Finite Group Databasebeta

← #6813399

Subgroups — #6813399

Order 512.

1388 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42925C211yesmaximal, characteristic
2#42452C211yesmaximal, characteristic, complemented
3#33142C211yesmaximal, characteristic, complemented
4#32388C211yesmaximal, characteristic, complemented
5#32376C211yesmaximal, characteristic, complemented
6#32362C211yesmaximal, characteristic, complemented
7#32358C211yesmaximal, characteristic, complemented
8#32299C211yesmaximal, characteristic, complemented
9#32296C211yesmaximal, characteristic, complemented
10#31093C211yesmaximal, characteristic, complemented
11#31086C211yesmaximal, characteristic, complemented
12#29919C211yesmaximal, characteristic, complemented
13#29916C211yesmaximal, characteristic, complemented
14#28837C211yesmaximal, characteristic, complemented
15#28530C211yesmaximal, characteristic, complemented
16#28018C211yesmaximal, characteristic, complemented
17#27993C211yesmaximal, characteristic, complemented
18#27946C211yesmaximal, characteristic, complemented
19#27853C211yesmaximal, characteristic, complemented
20#26343C211yesmaximal, characteristic, complemented
21#26340C211yesmaximal, characteristic, complemented
22#26135C211yesmaximal, characteristic, complemented
23#26130C211yesmaximal, characteristic
24#26072C211yesmaximal, characteristic, complemented
25#26072C211yesmaximal, characteristic, complemented
26#25036C211yesmaximal, characteristic, complemented
27#24794C211yesmaximal, characteristic
28#23035C211yesmaximal, characteristic, complemented
29#22663C211yesmaximal, characteristic, complemented
30#21571C211yesmaximal, characteristic, complemented
31#20802C211yesmaximal, characteristic, complemented
32C2×#498C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#427C2211yescharacteristic
45C22×#106C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2837—21no—
48#2835—21no—
49#2805—21no—
50#2802—21no—
51#2796—21no—
52#2771—21no—
53#2728—21no—
54#2711—21no—
55#2689—21no—
56#2681—21no—
57#2663—21no—
58#2654—21no—
59#2652—21no—
60#2638—21no—
61#2625C2211yescharacteristic
62#2624C2211yescharacteristic
63#2570C2211yescharacteristic
64#2567C2211yescharacteristic
65#2556—21no—
66#2552C2211yescharacteristic
67#2542C2211yescharacteristic
68#2513C2211yescharacteristic
69#2511C2211yescharacteristic
70#2509C2211yescharacteristic
71#2509C2211yescharacteristic
72#2503C2211yescharacteristic
73#2500C2211yescharacteristic
74#2497C2211yescharacteristic
75#2496C2211yescharacteristic
76#2466—21no—
77#2440C2211yescharacteristic
78#2440C2211yescharacteristic
79#2439C2211yescharacteristic
80#2439C2211yescharacteristic
81#2422C2211yescharacteristic
82#2421C2211yescharacteristic
83#2416C2211yescharacteristic
84#2415C2211yescharacteristic
85#2395C2211yescharacteristic
86#2363C2211yescharacteristic
87#2360C2211yescharacteristic
88#2354C2211yescharacteristic
89D4×C4⋊C4C2211yescharacteristic
90#2317C2211yescharacteristic
91#2317C2211yescharacteristic
92#2101C2211yescharacteristic
93#2101C2211yescharacteristic
94#2100C2211yescharacteristic
95#2099C2211yescharacteristic
96#2097C2211yescharacteristic
97#2096C2211yescharacteristic
98#2096C2211yescharacteristic
99#2096C2211yescharacteristic
100#2094C2211yescharacteristic
101#2094C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic
104#2088C2211yescharacteristic
105#2088C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2084C2211yescharacteristic
110#2084C2211yescharacteristic
111#2084C2211yescharacteristic
112#2084C2211yescharacteristic
113#2083C2211yescharacteristic
114#2077C2211yescharacteristic
115#2077C2211yescharacteristic
116#2074C2211yescharacteristic
117#2073C2211yescharacteristic
118#2072C2211yescharacteristic
119#2071C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2058C2211yescharacteristic
125#2058C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2036C2211yescharacteristic
129#2036C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1947C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic
168#1869C2211yescharacteristic
169#1865C2211yescharacteristic
170#1864C2211yescharacteristic
171#1863C2211yescharacteristic
172#1862C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1850C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1846C2211yescharacteristic
188#1846C2211yescharacteristic
189#1844C2211yescharacteristic
190#1844C2211yescharacteristic
191#1844C2211yescharacteristic
192#1818C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195#1809C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1771C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#125—21no—
211C2×#123—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232#498—42no—
233#485—42no—
234#481—42no—
235#476—42no—
236#475—42no—
237#468—24no—
238#468—42no—
239C4×SD16—42no—
240#436—24no—
241#428—42no—
242#428—42no—
243#428—42no—
244#427—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106—42no—
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295#405—24no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400D411yescharacteristic
317#399—21no—
318#399—21no—
319#399—21no—
320#399D411yescharacteristic
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398D411yescharacteristic
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397D411yescharacteristic
338#397D411yescharacteristic
339#397D411yescharacteristic
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394D411yescharacteristic
356#394D411yescharacteristic
357#393—21no—
358#393—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16#4114yes—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#126—82no—
531#125—82no—
532#123—82no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—82no—
538C22⋊Q8—82no—
539C22⋊Q8—82no—
540C22⋊Q8—82no—
541#121—22no—
542#121—22no—
543#121—41no—
544#121—41no—
545#121—82no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—82no—
553#117—22no—
554#117—22no—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
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—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊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×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667#107—22no—
668#107—22no—
669#107—22no—
670#107—22no—
671#107—41no—
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—22no—
680#106—22no—
681#106—22no—
682#106—22no—
683#106—22no—
684#106—41no—
685#106—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713C22⋊C8—22no—
714C22⋊C8—22no—
715C22⋊C8—22no—
716#97—22no—
717#97—22no—
718#97—22no—
719C4×C8—22no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—22no—
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#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24C22×D411yescharacteristic
775C24C22×D411yescharacteristic
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—42no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—41no—
797C2×D4—42no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
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—42no—
829C22×C4—42no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C2×#4112yes—
853C22×C42−1+412yes—
854C22×C4C2511yescharacteristic
855SD16—44no—
856M16—28no—
857M16—44no—
858C2×C8—28no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8C2×#4112yes—
878C2×C8C2×#4112yes—
879C2×C8H(5,𝔽2)12yes—
880C2×C8H(5,𝔽2)12yes—
881C2×C82−1+412yes—
882C2×C82−1+412yes—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—41no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23#54712yes—
1023C23C23×D411yescharacteristic
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—162no—
1029Q8—162no—
1030D4—44no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—162no—
1036D4—162no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—162no—
1124C2×C4—162no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4#54712yes—
1128C2×C4#57712yes—
1129C2×C4#57712yes—
1130C2×C4C22×#4111yescharacteristic
1131C2×C4C2×H(5,𝔽2)11yescharacteristic
1132C2×C4C2×H(5,𝔽2)11yescharacteristic
1133C2×C4C2×2−1+411yescharacteristic
1134C2×C4C2×2−1+411yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C8—22no—
1137C8—22no—
1138C8—22no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8#53914yes—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22C2×#54711yescharacteristic
1166C22#349811yescharacteristic
1167C22#349911yescharacteristic
1168C22C2×#57711yescharacteristic
1169C22C2×#57711yescharacteristic
1170C22#358511yescharacteristic
1171C22#358611yescharacteristic
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4C2×#53911yescharacteristic
1200C4#349211yescharacteristic
1201C4#355211yescharacteristic
1202C4#355211yescharacteristic
1203C2—42no—
1204C2—81no—
1205C2—161no—
1206C2#3934811yescharacteristic
1207C2#6127211yescharacteristic
1208C2#6128111yescharacteristic
1209C2#6243011yescharacteristic
1210C2#6244511yescharacteristic
1211C2#6252111yescharacteristic
1212C2#6252211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2416C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42452C2semidirect
3. #33142C2semidirect
4. #32388C2semidirect
5. #32376C2semidirect
6. #32362C2semidirect
7. #32358C2semidirect
8. #32299C2semidirect
9. #32296C2semidirect
10. #31093C2semidirect
11. #31086C2semidirect
12. #29919C2semidirect
13. #29916C2semidirect
14. #28837C2semidirect
15. #28530C2semidirect
16. #28018C2semidirect
17. #27993C2semidirect
18. #27946C2semidirect
19. #27853C2semidirect
20. #26343C2semidirect
21. #26340C2semidirect
22. #26135C2semidirect
24. #26072C2semidirect
25. #26072C2semidirect
26. #25036C2semidirect
28. #23035C2semidirect
29. #22663C2semidirect
30. #21571C2semidirect
31. #20802C2semidirect

Maximal subgroups

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

subgroupindex
#429252
#424522
#331422
#323882
#323762
#323622
#323582
#322992
#322962
#310932
#310862
#299192
#299162
#288372
#285302
#280182
#279932
#279462
#278532
#263432
#263402
#261352
#261302
#260722
#250362
#247942
#230352
#226632
#215712
#208022