Finite Group Databasebeta

← #25064578

Subgroups — #25064578

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148544C211yesmaximal, characteristic
2#19143604C211yesmaximal, characteristic, complemented
3#19143020C211yesmaximal, characteristic, complemented
4#19133214C211yesmaximal, characteristic, complemented
5#19133204C211yesmaximal, characteristic, complemented
6#19133201C211yesmaximal, characteristic, complemented
7#19133194C211yesmaximal, characteristic, complemented
8#19133191C211yesmaximal, characteristic, complemented
9#19133185C211yesmaximal, characteristic, complemented
10#19133183C211yesmaximal, characteristic, complemented
11#19133182C211yesmaximal, characteristic, complemented
12#19133182C211yesmaximal, characteristic, complemented
13C2×#14582638C211yesmaximal, characteristic, complemented
14#329×D43C211yesmaximal, characteristic, complemented
15C43×#1532C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583632C411yescharacteristic
18#14583621C411yescharacteristic
19#14583612—21no—
20#14583573—21no—
21#14583572—21no—
22#14583562C411yescharacteristic
23#14583561C411yescharacteristic
24#14583555C411yescharacteristic
25#14583544C411yescharacteristic
26#14583541—21no—
27#14583540C411yescharacteristic
28#14583533C411yescharacteristic
29#14583515—21no—
30#14583488—21no—
31#14583482—21no—
32#14583448C2211yescharacteristic
33#14583434C2211yescharacteristic
34#14583434C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36#124×D43C2211yescharacteristic
37#14583371—21no—
38C4×#10621898C2211yescharacteristic
39#14583028—21no—
40#14582969—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582954C2211yescharacteristic, complemented
44#14582954C2211yescharacteristic, complemented
45#14582856—21no—
46#14582856—21no—
47#14582854—21no—
48C4×#10621877C2211yescharacteristic, complemented
49#14582851C2211yescharacteristic, complemented
50#14582851C2211yescharacteristic, complemented
51#14582851C2211yescharacteristic, complemented
52C2×#13063236C2211yescharacteristic, complemented
53#97×D43C2211yescharacteristic, complemented
54#97×D43C2211yescharacteristic, complemented
55#97×D43C2211yescharacteristic, complemented
56#14582641C2211yescharacteristic, complemented
57#14582641C2211yescharacteristic, complemented
58#14582639C2211yescharacteristic, complemented
59#14582639C2211yescharacteristic, complemented
60#14582638C2211yescharacteristic
61#14582638C2211yescharacteristic
62#14582638C2211yescharacteristic
63#14582638C2211yescharacteristic
64#14582638C2211yescharacteristic, complemented
65#14582638C2211yescharacteristic, complemented
66#14582638C2211yescharacteristic, complemented
67#14582638C2211yescharacteristic, complemented
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C2×#97×C43C2211yescharacteristic, complemented
71C43×#330C2211yescharacteristic, complemented
72C43×#330C2211yescharacteristic, complemented
73C43×#329C2211yescharacteristic, complemented
74C43×#329C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898D411yescharacteristic
77C2×#10621900C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C2×Q8×D43C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83#13063331—28no—
84C2×#10621877—21no—
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×#10621872—21no—
88C22×C43⋊C8—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92#13063324—21no—
93#13063323C2×C411yescharacteristic
94#13063321C2×C411yescharacteristic
95#13063320—21no—
96#13063320—21no—
97#13063320—21no—
98#13063319—21no—
99#13063314C2×C411yescharacteristic
100#13063313—21no—
101#13063313—21no—
102#13063313—21no—
103#13063313C2×C411yescharacteristic
104#13063313C2×C411yescharacteristic
105#13063313C2311yescharacteristic
106#13063313C2311yescharacteristic
107#13063312C2×C411yescharacteristic
108#13063311—21no—
109#13063311—21no—
110#13063311—21no—
111#13063311—21no—
112#13063310—21no—
113#13063310—21no—
114#13063310—21no—
115#13063309—21no—
116#13063308—21no—
117#13063307—21no—
118#13063305—21no—
119#13063305C2×C411yescharacteristic
120#13063305C2×C411yescharacteristic
121#13063303—21no—
122#13063303—21no—
123#13063302—21no—
124#13063302—21no—
125#13063300—21no—
126#13063300—21no—
127#13063300C2×C411yescharacteristic
128#13063300C2×C411yescharacteristic
129#13063299—21no—
130#13063298—21no—
131#13063298—21no—
132#13063298—21no—
133#13063297—21no—
134#13063295—21no—
135#13063295—21no—
136#13063295—21no—
137#13063293—21no—
138C4×Dic86C2×C411yescharacteristic
139C4×Dic86D411yescharacteristic
140#13063290C2×C411yescharacteristic
141#13063290C2×C411yescharacteristic
142C4×D172—21no—
143C4×D172C2×C411yescharacteristic
144C4×D172D411yescharacteristic
145D4×Dic43—21no—
146#13063287—21no—
147#13063287—21no—
148#13063287C2×C411yescharacteristic
149#13063287C2×C411yescharacteristic
150C4×C22⋊D43—21no—
151C4×C22⋊D43C2×C411yescharacteristic
152C4×C22⋊D43C2×C411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155(C22⋊D43)⋊C4—21no—
156(C22⋊D43)⋊C4—21no—
157(C22⋊D43)⋊C4—21no—
158#13063284D411yescharacteristic
159#13063283—21no—
160#13063283—21no—
161#13063282—21no—
162#13063282D411yescharacteristic
163#13063282D411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C42×D43C2311yescharacteristic
171C42×D43C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176#13063236—21no—
177#13063236C2311yescharacteristic
178#13063236C2311yescharacteristic
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063235—21no—
182#13063235—21no—
183#13063235—21no—
184C4×C43⋊C8—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C22×C8×C43—21no—
189#126×C43—21no—
190#125×C43C2311yescharacteristic
191#124×C43C2311yescharacteristic
192#123×C43—21no—
193C22⋊Q8×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic
195C4×Q8×C43C2×C411yescharacteristic
196C4×D4×C43—21no—
197C4×D4×C43C2×C411yescharacteristic
198#117×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#97×C43—21no—
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206#97×C43C2311yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43C22×C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43C22⋊C411yescharacteristic
221C2×C22⋊D43C22⋊C411yescharacteristic
222C22×Dic43—21no—
223C22×Dic43—21no—
224#10621902—81no—
225Q8×D43—81no—
226#10621900—81no—
227D4×D43—44no—
228D4×D43—81no—
229#10621898—24no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—81no—
235C2×D172C22⋊C411yescharacteristic
236C2×D172C22×C411yescharacteristic
237C2×D172C22×C411yescharacteristic
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C22×C411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×C4×D43C2×D411yescharacteristic
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—81no—
251C2×Dic86C22⋊C411yescharacteristic
252C2×Dic86C22×C411yescharacteristic
253C2×Dic86C22×C411yescharacteristic
254C2×C8×C43—24no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C22×C411yescharacteristic
264C4⋊C4×C43C22×C411yescharacteristic
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C42×C43—21no—
271C42×C43C22×C411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2411yescharacteristic
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43C22⋊C411yescharacteristic
302C4⋊Dic43C22⋊C411yescharacteristic
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319#10621877—24no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—42no—
325#10621872—24no—
326#10621872—24no—
327#10621872—42no—
328C8×D43—24no—
329C8×D43—24no—
330C8×D43—42no—
331C23×C43—21no—
332C23×C43C2×C22⋊C411yescharacteristic
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—81no—
338C22×D43—81no—
339C22×D43—81no—
340C22×D43—81no—
341C22×D43C2×C22⋊C411yescharacteristic
342C22×D43C2×C22⋊C411yescharacteristic
343Q8×C43—41no—
344D4×C43—41no—
345D4×C43—42no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—81no—
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C23×C411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C22⋊D43—22no—
360C22⋊D43—42no—
361C22⋊D43—81no—
362C22⋊D43—81no—
363C22⋊D43—81no—
364C22⋊D43#10414yes—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—81no—
368C2×Dic43—81no—
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375D172—22no—
376D172—41no—
377D172—41no—
378D172—42no—
379D172—81no—
380D172—81no—
381D172—81no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—41no—
385C4×D43—41no—
386C4×D43—41no—
387C4×D43—41no—
388C4×D43—42no—
389C4×D43—81no—
390C4×D43—81no—
391C4×D43—81no—
392Dic86—22no—
393Dic86—41no—
394Dic86—41no—
395Dic86—81no—
396Dic86—81no—
397C8×C43—22no—
398C8×C43—22no—
399C8×C43—41no—
400C8×C43—41no—
401C43⋊C8—22no—
402C43⋊C8—22no—
403C43⋊C8—22no—
404C43⋊C8—41no—
405#17652—431nomaximal, Sylow
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43C2×#10412yes—
412C22×C43C22×C22⋊C411yescharacteristic
413C2×D43—21no—
414C2×D43—21no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—162no—
425C2×D43—162no—
426C2×D43C2×#10412yes—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—41no—
436Dic43—21no—
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—21no—
441Dic43—41no—
442Dic43—41no—
443Dic43C2×#10412yes—
444#3514—431no—
445#2970—431no—
446#2875—431no—
447#1532—431no—
448#1532D4311yescharacteristic, complemented
449#1530—431no—
450#1529—431no—
451#1527—431no—
452#1527—431no—
453#1525—431no—
454#1524—431no—
455#1524—431no—
456#1524—431no—
457C2×#329—431no—
458C2×#329—431no—
459C2×C43—22no—
460C2×C43—81no—
461C2×C43#288811yescharacteristic
462C2×C43C22×#10411yescharacteristic
463C2×C43#290111yescharacteristic
464D43—22no—
465D43—41no—
466D43—81no—
467D43—81no—
468C2×#131—861no—
469#559—431no—
470#556—431no—
471#555—861no—
472#551—861no—
473#551—861no—
474D4×Q8—431no—
475#548—431no—
476#548—431no—
477#546—431no—
478#546—431no—
479#546—861no—
480D42—431no—
481#542—861no—
482#538—861no—
483#538—861no—
484#532—431no—
485#529—431no—
486#529—431no—
487#529C2×D4311yescharacteristic
488C2×#124—431no—
489C2×#124—431no—
490#518—861no—
491C4×#41—431no—
492#446—861no—
493#435—861no—
494#435—861no—
495C8×D4—861no—
496#432—431no—
497#432—431no—
498#432C2×D4311yescharacteristic, complemented
499#405—861no—
500#405—861no—
501#405—861no—
502C4×M16—431no—
503C4×M16—431no—
504C4×M16—431no—
505C4×M16—431no—
506C2×#97—431no—
507C2×#97—431no—
508C2×#97—431no—
509C2×#97—431no—
510C2×#97C2×D4311yescharacteristic, complemented
511#330—431no—
512#330—431no—
513#330C2×D4311yescharacteristic, complemented
514#330C2×D4311yescharacteristic, complemented
515#329—431no—
516#329—431no—
517#329—431no—
518#329—431no—
519#329—431no—
520#329—431no—
521#329—431no—
522#329—431no—
523#329—431no—
524#329—431no—
525#329C2×D4311yescharacteristic, complemented
526#329C2×D4311yescharacteristic, complemented
527C43#1765211yescharacteristic, complemented, Sylow
528C2×#41—431no—
529C2×#41—431no—
530C2×#41—431no—
531C22×Q8—431no—
532C22×Q8—431no—
533C22×D4—431no—
534C22×D4—431no—
535C22×D4—861no—
536#131—868no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C22×C8—21no—
542C22×C8—861no—
543C22×C8—861no—
544C22×C8—861no—
545C22×C8—861no—
546C4⋊Q8—431no—
547C4⋊Q8—861no—
548#127—431no—
549#126—21no—
550#126—861no—
551#126—861no—
552#126—861no—
553#126—861no—
554#125C22×D4311yescharacteristic
555#124—431no—
556#124—431no—
557#124—431no—
558#124—431no—
559#124—431no—
560#124—431no—
561#124—861no—
562#124—861no—
563#124—861no—
564#124—861no—
565#124—861no—
566#124—861no—
567#124—861no—
568#124C22×D4311yescharacteristic
569#123—21no—
570#123—861no—
571#123—861no—
572#123—861no—
573#123—861no—
574#123—861no—
575#123—861no—
576C22⋊Q8—431no—
577C22⋊Q8—431no—
578C22⋊Q8—861no—
579C22⋊Q8—861no—
580C22⋊Q8—861no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8C4×D4311yescharacteristic
584#121—431no—
585#121—431no—
586#121—861no—
587#121—861no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121C4×D4311yescharacteristic
594#120—861no—
595#120—861no—
596#120—861no—
597#120—861no—
598C4×Q8—431no—
599C4×Q8—431no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8C4×D4311yescharacteristic
603C4×D4—21no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4C4×D4311yescharacteristic
621#117—21no—
622#117—431no—
623#117—431no—
624#117—431no—
625#117—861no—
626#117—861no—
627#117—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C22⋊C4—861no—
633C2×C22⋊C4—861no—
634C2×C42—431no—
635C2×C42—431no—
636C2×C42C22×D4311yescharacteristic
637C4⋊C8—21no—
638C4⋊C8—861no—
639C4⋊C8—861no—
640C22⋊C8—21no—
641C22⋊C8—861no—
642C22⋊C8—861no—
643#97—21no—
644#97—431no—
645#97—431no—
646#97—431no—
647#97—431no—
648#97—861no—
649#97—861no—
650#97—861no—
651#97—861no—
652#97C22×D4311yescharacteristic
653#97C22×D4311yescharacteristic
654#97C22×D4311yescharacteristic
655#97C22×D4311yescharacteristic
656C4×C8—861no—
657C4×C8—861no—
658C4×C8—861no—
659C4×C8—861no—
660C24—861no—
661C24—861no—
662#41—864no—
663#41—3441no—
664#41—3441no—
665C2×Q8—431no—
666C2×Q8—431no—
667C2×Q8—431no—
668C2×Q8—861no—
669C2×Q8—861no—
670C2×Q8—3441no—
671C2×Q8—3441no—
672C2×Q8C2×C4×D4311yescharacteristic
673C2×D4—21no—
674C2×D4—431no—
675C2×D4—431no—
676C2×D4—431no—
677C2×D4—431no—
678C2×D4—431no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—3441no—
688C2×D4—3441no—
689C2×D4—1724no—
690C2×D4C2×C4×D4311yescharacteristic
691C22×C4—21no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4C2×C4×D4311yescharacteristic
705C22×C4D4×D4311yescharacteristic
706C22×C4D4×D4311yescharacteristic
707M16—864no—
708M16—864no—
709M16—864no—
710M16—1722no—
711C2×C8—24no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—864no—
717C2×C8—864no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—1722no—
723C2×C8—1722no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—431no—
729C4⋊C4—431no—
730C4⋊C4—431no—
731C4⋊C4—431no—
732C4⋊C4—431no—
733C4⋊C4—431no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4C2×C4×D4311yescharacteristic
741C4⋊C4C2×C4×D4311yescharacteristic
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—431no—
748C22⋊C4—431no—
749C22⋊C4—431no—
750C22⋊C4—431no—
751C22⋊C4—431no—
752C22⋊C4—431no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4—861no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C22⋊C4—861no—
764C22⋊C4—861no—
765C22⋊C4—861no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C42—21no—
772C42—431no—
773C42—431no—
774C42—431no—
775C42—431no—
776C42—431no—
777C42—431no—
778C42—861no—
779C42—861no—
780C42C2×C4×D4311yescharacteristic
781C42D4×D4311yescharacteristic
782C42D4×D4311yescharacteristic
783C42C23×D4311yescharacteristic
784C23—21no—
785C23—431no—
786C23—431no—
787C23—861no—
788C23—861no—
789C23—3441no—
790C23—3441no—
791C23—3441no—
792C23—3441no—
793C23—1722no—
794C23—1722no—
795C23C22⋊C4×D4311yescharacteristic
796Q8—41no—
797Q8—862no—
798Q8—3441no—
799Q8—3441no—
800Q8—1721no—
801Q8—1721no—
802D4—41no—
803D4—42no—
804D4—434no—
805D4—862no—
806D4—862no—
807D4—3441no—
808D4—3441no—
809D4—3441no—
810D4—3441no—
811D4—3441no—
812D4—3441no—
813D4—1721no—
814D4—1721no—
815D4—1722no—
816D4—1722no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—81no—
824C2×C4—431no—
825C2×C4—431no—
826C2×C4—431no—
827C2×C4—431no—
828C2×C4—431no—
829C2×C4—431no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—3441no—
835C2×C4—3441no—
836C2×C4—3441no—
837C2×C4—3441no—
838C2×C4—3441no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1722no—
844C2×C4C22⋊C4×D4311yescharacteristic
845C2×C4C22⋊C4×D4311yescharacteristic
846C2×C4C22⋊C4×D4311yescharacteristic
847C2×C4C22×C4×D4311yescharacteristic
848C2×C4C2×D4×D4311yescharacteristic
849C2×C4C2×D4×D4311yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C8—862no—
855C8—862no—
856C8—862no—
857C8—1721no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—432no—
864C22—861no—
865C22—861no—
866C22—861no—
867C22—861no—
868C22—861no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22—1721no—
873C22—1721no—
874C22—1721no—
875C22—6882no—
876C22—6882no—
877C22#104×D4312yes—
878C22C2×C22⋊C4×D4311yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—432no—
889C4—861no—
890C4—861no—
891C4—861no—
892C4—861no—
893C4—861no—
894C4—1721no—
895C4—1721no—
896C2—22no—
897C2—81no—
898C2—862no—
899C2—3441no—
900C2—3441no—
901C2—1721no—
902C2#1914307211yescharacteristic
903C2C2×#104×D4311yescharacteristic
904C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1532C2
socleC22×C43C22×C22⋊C4
prime radical#19148544C2
cosocleC42×C43C24
hypercenter#1532D43
hypocenterC43#17652
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1532

Complements

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

NH ≅ G/Ntype
2. #19143604C2semidirect
3. #19143020C2semidirect
4. #19133214C2semidirect
5. #19133204C2semidirect
6. #19133201C2semidirect
7. #19133194C2semidirect
8. #19133191C2semidirect
9. #19133185C2semidirect
10. #19133183C2semidirect
11. #19133182C2semidirect
12. #19133182C2semidirect
13. C2×#14582638C2semidirect
14. #329×D43C2semidirect
15. C43×#1532C2semidirect
43. #14582954C22semidirect
44. #14582954C22semidirect
48. C4×#10621877C22semidirect
49. #14582851C22semidirect
50. #14582851C22semidirect
51. #14582851C22semidirect
52. C2×#13063236C22semidirect
53. #97×D43C22semidirect
54. #97×D43C22semidirect
55. #97×D43C22semidirect
56. #14582641C22semidirect
57. #14582641C22semidirect
58. #14582639C22semidirect
59. #14582639C22semidirect
64. #14582638C22semidirect
65. #14582638C22semidirect
66. #14582638C22semidirect
67. #14582638C22semidirect
69. C43×#432C22semidirect
70. C2×#97×C43C22semidirect
71. C43×#330C22semidirect
72. C43×#330C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
448. #1532D43semidirect
498. #432C2×D43semidirect
510. C2×#97C2×D43semidirect
513. #330C2×D43semidirect
514. #330C2×D43semidirect
525. #329C2×D43semidirect
526. #329C2×D43semidirect
527. C43#17652semidirect

Maximal subgroups

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

subgroupindex
#191485442
#191436042
#191430202
#191332142
#191332042
#191332012
#191331942
#191331912
#191331852
#191331832
#191331822
C2×#145826382
#329×D432
C43×#15322
#1765243