Finite Group Databasebeta

← #25974036

Subgroups — #25974036

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148305C211yesmaximal, characteristic, complemented
2#19148240C211yesmaximal, characteristic, complemented
3#19146908C212yesmaximal, complemented
4#19146897C212yesmaximal, complemented
5#19146808C212yesmaximal, complemented
6#19146793C212yesmaximal, complemented
7#19146688C212yesmaximal, complemented
8#19146673C212yesmaximal, complemented
9#19146568C212yesmaximal, complemented
10#19146553C212yesmaximal, complemented
11#19144965C211yesmaximal, characteristic, complemented
12#19144567C211yesmaximal, characteristic, complemented
13#19144521C211yesmaximal, characteristic, complemented
14#19144287C211yesmaximal, characteristic, complemented
15#19144205C211yesmaximal, characteristic, complemented
16#19144147C211yesmaximal, characteristic, complemented
17#19143904C211yesmaximal, characteristic, complemented
18#19143839C211yesmaximal, characteristic, complemented
19#19143427C211yesmaximal, characteristic, complemented
20#19143297C211yesmaximal, characteristic, complemented
21#19143120C211yesmaximal, characteristic, complemented
22C2×#14582897C211yesmaximal, characteristic, complemented
23C43×#3081C211yesmaximal, characteristic, complemented
24C2×#13063370C2211yescharacteristic
25C22×#10621900C2211yescharacteristic
26C2×#13063358C2211yescharacteristic, complemented
27C2×#13063351C2211yescharacteristic
28C2×#13063347C2211yescharacteristic
29C2×#13063333C2211yescharacteristic
30C22×#10621872C2211yescharacteristic, complemented
31#14583610—21no—
32#14583610C2212yescomplemented
33#14583602—21no—
34#14583602C2212yescomplemented
35#14583587—21no—
36#14583587C2212yescomplemented
37#14583553—21no—
38#14583553—21no—
39#14583553C2212yes—
40#14583553C2212yes—
41#14583552—21no—
42#14583552C2212yescomplemented
43#14583544—21no—
44#14583544—21no—
45#14583544C2212yes—
46#14583544C2212yes—
47#14583498—22no—
48#14583480C2211yescharacteristic
49#14583475C2211yescharacteristic
50#14583475C2211yescharacteristic
51#14583461—22no—
52#14583412—22no—
53#14583411C2211yescharacteristic
54#14583411C2211yescharacteristic
55#14583411C2211yescharacteristic, complemented
56C2×#13063309—22no—
57#14583379C2211yescharacteristic
58#14583379C2211yescharacteristic, complemented
59C2×C4⋊C4×D43C2211yescharacteristic, complemented
60#14583269C2212yescomplemented
61#14583261C2212yescomplemented
62#14583256C2212yescomplemented
63#14583251C2212yescomplemented
64#14583243C2212yescomplemented
65#14583242C2212yescomplemented
66#14583236C2212yescomplemented
67#14583236C2212yescomplemented
68#14583231C2212yescomplemented
69#14583231C2212yescomplemented
70#14583219C2212yescomplemented
71#14583214C2212yescomplemented
72#14583158C2211yescharacteristic, complemented
73#14583158C2211yescharacteristic, complemented
74#14583158C2212yescomplemented
75#14583153C2211yescharacteristic, complemented
76#14583153C2211yescharacteristic, complemented
77#14583146C2211yescharacteristic, complemented
78#14583146C2211yescharacteristic, complemented
79#14583146C2211yescharacteristic, complemented
80#14583146C2211yescharacteristic, complemented
81#14583146C2212yescomplemented
82#14583141C2212yescomplemented
83#14583129C2212yescomplemented
84#14583122C2212yescomplemented
85#14583115C2212yescomplemented
86#14583110C2212yescomplemented
87#14583105C2212yescomplemented
88#14583062C2212yescomplemented
89#14583062C2212yescomplemented
90#14583062C2212yescomplemented
91#14583051C2212yescomplemented
92#14583045C2212yescomplemented
93#14583045C2212yescomplemented
94#14583045C2212yescomplemented
95#14583034C2212yescomplemented
96#14583009C2212yescomplemented
97#14582999C2212yescomplemented
98C4×#10621883C2212yescomplemented
99C4×#10621882C2212yescomplemented
100#14582976C2212yescomplemented
101#14582976C2212yescomplemented
102#14582969C2212yescomplemented
103#14582969C2212yescomplemented
104#14582942C2211yescharacteristic, complemented
105#14582907C2211yescharacteristic, complemented
106#14582902C2212yescomplemented
107#14582901C2211yescharacteristic
108#14582898C2211yescharacteristic
109#14582897C2212yescomplemented
110#14582897C2212yescomplemented
111#14582897C2212yescomplemented
112#14582897C2212yescomplemented
113#14582897C2212yescomplemented
114#14582893C2211yescharacteristic
115#14582893C2211yescharacteristic, complemented
116#14582892C2212yescomplemented
117C2×#13063250C2211yescharacteristic, complemented
118C2×#13063248C2211yescharacteristic, complemented
119C2×#13063246C2211yescharacteristic
120#102×D43C2212yescomplemented
121#14582865C2211yescharacteristic
122#14582862C2211yescharacteristic, complemented
123#14582855C2211yescharacteristic, complemented
124C43×#544C2211yescharacteristic, complemented
125C43×#518C2211yescharacteristic
126C43×#478C2212yescomplemented
127C43×#478C2212yescomplemented
128C43×#476C2212yescomplemented
129C43×#474C2212yescomplemented
130C43×#428C2211yescharacteristic, complemented
131C43×#427C2211yescharacteristic, complemented
132C43×#424C2211yescharacteristic, complemented
133C43×#418C2211yescharacteristic
134C2×#102×C43C2211yescharacteristic
135#13063370—24no—
136#13063370—42no—
137C2×#10621902—22no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2311yescharacteristic
141C2×#10621900—24no—
142C2×#10621900—21no—
143C2×#10621900—21no—
144C2×#10621900—21no—
145C2×#10621900—42no—
146C2×#10621900C2312yes—
147C2×#10621900C2312yes—
148C2×#10621900C2312yes—
149C22×Dic86C2311yescharacteristic
150C22×C22⋊D43—21no—
151C22×C22⋊D43—22no—
152C2×D4×D43—21no—
153C2×D4×D43C2312yes—
154C23×Dic43—21no—
155C22×C4×D43—21no—
156C22×C4×D43C2311yescharacteristic
157#13063358—42no—
158#13063351—24no—
159#13063347—42no—
160C2×Dic172C2311yescharacteristic
161C2×Dic172C2312yes—
162C2×#10621873C2311yescharacteristic
163C2×#10621873C2312yes—
164C2×#10621873C2311yescharacteristic
165C2×#10621883C2312yes—
166C2×D344C2311yescharacteristic
167C2×#10621882C2312yes—
168#13063333—42no—
169C2×#10621877C2311yescharacteristic
170C2×#10621872—42no—
171C2×#10621872C2311yescharacteristic
172C2×#10621872C2311yescharacteristic
173C2×#10621872C2312yes—
174C2×#10621872C2311yescharacteristic
175C2×#10621872C2311yescharacteristic
176C22×C43⋊C8C2311yescharacteristic
177C2×C8×D43C2312yes—
178#13063325—21no—
179#13063325C2312yes—
180#13063320—22no—
181#13063320—22no—
182#13063316—22no—
183#13063316—22no—
184#13063313—21no—
185#13063313C2312yes—
186#13063310—22no—
187#13063310—22no—
188#13063310—22no—
189#13063310—22no—
190#13063309—22no—
191#13063309—21no—
192#13063309—21no—
193#13063309—22no—
194#13063309—22no—
195#13063309—22no—
196#13063309—22no—
197#13063309—22no—
198#13063309—22no—
199#13063309—22no—
200#13063309D412yes—
201#13063305—21no—
202#13063305—21no—
203#13063305—21no—
204#13063305D411yescharacteristic
205#13063305D411yescharacteristic
206#13063305C2311yescharacteristic
207#13063305C2311yescharacteristic
208#13063305C2312yes—
209#13063305C2312yes—
210#13063305C2312yes—
211#13063305C2311yescharacteristic
212#13063305C2311yescharacteristic
213#13063301—22no—
214#13063301—22no—
215#13063301—22no—
216#13063300—21no—
217#13063300—22no—
218#13063300D411yescharacteristic
219#13063300D411yescharacteristic
220#13063300C2311yescharacteristic
221#13063300C2312yes—
222#13063300C2311yescharacteristic
223#13063300C2311yescharacteristic
224#13063300C2311yescharacteristic
225#13063299—22no—
226#13063299—22no—
227#13063299—22no—
228#13063299—22no—
229#13063299—22no—
230#13063295—21no—
231#13063295—21no—
232#13063295—22no—
233#13063295—22no—
234#13063295D412yes—
235C4×Dic86—21no—
236C4×Dic86C2312yes—
237C4×D172—21no—
238C4×D172—21no—
239C4×D172—21no—
240C4×D172—21no—
241C4×D172—21no—
242C4×D172C2312yes—
243C4×D172C2312yes—
244C4×D172C2312yes—
245#13063287—22no—
246#13063287—22no—
247(C22⋊D43)⋊C4—22no—
248(C22⋊D43)⋊C4—22no—
249#13063283—21no—
250#13063283—22no—
251#13063283C2312yes—
252C2×C4⋊Dic43—22no—
253C2×C4⋊Dic43—22no—
254C2×C4⋊Dic43C2311yescharacteristic
255C2×Dic43⋊C4—21no—
256C4⋊C4×D43—21no—
257C4⋊C4×D43—21no—
258C4⋊C4×D43—21no—
259C4⋊C4×D43C2312yes—
260C4⋊C4×D43C2312yes—
261C4⋊C4×D43C2312yes—
262C2×(C2×D43)⋊C4—22no—
263C2×(C2×D43)⋊C4—22no—
264#13063258C2312yes—
265#13063256C2312yes—
266#13063250C2312yes—
267#13063250C2312yes—
268#13063250C2312yes—
269#13063248C2312yes—
270#13063248C2312yes—
271#13063248C2312yes—
272#13063248C2312yes—
273#13063248C2311yescharacteristic
274#13063248C2312yes—
275#13063248C2311yescharacteristic
276#13063248C2311yescharacteristic
277#13063248C2311yescharacteristic
278#13063247C2312yes—
279#13063246C2312yes—
280#13063246C2312yes—
281#13063245C2312yes—
282#13063245C2311yescharacteristic
283#13063245C2311yescharacteristic
284#13063245C2311yescharacteristic
285#13063245C2311yescharacteristic
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288(C2×D43)⋊C8C2312yes—
289(C2×D43)⋊C8C2312yes—
290#13063236C2312yes—
291C4×C43⋊C8C2312yes—
292C22×D4×C43C2311yescharacteristic
293C2×M16×C43C2311yescharacteristic
294C22×C8×C43C2311yescharacteristic
295C4⋊Q8×C43—21no—
296C4⋊Q8×C43C2312yes—
297#125×C43—21no—
298#125×C43C2312yes—
299C22⋊Q8×C43—22no—
300C4×D4×C43—21no—
301C4×D4×C43—21no—
302C4×D4×C43C2312yes—
303C4×D4×C43C2312yes—
304#117×C43C2311yescharacteristic
305#117×C43C2311yescharacteristic
306#117×C43C2311yescharacteristic
307C2×C4⋊C4×C43C2311yescharacteristic
308C2×C22⋊C4×C43—22no—
309#107×C43C2312yes—
310#107×C43C2311yescharacteristic
311#107×C43C2311yescharacteristic
312#106×C43C2312yes—
313#106×C43C2311yescharacteristic
314#106×C43C2311yescharacteristic
315C4⋊C8×C43C2312yes—
316C4⋊C8×C43C2312yes—
317#102×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321C24×C43—21no—
322C23×D43—22no—
323C23×D43C2×D411yescharacteristic
324C2×Q8×C43—22no—
325C2×D4×C43—21no—
326C2×D4×C43—22no—
327C2×D4×C43#4114yescomplemented
328C2×D4×C43C2412yes—
329C22×C4×C43—22no—
330C22×C4×C43—22no—
331C22×C4×C43—21no—
332C22×C4×C43C2411yescharacteristic
333C2×C22⋊D43—22no—
334C2×C22⋊D43—21no—
335C2×C22⋊D43—21no—
336C2×C22⋊D43—22no—
337C2×C22⋊D43—22no—
338C2×C22⋊D43—22no—
339C2×C22⋊D43—44no—
340C2×C22⋊D43—48no—
341C2×C22⋊D43C2×D412yes—
342C22×Dic43—22no—
343C22×Dic43—22no—
344C22×Dic43—22no—
345C22×Dic43—21no—
346C22×Dic43—21no—
347C22×Dic43—44no—
348C22×Dic43C2×D411yescharacteristic
349#10621902—84no—
350#10621900—24no—
351#10621900—24no—
352#10621900—24no—
353#10621900—42no—
354#10621900—42no—
355#10621900—42no—
356#10621900—44no—
357#10621900—44no—
358#10621900—44no—
359D4×D43—24no—
360D4×D43—42no—
361D4×D43—44no—
362#10621898—22no—
363#10621898—22no—
364#10621898—22no—
365#10621898—22no—
366#10621898—22no—
367#10621898—22no—
368C2×D172—21no—
369C2×D172—21no—
370C2×D172—21no—
371C2×D172—21no—
372C2×D172—22no—
373C2×D172C2×D411yescharacteristic
374C2×D172C2×D412yes—
375C2×D172C2×D412yes—
376C2×D172C2411yescharacteristic
377C2×D172C2411yescharacteristic
378C2×C4×D43—22no—
379C2×C4×D43—22no—
380C2×C4×D43—21no—
381C2×C4×D43—21no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—22no—
386C2×C4×D43—82no—
387C2×C4×D43C2×D411yescharacteristic
388C2×C4×D43C2×D411yescharacteristic
389C2×C4×D43C2411yescharacteristic
390C2×C4×D43C2411yescharacteristic
391C2×C4×D43C2412yes—
392C2×Dic86—22no—
393C2×Dic86—22no—
394C2×Dic86—21no—
395C2×Dic86C2×D411yescharacteristic
396C2×Dic86C2412yes—
397C2×Dic86C2411yescharacteristic
398C2×Dic86C2411yescharacteristic
399M16×C43—22no—
400C2×C8×C43—22no—
401C2×C8×C43C2411yescharacteristic
402C2×C8×C43C2412yes—
403C2×C8×C43C2411yescharacteristic
404C4⋊C4×C43—21no—
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43—22no—
408C4⋊C4×C43C2×D411yescharacteristic
409C4⋊C4×C43C2×D411yescharacteristic
410C4⋊C4×C43C2412yes—
411C4⋊C4×C43C2411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C22⋊C4×C43—22no—
416C22⋊C4×C43—22no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C22⋊C4×C43C2×D412yes—
420C42×C43—21no—
421C42×C43—21no—
422C42×C43C2412yes—
423#10621883—24no—
424#10621882—24no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—21no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—21no—
440(C2×D43)⋊C4—21no—
441(C2×D43)⋊C4C2×D412yes—
442(C2×D43)⋊C4C2×D412yes—
443(C2×D43)⋊C4C2×D412yes—
444(C2×D43)⋊C4C2×D412yes—
445C4⋊Dic43—21no—
446C4⋊Dic43—22no—
447C4⋊Dic43—22no—
448C4⋊Dic43—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—22no—
451C4⋊Dic43—22no—
452C4⋊Dic43—22no—
453C4⋊Dic43—21no—
454C4⋊Dic43—21no—
455C4⋊Dic43C2×D412yes—
456C4⋊Dic43C2×D412yes—
457C4⋊Dic43C2412yes—
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462C4×Dic43—22no—
463C4×Dic43—22no—
464#10621877—22no—
465C2×C43⋊C8—22no—
466C2×C43⋊C8C2411yescharacteristic
467C2×C43⋊C8C2412yes—
468C2×C43⋊C8C2411yescharacteristic
469Dic172—41no—
470Dic172—42no—
471D344—41no—
472#10621873—41no—
473#10621873—41no—
474#10621873—42no—
475#10621872—41no—
476#10621872—41no—
477#10621872—41no—
478#10621872—41no—
479#10621872—42no—
480C8×D43—42no—
481C23×C43—22no—
482C23×C43—24no—
483C23×C43—81no—
484C23×C43—81no—
485C23×C43C22×D411yescharacteristic
486C22×D43—22no—
487C22×D43—21no—
488C22×D43—21no—
489C22×D43—41no—
490C22×D43—41no—
491C22×D43—44no—
492C22×D43—82no—
493C22×D43—82no—
494C22×D43C22×D412yes—
495C22×D43C22×D411yescharacteristic
496C22×D43C22×D411yescharacteristic
497Q8×C43—82no—
498D4×C43—24no—
499D4×C43—22no—
500D4×C43C2×#4114yes—
501C2×C4×C43—21no—
502C2×C4×C43—21no—
503C2×C4×C43—22no—
504C2×C4×C43—21no—
505C2×C4×C43—21no—
506C2×C4×C43—82no—
507C2×C4×C43—82no—
508C2×C4×C43—81no—
509C2×C4×C43C22×D412yes—
510C2×C4×C43C22×D412yes—
511C2×C4×C43C22×D411yescharacteristic
512C2×C4×C43C2×#4112yes—
513C2×C4×C43H(5,𝔽2)12yes—
514C2×C4×C43C2511yescharacteristic
515C22⋊D43—24no—
516C22⋊D43—44no—
517C22⋊D43—44no—
518C22⋊D43—44no—
519C22⋊D43—44no—
520C22⋊D43—42no—
521C22⋊D43—42no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—21no—
525C2×Dic43—21no—
526C2×Dic43—22no—
527C2×Dic43—44no—
528C2×Dic43—44no—
529C2×Dic43—44no—
530C2×Dic43—42no—
531C2×Dic43—81no—
532C2×Dic43C22×D412yes—
533C2×Dic43C22×D411yescharacteristic
534C2×Dic43C22×D411yescharacteristic
535D172—22no—
536D172—21no—
537D172—21no—
538D172—21no—
539D172—21no—
540D172—42no—
541D172—42no—
542D172—42no—
543D172—42no—
544D172—81no—
545D172—81no—
546D172—82no—
547C4×D43—22no—
548C4×D43—22no—
549C4×D43—21no—
550C4×D43—21no—
551C4×D43—22no—
552C4×D43—22no—
553C4×D43—21no—
554C4×D43—21no—
555C4×D43—44no—
556C4×D43—42no—
557C4×D43—42no—
558C4×D43—82no—
559C4×D43—82no—
560C4×D43—82no—
561Dic86—22no—
562Dic86—21no—
563Dic86—22no—
564Dic86—21no—
565Dic86—21no—
566Dic86—22no—
567Dic86—21no—
568Dic86—42no—
569C8×C43—22no—
570C8×C43—21no—
571C8×C43—21no—
572C43⋊C8—22no—
573C43⋊C8—21no—
574C43⋊C8—21no—
575#61177—431nomaximal, Sylow
576C22×C43—21no—
577C22×C43—21no—
578C22×C43—24no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—84no—
582C22×C43#54612yes—
583C22×C43C23×D411yescharacteristic
584C2×D43—21no—
585C2×D43—21no—
586C2×D43—22no—
587C2×D43—21no—
588C2×D43—21no—
589C2×D43—22no—
590C2×D43—21no—
591C2×D43—21no—
592C2×D43—22no—
593C2×D43—44no—
594C2×D43—41no—
595C2×D43—41no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—41no—
600C2×D43—164no—
601C4×C43—22no—
602C4×C43—22no—
603C4×C43—42no—
604C4×C43—41no—
605C4×C43—41no—
606C4×C43—41no—
607C4×C43—41no—
608C4×C43#54612yes—
609C4×C43C22×#4111yescharacteristic
610C4×C43C2×H(5,𝔽2)11yescharacteristic
611Dic43—22no—
612Dic43—21no—
613Dic43—21no—
614Dic43—42no—
615Dic43—42no—
616Dic43—41no—
617Dic43—41no—
618#3492—431no—
619#3485—431no—
620#3331—432no—
621#3330—432no—
622#3323—432no—
623#3322—432no—
624#3315—432no—
625#3314—432no—
626#3307—432no—
627#3306—432no—
628#3137—431no—
629#3097—431no—
630#3092—431no—
631#3081D4311yescharacteristic, complemented
632#3063—431no—
633#3054—431no—
634#3046—431no—
635#3012—431no—
636#3005—431no—
637#2946—431no—
638#2930—431no—
639#2897—431no—
640C2×#417—431no—
641C2×C43—22no—
642C2×C43—44no—
643C2×C43C2×#54611yescharacteristic
644C2×C43#358511yescharacteristic
645C2×C43#358611yescharacteristic
646D43—41no—
647D43—41no—
648D43—42no—
649D43—81no—
650D43—81no—
651C2×H(5,𝔽2)—431no—
652C22×#41—431no—
653C2×#137—431no—
654C2×AGL(1,ℤ/8)—431no—
655C2×#135—431no—
656C2×#131—431no—
657C22×M16—431no—
658#554—432no—
659#554—861no—
660#553—432no—
661#553—861no—
662#552—432no—
663#552—861no—
664#547—432no—
665#547—432no—
666#547—432no—
667#547—861no—
668#547—861no—
669#547—861no—
670#546—432no—
671#546—432no—
672#546—861no—
673#546—861no—
674#544C2×D4311yescharacteristic, complemented
675#539—862no—
676#537—431no—
677#536—431no—
678#536—431no—
679#534—862no—
680#525—431no—
681#525—431no—
682#525—431no—
683#525—862no—
684C2×#123—862no—
685#520—431no—
686#520—431no—
687#518C2×D4311yescharacteristic
688C22×C4⋊C4—431no—
689#491—432no—
690#489—432no—
691#488—432no—
692#487—432no—
693#485—432no—
694#485—432no—
695#484—432no—
696#484—432no—
697#483—432no—
698#483—432no—
699#481—432no—
700#480—432no—
701#478C2×D4312yescomplemented
702#478C2×D4312yescomplemented
703#476C2×D4312yescomplemented
704#474C2×D4312yescomplemented
705#470—431no—
706#470—432no—
707#470—431no—
708#469—431no—
709#469—431no—
710#468—431no—
711#468—432no—
712#468—431no—
713#468—431no—
714#468—431no—
715#467—432no—
716#465—432no—
717#464—432no—
718#463—432no—
719#462—432no—
720#461—432no—
721#452—432no—
722#452—432no—
723#452—432no—
724#450—432no—
725#449—432no—
726#449—432no—
727#449—432no—
728#447—432no—
729#442—432no—
730#440—432no—
731C4×SD16—432no—
732C4×D8—432no—
733#436—432no—
734#436—432no—
735#435—432no—
736#435—432no—
737#428—431no—
738#428C2×D4311yescharacteristic, complemented
739#427C2×D4311yescharacteristic, complemented
740#424C2×D4311yescharacteristic, complemented
741#419—431no—
742#418—432no—
743#418C2×D4311yescharacteristic
744#417—431no—
745#417—431no—
746#417—432no—
747#417—432no—
748#417—432no—
749#417—432no—
750#417—432no—
751#416—431no—
752#416—431no—
753#416—432no—
754C2×#103—431no—
755C2×#103—431no—
756C2×#102—431no—
757C2×#102—432no—
758C2×#102C2×D4311yescharacteristic
759#408—431no—
760#407—431no—
761#405—431no—
762C43#6117711yescharacteristic, complemented, Sylow
763H(5,𝔽2)—864no—
764H(5,𝔽2)—1722no—
765C2×#41—431no—
766C2×#41—432no—
767C2×#41—432no—
768C2×#41—432no—
769C2×#41—431no—
770C2×#41—431no—
771C2×#41—861no—
772C2×#41—861no—
773C2×#41—861no—
774C2×#41—862no—
775C2×#41—864no—
776C2×#41—1722no—
777C22×Q8—431no—
778C22×D4—432no—
779C22×D4—861no—
780C22×D4—862no—
781C22×D4—861no—
782C22×D4C22×D4311yescharacteristic
783C23×C4—431no—
784C23×C4—861no—
785C23×C4—861no—
786#137—1722no—
787AGL(1,ℤ/8)—864no—
788#135—1722no—
789C2×Q16—431no—
790C2×Q16—432no—
791C2×SD16—432no—
792C2×SD16—431no—
793C2×SD16—431no—
794C2×SD16—432no—
795C2×D8—432no—
796C2×D8—431no—
797#131—1722no—
798C2×M16—431no—
799C2×M16—431no—
800C2×M16—431no—
801C2×M16—431no—
802C2×M16—431no—
803C2×M16—432no—
804C2×M16—1722no—
805C2×M16C22×D4311yescharacteristic
806C22×C8—431no—
807C22×C8—432no—
808C22×C8C22×D4311yescharacteristic
809C4⋊Q8—21no—
810C4⋊Q8—432no—
811C4⋊Q8—861no—
812C4⋊Q8C22×D4312yes—
813#126—862no—
814#126—862no—
815#125—21no—
816#125—862no—
817#125—862no—
818#125C22×D4312yes—
819#124—432no—
820#124—861no—
821#123—432no—
822#123—862no—
823#123—862no—
824#123—862no—
825#123—862no—
826#123—862no—
827#123—862no—
828#123—861no—
829#123—861no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—862no—
835#123—862no—
836C22⋊Q8—22no—
837C22⋊Q8—431no—
838C22⋊Q8—431no—
839C22⋊Q8—431no—
840C22⋊Q8—431no—
841C22⋊Q8—431no—
842C22⋊Q8—431no—
843C22⋊Q8—432no—
844C22⋊Q8—432no—
845C22⋊Q8—432no—
846C22⋊Q8—862no—
847C22⋊Q8—862no—
848C22⋊Q8—861no—
849C22⋊Q8—862no—
850C22⋊Q8—861no—
851C22⋊Q8—861no—
852#121—431no—
853#121—431no—
854#121—431no—
855#121—431no—
856#121—431no—
857#121—431no—
858#121—432no—
859#121—862no—
860#121—862no—
861#121—862no—
862#121—861no—
863#121—862no—
864#121—862no—
865#121—862no—
866#120—432no—
867#120—862no—
868#120—862no—
869#120—861no—
870#120—861no—
871C4×Q8—432no—
872C4×Q8—861no—
873C4×D4—21no—
874C4×D4—21no—
875C4×D4—432no—
876C4×D4—432no—
877C4×D4—432no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4—862no—
884C4×D4—862no—
885C4×D4—862no—
886C4×D4—862no—
887C4×D4C22×D4312yes—
888C4×D4C22×D4312yes—
889#117—432no—
890#117—862no—
891#117—861no—
892#117C22×D4311yescharacteristic
893#117C22×D4311yescharacteristic
894#117C22×D4311yescharacteristic
895C2×C4⋊C4—431no—
896C2×C4⋊C4—432no—
897C2×C4⋊C4—432no—
898C2×C4⋊C4—432no—
899C2×C4⋊C4—861no—
900C2×C4⋊C4—861no—
901C2×C4⋊C4—862no—
902C2×C4⋊C4—862no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4C22×D4311yescharacteristic
906C2×C22⋊C4—22no—
907C2×C22⋊C4—862no—
908C2×C22⋊C4—862no—
909#107—432no—
910#107C22×D4311yescharacteristic
911#107C22×D4311yescharacteristic
912#107C22×D4312yes—
913#106—432no—
914#106C22×D4311yescharacteristic
915#106C22×D4311yescharacteristic
916#106C22×D4312yes—
917C4⋊C8C22×D4312yes—
918C4⋊C8C22×D4312yes—
919#103—432no—
920#103—432no—
921#103—432no—
922#103—432no—
923#103—432no—
924#103—431no—
925#103—431no—
926#103—431no—
927#103—431no—
928#103—432no—
929#103—432no—
930#103—432no—
931#102—432no—
932#102—432no—
933#102—432no—
934#102—431no—
935#102—431no—
936#102—431no—
937#102—431no—
938#102—432no—
939#102C22×D4312yes—
940#102C22×D4312yes—
941#102C22×D4312yes—
942#102C22×D4312yes—
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8—432no—
946C22⋊C8—432no—
947#97—432no—
948C4×C8—432no—
949C24—21no—
950C24—431no—
951C24—862no—
952#41—862no—
953#41—862no—
954#41—864no—
955#41—864no—
956#41—864no—
957#41—862no—
958#41—862no—
959#41—862no—
960#41—862no—
961#41—3444no—
962#41—1722no—
963#41—1722no—
964#41—1722no—
965#41—1724no—
966#41—1724no—
967#41—1724no—
968C2×Q8—22no—
969C2×Q8—431no—
970C2×Q8—432no—
971C2×Q8—431no—
972C2×Q8—431no—
973C2×Q8—861no—
974C2×Q8—862no—
975C2×Q8—862no—
976C2×D4—21no—
977C2×D4—22no—
978C2×D4—432no—
979C2×D4—431no—
980C2×D4—432no—
981C2×D4—432no—
982C2×D4—431no—
983C2×D4—431no—
984C2×D4—861no—
985C2×D4—861no—
986C2×D4—862no—
987C2×D4—861no—
988C2×D4—861no—
989C2×D4—862no—
990C2×D4—864no—
991C2×D4—862no—
992C2×D4—862no—
993C2×D4—862no—
994C2×D4—861no—
995C2×D4—861no—
996C2×D4—1722no—
997C2×D4—1724no—
998C2×D4—1728no—
999C2×D4—1724no—
1000C2×D4#1062190214yescomplemented
1001C2×D4C23×D4312yes—
1002C22×C4—21no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—432no—
1011C22×C4—862no—
1012C22×C4—862no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—862no—
1016C22×C4—862no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—862no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—3442no—
1025C22×C4—1724no—
1026C22×C4C23×D4311yescharacteristic
1027Q16—1721no—
1028Q16—1722no—
1029SD16—864no—
1030SD16—1721no—
1031SD16—1721no—
1032SD16—1722no—
1033D8—864no—
1034D8—1721no—
1035M16—22no—
1036M16—862no—
1037M16—1721no—
1038M16—1721no—
1039M16—1721no—
1040M16—1721no—
1041M16—1722no—
1042C2×C8—22no—
1043C2×C8—431no—
1044C2×C8—432no—
1045C2×C8—431no—
1046C2×C8—862no—
1047C2×C8—1722no—
1048C2×C8C23×D4312yes—
1049C2×C8C23×D4311yescharacteristic
1050C2×C8C23×D4311yescharacteristic
1051C4⋊C4—21no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—432no—
1056C4⋊C4—432no—
1057C4⋊C4—432no—
1058C4⋊C4—862no—
1059C4⋊C4—862no—
1060C4⋊C4—862no—
1061C4⋊C4—861no—
1062C4⋊C4—861no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4D4×D4311yescharacteristic
1073C4⋊C4D4×D4311yescharacteristic
1074C4⋊C4C23×D4312yes—
1075C4⋊C4C23×D4311yescharacteristic
1076C4⋊C4C23×D4311yescharacteristic
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C22⋊C4—21no—
1080C22⋊C4—21no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—432no—
1084C22⋊C4—432no—
1085C22⋊C4—432no—
1086C22⋊C4—432no—
1087C22⋊C4—861no—
1088C22⋊C4—861no—
1089C22⋊C4—862no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—862no—
1100C22⋊C4—862no—
1101C22⋊C4—862no—
1102C22⋊C4—862no—
1103C22⋊C4D4×D4312yes—
1104C42—21no—
1105C42—21no—
1106C42—862no—
1107C42—862no—
1108C42C23×D4312yes—
1109C23—22no—
1110C23—24no—
1111C23—81no—
1112C23—81no—
1113C23—432no—
1114C23—431no—
1115C23—431no—
1116C23—862no—
1117C23—861no—
1118C23—861no—
1119C23—3442no—
1120C23—3442no—
1121C23—1721no—
1122C23—1721no—
1123C23—1724no—
1124C23C2×D4×D4311yescharacteristic
1125Q8—82no—
1126Q8—862no—
1127Q8—861no—
1128Q8—862no—
1129Q8—861no—
1130Q8—861no—
1131Q8—862no—
1132Q8—861no—
1133Q8—1722no—
1134D4—22no—
1135D4—24no—
1136D4—864no—
1137D4—861no—
1138D4—861no—
1139D4—861no—
1140D4—861no—
1141D4—862no—
1142D4—3442no—
1143D4—3441no—
1144D4—3441no—
1145D4—1722no—
1146D4—1722no—
1147D4—1722no—
1148D4—1722no—
1149D4—1724no—
1150D4—1724no—
1151D4—1724no—
1152D4—1724no—
1153D4—1722no—
1154D4—1722no—
1155D4C2×#1062190214yes—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—82no—
1162C2×C4—82no—
1163C2×C4—81no—
1164C2×C4—432no—
1165C2×C4—431no—
1166C2×C4—431no—
1167C2×C4—862no—
1168C2×C4—861no—
1169C2×C4—861no—
1170C2×C4—862no—
1171C2×C4—862no—
1172C2×C4—861no—
1173C2×C4—861no—
1174C2×C4—862no—
1175C2×C4—862no—
1176C2×C4—861no—
1177C2×C4—862no—
1178C2×C4—862no—
1179C2×C4—861no—
1180C2×C4—3442no—
1181C2×C4—3442no—
1182C2×C4—3442no—
1183C2×C4—3441no—
1184C2×C4—1724no—
1185C2×C4—1724no—
1186C2×C4—1724no—
1187C2×C4—1724no—
1188C2×C4—1722no—
1189C2×C4—1722no—
1190C2×C4—1722no—
1191C2×C4C2×D4×D4312yes—
1192C2×C4C2×D4×D4312yes—
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4C2×#1062190212yes—
1195C2×C4#1306337112yes—
1196C2×C4C24×D4311yescharacteristic
1197C8—21no—
1198C8—21no—
1199C8—22no—
1200C8—862no—
1201C8—861no—
1202C8—861no—
1203C22—21no—
1204C22—21no—
1205C22—24no—
1206C22—42no—
1207C22—42no—
1208C22—84no—
1209C22—861no—
1210C22—861no—
1211C22—862no—
1212C22—861no—
1213C22—862no—
1214C22—861no—
1215C22—861no—
1216C22—861no—
1217C22—862no—
1218C22—1724no—
1219C22—1721no—
1220C22—1721no—
1221C22—1721no—
1222C22—1721no—
1223C22—1721no—
1224C22—1721no—
1225C22—6884no—
1226C22#1458354012yes—
1227C22C22×D4×D4311yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—861no—
1236C4—861no—
1237C4—862no—
1238C4—1721no—
1239C4—1722no—
1240C4—1721no—
1241C4—1722no—
1242C4#1458354012yes—
1243C4C22×#1062190211yescharacteristic
1244C4C2×#1306337111yescharacteristic
1245C2—22no—
1246C2—44no—
1247C2—3441no—
1248C2—3441no—
1249C2—1721no—
1250C2—1721no—
1251C2—1722no—
1252C2C2×#1458354011yescharacteristic
1253C2#1914937011yescharacteristic
1254C2#1914937711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3081C2
socleC22×C43C23×D4
hypercenter#3081D43
hypocenterC43#61177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #19148305C2semidirect
2. #19148240C2semidirect
3. #19146908C2semidirect
4. #19146897C2semidirect
5. #19146808C2semidirect
6. #19146793C2semidirect
7. #19146688C2semidirect
8. #19146673C2semidirect
9. #19146568C2semidirect
10. #19146553C2semidirect
11. #19144965C2semidirect
12. #19144567C2semidirect
13. #19144521C2semidirect
14. #19144287C2semidirect
15. #19144205C2semidirect
16. #19144147C2semidirect
17. #19143904C2semidirect
18. #19143839C2semidirect
19. #19143427C2semidirect
20. #19143297C2semidirect
21. #19143120C2semidirect
22. C2×#14582897C2semidirect
23. C43×#3081C2semidirect
26. C2×#13063358C22semidirect
30. C22×#10621872C22semidirect
32. #14583610C22semidirect
34. #14583602C22semidirect
36. #14583587C22semidirect
42. #14583552C22semidirect
55. #14583411C22semidirect
58. #14583379C22semidirect
59. C2×C4⋊C4×D43C22semidirect
60. #14583269C22semidirect
61. #14583261C22semidirect
62. #14583256C22semidirect
63. #14583251C22semidirect
64. #14583243C22semidirect
65. #14583242C22semidirect
66. #14583236C22semidirect
67. #14583236C22semidirect
68. #14583231C22semidirect
69. #14583231C22semidirect
70. #14583219C22semidirect
71. #14583214C22semidirect
72. #14583158C22semidirect
73. #14583158C22semidirect
74. #14583158C22semidirect
75. #14583153C22semidirect
76. #14583153C22semidirect
77. #14583146C22semidirect
78. #14583146C22semidirect
79. #14583146C22semidirect
80. #14583146C22semidirect
81. #14583146C22semidirect
82. #14583141C22semidirect
83. #14583129C22semidirect
84. #14583122C22semidirect
85. #14583115C22semidirect
86. #14583110C22semidirect
87. #14583105C22semidirect
88. #14583062C22semidirect
89. #14583062C22semidirect
90. #14583062C22semidirect
91. #14583051C22semidirect
92. #14583045C22semidirect
93. #14583045C22semidirect
94. #14583045C22semidirect
95. #14583034C22semidirect
96. #14583009C22semidirect
97. #14582999C22semidirect
98. C4×#10621883C22semidirect
99. C4×#10621882C22semidirect
100. #14582976C22semidirect
101. #14582976C22semidirect
102. #14582969C22semidirect
103. #14582969C22semidirect
104. #14582942C22semidirect
105. #14582907C22semidirect
106. #14582902C22semidirect
109. #14582897C22semidirect
110. #14582897C22semidirect
111. #14582897C22semidirect
112. #14582897C22semidirect
113. #14582897C22semidirect
115. #14582893C22semidirect
116. #14582892C22semidirect
117. C2×#13063250C22semidirect
118. C2×#13063248C22semidirect
120. #102×D43C22semidirect
122. #14582862C22semidirect
123. #14582855C22semidirect
124. C43×#544C22semidirect
126. C43×#478C22semidirect
127. C43×#478C22semidirect
128. C43×#476C22semidirect
129. C43×#474C22semidirect
130. C43×#428C22semidirect
131. C43×#427C22semidirect
132. C43×#424C22semidirect
327. C2×D4×C43#41semidirect
631. #3081D43semidirect
674. #544C2×D43semidirect
701. #478C2×D43semidirect
702. #478C2×D43semidirect
703. #476C2×D43semidirect
704. #474C2×D43semidirect
738. #428C2×D43semidirect
739. #427C2×D43semidirect
740. #424C2×D43semidirect
762. C43#61177semidirect
1000. C2×D4#10621902semidirect

Maximal subgroups

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

subgroupindex
#191483052
#191482402
#191469082
#191468972
#191468082
#191467932
#191466882
#191466732
#191465682
#191465532
#191449652
#191445672
#191445212
#191442872
#191442052
#191441472
#191439042
#191438392
#191434272
#191432972
#191431202
C2×#145828972
C43×#30812
#6117743