Finite Group Databasebeta

← #7014329

Subgroups — #7014329

Order 512.

1467 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45046C211yesmaximal, characteristic, complemented
2#42548C211yesmaximal, characteristic, complemented
3#32337C211yesmaximal, characteristic, complemented
4#31996C211yesmaximal, characteristic, complemented
5#31870C211yesmaximal, characteristic, complemented
6#31626C211yesmaximal, characteristic, complemented
7#31557C211yesmaximal, characteristic, complemented
8#31514C211yesmaximal, characteristic, complemented
9#31086C211yesmaximal, characteristic, complemented
10#30567C211yesmaximal, characteristic, complemented
11#29174C211yesmaximal, characteristic, complemented
12#29043C211yesmaximal, characteristic, complemented
13#28152C211yesmaximal, characteristic, complemented
14#28056C211yesmaximal, characteristic, complemented
15#27835C211yesmaximal, characteristic, complemented
16#27550C211yesmaximal, characteristic, complemented
17#27473C211yesmaximal, characteristic, complemented
18#27299C211yesmaximal, characteristic, complemented
19#26961C211yesmaximal, characteristic, complemented
20#26904C211yesmaximal, characteristic, complemented
21#26633C211yesmaximal, characteristic, complemented
22#26547C211yesmaximal, characteristic, complemented
23#26529C211yesmaximal, characteristic, complemented
24#26408C211yesmaximal, characteristic, complemented
25#25252C211yesmaximal, characteristic, complemented
26#24716C211yesmaximal, characteristic, complemented
27#23712C211yesmaximal, characteristic, complemented
28#22918C211yesmaximal, characteristic, complemented
29#22905C211yesmaximal, characteristic, complemented
30#22670C211yesmaximal, characteristic, complemented
31#22193C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×C4×D8C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#433C2211yescharacteristic
41#2835—21no—
42#2797—21no—
43#2782—21no—
44#2779—21no—
45#2744—21no—
46#2723—21no—
47#2708—21no—
48#2696—21no—
49#2691—21no—
50#2636—21no—
51#2628C2211yescharacteristic
52#2623—21no—
53#2579—21no—
54#2571C2211yescharacteristic
55#2537C2211yescharacteristic
56#2535C2211yescharacteristic
57#2512C2211yescharacteristic
58#2508C2211yescharacteristic
59#2507C2211yescharacteristic
60#2497C2211yescharacteristic
61#2497C2211yescharacteristic
62#2496C2211yescharacteristic
63#2487C2211yescharacteristic
64#2467—21no—
65#2464—21no—
66#2452C2211yescharacteristic
67#2449—21no—
68#2440C2211yescharacteristic
69#2428C2211yescharacteristic
70#2428C2211yescharacteristic
71#2422C2211yescharacteristic
72#2422C2211yescharacteristic
73#2420C2211yescharacteristic
74#2416—21no—
75#2416C2211yescharacteristic
76#2395C2211yescharacteristic
77#2366C2211yescharacteristic
78#2361C2211yescharacteristic
79#2361C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82#2345C2211yescharacteristic
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic
85#2324C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2071C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2058C2211yescharacteristic
113#2054C2211yescharacteristic
114#2041C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2023C2211yescharacteristic
122#2011C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1988C2211yescharacteristic
127#1982C2211yescharacteristic
128#1957C2211yescharacteristic
129#1949C2211yescharacteristic
130#1947C2211yescharacteristic
131#1943C2211yescharacteristic
132#1943C2211yescharacteristic
133#1941C2211yescharacteristic
134#1941C2211yescharacteristic
135#1941C2211yescharacteristic
136#1939C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1924C2211yescharacteristic
146#1923C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1874C2211yescharacteristic
168#1869C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1851C2211yescharacteristic
183#1850C2211yescharacteristic
184#1844C2211yescharacteristic
185#1836C2211yescharacteristic
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4—21no—
239C22×C4⋊C4—21no—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242#481—24no—
243#481—42no—
244#476—42no—
245#466—24no—
246#442—42no—
247#442—42no—
248C4×D8—24no—
249#435—42no—
250#433—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
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
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400D411yescharacteristic
309#399—21no—
310#399—21no—
311#399D411yescharacteristic
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398D411yescharacteristic
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397D411yescharacteristic
324#397D411yescharacteristic
325#397D411yescharacteristic
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394D411yescharacteristic
342#394D411yescharacteristic
343#393—21no—
344#393—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
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#389C2311yescharacteristic
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#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×M16—41no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#127—22no—
537#127—41no—
538#126—82no—
539#126—82no—
540#123—82no—
541#123—82no—
542C22⋊Q8—82no—
543C22⋊Q8—82no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—82no—
557#121—82no—
558#121—82no—
559#121—82no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—82no—
577C4×D4—82no—
578C4×D4—82no—
579#117—41no—
580#117—41no—
581C2×C4⋊C4—22no—
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—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—82no—
611C2×C4⋊C4—82no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—41no—
688#107—41no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102#4114yes—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729#97—22no—
730#97—22no—
731C4×C8—22no—
732C4×C8—41no—
733C4×C8—41no—
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#95—21no—
764#95—21no—
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×D411yescharacteristic
779C24C22×D411yescharacteristic
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4C2×#4112yes—
827C2×D42−1+412yes—
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—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C2511yescharacteristic
893D8—28no—
894D8—82no—
895M16—82no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—82no—
919C2×C8—82no—
920C2×C8C2×#4112yes—
921C2×C8H(5,𝔽2)12yes—
922C4⋊C4—22no—
923C4⋊C4—22no—
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—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4C2×#4112yes—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—42no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—22no—
1046C23—21no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23#57712yes—
1073C23C23×D411yescharacteristic
1074Q8—162no—
1075D4—22no—
1076D4—22no—
1077D4—22no—
1078D4—22no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—84no—
1088D4—82no—
1089D4—84no—
1090D4—84no—
1091D4—162no—
1092D4—162no—
1093D4—162no—
1094D4—162no—
1095D4—162no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
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—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4—162no—
1184C2×C4—162no—
1185C2×C4—162no—
1186C2×C4#57612yes—
1187C2×C4#57712yes—
1188C2×C4C22×#4111yescharacteristic
1189C2×C4C2×H(5,𝔽2)11yescharacteristic
1190C2×C4C2×2−1+411yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C2×C4#58511yescharacteristic
1194C8—22no—
1195C8—22no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—41no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—42no—
1219C22—41no—
1220C22—42no—
1221C22—41no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22D4×#4111yescharacteristic
1238C22#348911yescharacteristic
1239C22#349611yescharacteristic
1240C22C2×#57611yescharacteristic
1241C22C2×#57711yescharacteristic
1242C22C2×#57711yescharacteristic
1243C22#358511yescharacteristic
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4#349211yescharacteristic
1270C4#352111yescharacteristic
1271C4#355311yescharacteristic
1272C4#356211yescharacteristic
1273C2—42no—
1274C2—81no—
1275C2—82no—
1276C2—82no—
1277C2—161no—
1278C2#4303711yescharacteristic
1279C2#6148311yescharacteristic
1280C2#6151911yescharacteristic
1281C2#6216611yescharacteristic
1282C2#6219911yescharacteristic
1283C2#6230811yescharacteristic
1284C2#6234211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #45046C2semidirect
2. #42548C2semidirect
3. #32337C2semidirect
4. #31996C2semidirect
5. #31870C2semidirect
6. #31626C2semidirect
7. #31557C2semidirect
8. #31514C2semidirect
9. #31086C2semidirect
10. #30567C2semidirect
11. #29174C2semidirect
12. #29043C2semidirect
13. #28152C2semidirect
14. #28056C2semidirect
15. #27835C2semidirect
16. #27550C2semidirect
17. #27473C2semidirect
18. #27299C2semidirect
19. #26961C2semidirect
20. #26904C2semidirect
21. #26633C2semidirect
22. #26547C2semidirect
23. #26529C2semidirect
24. #26408C2semidirect
25. #25252C2semidirect
26. #24716C2semidirect
27. #23712C2semidirect
28. #22918C2semidirect
29. #22905C2semidirect
30. #22670C2semidirect
31. #22193C2semidirect

Maximal subgroups

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

subgroupindex
#450462
#425482
#323372
#319962
#318702
#316262
#315572
#315142
#310862
#305672
#291742
#290432
#281522
#280562
#278352
#275502
#274732
#272992
#269612
#269042
#266332
#265472
#265292
#264082
#252522
#247162
#237122
#229182
#229052
#226702
#221932