Finite Group Databasebeta

← #25064739

Subgroups — #25064739

Order 11008.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148544C211yesmaximal, characteristic
2#19143610C211yesmaximal, characteristic, complemented
3#19143241C211yesmaximal, characteristic, complemented
4#19133228C211yesmaximal, characteristic, complemented
5#19133226C211yesmaximal, characteristic, complemented
6#19133225C211yesmaximal, characteristic, complemented
7#19133218C211yesmaximal, characteristic, complemented
8#19133214C211yesmaximal, characteristic, complemented
9#19133214C211yesmaximal, characteristic, complemented
10#19133204C211yesmaximal, characteristic, complemented
11#19133192C211yesmaximal, characteristic, complemented
12#19133191C211yesmaximal, characteristic, complemented
13#19133182C211yesmaximal, characteristic, complemented
14#329×D43C211yesmaximal, characteristic, complemented
15C43×#1529C211yesmaximal, characteristic, complemented
16#14583632C411yescharacteristic
17#14583621C411yescharacteristic
18#14583612—21no—
19#14583573—21no—
20#14583572—21no—
21#14583562C411yescharacteristic
22#14583561C411yescharacteristic
23#14583555C411yescharacteristic
24#14583544C411yescharacteristic
25#14583541—21no—
26#14583540C411yescharacteristic
27#14583533C411yescharacteristic
28#14583515—21no—
29#14583488—21no—
30#14583482—21no—
31#14583448C2211yescharacteristic
32#14583434C2211yescharacteristic
33#14583434C2211yescharacteristic
34C2×#13063313C2211yescharacteristic
35#124×D43C2211yescharacteristic
36#14583371—21no—
37C4×#10621898C2211yescharacteristic
38#14583029—21no—
39#14582968—21no—
40#14582968—21no—
41C8×D172—21no—
42#14582959—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic, complemented
45#14582956C2211yescharacteristic, complemented
46#14582954C2211yescharacteristic, complemented
47#14582954C2211yescharacteristic, complemented
48#14582954C2211yescharacteristic, complemented
49#14582954C2211yescharacteristic, complemented
50#14582924—21no—
51#14582864—21no—
52#14582851C2211yescharacteristic, 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
70C4×M16×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
83C2×#10621872—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063324—21no—
88#13063323C2×C411yescharacteristic
89#13063321C2×C411yescharacteristic
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063319—21no—
94#13063314C2×C411yescharacteristic
95#13063313—21no—
96#13063313—21no—
97#13063313—21no—
98#13063313C2×C411yescharacteristic
99#13063313C2×C411yescharacteristic
100#13063313C2311yescharacteristic
101#13063313C2311yescharacteristic
102#13063312C2×C411yescharacteristic
103#13063311—21no—
104#13063311—21no—
105#13063311—21no—
106#13063311—21no—
107#13063310—21no—
108#13063310—21no—
109#13063310—21no—
110#13063309—21no—
111#13063308—21no—
112#13063307—21no—
113#13063305—21no—
114#13063305C2×C411yescharacteristic
115#13063305C2×C411yescharacteristic
116#13063303—21no—
117#13063303—21no—
118#13063302—21no—
119#13063302—21no—
120#13063300—21no—
121#13063300—21no—
122#13063300C2×C411yescharacteristic
123#13063300C2×C411yescharacteristic
124#13063299—21no—
125#13063298—21no—
126#13063298—21no—
127#13063298—21no—
128#13063297—21no—
129#13063295—21no—
130#13063295—21no—
131#13063295—21no—
132#13063293—21no—
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135#13063290C2×C411yescharacteristic
136#13063290C2×C411yescharacteristic
137C4×D172—21no—
138C4×D172C2×C411yescharacteristic
139C4×D172D411yescharacteristic
140D4×Dic43—21no—
141#13063287—21no—
142#13063287—21no—
143#13063287C2×C411yescharacteristic
144#13063287C2×C411yescharacteristic
145C4×C22⋊D43—21no—
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063284D411yescharacteristic
154#13063283—21no—
155#13063283—21no—
156#13063282—21no—
157#13063282D411yescharacteristic
158#13063282D411yescharacteristic
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063235—21no—
184#13063235—21no—
185#13063235—21no—
186C8×Dic43—21no—
187C2×M16×C43—21no—
188#126×C43—21no—
189#125×C43C2311yescharacteristic
190#124×C43C2311yescharacteristic
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193#121×C43C2×C411yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic
197#117×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206C23×D43—21no—
207C23×D43—21no—
208C2×Q8×C43C22×C411yescharacteristic
209C2×D4×C43—21no—
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43C22⋊C411yescharacteristic
220C2×C22⋊D43C22⋊C411yescharacteristic
221C22×Dic43—21no—
222C22×Dic43—21no—
223#10621902—81no—
224Q8×D43—81no—
225#10621900—81no—
226D4×D43—44no—
227D4×D43—81no—
228#10621898—42no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—81no—
234C2×D172C22⋊C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×D172C22×C411yescharacteristic
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—81no—
250C2×Dic86C22⋊C411yescharacteristic
251C2×Dic86C22×C411yescharacteristic
252C2×Dic86C22×C411yescharacteristic
253M16×C43—42no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C22×C411yescharacteristic
263C4⋊C4×C43C22×C411yescharacteristic
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C42×C43—21no—
270C42×C43C22×C411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2411yescharacteristic
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43C22⋊C411yescharacteristic
277C22⋊Dic43C22⋊C411yescharacteristic
278(C2×D43)⋊C4—21no—
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)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43C22⋊C411yescharacteristic
301C4⋊Dic43C22⋊C411yescharacteristic
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43C22×C411yescharacteristic
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322#10621872—42no—
323C8×D43—42no—
324C8×D43—42no—
325C8×D43—42no—
326C23×C43—21no—
327C23×C43C2×C22⋊C411yescharacteristic
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—81no—
333C22×D43—81no—
334C22×D43—81no—
335C22×D43—81no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338Q8×C43—41no—
339D4×C43—41no—
340D4×C43—42no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—81no—
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C22⋊D43—22no—
355C22⋊D43—41no—
356C22⋊D43—42no—
357C22⋊D43—81no—
358C22⋊D43—81no—
359C22⋊D43—81no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—81no—
363C2×Dic43—81no—
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369C2×Dic43C2×C22⋊C411yescharacteristic
370D172—22no—
371D172—41no—
372D172—41no—
373D172—42no—
374D172—81no—
375D172—81no—
376D172—81no—
377C4×D43—22no—
378C4×D43—41no—
379C4×D43—41no—
380C4×D43—41no—
381C4×D43—41no—
382C4×D43—41no—
383C4×D43—42no—
384C4×D43—81no—
385C4×D43—81no—
386C4×D43—81no—
387Dic86—41no—
388Dic86—41no—
389Dic86—41no—
390Dic86—81no—
391Dic86—81no—
392C8×C43—22no—
393C8×C43—41no—
394C8×C43—41no—
395C8×C43—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398C43⋊C8—41no—
399C43⋊C8—41no—
400#17679—431nomaximal, Sylow
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43C22×C22⋊C411yescharacteristic
408C2×D43—21no—
409C2×D43—21no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—41no—
414C2×D43—41no—
415C2×D43—41no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—162no—
420C2×D43—162no—
421C2×D43#42112yes—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431Dic43—21no—
432Dic43—21no—
433Dic43—21no—
434Dic43—21no—
435Dic43—21no—
436Dic43—21no—
437Dic43—41no—
438Dic43—41no—
439#3514—431no—
440#2970—431no—
441#2923—431no—
442#1536—431no—
443#1535—431no—
444#1535—431no—
445#1533—431no—
446#1532—431no—
447#1532—431no—
448#1530—431no—
449#1529D4311yescharacteristic, complemented
450#1527—431no—
451#1527—431no—
452#1524—431no—
453C2×#329—431no—
454C2×C43—41no—
455C2×C43—81no—
456C2×C43#288811yescharacteristic
457C2×C43C2×#42111yescharacteristic
458C2×C43#290111yescharacteristic
459D43—22no—
460D43—41no—
461D43—81no—
462D43—81no—
463#559—431no—
464#556—431no—
465#555—861no—
466#551—861no—
467#551—861no—
468D4×Q8—431no—
469#548—431no—
470#548—431no—
471#546—431no—
472#546—431no—
473#546—861no—
474D42—431no—
475#542—861no—
476#538—861no—
477#538—861no—
478#532—431no—
479#529—431no—
480#529—431no—
481#529C2×D4311yescharacteristic
482C2×#124—431no—
483C2×#124—431no—
484#518—861no—
485C4×#41—431no—
486#446—861no—
487#435—861no—
488#435—861no—
489C8×D4—861no—
490#433—861no—
491#433—861no—
492#432—431no—
493#432—431no—
494#432—431no—
495#432—431no—
496#432—431no—
497#432—431no—
498#432C2×D4311yescharacteristic, complemented
499#424—861no—
500#408—861no—
501C4×M16—431no—
502C4×M16C2×D4311yescharacteristic, complemented
503C2×#97—431no—
504C2×#97—431no—
505C2×#97—431no—
506#330—431no—
507#330—431no—
508#330C2×D4311yescharacteristic, complemented
509#330C2×D4311yescharacteristic, complemented
510#329—431no—
511#329—431no—
512#329—431no—
513#329—431no—
514#329—431no—
515#329—431no—
516#329—431no—
517#329—431no—
518#329—431no—
519#329—431no—
520#329C2×D4311yescharacteristic, complemented
521#329C2×D4311yescharacteristic, complemented
522C43#1767911yescharacteristic, complemented, Sylow
523C2×#41—431no—
524C2×#41—431no—
525C2×#41—431no—
526C22×Q8—431no—
527C22×Q8—431no—
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—861no—
531C2×M16—21no—
532C2×M16—861no—
533C22×C8—861no—
534C22×C8—861no—
535C22×C8—861no—
536C4⋊Q8—431no—
537C4⋊Q8—861no—
538#127—431no—
539#126—21no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#125C22×D4311yescharacteristic
545#124—431no—
546#124—431no—
547#124—431no—
548#124—431no—
549#124—431no—
550#124—431no—
551#124—861no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556#124—861no—
557#124—861no—
558#124C22×D4311yescharacteristic
559#123—21no—
560#123—861no—
561#123—861no—
562#123—861no—
563#123—861no—
564#123—861no—
565#123—861no—
566C22⋊Q8—431no—
567C22⋊Q8—431no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8C4×D4311yescharacteristic
574#121—431no—
575#121—431no—
576#121—861no—
577#121—861no—
578#121—861no—
579#121—861no—
580#121—861no—
581#121—861no—
582#121—861no—
583#121C4×D4311yescharacteristic
584#120—861no—
585#120—861no—
586#120—861no—
587#120—861no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—431no—
592C4×Q8C4×D4311yescharacteristic
593C4×D4—21no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4C4×D4311yescharacteristic
611#117—21no—
612#117—431no—
613#117—431no—
614#117—431no—
615#117—861no—
616#117—861no—
617#117—861no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C42—431no—
625C2×C42—431no—
626C2×C42C22×D4311yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—861no—
629C4⋊C8—861no—
630C4⋊C8—861no—
631C4⋊C8—861no—
632C4⋊C8—861no—
633C4⋊C8—861no—
634C22⋊C8—21no—
635C22⋊C8—861no—
636C22⋊C8—861no—
637C22⋊C8—861no—
638C22⋊C8—861no—
639C22⋊C8—861no—
640C22⋊C8—861no—
641#97—431no—
642#97—431no—
643#97—431no—
644#97—431no—
645#97—861no—
646#97—861no—
647#97—861no—
648#97C22×D4311yescharacteristic
649#97C22×D4311yescharacteristic
650#97C22×D4311yescharacteristic
651#97C22×D4311yescharacteristic
652C4×C8—21no—
653C4×C8—861no—
654C24—861no—
655C24—861no—
656#41—3441no—
657#41—3441no—
658#41—1722no—
659C2×Q8—431no—
660C2×Q8—431no—
661C2×Q8—431no—
662C2×Q8—861no—
663C2×Q8—861no—
664C2×Q8—3441no—
665C2×Q8—3441no—
666C2×Q8C2×C4×D4311yescharacteristic
667C2×D4—21no—
668C2×D4—431no—
669C2×D4—431no—
670C2×D4—431no—
671C2×D4—431no—
672C2×D4—431no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—3441no—
682C2×D4—3441no—
683C2×D4—1724no—
684C2×D4C2×C4×D4311yescharacteristic
685C22×C4—21no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4C2×C4×D4311yescharacteristic
699C22×C4D4×D4311yescharacteristic
700C22×C4D4×D4311yescharacteristic
701M16—42no—
702M16—1722no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—1722no—
712C2×C8—1722no—
713C2×C8—1722no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
722C4⋊C4—431no—
723C4⋊C4—431no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4C2×C4×D4311yescharacteristic
731C4⋊C4C2×C4×D4311yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—431no—
738C22⋊C4—431no—
739C22⋊C4—431no—
740C22⋊C4—431no—
741C22⋊C4—431no—
742C22⋊C4—431no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4—861no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C42—21no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—431no—
768C42—861no—
769C42—861no—
770C42C2×C4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C42D4×D4311yescharacteristic
773C42C23×D4311yescharacteristic
774C23—21no—
775C23—431no—
776C23—431no—
777C23—861no—
778C23—861no—
779C23—3441no—
780C23—3441no—
781C23—3441no—
782C23—3441no—
783C23—1722no—
784C23—1722no—
785C23C22⋊C4×D4311yescharacteristic
786Q8—41no—
787Q8—3441no—
788Q8—3441no—
789Q8—1721no—
790Q8—1721no—
791Q8—1721no—
792D4—41no—
793D4—42no—
794D4—862no—
795D4—862no—
796D4—3441no—
797D4—3441no—
798D4—3441no—
799D4—3441no—
800D4—3441no—
801D4—3441no—
802D4—1721no—
803D4—1721no—
804D4—1722no—
805D4—1721no—
806D4—1722no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—81no—
814C2×C4—431no—
815C2×C4—431no—
816C2×C4—431no—
817C2×C4—431no—
818C2×C4—431no—
819C2×C4—431no—
820C2×C4—862no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—3441no—
824C2×C4—3441no—
825C2×C4—3441no—
826C2×C4—3441no—
827C2×C4—3441no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1722no—
834C2×C4C22⋊C4×D4311yescharacteristic
835C2×C4C22⋊C4×D4311yescharacteristic
836C2×C4C22⋊C4×D4311yescharacteristic
837C2×C4C22×C4×D4311yescharacteristic
838C2×C4C2×D4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1721no—
845C8—1721no—
846C8—1721no—
847C8—1721no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—432no—
855C22—861no—
856C22—861no—
857C22—861no—
858C22—861no—
859C22—861no—
860C22—1721no—
861C22—1721no—
862C22—1721no—
863C22—1721no—
864C22—1721no—
865C22—1721no—
866C22—6882no—
867C22—6882no—
868C22C2×C22⋊C4×D4311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—861no—
879C4—861no—
880C4—861no—
881C4—861no—
882C4—861no—
883C4—861no—
884C4—1721no—
885C4—1721no—
886C2—41no—
887C2—81no—
888C2—862no—
889C2—3441no—
890C2—3441no—
891C2—1721no—
892C2#1914307211yescharacteristic
893C2#421×D4311yescharacteristic
894C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1529C2
socleC22×C43C22×C22⋊C4
prime radical#19148544C2
cosocleC42×C43C24
hypercenter#1529D43
hypocenterC43#17679
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1529

Complements

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

NH ≅ G/Ntype
2. #19143610C2semidirect
3. #19143241C2semidirect
4. #19133228C2semidirect
5. #19133226C2semidirect
6. #19133225C2semidirect
7. #19133218C2semidirect
8. #19133214C2semidirect
9. #19133214C2semidirect
10. #19133204C2semidirect
11. #19133192C2semidirect
12. #19133191C2semidirect
13. #19133182C2semidirect
14. #329×D43C2semidirect
15. C43×#1529C2semidirect
44. #14582956C22semidirect
45. #14582956C22semidirect
46. #14582954C22semidirect
47. #14582954C22semidirect
48. #14582954C22semidirect
49. #14582954C22semidirect
52. #14582851C22semidirect
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. C4×M16×C43C22semidirect
71. C43×#330C22semidirect
72. C43×#330C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
449. #1529D43semidirect
498. #432C2×D43semidirect
502. C4×M16C2×D43semidirect
508. #330C2×D43semidirect
509. #330C2×D43semidirect
520. #329C2×D43semidirect
521. #329C2×D43semidirect
522. C43#17679semidirect

Maximal subgroups

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

subgroupindex
#191485442
#191436102
#191432412
#191332282
#191332262
#191332252
#191332182
#191332142
#191332042
#191331922
#191331912
#191331822
#329×D432
C43×#15292
#1767943