Finite Group Databasebeta

← #6776936

Subgroups — #6776936

Order 512.

1419 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39046C211yesmaximal, characteristic, complemented
2#35551C211yesmaximal, characteristic, complemented
3#33086C211yesmaximal, characteristic, complemented
4#32452C211yesmaximal, characteristic, complemented
5#32378C211yesmaximal, characteristic, complemented
6#32273C211yesmaximal, characteristic, complemented
7#32021C211yesmaximal, characteristic, complemented
8#31530C211yesmaximal, characteristic, complemented
9#31470C211yesmaximal, characteristic, complemented
10#31276C211yesmaximal, characteristic, complemented
11#30412C211yesmaximal, characteristic
12#30180C211yesmaximal, characteristic, complemented
13#30015C211yesmaximal, characteristic, complemented
14#29529C211yesmaximal, characteristic, complemented
15#29406C211yesmaximal, characteristic, complemented
16#28991C211yesmaximal, characteristic, complemented
17#28861C211yesmaximal, characteristic, complemented
18#28086C211yesmaximal, characteristic, complemented
19#27884C211yesmaximal, characteristic, complemented
20#27863C211yesmaximal, characteristic, complemented
21#27625C211yesmaximal, characteristic, complemented
22#27591C211yesmaximal, characteristic, complemented
23#27520C211yesmaximal, characteristic, complemented
24#27480C211yesmaximal, characteristic, complemented
25#27171C211yesmaximal, characteristic, complemented
26#25046C211yesmaximal, characteristic, complemented
27#24913C211yesmaximal, characteristic, complemented
28#22792C211yesmaximal, characteristic, complemented
29#22190C211yesmaximal, characteristic, complemented
30#22056C211yesmaximal, characteristic, complemented
31#21126C211yesmaximal, characteristic, complemented
32C2×#469C2211yescharacteristic
33C2×#447C2211yescharacteristic
34C2×#442C2211yescharacteristic
35#2854C2211yescharacteristic
36#2761—21no—
37#2735—21no—
38#2706—21no—
39#2697—21no—
40#2644C2211yescharacteristic
41#2629C2211yescharacteristic
42#2603—21no—
43#2577—21no—
44#2566C2211yescharacteristic, complemented
45#2562C2211yescharacteristic
46#2558—21no—
47#2552C2211yescharacteristic, complemented
48#2537C2211yescharacteristic
49#2534—21no—
50#2531—21no—
51#2518—21no—
52#2512C2211yescharacteristic
53#2505—21no—
54#2497C2211yescharacteristic
55#2495C2211yescharacteristic, complemented
56#2490C2211yescharacteristic
57#2485C2211yescharacteristic
58#2480—21no—
59#2476—21no—
60#2470—21no—
61#2460—21no—
62#2454C2211yescharacteristic
63#2425—21no—
64#2422C2211yescharacteristic
65#2422C2211yescharacteristic
66#2422C2211yescharacteristic, complemented
67#2408C2211yescharacteristic
68#2346C2211yescharacteristic
69D4×C22⋊C4C2211yescharacteristic
70#2330C2211yescharacteristic, complemented
71#2324C2211yescharacteristic
72#2319C2211yescharacteristic
73#2314C2211yescharacteristic
74#2309C2211yescharacteristic
75C4×#121C2211yescharacteristic
76C4×#121C2211yescharacteristic, complemented
77#2290C2211yescharacteristic
78#2285C2211yescharacteristic, complemented
79#2275C2211yescharacteristic, complemented
80#2100C2211yescharacteristic, complemented
81#2099C2211yescharacteristic, complemented
82#2094C2211yescharacteristic
83#2094C2211yescharacteristic
84#2092C2211yescharacteristic
85#2092C2211yescharacteristic
86#2087C2211yescharacteristic, complemented
87#2084C2211yescharacteristic, complemented
88#2084C2211yescharacteristic, complemented
89#2083C2211yescharacteristic, complemented
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic, complemented
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic, complemented
119#1999C2211yescharacteristic
120#1992C2211yescharacteristic, complemented
121#1991C2211yescharacteristic, complemented
122#1972C2211yescharacteristic
123#1970C2211yescharacteristic
124#1948C2211yescharacteristic, complemented
125#1948C2211yescharacteristic, complemented
126#1943C2211yescharacteristic, complemented
127#1941C2211yescharacteristic, complemented
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic, complemented
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1920C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1875C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1844C2211yescharacteristic, complemented
183#1840C2211yescharacteristic, complemented
184#1836C2211yescharacteristic, complemented
185#1818C2211yescharacteristic
186#1809C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1797C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#123—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#121—21no—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C42C2311yescharacteristic
235#469—24no—
236#447—24no—
237#442—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#400—21no—
285#400—21no—
286#400—21no—
287#399—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#392—21no—
320#390—21no—
321#390—21no—
322#390—21no—
323#390—21no—
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
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#388D411yescharacteristic
366#388D411yescharacteristic
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387D411yescharacteristic
374#387D411yescharacteristic
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386D411yescharacteristic
382#386D411yescharacteristic
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385D411yescharacteristic
391#385D411yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#383—21no—
398#382—21no—
399#382—21no—
400#382C2311yescharacteristic
401#381—21no—
402#380—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#379—21no—
417#379—21no—
418#379—21no—
419#379—21no—
420C4×C4⋊C4—21no—
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×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437#376C2311yescharacteristic
438C2×#95—21no—
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×D8—22no—
507C2×D8—41no—
508C2×D8—41no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8#4114yes—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526#126—82no—
527#125—41no—
528#125—41no—
529#125—41no—
530#125—41no—
531#125—82no—
532#123—82no—
533#123—82no—
534#123—82no—
535#123—82no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—41no—
540#121—41no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—82no—
545#120—82no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—82no—
559C4×D4—82no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—82no—
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—21no—
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—41no—
665C2×C42—41no—
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709C22⋊C8—22no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715#97—22no—
716#97—41no—
717C4×C8—41no—
718C4×C8—41no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95C2×D411yescharacteristic
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
758C24—21no—
759C24—21no—
760C24—21no—
761C24—42no—
762C24—42no—
763C24—81no—
764C24—81no—
765C24—81no—
766C24—81no—
767C24—81no—
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—81no—
798C2×D4—82no—
799C2×D4—82no—
800C2×D4—82no—
801C2×D4—82no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4C2×#4112yes—
809C2×D4C2×#4112yes—
810C22×C4—22no—
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—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C2511yescharacteristic
869D8—44no—
870D8—82no—
871M16—82no—
872M16—82no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8C2×#4112yes—
897C4⋊C4—22no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C22⋊C4—22no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—41no—
1011C42—41no—
1012C42—42no—
1013C42—42no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—84no—
1056C23—84no—
1057C23—162no—
1058C23—162no—
1059C23—162no—
1060C23—162no—
1061C23—162no—
1062C23C23×D411yescharacteristic
1063D4—22no—
1064D4—22no—
1065D4—22no—
1066D4—22no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—82no—
1076D4—84no—
1077D4—84no—
1078D4—84no—
1079D4—162no—
1080D4—162no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—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—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—44no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—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—82no—
1165C2×C4—162no—
1166C2×C4—162no—
1167C2×C4—162no—
1168C2×C4—162no—
1169C2×C4—162no—
1170C2×C4#57712yes—
1171C2×C4C22×#4111yescharacteristic
1172C2×C4#58511yescharacteristic
1173C2×C4#58511yescharacteristic
1174C2×C4#58511yescharacteristic
1175C2×C4#58511yescharacteristic
1176C2×C4#58511yescharacteristic
1177C8—22no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—42no—
1190C22—41no—
1191C22—41no—
1192C22—42no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22—42no—
1201C22—41no—
1202C22—41no—
1203C22—42no—
1204C22—42no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—168no—
1221C22#344911yescharacteristic
1222C22D4×#4111yescharacteristic
1223C22#348511yescharacteristic
1224C22C2×#57711yescharacteristic
1225C22#358511yescharacteristic
1226C22#358511yescharacteristic
1227C22#358511yescharacteristic
1228C4—22no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4#349111yescharacteristic
1254C4#352111yescharacteristic
1255C4#356611yescharacteristic
1256C4#356811yescharacteristic
1257C2—81no—
1258C2—81no—
1259C2—82no—
1260C2—82no—
1261C2—161no—
1262C2#3837611yescharacteristic
1263C2#6098911yescharacteristic
1264C2#6100311yescharacteristic
1265C2#6150611yescharacteristic
1266C2#6155111yescharacteristic
1267C2#6174611yescharacteristic
1268C2#6178311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30412C2
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
1. #39046C2semidirect
2. #35551C2semidirect
3. #33086C2semidirect
4. #32452C2semidirect
5. #32378C2semidirect
6. #32273C2semidirect
7. #32021C2semidirect
8. #31530C2semidirect
9. #31470C2semidirect
10. #31276C2semidirect
12. #30180C2semidirect
13. #30015C2semidirect
14. #29529C2semidirect
15. #29406C2semidirect
16. #28991C2semidirect
17. #28861C2semidirect
18. #28086C2semidirect
19. #27884C2semidirect
20. #27863C2semidirect
21. #27625C2semidirect
22. #27591C2semidirect
23. #27520C2semidirect
24. #27480C2semidirect
25. #27171C2semidirect
26. #25046C2semidirect
27. #24913C2semidirect
28. #22792C2semidirect
29. #22190C2semidirect
30. #22056C2semidirect
31. #21126C2semidirect
44. #2566C22semidirect
47. #2552C22semidirect
55. #2495C22semidirect
66. #2422C22semidirect
70. #2330C22semidirect
76. C4×#121C22semidirect
78. #2285C22semidirect
79. #2275C22semidirect
80. #2100C22semidirect
81. #2099C22semidirect
86. #2087C22semidirect
87. #2084C22semidirect
88. #2084C22semidirect
89. #2083C22semidirect
95. #2077C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
103. #2071C22semidirect
105. #2065C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
114. #2034C22semidirect
118. #2025C22semidirect
120. #1992C22semidirect
121. #1991C22semidirect
124. #1948C22semidirect
125. #1948C22semidirect
126. #1943C22semidirect
127. #1941C22semidirect
141. #1925C22semidirect
144. #1920C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
161. #1895C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
182. #1844C22semidirect
183. #1840C22semidirect
184. #1836C22semidirect
186. #1809C22semidirect
187. #1809C22semidirect
188. #1809C22semidirect
191. #1797C22semidirect
195. #1776C22semidirect
197. C4×#102C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
201. #1746C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#390462
#355512
#330862
#324522
#323782
#322732
#320212
#315302
#314702
#312762
#304122
#301802
#300152
#295292
#294062
#289912
#288612
#280862
#278842
#278632
#276252
#275912
#275202
#274802
#271712
#250462
#249132
#227922
#221902
#220562
#211262