Finite Group Databasebeta

← #6526545

Subgroups — #6526545

Order 512.

1404 conjugacy classes of subgroups.

The subgroup lattice has 1197 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37304C211yesmaximal, characteristic
2#35579C211yesmaximal, characteristic, complemented
3#29360C211yesmaximal, characteristic, complemented
4#29360C211yesmaximal, characteristic, complemented
5#29356C211yesmaximal, characteristic, complemented
6#29354C211yesmaximal, characteristic, complemented
7#29228C211yesmaximal, characteristic, complemented
8#29228C211yesmaximal, characteristic, complemented
9#29227C211yesmaximal, characteristic, complemented
10#29223C211yesmaximal, characteristic, complemented
11#27829C211yesmaximal, characteristic, complemented
12#27826C211yesmaximal, characteristic, complemented
13#27822C211yesmaximal, characteristic, complemented
14#27819C211yesmaximal, characteristic, complemented
15#27744C211yesmaximal, characteristic, complemented
16#27739C211yesmaximal, characteristic, complemented
17#27735C211yesmaximal, characteristic, complemented
18#27733C211yesmaximal, characteristic, complemented
19#27726C211yesmaximal, characteristic, complemented
20#27725C211yesmaximal, characteristic, complemented
21#27718C211yesmaximal, characteristic, complemented
22#27718C211yesmaximal, characteristic, complemented
23#27717C211yesmaximal, characteristic, complemented
24#27711C211yesmaximal, characteristic, complemented
25#27709C211yesmaximal, characteristic, complemented
26#27704C211yesmaximal, characteristic, complemented
27#21897C211yesmaximal, characteristic
28#21843C211yesmaximal, characteristic, complemented
29#21399C211yesmaximal, characteristic
30#21315C211yesmaximal, characteristic, complemented
31#20554C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#433C2211yescharacteristic
35C2×#424C2211yescharacteristic
36#2859C2211yescharacteristic
37#2858C2211yescharacteristic
38#2694—21no—
39#2694—21no—
40#2681—21no—
41#2681—21no—
42#2674—21no—
43#2674—21no—
44#2672—21no—
45#2672—21no—
46#2660C2211yescharacteristic
47#2641C2211yescharacteristic
48#2588—21no—
49#2587—21no—
50#2585—21no—
51#2570C2211yescharacteristic
52#2566C2211yescharacteristic
53#2566C2211yescharacteristic
54#2563C2211yescharacteristic
55#2556—21no—
56#2552C2211yescharacteristic
57#2552C2211yescharacteristic
58#2550C2211yescharacteristic
59#2542C2211yescharacteristic
60#2522—21no—
61#2507—21no—
62#2504C2211yescharacteristic
63#2501C2211yescharacteristic
64#2500C2211yescharacteristic
65#2500C2211yescharacteristic
66#2462—21no—
67#2442C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2440C2211yescharacteristic
71#2423—21no—
72#2330C2211yescharacteristic
73#2330C2211yescharacteristic
74#2314C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic
76C4×#125C2211yescharacteristic
77#2298C2211yescharacteristic
78#2274C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2025C2211yescharacteristic
104#2025C2211yescharacteristic
105#2025C2211yescharacteristic
106#2025C2211yescharacteristic
107#2025C2211yescharacteristic
108#2025C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#1993C2211yescharacteristic
112#1993C2211yescharacteristic
113#1993C2211yescharacteristic
114#1992C2211yescharacteristic
115#1992C2211yescharacteristic
116#1992C2211yescharacteristic
117#1992C2211yescharacteristic
118#1992C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1990C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1988C2211yescharacteristic
134#1988C2211yescharacteristic
135#1988C2211yescharacteristic
136#1987C2211yescharacteristic
137#1987C2211yescharacteristic
138#1987C2211yescharacteristic
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1982C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1836C2211yescharacteristic
168#1836C2211yescharacteristic
169#1836C2211yescharacteristic
170#1836C2211yescharacteristic
171#1836C2211yescharacteristic
172#1836C2211yescharacteristic
173#1834C2211yescharacteristic
174#1834C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1824C2211yescharacteristic
178#1823C2211yescharacteristic
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1770C2211yescharacteristic
186#1770C2211yescharacteristic
187#1768C2211yescharacteristic
188#1768C2211yescharacteristic
189#1767C2211yescharacteristic
190#1767C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#544—24no—
206#544—24no—
207#540—24no—
208#540—24no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×Q8—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245#433—24no—
246#424—24no—
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#400—21no—
282#400—21no—
283#399—21no—
284#399—21no—
285#399—21no—
286#399—21no—
287#399—21no—
288#399—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#390—21no—
324#390—21no—
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388D411yescharacteristic
362#388D411yescharacteristic
363#388D411yescharacteristic
364#388D411yescharacteristic
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387D411yescharacteristic
378#387D411yescharacteristic
379#387D411yescharacteristic
380#387D411yescharacteristic
381#386—21no—
382#386—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#384—21no—
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#380—21no—
405#380—21no—
406#380—21no—
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2311yescharacteristic
426#376C2311yescharacteristic
427C43C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2411yescharacteristic
498C2×M16—22no—
499C2×M16—41no—
500C2×M16—41no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—41no—
518C4⋊Q8—44no—
519#127—22no—
520#127—22no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—22no—
527#125—22no—
528#125—22no—
529#125—22no—
530#125—41no—
531#125—41no—
532#125—41no—
533#125—44no—
534#125—82no—
535#124—82no—
536#124—82no—
537#123—44no—
538#123—44no—
539#123—82no—
540#123—82no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543C22⋊Q8—82no—
544C22⋊Q8—82no—
545C22⋊Q8—82no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—44no—
551#121—44no—
552C4×Q8—82no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—22no—
558#117—22no—
559#117—22no—
560#117—41no—
561#117#4114yes—
562#117#4114yes—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698C22⋊C8—22no—
699C22⋊C8—22no—
700#97—22no—
701#97—41no—
702#97—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
709C4×C8—41no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750C24—21no—
751C24—21no—
752C24C22×D411yescharacteristic
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8—81no—
761C2×Q8—81no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—81no—
779C2×D4—81no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
784C2×D4—81no—
785C2×D4—81no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C2×#4112yes—
830C22×C4C2×#4112yes—
831C22×C4C2511yescharacteristic
832M16—82no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—82no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4#12414yes—
930C4⋊C4#12414yes—
931C4⋊C42−1+412yes—
932C4⋊C42−1+412yes—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4#12414yes—
962C22⋊C4#12414yes—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—41no—
972C42—41no—
973C42—41no—
974C42—41no—
975C42—42no—
976C42—42no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42C2×#4112yes—
984C42C2×#4112yes—
985C42C2×#4112yes—
986C42C2×#4112yes—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23C2×#12412yes—
1008C23C23×D411yescharacteristic
1009Q8—84no—
1010Q8—162no—
1011Q8—162no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—162no—
1021D4—162no—
1022D4—162no—
1023D4—162no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—162no—
1105C2×C4—162no—
1106C2×C4—162no—
1107C2×C4—162no—
1108C2×C4C2×#12412yes—
1109C2×C4C2×#12412yes—
1110C2×C4C2×#12412yes—
1111C2×C4C2×#12412yes—
1112C2×C4C2×#12412yes—
1113C2×C4C22×#4111yescharacteristic
1114C2×C4C22×#4111yescharacteristic
1115C2×C4C2×2−1+411yescharacteristic
1116C2×C4C2×2−1+411yescharacteristic
1117C2×C4#58511yescharacteristic
1118C2×C4#58511yescharacteristic
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22C22×#12411yescharacteristic
1149C22#348911yescharacteristic
1150C22#348911yescharacteristic
1151C22#358511yescharacteristic
1152C22#358511yescharacteristic
1153C22#358511yescharacteristic
1154C22#358611yescharacteristic
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—41no—
1161C4—41no—
1162C4—42no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4#350711yescharacteristic
1183C4#350711yescharacteristic
1184C4#350911yescharacteristic
1185C4#351011yescharacteristic
1186C2—42no—
1187C2—161no—
1188C2—161no—
1189C2#3562811yescharacteristic
1190C2#6062511yescharacteristic
1191C2#6062611yescharacteristic
1192C2#6223111yescharacteristic
1193C2#6223311yescharacteristic
1194C2#6223811yescharacteristic
1195C2#6224211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35579C2semidirect
3. #29360C2semidirect
4. #29360C2semidirect
5. #29356C2semidirect
6. #29354C2semidirect
7. #29228C2semidirect
8. #29228C2semidirect
9. #29227C2semidirect
10. #29223C2semidirect
11. #27829C2semidirect
12. #27826C2semidirect
13. #27822C2semidirect
14. #27819C2semidirect
15. #27744C2semidirect
16. #27739C2semidirect
17. #27735C2semidirect
18. #27733C2semidirect
19. #27726C2semidirect
20. #27725C2semidirect
21. #27718C2semidirect
22. #27718C2semidirect
23. #27717C2semidirect
24. #27711C2semidirect
25. #27709C2semidirect
26. #27704C2semidirect
28. #21843C2semidirect
30. #21315C2semidirect
31. #20554C2semidirect

Maximal subgroups

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

subgroupindex
#373042
#355792
#293602
#293562
#293542
#292282
#292272
#292232
#278292
#278262
#278222
#278192
#277442
#277392
#277352
#277332
#277262
#277252
#277182
#277172
#277112
#277092
#277042
#218972
#218432
#213992
#213152
#205542