Finite Group Databasebeta

← #35196720

Subgroups — #35196720

Order 20224.

7104 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#23777487C212yesmaximal, complemented
2#23777445C216yesmaximal, complemented
3#23777418C211yesmaximal, characteristic, complemented
4#23777412C211yesmaximal, characteristic, complemented
5#23777381C213yesmaximal, complemented
6#23777377C213yesmaximal, complemented
7#23777308C213yesmaximal, complemented
8#23777283C213yesmaximal, complemented
9#23777218C211yesmaximal, characteristic, complemented
10#23777184C211yesmaximal, characteristic, complemented
11#23777148C216yesmaximal, complemented
12#23777077C212yesmaximal, complemented
13#23777018C216yesmaximal, complemented
14#23777017C212yesmaximal, complemented
15Q8×#11929624C211yesmaximal, characteristic, complemented
16#23776967C213yesmaximal, complemented
17#23776964C213yesmaximal, complemented
18#23776831C216yesmaximal, complemented
19#23776693C213yesmaximal, complemented
20#533×D79C213yesmaximal, complemented
21C4×#14579209C212yesmaximal, complemented
22C2×C4×#11929625C211yesmaximal, characteristic, complemented
23Q8×#41×C79C211yesmaximal, characteristic, complemented
24C2×#14579209C2212yes—
25C22×#11929625C2211yescharacteristic
26Q8×Dic158C2211yescharacteristic, complemented
27#19099291C2213yescomplemented
28#19099289C2212yescomplemented
29#19099288C2216yescomplemented
30#19099287C2213yescomplemented
31#19099287C2216yescomplemented
32#19099286C2213yescomplemented
33#19099285C2216yescomplemented
34#19099284C2216yescomplemented
35#19099284C2216yescomplemented
36#19099279C2213yescomplemented
37#19099278C2213yescomplemented
38#19099274C2213yescomplemented
39#19099273C2213yescomplemented
40#19099273C2213yescomplemented
41#19099268C2216yes—
42#19099266C2216yescomplemented
43#19099263C2216yescomplemented
44#19099255C2216yes—
45#19099254C2216yescomplemented
46#19099254C2216yescomplemented
47#19099253C2216yes—
48#19099251C2216yescomplemented
49#19099248C2216yescomplemented
50#19099247C22112yescomplemented
51#19099245C22112yescomplemented
52#19099245C22112yescomplemented
53#19099242C22112yes—
54#19099240C22112yes—
55Q8×D316C2211yescharacteristic, complemented
56#19099228C2216yescomplemented
57Q8×C22⋊D79C2212yes—
58Q8×C22⋊D79C2212yescomplemented
59#19099225C2212yes—
60#19099224C2212yes—
61#19099223C22112yescomplemented
62#19099218C2213yescomplemented
63#19099216C2216yes—
64#19099216C2213yescomplemented
65#19099215C2216yes—
66#19099215C2216yescomplemented
67#19099214C2216yescomplemented
68#19099209C2216yes—
69#19099204C2216yes—
70#19099190C2216yescomplemented
71#19099187C2216yescomplemented
72#19099186C2216yescomplemented
73#19099183C22112yescomplemented
74#19099174C2216yescomplemented
75#19099173C2216yescomplemented
76#19099172C22112yescomplemented
77#19099161C22112yescomplemented
78#19099159C22112yescomplemented
79#19099143C2216yes—
80#19099138C2216yes—
81#19099136C2216yescomplemented
82#19099120C2213yes—
83#19099119C2216yescomplemented
84#19099118C2213yescomplemented
85#19099118C2213yescomplemented
86#19099117C2213yescomplemented
87#19099117C2213yescomplemented
88#19099117C2216yescomplemented
89#19099117C2216yescomplemented
90#19099117C2216yescomplemented
91#19099116C2213yes—
92#19099115C2216yes—
93#19099115C2216yes—
94#19099110C2213yescomplemented
95#19099110C2213yescomplemented
96#19099109C2211yescharacteristic
97C4⋊Q8×D79C2213yescomplemented
98C4⋊Q8×D79C2213yescomplemented
99#19099100C2216yescomplemented
100#19099100C22112yescomplemented
101#19099100C2213yescomplemented
102#19099100C2213yescomplemented
103#19099097C2216yescomplemented
104#19099095C2213yescomplemented
105#19099095C2213yescomplemented
106#19099093C2216yes—
107#19099093C2216yes—
108#19099091C2216yescomplemented
109#19099091C22112yescomplemented
110#19099091C2216yescomplemented
111#125×D79C2216yescomplemented
112#19099075C2213yes—
113#19099072C2216yes—
114#19099072C2216yes—
115#19099070C2213yes—
116C22⋊Q8×D79C2216yes—
117C22⋊Q8×D79C2216yes—
118#19099045C2212yes—
119#19099045C2216yescomplemented
120#19099044C2216yescomplemented
121#19099044C2216yescomplemented
122#19099041C2212yescomplemented
123#19099039C2216yescomplemented
124#19099039C2212yescomplemented
125C4×#11929625C2213yes—
126C4×#11929625C2213yes—
127C4×#11929625C2213yes—
128C4×#11929625C2211yescharacteristic
129C4×#11929625C2211yescharacteristic
130C4×#11929625C2211yescharacteristic
131C4×#11929625C2211yescharacteristic
132C4×#11929625C2213yes—
133C4×#11929625C2216yescomplemented
134C4×#11929624C2213yes—
135C4×#11929624C2216yescomplemented
136C4×#11929624C2216yescomplemented
137C4×#11929624C2216yescomplemented
138C2×Q8×Dic79C2211yescharacteristic
139C4×Q8×D79C2216yescomplemented
140C4×Q8×D79C2212yescomplemented
141C4×Q8×D79C2216yescomplemented
142C2×C4×D316C2213yes—
143C2×#14579123C2213yes—
144C2×#14579119C2213yes—
145#117×D79C2216yes—
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×#11929625—28no—
160C2×#11929625C2313yes—
161C2×#11929625C2316yes—
162C2×#11929625C2313yes—
163C2×#11929625C2311yescharacteristic
164C2×#11929625C2311yescharacteristic
165C2×#11929624C2316yes—
166C2×#11929624C2316yes—
167C2×#11929624C2311yescharacteristic
168C2×#11929624C2316yes—
169C2×Q8×D79C2316yes—
170C2×Q8×D79C2312yes—
171C2×Q8×D79C2316yes—
172C22×D316C2313yes—
173C22×C4×D79C2313yes—
174C22×C4×D79C2313yes—
175C22×C4×D79C2313yes—
176#14579161C2313yes—
177#14579161C2313yes—
178#14579160C2316yes—
179#14579160C2316yes—
180#14579160C2316yes—
181#14579160C2313yes—
182#14579160C2313yes—
183#14579159C2316yes—
184#14579159C2316yes—
185#14579159C2316yes—
186#14579159C2311yescharacteristic
187#14579157C2311yescharacteristic
188#14579156C23112yes—
189#14579156C2316yes—
190#14579156C23112yes—
191#14579156C23112yes—
192#14579156C23112yes—
193#14579156C2316yes—
194#14579155C23112yes—
195#14579154C2316yes—
196#14579154C23112yes—
197#14579154C2316yes—
198#14579153C2316yes—
199#14579153C2316yes—
200#14579152C23112yes—
201#14579152C2316yes—
202#14579152C2313yes—
203#14579152C2313yes—
204#14579151C23112yes—
205#14579151C23112yes—
206#14579151C2316yes—
207#14579151C23112yes—
208#14579151C2316yes—
209#14579151C23112yes—
210#14579150C2316yes—
211#14579150C23112yes—
212#14579150C2311yescharacteristic
213#14579149C2316yes—
214#14579148C2311yescharacteristic
215#14579147C2316yes—
216#14579147C23112yes—
217#14579147C2316yes—
218#14579146C23112yes—
219#14579146C23112yes—
220#14579146C23112yes—
221#14579146C2316yes—
222#14579146C23112yes—
223#14579146C2316yes—
224#14579145C2316yes—
225#14579144C23112yes—
226#14579143C23112yes—
227#14579143C2316yes—
228#14579143C2316yes—
229#14579142C2316yes—
230#14579141C2316yes—
231#14579141C2316yes—
232#14579141C2316yes—
233#14579141C2313yes—
234#14579141C2313yes—
235#14579140C2316yes—
236#14579140C2316yes—
237#14579140C2316yes—
238#14579139C2316yes—
239#14579139C23112yes—
240#14579139C23112yes—
241#14579139C23112yes—
242#14579139C23112yes—
243#14579139C2316yes—
244#14579138C2316yes—
245#14579138C2316yes—
246#14579137C2316yes—
247#14579137C2316yes—
248#14579137C2316yes—
249#14579137C23112yes—
250#14579137C2316yes—
251#14579137C2313yes—
252#14579137C2313yes—
253#14579136C23112yes—
254#14579136C2316yes—
255#14579136C2313yes—
256#14579136C2313yes—
257#14579135C2316yes—
258#14579134C2316yes—
259#14579134C23112yes—
260#14579134C2316yes—
261#14579133C2312yes—
262#14579133C2312yes—
263#14579132C2313yes—
264#14579132C2313yes—
265#14579131C2316yes—
266#14579129C2316yes—
267Q8×Dic79C2313yes—
268Q8×Dic79C2316yes—
269Q8×Dic79C2312yes—
270Q8×Dic79C2311yescharacteristic
271Q8×Dic79C2316yes—
272Q8×Dic79C2316yes—
273Q8×Dic79C2313yes—
274Q8×Dic79C2311yescharacteristic
275C4×Dic158C2316yes—
276C4×Dic158C2316yes—
277C4×Dic158C2313yes—
278C4×Dic158C2316yes—
279C4×Dic158C2313yes—
280C4×Dic158C2316yes—
281C4×Dic158C2316yes—
282C4×Dic158C2316yes—
283C4×Dic158C2316yes—
284#14579126C23112yes—
285#14579126C2316yes—
286#14579126C23112yes—
287#14579126C2316yes—
288#14579126C2316yes—
289C4×D316C2316yes—
290C4×D316C2316yes—
291C4×D316C2316yes—
292C4×D316C2313yes—
293C4×D316C2313yes—
294C4×D316C2316yes—
295C4×D316C2313yes—
296C4×D316C2313yes—
297C4×D316C2313yes—
298C4×D316C2316yes—
299C4×D316C2313yes—
300C4×D316C2316yes—
301C4×D316C2316yes—
302#14579123C2316yes—
303#14579123C2313yes—
304#14579123C2316yes—
305#14579123C2313yes—
306#14579123C2313yes—
307#14579123C2316yes—
308#14579123C23112yes—
309#14579123C2313yes—
310C4×C22⋊D79C2316yes—
311C4×C22⋊D79C2316yes—
312C4×C22⋊D79C2316yes—
313C4×C22⋊D79C2316yes—
314C4×C22⋊D79C2316yes—
315C4×C22⋊D79C23112yes—
316C4×C22⋊D79C2316yes—
317C4×C22⋊D79C2316yes—
318C4×C22⋊D79C2312yes—
319C4×C22⋊D79C2312yes—
320C4×C22⋊D79C2316yes—
321#14579120C2316yes—
322#14579120C2316yes—
323#14579120C2316yes—
324#14579120C2313yes—
325#14579119C2313yes—
326#14579119C2316yes—
327#14579119C23112yes—
328#14579119C2316yes—
329#14579119C2313yes—
330#14579119C2316yes—
331#14579119C2316yes—
332#14579119C2316yes—
333#14579119C2313yes—
334#14579119C2313yes—
335#14579118C2316yes—
336#14579118C2316yes—
337#14579118C23112yes—
338#14579118C2316yes—
339#14579118C2316yes—
340#14579118C23112yes—
341#14579118C2316yes—
342#14579117C23112yes—
343C2×C4⋊Dic79C2313yes—
344C4⋊C4×D79C2316yes—
345C4⋊C4×D79C23112yes—
346C4⋊C4×D79C2316yes—
347C4⋊C4×D79C23112yes—
348C4⋊C4×D79C2316yes—
349C4⋊C4×D79C2316yes—
350C4⋊C4×D79C2316yes—
351C2×(C2×D79)⋊C4C2316yes—
352C22⋊C4×D79C23112yes—
353C2×C4×Dic79C2311yescharacteristic
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×D79C2413yes—
401#11929625—212no—
402#11929625—224no—
403#11929625—212no—
404#11929625—24no—
405#11929625#4118yescomplemented
406#11929624—224no—
407#11929624—224no—
408#11929624—24no—
409#11929624—412no—
410C2×Dic158C2416yes—
411C2×Dic158C2416yes—
412C2×Dic158C2416yes—
413C2×Dic158C2411yescharacteristic
414C2×Dic158C2416yes—
415Q8×D79—224no—
416Q8×D79—28no—
417Q8×D79—412no—
418C2×D316—212no—
419C2×D316C2416yes—
420C2×D316C2411yescharacteristic
421C2×D316C2416yes—
422C2×D316C2413yes—
423C2×D316C2416yes—
424C2×D316C2413yes—
425C2×C22⋊D79C2416yes—
426C2×C22⋊D79C2412yes—
427C2×C22⋊D79C2412yes—
428C2×C22⋊D79C2412yes—
429C2×C22⋊D79C2416yes—
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2413yes—
433C2×C4×D79—212no—
434C2×C4×D79—212no—
435C2×C4×D79—46no—
436C2×C4×D79C2413yes—
437C2×C4×D79C24112yes—
438C2×C4×D79C2416yes—
439C2×C4×D79C2413yes—
440C2×C4×D79C2412yes—
441C2×C4×D79C2413yes—
442C2×C4×D79C2413yes—
443C2×C4×D79C2413yes—
444C2×C4×D79C2413yes—
445C2×C4×D79C2413yes—
446C2×C4×D79C2413yes—
447C2×C4×D79C2413yes—
448C2×C4×D79C24112yes—
449C2×C4×D79C2416yes—
450C2×C4×D79C2413yes—
451C2×C4×D79C2413yes—
452C2×C4×D79C2413yes—
453C4⋊Dic79C2413yes—
454C4⋊Dic79C2413yes—
455C4⋊Dic79C2416yes—
456C4⋊Dic79C2416yes—
457C4⋊Dic79C2416yes—
458C4⋊Dic79C2416yes—
459C4⋊Dic79C2413yes—
460C4⋊Dic79C2413yes—
461C4⋊Dic79C2416yes—
462C4⋊Dic79C2416yes—
463C4⋊Dic79C2416yes—
464Dic79⋊C4C2416yes—
465Dic79⋊C4C2416yes—
466Dic79⋊C4C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C24112yes—
469Dic79⋊C4C24112yes—
470Dic79⋊C4C24112yes—
471Dic79⋊C4C24112yes—
472Dic79⋊C4C2412yes—
473Dic79⋊C4C2412yes—
474Dic79⋊C4C2416yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2416yes—
477Dic79⋊C4C2416yes—
478C22⋊Dic79C2416yes—
479C22⋊Dic79C2416yes—
480C22⋊Dic79C2412yes—
481C22⋊Dic79C2412yes—
482C22⋊Dic79C2416yes—
483(C2×D79)⋊C4C24112yes—
484(C2×D79)⋊C4C24112yes—
485(C2×D79)⋊C4C2416yes—
486(C2×D79)⋊C4C2416yes—
487(C2×D79)⋊C4C2416yes—
488(C2×D79)⋊C4C2416yes—
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C2412yes—
491(C2×D79)⋊C4C2412yes—
492(C2×D79)⋊C4C2416yes—
493(C2×D79)⋊C4C2416yes—
494(C2×D79)⋊C4C2416yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498(C2×D79)⋊C4C2416yes—
499C4×Dic79C2411yescharacteristic
500C4×Dic79C2411yescharacteristic
501C4×Dic79C2411yescharacteristic
502C4×Dic79C2411yescharacteristic
503C4×Dic79C2416yes—
504C4×Dic79C2413yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2413yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C24112yes—
513C4×Dic79C24112yes—
514C4×Dic79C2416yes—
515C4×Dic79C2416yes—
516#41×C79—24no—
517C2×Q8×C79—24no—
518C2×Q8×C79—28no—
519C2×Q8×C79C2416yes—
520C2×Q8×C79C2413yes—
521C2×Q8×C79C2411yescharacteristic
522C2×Q8×C79C2416yes—
523C2×Q8×C79C2411yescharacteristic
524C2×D4×C79C2412yes—
525C2×D4×C79C2411yescharacteristic
526C22×C4×C79C2416yes—
527C22×C4×C79C2412yes—
528C22×C4×C79C2413yes—
529C22×C4×C79C2416yes—
530C22×C4×C79C2413yes—
531C22×C4×C79C2411yescharacteristic
532C4⋊C4×C79C2413yes—
533C4⋊C4×C79C24112yes—
534C4⋊C4×C79C2416yes—
535C4⋊C4×C79C2416yes—
536C4⋊C4×C79C2413yes—
537C4⋊C4×C79C2413yes—
538C4⋊C4×C79C2413yes—
539C4⋊C4×C79C2416yes—
540C4⋊C4×C79C2416yes—
541C4⋊C4×C79C24112yes—
542C4⋊C4×C79C2416yes—
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—26no—
556C22×D79—26no—
557C22×D79—43no—
558C22×D79C2513yes—
559C22×D79C2512yes—
560C22×D79C2513yes—
561Q8×C79—212no—
562Q8×C79—26no—
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—24no—
584C22⋊D79—212no—
585C22⋊D79—24no—
586C22⋊D79—24no—
587C22⋊D79—46no—
588C2×Dic79—26no—
589C2×Dic79—22no—
590C2×Dic79—22no—
591C2×Dic79C2513yes—
592C2×Dic79C2511yescharacteristic
593C2×Dic79C2511yescharacteristic
594C2×Dic79C2512yes—
595C2×Dic79C2513yes—
596C2×Dic79C2516yes—
597C2×Dic79C2516yes—
598C2×Dic79C2511yescharacteristic
599C2×Dic79C2511yescharacteristic
600D316—212no—
601D316—212no—
602D316—26no—
603D316—22no—
604D316—46no—
605D316C2×#41112yes—
606C4×D79—26no—
607C4×D79—224no—
608C4×D79—26no—
609C4×D79—212no—
610C4×D79—26no—
611C4×D79—26no—
612C4×D79—26no—
613C4×D79—26no—
614C4×D79—24no—
615C4×D79—26no—
616C4×D79—26no—
617C4×D79—26no—
618C4×D79—43no—
619C4×D79—43no—
620C4×D79—412no—
621C4×D79—46no—
622C4×D79C2×#41112yes—
623Dic158—212no—
624Dic158—22no—
625Dic158—212no—
626Dic158—212no—
627Dic158—46no—
628C22×C79—21no—
629C22×C79—21no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79—22no—
633C22×C79C2×2−1+412yes—
634C22×C79C2611yescharacteristic
635C2×D79—23no—
636C2×D79—23no—
637C2×D79—22no—
638C2×D79—23no—
639C2×D79—22no—
640C2×D79—23no—
641C2×D79—22no—
642C2×D79—23no—
643C2×D79—412no—
644C2×D79C22×#4116yes—
645C4×C79—26no—
646C4×C79—23no—
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—26no—
655Dic79—21no—
656Dic79—22no—
657Dic79—23no—
658Dic79—23no—
659Dic79—26no—
660Dic79—21no—
661Dic79C22×#4112yes—
662Dic79#58512yes—
663#62805—791nomaximal, Sylow
664C2×C79—22no—
665C2×C79—42no—
666C2×C79C23×#4111yescharacteristic
667C2×C79C22×2−1+411yescharacteristic
668C2×C79C2×#58511yescharacteristic
669D79—26no—
670D79—42no—
671D79—43no—
672#3523—792no—
673#3520—796no—
674#3518—791no—
675#3518—791no—
676#3515—793no—
677#3515—793no—
678#3511—793no—
679#3509—793no—
680#3503—791no—
681#3499—791no—
682#3495—796no—
683#3489—792no—
684#3482—796no—
685#3482—792no—
686Q8×#41—791no—
687Q8×#41D7911yescharacteristic, complemented
688#3475—793no—
689#3475—793no—
690#3461—796no—
691#3444—793no—
692C2×#533—793no—
693C4×2−1+4—792no—
694C2×C4×#41—791no—
695C79#6280511yescharacteristic, complemented, Sylow
696C2×2−1+4—792no—
697C22×#41—791no—
698Q82—791no—
699Q82C2×D7911yescharacteristic, complemented
700#557—796no—
701#557—793no—
702#557—792no—
703#557C2×D7913yescomplemented
704#556—793no—
705#556—796no—
706#556—796no—
707#556—796no—
708#556—793no—
709#556—796no—
710#555—793no—
711#555—793no—
712#554—793no—
713#554—793no—
714#554—793no—
715#554—796no—
716#554C2×D7916yes—
717#554C2×D7913yescomplemented
718#553—796no—
719#553—796no—
720#552—7912no—
721#552—7912no—
722#552—796no—
723#552—7912no—
724#552—796no—
725#552—796no—
726#552—796no—
727#552—796no—
728#552—796no—
729#551—7912no—
730#551—7912no—
731D4×Q8—792no—
732D4×Q8—792no—
733D4×Q8—796no—
734D4×Q8—791no—
735D4×Q8C2×D7912yes—
736D4×Q8C2×D7911yescharacteristic, complemented
737#548—792no—
738#548—7912no—
739#548—792no—
740#547—796no—
741#547—793no—
742#547—796no—
743#547—796no—
744#547—793no—
745#547—796no—
746#546—796no—
747#546—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—796no—
763#533—796no—
764#533—796no—
765#533—796no—
766#533—796no—
767#533—793no—
768#533—793no—
769#533—796no—
770#533—793no—
771#533—793no—
772#533C2×D7913yes—
773#533C2×D7916yescomplemented
774#532—791no—
775#532—793no—
776#532—793no—
777C2×C4⋊Q8—793no—
778C2×C4⋊Q8—793no—
779#529—793no—
780#529—793no—
781#529—7912no—
782#529—796no—
783#529—796no—
784#529—793no—
785#529—793no—
786#529—796no—
787#529—796no—
788#529—796no—
789#529—7912no—
790#529—796no—
791C2×#125—796no—
792#525—793no—
793#525—796no—
794#525—796no—
795#525—793no—
796C2×C22⋊Q8—796no—
797C2×C22⋊Q8—796no—
798#520—792no—
799#520—796no—
800#520—796no—
801#520—796no—
802#519—792no—
803#519—796no—
804#519—792no—
805C4×#41—791no—
806C4×#41—793no—
807C4×#41—793no—
808C4×#41—791no—
809C4×#41—791no—
810C4×#41—793no—
811C4×#41—793no—
812C4×#41—791no—
813C4×#41—796no—
814C4×#41—796no—
815C4×#41—796no—
816C4×#41—793no—
817C4×#41—796no—
818C4×#41C2×D7913yes—
819C2×C4×Q8—791no—
820C2×C4×Q8—796no—
821C2×C4×Q8—792no—
822C2×C4×Q8—796no—
823C2×C4×Q8C2×D7911yescharacteristic
824C2×C4×Q8C2×D7912yescomplemented
825C2×C4×D4—793no—
826C2×C4×D4—793no—
827C2×#117—796no—
828C2×#117—793no—
829C22×C42—793no—
8302−1+4—15816no—
831C2×#41—791no—
832C2×#41—793no—
833C2×#41—793no—
834C2×#41—791no—
835C2×#41—796no—
836C2×#41—796no—
837C2×#41—791no—
838C2×#41—796no—
839C2×#41—796no—
840C2×#41—1588no—
841C2×#41C22×D7911yescharacteristic
842C22×Q8—796no—
843C22×Q8—796no—
844C22×Q8—792no—
845C22×Q8C22×D7911yescharacteristic
846C22×Q8C22×D7912yes—
847C22×D4—793no—
848C23×C4—793no—
849C23×C4—793no—
850C23×C4—793no—
851C4⋊Q8—796no—
852C4⋊Q8—796no—
853C4⋊Q8—791no—
854C4⋊Q8—796no—
855C4⋊Q8—793no—
856C4⋊Q8—793no—
857C4⋊Q8—796no—
858C4⋊Q8—796no—
859C4⋊Q8—796no—
860C4⋊Q8—793no—
861C4⋊Q8—793no—
862C4⋊Q8C22×D7913yes—
863C4⋊Q8C22×D7913yes—
864C4⋊Q8C22×D7916yes—
865C4⋊Q8C22×D7916yes—
866#127—791no—
867#126—796no—
868#126—796no—
869#126—7912no—
870#126—7912no—
871#126—7912no—
872#126—7912no—
873#126—796no—
874#126—796no—
875#126—7912no—
876#126—7912no—
877#125—793no—
878#125—793no—
879#125—7912no—
880#125—7912no—
881#125—796no—
882#125—796no—
883#125—7912no—
884#125—7912no—
885#125—796no—
886#125—7912no—
887#125—796no—
888#125—796no—
889#125C22×D7916yes—
890#125C22×D79112yes—
891#124—791no—
892#124—796no—
893#124—7912no—
894#124—791no—
895#124—796no—
896#124—796no—
897#124—7912no—
898#124—796no—
899#123—796no—
900#123—7912no—
901#123—796no—
902#123—796no—
903#123—7912no—
904#123—7912no—
905#123—7912no—
906#123—7912no—
907#123—796no—
908#123—796no—
909#123—796no—
910#123—7912no—
911C22⋊Q8—796no—
912C22⋊Q8—796no—
913C22⋊Q8—793no—
914C22⋊Q8—793no—
915C22⋊Q8—796no—
916C22⋊Q8—7912no—
917C22⋊Q8—796no—
918C22⋊Q8—796no—
919C22⋊Q8—796no—
920C22⋊Q8—796no—
921C22⋊Q8—7912no—
922C22⋊Q8—796no—
923C22⋊Q8—7912no—
924C22⋊Q8—796no—
925C22⋊Q8—796no—
926C22⋊Q8—796no—
927C22⋊Q8—793no—
928C22⋊Q8—793no—
929C22⋊Q8—7912no—
930C22⋊Q8—796no—
931C22⋊Q8—7912no—
932C22⋊Q8—796no—
933C22⋊Q8—796no—
934C22⋊Q8C22×D7916yes—
935C22⋊Q8C22×D7916yes—
936C22⋊Q8C22×D7916yes—
937C22⋊Q8C22×D7916yes—
938C22⋊Q8C22×D79112yes—
939#121—792no—
940#121—792no—
941#121—793no—
942#121—793no—
943#121—796no—
944#121—793no—
945#121—793no—
946#121—7912no—
947#121—796no—
948#121—796no—
949#121—796no—
950#121—7912no—
951#120—796no—
952#120—796no—
953C4×Q8—791no—
954C4×Q8—793no—
955C4×Q8—791no—
956C4×Q8—793no—
957C4×Q8—796no—
958C4×Q8—792no—
959C4×Q8—796no—
960C4×Q8—796no—
961C4×Q8—7912no—
962C4×Q8—796no—
963C4×Q8—796no—
964C4×Q8—7912no—
965C4×Q8—796no—
966C4×Q8—796no—
967C4×Q8—796no—
968C4×Q8—796no—
969C4×Q8—796no—
970C4×Q8—796no—
971C4×Q8—796no—
972C4×Q8—796no—
973C4×Q8—793no—
974C4×Q8—793no—
975C4×Q8C22×D7911yescharacteristic
976C4×Q8C22×D7916yes—
977C4×Q8C22×D7916yes—
978C4×Q8C22×D7913yes—
979C4×Q8C22×D7911yescharacteristic
980C4×Q8C22×D7913yes—
981C4×Q8C22×D7912yes—
982C4×Q8C22×D7916yes—
983C4×Q8C22×D7913yes—
984C4×Q8C22×D7913yes—
985C4×D4—796no—
986C4×D4—792no—
987C4×D4—792no—
988C4×D4—796no—
989C4×D4—796no—
990C4×D4—7912no—
991C4×D4—796no—
992C4×D4—796no—
993C4×D4—796no—
994C4×D4—796no—
995C4×D4—796no—
996C4×D4—793no—
997C4×D4—796no—
998C4×D4—793no—
999C4×D4—793no—
1000C4×D4—793no—
1001C4×D4—796no—
1002C4×D4—796no—
1003C4×D4—7912no—
1004C4×D4—793no—
1005C4×D4—793no—
1006C4×D4—796no—
1007C4×D4—793no—
1008C4×D4—796no—
1009C4×D4—793no—
1010C4×D4—796no—
1011C4×D4—796no—
1012C4×D4—796no—
1013C4×D4—796no—
1014C4×D4—796no—
1015C4×D4—793no—
1016C4×D4—793no—
1017C4×D4C22×D7916yes—
1018C4×D4C22×D7916yes—
1019C4×D4C22×D7913yes—
1020C4×D4C22×D7913yes—
1021#117—793no—
1022#117—796no—
1023#117—796no—
1024#117—796no—
1025#117—793no—
1026#117—793no—
1027#117—796no—
1028#117—793no—
1029#117—796no—
1030#117—793no—
1031#117—796no—
1032#117—796no—
1033#117—7912no—
1034#117—796no—
1035#117—7912no—
1036#117—7912no—
1037#117—796no—
1038#117—796no—
1039#117—7912no—
1040#117—796no—
1041#117—796no—
1042#117—796no—
1043#117C22×D7913yes—
1044#117C22×D7916yes—
1045C2×C4⋊C4—793no—
1046C2×C4⋊C4—796no—
1047C2×C4⋊C4—796no—
1048C2×C4⋊C4—7912no—
1049C2×C4⋊C4—796no—
1050C2×C4⋊C4—796no—
1051C2×C4⋊C4—7912no—
1052C2×C4⋊C4—796no—
1053C2×C4⋊C4C22×D7913yes—
1054C2×C4⋊C4C22×D7916yes—
1055C2×C22⋊C4—796no—
1056C2×C22⋊C4—7912no—
1057C2×C42—793no—
1058C2×C42—793no—
1059C2×C42—791no—
1060C2×C42—7912no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—796no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—793no—
1067C2×C42—793no—
1068C2×C42—793no—
1069C2×C42—793no—
1070C2×C42C22×D7913yes—
1071C2×C42C22×D7916yes—
1072C24—793no—
1073#41—24no—
1074#41—31612no—
1075#41—798no—
1076#41—15824no—
1077#41—15824no—
1078#41—15812no—
1079#41—15812no—
1080#41—15824no—
1081#41—1584no—
1082#41—1584no—
1083C2×Q8—24no—
1084C2×Q8—28no—
1085C2×Q8—31612no—
1086C2×Q8—796no—
1087C2×Q8—791no—
1088C2×Q8—796no—
1089C2×Q8—796no—
1090C2×Q8—796no—
1091C2×Q8—15824no—
1092C2×Q8—1588no—
1093C2×Q8C23×D7916yes—
1094C2×Q8C23×D7913yes—
1095C2×Q8C23×D7911yescharacteristic
1096C2×Q8C23×D7916yes—
1097C2×Q8C23×D7911yescharacteristic
1098C2×D4—796no—
1099C2×D4—792no—
1100C2×D4—796no—
1101C2×D4—792no—
1102C2×D4—792no—
1103C2×D4—796no—
1104C2×D4—793no—
1105C2×D4—791no—
1106C2×D4—796no—
1107C2×D4—796no—
1108C2×D4—793no—
1109C2×D4—15812no—
1110C2×D4C23×D7912yes—
1111C2×D4C23×D7911yescharacteristic
1112C22×C4—3166no—
1113C22×C4—793no—
1114C22×C4—793no—
1115C22×C4—7912no—
1116C22×C4—796no—
1117C22×C4—793no—
1118C22×C4—791no—
1119C22×C4—791no—
1120C22×C4—793no—
1121C22×C4—793no—
1122C22×C4—793no—
1123C22×C4—793no—
1124C22×C4—793no—
1125C22×C4—793no—
1126C22×C4—793no—
1127C22×C4—793no—
1128C22×C4—7912no—
1129C22×C4—796no—
1130C22×C4—793no—
1131C22×C4—792no—
1132C22×C4—793no—
1133C22×C4—15812no—
1134C22×C4—15812no—
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—7912no—
1146C4⋊C4—7912no—
1147C4⋊C4—7912no—
1148C4⋊C4—7912no—
1149C4⋊C4—792no—
1150C4⋊C4—792no—
1151C4⋊C4—796no—
1152C4⋊C4—796no—
1153C4⋊C4—796no—
1154C4⋊C4—796no—
1155C4⋊C4—793no—
1156C4⋊C4—793no—
1157C4⋊C4—796no—
1158C4⋊C4—796no—
1159C4⋊C4—796no—
1160C4⋊C4—793no—
1161C4⋊C4—793no—
1162C4⋊C4—796no—
1163C4⋊C4—796no—
1164C4⋊C4—796no—
1165C4⋊C4—796no—
1166C4⋊C4C23×D7913yes—
1167C4⋊C4C23×D7913yes—
1168C4⋊C4C23×D7913yes—
1169C4⋊C4C23×D7916yes—
1170C4⋊C4C23×D79112yes—
1171C4⋊C4C23×D79112yes—
1172C4⋊C4C23×D7916yes—
1173C4⋊C4C23×D7916yes—
1174C4⋊C4C23×D7913yes—
1175C4⋊C4C23×D7916yes—
1176C4⋊C4C23×D7916yes—
1177C22⋊C4—796no—
1178C22⋊C4—792no—
1179C22⋊C4—792no—
1180C22⋊C4—796no—
1181C22⋊C4—796no—
1182C22⋊C4—796no—
1183C22⋊C4—796no—
1184C22⋊C4—796no—
1185C22⋊C4—796no—
1186C22⋊C4—7912no—
1187C22⋊C4—7912no—
1188C22⋊C4—796no—
1189C22⋊C4—796no—
1190C22⋊C4—792no—
1191C22⋊C4—792no—
1192C22⋊C4—796no—
1193C22⋊C4—796no—
1194C22⋊C4—796no—
1195C22⋊C4—796no—
1196C22⋊C4—796no—
1197C22⋊C4—796no—
1198C22⋊C4C23×D7916yes—
1199C22⋊C4C23×D7916yes—
1200C22⋊C4C23×D7916yes—
1201C42—791no—
1202C42—791no—
1203C42—793no—
1204C42—793no—
1205C42—793no—
1206C42—793no—
1207C42—793no—
1208C42—793no—
1209C42—793no—
1210C42—793no—
1211C42—796no—
1212C42—7912no—
1213C42—7912no—
1214C42—796no—
1215C42—791no—
1216C42—791no—
1217C42—796no—
1218C42C23×D7913yes—
1219C42C23×D7913yes—
1220C42C23×D7916yes—
1221C42C23×D7916yes—
1222C42C23×D7913yes—
1223C42C23×D7913yes—
1224C42C23×D7916yes—
1225C23—3163no—
1226C23—793no—
1227C23—793no—
1228C23—792no—
1229C23—1586no—
1230C23—1586no—
1231C23C24×D7912yes—
1232C23C24×D7911yescharacteristic
1233Q8—22no—
1234Q8—212no—
1235Q8—26no—
1236Q8—46no—
1237Q8—3166no—
1238Q8—15812no—
1239Q8—15812no—
1240Q8—1582no—
1241Q8—15812no—
1242Q8#41×D7914yes—
1243D4—24no—
1244D4—22no—
1245D4—3166no—
1246D4—3166no—
1247D4—7912no—
1248D4—15812no—
1249D4—15812no—
1250D4—1584no—
1251D4—1584no—
1252D4—15812no—
1253D4—1584no—
1254D4—1582no—
1255D4—1586no—
1256C2×C4—24no—
1257C2×C4—26no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—3163no—
1262C2×C4—3163no—
1263C2×C4—31612no—
1264C2×C4—3166no—
1265C2×C4—791no—
1266C2×C4—791no—
1267C2×C4—7912no—
1268C2×C4—793no—
1269C2×C4—791no—
1270C2×C4—791no—
1271C2×C4—792no—
1272C2×C4—793no—
1273C2×C4—796no—
1274C2×C4—796no—
1275C2×C4—1586no—
1276C2×C4—1586no—
1277C2×C4—1586no—
1278C2×C4—1586no—
1279C2×C4—15824no—
1280C2×C4—1582no—
1281C2×C4—1582no—
1282C2×C4—1586no—
1283C2×C4—1586no—
1284C2×C4—1586no—
1285C2×C4—1586no—
1286C2×C4—1586no—
1287C2×C4—1584no—
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—31612no—
1306C22—796no—
1307C22—1582no—
1308C22—1583no—
1309C22—1583no—
1310C22—1582no—
1311C22—1582no—
1312C22—1583no—
1313C22—1583no—
1314C22—1583no—
1315C22C2×#1457920912yes—
1316C22C25×D7911yescharacteristic
1317C4—23no—
1318C4—26no—
1319C4—22no—
1320C4—23no—
1321C4—26no—
1322C4—23no—
1323C4—792no—
1324C4—792no—
1325C4—1581no—
1326C4—1586no—
1327C4—1583no—
1328C4—1583no—
1329C4—1582no—
1330C4—1581no—
1331C4—1586no—
1332C4C2×#41×D7916yes—
1333C4C2×#1457920912yes—
1334C4C2×#1457920912yes—
1335C2—22no—
1336C2—42no—
1337C2—3163no—
1338C2—3162no—
1339C2—1586no—
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#62805
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #23777487C2semidirect
2. #23777445C2semidirect
3. #23777418C2semidirect
4. #23777412C2semidirect
5. #23777381C2semidirect
6. #23777377C2semidirect
7. #23777308C2semidirect
8. #23777283C2semidirect
9. #23777218C2semidirect
10. #23777184C2semidirect
11. #23777148C2semidirect
12. #23777077C2semidirect
13. #23777018C2semidirect
14. #23777017C2semidirect
15. Q8×#11929624C2semidirect
16. #23776967C2semidirect
17. #23776964C2semidirect
18. #23776831C2semidirect
19. #23776693C2semidirect
20. #533×D79C2semidirect
21. C4×#14579209C2semidirect
22. C2×C4×#11929625C2semidirect
23. Q8×#41×C79C2semidirect
26. Q8×Dic158C22semidirect
27. #19099291C22semidirect
28. #19099289C22semidirect
29. #19099288C22semidirect
30. #19099287C22semidirect
31. #19099287C22semidirect
32. #19099286C22semidirect
33. #19099285C22semidirect
34. #19099284C22semidirect
35. #19099284C22semidirect
36. #19099279C22semidirect
37. #19099278C22semidirect
38. #19099274C22semidirect
39. #19099273C22semidirect
40. #19099273C22semidirect
42. #19099266C22semidirect
43. #19099263C22semidirect
45. #19099254C22semidirect
46. #19099254C22semidirect
48. #19099251C22semidirect
49. #19099248C22semidirect
50. #19099247C22semidirect
51. #19099245C22semidirect
52. #19099245C22semidirect
55. Q8×D316C22semidirect
56. #19099228C22semidirect
58. Q8×C22⋊D79C22semidirect
61. #19099223C22semidirect
62. #19099218C22semidirect
64. #19099216C22semidirect
66. #19099215C22semidirect
67. #19099214C22semidirect
70. #19099190C22semidirect
71. #19099187C22semidirect
72. #19099186C22semidirect
73. #19099183C22semidirect
74. #19099174C22semidirect
75. #19099173C22semidirect
76. #19099172C22semidirect
77. #19099161C22semidirect
78. #19099159C22semidirect
81. #19099136C22semidirect
83. #19099119C22semidirect
84. #19099118C22semidirect
85. #19099118C22semidirect
86. #19099117C22semidirect
87. #19099117C22semidirect
88. #19099117C22semidirect
89. #19099117C22semidirect
90. #19099117C22semidirect
94. #19099110C22semidirect
95. #19099110C22semidirect
97. C4⋊Q8×D79C22semidirect
98. C4⋊Q8×D79C22semidirect
99. #19099100C22semidirect
100. #19099100C22semidirect
101. #19099100C22semidirect
102. #19099100C22semidirect
103. #19099097C22semidirect
104. #19099095C22semidirect
105. #19099095C22semidirect
108. #19099091C22semidirect
109. #19099091C22semidirect
110. #19099091C22semidirect
111. #125×D79C22semidirect
119. #19099045C22semidirect
120. #19099044C22semidirect
121. #19099044C22semidirect
122. #19099041C22semidirect
123. #19099039C22semidirect
124. #19099039C22semidirect
133. C4×#11929625C22semidirect
135. C4×#11929624C22semidirect
136. C4×#11929624C22semidirect
137. C4×#11929624C22semidirect
139. C4×Q8×D79C22semidirect
140. C4×Q8×D79C22semidirect
141. C4×Q8×D79C22semidirect
147. Q82×C79C22semidirect
148. #557×C79C22semidirect
150. #554×C79C22semidirect
152. D4×Q8×C79C22semidirect
154. #533×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
405. #11929625#41semidirect
573. C2×C4×C792−1+4semidirect
687. Q8×#41D79semidirect
695. C79#62805semidirect
699. Q82C2×D79semidirect
703. #557C2×D79semidirect
717. #554C2×D79semidirect
736. D4×Q8C2×D79semidirect
773. #533C2×D79semidirect
824. 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
#237774872
#237774452
#237774182
#237774122
#237773812
#237773772
#237773082
#237772832
#237772182
#237771842
#237771482
#237770772
#237770182
#237770172
Q8×#119296242
#237769672
#237769642
#237768312
#237766932
#533×D792
C4×#145792092
C2×C4×#119296252
Q8×#41×C792
#6280579