Finite Group Databasebeta

← #6709460

Subgroups — #6709460

Order 512.

1439 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39030C211yesmaximal, characteristic
2#36254C211yesmaximal, characteristic, complemented
3#33095C211yesmaximal, characteristic, complemented
4#32400C211yesmaximal, characteristic, complemented
5#32265C211yesmaximal, characteristic, complemented
6#32262C211yesmaximal, characteristic, complemented
7#31996C211yesmaximal, characteristic, complemented
8#31787C211yesmaximal, characteristic, complemented
9#31680C211yesmaximal, characteristic, complemented
10#31471C211yesmaximal, characteristic, complemented
11#31266C211yesmaximal, characteristic, complemented
12#30362C211yesmaximal, characteristic, complemented
13#30167C211yesmaximal, characteristic, complemented
14#28082C211yesmaximal, characteristic, complemented
15#27848C211yesmaximal, characteristic, complemented
16#27534C211yesmaximal, characteristic, complemented
17#27477C211yesmaximal, characteristic, complemented
18#27357C211yesmaximal, characteristic, complemented
19#27150C211yesmaximal, characteristic, complemented
20#27054C211yesmaximal, characteristic, complemented
21#27027C211yesmaximal, characteristic, complemented
22#26310C211yesmaximal, characteristic, complemented
23#26199C211yesmaximal, characteristic, complemented
24#25026C211yesmaximal, characteristic, complemented
25#24938C211yesmaximal, characteristic, complemented
26#24869C211yesmaximal, characteristic, complemented
27#24865C211yesmaximal, characteristic, complemented
28#22935C211yesmaximal, characteristic, complemented
29#22562C211yesmaximal, characteristic, complemented
30#22339C211yesmaximal, characteristic, complemented
31#21580C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C22×#102C2211yescharacteristic
35#2854C2211yescharacteristic
36#2852—21no—
37#2851C2211yescharacteristic, complemented
38#2779—21no—
39#2703—21no—
40#2697—21no—
41#2685—21no—
42#2648—21no—
43#2596—21no—
44#2575—21no—
45#2570C2211yescharacteristic, complemented
46#2562C2211yescharacteristic
47#2562C2211yescharacteristic
48#2537C2211yescharacteristic
49#2533—21no—
50#2512C2211yescharacteristic
51#2505—21no—
52#2497C2211yescharacteristic
53#2496C2211yescharacteristic, complemented
54#2495C2211yescharacteristic
55#2490C2211yescharacteristic
56#2487C2211yescharacteristic
57#2487C2211yescharacteristic, complemented
58#2485C2211yescharacteristic
59#2479—21no—
60#2467—21no—
61#2454C2211yescharacteristic
62#2444—21no—
63#2424—21no—
64#2414C2211yescharacteristic
65#2408C2211yescharacteristic
66#2408C2211yescharacteristic
67#2370C2211yescharacteristic, complemented
68#2363C2211yescharacteristic
69#2352C2211yescharacteristic
70#2352C2211yescharacteristic, complemented
71D4×C4⋊C4C2211yescharacteristic
72#2346C2211yescharacteristic, complemented
73#2344C2211yescharacteristic
74D4×C22⋊C4C2211yescharacteristic
75#2312—21no—
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78#2290—21no—
79C2×C4×C4⋊C4C2211yescharacteristic, complemented
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2099C2211yescharacteristic, complemented
83#2094C2211yescharacteristic
84#2092C2211yescharacteristic
85#2086C2211yescharacteristic, complemented
86#2085C2211yescharacteristic, complemented
87#2084C2211yescharacteristic, complemented
88#2077C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic, complemented
91#2077C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#1992C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1955C2211yescharacteristic
123#1955C2211yescharacteristic, complemented
124#1948C2211yescharacteristic, complemented
125#1948C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1944C2211yescharacteristic, complemented
128#1943C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1926C2211yescharacteristic
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1875C2211yescharacteristic
161#1874C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1869C2211yescharacteristic
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic
167#1869C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1854C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1854C2211yescharacteristic, complemented
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic, complemented
178#1853C2211yescharacteristic, complemented
179#1852C2211yescharacteristic, complemented
180#1847C2211yescharacteristic, complemented
181#1825C2211yescharacteristic, complemented
182#1824C2211yescharacteristic, complemented
183#1823C2211yescharacteristic
184#1817C2211yescharacteristic, complemented
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic, complemented
201#1749C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#121—21no—
212C2×#121D411yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#120—21no—
218C2×#120—21no—
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4—21no—
233C22×C42—21no—
234C22×C42C2311yescharacteristic
235#482—24no—
236#481—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#102—24no—
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×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#399—21no—
295#399—21no—
296#399—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#392—21no—
316#392—21no—
317#392—21no—
318#390—21no—
319#390—21no—
320#390—21no—
321#390D411yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#389—21no—
329#389—21no—
330#389D411yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388D411yescharacteristic
360#388D411yescharacteristic
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
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#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386D411yescharacteristic
384#386D411yescharacteristic
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#383—21no—
395#382—21no—
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#381—21no—
399#380—21no—
400#380—21no—
401#380D411yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#379—21no—
417#379—21no—
418#379—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×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437#376—21no—
438C2×#95—21no—
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2×D411yescharacteristic
495C22×D4C2×D411yescharacteristic
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522#126—82no—
523#126—82no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#123—82no—
529#121—22no—
530#121—22no—
531#121—42no—
532#121—41no—
533#121—41no—
534#121—41no—
535#121—41no—
536#121—41no—
537#121—41no—
538#121—82no—
539#120—82no—
540#120—82no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—44no—
552C4×D4—82no—
553#117—22no—
554#117—41no—
555#117—41no—
556#117—41no—
557#117—82no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
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—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
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—44no—
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—41no—
660C2×C42—41no—
661C2×C42—82no—
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#107—41no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102#4114yes—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706C22⋊C8—41no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—41no—
713#97—41no—
714#97—41no—
715#97—41no—
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#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24—21no—
760C24—42no—
761C24—42no—
762C24—81no—
763C24—81no—
764C24—81no—
765C24—81no—
766C24—81no—
767C24C22×D411yescharacteristic
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
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—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—82no—
799C2×D4—82no—
800C2×D4—82no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×#4112yes—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C2511yescharacteristic
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—82no—
899C2×C8—82no—
900C2×C8C2×#4112yes—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4C2×#4112yes—
955C22⋊C4—22no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—41no—
1008C42—41no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—22no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—84no—
1053C23—84no—
1054C23—162no—
1055C23—162no—
1056C23—162no—
1057C23—162no—
1058C23—162no—
1059C23#57512yes—
1060C23#57712yes—
1061C23C23×D411yescharacteristic
1062D4—22no—
1063D4—22no—
1064D4—44no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—82no—
1072D4—82no—
1073D4—84no—
1074D4—84no—
1075D4—162no—
1076D4—162no—
1077D4—162no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—44no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—82no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—162no—
1171C2×C4—162no—
1172C2×C4C22×#4111yescharacteristic
1173C2×C4#58511yescharacteristic
1174C2×C4#58511yescharacteristic
1175C2×C4#58511yescharacteristic
1176C2×C4#58511yescharacteristic
1177C2×C4#58511yescharacteristic
1178C8—22no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—42no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—42no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—168no—
1222C22D4×#4111yescharacteristic
1223C22#348511yescharacteristic
1224C22#348511yescharacteristic
1225C22C2×#57511yescharacteristic
1226C22C2×#57711yescharacteristic
1227C22#358511yescharacteristic
1228C22#358511yescharacteristic
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4#345511yescharacteristic
1255C4#352111yescharacteristic
1256C4#356611yescharacteristic
1257C4#356811yescharacteristic
1258C2—42no—
1259C2—42no—
1260C2—81no—
1261C2—82no—
1262C2—161no—
1263C2#3774011yescharacteristic
1264C2#6145411yescharacteristic
1265C2#6152111yescharacteristic
1266C2#6171411yescharacteristic
1267C2#6172911yescharacteristic
1268C2#6174611yescharacteristic
1269C2#6179511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39030C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36254C2semidirect
3. #33095C2semidirect
4. #32400C2semidirect
5. #32265C2semidirect
6. #32262C2semidirect
7. #31996C2semidirect
8. #31787C2semidirect
9. #31680C2semidirect
10. #31471C2semidirect
11. #31266C2semidirect
12. #30362C2semidirect
13. #30167C2semidirect
14. #28082C2semidirect
15. #27848C2semidirect
16. #27534C2semidirect
17. #27477C2semidirect
18. #27357C2semidirect
19. #27150C2semidirect
20. #27054C2semidirect
21. #27027C2semidirect
22. #26310C2semidirect
23. #26199C2semidirect
24. #25026C2semidirect
25. #24938C2semidirect
26. #24869C2semidirect
27. #24865C2semidirect
28. #22935C2semidirect
29. #22562C2semidirect
30. #22339C2semidirect
31. #21580C2semidirect
37. #2851C22semidirect
45. #2570C22semidirect
53. #2496C22semidirect
57. #2487C22semidirect
67. #2370C22semidirect
70. #2352C22semidirect
72. #2346C22semidirect
79. C2×C4×C4⋊C4C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2099C22semidirect
85. #2086C22semidirect
86. #2085C22semidirect
87. #2084C22semidirect
90. #2077C22semidirect
91. #2077C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
97. #2076C22semidirect
99. #2075C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
120. #1992C22semidirect
121. #1989C22semidirect
123. #1955C22semidirect
124. #1948C22semidirect
125. #1948C22semidirect
126. #1944C22semidirect
127. #1944C22semidirect
128. #1943C22semidirect
144. #1924C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1920C22semidirect
148. #1919C22semidirect
149. #1919C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
167. #1869C22semidirect
172. #1854C22semidirect
173. #1854C22semidirect
174. #1854C22semidirect
177. #1853C22semidirect
178. #1853C22semidirect
179. #1852C22semidirect
180. #1847C22semidirect
181. #1825C22semidirect
182. #1824C22semidirect
184. #1817C22semidirect
188. #1807C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
200. #1752C22semidirect
201. #1749C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#390302
#362542
#330952
#324002
#322652
#322622
#319962
#317872
#316802
#314712
#312662
#303622
#301672
#280822
#278482
#275342
#274772
#273572
#271502
#270542
#270272
#263102
#261992
#250262
#249382
#248692
#248652
#229352
#225622
#223392
#215802