Finite Group Databasebeta

← #25974475

Subgroups — #25974475

Order 11008.

2114 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#19148315C211yesmaximal, characteristic, complemented
2#19148260C211yesmaximal, characteristic, complemented
3#19146846C212yesmaximal, complemented
4#19146824C212yesmaximal, complemented
5#19146749C212yesmaximal, complemented
6#19146739C212yesmaximal, complemented
7#19146719C212yesmaximal, complemented
8#19146664C212yesmaximal, complemented
9#19146543C212yesmaximal, complemented
10#19146433C212yesmaximal, complemented
11#19144947C211yesmaximal, characteristic, complemented
12#19144589C211yesmaximal, characteristic, complemented
13#19144451C211yesmaximal, characteristic, complemented
14#19144267C211yesmaximal, characteristic, complemented
15#19144210C211yesmaximal, characteristic, complemented
16#19144139C211yesmaximal, characteristic, complemented
17#19143904C211yesmaximal, characteristic, complemented
18#19143817C211yesmaximal, characteristic, complemented
19#19143478C211yesmaximal, characteristic, complemented
20#19143316C211yesmaximal, characteristic, complemented
21#19143116C211yesmaximal, characteristic, complemented
22#19143112C211yesmaximal, characteristic, complemented
23C2×C43×#482C211yesmaximal, characteristic, complemented
24C2×#13063370C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#13063351C2211yescharacteristic, complemented
27C2×#13063347C2211yescharacteristic
28C2×#13063347C2211yescharacteristic, complemented
29C2×#13063331C2211yescharacteristic, complemented
30C22×#10621877C2211yescharacteristic, complemented
31#14583617—21no—
32#14583617C2212yescomplemented
33#14583612—21no—
34#14583612C2212yescomplemented
35#14583593—21no—
36#14583593C2212yescomplemented
37#14583588—21no—
38#14583588C2212yescomplemented
39#14583567C2212yes—
40#14583555C2212yes—
41#14583546C2212yes—
42#14583539—22no—
43#14583533C2212yes—
44D4×C22⋊D43—22no—
45#14583530C2211yescharacteristic, complemented
46#14583487—22no—
47#14583480C2211yescharacteristic
48#14583480C2211yescharacteristic, complemented
49#14583478—21no—
50#14583466C2211yescharacteristic
51#14583465—21no—
52#14583433—22no—
53#14583410C2211yescharacteristic
54#14583410C2211yescharacteristic, complemented
55#14583409—21no—
56#121×D43—21no—
57#14583380C2211yescharacteristic
58#14583380C2211yescharacteristic, complemented
59#14583380C2211yescharacteristic, complemented
60#14583262C2212yescomplemented
61#14583257C2212yescomplemented
62#14583252C2212yescomplemented
63#14583244C2212yescomplemented
64#14583243C2212yescomplemented
65#14583231C2212yescomplemented
66#14583225C2212yescomplemented
67#14583219C2212yescomplemented
68#14583205C2212yescomplemented
69#14583202C2212yescomplemented
70#14583193C2212yescomplemented
71#14583178C2212yescomplemented
72#14583150C2212yescomplemented
73#14583146C2212yescomplemented
74#14583146C2212yescomplemented
75#14583143C2212yescomplemented
76#14583141C2212yescomplemented
77#14583136C2212yescomplemented
78#14583133C2212yescomplemented
79#14583126C2212yescomplemented
80#14583120C2212yescomplemented
81#14583113C2212yescomplemented
82#14583098C2212yescomplemented
83#14583093C2212yescomplemented
84#14583063C2211yescharacteristic, complemented
85#14583063C2211yescharacteristic, complemented
86#14583062C2212yescomplemented
87#14583057C2211yescharacteristic, complemented
88#14583052C2211yescharacteristic, complemented
89#14583051C2212yescomplemented
90#14583046C2211yescharacteristic, complemented
91#14583046C2211yescharacteristic, complemented
92#14583045C2212yescomplemented
93#14583040C2211yescharacteristic, complemented
94#14583035C2211yescharacteristic, complemented
95#14583034C2212yescomplemented
96#14583010C2212yescomplemented
97#14583005C2212yescomplemented
98#14582986C2212yescomplemented
99#14582986C2212yescomplemented
100#14582974C2212yescomplemented
101#14582973C2212yescomplemented
102#14582967C2212yescomplemented
103(C22⋊D43)⋊C8C2212yescomplemented
104#14582939C2211yescharacteristic, complemented
105#14582925C2211yescharacteristic, complemented
106#14582907C2212yescomplemented
107#14582904C2211yescharacteristic, complemented
108#14582903C2212yescomplemented
109#14582902C2212yescomplemented
110#14582898C2211yescharacteristic
111#14582898C2211yescharacteristic
112#14582898C2211yescharacteristic, complemented
113#14582898C2211yescharacteristic, complemented
114#14582898C2211yescharacteristic, complemented
115#14582897C2212yescomplemented
116#14582896C2211yescharacteristic
117#14582896C2211yescharacteristic, complemented
118#14582893C2212yescomplemented
119#14582893C2212yescomplemented
120#14582892C2212yescomplemented
121#102×D43C2212yescomplemented
122#14582865C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×#121×C43C2211yescharacteristic
125C2×#117×C43C2211yescharacteristic, complemented
126C43×#482C2212yescomplemented
127C43×#482C2212yescomplemented
128C43×#482C2212yescomplemented
129C43×#482C2212yescomplemented
130C2×#107×C43C2211yescharacteristic, complemented
131C2×#106×C43C2211yescharacteristic, complemented
132C2×#102×C43C2211yescharacteristic, complemented
133C2×#102×C43C2211yescharacteristic, complemented
134C2×C22⋊C8×C43C2211yescharacteristic, complemented
135#13063370—24no—
136#13063370—42no—
137C2×#10621898—21no—
138C2×#10621898—21no—
139C2×#10621898—24no—
140C2×#10621898—42no—
141C2×#10621898C2311yescharacteristic
142C2×#10621898C2311yescharacteristic
143C2×#10621898C2311yescharacteristic
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621898C2311yescharacteristic
147C2×#10621900—21no—
148C2×#10621900C2312yes—
149C22×Dic86C2311yescharacteristic
150C22×D172C2311yescharacteristic
151C22×C22⋊D43—21no—
152C22×C22⋊D43—22no—
153C2×D4×D43—22no—
154C2×D4×D43—21no—
155C2×D4×D43C2312yes—
156C22×C4×D43—21no—
157#13063351—42no—
158#13063347—24no—
159#13063347—42no—
160C2×Dic172C2311yescharacteristic
161C2×Dic172C2311yescharacteristic
162C2×#10621873C2311yescharacteristic
163C2×#10621873C2311yescharacteristic
164C2×#10621873C2311yescharacteristic
165C2×#10621873C2311yescharacteristic
166C2×#10621883C2312yes—
167C2×D344C2311yescharacteristic
168C2×D344C2311yescharacteristic
169C2×#10621882C2312yes—
170#13063331—42no—
171C2×#10621877—42no—
172C2×#10621877C2311yescharacteristic
173C2×#10621877C2311yescharacteristic
174C2×#10621877C2312yes—
175C2×#10621872C2312yes—
176C22×C43⋊C8C2312yes—
177C2×C8×D43C2312yes—
178#13063324—21no—
179#13063324C2312yes—
180#13063321—22no—
181#13063321C2312yes—
182#13063319—22no—
183#13063319—22no—
184#13063318—22no—
185#13063318—22no—
186#13063317—22no—
187#13063316—21no—
188#13063316C2312yes—
189#13063313—22no—
190#13063312C2312yes—
191#13063311—22no—
192#13063311—22no—
193#13063311—22no—
194#13063308—21no—
195#13063308D412yes—
196#13063307—22no—
197#13063307—22no—
198#13063307—22no—
199#13063305—21no—
200#13063305—21no—
201#13063305C2312yes—
202#13063305C2312yes—
203#13063304—22no—
204#13063304D411yescharacteristic
205#13063304D411yescharacteristic
206#13063304C2311yescharacteristic
207#13063304C2311yescharacteristic
208#13063302—22no—
209#13063300—21no—
210#13063300—21no—
211#13063300C2312yes—
212#13063300C2312yes—
213#13063299—22no—
214#13063299—22no—
215#13063299D411yescharacteristic
216#13063299D411yescharacteristic
217#13063299C2311yescharacteristic
218#13063299C2311yescharacteristic
219#13063298—22no—
220#13063298—22no—
221#13063298—22no—
222#13063298—22no—
223#13063297—22no—
224#13063297—22no—
225#13063296—22no—
226#13063296—21no—
227#13063296—21no—
228#13063295—22no—
229#13063294—21no—
230#13063294—22no—
231#13063294D412yes—
232#13063293—22no—
233#13063293—22no—
234C4×Dic86—22no—
235#13063290—21no—
236#13063290C2312yes—
237#13063290C2312yes—
238C4×D172—22no—
239D4×Dic43—22no—
240#13063287—21no—
241#13063287C2312yes—
242#13063287C2312yes—
243C4×C22⋊D43—21no—
244C4×C22⋊D43—21no—
245C4×C22⋊D43—22no—
246C4×C22⋊D43—22no—
247C4×C22⋊D43—22no—
248C4×C22⋊D43C2312yes—
249C4×C22⋊D43C2312yes—
250(C22⋊D43)⋊C4—22no—
251#13063284C2311yescharacteristic
252#13063284C2311yescharacteristic
253#13063283—21no—
254#13063283—21no—
255#13063283C2312yes—
256#13063282—22no—
257#13063282—22no—
258C4⋊C4×D43—21no—
259C4⋊C4×D43—21no—
260C4⋊C4×D43C2312yes—
261C22⋊C4×D43—22no—
262#13063258C2312yes—
263#13063256C2312yes—
264Dic43⋊C8C2312yes—
265Dic43⋊C8C2312yes—
266#13063250C2311yescharacteristic
267#13063250C2311yescharacteristic
268#13063250C2311yescharacteristic
269#13063250C2311yescharacteristic
270#13063248C2312yes—
271#13063248C2312yes—
272#13063248C2312yes—
273#13063248C2312yes—
274#13063248C2312yes—
275#13063247C2311yescharacteristic
276#13063247C2311yescharacteristic
277#13063247C2311yescharacteristic
278#13063247C2311yescharacteristic
279#13063246C2312yes—
280#13063246C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283#13063245C2312yes—
284#13063245C2312yes—
285#13063245C2312yes—
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C22×D4×C43—21no—
291C22×D4×C43C2311yescharacteristic
292C23×C4×C43C2311yescharacteristic
293C22×C8×C43C2311yescharacteristic
294C22×C8×C43C2311yescharacteristic
295#121×C43—21no—
296#121×C43—21no—
297#121×C43C2312yes—
298#121×C43C2312yes—
299#117×C43—21no—
300#117×C43—21no—
301#117×C43C2312yes—
302#117×C43C2312yes—
303C2×C4⋊C4×C43C2311yescharacteristic
304C2×C4⋊C4×C43C2311yescharacteristic
305C2×C4⋊C4×C43C2311yescharacteristic
306C2×C22⋊C4×C43—21no—
307C2×C22⋊C4×C43—21no—
308C2×C42×C43—21no—
309#107×C43C2312yes—
310#107×C43C2312yes—
311#106×C43C2312yes—
312#106×C43C2312yes—
313#102×C43C2312yes—
314#102×C43C2312yes—
315#102×C43C2312yes—
316#102×C43C2312yes—
317C22⋊C8×C43C2311yescharacteristic
318C22⋊C8×C43C2311yescharacteristic
319C22⋊C8×C43C2311yescharacteristic
320C22⋊C8×C43C2311yescharacteristic
321C24×C43—21no—
322C24×C43C2×D411yescharacteristic
323C23×D43—21no—
324C23×D43—22no—
325C2×D4×C43—21no—
326C2×D4×C43—22no—
327C2×D4×C43—22no—
328C2×D4×C43—22no—
329C2×D4×C43—22no—
330C2×D4×C43—82no—
331C2×D4×C43C2412yes—
332C22×C4×C43—22no—
333C22×C4×C43—22no—
334C22×C4×C43—21no—
335C22×C4×C43—21no—
336C22×C4×C43—21no—
337C22×C4×C43C2×D411yescharacteristic
338C22×C4×C43C2×D411yescharacteristic
339C22×C4×C43C2×D411yescharacteristic
340C22×C4×C43C2411yescharacteristic
341C22×C4×C43C2411yescharacteristic
342C22×C4×C43C2411yescharacteristic
343C2×C22⋊D43—22no—
344C2×C22⋊D43—22no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43—21no—
347C2×C22⋊D43—21no—
348C2×C22⋊D43—21no—
349C2×C22⋊D43—21no—
350C2×C22⋊D43—21no—
351C2×C22⋊D43—21no—
352C2×C22⋊D43—21no—
353C2×C22⋊D43—22no—
354C2×C22⋊D43—44no—
355C2×C22⋊D43—48no—
356C2×C22⋊D43C2×D412yes—
357C2×C22⋊D43C2×D412yes—
358C2×C22⋊D43C2×D412yes—
359C22×Dic43—22no—
360C22×Dic43—21no—
361#10621900—24no—
362#10621900—42no—
363#10621900—44no—
364D4×D43—24no—
365D4×D43—42no—
366D4×D43—44no—
367D4×D43—84no—
368#10621898—22no—
369#10621898—22no—
370#10621898—22no—
371#10621898—22no—
372#10621898—22no—
373#10621898—22no—
374#10621898—22no—
375#10621898—22no—
376#10621898—22no—
377#10621898—41no—
378#10621898—41no—
379#10621898—44no—
380#10621898—44no—
381#10621898#4114yes—
382C2×D172—21no—
383C2×D172—22no—
384C2×D172—22no—
385C2×D172—22no—
386C2×D172—41no—
387C2×D172C2×D411yescharacteristic
388C2×D172C2411yescharacteristic
389C2×D172C2411yescharacteristic
390C2×D172C2411yescharacteristic
391C2×C4×D43—21no—
392C2×C4×D43—21no—
393C2×C4×D43—21no—
394C2×C4×D43—21no—
395C2×C4×D43—21no—
396C2×C4×D43—22no—
397C2×C4×D43—22no—
398C2×C4×D43—22no—
399C2×C4×D43—44no—
400C2×C4×D43C2412yes—
401C2×Dic86—22no—
402C2×Dic86—21no—
403C2×Dic86—22no—
404C2×Dic86—41no—
405C2×Dic86C2×D411yescharacteristic
406C2×Dic86C2411yescharacteristic
407C2×Dic86C2411yescharacteristic
408C2×Dic86C2411yescharacteristic
409C2×C8×C43—22no—
410C2×C8×C43—22no—
411C2×C8×C43C2411yescharacteristic
412C2×C8×C43C2411yescharacteristic
413C2×C8×C43C2411yescharacteristic
414C2×C8×C43C2411yescharacteristic
415C4⋊C4×C43—21no—
416C4⋊C4×C43—21no—
417C4⋊C4×C43—21no—
418C4⋊C4×C43C2412yes—
419C4⋊C4×C43C2412yes—
420C4⋊C4×C43C2412yes—
421C22⋊C4×C43—22no—
422C22⋊C4×C43—22no—
423C22⋊C4×C43—22no—
424C22⋊C4×C43—22no—
425C42×C43—22no—
426C42×C43—22no—
427C22⋊Dic43—22no—
428C22⋊Dic43—22no—
429C22⋊Dic43—21no—
430C22⋊Dic43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43C2×D412yes—
433C22⋊Dic43C2×D412yes—
434C22⋊Dic43C2×D412yes—
435#10621883—42no—
436#10621882—42no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4C2×D412yes—
447(C2×D43)⋊C4C2×D412yes—
448C4⋊Dic43—22no—
449C4⋊Dic43—22no—
450C4⋊Dic43—22no—
451C4⋊Dic43C2×D411yescharacteristic
452C4⋊Dic43C2×D411yescharacteristic
453C4⋊Dic43C2411yescharacteristic
454C4⋊Dic43C2411yescharacteristic
455Dic43⋊C4—21no—
456Dic43⋊C4—21no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4C2×D412yes—
463Dic43⋊C4C2×D412yes—
464C4×Dic43—21no—
465C4×Dic43—22no—
466C4×Dic43—22no—
467C4×Dic43—22no—
468C4×Dic43C2412yes—
469#10621877—22no—
470#10621877—22no—
471#10621877—42no—
472C2×C43⋊C8—42no—
473C2×C43⋊C8C2412yes—
474C2×C43⋊C8C2412yes—
475Dic172—22no—
476Dic172—41no—
477D344—22no—
478D344—41no—
479#10621873—22no—
480#10621873—22no—
481#10621873—41no—
482#10621873—41no—
483#10621872—42no—
484C8×D43—42no—
485C23×C43—22no—
486C23×C43—22no—
487C23×C43—41no—
488C23×C43—41no—
489C23×C43—42no—
490C23×C43—81no—
491C23×C43—81no—
492C23×C43C22×D411yescharacteristic
493C23×C43C22×D411yescharacteristic
494C23×C43C22×D411yescharacteristic
495C22×D43—21no—
496C22×D43—21no—
497C22×D43—21no—
498C22×D43—44no—
499C22×D43—42no—
500C22×D43—42no—
501C22×D43—82no—
502C22×D43—82no—
503C22×D43—81no—
504C22×D43C22×D412yes—
505D4×C43—22no—
506D4×C43—22no—
507D4×C43—44no—
508D4×C43—42no—
509D4×C43—82no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—22no—
513C2×C4×C43—21no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—21no—
517C2×C4×C43—22no—
518C2×C4×C43—22no—
519C2×C4×C43—22no—
520C2×C4×C43—81no—
521C2×C4×C43—81no—
522C2×C4×C43—81no—
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C22×D411yescharacteristic
525C2×C4×C43C22×D411yescharacteristic
526C2×C4×C43C2×#4112yes—
527C2×C4×C43H(5,𝔽2)12yes—
528C2×C4×C43C2511yescharacteristic
529C22⋊D43—24no—
530C22⋊D43—24no—
531C22⋊D43—42no—
532C22⋊D43—42no—
533C22⋊D43—44no—
534C22⋊D43—44no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—42no—
538C22⋊D43—42no—
539C22⋊D43—82no—
540C22⋊D43—82no—
541C22⋊D43—81no—
542C22⋊D43—81no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—21no—
548C2×Dic43—44no—
549C2×Dic43—42no—
550C2×Dic43C22×D412yes—
551C2×Dic43C22×D412yes—
552C2×Dic43C22×D412yes—
553D172—22no—
554D172—21no—
555D172—21no—
556D172—21no—
557D172—21no—
558D172—21no—
559D172—42no—
560D172—82no—
561D172—82no—
562D172C2×#4112yes—
563C4×D43—24no—
564C4×D43—22no—
565C4×D43—22no—
566C4×D43—42no—
567C4×D43—42no—
568C4×D43—42no—
569C4×D43—42no—
570C4×D43—82no—
571C4×D43—82no—
572C4×D43—82no—
573Dic86—22no—
574Dic86—21no—
575Dic86—21no—
576Dic86—21no—
577Dic86—21no—
578Dic86—21no—
579Dic86—42no—
580Dic86—82no—
581Dic86C2×#4112yes—
582C8×C43—21no—
583C8×C43—21no—
584C8×C43—21no—
585C8×C43—21no—
586C43⋊C8—22no—
587C43⋊C8—22no—
588#61196—431nomaximal, Sylow
589C22×C43—21no—
590C22×C43—21no—
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—82no—
601C22×C43—162no—
602C22×C43#54612yes—
603C22×C43C23×D411yescharacteristic
604C2×D43—22no—
605C2×D43—22no—
606C2×D43—22no—
607C2×D43—22no—
608C2×D43—41no—
609C2×D43—41no—
610C2×D43—41no—
611C2×D43—41no—
612C2×D43—41no—
613C2×D43—41no—
614C2×D43—41no—
615C2×D43—41no—
616C2×D43—84no—
617C2×D43—164no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—42no—
621C4×C43—42no—
622C4×C43—42no—
623C4×C43#54612yes—
624C4×C43C22×#4111yescharacteristic
625C4×C43C2×H(5,𝔽2)11yescharacteristic
626Dic43—22no—
627Dic43—22no—
628Dic43—22no—
629Dic43—22no—
630Dic43—41no—
631Dic43—41no—
632Dic43—41no—
633Dic43—41no—
634#3493—431no—
635#3488—431no—
636#3326—432no—
637#3324—432no—
638#3319—432no—
639#3318—432no—
640#3317—432no—
641#3313—432no—
642#3305—432no—
643#3296—432no—
644#3136—431no—
645#3099—431no—
646C2×#482D4311yescharacteristic, complemented
647#3083—431no—
648#3061—431no—
649#3055—431no—
650#3045—431no—
651#3012—431no—
652#3002—431no—
653#2952—431no—
654#2933—431no—
655#2897—431no—
656#2896—431no—
657C2×C43—22no—
658C2×C43—41no—
659C2×C43—41no—
660C2×C43—82no—
661C2×C43C2×#54611yescharacteristic
662C2×C43#358411yescharacteristic
663C2×C43#358511yescharacteristic
664D43—42no—
665D43—42no—
666D43—81no—
667D43—81no—
668C2×H(5,𝔽2)—431no—
669C22×#41—431no—
670C2×AGL(1,ℤ/8)—431no—
671C2×#135—431no—
672C2×#135—431no—
673C2×#131—431no—
674C22×M16—431no—
675#556—432no—
676#556—861no—
677#555—432no—
678#555—861no—
679#553—432no—
680#553—861no—
681#552—432no—
682#552—861no—
683#550—432no—
684#548—432no—
685#546—432no—
686#546—862no—
687D42—432no—
688D42—862no—
689#544—431no—
690#538—862no—
691#537—431no—
692#537—431no—
693#537—861no—
694#535—431no—
695#535—861no—
696#529—862no—
697#525—431no—
698#525—431no—
699#525—861no—
700C2×#121—861no—
701C2×#121C2×D4311yescharacteristic
702#520—431no—
703#520—431no—
704#520—431no—
705C2×#117C2×D4311yescharacteristic, complemented
706#490—432no—
707#489—432no—
708#488—432no—
709#486—432no—
710#485—432no—
711#483—432no—
712#482—432no—
713#482C2×D4312yescomplemented
714#482C2×D4312yescomplemented
715#482C2×D4312yescomplemented
716#482C2×D4312yescomplemented
717#481—432no—
718#479—432no—
719#478—432no—
720#477—432no—
721#474—432no—
722#469—432no—
723#468—432no—
724#468—432no—
725#468—432no—
726#467—432no—
727#466—432no—
728#466—432no—
729#465—432no—
730#464—432no—
731#463—432no—
732#460—432no—
733#459—432no—
734#452—432no—
735#452—431no—
736#452—431no—
737#451—431no—
738#450—432no—
739#450—431no—
740#449—432no—
741#449—431no—
742#449—431no—
743#448—431no—
744#447—432no—
745#447—431no—
746#442—432no—
747#441—432no—
748C4×SD16—432no—
749C4×SD16—432no—
750#436—432no—
751#435—432no—
752#435—432no—
753C8×D4—432no—
754#428—431no—
755C2×#107C2×D4311yescharacteristic, complemented
756C2×#106C2×D4311yescharacteristic, complemented
757#424—431no—
758#419—432no—
759#418—431no—
760#418—432no—
761#418—432no—
762#417—431no—
763#417—431no—
764#417—431no—
765#417—431no—
766#417—431no—
767#417—432no—
768#416—431no—
769#416—431no—
770#416—432no—
771#416—432no—
772#416—432no—
773C2×#102—432no—
774C2×#102C2×D4311yescharacteristic, complemented
775C2×#102C2×D4311yescharacteristic, complemented
776#408—431no—
777C2×C22⋊C8C2×D4311yescharacteristic, complemented
778#405—431no—
779C43#6119611yescharacteristic, complemented, Sylow
780H(5,𝔽2)—864no—
781H(5,𝔽2)—1722no—
782C2×#41—431no—
783C2×#41—432no—
784C2×#41—431no—
785C2×#41—431no—
786C2×#41—431no—
787C2×#41—431no—
788C2×#41—431no—
789C2×#41—864no—
790C2×#41—861no—
791C2×#41—861no—
792C2×#41—861no—
793C2×#41—1722no—
794C22×Q8—431no—
795C22×D4—21no—
796C22×D4—432no—
797C22×D4—431no—
798C22×D4—862no—
799C22×D4—861no—
800C22×D4—862no—
801C22×D4—861no—
802C22×D4C22×D4311yescharacteristic
803C23×C4—861no—
804C23×C4C22×D4311yescharacteristic
805AGL(1,ℤ/8)—1722no—
806#135—864no—
807#135—1722no—
808C2×Q16—431no—
809C2×Q16—431no—
810C2×SD16—432no—
811C2×SD16—431no—
812C2×SD16—431no—
813C2×SD16—431no—
814C2×SD16—431no—
815C2×D8—432no—
816C2×D8—431no—
817C2×D8—431no—
818#131—1722no—
819C2×M16—431no—
820C2×M16—431no—
821C2×M16—432no—
822C2×M16—432no—
823C2×M16—1722no—
824C22×C8—432no—
825C22×C8—432no—
826C22×C8C22×D4311yescharacteristic
827C22×C8C22×D4311yescharacteristic
828C4⋊Q8—432no—
829C4⋊Q8—861no—
830#127—432no—
831#127—862no—
832#126—862no—
833#126—862no—
834#126—862no—
835#126—862no—
836#125—432no—
837#125—862no—
838#125—861no—
839#124—432no—
840#124—862no—
841#124—862no—
842#124—862no—
843#124—862no—
844#123—432no—
845#123—862no—
846#123—862no—
847#123—862no—
848#123—861no—
849C22⋊Q8—431no—
850C22⋊Q8—431no—
851C22⋊Q8—431no—
852C22⋊Q8—431no—
853C22⋊Q8—432no—
854C22⋊Q8—432no—
855C22⋊Q8—862no—
856C22⋊Q8—862no—
857C22⋊Q8—861no—
858C22⋊Q8—861no—
859#121—21no—
860#121—21no—
861#121—431no—
862#121—431no—
863#121—431no—
864#121—431no—
865#121—432no—
866#121—432no—
867#121—862no—
868#121—862no—
869#121—862no—
870#121—862no—
871#121—862no—
872#121—862no—
873#121—861no—
874#121—861no—
875#121—861no—
876#121—861no—
877#121—862no—
878#121—862no—
879#121—862no—
880#121C22×D4312yes—
881#121C22×D4312yes—
882#120—432no—
883#120—862no—
884#120—862no—
885#120—862no—
886#120—862no—
887#120—861no—
888C4×Q8—432no—
889C4×Q8—432no—
890C4×Q8—862no—
891C4×Q8—861no—
892C4×D4—432no—
893C4×D4—432no—
894C4×D4—432no—
895C4×D4—432no—
896C4×D4—862no—
897C4×D4—862no—
898C4×D4—862no—
899C4×D4—862no—
900C4×D4—862no—
901C4×D4—861no—
902C4×D4—862no—
903C4×D4—861no—
904C4×D4—861no—
905#117—21no—
906#117—21no—
907#117—431no—
908#117—431no—
909#117—432no—
910#117—862no—
911#117—862no—
912#117—861no—
913#117—861no—
914#117C22×D4312yes—
915#117C22×D4312yes—
916C2×C4⋊C4—432no—
917C2×C4⋊C4—861no—
918C2×C4⋊C4—861no—
919C2×C4⋊C4C22×D4311yescharacteristic
920C2×C4⋊C4C22×D4311yescharacteristic
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C22⋊C4—21no—
923C2×C22⋊C4—21no—
924C2×C22⋊C4—862no—
925C2×C42—21no—
926#107—432no—
927#107C22×D4312yes—
928#107C22×D4312yes—
929#106—432no—
930#106C22×D4312yes—
931#106C22×D4312yes—
932C4⋊C8—432no—
933C4⋊C8—432no—
934#103—431no—
935#103—431no—
936#103—431no—
937#103—431no—
938#103—432no—
939#103—432no—
940#103—432no—
941#103—432no—
942#103—432no—
943#102—432no—
944#102—432no—
945#102—431no—
946#102—431no—
947#102—431no—
948#102—431no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102C22×D4312yes—
955#102C22×D4312yes—
956#102C22×D4312yes—
957#102C22×D4312yes—
958C22⋊C8—432no—
959C22⋊C8—432no—
960C22⋊C8C22×D4311yescharacteristic
961C22⋊C8C22×D4311yescharacteristic
962C22⋊C8C22×D4311yescharacteristic
963C22⋊C8C22×D4311yescharacteristic
964#97—432no—
965C4×C8—432no—
966C24—21no—
967C24—862no—
968C24—861no—
969C24D4×D4311yescharacteristic
970#41—434no—
971#41—862no—
972#41—862no—
973#41—862no—
974#41—862no—
975#41—862no—
976#41—864no—
977#41—862no—
978#41—862no—
979#41—862no—
980#41—862no—
981#41—1724no—
982#41—1721no—
983#41—1721no—
984#41—1724no—
985#41—1722no—
986#41—1724no—
987C2×Q8—431no—
988C2×Q8—431no—
989C2×Q8—431no—
990C2×Q8—431no—
991C2×Q8—862no—
992C2×Q8—862no—
993C2×Q8—861no—
994C2×Q8—1721no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—21no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—82no—
1001C2×D4—432no—
1002C2×D4—432no—
1003C2×D4—432no—
1004C2×D4—431no—
1005C2×D4—431no—
1006C2×D4—431no—
1007C2×D4—431no—
1008C2×D4—862no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—862no—
1012C2×D4—862no—
1013C2×D4—862no—
1014C2×D4—864no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4—862no—
1019C2×D4—861no—
1020C2×D4—861no—
1021C2×D4—861no—
1022C2×D4—861no—
1023C2×D4—861no—
1024C2×D4—3444no—
1025C2×D4—1721no—
1026C2×D4—1722no—
1027C2×D4—1724no—
1028C2×D4—1728no—
1029C2×D4—1724no—
1030C2×D4C23×D4312yes—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—21no—
1034C22×C4—21no—
1035C22×C4—21no—
1036C22×C4—432no—
1037C22×C4—862no—
1038C22×C4—862no—
1039C22×C4—862no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4—861no—
1043C22×C4—861no—
1044C22×C4—861no—
1045C22×C4—861no—
1046C22×C4—861no—
1047C22×C4—1724no—
1048C22×C4D4×D4311yescharacteristic
1049C22×C4D4×D4311yescharacteristic
1050C22×C4D4×D4311yescharacteristic
1051C22×C4C23×D4311yescharacteristic
1052C22×C4C23×D4311yescharacteristic
1053C22×C4C23×D4311yescharacteristic
1054Q16—862no—
1055Q16—1721no—
1056SD16—862no—
1057SD16—862no—
1058SD16—1721no—
1059SD16—1721no—
1060SD16—1722no—
1061D8—862no—
1062D8—1721no—
1063D8—1722no—
1064M16—862no—
1065M16—862no—
1066M16—1722no—
1067M16—1722no—
1068C2×C8—22no—
1069C2×C8—22no—
1070C2×C8—432no—
1071C2×C8—432no—
1072C2×C8—1722no—
1073C2×C8—1722no—
1074C2×C8C23×D4311yescharacteristic
1075C2×C8C23×D4311yescharacteristic
1076C2×C8C23×D4311yescharacteristic
1077C2×C8C23×D4311yescharacteristic
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—431no—
1082C4⋊C4—431no—
1083C4⋊C4—432no—
1084C4⋊C4—432no—
1085C4⋊C4—431no—
1086C4⋊C4—431no—
1087C4⋊C4—862no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—861no—
1096C4⋊C4—861no—
1097C4⋊C4C23×D4312yes—
1098C4⋊C4C23×D4312yes—
1099C4⋊C4C23×D4312yes—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—432no—
1105C22⋊C4—432no—
1106C22⋊C4—432no—
1107C22⋊C4—432no—
1108C22⋊C4—432no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—861no—
1119C22⋊C4—861no—
1120C22⋊C4—861no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C42—22no—
1124C42—22no—
1125C42—432no—
1126C42—862no—
1127C42—862no—
1128C42—862no—
1129C42—861no—
1130C23—22no—
1131C23—22no—
1132C23—41no—
1133C23—41no—
1134C23—42no—
1135C23—81no—
1136C23—81no—
1137C23—432no—
1138C23—861no—
1139C23—861no—
1140C23—861no—
1141C23—3441no—
1142C23—3442no—
1143C23—3442no—
1144C23—1722no—
1145C23—1722no—
1146C23—1724no—
1147C23C2×D4×D4311yescharacteristic
1148C23C2×D4×D4311yescharacteristic
1149C23C2×D4×D4311yescharacteristic
1150Q8—432no—
1151Q8—861no—
1152Q8—862no—
1153Q8—861no—
1154Q8—861no—
1155Q8—861no—
1156Q8—861no—
1157Q8—3442no—
1158Q8—1722no—
1159D4—22no—
1160D4—22no—
1161D4—44no—
1162D4—42no—
1163D4—82no—
1164D4—432no—
1165D4—864no—
1166D4—864no—
1167D4—861no—
1168D4—861no—
1169D4—861no—
1170D4—861no—
1171D4—861no—
1172D4—862no—
1173D4—3442no—
1174D4—3442no—
1175D4—3442no—
1176D4—3442no—
1177D4—3441no—
1178D4—3441no—
1179D4—1722no—
1180D4—1722no—
1181D4—1722no—
1182D4—1722no—
1183D4—1724no—
1184D4—1724no—
1185D4—1722no—
1186D4—1722no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—81no—
1199C2×C4—81no—
1200C2×C4—81no—
1201C2×C4—432no—
1202C2×C4—432no—
1203C2×C4—432no—
1204C2×C4—861no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—864no—
1208C2×C4—861no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—3442no—
1213C2×C4—3442no—
1214C2×C4—3442no—
1215C2×C4—1722no—
1216C2×C4—1722no—
1217C2×C4—1724no—
1218C2×C4—1722no—
1219C2×C4—1722no—
1220C2×C4—1722no—
1221C2×C4C2×D4×D4311yescharacteristic
1222C2×C4C2×D4×D4311yescharacteristic
1223C2×C4C2×D4×D4311yescharacteristic
1224C2×C4#41×D4312yes—
1225C2×C4#1306337112yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—21no—
1228C8—21no—
1229C8—21no—
1230C8—21no—
1231C8—862no—
1232C8—862no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—82no—
1245C22—162no—
1246C22—862no—
1247C22—862no—
1248C22—862no—
1249C22—862no—
1250C22—3444no—
1251C22—1721no—
1252C22—1721no—
1253C22—1721no—
1254C22—1721no—
1255C22—1721no—
1256C22—1721no—
1257C22—1721no—
1258C22—1721no—
1259C22—6884no—
1260C22#1458354112yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—862no—
1268C4—862no—
1269C4—862no—
1270C4—862no—
1271C4—1721no—
1272C4—1721no—
1273C4—1721no—
1274C4—1721no—
1275C4#1458354112yes—
1276C4C2×#41×D4311yescharacteristic
1277C4C2×#1306337111yescharacteristic
1278C2—22no—
1279C2—41no—
1280C2—41no—
1281C2—82no—
1282C2—3441no—
1283C2—3441no—
1284C2—1722no—
1285C2—1722no—
1286C2C2×#1458354111yescharacteristic
1287C2#1914936411yescharacteristic
1288C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC22×C43C23×D4
hypercenterC2×#482D43
hypocenterC43#61196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. #19148315C2semidirect
2. #19148260C2semidirect
3. #19146846C2semidirect
4. #19146824C2semidirect
5. #19146749C2semidirect
6. #19146739C2semidirect
7. #19146719C2semidirect
8. #19146664C2semidirect
9. #19146543C2semidirect
10. #19146433C2semidirect
11. #19144947C2semidirect
12. #19144589C2semidirect
13. #19144451C2semidirect
14. #19144267C2semidirect
15. #19144210C2semidirect
16. #19144139C2semidirect
17. #19143904C2semidirect
18. #19143817C2semidirect
19. #19143478C2semidirect
20. #19143316C2semidirect
21. #19143116C2semidirect
22. #19143112C2semidirect
23. C2×C43×#482C2semidirect
26. C2×#13063351C22semidirect
28. C2×#13063347C22semidirect
29. C2×#13063331C22semidirect
30. C22×#10621877C22semidirect
32. #14583617C22semidirect
34. #14583612C22semidirect
36. #14583593C22semidirect
38. #14583588C22semidirect
45. #14583530C22semidirect
48. #14583480C22semidirect
54. #14583410C22semidirect
58. #14583380C22semidirect
59. #14583380C22semidirect
60. #14583262C22semidirect
61. #14583257C22semidirect
62. #14583252C22semidirect
63. #14583244C22semidirect
64. #14583243C22semidirect
65. #14583231C22semidirect
66. #14583225C22semidirect
67. #14583219C22semidirect
68. #14583205C22semidirect
69. #14583202C22semidirect
70. #14583193C22semidirect
71. #14583178C22semidirect
72. #14583150C22semidirect
73. #14583146C22semidirect
74. #14583146C22semidirect
75. #14583143C22semidirect
76. #14583141C22semidirect
77. #14583136C22semidirect
78. #14583133C22semidirect
79. #14583126C22semidirect
80. #14583120C22semidirect
81. #14583113C22semidirect
82. #14583098C22semidirect
83. #14583093C22semidirect
84. #14583063C22semidirect
85. #14583063C22semidirect
86. #14583062C22semidirect
87. #14583057C22semidirect
88. #14583052C22semidirect
89. #14583051C22semidirect
90. #14583046C22semidirect
91. #14583046C22semidirect
92. #14583045C22semidirect
93. #14583040C22semidirect
94. #14583035C22semidirect
95. #14583034C22semidirect
96. #14583010C22semidirect
97. #14583005C22semidirect
98. #14582986C22semidirect
99. #14582986C22semidirect
100. #14582974C22semidirect
101. #14582973C22semidirect
102. #14582967C22semidirect
103. (C22⋊D43)⋊C8C22semidirect
104. #14582939C22semidirect
105. #14582925C22semidirect
106. #14582907C22semidirect
107. #14582904C22semidirect
108. #14582903C22semidirect
109. #14582902C22semidirect
112. #14582898C22semidirect
113. #14582898C22semidirect
114. #14582898C22semidirect
115. #14582897C22semidirect
117. #14582896C22semidirect
118. #14582893C22semidirect
119. #14582893C22semidirect
120. #14582892C22semidirect
121. #102×D43C22semidirect
122. #14582865C22semidirect
123. #14582854C22semidirect
125. C2×#117×C43C22semidirect
126. C43×#482C22semidirect
127. C43×#482C22semidirect
128. C43×#482C22semidirect
129. C43×#482C22semidirect
130. C2×#107×C43C22semidirect
131. C2×#106×C43C22semidirect
132. C2×#102×C43C22semidirect
133. C2×#102×C43C22semidirect
134. C2×C22⋊C8×C43C22semidirect
646. C2×#482D43semidirect
705. C2×#117C2×D43semidirect
713. #482C2×D43semidirect
714. #482C2×D43semidirect
715. #482C2×D43semidirect
716. #482C2×D43semidirect
755. C2×#107C2×D43semidirect
756. C2×#106C2×D43semidirect
774. C2×#102C2×D43semidirect
775. C2×#102C2×D43semidirect
777. C2×C22⋊C8C2×D43semidirect
779. C43#61196semidirect

Maximal subgroups

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

subgroupindex
#191483152
#191482602
#191468462
#191468242
#191467492
#191467392
#191467192
#191466642
#191465432
#191464332
#191449472
#191445892
#191444512
#191442672
#191442102
#191441392
#191439042
#191438172
#191434782
#191433162
#191431162
#191431122
C2×C43×#4822
#6119643