Finite Group Databasebeta

← #6804801

Subgroups — #6804801

Order 512.

1330 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39803C211yesmaximal, characteristic, complemented
2#39633C211yesmaximal, characteristic, complemented
3#33284C211yesmaximal, characteristic, complemented
4#32561C211yesmaximal, characteristic, complemented
5#32554C211yesmaximal, characteristic, complemented
6#32552C211yesmaximal, characteristic, complemented
7#32544C211yesmaximal, characteristic, complemented
8#31833C211yesmaximal, characteristic, complemented
9#31818C211yesmaximal, characteristic, complemented
10#31815C211yesmaximal, characteristic, complemented
11#31804C211yesmaximal, characteristic, complemented
12#30232C211yesmaximal, characteristic, complemented
13#30203C211yesmaximal, characteristic, complemented
14#29226C211yesmaximal, characteristic, complemented
15#29201C211yesmaximal, characteristic, complemented
16#29187C211yesmaximal, characteristic, complemented
17#28730C211yesmaximal, characteristic, complemented
18#28630C211yesmaximal, characteristic
19#28621C211yesmaximal, characteristic
20#27568C211yesmaximal, characteristic, complemented
21#27567C211yesmaximal, characteristic, complemented
22#27553C211yesmaximal, characteristic, complemented
23#27550C211yesmaximal, characteristic, complemented
24#27452C211yesmaximal, characteristic, complemented
25#27443C211yesmaximal, characteristic, complemented
26#27431C211yesmaximal, characteristic, complemented
27#27424C211yesmaximal, characteristic, complemented
28#22279C211yesmaximal, characteristic
29#22222C211yesmaximal, characteristic, complemented
30#21654C211yesmaximal, characteristic, complemented
31#21347C211yesmaximal, characteristic, complemented
32C2×#496C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#488C2211yescharacteristic
35#2868C2211yescharacteristic
36#2858C2211yescharacteristic
37#2790—21no—
38#2790—21no—
39#2786—21no—
40#2740—21no—
41#2729—21no—
42#2729—21no—
43#2715—21no—
44#2700—21no—
45#2660C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2641C2211yescharacteristic
49#2601—21no—
50#2582C2211yescharacteristic
51#2580C2211yescharacteristic
52#2560—21no—
53#2538C2211yescharacteristic
54#2538C2211yescharacteristic
55#2521—21no—
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2512C2211yescharacteristic
59#2512C2211yescharacteristic
60#2502—21no—
61#2497—21no—
62#2492—21no—
63#2474—21no—
64#2452C2211yescharacteristic
65#2452C2211yescharacteristic
66#2451C2211yescharacteristic
67#2451C2211yescharacteristic
68#2440—21no—
69#2357C2211yescharacteristic
70#2354C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72D4×C4⋊C4C2211yescharacteristic
73#2331C2211yescharacteristic
74#2328C2211yescharacteristic
75#2326C2211yescharacteristic
76#2326C2211yescharacteristic
77C4×#125C2211yescharacteristic
78C4×#124C2211yescharacteristic
79#2295C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#1993C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1991C2211yescharacteristic
124#1990C2211yescharacteristic
125#1990C2211yescharacteristic
126#1987C2211yescharacteristic
127#1987C2211yescharacteristic
128#1987C2211yescharacteristic
129#1987C2211yescharacteristic
130#1985C2211yescharacteristic
131#1984C2211yescharacteristic
132#1961C2211yescharacteristic
133#1958C2211yescharacteristic
134#1957C2211yescharacteristic
135#1957C2211yescharacteristic
136#1940C2211yescharacteristic
137#1939C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1846C2211yescharacteristic
187#1836C2211yescharacteristic
188#1836C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1767C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1746C2211yescharacteristic
201#1744C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C22×C4⋊C4—21no—
234#496—24no—
235#489—24no—
236#488—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#399—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391D411yescharacteristic
325#391D411yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389D411yescharacteristic
348#389D411yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387D411yescharacteristic
384#387D411yescharacteristic
385#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384—21no—
402#384—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432#376C2311yescharacteristic
433#376C2311yescharacteristic
434C43C2311yescharacteristic
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C2411yescharacteristic
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16—41no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—41no—
505C2×D8—41no—
506C2×D8—41no—
507C2×D8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—82no—
523C4⋊Q8—82no—
524#127—22no—
525#127—22no—
526#126—82no—
527#126—82no—
528#125—22no—
529#125—22no—
530#124—22no—
531#124—82no—
532#124—82no—
533#124#4114yes—
534C22⋊Q8—82no—
535C22⋊Q8—82no—
536C22⋊Q8—82no—
537C22⋊Q8—82no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556#117—82no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
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—82no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
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×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#107—41no—
663#107—41no—
664#106—41no—
665#106—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
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#97—22no—
697#97—22no—
698#97—41no—
699#97—41no—
700C4×C8—22no—
701C4×C8—22no—
702C4×C8—41no—
703C4×C8—41no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
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#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
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
748C24—21no—
749C24—21no—
750C24—21no—
751C2×Q8—22no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—41no—
758C2×Q8—41no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8C2×#4112yes—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4C2×#4112yes—
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—21no—
805C22×C4—21no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
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×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C2511yescharacteristic
836SD16—82no—
837SD16—82no—
838D8—82no—
839D8—82no—
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—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
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—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
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—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
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—81no—
962C42—22no—
963C42—22no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—41no—
977C42—41no—
978C42—42no—
979C42—42no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42C2×#4112yes—
986C422−1+412yes—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
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—
1007C23—41no—
1008C23C23×D411yescharacteristic
1009Q8—22no—
1010Q8—22no—
1011Q8—41no—
1012Q8—41no—
1013Q8—82no—
1014Q8—162no—
1015Q8—162no—
1016Q8—162no—
1017D4—22no—
1018D4—22no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—162no—
1030D4—162no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
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—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
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—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—84no—
1109C2×C4—84no—
1110C2×C4—162no—
1111C2×C4—162no—
1112C2×C4—162no—
1113C2×C4#54812yes—
1114C2×C4#54812yes—
1115C2×C4#57612yes—
1116C2×C4#57712yes—
1117C2×C4C22×#4111yescharacteristic
1118C2×C4C2×2−1+411yescharacteristic
1119C2×C4#58511yescharacteristic
1120C2×C4#58511yescharacteristic
1121C2×C4#58511yescharacteristic
1122C2×C4#58511yescharacteristic
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
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—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22#344911yescharacteristic
1153C22C2×#54811yescharacteristic
1154C22#350011yescharacteristic
1155C22C2×#57611yescharacteristic
1156C22C2×#57711yescharacteristic
1157C22#358511yescharacteristic
1158C22#358611yescharacteristic
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4#352111yescharacteristic
1187C4#352111yescharacteristic
1188C4#355711yescharacteristic
1189C4#355711yescharacteristic
1190C2—82no—
1191C2—161no—
1192C2—161no—
1193C2#3916311yescharacteristic
1194C2#6097611yescharacteristic
1195C2#6098911yescharacteristic
1196C2#6132911yescharacteristic
1197C2#6133611yescharacteristic
1198C2#6259711yescharacteristic
1199C2#6261011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#496C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39803C2semidirect
2. #39633C2semidirect
3. #33284C2semidirect
4. #32561C2semidirect
5. #32554C2semidirect
6. #32552C2semidirect
7. #32544C2semidirect
8. #31833C2semidirect
9. #31818C2semidirect
10. #31815C2semidirect
11. #31804C2semidirect
12. #30232C2semidirect
13. #30203C2semidirect
14. #29226C2semidirect
15. #29201C2semidirect
16. #29187C2semidirect
17. #28730C2semidirect
20. #27568C2semidirect
21. #27567C2semidirect
22. #27553C2semidirect
23. #27550C2semidirect
24. #27452C2semidirect
25. #27443C2semidirect
26. #27431C2semidirect
27. #27424C2semidirect
29. #22222C2semidirect
30. #21654C2semidirect
31. #21347C2semidirect

Maximal subgroups

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

subgroupindex
#398032
#396332
#332842
#325612
#325542
#325522
#325442
#318332
#318182
#318152
#318042
#302322
#302032
#292262
#292012
#291872
#287302
#286302
#286212
#275682
#275672
#275532
#275502
#274522
#274432
#274312
#274242
#222792
#222222
#216542
#213472