Finite Group Databasebeta

← #6570029

Subgroups — #6570029

Order 512.

1373 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38111C211yesmaximal, characteristic
2#37882C211yesmaximal, characteristic
3#30393C211yesmaximal, characteristic, complemented
4#30375C211yesmaximal, characteristic, complemented
5#30294C211yesmaximal, characteristic, complemented
6#29589C211yesmaximal, characteristic, complemented
7#29528C211yesmaximal, characteristic, complemented
8#29172C211yesmaximal, characteristic, complemented
9#29106C211yesmaximal, characteristic, complemented
10#28970C211yesmaximal, characteristic, complemented
11#28947C211yesmaximal, characteristic, complemented
12#28867C211yesmaximal, characteristic, complemented
13#28847C211yesmaximal, characteristic, complemented
14#28108C211yesmaximal, characteristic
15#28095C211yesmaximal, characteristic
16#28087C211yesmaximal, characteristic, complemented
17#28066C211yesmaximal, characteristic, complemented
18#28050C211yesmaximal, characteristic, complemented
19#28030C211yesmaximal, characteristic, complemented
20#27961C211yesmaximal, characteristic, complemented
21#27867C211yesmaximal, characteristic, complemented
22#27663C211yesmaximal, characteristic
23#27658C211yesmaximal, characteristic
24#23793C211yesmaximal, characteristic, complemented
25#23772C211yesmaximal, characteristic, complemented
26C2×#2096C211yesmaximal, characteristic, complemented
27#22615C211yesmaximal, characteristic, complemented
28#22609C211yesmaximal, characteristic, complemented
29#22575C211yesmaximal, characteristic, complemented
30#22567C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic
32C2×#435C2211yescharacteristic
33C2×C8×D4C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×#106C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38#2857C2211yescharacteristic
39#2851C2211yescharacteristic
40#2799—21no—
41#2798—21no—
42#2794—21no—
43#2794—21no—
44#2759—21no—
45#2755—21no—
46#2721—21no—
47#2721—21no—
48#2647C2211yescharacteristic
49#2645C2211yescharacteristic
50#2629C2211yescharacteristic
51#2625C2211yescharacteristic
52#2511C2211yescharacteristic
53#2506C2211yescharacteristic
54#2506C2211yescharacteristic
55#2498—21no—
56#2496C2211yescharacteristic
57#2496C2211yescharacteristic
58#2493—21no—
59#2492C2211yescharacteristic
60#2488—21no—
61#2487C2211yescharacteristic
62#2487C2211yescharacteristic
63#2486C2211yescharacteristic
64#2481—21no—
65#2481—21no—
66#2473—21no—
67#2473—21no—
68#2451C2211yescharacteristic
69#2438—21no—
70#2423C2211yescharacteristic
71#2409C2211yescharacteristic
72#2345C2211yescharacteristic
73#2345C2211yescharacteristic
74#2344C2211yescharacteristic
75Q8×C22⋊C4C2211yescharacteristic
76#2330C2211yescharacteristic
77#2323C2211yescharacteristic
78#2320C2211yescharacteristic
79#2314C2211yescharacteristic
80C2×#391C2211yescharacteristic
81#2290C2211yescharacteristic
82C2×#384C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2096C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2096C2211yescharacteristic
93#2096C2211yescharacteristic
94#2096C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2057C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2026C2211yescharacteristic
122#2026C2211yescharacteristic
123#1990C2211yescharacteristic
124#1990C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1943C2211yescharacteristic
128#1943C2211yescharacteristic
129#1941C2211yescharacteristic
130#1941C2211yescharacteristic
131#1941C2211yescharacteristic
132#1941C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1933C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1933C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1834C2211yescharacteristic
166#1834C2211yescharacteristic
167#1824C2211yescharacteristic
168#1824C2211yescharacteristic
169#1824C2211yescharacteristic
170#1824C2211yescharacteristic
171#1823C2211yescharacteristic
172#1823C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1808C2211yescharacteristic
176#1808C2211yescharacteristic
177#1807C2211yescharacteristic
178#1807C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1787C2211yescharacteristic
182#1787C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#106C2211yescharacteristic
186C4×#106C2211yescharacteristic
187#1771C2211yescharacteristic
188C8×C4⋊C4C2211yescharacteristic
189#1768C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194#1753C2211yescharacteristic
195#1752C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1750C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200#1746C2211yescharacteristic
201#1729C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C22×C4⋊C4—21no—
224C22×C4⋊C4—21no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#435—24no—
230C8×D4—24no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106—24no—
236C2×#106—24no—
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#103—24no—
252C2×#103—24no—
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#401—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
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#400—21no—
295#400—21no—
296#400—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#395—21no—
318#395—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388D411yescharacteristic
363#388D411yescharacteristic
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#387—21no—
375#387—21no—
376#387—21no—
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#386D411yescharacteristic
393#386D411yescharacteristic
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385D411yescharacteristic
400#385D411yescharacteristic
401#384—21no—
402#384—21no—
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#383—21no—
409#382—21no—
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376C2311yescharacteristic
440C2×#95—21no—
441C2×#95—21no—
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—22no—
487C22×Q8—22no—
488C22×Q8—22no—
489C22×Q8—41no—
490C22×Q8—41no—
491C22×Q8—41no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4C2×D411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8#4114yes—
514C22×C8#4114yes—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#126—82no—
526#126—82no—
527#125—41no—
528#125—41no—
529#125—82no—
530#125—82no—
531#123—82no—
532C22⋊Q8—22no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—82no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×D4—22no—
542C4×D4—22no—
543#117—41no—
544#117—41no—
545#117—82no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
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⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—82no—
589C2×C4⋊C4—82no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊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×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⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—41no—
638C2×C42—41no—
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680C22⋊C8—22no—
681C22⋊C8—22no—
682C22⋊C8—22no—
683C22⋊C8—22no—
684#97—22no—
685#97—41no—
686#97—41no—
687C4×C8—22no—
688C4×C8—41no—
689C4×C8—41no—
690C4×C8—41no—
691C4×C8—41no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24C22×D411yescharacteristic
753C24C22×D411yescharacteristic
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—82no—
774C2×Q8—82no—
775C2×Q82−1+412yes—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C2×#4112yes—
836C22×C4C2×#4112yes—
837C22×C4C2511yescharacteristic
838M16—82no—
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×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—44no—
860C2×C8—44no—
861C2×C8—82no—
862C2×C8C2×#4112yes—
863C2×C8C2×#4112yes—
864C2×C8C2×#4112yes—
865C2×C8C2×#4112yes—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
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—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—41no—
966C42—41no—
967C42—42no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23#53212yes—
987C23#57712yes—
988C23#57812yes—
989C23C23×D411yescharacteristic
990Q8—22no—
991Q8—22no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—84no—
999Q8—162no—
1000D4—44no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
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—84no—
1093C2×C4—84no—
1094C2×C4—162no—
1095C2×C4—162no—
1096C2×C4#53212yes—
1097C2×C4#57712yes—
1098C2×C4#57712yes—
1099C2×C4C22×#4111yescharacteristic
1100C2×C4C22×#4111yescharacteristic
1101C2×C4C2×2−1+411yescharacteristic
1102C2×C4#58511yescharacteristic
1103C2×C4#58511yescharacteristic
1104C2×C4#58511yescharacteristic
1105C8—22no—
1106C8—22no—
1107C8—22no—
1108C8—22no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22#317814yes—
1127C22C2×#53211yescharacteristic
1128C22#348511yescharacteristic
1129C22#348911yescharacteristic
1130C22C2×#57711yescharacteristic
1131C22C2×#57711yescharacteristic
1132C22C2×#57711yescharacteristic
1133C22C2×#57811yescharacteristic
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4#349111yescharacteristic
1163C4#349111yescharacteristic
1164C4#349511yescharacteristic
1165C4#349511yescharacteristic
1166C2—24no—
1167C2—81no—
1168C2#3606111yescharacteristic
1169C2C2×#317811yescharacteristic
1170C2#6071211yescharacteristic
1171C2#6176511yescharacteristic
1172C2#6176711yescharacteristic
1173C2#6220311yescharacteristic
1174C2#6220511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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
3. #30393C2semidirect
4. #30375C2semidirect
5. #30294C2semidirect
6. #29589C2semidirect
7. #29528C2semidirect
8. #29172C2semidirect
9. #29106C2semidirect
10. #28970C2semidirect
11. #28947C2semidirect
12. #28867C2semidirect
13. #28847C2semidirect
16. #28087C2semidirect
17. #28066C2semidirect
18. #28050C2semidirect
19. #28030C2semidirect
20. #27961C2semidirect
21. #27867C2semidirect
24. #23793C2semidirect
25. #23772C2semidirect
26. C2×#2096C2semidirect
27. #22615C2semidirect
28. #22609C2semidirect
29. #22575C2semidirect
30. #22567C2semidirect

Maximal subgroups

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

subgroupindex
#381112
#378822
#303932
#303752
#302942
#295892
#295282
#291722
#291062
#289702
#289472
#288672
#288472
#281082
#280952
#280872
#280662
#280502
#280302
#279612
#278672
#276632
#276582
#237932
#237722
C2×#20962
#226152
#226092
#225752
#225672
#205572