Finite Group Databasebeta

← #25974040

Subgroups — #25974040

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#19148238C211yesmaximal, characteristic, complemented
3#19146910C212yesmaximal, complemented
4#19146899C212yesmaximal, complemented
5#19146810C212yesmaximal, complemented
6#19146795C212yesmaximal, complemented
7#19146690C212yesmaximal, complemented
8#19146675C212yesmaximal, complemented
9#19146570C212yesmaximal, complemented
10#19146555C212yesmaximal, complemented
11#19144562C211yesmaximal, characteristic, complemented
12#19144516C211yesmaximal, characteristic, complemented
13#19144420C211yesmaximal, characteristic, complemented
14#19144284C211yesmaximal, characteristic, complemented
15#19144203C211yesmaximal, characteristic, complemented
16#19144141C211yesmaximal, characteristic, complemented
17#19143901C211yesmaximal, characteristic, complemented
18#19143841C211yesmaximal, characteristic, complemented
19#19143429C211yesmaximal, characteristic, complemented
20#19143300C211yesmaximal, characteristic, complemented
21#19143117C211yesmaximal, characteristic, complemented
22C2×#14582899C211yesmaximal, characteristic, complemented
23C43×#3137C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C22×#10621902C2211yescharacteristic
26C2×#13063356C2211yescharacteristic, complemented
27C2×#13063353C2211yescharacteristic
28C2×#13063345C2211yescharacteristic
29C2×#13063331C2211yescharacteristic
30C22×#10621872C2211yescharacteristic, complemented
31#14583610—21no—
32#14583610C2212yescomplemented
33#14583602—21no—
34#14583602C2212yescomplemented
35#14583587—21no—
36#14583587C2212yescomplemented
37#14583552—21no—
38#14583552C2212yes—
39#14583552C2212yes—
40#14583552C2212yescomplemented
41#14583551—21no—
42#14583551—21no—
43#14583542C2212yes—
44#14583542C2212yes—
45#14583540—21no—
46#14583540—21no—
47#14583498—22no—
48#14583480C2211yescharacteristic
49#14583473C2211yescharacteristic
50#14583460—22no—
51#14583412—22no—
52#14583411C2211yescharacteristic
53#14583411C2211yescharacteristic, complemented
54#14583406C2211yescharacteristic
55#123×D43—22no—
56#14583379C2211yescharacteristic
57#14583379C2211yescharacteristic, complemented
58#14583373C2211yescharacteristic
59C2×C4⋊C4×D43C2211yescharacteristic, complemented
60#14583239C2212yescomplemented
61#14583238C2212yescomplemented
62#14583233C2212yescomplemented
63#14583233C2212yescomplemented
64#14583228C2212yescomplemented
65#14583228C2212yescomplemented
66#14583216C2212yescomplemented
67#14583211C2212yescomplemented
68#14583196C2212yescomplemented
69#14583196C2212yescomplemented
70#14583186C2212yescomplemented
71#14583176C2212yescomplemented
72#14583156C2211yescharacteristic, complemented
73#14583156C2211yescharacteristic, complemented
74#14583156C2212yescomplemented
75#14583151C2211yescharacteristic, complemented
76#14583151C2211yescharacteristic, complemented
77#14583148C2211yescharacteristic, complemented
78#14583148C2211yescharacteristic, complemented
79#14583148C2212yescomplemented
80#14583144C2211yescharacteristic, complemented
81#14583144C2211yescharacteristic, complemented
82#14583139C2212yescomplemented
83#14583131C2212yescomplemented
84#14583118C2212yescomplemented
85#14583111C2212yescomplemented
86#14583106C2212yescomplemented
87#14583101C2212yescomplemented
88#14583064C2212yescomplemented
89#14583064C2212yescomplemented
90#14583064C2212yescomplemented
91#14583051C2212yescomplemented
92#14583047C2212yescomplemented
93#14583047C2212yescomplemented
94#14583047C2212yescomplemented
95#14583034C2212yescomplemented
96#14583012C2212yescomplemented
97#14583001C2212yescomplemented
98C4×#10621873C2212yescomplemented
99C4×D344C2212yescomplemented
100#14582978C2212yescomplemented
101#14582978C2212yescomplemented
102#14582972C2212yescomplemented
103#14582972C2212yescomplemented
104#14582941C2211yescharacteristic, complemented
105#14582939C2211yescharacteristic, complemented
106#14582935C2211yescharacteristic, complemented
107#14582926C2211yescharacteristic, complemented
108#14582903C2211yescharacteristic
109#14582902C2212yescomplemented
110#14582900C2211yescharacteristic
111#14582899C2212yescomplemented
112#14582899C2212yescomplemented
113#14582899C2212yescomplemented
114#14582899C2212yescomplemented
115#14582899C2212yescomplemented
116#14582896C2211yescharacteristic, complemented
117#14582894C2212yescomplemented
118C2×#13063249C2211yescharacteristic, complemented
119C2×#13063247C2211yescharacteristic
120C2×#13063245C2211yescharacteristic
121#102×D43C2212yescomplemented
122#14582867C2211yescharacteristic
123#14582862C2211yescharacteristic, complemented
124C43×#544C2211yescharacteristic, complemented
125C43×#536C2211yescharacteristic
126C43×#491C2212yescomplemented
127C43×#489C2212yescomplemented
128C43×#488C2212yescomplemented
129C43×#487C2212yescomplemented
130C43×#419C2211yescharacteristic, complemented
131C43×#417C2211yescharacteristic
132C43×#416C2211yescharacteristic
133C2×#103×C43C2211yescharacteristic, complemented
134C43×#405C2211yescharacteristic, complemented
135#13063371—24no—
136#13063371—42no—
137C2×#10621902—22no—
138C2×#10621902—21no—
139C2×#10621902—21no—
140C2×#10621902—24no—
141C2×#10621902—42no—
142C2×#10621902C2312yes—
143C2×#10621902C2312yes—
144C2×#10621902C2312yes—
145C2×#10621898—21no—
146C2×#10621898C2311yescharacteristic
147C2×#10621898C2311yescharacteristic
148C22×D172—21no—
149C22×D172—21no—
150C22×D172C2311yescharacteristic
151C2×D4×D43—22no—
152C2×D4×D43C2312yes—
153C22×C4×D43—21no—
154C22×C4×D43—21no—
155C22×C4×D43C2311yescharacteristic
156#13063356—42no—
157#13063353—24no—
158#13063345—42no—
159C2×#10621885C2311yescharacteristic
160C2×#10621885C2312yes—
161C2×#10621873C2312yes—
162C2×#10621883C2311yescharacteristic
163C2×#10621884C2311yescharacteristic
164C2×#10621884C2312yes—
165C2×D344C2312yes—
166C2×#10621882C2311yescharacteristic
167#13063331—42no—
168C2×#10621877C2311yescharacteristic
169C2×#10621872—42no—
170C2×#10621872C2311yescharacteristic
171C2×#10621872C2311yescharacteristic
172C2×#10621872C2311yescharacteristic
173C2×#10621872C2311yescharacteristic
174C2×#10621872C2312yes—
175C22×C43⋊C8C2311yescharacteristic
176C2×C8×D43C2312yes—
177#13063323—21no—
178#13063320—22no—
179#13063320—22no—
180#13063316—22no—
181#13063316—22no—
182#13063314—21no—
183#13063310—22no—
184#13063310—22no—
185#13063310—22no—
186#13063310—22no—
187#13063310—22no—
188#13063310—22no—
189#13063310—22no—
190#13063310—22no—
191#13063309—21no—
192#13063309D412yes—
193#13063308—22no—
194#13063307—22no—
195#13063307—22no—
196#13063306—21no—
197#13063305—21no—
198#13063305D411yescharacteristic
199#13063305D411yescharacteristic
200#13063305C2312yes—
201#13063305C2311yescharacteristic
202#13063305C2311yescharacteristic
203#13063301—22no—
204#13063301—22no—
205#13063301—22no—
206#13063301C2311yescharacteristic
207#13063301C2311yescharacteristic
208#13063301C2312yes—
209#13063301C2312yes—
210#13063300—21no—
211#13063300—22no—
212#13063300—22no—
213#13063300—22no—
214#13063300D411yescharacteristic
215#13063300D411yescharacteristic
216#13063300C2311yescharacteristic
217#13063300C2312yes—
218#13063300C2311yescharacteristic
219#13063299—22no—
220#13063298—22no—
221#13063298—22no—
222#13063296C2311yescharacteristic
223#13063296C2311yescharacteristic
224#13063295—21no—
225#13063295—22no—
226#13063295—22no—
227#13063295D412yes—
228#13063293—21no—
229C4×Dic86—21no—
230C4×Dic86C2312yes—
231C4×D172—21no—
232C4×D172—21no—
233C4×D172—21no—
234C4×D172C2312yes—
235C4×D172C2312yes—
236C4×D172C2312yes—
237C4×D172C2312yes—
238C4×D172C2312yes—
239#13063287—22no—
240#13063287—21no—
241#13063287—21no—
242#13063287—22no—
243C4×C22⋊D43—21no—
244C4×C22⋊D43—21no—
245(C22⋊D43)⋊C4—22no—
246(C22⋊D43)⋊C4—22no—
247#13063284C2311yescharacteristic
248#13063283—21no—
249#13063283—22no—
250#13063283C2312yes—
251C2×C4⋊Dic43C2311yescharacteristic
252C2×Dic43⋊C4—21no—
253C4⋊C4×D43—21no—
254C4⋊C4×D43—21no—
255C4⋊C4×D43—21no—
256C4⋊C4×D43—22no—
257C4⋊C4×D43—22no—
258C4⋊C4×D43C2312yes—
259C4⋊C4×D43C2312yes—
260C4⋊C4×D43C2312yes—
261C22⋊C4×D43—22no—
262C22⋊C4×D43—22no—
263C22⋊C4×D43—22no—
264#13063259C2312yes—
265#13063258C2312yes—
266#13063258C2311yescharacteristic
267#13063258C2311yescharacteristic
268#13063257C2312yes—
269#13063256C2312yes—
270#13063256C2311yescharacteristic
271#13063256C2311yescharacteristic
272C4⋊(C43⋊C8)C2312yes—
273C4⋊(C43⋊C8)C2312yes—
274#13063250C2311yescharacteristic
275#13063250C2311yescharacteristic
276#13063249C2312yes—
277#13063249C2312yes—
278#13063249C2312yes—
279#13063247C2311yescharacteristic
280#13063247C2312yes—
281#13063247C2312yes—
282#13063247C2311yescharacteristic
283#13063246C2312yes—
284#13063245C2312yes—
285#13063245C2312yes—
286#13063245C2312yes—
287#13063245C2312yes—
288(C2×D43)⋊C8C2312yes—
289(C2×D43)⋊C8C2312yes—
290(C2×D43)⋊C8C2312yes—
291(C2×D43)⋊C8C2312yes—
292C2×#41×C43C2311yescharacteristic
293C22×Q8×C43C2311yescharacteristic
294C2×M16×C43C2311yescharacteristic
295C22×C8×C43C2311yescharacteristic
296C4⋊Q8×C43—21no—
297C4⋊Q8×C43C2312yes—
298C4⋊Q8×C43C2312yes—
299#125×C43—21no—
300#125×C43C2312yes—
301#124×C43C2312yes—
302#123×C43—22no—
303C22⋊Q8×C43—21no—
304C22⋊Q8×C43—21no—
305C22⋊Q8×C43—22no—
306#117×C43C2311yescharacteristic
307#117×C43C2311yescharacteristic
308C2×C4⋊C4×C43C2311yescharacteristic
309#103×C43C2312yes—
310#103×C43C2312yes—
311#103×C43C2312yes—
312#103×C43C2312yes—
313#103×C43C2311yescharacteristic
314#103×C43C2312yes—
315#103×C43C2311yescharacteristic
316#102×C43C2312yes—
317#102×C43C2311yescharacteristic
318#102×C43C2311yescharacteristic
319#97×C43C2312yes—
320C4×C8×C43C2312yes—
321C23×D43—21no—
322C23×D43—22no—
323C23×D43C2×D411yescharacteristic
324#41×C43—22no—
325#41×C43—22no—
326C2×Q8×C43—21no—
327C2×Q8×C43—22no—
328C2×Q8×C43—22no—
329C2×Q8×C43—22no—
330C2×Q8×C43C2412yes—
331C2×Q8×C43C2411yescharacteristic
332C2×D4×C43—21no—
333C2×D4×C43C2411yescharacteristic
334C22×C4×C43—21no—
335C22×C4×C43—21no—
336C22×C4×C43—21no—
337C22×C4×C43C2411yescharacteristic
338C2×C22⋊D43—22no—
339C2×C22⋊D43—21no—
340C2×C22⋊D43—21no—
341C2×C22⋊D43—21no—
342C2×C22⋊D43C2×D412yes—
343C22×Dic43—21no—
344C22×Dic43C2×D411yescharacteristic
345#10621902—24no—
346#10621902—24no—
347#10621902—24no—
348#10621902—42no—
349#10621902—42no—
350#10621902—42no—
351#10621902—44no—
352#10621902—44no—
353#10621902—84no—
354D4×D43—24no—
355D4×D43—48no—
356D4×D43—42no—
357#10621898—22no—
358#10621898—22no—
359#10621898—22no—
360#10621898—22no—
361#10621898—44no—
362C2×D172—21no—
363C2×D172—22no—
364C2×D172—21no—
365C2×D172—21no—
366C2×D172—22no—
367C2×D172—22no—
368C2×D172—22no—
369C2×D172—22no—
370C2×D172—44no—
371C2×D172—44no—
372C2×D172C2×D411yescharacteristic
373C2×D172C2×D412yes—
374C2×D172C2×D412yes—
375C2×D172#4114yescomplemented
376C2×D172C2411yescharacteristic
377C2×D172C2412yes—
378C2×C4×D43—22no—
379C2×C4×D43—22no—
380C2×C4×D43—21no—
381C2×C4×D43—22no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—22no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—44no—
391C2×C4×D43—82no—
392C2×C4×D43C2×D411yescharacteristic
393C2×C4×D43C2×D411yescharacteristic
394C2×C4×D43C2411yescharacteristic
395C2×C4×D43C2411yescharacteristic
396C2×C4×D43C2412yes—
397C2×Dic86C2×D411yescharacteristic
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×C43—22no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43C2×D411yescharacteristic
411C4⋊C4×C43C2×D411yescharacteristic
412C4⋊C4×C43C2412yes—
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C22⋊C4×C43—22no—
416C22⋊C4×C43—22no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43C2×D412yes—
419C42×C43—21no—
420C42×C43C2412yes—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424#10621885—41no—
425#10621885—42no—
426#10621884—41no—
427#10621884—42no—
428#10621883—41no—
429#10621882—41no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—21no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4C2×D412yes—
445(C2×D43)⋊C4C2×D412yes—
446(C2×D43)⋊C4C2×D412yes—
447(C2×D43)⋊C4C2×D412yes—
448C4⋊Dic43—21no—
449C4⋊Dic43—22no—
450C4⋊Dic43—21no—
451C4⋊Dic43—21no—
452C4⋊Dic43C2×D412yes—
453C4⋊Dic43C2×D412yes—
454C4⋊Dic43C2412yes—
455C4⋊Dic43C2411yescharacteristic
456C4⋊Dic43C2411yescharacteristic
457Dic43⋊C4—22no—
458Dic43⋊C4—21no—
459Dic43⋊C4—21no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465C4×Dic43—22no—
466C4×Dic43—21no—
467C4×Dic43—22no—
468#10621877—22no—
469C2×C43⋊C8—22no—
470C2×C43⋊C8C2412yes—
471C2×C43⋊C8C2411yescharacteristic
472C2×C43⋊C8C2411yescharacteristic
473D344—24no—
474#10621873—24no—
475#10621872—41no—
476#10621872—41no—
477#10621872—41no—
478#10621872—41no—
479#10621872—42no—
480C8×D43—42no—
481C23×C43—21no—
482C23×C43C22×D411yescharacteristic
483C22×D43—22no—
484C22×D43—22no—
485C22×D43—24no—
486C22×D43—21no—
487C22×D43—41no—
488C22×D43—41no—
489C22×D43—44no—
490C22×D43—82no—
491C22×D43—82no—
492C22×D43—81no—
493C22×D43—81no—
494C22×D43C22×D412yes—
495C22×D43C22×D411yescharacteristic
496C22×D43C22×D411yescharacteristic
497Q8×C43—22no—
498Q8×C43—21no—
499Q8×C43—22no—
500Q8×C43—21no—
501Q8×C43—42no—
502Q8×C43—82no—
503D4×C43—21no—
504D4×C43—21no—
505D4×C43—42no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—21no—
511C2×C4×C43—42no—
512C2×C4×C43—42no—
513C2×C4×C43—81no—
514C2×C4×C43C22×D412yes—
515C2×C4×C43C22×D412yes—
516C2×C4×C43C22×D411yescharacteristic
517C2×C4×C43C2×#4112yes—
518C2×C4×C43H(5,𝔽2)12yes—
519C2×C4×C43C2511yescharacteristic
520C22⋊D43—24no—
521C22⋊D43—44no—
522C22⋊D43—42no—
523C22⋊D43—81no—
524C22⋊D43—81no—
525C2×Dic43—22no—
526C2×Dic43—22no—
527C2×Dic43—21no—
528C2×Dic43—21no—
529C2×Dic43—21no—
530C2×Dic43—81no—
531C2×Dic43C22×D412yes—
532C2×Dic43C22×D411yescharacteristic
533C2×Dic43C22×D411yescharacteristic
534D172—24no—
535D172—22no—
536D172—21no—
537D172—22no—
538D172—21no—
539D172—42no—
540D172—42no—
541D172—44no—
542D172—44no—
543D172—44no—
544D172—42no—
545D172—42no—
546D172—82no—
547D172C2×#4114yes—
548C4×D43—22no—
549C4×D43—22no—
550C4×D43—21no—
551C4×D43—21no—
552C4×D43—22no—
553C4×D43—22no—
554C4×D43—21no—
555C4×D43—21no—
556C4×D43—44no—
557C4×D43—44no—
558C4×D43—44no—
559C4×D43—44no—
560C4×D43—42no—
561C4×D43—82no—
562C4×D43—82no—
563C4×D43—82no—
564C4×D43—82no—
565C4×D43—82no—
566Dic86—22no—
567Dic86—21no—
568Dic86—21no—
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—41no—
579C22×C43—41no—
580C22×C43—41no—
581C22×C43#54612yes—
582C22×C43C23×D411yescharacteristic
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—22no—
586C2×D43—21no—
587C2×D43—21no—
588C2×D43—22no—
589C2×D43—24no—
590C2×D43—21no—
591C2×D43—21no—
592C2×D43—22no—
593C2×D43—44no—
594C2×D43—42no—
595C2×D43—42no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—84no—
600C2×D43—164no—
601C4×C43—22no—
602C4×C43—22no—
603C4×C43—42no—
604C4×C43—41no—
605C4×C43—41no—
606C4×C43—41no—
607C4×C43—42no—
608C4×C43#54612yes—
609C4×C43C22×#4111yescharacteristic
610C4×C43C2×H(5,𝔽2)11yescharacteristic
611Dic43—22no—
612Dic43—21no—
613Dic43—21no—
614Dic43—42no—
615Dic43—41no—
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#3137D4311yescharacteristic, complemented
629#3097—431no—
630#3092—431no—
631#3081—431no—
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—81no—
643C2×C43C2×#54611yescharacteristic
644C2×C43#358511yescharacteristic
645C2×C43#358611yescharacteristic
646D43—41no—
647D43—41no—
648D43—42no—
649D43—44no—
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#536C2×D4311yescharacteristic
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#518—431no—
688C22×C4⋊C4—431no—
689#491C2×D4312yescomplemented
690#489C2×D4312yescomplemented
691#488C2×D4312yescomplemented
692#487C2×D4312yescomplemented
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#478—432no—
702#478—432no—
703#476—432no—
704#474—432no—
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#428—431no—
739#427—431no—
740#424—431no—
741#419C2×D4311yescharacteristic, complemented
742#418—431no—
743#418—432no—
744#417—431no—
745#417—432no—
746#417—432no—
747#417—432no—
748#417—432no—
749#417—432no—
750#417C2×D4311yescharacteristic
751#416—431no—
752#416—432no—
753#416C2×D4311yescharacteristic
754C2×#103—431no—
755C2×#103C2×D4311yescharacteristic, complemented
756C2×#102—431no—
757C2×#102—431no—
758C2×#102—432no—
759#408—431no—
760#407—431no—
761#405C2×D4311yescharacteristic, complemented
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—861no—
771C2×#41—861no—
772C2×#41—861no—
773C2×#41—862no—
774C2×#41—864no—
775C2×#41—1722no—
776C2×#41C22×D4311yescharacteristic
777C22×Q8C22×D4311yescharacteristic
778C22×D4—432no—
779C22×D4—431no—
780C22×D4—861no—
781C22×D4—861no—
782C22×D4—862no—
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—431no—
792C2×SD16—432no—
793C2×SD16—431no—
794C2×SD16—432no—
795C2×D8—431no—
796C2×D8—432no—
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—861no—
811C4⋊Q8C22×D4312yes—
812C4⋊Q8C22×D4312yes—
813#126—862no—
814#126—862no—
815#125—21no—
816#125—862no—
817#125—862no—
818#125C22×D4312yes—
819#124—861no—
820#124C22×D4312yes—
821#123—22no—
822#123—432no—
823#123—862no—
824#123—862no—
825#123—861no—
826#123—862no—
827#123—862no—
828#123—862no—
829#123—862no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—862no—
835#123—861no—
836C22⋊Q8—21no—
837C22⋊Q8—21no—
838C22⋊Q8—22no—
839C22⋊Q8—431no—
840C22⋊Q8—431no—
841C22⋊Q8—431no—
842C22⋊Q8—431no—
843C22⋊Q8—432no—
844C22⋊Q8—432no—
845C22⋊Q8—431no—
846C22⋊Q8—431no—
847C22⋊Q8—432no—
848C22⋊Q8—862no—
849C22⋊Q8—862no—
850C22⋊Q8—861no—
851C22⋊Q8—862no—
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—862no—
863#121—862no—
864#121—861no—
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—432no—
874C4×D4—432no—
875C4×D4—432no—
876C4×D4—432no—
877C4×D4—432no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—861no—
881C4×D4—862no—
882C4×D4—862no—
883C4×D4—862no—
884C4×D4—861no—
885C4×D4—861no—
886C4×D4—861no—
887C4×D4—861no—
888C4×D4—862no—
889#117—431no—
890#117—432no—
891#117—862no—
892#117—861no—
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—862no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—861no—
902C2×C4⋊C4—861no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4C22×D4311yescharacteristic
906C2×C22⋊C4—862no—
907C2×C22⋊C4—862no—
908C2×C22⋊C4—862no—
909#107—432no—
910#107—431no—
911#107—431no—
912#107—432no—
913#106—432no—
914#106—431no—
915#106—431no—
916#106—432no—
917C4⋊C8—432no—
918C4⋊C8—432no—
919#103—432no—
920#103—432no—
921#103—432no—
922#103—431no—
923#103—431no—
924#103C22×D4312yes—
925#103C22×D4312yes—
926#103C22×D4311yescharacteristic
927#103C22×D4311yescharacteristic
928#103C22×D4312yes—
929#103C22×D4312yes—
930#103C22×D4312yes—
931#102—432no—
932#102—432no—
933#102—432no—
934#102—431no—
935#102—431no—
936#102—432no—
937#102—432no—
938#102—432no—
939#102—432no—
940#102C22×D4311yescharacteristic
941#102C22×D4311yescharacteristic
942#102C22×D4312yes—
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8—432no—
946C22⋊C8—432no—
947#97C22×D4312yes—
948C4×C8C22×D4312yes—
949C24—431no—
950C24—862no—
951C24—861no—
952#41—22no—
953#41—22no—
954#41—862no—
955#41—862no—
956#41—864no—
957#41—864no—
958#41—864no—
959#41—862no—
960#41—862no—
961#41—3444no—
962#41—1724no—
963#41—1722no—
964#41—1722no—
965#41—1722no—
966#41—1724no—
967#41—1724no—
968C2×Q8—21no—
969C2×Q8—22no—
970C2×Q8—22no—
971C2×Q8—22no—
972C2×Q8—431no—
973C2×Q8—431no—
974C2×Q8C23×D4312yes—
975C2×Q8C23×D4311yescharacteristic
976C2×D4—21no—
977C2×D4—432no—
978C2×D4—431no—
979C2×D4—432no—
980C2×D4—432no—
981C2×D4—434no—
982C2×D4—432no—
983C2×D4—431no—
984C2×D4—862no—
985C2×D4—861no—
986C2×D4—861no—
987C2×D4—862no—
988C2×D4—862no—
989C2×D4—862no—
990C2×D4—862no—
991C2×D4—864no—
992C2×D4—861no—
993C2×D4—861no—
994C2×D4—861no—
995C2×D4—861no—
996C2×D4—862no—
997C2×D4—1724no—
998C2×D4—1724no—
999C2×D4—1722no—
1000C2×D4—1728no—
1001C2×D4C23×D4311yescharacteristic
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
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—862no—
1021C22×C4—862no—
1022C22×C4—862no—
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—432no—
1044C2×C8—431no—
1045C2×C8—431no—
1046C2×C8—862no—
1047C2×C8—1722no—
1048C2×C8C23×D4311yescharacteristic
1049C2×C8C23×D4312yes—
1050C2×C8C23×D4311yescharacteristic
1051C4⋊C4—21no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—432no—
1058C4⋊C4—432no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—862no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—861no—
1066C4⋊C4—861no—
1067C4⋊C4—862no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—862no—
1074C4⋊C4D4×D4311yescharacteristic
1075C4⋊C4D4×D4311yescharacteristic
1076C4⋊C4C23×D4312yes—
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C22⋊C4—21no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—432no—
1083C22⋊C4—432no—
1084C22⋊C4—432no—
1085C22⋊C4—432no—
1086C22⋊C4—862no—
1087C22⋊C4—861no—
1088C22⋊C4—861no—
1089C22⋊C4—862no—
1090C22⋊C4—862no—
1091C22⋊C4—862no—
1092C22⋊C4—861no—
1093C22⋊C4—861no—
1094C22⋊C4—861no—
1095C22⋊C4—861no—
1096C22⋊C4—862no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—862no—
1101C22⋊C4—862no—
1102C22⋊C4—862no—
1103C22⋊C4D4×D4312yes—
1104C42—21no—
1105C42—862no—
1106C42—861no—
1107C42—862no—
1108C42C23×D4312yes—
1109C23—21no—
1110C23—432no—
1111C23—431no—
1112C23—431no—
1113C23—864no—
1114C23—862no—
1115C23—862no—
1116C23—861no—
1117C23—3441no—
1118C23—3441no—
1119C23—3442no—
1120C23—3442no—
1121C23—1721no—
1122C23—1721no—
1123C23—1724no—
1124C23C2×D4×D4311yescharacteristic
1125Q8—22no—
1126Q8—21no—
1127Q8—22no—
1128Q8—21no—
1129Q8—42no—
1130Q8—82no—
1131Q8—862no—
1132Q8—861no—
1133Q8—861no—
1134D4—21no—
1135D4—21no—
1136D4—42no—
1137D4—434no—
1138D4—864no—
1139D4—861no—
1140D4—862no—
1141D4—861no—
1142D4—864no—
1143D4—862no—
1144D4—3442no—
1145D4—3441no—
1146D4—3441no—
1147D4—1722no—
1148D4—1722no—
1149D4—1724no—
1150D4—1724no—
1151D4—1724no—
1152D4—1722no—
1153D4—1722no—
1154D4—1724no—
1155D4—1722no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—42no—
1162C2×C4—42no—
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—861no—
1179C2×C4—861no—
1180C2×C4—3442no—
1181C2×C4—3442no—
1182C2×C4—3442no—
1183C2×C4—3442no—
1184C2×C4—3442no—
1185C2×C4—3441no—
1186C2×C4—1724no—
1187C2×C4—1724no—
1188C2×C4—1724no—
1189C2×C4—1724no—
1190C2×C4—1722no—
1191C2×C4C2×D4×D4312yes—
1192C2×C4C2×D4×D4312yes—
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4#41×D4312yes—
1195C2×C4#1306337112yes—
1196C2×C4C24×D4311yescharacteristic
1197C8—22no—
1198C8—21no—
1199C8—21no—
1200C8—861no—
1201C8—861no—
1202C8—862no—
1203C22—21no—
1204C22—21no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—861no—
1209C22—861no—
1210C22—862no—
1211C22—864no—
1212C22—861no—
1213C22—862no—
1214C22—861no—
1215C22—861no—
1216C22—861no—
1217C22—862no—
1218C22—3444no—
1219C22—1724no—
1220C22—1721no—
1221C22—1721no—
1222C22—1721no—
1223C22—1722no—
1224C22—1722no—
1225C22—6884no—
1226C22#1458354212yes—
1227C22C22×D4×D4311yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—41no—
1231C4—42no—
1232C4—42no—
1233C4—41no—
1234C4—41no—
1235C4—861no—
1236C4—861no—
1237C4—862no—
1238C4—1721no—
1239C4—1722no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458354212yes—
1243C4C2×#41×D4311yescharacteristic
1244C4C2×#1306337111yescharacteristic
1245C2—22no—
1246C2—81no—
1247C2—3441no—
1248C2—1721no—
1249C2—1721no—
1250C2—1722no—
1251C2—1724no—
1252C2C2×#1458354211yescharacteristic
1253C2#1914937311yescharacteristic
1254C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3137C2
socleC22×C43C23×D4
hypercenter#3137D43
hypocenterC43#61177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #3137

Complements

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

NH ≅ G/Ntype
1. #19148305C2semidirect
2. #19148238C2semidirect
3. #19146910C2semidirect
4. #19146899C2semidirect
5. #19146810C2semidirect
6. #19146795C2semidirect
7. #19146690C2semidirect
8. #19146675C2semidirect
9. #19146570C2semidirect
10. #19146555C2semidirect
11. #19144562C2semidirect
12. #19144516C2semidirect
13. #19144420C2semidirect
14. #19144284C2semidirect
15. #19144203C2semidirect
16. #19144141C2semidirect
17. #19143901C2semidirect
18. #19143841C2semidirect
19. #19143429C2semidirect
20. #19143300C2semidirect
21. #19143117C2semidirect
22. C2×#14582899C2semidirect
23. C43×#3137C2semidirect
26. C2×#13063356C22semidirect
30. C22×#10621872C22semidirect
32. #14583610C22semidirect
34. #14583602C22semidirect
36. #14583587C22semidirect
40. #14583552C22semidirect
53. #14583411C22semidirect
57. #14583379C22semidirect
59. C2×C4⋊C4×D43C22semidirect
60. #14583239C22semidirect
61. #14583238C22semidirect
62. #14583233C22semidirect
63. #14583233C22semidirect
64. #14583228C22semidirect
65. #14583228C22semidirect
66. #14583216C22semidirect
67. #14583211C22semidirect
68. #14583196C22semidirect
69. #14583196C22semidirect
70. #14583186C22semidirect
71. #14583176C22semidirect
72. #14583156C22semidirect
73. #14583156C22semidirect
74. #14583156C22semidirect
75. #14583151C22semidirect
76. #14583151C22semidirect
77. #14583148C22semidirect
78. #14583148C22semidirect
79. #14583148C22semidirect
80. #14583144C22semidirect
81. #14583144C22semidirect
82. #14583139C22semidirect
83. #14583131C22semidirect
84. #14583118C22semidirect
85. #14583111C22semidirect
86. #14583106C22semidirect
87. #14583101C22semidirect
88. #14583064C22semidirect
89. #14583064C22semidirect
90. #14583064C22semidirect
91. #14583051C22semidirect
92. #14583047C22semidirect
93. #14583047C22semidirect
94. #14583047C22semidirect
95. #14583034C22semidirect
96. #14583012C22semidirect
97. #14583001C22semidirect
98. C4×#10621873C22semidirect
99. C4×D344C22semidirect
100. #14582978C22semidirect
101. #14582978C22semidirect
102. #14582972C22semidirect
103. #14582972C22semidirect
104. #14582941C22semidirect
105. #14582939C22semidirect
106. #14582935C22semidirect
107. #14582926C22semidirect
109. #14582902C22semidirect
111. #14582899C22semidirect
112. #14582899C22semidirect
113. #14582899C22semidirect
114. #14582899C22semidirect
115. #14582899C22semidirect
116. #14582896C22semidirect
117. #14582894C22semidirect
118. C2×#13063249C22semidirect
121. #102×D43C22semidirect
123. #14582862C22semidirect
124. C43×#544C22semidirect
126. C43×#491C22semidirect
127. C43×#489C22semidirect
128. C43×#488C22semidirect
129. C43×#487C22semidirect
130. C43×#419C22semidirect
133. C2×#103×C43C22semidirect
134. C43×#405C22semidirect
375. C2×D172#41semidirect
628. #3137D43semidirect
674. #544C2×D43semidirect
689. #491C2×D43semidirect
690. #489C2×D43semidirect
691. #488C2×D43semidirect
692. #487C2×D43semidirect
741. #419C2×D43semidirect
755. C2×#103C2×D43semidirect
761. #405C2×D43semidirect
762. C43#61177semidirect

Maximal subgroups

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

subgroupindex
#191483052
#191482382
#191469102
#191468992
#191468102
#191467952
#191466902
#191466752
#191465702
#191465552
#191445622
#191445162
#191444202
#191442842
#191442032
#191441412
#191439012
#191438412
#191434292
#191433002
#191431172
C2×#145828992
C43×#31372
#6117743