Finite Group Databasebeta

← #6611496

Subgroups — #6611496

Order 512.

1685 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#37862C211yesmaximal, characteristic
2#37686C211yesmaximal, characteristic, complemented
3#33292C211yesmaximal, characteristic, complemented
4#33054C211yesmaximal, characteristic, complemented
5#33044C211yesmaximal, characteristic, complemented
6#29229C211yesmaximal, characteristic, complemented
7#28730C211yesmaximal, characteristic, complemented
8#27971C211yesmaximal, characteristic, complemented
9#27965C211yesmaximal, characteristic, complemented
10#27830C211yesmaximal, characteristic, complemented
11#27827C211yesmaximal, characteristic, complemented
12#27818C211yesmaximal, characteristic, complemented
13#27813C211yesmaximal, characteristic, complemented
14#27722C211yesmaximal, characteristic, complemented
15#27719C211yesmaximal, characteristic, complemented
16#27715C211yesmaximal, characteristic, complemented
17#27711C211yesmaximal, characteristic, complemented
18#27701C211yesmaximal, characteristic, complemented
19#27698C211yesmaximal, characteristic, complemented
20#27697C211yesmaximal, characteristic, complemented
21#27695C211yesmaximal, characteristic, complemented
22#25916C211yesmaximal, characteristic, complemented
23#25908C211yesmaximal, characteristic, complemented
24#22497C211yesmaximal, characteristic, complemented
25#22493C211yesmaximal, characteristic
26#22488C211yesmaximal, characteristic
27#22487C211yesmaximal, characteristic, complemented
28#21654C211yesmaximal, characteristic, complemented
29#21326C211yesmaximal, characteristic, complemented
30C2×#1990C211yesmaximal, characteristic, complemented
31#20484C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#489C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×C8×D4C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2851C2211yescharacteristic
44#2850C2211yescharacteristic
45#2734—21no—
46#2729—21no—
47#2721—21no—
48#2721—21no—
49#2713—21no—
50#2680—21no—
51#2680—21no—
52#2677—21no—
53#2660C2211yescharacteristic
54#2660C2211yescharacteristic
55#2628C2211yescharacteristic
56#2620C2211yescharacteristic
57#2565C2211yescharacteristic
58#2551C2211yescharacteristic
59#2550C2211yescharacteristic
60#2542C2211yescharacteristic
61#2504C2211yescharacteristic
62#2502C2211yescharacteristic
63#2501C2211yescharacteristic
64#2499C2211yescharacteristic
65#2473—21no—
66#2449—21no—
67#2449—21no—
68#2449—21no—
69#2443—21no—
70#2443—21no—
71#2442C2211yescharacteristic
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic
74#2439C2211yescharacteristic
75#2434—21no—
76#2409—21no—
77#2352C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79#2331C2211yescharacteristic
80#2326C2211yescharacteristic
81#2317C2211yescharacteristic
82#2290C2211yescharacteristic
83C2×#384C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2099C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2026C2211yescharacteristic
101#2025C2211yescharacteristic
102#2024C2211yescharacteristic
103#2024C2211yescharacteristic
104#2024C2211yescharacteristic
105#2023C2211yescharacteristic
106#2023C2211yescharacteristic
107#2023C2211yescharacteristic
108#1993C2211yescharacteristic
109#1993C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1992C2211yescharacteristic
113#1992C2211yescharacteristic
114#1992C2211yescharacteristic
115#1992C2211yescharacteristic
116#1991C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1990C2211yescharacteristic
120#1990C2211yescharacteristic
121#1990C2211yescharacteristic
122#1990C2211yescharacteristic
123#1990C2211yescharacteristic
124#1990C2211yescharacteristic
125#1990C2211yescharacteristic
126#1990C2211yescharacteristic
127#1990C2211yescharacteristic
128#1990C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1987C2211yescharacteristic
133#1958C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1895C2211yescharacteristic
147#1894C2211yescharacteristic
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1893C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1875C2211yescharacteristic
155#1874C2211yescharacteristic
156#1874C2211yescharacteristic
157#1874C2211yescharacteristic
158#1873C2211yescharacteristic
159#1872C2211yescharacteristic
160#1872C2211yescharacteristic
161#1872C2211yescharacteristic
162#1836C2211yescharacteristic
163#1836C2211yescharacteristic
164#1836C2211yescharacteristic
165#1836C2211yescharacteristic
166#1835C2211yescharacteristic
167#1835C2211yescharacteristic
168#1834C2211yescharacteristic
169#1825C2211yescharacteristic
170#1825C2211yescharacteristic
171#1824C2211yescharacteristic
172#1824C2211yescharacteristic
173#1824C2211yescharacteristic
174#1824C2211yescharacteristic
175#1824C2211yescharacteristic
176#1823C2211yescharacteristic
177#1805C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic
180#1802C2211yescharacteristic
181#1771C2211yescharacteristic
182C8×C4⋊C4C2211yescharacteristic
183#1768C2211yescharacteristic
184#1763C2211yescharacteristic
185#1762C2211yescharacteristic
186C4×#103C2211yescharacteristic
187C4×#102C2211yescharacteristic
188#1753C2211yescharacteristic
189#1752C2211yescharacteristic
190C8×C22⋊C4C2211yescharacteristic
191C8×C22⋊C4C2211yescharacteristic
192#1750C2211yescharacteristic
193#1749C2211yescharacteristic
194#1736C2211yescharacteristic
195#1736C2211yescharacteristic
196#1735C2211yescharacteristic
197C2×#340C2211yescharacteristic
198C2×#340C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1726C2211yescharacteristic
203C23×Q8—21no—
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#554—24no—
209#554—24no—
210#553—24no—
211#553—24no—
212#544—24no—
213#544—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—24no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—21no—
259C22×C4⋊C4—21no—
260C22×C4⋊C4—21no—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#489—24no—
269#489—42no—
270#488—42no—
271#435—24no—
272C8×D4—24no—
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295#405—42no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8—42no—
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#399—21no—
312#399—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#393—21no—
348#393—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388D411yescharacteristic
376#388D411yescharacteristic
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386D411yescharacteristic
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—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#385—21no—
409#385D411yescharacteristic
410#385D411yescharacteristic
411#384—21no—
412#384—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438#376C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—44no—
500C22×Q8—82no—
501C22×Q8—82no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—41no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—82no—
553C4⋊Q8#4114yes—
554#126—44no—
555#125—22no—
556#125—22no—
557#125—22no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125—44no—
562#125—44no—
563#124—22no—
564#124—22no—
565#123—44no—
566#123—82no—
567#123—82no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—82no—
577C22⋊Q8—82no—
578C22⋊Q8—82no—
579C22⋊Q8—82no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—44no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—82no—
592C4×D4#4114yes—
593C4×D4#4114yes—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4—82no—
657C2×C4⋊C4—82no—
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C4⋊C8—22no—
719C4⋊C8—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740#97—22no—
741#97—22no—
742#97—22no—
743#97—22no—
744#97—41no—
745C4×C8—22no—
746C4×C8—22no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—41no—
750C4×C8—41no—
751C4×C8—41no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792C24—21no—
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C2×Q8—24no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—816no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4#12414yes—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4C2511yescharacteristic
902M16—44no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—44no—
926C2×C8—44no—
927C2×C8—44no—
928C2×C82−1+412yes—
929C2×C82−1+412yes—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4#12414yes—
1004C4⋊C4C2×#4112yes—
1005C4⋊C4C2×#4112yes—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4#12414yes—
1032C22⋊C4#12414yes—
1033C42—22no—
1034C42—22no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42C2×#4112yes—
1047C42C2×#4112yes—
1048C42C2×#4112yes—
1049C42H(5,𝔽2)12yes—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23C2×#12412yes—
1068C23C2×#12412yes—
1069C23#57712yes—
1070C23#57812yes—
1071C23C23×D411yescharacteristic
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—84no—
1077Q8—84no—
1078Q8—84no—
1079Q8—84no—
1080Q8—162no—
1081Q8—162no—
1082D4—28no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—84no—
1088D4—162no—
1089C2×C4—28no—
1090C2×C4—28no—
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—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
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—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—84no—
1173C2×C4—84no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4—162no—
1179C2×C4C2×#12412yes—
1180C2×C4C2×#12412yes—
1181C2×C4C2×#12412yes—
1182C2×C4C2×#12412yes—
1183C2×C4#54612yes—
1184C2×C4#54612yes—
1185C2×C4#57612yes—
1186C2×C4#57712yes—
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C22×#4111yescharacteristic
1189C2×C4C22×#4111yescharacteristic
1190C2×C4C2×H(5,𝔽2)11yescharacteristic
1191C2×C4C2×2−1+411yescharacteristic
1192C2×C4C2×2−1+411yescharacteristic
1193C8—22no—
1194C8—22no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22#313714yes—
1222C22C22×#12411yescharacteristic
1223C22C2×#54611yescharacteristic
1224C22#349911yescharacteristic
1225C22C2×#57611yescharacteristic
1226C22C2×#57711yescharacteristic
1227C22C2×#57711yescharacteristic
1228C22C2×#57811yescharacteristic
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—42no—
1242C4—41no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4#348211yescharacteristic
1257C4#348211yescharacteristic
1258C4#352011yescharacteristic
1259C4#352011yescharacteristic
1260C2—24no—
1261C2—42no—
1262C2—161no—
1263C2#3630311yescharacteristic
1264C2C2×#313711yescharacteristic
1265C2#6062211yescharacteristic
1266C2#6116711yescharacteristic
1267C2#6116811yescharacteristic
1268C2#6248611yescharacteristic
1269C2#6248811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#553C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37686C2semidirect
3. #33292C2semidirect
4. #33054C2semidirect
5. #33044C2semidirect
6. #29229C2semidirect
7. #28730C2semidirect
8. #27971C2semidirect
9. #27965C2semidirect
10. #27830C2semidirect
11. #27827C2semidirect
12. #27818C2semidirect
13. #27813C2semidirect
14. #27722C2semidirect
15. #27719C2semidirect
16. #27715C2semidirect
17. #27711C2semidirect
18. #27701C2semidirect
19. #27698C2semidirect
20. #27697C2semidirect
21. #27695C2semidirect
22. #25916C2semidirect
23. #25908C2semidirect
24. #22497C2semidirect
27. #22487C2semidirect
28. #21654C2semidirect
29. #21326C2semidirect
30. C2×#1990C2semidirect
31. #20484C2semidirect

Maximal subgroups

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

subgroupindex
#378622
#376862
#332922
#330542
#330442
#292292
#287302
#279712
#279652
#278302
#278272
#278182
#278132
#277222
#277192
#277152
#277112
#277012
#276982
#276972
#276952
#259162
#259082
#224972
#224932
#224882
#224872
#216542
#213262
C2×#19902
#204842