Finite Group Databasebeta

← #7300864

Subgroups — #7300864

Order 512.

1190 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42699C211yesmaximal, characteristic
2#42689C211yesmaximal, characteristic, complemented
3#32830C211yesmaximal, characteristic, complemented
4#32649C211yesmaximal, characteristic, complemented
5#32617C211yesmaximal, characteristic
6#32609C211yesmaximal, characteristic, complemented
7#32557C211yesmaximal, characteristic, complemented
8#32530C211yesmaximal, characteristic, complemented
9#32484C211yesmaximal, characteristic, complemented
10#32428C211yesmaximal, characteristic, complemented
11#32364C211yesmaximal, characteristic, complemented
12#32170C211yesmaximal, characteristic
13#32097C211yesmaximal, characteristic
14#31966C211yesmaximal, characteristic
15#31903C211yesmaximal, characteristic, complemented
16#29590C211yesmaximal, characteristic, complemented
17#29567C211yesmaximal, characteristic, complemented
18#29544C211yesmaximal, characteristic, complemented
19#29037C211yesmaximal, characteristic, complemented
20#28894C211yesmaximal, characteristic
21#28048C211yesmaximal, characteristic, complemented
22#28019C211yesmaximal, characteristic, complemented
23#27146C211yesmaximal, characteristic, complemented
24#27092C211yesmaximal, characteristic, complemented
25#26863C211yesmaximal, characteristic, complemented
26#26760C211yesmaximal, characteristic, complemented
27#26334C211yesmaximal, characteristic
28#26325C211yesmaximal, characteristic, complemented
29#25074C211yesmaximal, characteristic, complemented
30#24993C211yesmaximal, characteristic, complemented
31#22316C211yesmaximal, characteristic, complemented
32#2837—21no—
33#2833—21no—
34#2769—21no—
35#2766—21no—
36#2762—21no—
37#2762—21no—
38#2702—21no—
39#2700—21no—
40#2692—21no—
41#2687—21no—
42#2666—21no—
43#2663—21no—
44#2655—21no—
45#2651—21no—
46#2647C2211yescharacteristic
47#2640C2211yescharacteristic
48#2592C2211yescharacteristic
49#2582C2211yescharacteristic
50#2582C2211yescharacteristic
51#2581C2211yescharacteristic
52#2548C2211yescharacteristic
53#2544C2211yescharacteristic
54#2542C2211yescharacteristic
55#2538C2211yescharacteristic
56#2524—21no—
57#2521—21no—
58#2514C2211yescharacteristic
59#2514C2211yescharacteristic
60#2514C2211yescharacteristic
61#2512C2211yescharacteristic
62#2511C2211yescharacteristic
63#2511C2211yescharacteristic
64#2509C2211yescharacteristic
65#2508C2211yescharacteristic
66#2508C2211yescharacteristic
67#2507C2211yescharacteristic
68#2448C2211yescharacteristic
69#2445C2211yescharacteristic
70#2399C2211yescharacteristic
71#2369C2211yescharacteristic
72#2367C2211yescharacteristic
73#2355C2211yescharacteristic
74#2355C2211yescharacteristic
75#2320C2211yescharacteristic
76#2319C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2100C2211yescharacteristic
80#2097C2211yescharacteristic
81#2096C2211yescharacteristic
82#2096C2211yescharacteristic
83#2095C2211yescharacteristic
84#2094C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2084C2211yescharacteristic
91#2084C2211yescharacteristic
92#2074C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2057C2211yescharacteristic
112#2056C2211yescharacteristic
113#2056C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2041C2211yescharacteristic
121#2024C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2014C2211yescharacteristic
125#1985C2211yescharacteristic
126#1985C2211yescharacteristic
127#1984C2211yescharacteristic
128#1984C2211yescharacteristic
129#1983C2211yescharacteristic
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1969C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1961C2211yescharacteristic
137#1958C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1947C2211yescharacteristic
142#1944C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1939C2211yescharacteristic
146#1939C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1921C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1880C2211yescharacteristic
180#1880C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic
190#1862C2211yescharacteristic
191#1847C2211yescharacteristic
192#1834C2211yescharacteristic
193#1832C2211yescharacteristic
194#1805C2211yescharacteristic
195#1802C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#126—21no—
209C2×#124—21no—
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273#401—21no—
274#401—21no—
275#401—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#399—21no—
291#399—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398D411yescharacteristic
304#398D411yescharacteristic
305#398D411yescharacteristic
306#398D411yescharacteristic
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#395—21no—
316#395D411yescharacteristic
317#395D411yescharacteristic
318#395D411yescharacteristic
319#395D411yescharacteristic
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#393—21no—
328#393—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
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#388—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#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#383—21no—
412#383—21no—
413#382—21no—
414#382—21no—
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#380—21no—
422#380—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×C22⋊C4—21no—
439#376C2311yescharacteristic
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#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8—21no—
479C22×Q8C2×D411yescharacteristic
480C22×Q8C2×D411yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×Q8C2411yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2411yescharacteristic
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C2×Q16—41no—
490C2×Q16—41no—
491C2×Q16—41no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C2×SD16—41no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508#127—41no—
509#127—41no—
510#126—82no—
511#124—41no—
512#124—41no—
513#124—41no—
514#124—41no—
515#124—82no—
516#123—82no—
517C22⋊Q8—82no—
518C22⋊Q8—82no—
519C22⋊Q8—82no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×D4—41no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—41no—
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⋊C4—21no—
556C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622#107—22no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635C4⋊C8—41no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638C4⋊C8—41no—
639C4⋊C8—41no—
640C4⋊C8—41no—
641#103—22no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#102—22no—
654#102—41no—
655#102—41no—
656#102—41no—
657#102—41no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665#102—41no—
666#102—41no—
667#97—22no—
668#97—41no—
669#97—41no—
670C4×C8—41no—
671C4×C8—41no—
672C4×C8—41no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735C24—21no—
736C24—21no—
737C2×Q8—22no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—41no—
751C2×Q8—41no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—41no—
755C2×Q8—42no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—42no—
771C2×D4—81no—
772C2×D4—81no—
773C2×D4—81no—
774C2×D4—81no—
775C2×D4—81no—
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—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
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×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C2511yescharacteristic
811Q16—82no—
812SD16—82no—
813SD16—82no—
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×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C82−1+412yes—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—21no—
841C4⋊C4—21no—
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—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—81no—
881C4⋊C4—81no—
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—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
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—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—42no—
938C42—42no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42—81no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23C23×D411yescharacteristic
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—41no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—82no—
971Q8—82no—
972Q8—162no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—41no—
981D4—162no—
982D4—162no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
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—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
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—162no—
1067C2×C4—162no—
1068C2×C4#57712yes—
1069C2×C4C2×2−1+411yescharacteristic
1070C2×C4#58511yescharacteristic
1071C2×C4#58511yescharacteristic
1072C2×C4#58511yescharacteristic
1073C2×C4#58511yescharacteristic
1074C2×C4#58511yescharacteristic
1075C8—22no—
1076C8—41no—
1077C8—41no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22#348511yescharacteristic
1098C22#348711yescharacteristic
1099C22#349711yescharacteristic
1100C22C2×#57711yescharacteristic
1101C22#358411yescharacteristic
1102C22#358511yescharacteristic
1103C22#358611yescharacteristic
1104C4—22no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—41no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4#356411yescharacteristic
1133C4#356511yescharacteristic
1134C4#356611yescharacteristic
1135C4#356611yescharacteristic
1136C2—161no—
1137C2—161no—
1138C2#4782311yescharacteristic
1139C2#6177011yescharacteristic
1140C2#6177611yescharacteristic
1141C2#6191811yescharacteristic
1142C2#6192111yescharacteristic
1143C2#6240711yescharacteristic
1144C2#6241011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42689C2semidirect
3. #32830C2semidirect
4. #32649C2semidirect
6. #32609C2semidirect
7. #32557C2semidirect
8. #32530C2semidirect
9. #32484C2semidirect
10. #32428C2semidirect
11. #32364C2semidirect
15. #31903C2semidirect
16. #29590C2semidirect
17. #29567C2semidirect
18. #29544C2semidirect
19. #29037C2semidirect
21. #28048C2semidirect
22. #28019C2semidirect
23. #27146C2semidirect
24. #27092C2semidirect
25. #26863C2semidirect
26. #26760C2semidirect
28. #26325C2semidirect
29. #25074C2semidirect
30. #24993C2semidirect
31. #22316C2semidirect

Maximal subgroups

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

subgroupindex
#426992
#426892
#328302
#326492
#326172
#326092
#325572
#325302
#324842
#324282
#323642
#321702
#320972
#319662
#319032
#295902
#295672
#295442
#290372
#288942
#280482
#280192
#271462
#270922
#268632
#267602
#263342
#263252
#250742
#249932
#223162