Finite Group Databasebeta

← #6802998

Subgroups — #6802998

Order 512.

1390 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39818C211yesmaximal, characteristic
2#35543C211yesmaximal, characteristic, complemented
3#33116C211yesmaximal, characteristic, complemented
4#32401C211yesmaximal, characteristic, complemented
5#32400C211yesmaximal, characteristic, complemented
6#32390C211yesmaximal, characteristic, complemented
7#32384C211yesmaximal, characteristic, complemented
8#31601C211yesmaximal, characteristic, complemented
9#31598C211yesmaximal, characteristic, complemented
10#31598C211yesmaximal, characteristic, complemented
11#31574C211yesmaximal, characteristic, complemented
12#29765C211yesmaximal, characteristic, complemented
13#29755C211yesmaximal, characteristic, complemented
14#28840C211yesmaximal, characteristic, complemented
15#28834C211yesmaximal, characteristic, complemented
16#27923C211yesmaximal, characteristic, complemented
17#27923C211yesmaximal, characteristic, complemented
18#27917C211yesmaximal, characteristic, complemented
19#27760C211yesmaximal, characteristic, complemented
20#27755C211yesmaximal, characteristic, complemented
21#27654C211yesmaximal, characteristic, complemented
22#27654C211yesmaximal, characteristic, complemented
23#27646C211yesmaximal, characteristic, complemented
24#26541C211yesmaximal, characteristic, complemented
25#26530C211yesmaximal, characteristic, complemented
26#26102C211yesmaximal, characteristic, complemented
27#26094C211yesmaximal, characteristic, complemented
28#22631C211yesmaximal, characteristic, complemented
29#22090C211yesmaximal, characteristic, complemented
30#22081C211yesmaximal, characteristic, complemented
31#21588C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#480C2211yescharacteristic
41#2856C2211yescharacteristic
42#2803—21no—
43#2714—21no—
44#2701—21no—
45#2688—21no—
46#2619C2211yescharacteristic
47#2619C2211yescharacteristic
48#2602—21no—
49#2571C2211yescharacteristic
50#2571C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2570C2211yescharacteristic
55#2570C2211yescharacteristic
56#2559—21no—
57#2552C2211yescharacteristic
58#2552C2211yescharacteristic
59#2541C2211yescharacteristic
60#2513C2211yescharacteristic
61#2512C2211yescharacteristic
62#2509—21no—
63#2508—21no—
64#2507—21no—
65#2506—21no—
66#2505—21no—
67#2505—21no—
68#2473—21no—
69#2473—21no—
70#2464—21no—
71#2456—21no—
72#2445C2211yescharacteristic
73#2445C2211yescharacteristic
74#2366C2211yescharacteristic
75#2357C2211yescharacteristic
76#2324C2211yescharacteristic
77#2324C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic
80#2317C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2296C2211yescharacteristic
83C2×#389C2211yescharacteristic
84#2285C2211yescharacteristic
85#2274C2211yescharacteristic
86#2094C2211yescharacteristic
87#2094C2211yescharacteristic
88#2094C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2071C2211yescharacteristic
113#2071C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#1982C2211yescharacteristic
127#1982C2211yescharacteristic
128#1961C2211yescharacteristic
129#1961C2211yescharacteristic
130#1961C2211yescharacteristic
131#1961C2211yescharacteristic
132#1957C2211yescharacteristic
133#1957C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1947C2211yescharacteristic
142#1943C2211yescharacteristic
143#1943C2211yescharacteristic
144#1943C2211yescharacteristic
145#1941C2211yescharacteristic
146#1940C2211yescharacteristic
147#1939C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1934C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1853C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1846C2211yescharacteristic
181#1846C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1823C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×#127C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#126—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#123—21no—
210C2×#123—21no—
211C2×#121—21no—
212C2×#121—21no—
213C2×#121—21no—
214C2×#121—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C42C2311yescharacteristic
231#482—24no—
232#482—24no—
233#482—42no—
234#482—42no—
235#482—42no—
236#482—42no—
237#481—42no—
238#481—42no—
239#480—24no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#392—21no—
331#392—21no—
332#392—21no—
333#392—21no—
334#392—21no—
335#392—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389D411yescharacteristic
361#389D411yescharacteristic
362#389D411yescharacteristic
363#389D411yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385D411yescharacteristic
409#385D411yescharacteristic
410#385D411yescharacteristic
411#385D411yescharacteristic
412#384—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C2×#95—21no—
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515#127—22no—
516#127—22no—
517#127—41no—
518#127—41no—
519#127—41no—
520#127—41no—
521#126—82no—
522#125—82no—
523#125—82no—
524#123—82no—
525#123—82no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—82no—
533#121—82no—
534#121—82no—
535#121—82no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—82no—
543C4×D4—82no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—22no—
549#117—22no—
550#117—41no—
551#117—41no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
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—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—82no—
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#102—22no—
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—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8#4114yes—
713#97—22no—
714#97—41no—
715#97—41no—
716#97—41no—
717C4×C8—22no—
718C4×C8—41no—
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#95—21no—
753#95—21no—
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762C24—21no—
763C24—21no—
764C24—21no—
765C24C22×D411yescharacteristic
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—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—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
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×D4—81no—
810C2×D4—81no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
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—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C2×#4112yes—
863C22×C4H(5,𝔽2)12yes—
864C22×C4C2511yescharacteristic
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
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×C8C2×#4112yes—
888C2×C8C2×#4112yes—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
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—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
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—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—41no—
996C42—41no—
997C42—42no—
998C42—42no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C422−1+412yes—
1007C422−1+412yes—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23#55012yes—
1036C23C23×D411yescharacteristic
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—84no—
1050D4—84no—
1051D4—162no—
1052D4—162no—
1053D4—162no—
1054D4—162no—
1055D4—162no—
1056D4—162no—
1057D4—162no—
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—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
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—21no—
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—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—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
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—82no—
1137C2×C4—82no—
1138C2×C4—84no—
1139C2×C4—162no—
1140C2×C4—162no—
1141C2×C4—162no—
1142C2×C4—162no—
1143C2×C4#53612yes—
1144C2×C4#53612yes—
1145C2×C4#55012yes—
1146C2×C4#57712yes—
1147C2×C4C22×#4111yescharacteristic
1148C2×C4C2×H(5,𝔽2)11yescharacteristic
1149C2×C4C2×2−1+411yescharacteristic
1150C2×C4C2×2−1+411yescharacteristic
1151C2×C4#58511yescharacteristic
1152C2×C4#58511yescharacteristic
1153C8—22no—
1154C8—22no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22C2×#53611yescharacteristic
1190C22C2×#55011yescharacteristic
1191C22#348511yescharacteristic
1192C22C2×#57711yescharacteristic
1193C22#358511yescharacteristic
1194C22#358511yescharacteristic
1195C22#358511yescharacteristic
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4#351511yescharacteristic
1223C4#351511yescharacteristic
1224C4#355911yescharacteristic
1225C4#355911yescharacteristic
1226C2—42no—
1227C2—161no—
1228C2—161no—
1229C2—161no—
1230C2#3913411yescharacteristic
1231C2#6088311yescharacteristic
1232C2#6089211yescharacteristic
1233C2#6141411yescharacteristic
1234C2#6142111yescharacteristic
1235C2#6175611yescharacteristic
1236C2#6178311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39818C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35543C2semidirect
3. #33116C2semidirect
4. #32401C2semidirect
5. #32400C2semidirect
6. #32390C2semidirect
7. #32384C2semidirect
8. #31601C2semidirect
9. #31598C2semidirect
10. #31598C2semidirect
11. #31574C2semidirect
12. #29765C2semidirect
13. #29755C2semidirect
14. #28840C2semidirect
15. #28834C2semidirect
16. #27923C2semidirect
17. #27923C2semidirect
18. #27917C2semidirect
19. #27760C2semidirect
20. #27755C2semidirect
21. #27654C2semidirect
22. #27654C2semidirect
23. #27646C2semidirect
24. #26541C2semidirect
25. #26530C2semidirect
26. #26102C2semidirect
27. #26094C2semidirect
28. #22631C2semidirect
29. #22090C2semidirect
30. #22081C2semidirect
31. #21588C2semidirect

Maximal subgroups

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

subgroupindex
#398182
#355432
#331162
#324012
#324002
#323902
#323842
#316012
#315982
#315742
#297652
#297552
#288402
#288342
#279232
#279172
#277602
#277552
#276542
#276462
#265412
#265302
#261022
#260942
#226312
#220902
#220812
#215882