesmaximal, complemented
19#23776697C213yesmaximal, complemented
20#23776693C213yesmaximal, complemented
21C4×#14579209C212yesmaximal, complemented
22C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
23Q8×#41×C79C211yesmaximal, characteristic, complemented
24C2×#14579209C2212yes—
25C22×Q8×D79C2211yescharacteristic
26#19099298C2213yescomplemented
27#19099298C2213yescomplemented
28#19099296C2216yescomplemented
29#19099293C2213yescomplemented
30#19099292C2211yescharacteristic, complemented
31#19099291C2213yescomplemented
32#19099290C2216yescomplemented
33#19099289C2212yescomplemented
34#19099288C2216yescomplemented
35#19099288C2213yescomplemented
36#19099287C2216yescomplemented
37#19099286C2213yescomplemented
38#19099285C2216yescomplemented
39#19099285C2216yescomplemented
40#19099284C22112yescomplemented
41#19099283C2213yescomplemented
42#19099274C2213yescomplemented
43#19099271C2216yes—
44#19099269C2216yescomplemented
45#19099267C22112yes—
46#19099262C22112yes—
47#19099261C2216yes—
48#19099259C2216yes—
49#19099254C2216yes—
50#19099248C2216yescomplemented
51#19099247C2216yes—
52#19099247C2216yescomplemented
53#19099245C22112yes—
54#19099245C22112yescomplemented
55#19099235C2211yescharacteristic, complemented
56#19099234C2213yescomplemented
57#19099228C2216yes—
58#19099228C2213yescomplemented
59Q8×C22⋊D79C2212yes—
60#19099226C2216yes—
61#19099225C2212yes—
62#19099224C2212yes—
63#19099224C2212yescomplemented
64#19099223C2216yes—
65#19099223C2216yescomplemented
66#19099222C2216yes—
67#19099216C2216yes—
68#19099215C22112yes—
69#19099214C2216yes—
70#19099190C2216yes—
71#19099187C2216yescomplemented
72#19099186C2216yescomplemented
73#19099183C22112yescomplemented
74#19099174C2216yescomplemented
75#19099173C2216yescomplemented
76#19099172C22112yescomplemented
77#19099161C22112yes—
78#19099159C22112yes—
79#19099143C2216yes—
80#19099138C2216yes—
81#19099136C2216yes—
82#19099118C2213yes—
83#19099118C2213yes—
84#19099117C2213yes—
85#19099117C2213yes—
86#19099117C2216yescomplemented
87#19099117C22112yescomplemented
88#19099116C2213yes—
89#19099114C2213yes—
90#19099114C2213yes—
91#19099113C2213yes—
92#19099110C2213yes—
93#19099110C2213yes—
94#19099109C2213yes—
95#19099100C2216yes—
96#19099100C2213yes—
97#19099100C2213yes—
98#19099100C2216yes—
99#19099100C2216yescomplemented
100#19099099C2216yes—
101#19099099C2216yes—
102#19099098C2216yes—
103#19099098C2216yes—
104#19099097C2216yescomplemented
105#19099095C2213yes—
106#19099095C2213yes—
107#19099093C2216yes—
108#19099093C2216yes—
109#19099091C2216yes—
110#19099091C2216yes—
111#19099091C22112yescomplemented
112#19099076C2216yes—
113#19099076C2216yes—
114#19099075C2213yes—
115#19099072C2216yes—
116#19099072C2216yes—
117#19099070C2211yescharacteristic
118#19099045C2216yes—
119#19099045C2212yescomplemented
120#19099044C2216yes—
121#19099044C2216yescomplemented
122#19099041C2212yescomplemented
123#19099039C2212yes—
124#19099039C2216yescomplemented
125C4×#11929625C2216yes—
126C4×#11929625C2216yes—
127C4×#11929625C2212yescomplemented
128C4×#11929624C2216yes—
129C4×#11929624C2213yes—
130C4×#11929624C2216yes—
131C4×#11929624C2216yescomplemented
132#19099031C2216yes—
133C2×Q8×Dic79C2211yescharacteristic
134C2×C4×Dic158C2213yes—
135C2×#14579126C2213yes—
136C4×Q8×D79C2213yes—
137C4×Q8×D79C2211yescharacteristic
138C4×Q8×D79C2211yescharacteristic
139C4×Q8×D79C2213yes—
140C4×Q8×D79C2211yescharacteristic
141C4×Q8×D79C2213yes—
142C4×Q8×D79C2211yescharacteristic
143C4×Q8×D79C2213yes—
144C4×Q8×D79C2216yescomplemented
145C2×C4⋊C4×D79C2213yes—
146C2×C42×D79C2213yes—
147Q82×C79C2211yescharacteristic, complemented
148#557×C79C2213yescomplemented
149#554×C79C2216yes—
150#554×C79C2213yescomplemented
151D4×Q8×C79C2212yes—
152D4×Q8×C79C2211yescharacteristic, complemented
153#533×C79C2213yes—
154#533×C79C2216yescomplemented
155C4×#41×C79C2213yes—
156C2×C4×Q8×C79C2211yescharacteristic
157C2×C4×Q8×C79C2212yescomplemented
158#14579209—216no—
159C2×#11929625C2316yes—
160C2×#11929625C2312yes—
161C2×#11929625C2316yes—
162C2×#11929624C2316yes—
163C2×#11929624C2316yes—
164C2×#11929624C2313yes—
165C2×#11929624C2316yes—
166C22×Dic158C2313yes—
167C2×Q8×D79—28no—
168C2×Q8×D79C2313yes—
169C2×Q8×D79C2316yes—
170C2×Q8×D79C2313yes—
171C2×Q8×D79C2311yescharacteristic
172C2×Q8×D79C2311yescharacteristic
173C22×C4×D79C2311yescharacteristic
174C22×C4×D79C2313yes—
175C22×C4×D79C2313yes—
176#14579161C2313yes—
177#14579160C23112yes—
178#14579160C2316yes—
179#14579160C2313yes—
180#14579160C2313yes—
181#14579159C2316yes—
182#14579159C23112yes—
183#14579159C2313yes—
184#14579158C2313yes—
185#14579157C2313yes—
186#14579156C23112yes—
187#14579156C23112yes—
188#14579156C2316yes—
189#14579156C23112yes—
190#14579156C2316yes—
191#14579156C23112yes—
192#14579155C23112yes—
193#14579154C23112yes—
194#14579154C2316yes—
195#14579154C2316yes—
196#14579153C2316yes—
197#14579152C2316yes—
198#14579152C2316yes—
199#14579152C2316yes—
200#14579152C2313yes—
201#14579152C2313yes—
202#14579151C23112yes—
203#14579151C23112yes—
204#14579151C23112yes—
205#14579151C2316yes—
206#14579151C23112yes—
207#14579151C2316yes—
208#14579150C2316yes—
209#14579150C2316yes—
210#14579150C2316yes—
211#14579150C2313yes—
212#14579149C2316yes—
213#14579149C2316yes—
214#14579148C2313yes—
215#14579147C23112yes—
216#14579147C2316yes—
217#14579147C2316yes—
218#14579146C23112yes—
219#14579146C2316yes—
220#14579146C23112yes—
221#14579146C23112yes—
222#14579146C23112yes—
223#14579146C2316yes—
224#14579145C2316yes—
225#14579144C23112yes—
226#14579143C2316yes—
227#14579143C23112yes—
228#14579143C2316yes—
229#14579142C2312yes—
230#14579141C2316yes—
231#14579141C23112yes—
232#14579141C2313yes—
233#14579141C2313yes—
234#14579140C2316yes—
235#14579139C23112yes—
236#14579139C23112yes—
237#14579139C23112yes—
238#14579139C2316yes—
239#14579139C23112yes—
240#14579139C2316yes—
241#14579138C2316yes—
242#14579138C2316yes—
243#14579137C2316yes—
244#14579137C2316yes—
245#14579137C2316yes—
246#14579137C23112yes—
247#14579137C2316yes—
248#14579137C2311yescharacteristic
249#14579137C2311yescharacteristic
250#14579136C2316yes—
251#14579136C2316yes—
252#14579136C2316yes—
253#14579136C2313yes—
254#14579136C2313yes—
255#14579135C2316yes—
256#14579135C2316yes—
257#14579135C2316yes—
258#14579134C2316yes—
259#14579134C23112yes—
260#14579134C2316yes—
261#14579133C2316yes—
262#14579133C2316yes—
263#14579132C2311yescharacteristic
264#14579132C2311yescharacteristic
265#14579131C2316yes—
266#14579129C2312yes—
267Q8×Dic79C2316yes—
268Q8×Dic79C2313yes—
269Q8×Dic79C2312yes—
270Q8×Dic79C2311yescharacteristic
271Q8×Dic79C2316yes—
272Q8×Dic79C2313yes—
273Q8×Dic79C2311yescharacteristic
274Q8×Dic79C2316yes—
275C4×Dic158C2316yes—
276C4×Dic158C2316yes—
277C4×Dic158C2313yes—
278C4×Dic158C2316yes—
279C4×Dic158C2313yes—
280C4×Dic158C2313yes—
281C4×Dic158C2316yes—
282C4×Dic158C2313yes—
283C4×Dic158C2316yes—
284C4×Dic158C2316yes—
285C4×Dic158C2313yes—
286C4×Dic158C2313yes—
287C4×Dic158C2316yes—
288#14579126C2316yes—
289#14579126C2313yes—
290#14579126C2316yes—
291#14579126C2313yes—
292#14579126C23112yes—
293#14579126C2316yes—
294#14579126C2313yes—
295#14579126C2313yes—
296#14579126C2316yes—
297#14579126C2316yes—
298C4×D316C2316yes—
299C4×D316C2316yes—
300C4×D316C2316yes—
301C4×D316C2313yes—
302C4×D316C2313yes—
303C4×D316C2316yes—
304C4×D316C2316yes—
305C4×D316C2316yes—
306C4×D316C2316yes—
307#14579123C23112yes—
308#14579123C2316yes—
309#14579123C2316yes—
310#14579123C23112yes—
311#14579123C2316yes—
312#14579123C2316yes—
313#14579123C2316yes—
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⋊D79C2312yes—
323C4×C22⋊D79C2316yes—
324C4×C22⋊D79C2316yes—
325(C22⋊D79)⋊C4C23112yes—
326(C22⋊D79)⋊C4C23112yes—
327#14579120C2316yes—
328#14579120C2316yes—
329#14579120C2316yes—
330#14579120C2311yescharacteristic
331#14579119C2316yes—
332#14579119C23112yes—
333#14579119C2316yes—
334#14579119C23112yes—
335#14579119C2316yes—
336#14579118C2316yes—
337#14579118C2316yes—
338#14579118C2316yes—
339#14579118C23112yes—
340#14579118C2316yes—
341#14579118C23112yes—
342#14579118C2316yes—
343C2×C4⋊Dic79C2313yes—
344C2×Dic79⋊C4C2316yes—
345C4⋊C4×D79C2313yes—
346C4⋊C4×D79C2316yes—
347C4⋊C4×D79C2313yes—
348C4⋊C4×D79C2316yes—
349C4⋊C4×D79C23112yes—
350C4⋊C4×D79C2313yes—
351C4⋊C4×D79C2316yes—
352C4⋊C4×D79C2313yes—
353C2×C4×Dic79C2313yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2313yes—
356C42×D79C2313yes—
357C42×D79C2313yes—
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C23112yes—
365C42×D79C2316yes—
366C2×#41×C79C2311yescharacteristic
367C22×Q8×C79C2312yes—
368C22×Q8×C79C2311yescharacteristic
369C4⋊Q8×C79C2316yes—
370C4⋊Q8×C79C2316yes—
371C4⋊Q8×C79C2313yes—
372C4⋊Q8×C79C2313yes—
373#125×C79C23112yes—
374#125×C79C2316yes—
375C22⋊Q8×C79C2316yes—
376C22⋊Q8×C79C2316yes—
377C22⋊Q8×C79C23112yes—
378C22⋊Q8×C79C2316yes—
379C22⋊Q8×C79C2316yes—
380C4×Q8×C79C2312yes—
381C4×Q8×C79C2311yescharacteristic
382C4×Q8×C79C2311yescharacteristic
383C4×Q8×C79C2313yes—
384C4×Q8×C79C2313yes—
385C4×Q8×C79C2316yes—
386C4×Q8×C79C2316yes—
387C4×Q8×C79C2313yes—
388C4×Q8×C79C2313yes—
389C4×Q8×C79C2316yes—
390C4×D4×C79C2316yes—
391C4×D4×C79C2313yes—
392C4×D4×C79C2316yes—
393C4×D4×C79C2313yes—
394#117×C79C2313yes—
395#117×C79C2316yes—
396C2×C4⋊C4×C79C2316yes—
397C2×C4⋊C4×C79C2313yes—
398C2×C42×C79C2313yes—
399C2×C42×C79C2316yes—
400C23×D79C2411yescharacteristic
401#11929625—224no—
402#11929625—28no—
403#11929625—412no—
404#11929624—224no—
405#11929624—224no—
406#11929624—212no—
407#11929624—412no—
408C2×Dic158—212no—
409C2×Dic158C2416yes—
410C2×Dic158C2413yes—
411C2×Dic158C2416yes—
412C2×Dic158C2413yes—
413C2×Dic158C2416yes—
414C2×Dic158C2413yes—
415Q8×D79—212no—
416Q8×D79—212no—
417Q8×D79—224no—
418Q8×D79—24no—
419Q8×D79#4118yescomplemented
420C2×D316C2416yes—
421C2×D316C2416yes—
422C2×D316C2416yes—
423C2×D316C2413yes—
424C2×D316C2416yes—
425C2×C22⋊D79C2412yes—
426C2×C22⋊D79C2412yes—
427C2×C22⋊D79C2416yes—
428C2×C22⋊D79C2416yes—
429C2×C22⋊D79C2416yes—
430C22×Dic79C2413yes—
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2413yes—
433C2×C4×D79—212no—
434C2×C4×D79—24no—
435C2×C4×D79—46no—
436C2×C4×D79C2413yes—
437C2×C4×D79C2413yes—
438C2×C4×D79C2413yes—
439C2×C4×D79C24112yes—
440C2×C4×D79C2416yes—
441C2×C4×D79C2413yes—
442C2×C4×D79C2416yes—
443C2×C4×D79C2413yes—
444C2×C4×D79C2411yescharacteristic
445C2×C4×D79C2411yescharacteristic
446C2×C4×D79C2411yescharacteristic
447C2×C4×D79C2411yescharacteristic
448C2×C4×D79C2416yes—
449C2×C4×D79C24112yes—
450C2×C4×D79C2413yes—
451C2×C4×D79C2413yes—
452C2×C4×D79C2413yes—
453C4⋊Dic79C2413yes—
454C4⋊Dic79C2413yes—
455C4⋊Dic79C2416yes—
456C4⋊Dic79C2416yes—
457C4⋊Dic79C2416yes—
458C4⋊Dic79C2416yes—
459C4⋊Dic79C2416yes—
460C4⋊Dic79C2416yes—
461C4⋊Dic79C2411yescharacteristic
462C4⋊Dic79C2411yescharacteristic
463C4⋊Dic79C2416yes—
464Dic79⋊C4C2416yes—
465Dic79⋊C4C2416yes—
466Dic79⋊C4C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C2416yes—
470Dic79⋊C4C2416yes—
471Dic79⋊C4C2412yes—
472Dic79⋊C4C2412yes—
473Dic79⋊C4C24112yes—
474Dic79⋊C4C24112yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2416yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2416yes—
479Dic79⋊C4C2416yes—
480C22⋊Dic79C2412yes—
481C22⋊Dic79C2412yes—
482C22⋊Dic79C2416yes—
483C22⋊Dic79C2412yes—
484C22⋊Dic79C2416yes—
485(C2×D79)⋊C4C2412yes—
486(C2×D79)⋊C4C2412yes—
487(C2×D79)⋊C4C2416yes—
488(C2×D79)⋊C4C2416yes—
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C24112yes—
491(C2×D79)⋊C4C2416yes—
492(C2×D79)⋊C4C2416yes—
493(C2×D79)⋊C4C24112yes—
494(C2×D79)⋊C4C24112yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498(C2×D79)⋊C4C24112yes—
499C4×Dic79C2413yes—
500C4×Dic79C2412yes—
501C4×Dic79C2413yes—
502C4×Dic79C2413yes—
503C4×Dic79C2413yes—
504C4×Dic79C2413yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2413yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C24112yes—
513C4×Dic79C2416yes—
514C4×Dic79C2416yes—
515C4×Dic79C24112yes—
516#41×C79—24no—
517C2×Q8×C79—24no—
518C2×Q8×C79—28no—
519C2×Q8×C79C2413yes—
520C2×Q8×C79C2416yes—
521C2×Q8×C79C2411yescharacteristic
522C2×Q8×C79C2416yes—
523C2×Q8×C79C2411yescharacteristic
524C2×D4×C79C2412yes—
525C2×D4×C79C2411yescharacteristic
526C22×C4×C79C2413yes—
527C22×C4×C79C2416yes—
528C22×C4×C79C2412yes—
529C22×C4×C79C2416yes—
530C22×C4×C79C2413yes—
531C22×C4×C79C2411yescharacteristic
532C4⋊C4×C79C2413yes—
533C4⋊C4×C79C2416yes—
534C4⋊C4×C79C24112yes—
535C4⋊C4×C79C2413yes—
536C4⋊C4×C79C2416yes—
537C4⋊C4×C79C2413yes—
538C4⋊C4×C79C2413yes—
539C4⋊C4×C79C2416yes—
540C4⋊C4×C79C2416yes—
541C4⋊C4×C79C2416yes—
542C4⋊C4×C79C24112yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2416yes—
545C22⋊C4×C79C2416yes—
546C42×C79C2413yes—
547C42×C79C2413yes—
548C42×C79C2416yes—
549C42×C79C2413yes—
550C42×C79C2416yes—
551C42×C79C2413yes—
552C42×C79C2416yes—
553C23×C79C2512yes—
554C23×C79C2511yescharacteristic
555C22×D79—22no—
556C22×D79—22no—
557C22×D79—22no—
558C22×D79C2516yes—
559C22×D79C2511yescharacteristic
560C22×D79C2511yescharacteristic
561Q8×C79—26no—
562Q8×C79—212no—
563Q8×C79—22no—
564Q8×C79—46no—
565Q8×C79C2×#4114yes—
566D4×C79—24no—
567D4×C79—22no—
568C2×C4×C79—26no—
569C2×C4×C79—212no—
570C2×C4×C79—24no—
571C2×C4×C79—43no—
572C2×C4×C79—46no—
573C2×C4×C792−1+414yescomplemented
574C2×C4×C79C2513yes—
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—212no—
584C22⋊D79—24no—
585C22⋊D79—24no—
586C22⋊D79—212no—
587C22⋊D79—46no—
588C2×Dic79—22no—
589C2×Dic79—26no—
590C2×Dic79—43no—
591C2×Dic79C2511yescharacteristic
592C2×Dic79C2511yescharacteristic
593C2×Dic79C2513yes—
594C2×Dic79C2516yes—
595C2×Dic79C2513yes—
596C2×Dic79C2512yes—
597C2×Dic79C2512yes—
598C2×Dic79C2513yes—
599C2×Dic79C2513yes—
600D316—212no—
601D316—212no—
602D316—212no—
603D316—26no—
604D316—46no—
605C4×D79—26no—
606C4×D79—26no—
607C4×D79—26no—
608C4×D79—26no—
609C4×D79—212no—
610C4×D79—22no—
611C4×D79—22no—
612C4×D79—22no—
613C4×D79—22no—
614C4×D79—212no—
615C4×D79—26no—
616C4×D79—224no—
617C4×D79—43no—
618C4×D79—43no—
619C4×D79—46no—
620C4×D79—412no—
621C4×D79C2×#41112yes—
622Dic158—26no—
623Dic158—26no—
624Dic158—212no—
625Dic158—212no—
626Dic158—46no—
627Dic158C2×#41112yes—
628C22×C79—21no—
629C22×C79—21no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79—22no—
633C22×C79C2×2−1+412yes—
634C22×C79C2611yescharacteristic
635C2×D79—28no—
636C2×D79—21no—
637C2×D79—21no—
638C2×D79—21no—
639C2×D79—21no—
640C2×D79—26no—
641C2×D79—26no—
642C2×D79—26no—
643C2×D79C22×#4112yes—
644C2×D79#58512yes—
645C4×C79—23no—
646C4×C79—26no—
647C4×C79—22no—
648C4×C79—23no—
649C4×C79—26no—
650C4×C79—23no—
651C4×C79C22×#4116yes—
652C4×C79C2×2−1+412yes—
653C4×C79C2×2−1+412yes—
654Dic79—22no—
655Dic79—23no—
656Dic79—26no—
657Dic79—21no—
658Dic79—21no—
659Dic79—22no—
660Dic79—23no—
661Dic79—23no—
662Dic79C22×#4116yes—
663#62788—791nomaximal, Sylow
664C2×C79—22no—
665C2×C79—42no—
666C2×C79C23×#4111yescharacteristic
667C2×C79C22×2−1+411yescharacteristic
668C2×C79C2×#58511yescharacteristic
669D79—22no—
670D79—22no—
671D79—46no—
672#3523—793no—
673#3523—791no—
674#3522—791no—
675#3522—793no—
676#3516—796no—
677#3516—792no—
678#3507—793no—
679#3507—793no—
680#3502—791no—
681#3497—791no—
682#3492—796no—
683#3486—792no—
684#3482—796no—
685#3482—792no—
686#3480—793no—
687#3480—791no—
688Q8×#41—793no—
689Q8×#41D7911yescharacteristic, complemented
690#3461—796no—
691#3444—793no—
692#3444—793no—
693C4×2−1+4—792no—
694C22×C4×Q8—791no—
695C79#6278811yescharacteristic, complemented, Sylow
696C2×2−1+4—792no—
697C23×Q8—791no—
698#559—793no—
699#559—793no—
700#559—796no—
701Q82—793no—
702Q82C2×D7911yescharacteristic, complemented
703#557—793no—
704#557—796no—
705#557—796no—
706#557—793no—
707#557—791no—
708#557—792no—
709#557C2×D7913yescomplemented
710#556—796no—
711#556—7912no—
712#556—796no—
713#556—796no—
714#556—793no—
715#556—793no—
716#554—793no—
717#554—796no—
718#554—7912no—
719#554—796no—
720#554C2×D7916yes—
721#554C2×D7913yescomplemented
722#553—796no—
723#553—7912no—
724#553—796no—
725#552—7912no—
726#552—7912no—
727#552—796no—
728#552—796no—
729#552—796no—
730#552—796no—
731#550—791no—
732#550—793no—
733D4×Q8—792no—
734D4×Q8—796no—
735D4×Q8—793no—
736D4×Q8—796no—
737D4×Q8C2×D7912yes—
738D4×Q8C2×D7911yescharacteristic, complemented
739#548—792no—
740#548—792no—
741#548—796no—
742#548—796no—
743#548—792no—
744#548—796no—
745#547—796no—
746#547—7912no—
747#547—796no—
748#544—796no—
749#542—796no—
750#542—7912no—
751#542—796no—
752#541—796no—
753#541—7912no—
754#541—796no—
755#539—7912no—
756#539—7912no—
757#537—796no—
758#536—796no—
759#536—796no—
760#533—793no—
761#533—793no—
762#533—793no—
763#533—793no—
764#533—7912no—
765#533—796no—
766#533—793no—
767#533C2×D7913yes—
768#533C2×D7916yescomplemented
769#532—793no—
770#532—793no—
771#532—793no—
772#532—793no—
773#532—793no—
774#532—793no—
775#529—796no—
776#529—796no—
777#529—796no—
778#529—796no—
779#529—796no—
780#529—796no—
781#529—793no—
782#529—793no—
783#529—796no—
784#529—793no—
785#529—796no—
786#529—796no—
787#529—793no—
788#529—796no—
789#529—796no—
790#529—7912no—
791#529—796no—
792#525—791no—
793#525—796no—
794#525—796no—
795#525—796no—
796#525—796no—
797#525—793no—
798#520—796no—
799#520—792no—
800#520—796no—
801#520—796no—
802#519—792no—
803#519—792no—
804#519—796no—
805C4×#41—796no—
806C4×#41—792no—
807C4×#41—796no—
808C4×#41—796no—
809C4×#41—796no—
810C4×#41—796no—
811C4×#41—793no—
812C4×#41—796no—
813C4×#41C2×D7913yes—
814C2×C4×Q8—791no—
815C2×C4×Q8—791no—
816C2×C4×Q8—793no—
817C2×C4×Q8—791no—
818C2×C4×Q8—793no—
819C2×C4×Q8—791no—
820C2×C4×Q8—793no—
821C2×C4×Q8—791no—
822C2×C4×Q8—793no—
823C2×C4×Q8—796no—
824C2×C4×Q8—793no—
825C2×C4×Q8—793no—
826C2×C4×Q8C2×D7911yescharacteristic
827C2×C4×Q8C2×D7912yescomplemented
828C22×C4⋊C4—793no—
829C22×C42—793no—
8302−1+4—15816no—
831C2×#41—796no—
832C2×#41—796no—
833C2×#41—792no—
834C2×#41—796no—
835C2×#41—793no—
836C2×#41—796no—
837C2×#41—796no—
838C2×#41C22×D7911yescharacteristic
839C22×Q8—791no—
840C22×Q8—793no—
841C22×Q8—793no—
842C22×Q8—791no—
843C22×Q8—796no—
844C22×Q8—793no—
845C22×Q8—1588no—
846C22×Q8C22×D7911yescharacteristic
847C22×Q8C22×D7912yes—
848C23×C4—793no—
849C23×C4—793no—
850C23×C4—791no—
851C4⋊Q8—793no—
852C4⋊Q8—796no—
853C4⋊Q8—7912no—
854C4⋊Q8—793no—
855C4⋊Q8—793no—
856C4⋊Q8—7912no—
857C4⋊Q8—796no—
858C4⋊Q8—793no—
859C4⋊Q8C22×D7913yes—
860C4⋊Q8C22×D7913yes—
861C4⋊Q8C22×D7916yes—
862C4⋊Q8C22×D7916yes—
863#127—793no—
864#127—793no—
865#126—796no—
866#126—7912no—
867#126—796no—
868#126—7912no—
869#126—7912no—
870#126—7912no—
871#126—796no—
872#126—796no—
873#126—7912no—
874#126—7912no—
875#125—796no—
876#125—796no—
877#125—796no—
878#125—796no—
879#125—793no—
880#125—793no—
881#125—7912no—
882#125—796no—
883#125—7912no—
884#125—7912no—
885#125—7912no—
886#125—796no—
887#125C22×D7916yes—
888#125C22×D79112yes—
889#124—796no—
890#124—796no—
891#124—793no—
892#124—796no—
893#124—793no—
894#124—796no—
895#124—796no—
896#124—7912no—
897#124—796no—
898#124—796no—
899#123—792no—
900#123—7912no—
901#123—796no—
902#123—7912no—
903#123—796no—
904#123—7912no—
905#123—7912no—
906#123—7912no—
907#123—796no—
908#123—796no—
909#123—796no—
910#123—7912no—
911C22⋊Q8—791no—
912C22⋊Q8—791no—
913C22⋊Q8—796no—
914C22⋊Q8—796no—
915C22⋊Q8—796no—
916C22⋊Q8—796no—
917C22⋊Q8—7912no—
918C22⋊Q8—796no—
919C22⋊Q8—793no—
920C22⋊Q8—793no—
921C22⋊Q8—796no—
922C22⋊Q8—796no—
923C22⋊Q8—7912no—
924C22⋊Q8—7912no—
925C22⋊Q8—796no—
926C22⋊Q8—7912no—
927C22⋊Q8—7912no—
928C22⋊Q8—7912no—
929C22⋊Q8—796no—
930C22⋊Q8—796no—
931C22⋊Q8C22×D7916yes—
932C22⋊Q8C22×D7916yes—
933C22⋊Q8C22×D7916yes—
934C22⋊Q8C22×D7916yes—
935C22⋊Q8C22×D79112yes—
936#121—791no—
937#121—791no—
938#121—796no—
939#121—796no—
940#121—796no—
941#121—796no—
942#121—796no—
943#121—793no—
944#121—793no—
945#121—796no—
946#121—796no—
947#121—796no—
948#121—796no—
949#121—796no—
950#121—7912no—
951#120—792no—
952#120—796no—
953C4×Q8—791no—
954C4×Q8—793no—
955C4×Q8—791no—
956C4×Q8—793no—
957C4×Q8—796no—
958C4×Q8—796no—
959C4×Q8—792no—
960C4×Q8—796no—
961C4×Q8—793no—
962C4×Q8—796no—
963C4×Q8—793no—
964C4×Q8—793no—
965C4×Q8—796no—
966C4×Q8—793no—
967C4×Q8—796no—
968C4×Q8—7912no—
969C4×Q8—796no—
970C4×Q8—796no—
971C4×Q8—793no—
972C4×Q8—796no—
973C4×Q8—793no—
974C4×Q8—793no—
975C4×Q8—793no—
976C4×Q8—796no—
977C4×Q8—796no—
978C4×Q8—796no—
979C4×Q8—796no—
980C4×Q8—796no—
981C4×Q8—796no—
982C4×Q8—793no—
983C4×Q8—793no—
984C4×Q8C22×D7911yescharacteristic
985C4×Q8C22×D7913yes—
986C4×Q8C22×D7911yescharacteristic
987C4×Q8C22×D7913yes—
988C4×Q8C22×D7916yes—
989C4×Q8C22×D7912yes—
990C4×Q8C22×D7916yes—
991C4×Q8C22×D7916yes—
992C4×Q8C22×D7913yes—
993C4×Q8C22×D7913yes—
994C4×D4—792no—
995C4×D4—792no—
996C4×D4—796no—
997C4×D4—796no—
998C4×D4—796no—
999C4×D4—7912no—
1000C4×D4—796no—
1001C4×D4—796no—
1002C4×D4—796no—
1003C4×D4—796no—
1004C4×D4—796no—
1005C4×D4—7912no—
1006C4×D4—796no—
1007C4×D4—796no—
1008C4×D4—7912no—
1009C4×D4—796no—
1010C4×D4—796no—
1011C4×D4—796no—
1012C4×D4—7912no—
1013C4×D4—7912no—
1014C4×D4—796no—
1015C4×D4—796no—
1016C4×D4—796no—
1017C4×D4—796no—
1018C4×D4—796no—
1019C4×D4—796no—
1020C4×D4—796no—
1021C4×D4—793no—
1022C4×D4—793no—
1023C4×D4C22×D7916yes—
1024C4×D4C22×D7916yes—
1025C4×D4C22×D7913yes—
1026C4×D4C22×D7913yes—
1027#117—791no—
1028#117—796no—
1029#117—796no—
1030#117—796no—
1031#117—796no—
1032#117—7912no—
1033#117—796no—
1034#117—796no—
1035#117—7912no—
1036#117—796no—
1037#117—796no—
1038#117—7912no—
1039#117—796no—
1040#117—7912no—
1041#117—796no—
1042#117—796no—
1043#117C22×D7913yes—
1044#117C22×D7916yes—
1045C2×C4⋊C4—796no—
1046C2×C4⋊C4—793no—
1047C2×C4⋊C4—793no—
1048C2×C4⋊C4—793no—
1049C2×C4⋊C4—796no—
1050C2×C4⋊C4—796no—
1051C2×C4⋊C4—793no—
1052C2×C4⋊C4—793no—
1053C2×C4⋊C4—7912no—
1054C2×C4⋊C4—796no—
1055C2×C4⋊C4C22×D7913yes—
1056C2×C4⋊C4C22×D7916yes—
1057C2×C42—793no—
1058C2×C42—793no—
1059C2×C42—793no—
1060C2×C42—793no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—793no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—793no—
1067C2×C42—793no—
1068C2×C42—7912no—
1069C2×C42—796no—
1070C2×C42C22×D7913yes—
1071C2×C42C22×D7916yes—
1072C24—791no—
1073#41—24no—
1074#41—31612no—
1075#41—31612no—
1076#41—15824no—
1077#41—15824no—
1078#41—15824no—
1079#41—1588no—
1080#41—15812no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—798no—
1084C2×Q8—796no—
1085C2×Q8—793no—
1086C2×Q8—793no—
1087C2×Q8—796no—
1088C2×Q8—793no—
1089C2×Q8—796no—
1090C2×Q8—15812no—
1091C2×Q8—15812no—
1092C2×Q8—15812no—
1093C2×Q8—15824no—
1094C2×Q8—1584no—
1095C2×Q8C23×D7913yes—
1096C2×Q8C23×D7916yes—
1097C2×Q8C23×D7911yescharacteristic
1098C2×Q8C23×D7916yes—
1099C2×Q8C23×D7911yescharacteristic
1100C2×D4—796no—
1101C2×D4—796no—
1102C2×D4—792no—
1103C2×D4—792no—
1104C2×D4—796no—
1105C2×D4—796no—
1106C2×D4—793no—
1107C2×D4—796no—
1108C2×D4—796no—
1109C2×D4—796no—
1110C2×D4C23×D7912yes—
1111C2×D4C23×D7911yescharacteristic
1112C22×C4—3166no—
1113C22×C4—793no—
1114C22×C4—793no—
1115C22×C4—793no—
1116C22×C4—7912no—
1117C22×C4—796no—
1118C22×C4—793no—
1119C22×C4—791no—
1120C22×C4—793no—
1121C22×C4—791no—
1122C22×C4—791no—
1123C22×C4—793no—
1124C22×C4—793no—
1125C22×C4—793no—
1126C22×C4—793no—
1127C22×C4—793no—
1128C22×C4—7912no—
1129C22×C4—796no—
1130C22×C4—791no—
1131C22×C4—791no—
1132C22×C4—796no—
1133C22×C4—15812no—
1134C22×C4—1584no—
1135C22×C4C23×D7913yes—
1136C22×C4C23×D7916yes—
1137C22×C4C23×D7912yes—
1138C22×C4C23×D7913yes—
1139C22×C4C23×D7916yes—
1140C22×C4C23×D7911yescharacteristic
1141C4⋊C4—796no—
1142C4⋊C4—796no—
1143C4⋊C4—796no—
1144C4⋊C4—796no—
1145C4⋊C4—796no—
1146C4⋊C4—796no—
1147C4⋊C4—796no—
1148C4⋊C4—792no—
1149C4⋊C4—792no—
1150C4⋊C4—796no—
1151C4⋊C4—796no—
1152C4⋊C4—796no—
1153C4⋊C4—7912no—
1154C4⋊C4—796no—
1155C4⋊C4—796no—
1156C4⋊C4—7912no—
1157C4⋊C4—793no—
1158C4⋊C4—793no—
1159C4⋊C4—796no—
1160C4⋊C4—796no—
1161C4⋊C4—796no—
1162C4⋊C4—796no—
1163C4⋊C4—796no—
1164C4⋊C4—791no—
1165C4⋊C4—791no—
1166C4⋊C4—796no—
1167C4⋊C4—796no—
1168C4⋊C4C23×D7913yes—
1169C4⋊C4C23×D7913yes—
1170C4⋊C4C23×D7916yes—
1171C4⋊C4C23×D7916yes—
1172C4⋊C4C23×D79112yes—
1173C4⋊C4C23×D7916yes—
1174C4⋊C4C23×D79112yes—
1175C4⋊C4C23×D7913yes—
1176C4⋊C4C23×D7913yes—
1177C4⋊C4C23×D7916yes—
1178C4⋊C4C23×D7916yes—
1179C22⋊C4—796no—
1180C22⋊C4—792no—
1181C22⋊C4—792no—
1182C22⋊C4—792no—
1183C22⋊C4—796no—
1184C22⋊C4—796no—
1185C22⋊C4—796no—
1186C22⋊C4—792no—
1187C22⋊C4—792no—
1188C22⋊C4—796no—
1189C22⋊C4—7912no—
1190C22⋊C4—796no—
1191C22⋊C4—796no—
1192C22⋊C4—796no—
1193C22⋊C4—7912no—
1194C22⋊C4—7912no—
1195C22⋊C4—796no—
1196C22⋊C4—7912no—
1197C22⋊C4—796no—
1198C22⋊C4C23×D7916yes—
1199C22⋊C4C23×D7916yes—
1200C22⋊C4C23×D7916yes—
1201C42—793no—
1202C42—793no—
1203C42—793no—
1204C42—793no—
1205C42—793no—
1206C42—793no—
1207C42—793no—
1208C42—793no—
1209C42—793no—
1210C42—793no—
1211C42—7912no—
1212C42—796no—
1213C42—7912no—
1214C42—796no—
1215C42—793no—
1216C42—793no—
1217C42—792no—
1218C42C23×D7913yes—
1219C42C23×D7913yes—
1220C42C23×D7916yes—
1221C42C23×D7916yes—
1222C42C23×D7913yes—
1223C42C23×D7913yes—
1224C42C23×D7916yes—
1225C23—791no—
1226C23—791no—
1227C23—796no—
1228C23—1582no—
1229C23—1582no—
1230C23—1582no—
1231C23C24×D7912yes—
1232C23C24×D7911yescharacteristic
1233Q8—22no—
1234Q8—26no—
1235Q8—212no—
1236Q8—46no—
1237Q8—3166no—
1238Q8—7912no—
1239Q8—15812no—
1240Q8—15812no—
1241Q8—1586no—
1242Q8—1586no—
1243Q8#41×D7914yes—
1244D4—24no—
1245D4—22no—
1246D4—3166no—
1247D4—3166no—
1248D4—15812no—
1249D4—15812no—
1250D4—15812no—
1251D4—1584no—
1252D4—1584no—
1253D4—15812no—
1254D4—1586no—
1255D4—15812no—
1256C2×C4—24no—
1257C2×C4—26no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—3163no—
1262C2×C4—3163no—
1263C2×C4—3166no—
1264C2×C4—31612no—
1265C2×C4—3163no—
1266C2×C4—793no—
1267C2×C4—7912no—
1268C2×C4—791no—
1269C2×C4—791no—
1270C2×C4—793no—
1271C2×C4—796no—
1272C2×C4—793no—
1273C2×C4—792no—
1274C2×C4—792no—
1275C2×C4—793no—
1276C2×C4—1586no—
1277C2×C4—15824no—
1278C2×C4—1586no—
1279C2×C4—1586no—
1280C2×C4—1586no—
1281C2×C4—1586no—
1282C2×C4—1582no—
1283C2×C4—1582no—
1284C2×C4—1582no—
1285C2×C4—1582no—
1286C2×C4—1582no—
1287C2×C4—15812no—
1288C2×C4—1586no—
1289C2×C4—15812no—
1290C2×C4#1457920914yescomplemented
1291C2×C4C24×D7913yes—
1292C2×C4C24×D7913yes—
1293C2×C4C24×D7916yes—
1294C2×C4C24×D7916yes—
1295C2×C4C24×D7913yes—
1296C2×C4C24×D7912yes—
1297C2×C4C24×D7911yescharacteristic
1298C2×C4C24×D7913yes—
1299C2×C4C24×D7911yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—792no—
1306C22—792no—
1307C22—1588no—
1308C22—1586no—
1309C22—1586no—
1310C22—1586no—
1311C22—1581no—
1312C22—1581no—
1313C22—1581no—
1314C22—1581no—
1315C22C2×#1457920912yes—
1316C22C25×D7911yescharacteristic
1317C4—26no—
1318C4—23no—
1319C4—22no—
1320C4—23no—
1321C4—26no—
1322C4—23no—
1323C4—796no—
1324C4—1582no—
1325C4—1583no—
1326C4—1581no—
1327C4—1581no—
1328C4—1586no—
1329C4—1583no—
1330C4—1582no—
1331C4—1583no—
1332C4C2×#41×D7916yes—
1333C4C2×#1457920912yes—
1334C4C2×#1457920912yes—
1335C2—22no—
1336C2—42no—
1337C2—3166no—
1338C2—1582no—
1339C2—1582no—
1340C2C22×#41×D7911yescharacteristic
1341C2C22×#1457920911yescharacteristic
1342C2#585×D7911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingQ8×#41×C79C2
hypercenterQ8×#41D79
hypocenterC79#62788
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #23777493C2semidirect
2. #23777491C2semidirect
3. #23777486C2semidirect
4. #23777484C2semidirect
5. #23777394C2semidirect
6. #23777390C2semidirect
7. #23777266C2semidirect
8. #23777263C2semidirect
9. #23777209C2semidirect
10. #23777170C2semidirect
11. #23777108C2semidirect
12. #23777050C2semidirect
13. #23777018C2semidirect
14. #23777017C2semidirect
15. #23776995C2semidirect
16. #23776993C2semidirect
17. #23776978C2semidirect
18. #23776831C2semidirect
19. #23776697C2semidirect
20. #23776693C2semidirect
21. C4×#14579209C2semidirect
22. C2×C4×Q8×D79C2semidirect
23. Q8×#41×C79C2semidirect
26. #19099298C22semidirect
27. #19099298C22semidirect
28. #19099296C22semidirect
29. #19099293C22semidirect
30. #19099292C22semidirect
31. #19099291C22semidirect
32. #19099290C22semidirect
33. #19099289C22semidirect
34. #19099288C22semidirect
35. #19099288C22semidirect
36. #19099287C22semidirect
37. #19099286C22semidirect
38. #19099285C22semidirect
39. #19099285C22semidirect
40. #19099284C22semidirect
41. #19099283C22semidirect
42. #19099274C22semidirect
44. #19099269C22semidirect
50. #19099248C22semidirect
52. #19099247C22semidirect
54. #19099245C22semidirect
55. #19099235C22semidirect
56. #19099234C22semidirect
58. #19099228C22semidirect
63. #19099224C22semidirect
65. #19099223C22semidirect
71. #19099187C22semidirect
72. #19099186C22semidirect
73. #19099183C22semidirect
74. #19099174C22semidirect
75. #19099173C22semidirect
76. #19099172C22semidirect
86. #19099117C22semidirect
87. #19099117C22semidirect
99. #19099100C22semidirect
104. #19099097C22semidirect
111. #19099091C22semidirect
119. #19099045C22semidirect
121. #19099044C22semidirect
122. #19099041C22semidirect
124. #19099039C22semidirect
127. C4×#11929625C22semidirect
131. C4×#11929624C22semidirect
144. C4×Q8×D79C22semidirect
147. Q82×C79C22semidirect
148. #557×C79C22semidirect
150. #554×C79C22semidirect
152. D4×Q8×C79C22semidirect
154. #533×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
419. Q8×D79#41semidirect
573. C2×C4×C792−1+4semidirect
689. Q8×#41D79semidirect
695. C79#62788semidirect
702. Q82C2×D79semidirect
709. #557C2×D79semidirect
721. #554C2×D79semidirect
738. D4×Q8C2×D79semidirect
768. #533C2×D79semidirect
827. C2×C4×Q8C2×D79semidirect
1290. C2×C4#14579209semidirect

Maximal subgroups

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

subgroupindex
#237774932
#237774912
#237774862
#237774842
#237773942
#237773902
#237772662
#237772632
#237772092
#237771702
#237771082
#237770502
#237770182
#237770172
#237769952
#237769932
#237769782
#237768312
#237766972
#237766932
C4×#145792092
C2×C4×Q8×D792
Q8×#41×C792
#6278879