Finite Group Databasebeta

← #25971469

Subgroups — #25971469

Order 11008.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148493C211yesmaximal, characteristic, complemented
2#19148464C211yesmaximal, characteristic, complemented
3#19146013C212yesmaximal, complemented
4#19146005C212yesmaximal, complemented
5#19145838C211yesmaximal, characteristic, complemented
6#19145836C211yesmaximal, characteristic, complemented
7#19145793C211yesmaximal, characteristic, complemented
8#19145614C211yesmaximal, characteristic, complemented
9#19145614C211yesmaximal, characteristic, complemented
10#19145584C211yesmaximal, characteristic, complemented
11#19145578C211yesmaximal, characteristic, complemented
12#19145469C212yesmaximal, complemented
13#19145459C212yesmaximal, complemented
14#19145295C211yesmaximal, characteristic, complemented
15#19145292C211yesmaximal, characteristic, complemented
16#19145192C211yesmaximal, characteristic, complemented
17#19145189C211yesmaximal, characteristic, complemented
18#19144882C212yesmaximal, complemented
19#19144834C212yesmaximal, complemented
20#19144786C212yesmaximal, complemented
21#19144784C212yesmaximal, complemented
22#19143241C211yesmaximal, characteristic, complemented
23C43×#3235C211yesmaximal, characteristic, complemented
24#14583634—21no—
25#14583634—21no—
26#14583632—21no—
27#14583631—21no—
28#14583622—21no—
29#14583622—21no—
30#14583576—21no—
31#14583576—21no—
32#14583576—21no—
33#14583576—21no—
34#14583568—21no—
35#14583567—21no—
36#14583546—21no—
37#14583544—21no—
38#14583542—21no—
39#14583537—21no—
40#14583523C2211yescharacteristic
41#14583523C2211yescharacteristic
42#14583523C2211yescharacteristic, complemented
43#14583523C2211yescharacteristic, complemented
44#14583502C2212yes—
45#14583500C2212yescomplemented
46#14583475C2211yescharacteristic
47#14583468C2211yescharacteristic
48#14583465C2212yes—
49#14583454C2211yescharacteristic, complemented
50#14583450C2211yescharacteristic, complemented
51#14583449C2211yescharacteristic
52#14583447C2211yescharacteristic, complemented
53#127×D43C2211yescharacteristic, complemented
54#14583434C2211yescharacteristic
55#14583434C2211yescharacteristic
56#14583434C2211yescharacteristic, complemented
57#14583434C2211yescharacteristic, complemented
58C2×#13063313C2211yescharacteristic, complemented
59#14583376C2211yescharacteristic, complemented
60#14583373C2211yescharacteristic, complemented
61#14583371C2212yescomplemented
62C4×#10621898C2211yescharacteristic
63#14583309C2211yescharacteristic, complemented
64#14583309C2211yescharacteristic, complemented
65#14583288C2211yescharacteristic
66#14583288C2211yescharacteristic
67#14583286C2211yescharacteristic
68#14583286C2211yescharacteristic
69#14583265C2211yescharacteristic, complemented
70#14583265C2211yescharacteristic, complemented
71#14583261C2211yescharacteristic, complemented
72#14583261C2211yescharacteristic, complemented
73#14583259C2211yescharacteristic, complemented
74#14583259C2211yescharacteristic, complemented
75#14583243C2212yescomplemented
76#14583242C2212yescomplemented
77#14583226C2212yes—
78#14583225C2212yes—
79#14583223C2212yescomplemented
80#14583223C2212yescomplemented
81#14583209C2212yescomplemented
82#14583205C2212yescomplemented
83#14583202C2212yescomplemented
84#14583198C2212yescomplemented
85#14583186C2212yescomplemented
86#14583176C2212yescomplemented
87#14583153C2212yescomplemented
88#14583151C2212yescomplemented
89#14583146C2212yescomplemented
90#14583144C2212yescomplemented
91#14583136C2212yescomplemented
92#14583134C2212yescomplemented
93#14583129C2212yescomplemented
94#14583127C2212yescomplemented
95#14583115C2212yescomplemented
96#14583115C2212yescomplemented
97#14583114C2212yescomplemented
98#14583114C2212yescomplemented
99#14583098C2212yescomplemented
100#14583098C2212yescomplemented
101#14583093C2212yes—
102#14583093C2212yes—
103#14583051C2212yescomplemented
104#14583051C2212yescomplemented
105#14583040C2212yescomplemented
106#14583037C2212yescomplemented
107#14583035C2212yescomplemented
108#14583034C2212yes—
109#14583034C2212yes—
110#14583032C2212yescomplemented
111#14583010C2212yescomplemented
112#14583008C2212yescomplemented
113#14582998C2212yescomplemented
114#14582996C2212yescomplemented
115#14582990C2212yescomplemented
116#14582986C2212yescomplemented
117#14582981C2212yescomplemented
118#14582979C2212yescomplemented
119#14582959C2212yescomplemented
120#14582957C2212yescomplemented
121#14582956C2211yescharacteristic, complemented
122#14582954C2211yescharacteristic, complemented
123#14582954C2211yescharacteristic, complemented
124#14582924C2212yescomplemented
125#14582864C2212yes—
126#14582851C2211yescharacteristic, complemented
127#97×D43C2211yescharacteristic, complemented
128C43×#533C2211yescharacteristic, complemented
129C43×#532C2211yescharacteristic
130C43×#501C2211yescharacteristic, complemented
131C43×#501C2211yescharacteristic, complemented
132C43×#490C2211yescharacteristic, complemented
133C43×#490C2211yescharacteristic, complemented
134C43×#482C2212yescomplemented
135C43×#482C2212yescomplemented
136C43×#476C2212yescomplemented
137C43×#474C2212yescomplemented
138C43×#432C2211yescharacteristic, complemented
139C2×#10621902—21no—
140C2×#10621898—21no—
141C2×#10621898C2311yescharacteristic
142C2×#10621900—21no—
143C22×Dic86C2311yescharacteristic
144C22×D172C2311yescharacteristic
145C2×D4×D43—21no—
146C2×D4×D43—21no—
147C2×D4×D43C2312yes—
148C2×#10621873C2312yes—
149C2×#10621873C2312yes—
150C2×#10621883C2312yes—
151C2×#10621883C2312yes—
152C2×D344C2312yes—
153C2×D344C2312yes—
154C2×#10621882C2312yes—
155C2×#10621882C2312yes—
156C2×#10621872C2312yes—
157C2×C8×D43C2312yes—
158#13063325—21no—
159#13063325C2311yescharacteristic
160#13063322—21no—
161#13063322C2311yescharacteristic
162#13063321—22no—
163#13063321—21no—
164#13063321—21no—
165#13063321C2312yes—
166#13063320—21no—
167#13063320—21no—
168#13063320—21no—
169#13063320—21no—
170#13063320—21no—
171#13063320—21no—
172#13063320—21no—
173#13063320—21no—
174#13063316C2312yes—
175#13063314—21no—
176#13063314—21no—
177#13063314—21no—
178#13063314—21no—
179#13063314—21no—
180#13063313—21no—
181#13063313—21no—
182#13063313—21no—
183#13063313—21no—
184#13063313—21no—
185#13063313C2311yescharacteristic
186#13063313C2311yescharacteristic
187#13063313C2311yescharacteristic
188#13063313C2311yescharacteristic
189#13063312—21no—
190#13063311—22no—
191#13063310—21no—
192#13063310—21no—
193#13063310—21no—
194#13063310—21no—
195#13063310—21no—
196#13063310—21no—
197#13063310—21no—
198#13063310—21no—
199#13063309—21no—
200#13063309—21no—
201#13063309—22no—
202#13063308—22no—
203#13063307—22no—
204#13063307—22no—
205#13063305—21no—
206#13063305C2311yescharacteristic
207#13063305C2311yescharacteristic
208#13063305C2311yescharacteristic
209#13063305C2311yescharacteristic
210#13063301—21no—
211#13063301—21no—
212#13063301—21no—
213#13063301—21no—
214#13063301—21no—
215#13063300—21no—
216#13063300C2312yes—
217#13063300C2311yescharacteristic
218#13063300C2311yescharacteristic
219#13063300C2311yescharacteristic
220#13063300C2311yescharacteristic
221#13063299—21no—
222#13063299—22no—
223#13063299C2312yes—
224#13063298—22no—
225#13063297—22no—
226#13063296—21no—
227#13063296—22no—
228#13063296C2312yes—
229#13063295—21no—
230#13063295—21no—
231#13063295—22no—
232#13063293—22no—
233Q8×Dic43—21no—
234C4×Dic86—21no—
235C4×Dic86—21no—
236C4×Dic86D411yescharacteristic
237C4×Dic86D411yescharacteristic
238#13063290—21no—
239#13063290C2311yescharacteristic
240#13063290C2311yescharacteristic
241#13063290C2311yescharacteristic
242#13063290C2311yescharacteristic
243C4×D172—21no—
244C4×D172—21no—
245C4×D172—21no—
246C4×D172D411yescharacteristic
247C4×D172D411yescharacteristic
248C4×D172C2312yes—
249D4×Dic43—21no—
250D4×Dic43C2312yes—
251#13063287—21no—
252#13063287—21no—
253#13063287—21no—
254#13063287—21no—
255#13063287—21no—
256#13063287C2311yescharacteristic
257#13063287C2311yescharacteristic
258#13063287C2312yes—
259#13063287C2311yescharacteristic
260#13063287C2311yescharacteristic
261C4×C22⋊D43—22no—
262C4×C22⋊D43D411yescharacteristic
263C4×C22⋊D43D411yescharacteristic
264C4×C22⋊D43D411yescharacteristic
265C4×C22⋊D43D411yescharacteristic
266(C22⋊D43)⋊C4—22no—
267#13063284C2311yescharacteristic
268#13063283—21no—
269#13063283—21no—
270#13063283—21no—
271#13063283—21no—
272#13063283C2312yes—
273#13063282C2311yescharacteristic
274#13063282C2311yescharacteristic
275#13063281—21no—
276#13063281—21no—
277C2×(C2×D43)⋊C4—21no—
278C2×(C2×D43)⋊C4—21no—
279C2×(C2×D43)⋊C4—22no—
280C22⋊C4×D43—21no—
281C22⋊C4×D43—21no—
282C22⋊C4×D43—22no—
283C42×D43C2311yescharacteristic
284C42×D43C2311yescharacteristic
285#13063258C2312yes—
286#13063258C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289C4⋊(C43⋊C8)C2312yes—
290Dic43⋊C8C2312yes—
291Dic43⋊C8C2312yes—
292#13063250C2312yes—
293#13063250C2312yes—
294#13063248C2312yes—
295#13063248C2312yes—
296#13063247C2312yes—
297#13063247C2312yes—
298#13063245C2312yes—
299#13063245C2312yes—
300#13063245C2312yes—
301#13063245C2312yes—
302#13063245C2312yes—
303#13063245C2312yes—
304C22⋊(C43⋊C8)C2312yes—
305(C2×D43)⋊C8C2312yes—
306(C2×D43)⋊C8C2312yes—
307#13063236C2311yescharacteristic
308#13063236C2311yescharacteristic
309#13063235C2312yes—
310C8×Dic43C2312yes—
311C2×#41×C43—21no—
312C4⋊Q8×C43C2311yescharacteristic
313C4⋊Q8×C43C2311yescharacteristic
314C4⋊Q8×C43C2311yescharacteristic
315#127×C43C2311yescharacteristic
316#125×C43C2311yescharacteristic
317#125×C43C2311yescharacteristic
318#124×C43—21no—
319C22⋊Q8×C43—21no—
320C22⋊Q8×C43—21no—
321#121×C43—21no—
322#121×C43C2312yes—
323C4×Q8×C43—21no—
324C4×Q8×C43—21no—
325C4×D4×C43—21no—
326C4×D4×C43C2312yes—
327#117×C43C2311yescharacteristic
328#117×C43C2311yescharacteristic
329C2×C42×C43C2311yescharacteristic
330#107×C43C2312yes—
331#107×C43C2312yes—
332#106×C43C2312yes—
333#106×C43C2312yes—
334C4⋊C8×C43C2312yes—
335#102×C43C2312yes—
336#102×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339C22⋊C8×C43C2312yes—
340#97×C43C2311yescharacteristic
341#97×C43C2311yescharacteristic
342C23×D43—21no—
343C23×D43—22no—
344#41×C43—82no—
345C2×Q8×C43—21no—
346C2×Q8×C43—21no—
347C2×Q8×C43—21no—
348C2×D4×C43—21no—
349C2×D4×C43—21no—
350C2×D4×C43—22no—
351C2×D4×C43C2412yes—
352C22×C4×C43—22no—
353C22×C4×C43C2×D411yescharacteristic
354C22×C4×C43C2×D411yescharacteristic
355C22×C4×C43C2411yescharacteristic
356C2×C22⋊D43—22no—
357C2×C22⋊D43—22no—
358C2×C22⋊D43—22no—
359C2×C22⋊D43—22no—
360C2×C22⋊D43—22no—
361C2×C22⋊D43C2×D411yescharacteristic
362C2×C22⋊D43C2×D411yescharacteristic
363C22×Dic43—22no—
364C22×Dic43—21no—
365#10621902—82no—
366#10621900—82no—
367D4×D43—42no—
368D4×D43—42no—
369D4×D43—82no—
370D4×D43—82no—
371#10621898—42no—
372#10621898—82no—
373C2×D172—21no—
374C2×D172—21no—
375C2×D172—21no—
376C2×D172—21no—
377C2×D172—21no—
378C2×D172—21no—
379C2×D172—21no—
380C2×D172—22no—
381C2×D172—42no—
382C2×D172C2×D411yescharacteristic
383C2×D172C2412yes—
384C2×D172C2411yescharacteristic
385C2×D172C2411yescharacteristic
386C2×C4×D43—22no—
387C2×C4×D43—21no—
388C2×C4×D43—21no—
389C2×C4×D43—21no—
390C2×C4×D43—21no—
391C2×C4×D43—22no—
392C2×C4×D43C2×D411yescharacteristic
393C2×C4×D43C2×D411yescharacteristic
394C2×C4×D43C2×D411yescharacteristic
395C2×C4×D43C2×D411yescharacteristic
396C2×C4×D43C2411yescharacteristic
397C2×C4×D43C2411yescharacteristic
398C2×Dic86—21no—
399C2×Dic86—21no—
400C2×Dic86—42no—
401C2×Dic86C2×D411yescharacteristic
402C2×Dic86C2411yescharacteristic
403C2×Dic86C2411yescharacteristic
404C2×C8×C43C2412yes—
405C2×C8×C43C2412yes—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43—21no—
410C4⋊C4×C43—21no—
411C4⋊C4×C43—21no—
412C4⋊C4×C43—21no—
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C4⋊C4×C43C2411yescharacteristic
416C4⋊C4×C43C2411yescharacteristic
417C4⋊C4×C43C2412yes—
418C22⋊C4×C43—22no—
419C22⋊C4×C43—22no—
420C22⋊C4×C43—21no—
421C22⋊C4×C43—21no—
422C42×C43—21no—
423C42×C43—21no—
424C42×C43C2×D411yescharacteristic
425C42×C43C2×D411yescharacteristic
426C42×C43C2411yescharacteristic
427C42×C43C2411yescharacteristic
428C22⋊Dic43—22no—
429C22⋊Dic43—22no—
430C22⋊Dic43C2×D411yescharacteristic
431C22⋊Dic43C2×D411yescharacteristic
432#10621883—42no—
433#10621883—42no—
434#10621882—42no—
435#10621882—42no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—21no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—21no—
447(C2×D43)⋊C4—21no—
448(C2×D43)⋊C4—21no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—22no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—21no—
454(C2×D43)⋊C4—21no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4—21no—
459(C2×D43)⋊C4—21no—
460(C2×D43)⋊C4—21no—
461(C2×D43)⋊C4C2×D411yescharacteristic
462(C2×D43)⋊C4C2×D411yescharacteristic
463(C2×D43)⋊C4C2×D411yescharacteristic
464(C2×D43)⋊C4C2×D411yescharacteristic
465C4⋊Dic43—21no—
466C4⋊Dic43—21no—
467C4⋊Dic43—21no—
468C4⋊Dic43—21no—
469C4⋊Dic43—21no—
470C4⋊Dic43—22no—
471C4⋊Dic43C2×D411yescharacteristic
472C4⋊Dic43C2×D411yescharacteristic
473C4⋊Dic43C2412yes—
474Dic43⋊C4—21no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4—21no—
478Dic43⋊C4—22no—
479Dic43⋊C4C2×D411yescharacteristic
480Dic43⋊C4C2×D411yescharacteristic
481Dic43⋊C4C2×D411yescharacteristic
482Dic43⋊C4C2×D411yescharacteristic
483C4×Dic43—21no—
484C4×Dic43—21no—
485C4×Dic43—21no—
486C4×Dic43—21no—
487C4×Dic43—22no—
488C4×Dic43C2×D411yescharacteristic
489C4×Dic43C2×D411yescharacteristic
490C4×Dic43C2×D411yescharacteristic
491C4×Dic43C2×D411yescharacteristic
492C4×Dic43C2411yescharacteristic
493C4×Dic43C2411yescharacteristic
494C2×C43⋊C8C2412yes—
495C2×C43⋊C8C2412yes—
496D344—42no—
497D344—42no—
498#10621873—42no—
499#10621873—42no—
500#10621872—42no—
501C8×D43—42no—
502C23×C43—22no—
503C23×C43C22×D411yescharacteristic
504C22×D43—21no—
505C22×D43—21no—
506C22×D43—22no—
507C22×D43—44no—
508C22×D43—42no—
509C22×D43—82no—
510C22×D43—82no—
511C22×D43—81no—
512C22×D43—81no—
513C22×D43C22×D411yescharacteristic
514C22×D43C22×D411yescharacteristic
515Q8×C43—42no—
516Q8×C43—81no—
517Q8×C43—81no—
518D4×C43—22no—
519D4×C43—22no—
520D4×C43—42no—
521D4×C43—42no—
522D4×C43—82no—
523C2×C4×C43—22no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—22no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—41no—
530C2×C4×C43—41no—
531C2×C4×C43—82no—
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43C22×D411yescharacteristic
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43C2511yescharacteristic
538C22⋊D43—41no—
539C22⋊D43—41no—
540C22⋊D43—44no—
541C22⋊D43—82no—
542C22⋊D43—82no—
543C22⋊D43—82no—
544C22⋊D43—82no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—22no—
548C2×Dic43—42no—
549C2×Dic43—82no—
550C2×Dic43C22×D411yescharacteristic
551C2×Dic43C22×D411yescharacteristic
552C2×Dic43C22×D411yescharacteristic
553C2×Dic43C22×D411yescharacteristic
554C2×Dic43C22×D411yescharacteristic
555C2×Dic43C22×D411yescharacteristic
556D172—22no—
557D172—22no—
558D172—22no—
559D172—22no—
560D172—41no—
561D172—42no—
562D172—42no—
563D172—42no—
564D172—81no—
565D172—81no—
566D172—81no—
567D172—81no—
568D172—82no—
569C4×D43—22no—
570C4×D43—22no—
571C4×D43—41no—
572C4×D43—41no—
573C4×D43—41no—
574C4×D43—41no—
575C4×D43—81no—
576C4×D43—81no—
577C4×D43—81no—
578C4×D43—81no—
579C4×D43—82no—
580C4×D43—82no—
581Dic86—22no—
582Dic86—22no—
583Dic86—41no—
584Dic86—42no—
585Dic86—42no—
586C8×C43—22no—
587C8×C43—22no—
588C43⋊C8—22no—
589C43⋊C8—22no—
590#61017—431nomaximal, Sylow
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—21no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43C23×D411yescharacteristic
598C2×D43—21no—
599C2×D43—21no—
600C2×D43—21no—
601C2×D43—21no—
602C2×D43—21no—
603C2×D43—21no—
604C2×D43—42no—
605C2×D43—42no—
606C2×D43—41no—
607C2×D43—41no—
608C2×D43—41no—
609C2×D43—41no—
610C2×D43—41no—
611C2×D43—41no—
612C2×D43—42no—
613C2×D43—164no—
614C2×D43—162no—
615C4×C43—21no—
616C4×C43—21no—
617C4×C43—21no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—41no—
621C4×C43—41no—
622C4×C43—42no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43#58512yes—
626Dic43—21no—
627Dic43—21no—
628Dic43—21no—
629Dic43—21no—
630Dic43—21no—
631Dic43—21no—
632Dic43—42no—
633Dic43—41no—
634Dic43—41no—
635#3510—431no—
636#3508—431no—
637#3257—432no—
638#3257—432no—
639#3240—431no—
640#3240—431no—
641#3235—431no—
642#3235D4311yescharacteristic, complemented
643#3217—431no—
644#3217—431no—
645#3213—431no—
646#3213—431no—
647#3200—432no—
648#3199—432no—
649#3180—431no—
650#3180—431no—
651#3171—431no—
652#3171—431no—
653#3126—432no—
654#3122—432no—
655#3118—432no—
656#3118—432no—
657#2923—431no—
658C2×C43—41no—
659C2×C43—82no—
660C2×C43#344911yescharacteristic
661C2×C43#358511yescharacteristic
662C2×C43#358511yescharacteristic
663D43—41no—
664D43—41no—
665D43—82no—
666D43—81no—
667D43—81no—
668#559—861no—
669#559—861no—
670#559—861no—
671#559—861no—
672#556—861no—
673#556—861no—
674#551—861no—
675#551—861no—
676#551—861no—
677#551—861no—
678#550—861no—
679#550—861no—
680#546—861no—
681#546—861no—
682#546—861no—
683#546—861no—
684#542—431no—
685#542—431no—
686#542—431no—
687#542—431no—
688#540—432no—
689#540—432no—
690#536—431no—
691#535—432no—
692#535—431no—
693#533—431no—
694#533C2×D4311yescharacteristic, complemented
695#532—431no—
696#532—431no—
697#532—431no—
698#532C2×D4311yescharacteristic
699C2×#127—431no—
700#529—431no—
701#529—431no—
702#529—431no—
703#529—431no—
704C2×#124—431no—
705#519—431no—
706#518—432no—
707#518—431no—
708C4×#41—431no—
709#501—431no—
710#501—431no—
711#501C2×D4311yescharacteristic, complemented
712#501C2×D4311yescharacteristic, complemented
713#496—431no—
714#496—431no—
715#496—431no—
716#496—431no—
717#490—431no—
718#490—431no—
719#490C2×D4311yescharacteristic, complemented
720#490C2×D4311yescharacteristic, complemented
721#489—431no—
722#489—431no—
723#489—431no—
724#489—431no—
725#485—432no—
726#485—432no—
727#482—432no—
728#482—432no—
729#482—432no—
730#482—432no—
731#482C2×D4312yescomplemented
732#482C2×D4312yescomplemented
733#479—432no—
734#479—432no—
735#478—432no—
736#478—432no—
737#476—432no—
738#476C2×D4312yescomplemented
739#474—432no—
740#474C2×D4312yescomplemented
741#469—432no—
742#469—432no—
743#468—432no—
744#468—432no—
745#466—432no—
746#466—432no—
747#465—432no—
748#465—432no—
749#463—432no—
750#463—432no—
751#463—432no—
752#463—432no—
753#460—432no—
754#460—432no—
755#459—432no—
756#459—432no—
757#450—432no—
758#450—432no—
759#448—432no—
760#448—432no—
761#447—432no—
762#447—432no—
763#447—432no—
764#447—432no—
765#442—432no—
766#442—432no—
767#440—432no—
768#440—432no—
769C4×SD16—432no—
770C4×SD16—432no—
771C4×D8—432no—
772C4×D8—432no—
773#433—432no—
774#433—432no—
775#432—431no—
776#432—431no—
777#432—431no—
778#432C2×D4311yescharacteristic, complemented
779#424—432no—
780#408—432no—
781C4×M16—431no—
782C2×#97—431no—
783C43#6101711yescharacteristic, complemented, Sylow
784C2×#41—21no—
785C2×#41—431no—
786C2×#41—861no—
787C2×#41—861no—
788C2×#41—861no—
789C22×Q8—431no—
790C22×D4—432no—
791C22×D4—431no—
792C22×D4—861no—
793C22×D4—861no—
794C2×SD16—432no—
795C2×SD16—432no—
796C2×SD16—432no—
797C2×SD16—432no—
798C2×D8—432no—
799C2×D8—432no—
800C2×D8—432no—
801C2×D8—432no—
802C2×M16—432no—
803C22×C8—432no—
804C4⋊Q8—431no—
805C4⋊Q8—861no—
806C4⋊Q8C22×D4311yescharacteristic
807C4⋊Q8C22×D4311yescharacteristic
808C4⋊Q8C22×D4311yescharacteristic
809#127—432no—
810#127—431no—
811#127—861no—
812#127—861no—
813#127—861no—
814#127—862no—
815#127C22×D4311yescharacteristic
816#126—861no—
817#126—861no—
818#126—861no—
819#126—861no—
820#126—861no—
821#126—861no—
822#126—861no—
823#126—861no—
824#125—432no—
825#125C22×D4311yescharacteristic
826#125C22×D4311yescharacteristic
827#124—21no—
828#124—431no—
829#124—431no—
830#124—431no—
831#124—431no—
832#124—861no—
833#124—861no—
834#124—861no—
835#124—861no—
836#124—862no—
837#124—861no—
838#124—861no—
839#124—861no—
840#124—861no—
841#124—861no—
842#124—861no—
843#124—861no—
844#123—862no—
845#123—862no—
846#123—862no—
847#123—861no—
848#123—861no—
849#123—861no—
850#123—861no—
851#123—861no—
852#123—861no—
853#123—861no—
854#123—861no—
855#123—861no—
856#123—861no—
857#123—862no—
858C22⋊Q8—21no—
859C22⋊Q8—21no—
860C22⋊Q8—431no—
861C22⋊Q8—431no—
862C22⋊Q8—431no—
863C22⋊Q8—431no—
864C22⋊Q8—861no—
865C22⋊Q8—861no—
866C22⋊Q8—861no—
867C22⋊Q8—861no—
868C22⋊Q8—861no—
869C22⋊Q8—861no—
870#121—21no—
871#121—432no—
872#121—432no—
873#121—431no—
874#121—431no—
875#121—431no—
876#121—431no—
877#121—432no—
878#121—862no—
879#121—862no—
880#121—862no—
881#121—862no—
882#121—861no—
883#121—861no—
884#121—861no—
885#121C22×D4312yes—
886#120—862no—
887#120—861no—
888#120—861no—
889#120—862no—
890C4×Q8—21no—
891C4×Q8—21no—
892C4×Q8—431no—
893C4×Q8—431no—
894C4×Q8—431no—
895C4×Q8—431no—
896C4×Q8—431no—
897C4×Q8—431no—
898C4×Q8—861no—
899C4×Q8—861no—
900C4×Q8—861no—
901C4×Q8—861no—
902C4×D4—21no—
903C4×D4—431no—
904C4×D4—431no—
905C4×D4—431no—
906C4×D4—431no—
907C4×D4—432no—
908C4×D4—431no—
909C4×D4—431no—
910C4×D4—431no—
911C4×D4—431no—
912C4×D4—432no—
913C4×D4—431no—
914C4×D4—431no—
915C4×D4—432no—
916C4×D4—861no—
917C4×D4—861no—
918C4×D4—861no—
919C4×D4—861no—
920C4×D4—862no—
921C4×D4—861no—
922C4×D4—861no—
923C4×D4—861no—
924C4×D4—861no—
925C4×D4—862no—
926C4×D4—861no—
927C4×D4C22×D4312yes—
928#117—431no—
929#117—431no—
930#117—431no—
931#117—432no—
932#117—861no—
933#117—861no—
934#117—861no—
935#117—861no—
936#117—861no—
937#117—861no—
938#117C22×D4311yescharacteristic
939#117C22×D4311yescharacteristic
940C2×C22⋊C4—862no—
941C2×C22⋊C4—861no—
942C2×C22⋊C4—861no—
943C2×C22⋊C4—862no—
944C2×C22⋊C4—861no—
945C2×C22⋊C4—861no—
946C2×C42—431no—
947C2×C42—431no—
948C2×C42C22×D4311yescharacteristic
949#107—432no—
950#107—432no—
951#107C22×D4312yes—
952#107C22×D4312yes—
953#106—432no—
954#106—432no—
955#106C22×D4312yes—
956#106C22×D4312yes—
957C4⋊C8—432no—
958C4⋊C8—432no—
959C4⋊C8—432no—
960C4⋊C8C22×D4312yes—
961#103—432no—
962#103—432no—
963#103—432no—
964#103—432no—
965#102—432no—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102—432no—
971#102—432no—
972#102—432no—
973#102C22×D4312yes—
974#102C22×D4312yes—
975#102C22×D4312yes—
976#102C22×D4312yes—
977C22⋊C8—432no—
978C22⋊C8—432no—
979C22⋊C8—432no—
980C22⋊C8C22×D4312yes—
981#97—432no—
982#97—431no—
983#97—431no—
984#97C22×D4311yescharacteristic
985#97C22×D4311yescharacteristic
986C4×C8—432no—
987C24—862no—
988C24—861no—
989#41—82no—
990#41—3442no—
991#41—3442no—
992#41—3442no—
993#41—1722no—
994C2×Q8—21no—
995C2×Q8—21no—
996C2×Q8—21no—
997C2×Q8—431no—
998C2×Q8—431no—
999C2×Q8—431no—
1000C2×Q8—861no—
1001C2×Q8—861no—
1002C2×Q8—1722no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—431no—
1007C2×D4—431no—
1008C2×D4—431no—
1009C2×D4—431no—
1010C2×D4—431no—
1011C2×D4—432no—
1012C2×D4—861no—
1013C2×D4—861no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—862no—
1017C2×D4—862no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C2×D4—862no—
1021C2×D4—862no—
1022C2×D4—861no—
1023C2×D4—861no—
1024C2×D4—861no—
1025C2×D4—3442no—
1026C2×D4—3442no—
1027C2×D4—1722no—
1028C2×D4—1722no—
1029C2×D4—1722no—
1030C2×D4C23×D4312yes—
1031C22×C4—22no—
1032C22×C4—431no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—861no—
1039C22×C4—861no—
1040C22×C4—861no—
1041C22×C4—861no—
1042C22×C4—862no—
1043C22×C4—862no—
1044C22×C4—861no—
1045C22×C4—862no—
1046C22×C4D4×D4311yescharacteristic
1047C22×C4D4×D4311yescharacteristic
1048C22×C4C23×D4311yescharacteristic
1049SD16—1722no—
1050SD16—1722no—
1051SD16—1722no—
1052SD16—1722no—
1053D8—1722no—
1054D8—1722no—
1055D8—1722no—
1056D8—1722no—
1057M16—1722no—
1058C2×C8—432no—
1059C2×C8—432no—
1060C2×C8—1722no—
1061C2×C8C23×D4312yes—
1062C2×C8C23×D4312yes—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—431no—
1071C4⋊C4—431no—
1072C4⋊C4—431no—
1073C4⋊C4—431no—
1074C4⋊C4—431no—
1075C4⋊C4—431no—
1076C4⋊C4—432no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—861no—
1084C4⋊C4—861no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—861no—
1088C4⋊C4C23×D4311yescharacteristic
1089C4⋊C4C23×D4311yescharacteristic
1090C4⋊C4C23×D4311yescharacteristic
1091C4⋊C4C23×D4311yescharacteristic
1092C4⋊C4C23×D4312yes—
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—431no—
1098C22⋊C4—431no—
1099C22⋊C4—431no—
1100C22⋊C4—431no—
1101C22⋊C4—431no—
1102C22⋊C4—431no—
1103C22⋊C4—862no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—861no—
1109C22⋊C4—861no—
1110C22⋊C4—861no—
1111C22⋊C4—861no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C22⋊C4—861no—
1117C22⋊C4—861no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—861no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C22⋊C4—861no—
1124C22⋊C4—862no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—862no—
1130C42—21no—
1131C42—21no—
1132C42—431no—
1133C42—431no—
1134C42—431no—
1135C42—431no—
1136C42—431no—
1137C42—431no—
1138C42—862no—
1139C42—861no—
1140C42—861no—
1141C42—861no—
1142C42—861no—
1143C42D4×D4311yescharacteristic
1144C42D4×D4311yescharacteristic
1145C42C23×D4311yescharacteristic
1146C42C23×D4311yescharacteristic
1147C23—22no—
1148C23—431no—
1149C23—431no—
1150C23—861no—
1151C23—861no—
1152C23—862no—
1153C23—3441no—
1154C23—3441no—
1155C23—3442no—
1156C23—3442no—
1157C23—1722no—
1158C23—1724no—
1159C23C2×D4×D4311yescharacteristic
1160Q8—42no—
1161Q8—81no—
1162Q8—81no—
1163Q8—862no—
1164Q8—862no—
1165Q8—1721no—
1166Q8—1722no—
1167Q8—1722no—
1168D4—22no—
1169D4—22no—
1170D4—42no—
1171D4—42no—
1172D4—82no—
1173D4—862no—
1174D4—862no—
1175D4—862no—
1176D4—862no—
1177D4—3442no—
1178D4—3441no—
1179D4—3441no—
1180D4—3441no—
1181D4—3441no—
1182D4—3442no—
1183D4—3442no—
1184D4—3442no—
1185D4—3442no—
1186D4—1721no—
1187D4—1722no—
1188D4—1722no—
1189D4—1722no—
1190D4—1721no—
1191D4—1721no—
1192D4—1724no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—82no—
1202C2×C4—431no—
1203C2×C4—431no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—431no—
1207C2×C4—431no—
1208C2×C4—862no—
1209C2×C4—862no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—862no—
1213C2×C4—3442no—
1214C2×C4—3442no—
1215C2×C4—3441no—
1216C2×C4—3441no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—3442no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1722no—
1225C2×C4C2×D4×D4311yescharacteristic
1226C2×C4C2×D4×D4311yescharacteristic
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4C2×D4×D4311yescharacteristic
1229C2×C4C2×D4×D4311yescharacteristic
1230C2×C4C24×D4311yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—862no—
1234C8—862no—
1235C22—21no—
1236C22—21no—
1237C22—21no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—861no—
1242C22—861no—
1243C22—861no—
1244C22—861no—
1245C22—861no—
1246C22—861no—
1247C22—1722no—
1248C22—1721no—
1249C22—1721no—
1250C22—1722no—
1251C22—1721no—
1252C22—1721no—
1253C22—1721no—
1254C22—1721no—
1255C22—1722no—
1256C22—6882no—
1257C22—6884no—
1258C22C22×D4×D4311yescharacteristic
1259C4—21no—
1260C4—21no—
1261C4—21no—
1262C4—21no—
1263C4—21no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—861no—
1270C4—861no—
1271C4—861no—
1272C4—861no—
1273C4—861no—
1274C4—861no—
1275C4—1722no—
1276C4—1721no—
1277C4—1721no—
1278C4#1458373612yes—
1279C2—41no—
1280C2—82no—
1281C2—3442no—
1282C2—3441no—
1283C2—3441no—
1284C2—1721no—
1285C2—1721no—
1286C2#1914792711yescharacteristic
1287C2#1914937111yescharacteristic
1288C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3235C2
socleC22×C43C23×D4
hypercenter#3235D43
hypocenterC43#61017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
1. #19148493C2semidirect
2. #19148464C2semidirect
3. #19146013C2semidirect
4. #19146005C2semidirect
5. #19145838C2semidirect
6. #19145836C2semidirect
7. #19145793C2semidirect
8. #19145614C2semidirect
9. #19145614C2semidirect
10. #19145584C2semidirect
11. #19145578C2semidirect
12. #19145469C2semidirect
13. #19145459C2semidirect
14. #19145295C2semidirect
15. #19145292C2semidirect
16. #19145192C2semidirect
17. #19145189C2semidirect
18. #19144882C2semidirect
19. #19144834C2semidirect
20. #19144786C2semidirect
21. #19144784C2semidirect
22. #19143241C2semidirect
23. C43×#3235C2semidirect
42. #14583523C22semidirect
43. #14583523C22semidirect
45. #14583500C22semidirect
49. #14583454C22semidirect
50. #14583450C22semidirect
52. #14583447C22semidirect
53. #127×D43C22semidirect
56. #14583434C22semidirect
57. #14583434C22semidirect
58. C2×#13063313C22semidirect
59. #14583376C22semidirect
60. #14583373C22semidirect
61. #14583371C22semidirect
63. #14583309C22semidirect
64. #14583309C22semidirect
69. #14583265C22semidirect
70. #14583265C22semidirect
71. #14583261C22semidirect
72. #14583261C22semidirect
73. #14583259C22semidirect
74. #14583259C22semidirect
75. #14583243C22semidirect
76. #14583242C22semidirect
79. #14583223C22semidirect
80. #14583223C22semidirect
81. #14583209C22semidirect
82. #14583205C22semidirect
83. #14583202C22semidirect
84. #14583198C22semidirect
85. #14583186C22semidirect
86. #14583176C22semidirect
87. #14583153C22semidirect
88. #14583151C22semidirect
89. #14583146C22semidirect
90. #14583144C22semidirect
91. #14583136C22semidirect
92. #14583134C22semidirect
93. #14583129C22semidirect
94. #14583127C22semidirect
95. #14583115C22semidirect
96. #14583115C22semidirect
97. #14583114C22semidirect
98. #14583114C22semidirect
99. #14583098C22semidirect
100. #14583098C22semidirect
103. #14583051C22semidirect
104. #14583051C22semidirect
105. #14583040C22semidirect
106. #14583037C22semidirect
107. #14583035C22semidirect
110. #14583032C22semidirect
111. #14583010C22semidirect
112. #14583008C22semidirect
113. #14582998C22semidirect
114. #14582996C22semidirect
115. #14582990C22semidirect
116. #14582986C22semidirect
117. #14582981C22semidirect
118. #14582979C22semidirect
119. #14582959C22semidirect
120. #14582957C22semidirect
121. #14582956C22semidirect
122. #14582954C22semidirect
123. #14582954C22semidirect
124. #14582924C22semidirect
126. #14582851C22semidirect
127. #97×D43C22semidirect
128. C43×#533C22semidirect
130. C43×#501C22semidirect
131. C43×#501C22semidirect
132. C43×#490C22semidirect
133. C43×#490C22semidirect
134. C43×#482C22semidirect
135. C43×#482C22semidirect
136. C43×#476C22semidirect
137. C43×#474C22semidirect
138. C43×#432C22semidirect
642. #3235D43semidirect
694. #533C2×D43semidirect
711. #501C2×D43semidirect
712. #501C2×D43semidirect
719. #490C2×D43semidirect
720. #490C2×D43semidirect
731. #482C2×D43semidirect
732. #482C2×D43semidirect
738. #476C2×D43semidirect
740. #474C2×D43semidirect
778. #432C2×D43semidirect
783. C43#61017semidirect

Maximal subgroups

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

subgroupindex
#191484932
#191484642
#191460132
#191460052
#191458382
#191458362
#191457932
#191456142
#191455842
#191455782
#191454692
#191454592
#191452952
#191452922
#191451922
#191451892
#191448822
#191448342
#191447862
#191447842
#191432412
C43×#32352
#6101743