Finite Group Databasebeta

← #7590310

Subgroups — #7590310

Order 512.

1503 conjugacy classes of subgroups.

The subgroup lattice has 1243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44914C211yesmaximal, characteristic
2#44898C211yesmaximal, characteristic
3#32412C211yesmaximal, characteristic, complemented
4#32408C211yesmaximal, characteristic, complemented
5#32266C211yesmaximal, characteristic, complemented
6#32260C211yesmaximal, characteristic, complemented
7#28713C211yesmaximal, characteristic, complemented
8#27853C211yesmaximal, characteristic, complemented
9#27843C211yesmaximal, characteristic, complemented
10#27671C211yesmaximal, characteristic, complemented
11#27671C211yesmaximal, characteristic, complemented
12#27665C211yesmaximal, characteristic, complemented
13#27609C211yesmaximal, characteristic, complemented
14#27606C211yesmaximal, characteristic, complemented
15#26072C211yesmaximal, characteristic, complemented
16#26060C211yesmaximal, characteristic, complemented
17#26011C211yesmaximal, characteristic, complemented
18#26009C211yesmaximal, characteristic, complemented
19#25993C211yesmaximal, characteristic, complemented
20#25990C211yesmaximal, characteristic, complemented
21#24961C211yesmaximal, characteristic, complemented
22#24949C211yesmaximal, characteristic, complemented
23#24946C211yesmaximal, characteristic, complemented
24#24935C211yesmaximal, characteristic, complemented
25#22663C211yesmaximal, characteristic, complemented
26#22659C211yesmaximal, characteristic, complemented
27#22624C211yesmaximal, characteristic, complemented
28#22613C211yesmaximal, characteristic, complemented
29#21445C211yesmaximal, characteristic
30#20664C211yesmaximal, characteristic, complemented
31#20662C211yesmaximal, characteristic, complemented
32C22×#131C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#436C2211yescharacteristic
35C2×#436C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#427C2211yescharacteristic
41C22×#106C2211yescharacteristic
42#2782—21no—
43#2763—21no—
44#2761—21no—
45#2754—21no—
46#2749—21no—
47#2730—21no—
48#2723—21no—
49#2723—21no—
50#2612—21no—
51#2610—21no—
52#2605—21no—
53#2603—21no—
54#2603—21no—
55#2595—21no—
56#2563C2211yescharacteristic
57#2547C2211yescharacteristic
58#2497C2211yescharacteristic
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2495C2211yescharacteristic
62#2487C2211yescharacteristic
63#2487C2211yescharacteristic
64#2485C2211yescharacteristic
65#2485C2211yescharacteristic
66#2485C2211yescharacteristic
67#2485C2211yescharacteristic
68#2477—21no—
69#2463—21no—
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2440C2211yescharacteristic
73#2439C2211yescharacteristic
74#2388C2211yescharacteristic
75#2354C2211yescharacteristic
76#2352C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79#2346C2211yescharacteristic
80#2346C2211yescharacteristic
81#2346C2211yescharacteristic
82#2344C2211yescharacteristic
83#2311C2211yescharacteristic
84#2311C2211yescharacteristic
85#2311C2211yescharacteristic
86#2311C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2077C2211yescharacteristic
108#2077C2211yescharacteristic
109#2077C2211yescharacteristic
110#2077C2211yescharacteristic
111#2077C2211yescharacteristic
112#2076C2211yescharacteristic
113#2075C2211yescharacteristic
114#2075C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2057C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1949C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1942C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1941C2211yescharacteristic
131#1921C2211yescharacteristic
132#1920C2211yescharacteristic
133#1920C2211yescharacteristic
134#1920C2211yescharacteristic
135#1920C2211yescharacteristic
136#1920C2211yescharacteristic
137#1920C2211yescharacteristic
138#1920C2211yescharacteristic
139#1919C2211yescharacteristic
140#1919C2211yescharacteristic
141#1918C2211yescharacteristic
142#1918C2211yescharacteristic
143#1870C2211yescharacteristic
144#1869C2211yescharacteristic
145#1869C2211yescharacteristic
146#1854C2211yescharacteristic
147#1854C2211yescharacteristic
148#1854C2211yescharacteristic
149#1854C2211yescharacteristic
150#1853C2211yescharacteristic
151#1853C2211yescharacteristic
152#1853C2211yescharacteristic
153#1853C2211yescharacteristic
154#1853C2211yescharacteristic
155#1853C2211yescharacteristic
156#1853C2211yescharacteristic
157#1852C2211yescharacteristic
158#1851C2211yescharacteristic
159#1850C2211yescharacteristic
160#1850C2211yescharacteristic
161#1847C2211yescharacteristic
162#1844C2211yescharacteristic
163#1825C2211yescharacteristic
164#1825C2211yescharacteristic
165#1825C2211yescharacteristic
166#1825C2211yescharacteristic
167#1825C2211yescharacteristic
168#1825C2211yescharacteristic
169#1825C2211yescharacteristic
170#1824C2211yescharacteristic
171#1823C2211yescharacteristic
172#1823C2211yescharacteristic
173#1809C2211yescharacteristic
174#1809C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1808C2211yescharacteristic
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1780C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C2×#131—24no—
205C2×#131—24no—
206C2×#131—42no—
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#124—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238#498—42no—
239#436—24no—
240#436—42no—
241#435—24no—
242#428—24no—
243#428—42no—
244#428—42no—
245#427—24no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106—42no—
255C2×#106C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395D411yescharacteristic
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394D411yescharacteristic
317#394D411yescharacteristic
318#394D411yescharacteristic
319#393—21no—
320#393—21no—
321#393—21no—
322#393D411yescharacteristic
323#392D411yescharacteristic
324#392D411yescharacteristic
325#392D411yescharacteristic
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#383—21no—
402#382—21no—
403#382—21no—
404#382—21no—
405#382—21no—
406#382C2311yescharacteristic
407#381—21no—
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
443#376—21no—
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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×D4C2×D411yescharacteristic
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514#131—416no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16#4114yes—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8#4114yes—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#126—82no—
549#126—82no—
550#124—82no—
551C22⋊Q8—82no—
552C22⋊Q8—82no—
553C22⋊Q8—82no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—82no—
561C4×D4—82no—
562#117—22no—
563#117—22no—
564#117—22no—
565#117—22no—
566#117—22no—
567#117—22no—
568#117—41no—
569#117—41no—
570#117—41no—
571#117—41no—
572#117—82no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
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—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—22no—
683#107—22no—
684#107—22no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—41no—
707C22⋊C8—22no—
708C22⋊C8—22no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716#97—22no—
717C4×C8—22no—
718C4×C8—22no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#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#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24C22×D411yescharacteristic
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C24C22×D411yescharacteristic
771#41—44no—
772#41—44no—
773#41—44no—
774#41—44no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—41no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C22×C4—21no—
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—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—42no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C42−1+412yes—
866C22×C42−1+412yes—
867C22×C4C2511yescharacteristic
868M16—28no—
869M16—44no—
870M16—44no—
871M16—44no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—28no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—44no—
893C2×C8—44no—
894C2×C8C2×#4112yes—
895C2×C8C2×#4112yes—
896C2×C8C2×#4112yes—
897C2×C8C2×#4112yes—
898C2×C8H(5,𝔽2)12yes—
899C4⋊C4—22no—
900C4⋊C4—22no—
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—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—41no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
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—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23#54712yes—
1042C23#54712yes—
1043C23C23×D411yescharacteristic
1044Q8—44no—
1045Q8—162no—
1046Q8—162no—
1047D4—44no—
1048D4—44no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—82no—
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—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
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—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—84no—
1144C2×C4—162no—
1145C2×C4—162no—
1146C2×C4—162no—
1147C2×C4—162no—
1148C2×C4#54712yes—
1149C2×C4#54712yes—
1150C2×C4#57712yes—
1151C2×C4#57712yes—
1152C2×C4C22×#4111yescharacteristic
1153C2×C4C22×#4111yescharacteristic
1154C2×C4C2×H(5,𝔽2)11yescharacteristic
1155C2×C4C2×2−1+411yescharacteristic
1156C2×C4C2×2−1+411yescharacteristic
1157C2×C4#58511yescharacteristic
1158C8—22no—
1159C8—22no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8#55114yes—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22C2×#54711yescharacteristic
1195C22C2×#54711yescharacteristic
1196C22#349611yescharacteristic
1197C22C2×#57711yescharacteristic
1198C22C2×#57711yescharacteristic
1199C22#358511yescharacteristic
1200C22#358611yescharacteristic
1201C4—22no—
1202C4—22no—
1203C4—22no—
1204C4—22no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4C2×#55111yescharacteristic
1228C4#349511yescharacteristic
1229C4#349511yescharacteristic
1230C4#353811yescharacteristic
1231C2—42no—
1232C2—42no—
1233C2—81no—
1234C2—81no—
1235C2#5919811yescharacteristic
1236C2#6126611yescharacteristic
1237C2#6127111yescharacteristic
1238C2#6127911yescharacteristic
1239C2#6128811yescharacteristic
1240C2#6230711yescharacteristic
1241C2#6234611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2388C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32412C2semidirect
4. #32408C2semidirect
5. #32266C2semidirect
6. #32260C2semidirect
7. #28713C2semidirect
8. #27853C2semidirect
9. #27843C2semidirect
10. #27671C2semidirect
11. #27671C2semidirect
12. #27665C2semidirect
13. #27609C2semidirect
14. #27606C2semidirect
15. #26072C2semidirect
16. #26060C2semidirect
17. #26011C2semidirect
18. #26009C2semidirect
19. #25993C2semidirect
20. #25990C2semidirect
21. #24961C2semidirect
22. #24949C2semidirect
23. #24946C2semidirect
24. #24935C2semidirect
25. #22663C2semidirect
26. #22659C2semidirect
27. #22624C2semidirect
28. #22613C2semidirect
30. #20664C2semidirect
31. #20662C2semidirect

Maximal subgroups

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

subgroupindex
#449142
#448982
#324122
#324082
#322662
#322602
#287132
#278532
#278432
#276712
#276652
#276092
#276062
#260722
#260602
#260112
#260092
#259932
#259902
#249612
#249492
#249462
#249352
#226632
#226592
#226242
#226132
#214452
#206642
#206622