Finite Group Databasebeta

← #7181416

Subgroups — #7181416

Order 512.

1297 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C211yesmaximal, characteristic, complemented
2#39997C211yesmaximal, characteristic, complemented
3#32541C211yesmaximal, characteristic, complemented
4#32537C211yesmaximal, characteristic, complemented
5#32500C211yesmaximal, characteristic, complemented
6#32488C211yesmaximal, characteristic, complemented
7#32452C211yesmaximal, characteristic, complemented
8#32440C211yesmaximal, characteristic, complemented
9#32359C211yesmaximal, characteristic, complemented
10#32349C211yesmaximal, characteristic, complemented
11#29318C211yesmaximal, characteristic, complemented
12#29195C211yesmaximal, characteristic, complemented
13#28049C211yesmaximal, characteristic, complemented
14#28041C211yesmaximal, characteristic, complemented
15#28021C211yesmaximal, characteristic, complemented
16#28017C211yesmaximal, characteristic, complemented
17#27514C211yesmaximal, characteristic, complemented
18#27500C211yesmaximal, characteristic, complemented
19#27383C211yesmaximal, characteristic, complemented
20#27367C211yesmaximal, characteristic, complemented
21#26332C211yesmaximal, characteristic, complemented
22#26332C211yesmaximal, characteristic, complemented
23#25304C211yesmaximal, characteristic
24#25304C211yesmaximal, characteristic
25#25069C211yesmaximal, characteristic, complemented
26#25002C211yesmaximal, characteristic, complemented
27#23784C211yesmaximal, characteristic, complemented
28#23152C211yesmaximal, characteristic, complemented
29#22745C211yesmaximal, characteristic, complemented
30#22729C211yesmaximal, characteristic, complemented
31#22151C211yesmaximal, characteristic
32C2×#459C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×#446C2211yescharacteristic
35#2864C2211yescharacteristic
36#2800—21no—
37#2800—21no—
38#2798—21no—
39#2754—21no—
40#2721—21no—
41#2716—21no—
42#2652—21no—
43#2580C2211yescharacteristic
44#2580C2211yescharacteristic
45#2566C2211yescharacteristic
46#2566C2211yescharacteristic
47#2548C2211yescharacteristic
48#2548C2211yescharacteristic
49#2545—21no—
50#2513C2211yescharacteristic
51#2513C2211yescharacteristic
52#2513C2211yescharacteristic
53#2513C2211yescharacteristic
54#2512—21no—
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2509C2211yescharacteristic
60#2508C2211yescharacteristic
61#2507C2211yescharacteristic
62#2506C2211yescharacteristic
63#2478—21no—
64#2475—21no—
65#2466—21no—
66#2466—21no—
67#2447—21no—
68#2367—21no—
69#2357C2211yescharacteristic
70#2357C2211yescharacteristic
71#2355C2211yescharacteristic
72#2355C2211yescharacteristic
73#2355C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75#2334—21no—
76C4×C4⋊Q8C2211yescharacteristic
77C4×#127C2211yescharacteristic
78C4×#125C2211yescharacteristic
79#2293C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2093C2211yescharacteristic
84#2093C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2025C2211yescharacteristic
120#1985C2211yescharacteristic
121#1985C2211yescharacteristic
122#1982C2211yescharacteristic
123#1972C2211yescharacteristic
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1961C2211yescharacteristic
130#1961C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1947C2211yescharacteristic
144#1944C2211yescharacteristic
145#1944C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1940C2211yescharacteristic
149#1940C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1844C2211yescharacteristic
187#1836C2211yescharacteristic
188#1836C2211yescharacteristic
189#1835C2211yescharacteristic
190#1802C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1767C2211yescharacteristic
200#1767C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C2×C4⋊Q8D411yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224#459—24no—
225#446—24no—
226#446—24no—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
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
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#397—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#397—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#393—21no—
316#393—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391D411yescharacteristic
321#391D411yescharacteristic
322#390—21no—
323#390—21no—
324#390—21no—
325#390—21no—
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389D411yescharacteristic
348#389D411yescharacteristic
349#389D411yescharacteristic
350#389D411yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384D411yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C43C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2×D411yescharacteristic
482C22×Q8C2×D411yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2411yescharacteristic
486C22×D4C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—42no—
506#127—22no—
507#127—22no—
508#126—44no—
509#126—82no—
510#126—82no—
511#126—82no—
512#125—41no—
513#125—41no—
514#125—82no—
515#124—44no—
516#124—82no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—82no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C4×D4—41no—
528C4×D4—82no—
529C4×D4—82no—
530#117—82no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
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×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639#107—22no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—41no—
664C4⋊C8#4114yes—
665#102—22no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#97—22no—
686#97—22no—
687#97—22no—
688#97—22no—
689#97—41no—
690#97—41no—
691C4×C8—22no—
692C4×C8—22no—
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#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738C24—21no—
739C24—21no—
740C24—21no—
741C2×Q8—22no—
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8—41no—
745C2×Q8—41no—
746C2×Q8—41no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—81no—
770C2×D4—81no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4—81no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C2511yescharacteristic
808D8—82no—
809D8—82no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8C2×#4112yes—
832C2×C8C2×#4112yes—
833C2×C82−1+412yes—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42C2×#4112yes—
961C422−1+412yes—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23C23×D411yescharacteristic
984Q8—44no—
985Q8—82no—
986D4—41no—
987D4—41no—
988D4—41no—
989D4—41no—
990D4—41no—
991D4—41no—
992D4—41no—
993D4—41no—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—84no—
999D4—84no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
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—21no—
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—41no—
1040C2×C4—41no—
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—84no—
1079C2×C4—162no—
1080C2×C4—162no—
1081C2×C4#54712yes—
1082C2×C4#54712yes—
1083C2×C4#57512yes—
1084C2×C4C22×#4111yescharacteristic
1085C2×C4C2×2−1+411yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4#58511yescharacteristic
1088C2×C4#58511yescharacteristic
1089C2×C4#58511yescharacteristic
1090C8—22no—
1091C8—22no—
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22C2×#54711yescharacteristic
1120C22#348711yescharacteristic
1121C22#349711yescharacteristic
1122C22C2×#57511yescharacteristic
1123C22#358511yescharacteristic
1124C22#358511yescharacteristic
1125C22#358511yescharacteristic
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4#351611yescharacteristic
1154C4#352111yescharacteristic
1155C4#355511yescharacteristic
1156C4#355711yescharacteristic
1157C2—161no—
1158C2—161no—
1159C2—161no—
1160C2#4524211yescharacteristic
1161C2#6125511yescharacteristic
1162C2#6129311yescharacteristic
1163C2#6189611yescharacteristic
1164C2#6194511yescharacteristic
1165C2#6239211yescharacteristic
1166C2#6240011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59679C2semidirect
2. #39997C2semidirect
3. #32541C2semidirect
4. #32537C2semidirect
5. #32500C2semidirect
6. #32488C2semidirect
7. #32452C2semidirect
8. #32440C2semidirect
9. #32359C2semidirect
10. #32349C2semidirect
11. #29318C2semidirect
12. #29195C2semidirect
13. #28049C2semidirect
14. #28041C2semidirect
15. #28021C2semidirect
16. #28017C2semidirect
17. #27514C2semidirect
18. #27500C2semidirect
19. #27383C2semidirect
20. #27367C2semidirect
21. #26332C2semidirect
22. #26332C2semidirect
25. #25069C2semidirect
26. #25002C2semidirect
27. #23784C2semidirect
28. #23152C2semidirect
29. #22745C2semidirect
30. #22729C2semidirect

Maximal subgroups

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

subgroupindex
#596792
#399972
#325412
#325372
#325002
#324882
#324522
#324402
#323592
#323492
#293182
#291952
#280492
#280412
#280212
#280172
#275142
#275002
#273832
#273672
#263322
#253042
#250692
#250022
#237842
#231522
#227452
#227292
#221512