Finite Group Databasebeta

← #7566583

Subgroups — #7566583

Order 512.

1410 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59549C211yesmaximal, characteristic
2#36480C211yesmaximal, characteristic, complemented
3#32638C211yesmaximal, characteristic, complemented
4#32568C211yesmaximal, characteristic, complemented
5#32244C211yesmaximal, characteristic, complemented
6#30813C211yesmaximal, characteristic, complemented
7#29156C211yesmaximal, characteristic, complemented
8#29113C211yesmaximal, characteristic, complemented
9#29035C211yesmaximal, characteristic, complemented
10#28060C211yesmaximal, characteristic, complemented
11#27712C211yesmaximal, characteristic, complemented
12#27385C211yesmaximal, characteristic, complemented
13#27257C211yesmaximal, characteristic
14#27145C211yesmaximal, characteristic, complemented
15#27131C211yesmaximal, characteristic, complemented
16#26770C211yesmaximal, characteristic, complemented
17#26709C211yesmaximal, characteristic, complemented
18#26704C211yesmaximal, characteristic, complemented
19#26327C211yesmaximal, characteristic, complemented
20#25993C211yesmaximal, characteristic, complemented
21#25962C211yesmaximal, characteristic, complemented
22#25007C211yesmaximal, characteristic, complemented
23#24585C211yesmaximal, characteristic, complemented
24#24484C211yesmaximal, characteristic
25#23238C211yesmaximal, characteristic, complemented
26#23220C211yesmaximal, characteristic, complemented
27#23075C211yesmaximal, characteristic, complemented
28#22610C211yesmaximal, characteristic, complemented
29#22568C211yesmaximal, characteristic, complemented
30#21582C211yesmaximal, characteristic, complemented
31#21058C211yesmaximal, characteristic, complemented
32C2×#486C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#427C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C2×#416C2211yescharacteristic
38#2863—21no—
39#2857C2211yescharacteristic
40#2778—21no—
41#2749—21no—
42#2605—21no—
43#2605—21no—
44#2592C2211yescharacteristic
45#2576—21no—
46#2567C2211yescharacteristic
47#2551C2211yescharacteristic
48#2538C2211yescharacteristic
49#2526—21no—
50#2514C2211yescharacteristic
51#2511C2211yescharacteristic
52#2509C2211yescharacteristic
53#2509C2211yescharacteristic
54#2500C2211yescharacteristic
55#2497—21no—
56#2492—21no—
57#2488—21no—
58#2465—21no—
59#2465—21no—
60#2463—21no—
61#2457—21no—
62#2447C2211yescharacteristic
63#2445C2211yescharacteristic
64#2439C2211yescharacteristic
65#2439C2211yescharacteristic
66#2431C2211yescharacteristic
67#2369C2211yescharacteristic
68#2366C2211yescharacteristic
69#2365C2211yescharacteristic
70#2365C2211yescharacteristic
71#2357C2211yescharacteristic
72#2355C2211yescharacteristic
73#2353—21no—
74#2347C2211yescharacteristic
75#2347C2211yescharacteristic
76#2346C2211yescharacteristic
77#2339C2211yescharacteristic
78C4×C4⋊Q8—21no—
79C4×C22⋊Q8C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2297C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2094C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2071C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2024C2211yescharacteristic
110#2024C2211yescharacteristic
111#2024C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1993C2211yescharacteristic
116#1988C2211yescharacteristic
117#1985C2211yescharacteristic
118#1984C2211yescharacteristic
119#1983C2211yescharacteristic
120#1982C2211yescharacteristic
121#1958C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1947C2211yescharacteristic
125#1941C2211yescharacteristic
126#1941C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1934C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1875C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1850C2211yescharacteristic
178#1850C2211yescharacteristic
179#1836C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1807C2211yescharacteristic
184#1807C2211yescharacteristic
185#1804C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190C4×#106C2211yescharacteristic
191C4×#106C2211yescharacteristic
192#1771C2211yescharacteristic
193#1770C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1749C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8D411yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#486—24no—
230#482—24no—
231#476—24no—
232#427—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249#416—24no—
250#416—24no—
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#395—21no—
299#395—21no—
300#395—21no—
301#395—21no—
302#394—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#393—21no—
307#393—21no—
308#393—21no—
309#392—21no—
310#392—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391D411yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389D411yescharacteristic
339#389C2311yescharacteristic
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#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—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#387D411yescharacteristic
379#387D411yescharacteristic
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#385—21no—
391#385D411yescharacteristic
392#385D411yescharacteristic
393#384—21no—
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#383—21no—
397#383—21no—
398#383—21no—
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#381—21no—
406#380—21no—
407#380—21no—
408#380D411yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438#376—21no—
439#376—21no—
440C2×#95—21no—
441C43—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#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—44no—
529#127—22no—
530#127—41no—
531#124—41no—
532#124—41no—
533#123—82no—
534C22⋊Q8—42no—
535C22⋊Q8—82no—
536C22⋊Q8—82no—
537#121—22no—
538#121—22no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—82no—
542C4×Q8—82no—
543C4×D4—22no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—44no—
550C4×D4—82no—
551#117—22no—
552#117—22no—
553#117—22no—
554#117—22no—
555#117—41no—
556#117#4114yes—
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⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C42—21no—
628C2×C42—21no—
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—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—41no—
642C2×C42—41no—
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—22no—
652#107—22no—
653#107—22no—
654#107—41no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—22no—
659#106—22no—
660#106—41no—
661#106—41no—
662#106—41no—
663C4⋊C8—22no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102#4114yes—
691C22⋊C8—22no—
692C22⋊C8—22no—
693#97—41no—
694#97—41no—
695#97—41no—
696#97—41no—
697C4×C8—22no—
698C4×C8—41no—
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
752C24—21no—
753C24—21no—
754C24C22×D411yescharacteristic
755#41—44no—
756#41—44no—
757#41—82no—
758#41—82no—
759C2×Q8—22no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—41no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4C2×#4112yes—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C2×#4112yes—
851C22×C42−1+412yes—
852C22×C4C2511yescharacteristic
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
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—44no—
877C2×C8—82no—
878C2×C8C2×#4112yes—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
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—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
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⋊C4C2×#4112yes—
932C4⋊C4C2×#4112yes—
933C4⋊C4C2×#4112yes—
934C22⋊C4—24no—
935C22⋊C4—22no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
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—
961C22⋊C4—81no—
962C42—24no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—41no—
976C42—41no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23#54812yes—
1011C23C23×D411yescharacteristic
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—82no—
1017Q8—84no—
1018Q8—84no—
1019Q8—162no—
1020D4—22no—
1021D4—22no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—84no—
1029D4—84no—
1030D4—84no—
1031D4—162no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
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—22no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
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—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—82no—
1115C2×C4—84no—
1116C2×C4—82no—
1117C2×C4—162no—
1118C2×C4—162no—
1119C2×C4—162no—
1120C2×C4#54812yes—
1121C2×C4#57512yes—
1122C2×C4#57712yes—
1123C2×C4C22×#4111yescharacteristic
1124C2×C4C22×#4111yescharacteristic
1125C2×C4C2×2−1+411yescharacteristic
1126C2×C4#58511yescharacteristic
1127C2×C4#58511yescharacteristic
1128C2×C4#58511yescharacteristic
1129C8—22no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22C2×#54811yescharacteristic
1159C22D4×#4111yescharacteristic
1160C22#348511yescharacteristic
1161C22C2×#57511yescharacteristic
1162C22C2×#57711yescharacteristic
1163C22#358411yescharacteristic
1164C22#358511yescharacteristic
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—41no—
1169C4—42no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4—42no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4#347511yescharacteristic
1193C4#349511yescharacteristic
1194C4#351011yescharacteristic
1195C4#356411yescharacteristic
1196C2—42no—
1197C2—82no—
1198C2—161no—
1199C2#5913211yescharacteristic
1200C2#6131611yescharacteristic
1201C2#6134711yescharacteristic
1202C2#6145411yescharacteristic
1203C2#6147411yescharacteristic
1204C2#6173911yescharacteristic
1205C2#6176111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2431C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36480C2semidirect
3. #32638C2semidirect
4. #32568C2semidirect
5. #32244C2semidirect
6. #30813C2semidirect
7. #29156C2semidirect
8. #29113C2semidirect
9. #29035C2semidirect
10. #28060C2semidirect
11. #27712C2semidirect
12. #27385C2semidirect
14. #27145C2semidirect
15. #27131C2semidirect
16. #26770C2semidirect
17. #26709C2semidirect
18. #26704C2semidirect
19. #26327C2semidirect
20. #25993C2semidirect
21. #25962C2semidirect
22. #25007C2semidirect
23. #24585C2semidirect
25. #23238C2semidirect
26. #23220C2semidirect
27. #23075C2semidirect
28. #22610C2semidirect
29. #22568C2semidirect
30. #21582C2semidirect
31. #21058C2semidirect

Maximal subgroups

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

subgroupindex
#595492
#364802
#326382
#325682
#322442
#308132
#291562
#291132
#290352
#280602
#277122
#273852
#272572
#271452
#271312
#267702
#267092
#267042
#263272
#259932
#259622
#250072
#245852
#244842
#232382
#232202
#230752
#226102
#225682
#215822
#210582