Finite Group Databasebeta

← #25969257

Subgroups — #25969257

Order 11008.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148407C211yesmaximal, characteristic, complemented
2#19148009C211yesmaximal, characteristic
3#19145879C212yesmaximal, complemented
4#19145876C212yesmaximal, complemented
5#19145846C212yesmaximal, complemented
6#19145843C212yesmaximal, complemented
7#19145827C211yesmaximal, characteristic, complemented
8#19145824C211yesmaximal, characteristic, complemented
9#19145791C211yesmaximal, characteristic, complemented
10#19145774C211yesmaximal, characteristic, complemented
11#19145773C211yesmaximal, characteristic, complemented
12#19145715C211yesmaximal, characteristic, complemented
13#19145713C211yesmaximal, characteristic, complemented
14#19145130C212yesmaximal, complemented
15#19144950C212yesmaximal, complemented
16#19144570C212yesmaximal, complemented
17#19144548C212yesmaximal, complemented
18#19144403C211yesmaximal, characteristic, complemented
19#19144393C211yesmaximal, characteristic, complemented
20#19144384C211yesmaximal, characteristic, complemented
21#474×D43C211yesmaximal, characteristic, complemented
22#19143262C211yesmaximal, characteristic, complemented
23C43×#3235C211yesmaximal, characteristic, complemented
24Q8×Dic86—21no—
25#14583627—21no—
26#14583609—21no—
27#14583607—21no—
28#14583607—21no—
29Q8×D172—21no—
30#14583562—21no—
31#14583562—21no—
32#14583529C2212yes—
33#14583529C2212yescomplemented
34#14583527C2212yescomplemented
35#14583526C2211yescharacteristic
36#14583523C2211yescharacteristic
37#14583516C2211yescharacteristic
38#14583513—21no—
39#14583503C2211yescharacteristic
40#14583502C2211yescharacteristic
41#14583499—21no—
42#14583483—21no—
43#14583481—21no—
44#14583478C2211yescharacteristic
45#14583465C2211yescharacteristic
46#14583462C2211yescharacteristic
47#14583454C2211yescharacteristic
48#14583454C2211yescharacteristic, complemented
49#14583446C2211yescharacteristic
50#14583445—21no—
51C2×#13063325C2211yescharacteristic, complemented
52C4⋊Q8×D43C2211yescharacteristic
53C4⋊Q8×D43C2211yescharacteristic, complemented
54#14583433C2211yescharacteristic
55#14583431C2211yescharacteristic
56#14583429—21no—
57#14583408—21no—
58#14583406—21no—
59#14583379C2212yes—
60C4×#10621898C2211yescharacteristic
61C4×#10621900C2211yescharacteristic
62C4×D4×D43C2211yescharacteristic
63#14583308C2212yescomplemented
64#14583307C2212yescomplemented
65#14583306C2212yescomplemented
66#14583303C2212yescomplemented
67#14583302C2212yescomplemented
68#14583299C2212yescomplemented
69#14583298C2212yescomplemented
70#14583262C2212yes—
71#14583259C2212yes—
72#14583257C2212yes—
73#14583256C2212yes—
74#14583252C2212yes—
75#14583245C2212yes—
76#14583244C2212yes—
77#14583243C2212yescomplemented
78#14583240C2212yescomplemented
79#14583236C2212yescomplemented
80#14583235C2212yescomplemented
81#14583225C2212yes—
82#14583223C2212yes—
83#14583222C2212yes—
84#14583221C2212yescomplemented
85#14583218C2212yes—
86#14583216C2212yes—
87#14583214C2212yes—
88#14583211C2212yescomplemented
89#14583210C2212yes—
90#14583210C2212yescomplemented
91#14583209C2212yescomplemented
92#14583201C2212yescomplemented
93#14583198C2212yes—
94#14583197C2212yes—
95#14583193C2212yescomplemented
96#14583191C2211yescharacteristic, complemented
97#14583187C2212yescomplemented
98#14583186C2211yescharacteristic
99#14583185C2211yescharacteristic, complemented
100#14583185C2211yescharacteristic, complemented
101#14583181C2211yescharacteristic, complemented
102#14583180C2211yescharacteristic
103#14583180C2211yescharacteristic
104#14583179C2211yescharacteristic
105#14583179C2211yescharacteristic
106#14583179C2211yescharacteristic, complemented
107#14583179C2211yescharacteristic, complemented
108#14583178C2212yes—
109#14583177C2212yes—
110#14583176C2211yescharacteristic
111#14582961C2212yescomplemented
112#14582957C2212yescomplemented
113#14582955C2211yescharacteristic, complemented
114#14582952C2211yescharacteristic, complemented
115#14582951C2211yescharacteristic, complemented
116#14582940C2212yes—
117#14582938C2212yes—
118#14582934C2212yes—
119#107×D43C2212yes—
120#14582921C2211yescharacteristic
121C4⋊C8×D43C2211yescharacteristic
122#14582902C2212yes—
123#14582897C2212yes—
124#14582892C2212yes—
125#102×D43C2212yes—
126#14582864C2212yes—
127#14582856C2212yes—
128C43×#533C2211yescharacteristic, complemented
129C43×#532C2211yescharacteristic
130C43×#501C2212yescomplemented
131C43×#490C2212yes—
132C43×#482C2212yes—
133C43×#482C2212yescomplemented
134C43×#476C2211yescharacteristic
135C43×#476C2211yescharacteristic, complemented
136C43×#474C2211yescharacteristic
137C43×#474C2211yescharacteristic, complemented
138C43×#432C2211yescharacteristic, complemented
139C2×#10621898—21no—
140C2×#10621898C2311yescharacteristic
141C2×#10621900C2311yescharacteristic
142C22×Dic86—21no—
143C2×Q8×D43—21no—
144C2×Q8×D43—21no—
145C2×D4×D43C2311yescharacteristic
146C22×C4×D43—21no—
147C2×#10621872C2312yes—
148C2×C8×D43C2312yes—
149#13063325—21no—
150#13063325—21no—
151#13063325—22no—
152#13063325C2312yes—
153#13063325C2311yescharacteristic
154#13063325C2311yescharacteristic
155#13063324—22no—
156#13063324—22no—
157#13063324—21no—
158#13063324—21no—
159#13063324C2311yescharacteristic
160#13063324C2312yes—
161#13063324C2312yes—
162#13063323—21no—
163#13063323—21no—
164#13063323—21no—
165#13063321—21no—
166#13063321C2311yescharacteristic
167#13063320—21no—
168#13063319—21no—
169#13063318—21no—
170#13063318—21no—
171#13063317—22no—
172#13063317C2311yescharacteristic
173#13063316C2311yescharacteristic
174#13063316C2312yes—
175#13063316C2312yes—
176#13063315—22no—
177#13063315—22no—
178#13063315—21no—
179#13063314—21no—
180#13063313C2311yescharacteristic
181#13063312—21no—
182#13063312C2311yescharacteristic
183#13063311—21no—
184#13063311—21no—
185#13063310—21no—
186#13063309—21no—
187#13063308—21no—
188#13063307—21no—
189#13063307—21no—
190#13063306—21no—
191#13063306—21no—
192#13063306—21no—
193#13063305—21no—
194#13063305—21no—
195#13063305—22no—
196#13063305—22no—
197#13063305C2311yescharacteristic
198#13063304C2311yescharacteristic
199#13063303—22no—
200#13063303—22no—
201#13063303—21no—
202#13063302—21no—
203#13063302—22no—
204#13063302—22no—
205#13063302—21no—
206#13063301—21no—
207#13063301—21no—
208#13063301—21no—
209#13063301—21no—
210#13063300C2311yescharacteristic
211#13063299C2311yescharacteristic
212#13063298—21no—
213#13063298—21no—
214#13063297—21no—
215#13063297—21no—
216#13063297—21no—
217#13063297—21no—
218#13063297—21no—
219#13063297—21no—
220#13063296—21no—
221#13063296—21no—
222#13063296C2311yescharacteristic
223#13063296C2311yescharacteristic
224#13063295—21no—
225#13063293—21no—
226#13063293—21no—
227#13063293—21no—
228Q8×Dic43—21no—
229Q8×Dic43—21no—
230C4×Dic86—22no—
231C4×Dic86D411yescharacteristic
232C4×Dic86D411yescharacteristic
233C4×Dic86C2311yescharacteristic
234#13063290—21no—
235#13063290—21no—
236#13063290C2311yescharacteristic
237C4×D172—22no—
238C4×D172D411yescharacteristic
239C4×D172D411yescharacteristic
240C4×D172C2311yescharacteristic
241D4×Dic43C2311yescharacteristic
242D4×Dic43C2311yescharacteristic
243#13063287C2311yescharacteristic
244C4×C22⋊D43—21no—
245C4×C22⋊D43—21no—
246C4×C22⋊D43—21no—
247C4×C22⋊D43—21no—
248C4×C22⋊D43—21no—
249C4×C22⋊D43D411yescharacteristic
250C4×C22⋊D43D411yescharacteristic
251C4×C22⋊D43D411yescharacteristic
252C4×C22⋊D43D411yescharacteristic
253(C22⋊D43)⋊C4—22no—
254(C22⋊D43)⋊C4—22no—
255(C22⋊D43)⋊C4—21no—
256(C22⋊D43)⋊C4—21no—
257#13063284—21no—
258#13063284C2311yescharacteristic
259#13063283C2311yescharacteristic
260#13063283C2312yes—
261#13063283C2312yes—
262#13063282—21no—
263#13063282C2311yescharacteristic
264#13063282C2311yescharacteristic
265#13063281—21no—
266C2×C4⋊Dic43—21no—
267C2×C4⋊Dic43C2312yes—
268C4⋊C4×D43—21no—
269C4⋊C4×D43—21no—
270C4⋊C4×D43C2311yescharacteristic
271C4⋊C4×D43C2312yes—
272C4⋊C4×D43C2312yes—
273C22⋊C4×D43—21no—
274C2×C4×Dic43—21no—
275C42×D43C2311yescharacteristic
276C42×D43C2311yescharacteristic
277#13063259C2312yes—
278#13063259C2312yes—
279#13063258C2312yes—
280#13063258C2312yes—
281#13063258C2312yes—
282#13063258C2312yes—
283#13063258C2312yes—
284#13063258C2312yes—
285#13063257C2312yes—
286#13063257C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289C4⋊(C43⋊C8)C2311yescharacteristic
290C4⋊(C43⋊C8)C2311yescharacteristic
291Dic43⋊C8C2312yes—
292Dic43⋊C8C2312yes—
293#13063250C2312yes—
294#13063250C2312yes—
295#13063248C2312yes—
296#13063248C2312yes—
297#13063247C2312yes—
298#13063247C2312yes—
299#13063246C2312yes—
300#13063246C2312yes—
301#13063246C2312yes—
302#13063246C2312yes—
303#13063245C2312yes—
304#13063245C2312yes—
305C22⋊(C43⋊C8)C2312yes—
306(C2×D43)⋊C8C2312yes—
307(C2×D43)⋊C8C2312yes—
308#13063235C2312yes—
309C4×C43⋊C8C2312yes—
310C8×Dic43C2312yes—
311C2×#41×C43—21no—
312C4⋊Q8×C43C2311yescharacteristic
313C4⋊Q8×C43C2311yescharacteristic
314C4⋊Q8×C43C2311yescharacteristic
315#127×C43C2311yescharacteristic
316#125×C43C2312yes—
317#124×C43—21no—
318C22⋊Q8×C43—21no—
319C22⋊Q8×C43—21no—
320#121×C43—21no—
321#121×C43C2311yescharacteristic
322#121×C43C2311yescharacteristic
323C4×Q8×C43—21no—
324C4×Q8×C43—21no—
325C4×D4×C43—21no—
326C4×D4×C43C2311yescharacteristic
327C4×D4×C43C2311yescharacteristic
328#117×C43C2312yes—
329C2×C42×C43C2311yescharacteristic
330#107×C43C2312yes—
331#107×C43C2312yes—
332#106×C43C2312yes—
333#106×C43C2312yes—
334C4⋊C8×C43C2311yescharacteristic
335C4⋊C8×C43C2311yescharacteristic
336#102×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339#102×C43C2312yes—
340C22⋊C8×C43C2312yes—
341#97×C43C2312yes—
342C23×D43—21no—
343#41×C43—82no—
344C2×Q8×C43—21no—
345C2×Q8×C43—21no—
346C2×Q8×C43—21no—
347C2×D4×C43—21no—
348C2×D4×C43—21no—
349C2×D4×C43—21no—
350C2×D4×C43—21no—
351C2×D4×C43C2411yescharacteristic
352C2×D4×C43C2411yescharacteristic
353C22×C4×C43—21no—
354C22×C4×C43—21no—
355C22×C4×C43C2×D411yescharacteristic
356C22×C4×C43C2×D411yescharacteristic
357C22×C4×C43C2411yescharacteristic
358C2×C22⋊D43—21no—
359C2×C22⋊D43—21no—
360C2×C22⋊D43—21no—
361C2×C22⋊D43—21no—
362C2×C22⋊D43—21no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43C2×D411yescharacteristic
366C2×C22⋊D43C2×D411yescharacteristic
367C22×Dic43—21no—
368C22×Dic43—21no—
369C22×Dic43—21no—
370C22×Dic43—22no—
371Q8×D43—82no—
372Q8×D43—82no—
373#10621900—22no—
374#10621900—22no—
375D4×D43—22no—
376D4×D43—22no—
377#10621898—22no—
378#10621898—22no—
379#10621898—82no—
380C2×D172—21no—
381C2×D172C2×D411yescharacteristic
382C2×D172C2411yescharacteristic
383C2×C4×D43—21no—
384C2×C4×D43—21no—
385C2×C4×D43—21no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—82no—
389C2×C4×D43C2×D411yescharacteristic
390C2×C4×D43C2×D411yescharacteristic
391C2×C4×D43C2×D411yescharacteristic
392C2×C4×D43C2×D411yescharacteristic
393C2×C4×D43C2411yescharacteristic
394C2×C4×D43C2411yescharacteristic
395C2×Dic86—21no—
396C2×Dic86—21no—
397C2×Dic86—22no—
398C2×Dic86—21no—
399C2×Dic86—22no—
400C2×Dic86—22no—
401C2×Dic86—82no—
402C2×Dic86C2×D411yescharacteristic
403C2×Dic86C2411yescharacteristic
404C2×C8×C43C2412yes—
405C2×C8×C43C2412yes—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—22no—
408C4⋊C4×C43—22no—
409C4⋊C4×C43—21no—
410C4⋊C4×C43—21no—
411C4⋊C4×C43C2412yes—
412C4⋊C4×C43C2412yes—
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C22⋊C4×C43—22no—
420C42×C43—22no—
421C42×C43C2×D411yescharacteristic
422C42×C43C2×D411yescharacteristic
423C42×C43C2411yescharacteristic
424C42×C43C2411yescharacteristic
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—21no—
430C22⋊Dic43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43C2×D411yescharacteristic
433C22⋊Dic43C2×D411yescharacteristic
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—21no—
440(C2×D43)⋊C4—21no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4C2×D411yescharacteristic
445(C2×D43)⋊C4C2×D411yescharacteristic
446(C2×D43)⋊C4C2×D411yescharacteristic
447(C2×D43)⋊C4C2×D411yescharacteristic
448C4⋊Dic43—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—22no—
451C4⋊Dic43—22no—
452C4⋊Dic43—21no—
453C4⋊Dic43—21no—
454C4⋊Dic43—22no—
455C4⋊Dic43—22no—
456C4⋊Dic43C2×D411yescharacteristic
457C4⋊Dic43C2×D411yescharacteristic
458C4⋊Dic43C2412yes—
459C4⋊Dic43C2412yes—
460C4⋊Dic43C2411yescharacteristic
461C4⋊Dic43C2411yescharacteristic
462Dic43⋊C4—21no—
463Dic43⋊C4—21no—
464Dic43⋊C4—21no—
465Dic43⋊C4—21no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—21no—
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—21no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4C2×D411yescharacteristic
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—22no—
484C4×Dic43—22no—
485C4×Dic43C2×D411yescharacteristic
486C4×Dic43C2×D411yescharacteristic
487C4×Dic43C2×D411yescharacteristic
488C4×Dic43C2×D411yescharacteristic
489C4×Dic43C2411yescharacteristic
490C4×Dic43C2411yescharacteristic
491C2×C43⋊C8C2412yes—
492C2×C43⋊C8C2412yes—
493#10621872—24no—
494C8×D43—24no—
495C23×C43—21no—
496C23×C43—21no—
497C23×C43C22×D411yescharacteristic
498C22×D43—21no—
499C22×D43—42no—
500C22×D43—81no—
501C22×D43—81no—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D411yescharacteristic
504Q8×C43—42no—
505Q8×C43—42no—
506Q8×C43—81no—
507D4×C43—21no—
508D4×C43—21no—
509D4×C43—21no—
510D4×C43—21no—
511D4×C43—81no—
512D4×C43—81no—
513D4×C43—81no—
514D4×C43—81no—
515C2×C4×C43—22no—
516C2×C4×C43—21no—
517C2×C4×C43—21no—
518C2×C4×C43—22no—
519C2×C4×C43—21no—
520C2×C4×C43—22no—
521C2×C4×C43—21no—
522C2×C4×C43—41no—
523C2×C4×C43—42no—
524C2×C4×C43—42no—
525C2×C4×C43C22×D411yescharacteristic
526C2×C4×C43C22×D411yescharacteristic
527C2×C4×C43C22×D411yescharacteristic
528C2×C4×C43C22×D411yescharacteristic
529C2×C4×C43C22×D411yescharacteristic
530C2×C4×C43C2511yescharacteristic
531C22⋊D43—22no—
532C22⋊D43—22no—
533C22⋊D43—42no—
534C22⋊D43—42no—
535C22⋊D43—81no—
536C22⋊D43—81no—
537C22⋊D43—81no—
538C22⋊D43—81no—
539C22⋊D43—81no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—21no—
545C2×Dic43—42no—
546C2×Dic43—81no—
547C2×Dic43—81no—
548C2×Dic43—82no—
549C2×Dic43C22×D411yescharacteristic
550C2×Dic43C22×D411yescharacteristic
551C2×Dic43C22×D411yescharacteristic
552C2×Dic43C22×D411yescharacteristic
553C2×Dic43C22×D411yescharacteristic
554C2×Dic43C22×D411yescharacteristic
555D172—22no—
556D172—21no—
557D172—21no—
558D172—81no—
559C4×D43—22no—
560C4×D43—22no—
561C4×D43—21no—
562C4×D43—21no—
563C4×D43—41no—
564C4×D43—41no—
565C4×D43—42no—
566C4×D43—81no—
567C4×D43—81no—
568C4×D43—82no—
569C4×D43—82no—
570C4×D432−1+412yes—
571C4×D432−1+412yes—
572Dic86—22no—
573Dic86—21no—
574Dic86—21no—
575Dic86—42no—
576Dic86—42no—
577Dic86—81no—
578Dic86—82no—
579Dic86—82no—
580Dic86—82no—
581C8×C43—22no—
582C8×C43—22no—
583C43⋊C8—22no—
584C43⋊C8—22no—
585#60888—431nomaximal, Sylow
586C22×C43—21no—
587C22×C43—21no—
588C22×C43—21no—
589C22×C43—41no—
590C22×C43—41no—
591C22×C43—41no—
592C22×C43—41no—
593C22×C43—41no—
594C22×C43—41no—
595C22×C43C23×D411yescharacteristic
596C2×D43—21no—
597C2×D43—21no—
598C2×D43—21no—
599C2×D43—21no—
600C2×D43—21no—
601C2×D43—41no—
602C2×D43—41no—
603C2×D43—41no—
604C2×D43—84no—
605C2×D43#53612yes—
606C4×C43—21no—
607C4×C43—21no—
608C4×C43—21no—
609C4×C43—21no—
610C4×C43—42no—
611C4×C43—42no—
612C4×C43—41no—
613C4×C43—41no—
614C4×C43#57612yes—
615C4×C43C2×2−1+411yescharacteristic
616C4×C43C2×2−1+411yescharacteristic
617Dic43—21no—
618Dic43—21no—
619Dic43—21no—
620Dic43—21no—
621Dic43—21no—
622Dic43—41no—
623Dic43—41no—
624Dic43—42no—
625Dic43—42no—
626Dic43—41no—
627Dic43#53612yes—
628#3503—431no—
629#3460—431no—
630#3243—432no—
631#3243—432no—
632#3241—432no—
633#3241—432no—
634#3239—431no—
635#3239—431no—
636#3235—431no—
637#3235D4311yescharacteristic, complemented
638#3233—431no—
639#3233—431no—
640#3226—431no—
641#3226—431no—
642#3164—432no—
643#3136—432no—
644#3098—432no—
645#3096—432no—
646#3079—431no—
647#3077—431no—
648#3076—431no—
649C2×#474—431no—
650#2925—431no—
651C2×C43—41no—
652C2×C43—81no—
653C2×C43—81no—
654C2×C43C2×#53611yescharacteristic
655C2×C43C2×#57611yescharacteristic
656C2×C43#358611yescharacteristic
657D43—22no—
658D43—41no—
659D43—81no—
660Q82—861no—
661#557—861no—
662#554—861no—
663#554—861no—
664#554—861no—
665D4×Q8—861no—
666D4×Q8—861no—
667D4×Q8—861no—
668#544—431no—
669#544—432no—
670#544—432no—
671#544—432no—
672#542—431no—
673#542—431no—
674#542—861no—
675#540—431no—
676#540—431no—
677#540—861no—
678#538—861no—
679#538—861no—
680#537—431no—
681#535—431no—
682#535—431no—
683#533—431no—
684#533—431no—
685#533C2×D4311yescharacteristic, complemented
686#532—431no—
687#532—861no—
688#532C2×D4311yescharacteristic
689C2×C4⋊Q8—431no—
690C2×C4⋊Q8—431no—
691C2×C4⋊Q8—431no—
692#529—431no—
693#529—431no—
694#529—861no—
695#525—861no—
696#525—861no—
697#520—432no—
698C4×#41—431no—
699C4×#41—431no—
700C2×C4×D4—431no—
701#501—432no—
702#501—432no—
703#501—432no—
704#501C2×D4312yescomplemented
705#500—432no—
706#500—432no—
707#499—432no—
708#499—432no—
709#490—432no—
710#490C2×D4312yes—
711#489—432no—
712#489—432no—
713#488—432no—
714#488—432no—
715#486—432no—
716#486—432no—
717#485—432no—
718#485—432no—
719#484—432no—
720#484—432no—
721#482—432no—
722#482—432no—
723#482—432no—
724#482—432no—
725#482C2×D4312yes—
726#482C2×D4312yescomplemented
727#481—432no—
728#481—432no—
729#480—432no—
730#480—432no—
731#480—432no—
732#480—432no—
733#479—432no—
734#478—432no—
735#478—432no—
736#478—432no—
737#477—431no—
738#477—432no—
739#476—431no—
740#476—432no—
741#476C2×D4311yescharacteristic
742#476C2×D4311yescharacteristic, complemented
743#475—431no—
744#475—431no—
745#475—431no—
746#474—431no—
747#474—431no—
748#474—431no—
749#474—431no—
750#474—431no—
751#474—432no—
752#474—431no—
753#474—431no—
754#474—432no—
755#474C2×D4311yescharacteristic
756#474C2×D4311yescharacteristic, complemented
757#433—432no—
758#433—432no—
759#432—431no—
760#432C2×D4311yescharacteristic, complemented
761#431—431no—
762#431—431no—
763#428—432no—
764#428—432no—
765#427—432no—
766C2×#107—432no—
767#423—431no—
768C2×C4⋊C8—431no—
769#418—432no—
770#417—432no—
771#416—432no—
772C2×#102—432no—
773#408—432no—
774#405—432no—
775C43#6088811yescharacteristic, complemented, Sylow
776C2×#41—21no—
777C2×#41—431no—
778C2×#41—431no—
779C2×#41—861no—
780C22×Q8—861no—
781C22×Q8—861no—
782C22×Q8—861no—
783C22×D4—431no—
784C23×C4—861no—
785C2×M16—432no—
786C22×C8—432no—
787C4⋊Q8—432no—
788C4⋊Q8—432no—
789C4⋊Q8—431no—
790C4⋊Q8—431no—
791C4⋊Q8—431no—
792C4⋊Q8—432no—
793C4⋊Q8—862no—
794C4⋊Q8—861no—
795C4⋊Q8—861no—
796C4⋊Q8—861no—
797C4⋊Q8—861no—
798C4⋊Q8—862no—
799C4⋊Q8—862no—
800C4⋊Q8—861no—
801C4⋊Q8—861no—
802C4⋊Q8—861no—
803C4⋊Q8C22×D4311yescharacteristic
804C4⋊Q8C22×D4311yescharacteristic
805C4⋊Q8C22×D4311yescharacteristic
806#127—431no—
807#127—861no—
808#127C22×D4311yescharacteristic
809#126—861no—
810#126—861no—
811#126—861no—
812#126—861no—
813#125—431no—
814#125—432no—
815#125—432no—
816#125—431no—
817#125—862no—
818#125—861no—
819#125—862no—
820#125—862no—
821#125C22×D4312yes—
822#124—21no—
823#124—431no—
824#124—431no—
825#124—861no—
826#124—861no—
827#124—861no—
828#124—861no—
829#123—861no—
830#123—861no—
831#123—861no—
832#123—861no—
833#123—861no—
834#123—861no—
835#123—861no—
836#123—861no—
837C22⋊Q8—21no—
838C22⋊Q8—21no—
839C22⋊Q8—431no—
840C22⋊Q8—431no—
841C22⋊Q8—862no—
842C22⋊Q8—862no—
843C22⋊Q8—861no—
844C22⋊Q8—861no—
845C22⋊Q8—861no—
846C22⋊Q8—862no—
847C22⋊Q8—862no—
848C22⋊Q8—862no—
849C22⋊Q8—862no—
850C22⋊Q8—861no—
851C22⋊Q8—861no—
852C22⋊Q8—861no—
853C22⋊Q8—861no—
854C22⋊Q8—861no—
855C22⋊Q8—861no—
856#121—21no—
857#121—431no—
858#121—431no—
859#121—431no—
860#121—431no—
861#121—861no—
862#121—861no—
863#121—861no—
864#121—861no—
865#121—861no—
866#121—861no—
867#121—861no—
868#121—861no—
869#121—861no—
870#121—861no—
871#121C22×D4311yescharacteristic
872#121C22×D4311yescharacteristic
873#120—861no—
874#120—861no—
875#120—861no—
876#120—861no—
877C4×Q8—21no—
878C4×Q8—21no—
879C4×Q8—431no—
880C4×Q8—431no—
881C4×Q8—431no—
882C4×Q8—431no—
883C4×Q8—862no—
884C4×Q8—861no—
885C4×Q8—861no—
886C4×Q8—861no—
887C4×Q8—861no—
888C4×D4—21no—
889C4×D4—431no—
890C4×D4—431no—
891C4×D4—431no—
892C4×D4—431no—
893C4×D4—431no—
894C4×D4—431no—
895C4×D4—431no—
896C4×D4—431no—
897C4×D4—431no—
898C4×D4—431no—
899C4×D4—862no—
900C4×D4—861no—
901C4×D4—861no—
902C4×D4—861no—
903C4×D4—861no—
904C4×D4—862no—
905C4×D4—862no—
906C4×D4—861no—
907C4×D4—861no—
908C4×D4—861no—
909C4×D4C22×D4311yescharacteristic
910C4×D4C22×D4311yescharacteristic
911#117—431no—
912#117—431no—
913#117—431no—
914#117—431no—
915#117—432no—
916#117—432no—
917#117—861no—
918#117—861no—
919#117—861no—
920#117C22×D4312yes—
921C2×C4⋊C4—432no—
922C2×C4⋊C4—431no—
923C2×C4⋊C4—432no—
924C2×C4⋊C4—432no—
925C2×C4⋊C4—861no—
926C2×C4⋊C4—861no—
927C2×C4⋊C4—861no—
928C2×C22⋊C4—861no—
929C2×C42—431no—
930C2×C42—431no—
931C2×C42—861no—
932C2×C42C22×D4311yescharacteristic
933#107—432no—
934#107—432no—
935#107—432no—
936#107—432no—
937#107—432no—
938#107—432no—
939#107—432no—
940#107—432no—
941#107C22×D4312yes—
942#107C22×D4312yes—
943#106—432no—
944#106—432no—
945#106—432no—
946#106—432no—
947#106C22×D4312yes—
948#106C22×D4312yes—
949C4⋊C8—432no—
950C4⋊C8—432no—
951C4⋊C8—431no—
952C4⋊C8—431no—
953C4⋊C8C22×D4311yescharacteristic
954C4⋊C8C22×D4311yescharacteristic
955#103—432no—
956#103—432no—
957#103—432no—
958#103—432no—
959#102—432no—
960#102—432no—
961#102—432no—
962#102—432no—
963#102—432no—
964#102—432no—
965#102—432no—
966#102—432no—
967#102C22×D4312yes—
968#102C22×D4312yes—
969#102C22×D4312yes—
970#102C22×D4312yes—
971C22⋊C8—432no—
972C22⋊C8—432no—
973C22⋊C8—432no—
974C22⋊C8C22×D4312yes—
975#97—432no—
976#97C22×D4312yes—
977C4×C8—432no—
978C4×C8—432no—
979C24—861no—
980#41—82no—
981#41—862no—
982#41—862no—
983#41—862no—
984#41—862no—
985#41—3442no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—21no—
989C2×Q8—431no—
990C2×Q8—431no—
991C2×Q8—861no—
992C2×Q8—862no—
993C2×Q8—862no—
994C2×Q8—862no—
995C2×Q8—861no—
996C2×Q8—861no—
997C2×Q8—3442no—
998C2×Q8—3442no—
999C2×Q8—3442no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—431no—
1005C2×D4—431no—
1006C2×D4—431no—
1007C2×D4—431no—
1008C2×D4—861no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—861no—
1012C2×D4—861no—
1013C2×D4—861no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4C23×D4311yescharacteristic
1019C2×D4C23×D4311yescharacteristic
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—431no—
1023C22×C4—431no—
1024C22×C4—431no—
1025C22×C4—431no—
1026C22×C4—431no—
1027C22×C4—431no—
1028C22×C4—861no—
1029C22×C4—861no—
1030C22×C4—862no—
1031C22×C4—862no—
1032C22×C4—861no—
1033C22×C4—861no—
1034C22×C4—861no—
1035C22×C4—862no—
1036C22×C4—861no—
1037C22×C4—3442no—
1038C22×C4D4×D4311yescharacteristic
1039C22×C4D4×D4311yescharacteristic
1040C22×C4C23×D4311yescharacteristic
1041M16—864no—
1042C2×C8—432no—
1043C2×C8—432no—
1044C2×C8—864no—
1045C2×C8C23×D4312yes—
1046C2×C8C23×D4312yes—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—431no—
1053C4⋊C4—431no—
1054C4⋊C4—431no—
1055C4⋊C4—431no—
1056C4⋊C4—431no—
1057C4⋊C4—431no—
1058C4⋊C4—432no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—861no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—862no—
1073C4⋊C4—862no—
1074C4⋊C4—862no—
1075C4⋊C4—862no—
1076C4⋊C4—862no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—862no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—861no—
1084C4⋊C4C23×D4312yes—
1085C4⋊C4C23×D4312yes—
1086C4⋊C4C23×D4311yescharacteristic
1087C4⋊C4C23×D4311yescharacteristic
1088C22⋊C4—22no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—21no—
1093C22⋊C4—431no—
1094C22⋊C4—431no—
1095C22⋊C4—431no—
1096C22⋊C4—431no—
1097C22⋊C4—431no—
1098C22⋊C4—431no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—862no—
1103C22⋊C4—862no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—861no—
1109C22⋊C4—861no—
1110C22⋊C4—861no—
1111C22⋊C4—861no—
1112C22⋊C4—861no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C42—22no—
1117C42—431no—
1118C42—431no—
1119C42—431no—
1120C42—431no—
1121C42—431no—
1122C42—431no—
1123C42—861no—
1124C42—861no—
1125C42—862no—
1126C42—862no—
1127C42—861no—
1128C42D4×D4311yescharacteristic
1129C42D4×D4311yescharacteristic
1130C42C23×D4311yescharacteristic
1131C42C23×D4311yescharacteristic
1132C23—21no—
1133C23—21no—
1134C23—431no—
1135C23—431no—
1136C23—861no—
1137C23—3441no—
1138C23—3441no—
1139C23—1722no—
1140C23C2×D4×D4311yescharacteristic
1141Q8—42no—
1142Q8—42no—
1143Q8—81no—
1144Q8—862no—
1145Q8—861no—
1146Q8—861no—
1147Q8—3442no—
1148Q8—3442no—
1149Q8—3442no—
1150Q8—3441no—
1151Q8—1722no—
1152Q8—1722no—
1153D4—21no—
1154D4—21no—
1155D4—21no—
1156D4—21no—
1157D4—81no—
1158D4—81no—
1159D4—81no—
1160D4—81no—
1161D4—862no—
1162D4—862no—
1163D4—862no—
1164D4—861no—
1165D4—861no—
1166D4—3441no—
1167D4—3441no—
1168D4—3441no—
1169D4—3441no—
1170D4—3441no—
1171D4—3441no—
1172D4—1722no—
1173D4—1722no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—431no—
1185C2×C4—432no—
1186C2×C4—432no—
1187C2×C4—431no—
1188C2×C4—431no—
1189C2×C4—431no—
1190C2×C4—431no—
1191C2×C4—431no—
1192C2×C4—862no—
1193C2×C4—862no—
1194C2×C4—861no—
1195C2×C4—861no—
1196C2×C4—861no—
1197C2×C4—861no—
1198C2×C4—862no—
1199C2×C4—862no—
1200C2×C4—861no—
1201C2×C4—3441no—
1202C2×C4—3441no—
1203C2×C4—3442no—
1204C2×C4—3442no—
1205C2×C4—3441no—
1206C2×C4—3441no—
1207C2×C4—3442no—
1208C2×C4—1721no—
1209C2×C4—1721no—
1210C2×C4—1722no—
1211C2×C4—1722no—
1212C2×C4C2×D4×D4311yescharacteristic
1213C2×C4C2×D4×D4311yescharacteristic
1214C2×C4C2×D4×D4311yescharacteristic
1215C2×C4C2×D4×D4311yescharacteristic
1216C2×C4C2×D4×D4311yescharacteristic
1217C2×C4C24×D4311yescharacteristic
1218C8—22no—
1219C8—22no—
1220C8—862no—
1221C8—862no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—432no—
1232C22—861no—
1233C22—861no—
1234C22—861no—
1235C22—861no—
1236C22—861no—
1237C22—3444no—
1238C22—1721no—
1239C22—1721no—
1240C22—1721no—
1241C22C22×D4×D4311yescharacteristic
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—42no—
1250C4—432no—
1251C4—861no—
1252C4—861no—
1253C4—861no—
1254C4—861no—
1255C4—861no—
1256C4—1721no—
1257C4—1722no—
1258C4—1722no—
1259C4—1721no—
1260C4—1721no—
1261C4#1458370312yes—
1262C42−1+4×D4311yescharacteristic
1263C42−1+4×D4311yescharacteristic
1264C2—41no—
1265C2—81no—
1266C2—81no—
1267C2—862no—
1268C2—3441no—
1269C2—1721no—
1270C2#536×D4311yescharacteristic
1271C2C2×#1458370311yescharacteristic
1272C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3235C2
socleC22×C43C23×D4
prime radical#19148009C2
hypercenter#3235D43
hypocenterC43#60888
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
1. #19148407C2semidirect
3. #19145879C2semidirect
4. #19145876C2semidirect
5. #19145846C2semidirect
6. #19145843C2semidirect
7. #19145827C2semidirect
8. #19145824C2semidirect
9. #19145791C2semidirect
10. #19145774C2semidirect
11. #19145773C2semidirect
12. #19145715C2semidirect
13. #19145713C2semidirect
14. #19145130C2semidirect
15. #19144950C2semidirect
16. #19144570C2semidirect
17. #19144548C2semidirect
18. #19144403C2semidirect
19. #19144393C2semidirect
20. #19144384C2semidirect
21. #474×D43C2semidirect
22. #19143262C2semidirect
23. C43×#3235C2semidirect
33. #14583529C22semidirect
34. #14583527C22semidirect
48. #14583454C22semidirect
51. C2×#13063325C22semidirect
53. C4⋊Q8×D43C22semidirect
63. #14583308C22semidirect
64. #14583307C22semidirect
65. #14583306C22semidirect
66. #14583303C22semidirect
67. #14583302C22semidirect
68. #14583299C22semidirect
69. #14583298C22semidirect
77. #14583243C22semidirect
78. #14583240C22semidirect
79. #14583236C22semidirect
80. #14583235C22semidirect
84. #14583221C22semidirect
88. #14583211C22semidirect
90. #14583210C22semidirect
91. #14583209C22semidirect
92. #14583201C22semidirect
95. #14583193C22semidirect
96. #14583191C22semidirect
97. #14583187C22semidirect
99. #14583185C22semidirect
100. #14583185C22semidirect
101. #14583181C22semidirect
106. #14583179C22semidirect
107. #14583179C22semidirect
111. #14582961C22semidirect
112. #14582957C22semidirect
113. #14582955C22semidirect
114. #14582952C22semidirect
115. #14582951C22semidirect
128. C43×#533C22semidirect
130. C43×#501C22semidirect
133. C43×#482C22semidirect
135. C43×#476C22semidirect
137. C43×#474C22semidirect
138. C43×#432C22semidirect
637. #3235D43semidirect
685. #533C2×D43semidirect
704. #501C2×D43semidirect
726. #482C2×D43semidirect
742. #476C2×D43semidirect
756. #474C2×D43semidirect
760. #432C2×D43semidirect
775. C43#60888semidirect

Maximal subgroups

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

subgroupindex
#191484072
#191480092
#191458792
#191458762
#191458462
#191458432
#191458272
#191458242
#191457912
#191457742
#191457732
#191457152
#191457132
#191451302
#191449502
#191445702
#191445482
#191444032
#191443932
#191443842
#474×D432
#191432622
C43×#32352
#6088843