Finite Group Databasebeta

← #7037524

Subgroups — #7037524

Order 512.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59208C211yesmaximal, characteristic, complemented
2#38996C211yesmaximal, characteristic, complemented
3#32389C211yesmaximal, characteristic, complemented
4#31945C211yesmaximal, characteristic, complemented
5#31698C211yesmaximal, characteristic, complemented
6#31681C211yesmaximal, characteristic, complemented
7#31530C211yesmaximal, characteristic, complemented
8#31370C211yesmaximal, characteristic, complemented
9#31362C211yesmaximal, characteristic, complemented
10#30400C211yesmaximal, characteristic
11#29110C211yesmaximal, characteristic, complemented
12#29096C211yesmaximal, characteristic, complemented
13#28085C211yesmaximal, characteristic, complemented
14#28058C211yesmaximal, characteristic, complemented
15#27879C211yesmaximal, characteristic, complemented
16#27743C211yesmaximal, characteristic, complemented
17#27701C211yesmaximal, characteristic, complemented
18#27574C211yesmaximal, characteristic, complemented
19#27534C211yesmaximal, characteristic, complemented
20#27385C211yesmaximal, characteristic, complemented
21#27113C211yesmaximal, characteristic, complemented
22#26738C211yesmaximal, characteristic, complemented
23#25032C211yesmaximal, characteristic, complemented
24#24977C211yesmaximal, characteristic, complemented
25#24933C211yesmaximal, characteristic, complemented
26#24893C211yesmaximal, characteristic, complemented
27#23764C211yesmaximal, characteristic, complemented
28#23300C211yesmaximal, characteristic, complemented
29#23132C211yesmaximal, characteristic, complemented
30#22764C211yesmaximal, characteristic, complemented
31#22040C211yesmaximal, characteristic, complemented
32C2×#466C2211yescharacteristic
33C2×#447C2211yescharacteristic
34C2×C4×D8C2211yescharacteristic
35#2851C2211yescharacteristic
36#2782—21no—
37#2757—21no—
38#2750—21no—
39#2749—21no—
40#2738—21no—
41#2693—21no—
42#2652—21no—
43#2603—21no—
44#2571C2211yescharacteristic, complemented
45#2566C2211yescharacteristic
46#2535C2211yescharacteristic
47#2534—21no—
48#2526—21no—
49#2513C2211yescharacteristic
50#2512C2211yescharacteristic
51#2509C2211yescharacteristic, complemented
52#2504C2211yescharacteristic
53#2497C2211yescharacteristic, complemented
54#2495C2211yescharacteristic
55#2490C2211yescharacteristic
56#2486C2211yescharacteristic
57#2483—21no—
58#2480—21no—
59#2455—21no—
60#2454C2211yescharacteristic, complemented
61#2442C2211yescharacteristic
62#2442C2211yescharacteristic, complemented
63#2422C2211yescharacteristic
64#2420C2211yescharacteristic
65#2420C2211yescharacteristic, complemented
66#2419—21no—
67#2408C2211yescharacteristic
68#2361C2211yescharacteristic
69#2361C2211yescharacteristic, complemented
70#2358—21no—
71#2357C2211yescharacteristic
72#2349C2211yescharacteristic, complemented
73D4×C4⋊C4C2211yescharacteristic
74D4×C22⋊C4C2211yescharacteristic
75#2318—21no—
76C4×#123C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2283C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2101C2211yescharacteristic, complemented
83#2099C2211yescharacteristic, complemented
84#2093C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2086C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
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#1991C2211yescharacteristic, complemented
123#1989C2211yescharacteristic, complemented
124#1970C2211yescharacteristic
125#1970C2211yescharacteristic
126#1955C2211yescharacteristic
127#1949C2211yescharacteristic, complemented
128#1942C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1917C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic, complemented
167#1869C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic, complemented
174#1846C2211yescharacteristic, complemented
175#1836C2211yescharacteristic, complemented
176#1835C2211yescharacteristic, complemented
177#1835C2211yescharacteristic, complemented
178#1824C2211yescharacteristic, complemented
179#1823C2211yescharacteristic
180#1823C2211yescharacteristic
181#1823C2211yescharacteristic, complemented
182#1808C2211yescharacteristic, complemented
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic, complemented
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×#123D411yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#120—21no—
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C22⋊C4—21no—
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234C22×C42C2311yescharacteristic
235#466—24no—
236#447—24no—
237C4×D8—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
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#399—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#392—21no—
320#392—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#388D411yescharacteristic
359#388D411yescharacteristic
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387D411yescharacteristic
365#387D411yescharacteristic
366#386—21no—
367#386—21no—
368#386—21no—
369#386—21no—
370#386—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386D411yescharacteristic
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385D411yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#383—21no—
396#383—21no—
397#382—21no—
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#381—21no—
409#381D411yescharacteristic
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#379—21no—
423#379—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437#376—21no—
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#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
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×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×D8—22no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8#4114yes—
515C22×C8—22no—
516C22×C8—41no—
517C22×C8—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#123—42no—
532#123—82no—
533#123—82no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—41no—
538#121—41no—
539#121—41no—
540#121—41no—
541#121—41no—
542#120—44no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—44no—
556C4×D4—82no—
557C4×D4—82no—
558C4×D4—82no—
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—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
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⋊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—82no—
642C2×C22⋊C4—82no—
643C2×C22⋊C4—82no—
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42C2×D411yescharacteristic
660C2×C42C2×D411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699C22⋊C8—22no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706#97—41no—
707#97—41no—
708#97—41no—
709#97—41no—
710C4×C8—22no—
711C4×C8—41no—
712C4×C8—41no—
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#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—42no—
764C24—42no—
765C24—81no—
766C24—81no—
767C24—81no—
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×D4—22no—
771C2×D4—22no—
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—21no—
787C2×D4—21no—
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—42no—
798C2×D4—81no—
799C2×D4—82no—
800C2×D4—82no—
801C2×D4—82no—
802C2×D4—82no—
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×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C2511yescharacteristic
878D8—44no—
879D8—82no—
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×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—82no—
904C2×C8C2×#4112yes—
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—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—42no—
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—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
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—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
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—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—41no—
1013C42—41no—
1014C42—42no—
1015C42—42no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
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—84no—
1053C23—84no—
1054C23—84no—
1055C23—84no—
1056C23—162no—
1057C23—162no—
1058C23—162no—
1059C23#57512yes—
1060C23#57612yes—
1061C23C23×D411yescharacteristic
1062D4—22no—
1063D4—22no—
1064D4—22no—
1065D4—22no—
1066D4—44no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—84no—
1076D4—84no—
1077D4—84no—
1078D4—84no—
1079D4—162no—
1080C2×C4—21no—
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—41no—
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—82no—
1164C2×C4—82no—
1165C2×C4—162no—
1166C2×C4—162no—
1167C2×C4—162no—
1168C2×C4—162no—
1169C2×C4—162no—
1170C2×C4—162no—
1171C2×C4—162no—
1172C2×C4—162no—
1173C2×C4C22×#4111yescharacteristic
1174C2×C4#58511yescharacteristic
1175C2×C4#58511yescharacteristic
1176C2×C4#58511yescharacteristic
1177C2×C4#58511yescharacteristic
1178C2×C4#58511yescharacteristic
1179C8—22no—
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C8—41no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—22no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
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—81no—
1221C22—81no—
1222C22—168no—
1223C22D4×#4111yescharacteristic
1224C22#348511yescharacteristic
1225C22#350011yescharacteristic
1226C22C2×#57511yescharacteristic
1227C22C2×#57611yescharacteristic
1228C22#358411yescharacteristic
1229C22#358511yescharacteristic
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—81no—
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#349111yescharacteristic
1256C4#352111yescharacteristic
1257C4#356611yescharacteristic
1258C4#356611yescharacteristic
1259C2—42no—
1260C2—42no—
1261C2—82no—
1262C2—82no—
1263C2—161no—
1264C2#4350011yescharacteristic
1265C2#6145411yescharacteristic
1266C2#6147111yescharacteristic
1267C2#6172711yescharacteristic
1268C2#6176211yescharacteristic
1269C2#6254711yescharacteristic
1270C2#6259811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30400C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59208C2semidirect
2. #38996C2semidirect
3. #32389C2semidirect
4. #31945C2semidirect
5. #31698C2semidirect
6. #31681C2semidirect
7. #31530C2semidirect
8. #31370C2semidirect
9. #31362C2semidirect
11. #29110C2semidirect
12. #29096C2semidirect
13. #28085C2semidirect
14. #28058C2semidirect
15. #27879C2semidirect
16. #27743C2semidirect
17. #27701C2semidirect
18. #27574C2semidirect
19. #27534C2semidirect
20. #27385C2semidirect
21. #27113C2semidirect
22. #26738C2semidirect
23. #25032C2semidirect
24. #24977C2semidirect
25. #24933C2semidirect
26. #24893C2semidirect
27. #23764C2semidirect
28. #23300C2semidirect
29. #23132C2semidirect
30. #22764C2semidirect
31. #22040C2semidirect
44. #2571C22semidirect
51. #2509C22semidirect
53. #2497C22semidirect
60. #2454C22semidirect
62. #2442C22semidirect
65. #2420C22semidirect
69. #2361C22semidirect
72. #2349C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2101C22semidirect
83. #2099C22semidirect
86. #2092C22semidirect
87. #2088C22semidirect
88. #2086C22semidirect
89. #2085C22semidirect
90. #2085C22semidirect
91. #2084C22semidirect
92. #2083C22semidirect
97. #2076C22semidirect
104. #2073C22semidirect
108. #2059C22semidirect
114. #2034C22semidirect
118. #2025C22semidirect
120. #1992C22semidirect
121. #1991C22semidirect
122. #1991C22semidirect
123. #1989C22semidirect
127. #1949C22semidirect
128. #1942C22semidirect
136. #1936C22semidirect
144. #1924C22semidirect
146. #1923C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
154. #1917C22semidirect
155. #1916C22semidirect
166. #1874C22semidirect
169. #1864C22semidirect
173. #1852C22semidirect
174. #1846C22semidirect
175. #1836C22semidirect
176. #1835C22semidirect
177. #1835C22semidirect
178. #1824C22semidirect
181. #1823C22semidirect
182. #1808C22semidirect
184. #1804C22semidirect
186. #1802C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1770C22semidirect
195. #1762C22semidirect
196. #1762C22semidirect
197. #1762C22semidirect
198. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#592082
#389962
#323892
#319452
#316982
#316812
#315302
#313702
#313622
#304002
#291102
#290962
#280852
#280582
#278792
#277432
#277012
#275742
#275342
#273852
#271132
#267382
#250322
#249772
#249332
#248932
#237642
#233002
#231322
#227642
#220402