Finite Group Databasebeta

← #7592812

Subgroups — #7592812

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45147C211yesmaximal, characteristic, complemented
2#44905C211yesmaximal, characteristic, complemented
3#32401C211yesmaximal, characteristic, complemented
4#32400C211yesmaximal, characteristic, complemented
5#32394C211yesmaximal, characteristic, complemented
6#32390C211yesmaximal, characteristic, complemented
7#28840C211yesmaximal, characteristic, complemented
8#28837C211yesmaximal, characteristic, complemented
9#28829C211yesmaximal, characteristic, complemented
10#28276C211yesmaximal, characteristic, complemented
11#28021C211yesmaximal, characteristic, complemented
12#28013C211yesmaximal, characteristic, complemented
13#27941C211yesmaximal, characteristic
14#27941C211yesmaximal, characteristic
15#27654C211yesmaximal, characteristic, complemented
16#27654C211yesmaximal, characteristic, complemented
17#26094C211yesmaximal, characteristic, complemented
18#26090C211yesmaximal, characteristic, complemented
19#25064C211yesmaximal, characteristic, complemented
20#25058C211yesmaximal, characteristic, complemented
21#24587C211yesmaximal, characteristic, complemented
22#24585C211yesmaximal, characteristic, complemented
23#24578C211yesmaximal, characteristic, complemented
24#24578C211yesmaximal, characteristic, complemented
25#22817C211yesmaximal, characteristic, complemented
26#22729C211yesmaximal, characteristic, complemented
27#22623C211yesmaximal, characteristic, complemented
28#22621C211yesmaximal, characteristic, complemented
29#21606C211yesmaximal, characteristic, complemented
30#21541C211yesmaximal, characteristic
31#20802C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#446C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#427C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C2×#405C2211yescharacteristic
44#2777—21no—
45#2773—21no—
46#2768—21no—
47#2738—21no—
48#2707—21no—
49#2695—21no—
50#2694—21no—
51#2687—21no—
52#2611—21no—
53#2604—21no—
54#2580C2211yescharacteristic
55#2571C2211yescharacteristic
56#2570C2211yescharacteristic
57#2570C2211yescharacteristic
58#2558—21no—
59#2556—21no—
60#2553—21no—
61#2552C2211yescharacteristic
62#2552C2211yescharacteristic
63#2552C2211yescharacteristic
64#2538C2211yescharacteristic
65#2519—21no—
66#2513C2211yescharacteristic
67#2513C2211yescharacteristic
68#2512C2211yescharacteristic
69#2512C2211yescharacteristic
70#2501C2211yescharacteristic
71#2501C2211yescharacteristic
72#2500C2211yescharacteristic
73#2500C2211yescharacteristic
74#2470—21no—
75#2458—21no—
76#2396C2211yescharacteristic
77#2357C2211yescharacteristic
78#2355C2211yescharacteristic
79#2354C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81#2347C2211yescharacteristic
82#2346C2211yescharacteristic
83#2345C2211yescharacteristic
84#2345C2211yescharacteristic
85#2324C2211yescharacteristic
86#2324C2211yescharacteristic
87#2317C2211yescharacteristic
88#2317C2211yescharacteristic
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2083C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2071C2211yescharacteristic
112#2071C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#1984C2211yescharacteristic
122#1972C2211yescharacteristic
123#1972C2211yescharacteristic
124#1970C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1947C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1939C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1850C2211yescharacteristic
168#1850C2211yescharacteristic
169#1847C2211yescharacteristic
170#1847C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1846C2211yescharacteristic
176#1846C2211yescharacteristic
177#1844C2211yescharacteristic
178#1844C2211yescharacteristic
179#1844C2211yescharacteristic
180#1844C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1809C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#123—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228#482—42no—
229#482—42no—
230#481—42no—
231#481—42no—
232#469—24no—
233#446—24no—
234#442—24no—
235#428—24no—
236#428—24no—
237#427—42no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106—42no—
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×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288#405—24no—
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400D411yescharacteristic
302#399—21no—
303#399—21no—
304#399—21no—
305#399—21no—
306#399—21no—
307#399D411yescharacteristic
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398D411yescharacteristic
317#398D411yescharacteristic
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396D411yescharacteristic
329#396D411yescharacteristic
330#395D411yescharacteristic
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#393—21no—
336#393D411yescharacteristic
337#391—21no—
338#390—21no—
339#390—21no—
340#390C2311yescharacteristic
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#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
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#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#383—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376—21no—
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8C2×D411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16#4114yes—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517#126—82no—
518#126—82no—
519#125—82no—
520#125—82no—
521#125—82no—
522#123—82no—
523#123—82no—
524#123—82no—
525#123—82no—
526C22⋊Q8—82no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—82no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538#117—22no—
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—22no—
544#117—82no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
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⋊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×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
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—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
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—22no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707#97—22no—
708#97—22no—
709#97—22no—
710#97#4114yes—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—22no—
714C4×C8—22no—
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#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#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759C24—21no—
760C24—21no—
761C24C22×D411yescharacteristic
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—41no—
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—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—81no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
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—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
827C22×C4H(5,𝔽2)12yes—
828C22×C4C2511yescharacteristic
829D8—44no—
830M16—28no—
831C2×C8—28no—
832C2×C8—21no—
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×C8C2×#4112yes—
851C2×C8C2×#4112yes—
852C2×C8C2×#4112yes—
853C2×C8C2×#4112yes—
854C2×C82−1+412yes—
855C2×C82−1+412yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
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—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
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—81no—
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—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
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—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—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42C2×#4112yes—
984C422−1+412yes—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
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#55012yes—
1006C23C23×D411yescharacteristic
1007Q8—44no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—162no—
1017D4—162no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
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—21no—
1055C2×C4—21no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
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—84no—
1099C2×C4—162no—
1100C2×C4—162no—
1101C2×C4—162no—
1102C2×C4#54712yes—
1103C2×C4#54712yes—
1104C2×C4#55012yes—
1105C2×C4#57712yes—
1106C2×C4#57712yes—
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C22×#4111yescharacteristic
1109C2×C4C2×H(5,𝔽2)11yescharacteristic
1110C2×C4C2×2−1+411yescharacteristic
1111C2×C4C2×2−1+411yescharacteristic
1112C2×C4C2×2−1+411yescharacteristic
1113C8—22no—
1114C8—22no—
1115C8—22no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8#55214yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22C2×#54711yescharacteristic
1143C22C2×#55011yescharacteristic
1144C22#349911yescharacteristic
1145C22C2×#57711yescharacteristic
1146C22C2×#57711yescharacteristic
1147C22#358511yescharacteristic
1148C22#358511yescharacteristic
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—22no—
1153C4—22no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4C2×#55211yescharacteristic
1177C4#349211yescharacteristic
1178C4#350911yescharacteristic
1179C4#354411yescharacteristic
1180C2—42no—
1181C2—161no—
1182C2—161no—
1183C2#5931211yescharacteristic
1184C2#6127211yescharacteristic
1185C2#6127911yescharacteristic
1186C2#6142111yescharacteristic
1187C2#6142111yescharacteristic
1188C2#6248611yescharacteristic
1189C2#6250111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45147C2semidirect
2. #44905C2semidirect
3. #32401C2semidirect
4. #32400C2semidirect
5. #32394C2semidirect
6. #32390C2semidirect
7. #28840C2semidirect
8. #28837C2semidirect
9. #28829C2semidirect
10. #28276C2semidirect
11. #28021C2semidirect
12. #28013C2semidirect
15. #27654C2semidirect
16. #27654C2semidirect
17. #26094C2semidirect
18. #26090C2semidirect
19. #25064C2semidirect
20. #25058C2semidirect
21. #24587C2semidirect
22. #24585C2semidirect
23. #24578C2semidirect
24. #24578C2semidirect
25. #22817C2semidirect
26. #22729C2semidirect
27. #22623C2semidirect
28. #22621C2semidirect
29. #21606C2semidirect
31. #20802C2semidirect

Maximal subgroups

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

subgroupindex
#451472
#449052
#324012
#324002
#323942
#323902
#288402
#288372
#288292
#282762
#280212
#280132
#279412
#276542
#260942
#260902
#250642
#250582
#245872
#245852
#245782
#228172
#227292
#226232
#226212
#216062
#215412
#208022