Finite Group Databasebeta

← #6794803

Subgroups — #6794803

Order 512.

1270 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39546C211yesmaximal, characteristic, complemented
2#35218C211yesmaximal, characteristic
3#33072C211yesmaximal, characteristic, complemented
4#32359C211yesmaximal, characteristic, complemented
5#32347C211yesmaximal, characteristic, complemented
6#32338C211yesmaximal, characteristic, complemented
7#32322C211yesmaximal, characteristic, complemented
8#32273C211yesmaximal, characteristic, complemented
9#32265C211yesmaximal, characteristic, complemented
10#32018C211yesmaximal, characteristic
11#31995C211yesmaximal, characteristic
12#29946C211yesmaximal, characteristic, complemented
13#29946C211yesmaximal, characteristic, complemented
14#29321C211yesmaximal, characteristic, complemented
15#29279C211yesmaximal, characteristic, complemented
16#28866C211yesmaximal, characteristic, complemented
17#28850C211yesmaximal, characteristic, complemented
18#27852C211yesmaximal, characteristic, complemented
19#27847C211yesmaximal, characteristic, complemented
20#27688C211yesmaximal, characteristic, complemented
21#27636C211yesmaximal, characteristic, complemented
22#27479C211yesmaximal, characteristic, complemented
23#27470C211yesmaximal, characteristic, complemented
24#27186C211yesmaximal, characteristic, complemented
25#27179C211yesmaximal, characteristic, complemented
26#24848C211yesmaximal, characteristic, complemented
27#24717C211yesmaximal, characteristic, complemented
28#22757C211yesmaximal, characteristic, complemented
29#21991C211yesmaximal, characteristic, complemented
30#21967C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic, complemented
32C2×#478C2211yescharacteristic
33C2×#433C2211yescharacteristic
34C2×#424C2211yescharacteristic
35#2859C2211yescharacteristic
36#2853—21no—
37#2852—21no—
38#2777—21no—
39#2766—21no—
40#2765—21no—
41#2761—21no—
42#2652—21no—
43#2648—21no—
44#2629C2211yescharacteristic
45#2629C2211yescharacteristic
46#2601—21no—
47#2597—21no—
48#2595—21no—
49#2590—21no—
50#2573—21no—
51#2570C2211yescharacteristic
52#2566C2211yescharacteristic
53#2562C2211yescharacteristic
54#2554—21no—
55#2535C2211yescharacteristic
56#2519—21no—
57#2508C2211yescharacteristic
58#2507C2211yescharacteristic
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2495C2211yescharacteristic
62#2494C2211yescharacteristic
63#2487C2211yescharacteristic
64#2485C2211yescharacteristic
65#2475—21no—
66#2422C2211yescharacteristic
67#2420C2211yescharacteristic
68#2347C2211yescharacteristic
69#2344C2211yescharacteristic
70#2324C2211yescharacteristic
71#2324C2211yescharacteristic
72#2317C2211yescharacteristic
73#2314C2211yescharacteristic
74#2314C2211yescharacteristic
75#2314C2211yescharacteristic
76C4×#125C2211yescharacteristic
77C4×#125C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic
107#2075C2211yescharacteristic
108#2075C2211yescharacteristic
109#2075C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1948C2211yescharacteristic
132#1948C2211yescharacteristic
133#1947C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1941C2211yescharacteristic
142#1936C2211yescharacteristic
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1895C2211yescharacteristic
163#1893C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1870C2211yescharacteristic
167#1869C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1847C2211yescharacteristic
181#1845C2211yescharacteristic
182#1836C2211yescharacteristic
183#1835C2211yescharacteristic
184#1831C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1804C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1798C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1767C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1752C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×#126—21no—
206C2×#126—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#121C2311yescharacteristic
212C2×#121C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×#117—21no—
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C42—21no—
223#478—24no—
224#433—24no—
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
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
245#424—24no—
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270#401—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#399—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#397—21no—
288#397—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#396—21no—
299#396—21no—
300#396—21no—
301#394—21no—
302#394—21no—
303#394—21no—
304#394—21no—
305#392—21no—
306#390—21no—
307#390—21no—
308#390D411yescharacteristic
309#390D411yescharacteristic
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389D411yescharacteristic
318#389D411yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388D411yescharacteristic
349#388D411yescharacteristic
350#388D411yescharacteristic
351#388D411yescharacteristic
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
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#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#383—21no—
392#383—21no—
393#382—21no—
394#382—21no—
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#381—21no—
401#381—21no—
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434C43C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
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
481C22×D4—21no—
482C22×D4—21no—
483C22×D4C2×D411yescharacteristic
484C22×D4C2411yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C22×C8—22no—
495C22×C8—41no—
496C22×C8—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505#126—82no—
506#126—82no—
507#125—22no—
508#125—22no—
509#125—41no—
510#125—41no—
511#125—82no—
512#123—82no—
513#121—22no—
514#121—22no—
515#121—41no—
516#121—41no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—41no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525#117—22no—
526#117—22no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
531#117—82no—
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⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
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⋊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×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
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—82no—
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637#107—22no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#106—22no—
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#4114yes—
663#102—22no—
664#102—22no—
665#102—22no—
666#102—22no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671C22⋊C8—22no—
672C22⋊C8—22no—
673C22⋊C8—41no—
674C22⋊C8—41no—
675C22⋊C8—41no—
676C22⋊C8—41no—
677#97—22no—
678#97—41no—
679#97—41no—
680C4×C8—22no—
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#95—21no—
724#95—21no—
725#95—21no—
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732C24—21no—
733C24C22×D411yescharacteristic
734C24C22×D411yescharacteristic
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D42−1+412yes—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4—81no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
802M16—82no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
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—82no—
826C2×C8C2×#4112yes—
827C2×C8C2×#4112yes—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
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—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
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—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—41no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
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—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—41no—
935C42—41no—
936C42—41no—
937C42—41no—
938C42—42no—
939C42—42no—
940C42—42no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42—81no—
947C42—81no—
948C42C2×#4112yes—
949C422−1+412yes—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—22no—
963C23—21no—
964C23—21no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C23×D411yescharacteristic
972D4—22no—
973D4—22no—
974D4—41no—
975D4—41no—
976D4—82no—
977D4—162no—
978D4—162no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
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—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
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—84no—
1067C2×C4—84no—
1068C2×C4—84no—
1069C2×C4—84no—
1070C2×C4#54712yes—
1071C2×C4#54712yes—
1072C2×C4C22×#4111yescharacteristic
1073C2×C4C2×2−1+411yescharacteristic
1074C2×C4C2×2−1+411yescharacteristic
1075C2×C4#58511yescharacteristic
1076C2×C4#58511yescharacteristic
1077C2×C4#58511yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C8—41no—
1085C8—41no—
1086C22—41no—
1087C22—41no—
1088C22—42no—
1089C22—42no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—42no—
1102C22—41no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22#344911yescharacteristic
1108C22C2×#54711yescharacteristic
1109C22#348911yescharacteristic
1110C22#358411yescharacteristic
1111C22#358511yescharacteristic
1112C22#358511yescharacteristic
1113C22#358611yescharacteristic
1114C4—22no—
1115C4—22no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4#351611yescharacteristic
1142C4#352111yescharacteristic
1143C4#356311yescharacteristic
1144C4#356511yescharacteristic
1145C2—81no—
1146C2—81no—
1147C2—82no—
1148C2#3891511yescharacteristic
1149C2#6097411yescharacteristic
1150C2#6098711yescharacteristic
1151C2#6128311yescharacteristic
1152C2#6129411yescharacteristic
1153C2#6219511yescharacteristic
1154C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39546C2semidirect
3. #33072C2semidirect
4. #32359C2semidirect
5. #32347C2semidirect
6. #32338C2semidirect
7. #32322C2semidirect
8. #32273C2semidirect
9. #32265C2semidirect
12. #29946C2semidirect
13. #29946C2semidirect
14. #29321C2semidirect
15. #29279C2semidirect
16. #28866C2semidirect
17. #28850C2semidirect
18. #27852C2semidirect
19. #27847C2semidirect
20. #27688C2semidirect
21. #27636C2semidirect
22. #27479C2semidirect
23. #27470C2semidirect
24. #27186C2semidirect
25. #27179C2semidirect
26. #24848C2semidirect
27. #24717C2semidirect
28. #22757C2semidirect
29. #21991C2semidirect
30. #21967C2semidirect
31. #21617C2semidirect

Maximal subgroups

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

subgroupindex
#395462
#352182
#330722
#323592
#323472
#323382
#323222
#322732
#322652
#320182
#319952
#299462
#293212
#292792
#288662
#288502
#278522
#278472
#276882
#276362
#274792
#274702
#271862
#271792
#248482
#247172
#227572
#219912
#219672
#216172