Finite Group Databasebeta

← #7230776

Subgroups — #7230776

Order 512.

1351 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46074C211yesmaximal, characteristic, complemented
2#36479C211yesmaximal, characteristic, complemented
3#33028C211yesmaximal, characteristic, complemented
4#33028C211yesmaximal, characteristic, complemented
5#32822C211yesmaximal, characteristic, complemented
6#32822C211yesmaximal, characteristic, complemented
7#31250C211yesmaximal, characteristic, complemented
8#31244C211yesmaximal, characteristic, complemented
9#31243C211yesmaximal, characteristic, complemented
10#31238C211yesmaximal, characteristic, complemented
11#30899C211yesmaximal, characteristic, complemented
12#30895C211yesmaximal, characteristic, complemented
13#30887C211yesmaximal, characteristic
14#30875C211yesmaximal, characteristic
15#30830C211yesmaximal, characteristic, complemented
16#30828C211yesmaximal, characteristic, complemented
17#30815C211yesmaximal, characteristic, complemented
18#30809C211yesmaximal, characteristic, complemented
19#27218C211yesmaximal, characteristic
20#27215C211yesmaximal, characteristic, complemented
21#27204C211yesmaximal, characteristic, complemented
22#27201C211yesmaximal, characteristic, complemented
23#27027C211yesmaximal, characteristic, complemented
24#27023C211yesmaximal, characteristic, complemented
25#27005C211yesmaximal, characteristic, complemented
26#27001C211yesmaximal, characteristic, complemented
27#25289C211yesmaximal, characteristic, complemented
28#25285C211yesmaximal, characteristic, complemented
29#25283C211yesmaximal, characteristic, complemented
30#25279C211yesmaximal, characteristic, complemented
31#23370C211yesmaximal, characteristic, complemented
32C2×#491C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44#2864C2211yescharacteristic
45#2861C2211yescharacteristic
46#2861C2211yescharacteristic
47#2855—21no—
48#2837—21no—
49#2800—21no—
50#2781—21no—
51#2750—21no—
52#2741—21no—
53#2740—21no—
54#2694—21no—
55#2608—21no—
56#2607—21no—
57#2574—21no—
58#2556—21no—
59#2550C2211yescharacteristic
60#2550C2211yescharacteristic
61#2548C2211yescharacteristic
62#2547C2211yescharacteristic
63#2545C2211yescharacteristic
64#2544C2211yescharacteristic
65#2522—21no—
66#2465—21no—
67#2454C2211yescharacteristic
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2453C2211yescharacteristic
72#2453C2211yescharacteristic
73#2452C2211yescharacteristic
74#2452C2211yescharacteristic
75#2448C2211yescharacteristic
76#2447C2211yescharacteristic
77#2446C2211yescharacteristic
78#2445C2211yescharacteristic
79#2376—21no—
80#2370C2211yescharacteristic
81#2370C2211yescharacteristic
82#2369C2211yescharacteristic
83#2365C2211yescharacteristic
84#2357C2211yescharacteristic
85#2357C2211yescharacteristic
86C4×#125C2211yescharacteristic
87C4×C22⋊Q8—21no—
88C42×D4C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2057C2211yescharacteristic
121#2043C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2042C2211yescharacteristic
127#2042C2211yescharacteristic
128#2041C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2024C2211yescharacteristic
132#2024C2211yescharacteristic
133#2013C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic
136#2011C2211yescharacteristic
137#1989C2211yescharacteristic
138#1989C2211yescharacteristic
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1982C2211yescharacteristic
144#1981C2211yescharacteristic
145#1973C2211yescharacteristic
146#1972C2211yescharacteristic
147#1970C2211yescharacteristic
148#1968C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1942C2211yescharacteristic
152#1941C2211yescharacteristic
153#1940C2211yescharacteristic
154#1940C2211yescharacteristic
155#1939C2211yescharacteristic
156#1939C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1917C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1916C2211yescharacteristic
180#1916C2211yescharacteristic
181#1880C2211yescharacteristic
182#1880C2211yescharacteristic
183#1879C2211yescharacteristic
184#1879C2211yescharacteristic
185#1879C2211yescharacteristic
186#1879C2211yescharacteristic
187#1879C2211yescharacteristic
188#1879C2211yescharacteristic
189#1877C2211yescharacteristic
190#1877C2211yescharacteristic
191#1877C2211yescharacteristic
192#1877C2211yescharacteristic
193#1865C2211yescharacteristic
194#1864C2211yescharacteristic
195#1863C2211yescharacteristic
196#1862C2211yescharacteristic
197#1831C2211yescharacteristic
198#1831C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#125D411yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C22×C42—21no—
232#491—42no—
233#489—42no—
234#488—42no—
235#486—42no—
236#479—42no—
237#478—42no—
238#478—42no—
239#478—42no—
240#475—42no—
241#474—42no—
242#463—42no—
243#463—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#399—21no—
305#399—21no—
306#399—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#395—21no—
327#395—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#393—21no—
335#393—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389D411yescharacteristic
367#389D411yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#386—21no—
415#386—21no—
416#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#382D411yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#381—21no—
429#381—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C43C2311yescharacteristic
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#127—41no—
531#127—41no—
532#125—22no—
533#125—22no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#125—42no—
541#124—41no—
542#124—41no—
543#124—41no—
544#124—41no—
545#124—41no—
546#124—41no—
547#124—41no—
548#124—41no—
549#123—44no—
550C22⋊Q8—44no—
551C22⋊Q8—82no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—82no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
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⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
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⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—82no—
659C2×C42C2×D411yescharacteristic
660C2×C42C2×D411yescharacteristic
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#107—22no—
671#107—22no—
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#106—22no—
677#106—22no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
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#97—41no—
723#97—41no—
724C4×C8—41no—
725C4×C8—41no—
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
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C24—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—42no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D42−1+412yes—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—24no—
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—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C2511yescharacteristic
861SD16—82no—
862SD16—82no—
863D8—82no—
864D8—82no—
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×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—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
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—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
947C4⋊C4H(5,𝔽2)12yes—
948C4⋊C42−1+412yes—
949C22⋊C4—24no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
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—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—42no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23C23×D411yescharacteristic
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—84no—
1040Q8—162no—
1041D4—22no—
1042D4—22no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—162no—
1054D4—162no—
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—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
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—84no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—162no—
1139C2×C4—162no—
1140C2×C4#57512yes—
1141C2×C4C2×H(5,𝔽2)11yescharacteristic
1142C2×C4C2×H(5,𝔽2)11yescharacteristic
1143C2×C4C2×2−1+411yescharacteristic
1144C2×C4C2×2−1+411yescharacteristic
1145C2×C4#58511yescharacteristic
1146C2×C4#58511yescharacteristic
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22#348611yescharacteristic
1177C22#348811yescharacteristic
1178C22#348811yescharacteristic
1179C22C2×#57511yescharacteristic
1180C22#358411yescharacteristic
1181C22#358411yescharacteristic
1182C22#358511yescharacteristic
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—42no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—42no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4#353111yescharacteristic
1211C4#354811yescharacteristic
1212C4#356111yescharacteristic
1213C4#356111yescharacteristic
1214C2—82no—
1215C2—161no—
1216C2—161no—
1217C2#4622611yescharacteristic
1218C2#6184511yescharacteristic
1219C2#6185511yescharacteristic
1220C2#6197111yescharacteristic
1221C2#6199411yescharacteristic
1222C2#6202811yescharacteristic
1223C2#6206211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46074C2semidirect
2. #36479C2semidirect
3. #33028C2semidirect
4. #33028C2semidirect
5. #32822C2semidirect
6. #32822C2semidirect
7. #31250C2semidirect
8. #31244C2semidirect
9. #31243C2semidirect
10. #31238C2semidirect
11. #30899C2semidirect
12. #30895C2semidirect
15. #30830C2semidirect
16. #30828C2semidirect
17. #30815C2semidirect
18. #30809C2semidirect
20. #27215C2semidirect
21. #27204C2semidirect
22. #27201C2semidirect
23. #27027C2semidirect
24. #27023C2semidirect
25. #27005C2semidirect
26. #27001C2semidirect
27. #25289C2semidirect
28. #25285C2semidirect
29. #25283C2semidirect
30. #25279C2semidirect
31. #23370C2semidirect

Maximal subgroups

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

subgroupindex
#460742
#364792
#330282
#328222
#312502
#312442
#312432
#312382
#308992
#308952
#308872
#308752
#308302
#308282
#308152
#308092
#272182
#272152
#272042
#272012
#270272
#270232
#270052
#270012
#252892
#252852
#252832
#252792
#233702