Finite Group Databasebeta

← #6911614

Subgroups — #6911614

Order 512.

1381 conjugacy classes of subgroups.

The subgroup lattice has 1215 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38118C211yesmaximal, characteristic
2#37691C211yesmaximal, characteristic, complemented
3#32847C211yesmaximal, characteristic, complemented
4#32753C211yesmaximal, characteristic, complemented
5#32238C211yesmaximal, characteristic, complemented
6#32235C211yesmaximal, characteristic, complemented
7#31364C211yesmaximal, characteristic, complemented
8#31361C211yesmaximal, characteristic, complemented
9#30959C211yesmaximal, characteristic, complemented
10#30950C211yesmaximal, characteristic, complemented
11#30785C211yesmaximal, characteristic, complemented
12#30782C211yesmaximal, characteristic, complemented
13#30292C211yesmaximal, characteristic, complemented
14#30179C211yesmaximal, characteristic, complemented
15#30159C211yesmaximal, characteristic, complemented
16#29991C211yesmaximal, characteristic, complemented
17#29648C211yesmaximal, characteristic, complemented
18#29400C211yesmaximal, characteristic, complemented
19#29108C211yesmaximal, characteristic, complemented
20#25997C211yesmaximal, characteristic, complemented
21#25991C211yesmaximal, characteristic, complemented
22#25964C211yesmaximal, characteristic, complemented
23#25954C211yesmaximal, characteristic, complemented
24#25814C211yesmaximal, characteristic, complemented
25#24946C211yesmaximal, characteristic, complemented
26#24934C211yesmaximal, characteristic, complemented
27#24872C211yesmaximal, characteristic
28#24868C211yesmaximal, characteristic
29#24308C211yesmaximal, characteristic, complemented
30#23451C211yesmaximal, characteristic, complemented
31#21997C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C2×#416C2211yescharacteristic
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2782—21no—
45#2778—21no—
46#2749—21no—
47#2746—21no—
48#2732—21no—
49#2729—21no—
50#2720—21no—
51#2692—21no—
52#2660C2211yescharacteristic
53#2645C2211yescharacteristic
54#2628C2211yescharacteristic
55#2625C2211yescharacteristic
56#2552C2211yescharacteristic
57#2550C2211yescharacteristic
58#2516—21no—
59#2515—21no—
60#2514C2211yescharacteristic
61#2510—21no—
62#2493—21no—
63#2489C2211yescharacteristic
64#2485C2211yescharacteristic
65#2465—21no—
66#2462—21no—
67#2454C2211yescharacteristic
68#2446—21no—
69#2442C2211yescharacteristic
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2439C2211yescharacteristic
73#2423—21no—
74#2420C2211yescharacteristic
75#2407C2211yescharacteristic
76#2354C2211yescharacteristic
77#2352C2211yescharacteristic
78#2347C2211yescharacteristic
79#2339C2211yescharacteristic
80#2331C2211yescharacteristic
81#2324C2211yescharacteristic
82#2319C2211yescharacteristic
83#2297C2211yescharacteristic
84#2290C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2097C2211yescharacteristic
90#2096C2211yescharacteristic
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2075C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2073C2211yescharacteristic
110#2072C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2066C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2058C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2034C2211yescharacteristic
128#2033C2211yescharacteristic
129#2026C2211yescharacteristic
130#2026C2211yescharacteristic
131#2026C2211yescharacteristic
132#2026C2211yescharacteristic
133#2025C2211yescharacteristic
134#2025C2211yescharacteristic
135#2025C2211yescharacteristic
136#2024C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#1991C2211yescharacteristic
142#1991C2211yescharacteristic
143#1989C2211yescharacteristic
144#1987C2211yescharacteristic
145#1949C2211yescharacteristic
146#1947C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1875C2211yescharacteristic
168#1874C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1852C2211yescharacteristic
181#1850C2211yescharacteristic
182#1850C2211yescharacteristic
183#1840C2211yescharacteristic
184#1832C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1824C2211yescharacteristic
189#1818C2211yescharacteristic
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#544—42no—
207#544—42no—
208#533—42no—
209#533—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#499—42no—
239#499—42no—
240#485—42no—
241#483—42no—
242#478—42no—
243#474—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264#416—42no—
265#416—42no—
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290#401—21no—
291#401—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#399—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#393—21no—
328#393—21no—
329#392—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388D411yescharacteristic
371#388D411yescharacteristic
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387D411yescharacteristic
385#387D411yescharacteristic
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386D411yescharacteristic
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385D411yescharacteristic
405#385D411yescharacteristic
406#384—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376C2311yescharacteristic
443C2×#95—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#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
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—44no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—44no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550#121—22no—
551#121—41no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—22no—
564#117—22no—
565#117—41no—
566#117—41no—
567#117—41no—
568#117—41no—
569#117—41no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
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—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—41no—
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×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—41no—
661C2×C42—41no—
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
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—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#103—22no—
690#103—22no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C4×C8—41no—
712C4×C8—41no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#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#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765C24—21no—
766C24C22×D411yescharacteristic
767C24C22×D411yescharacteristic
768#41—44no—
769#41—44no—
770#41—82no—
771#41—82no—
772C2×Q8—24no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×D4—22no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D42−1+412yes—
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—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
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×C4C22×D411yescharacteristic
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×C42−1+412yes—
858C22×C42−1+412yes—
859C22×C4C2511yescharacteristic
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×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—82no—
885C2×C8—82no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—21no—
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—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—42no—
919C4⋊C4—42no—
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—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⋊C4H(5,𝔽2)12yes—
949C4⋊C4H(5,𝔽2)12yes—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
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—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—41no—
991C42—41no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—42no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—21no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#53612yes—
1021C23C23×D411yescharacteristic
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—84no—
1027Q8—84no—
1028Q8—162no—
1029D4—22no—
1030D4—22no—
1031D4—41no—
1032D4—41no—
1033D4—82no—
1034D4—84no—
1035D4—162no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
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—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
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—41no—
1124C2×C4—84no—
1125C2×C4—82no—
1126C2×C4—82no—
1127C2×C4—162no—
1128C2×C4—162no—
1129C2×C4—162no—
1130C2×C4#53612yes—
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
1136C2×C4#58511yescharacteristic
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—42no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—42no—
1159C22—41no—
1160C22—42no—
1161C22—41no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22C2×#53611yescharacteristic
1167C22#348411yescharacteristic
1168C22#348911yescharacteristic
1169C22#358411yescharacteristic
1170C22#358411yescharacteristic
1171C22#358411yescharacteristic
1172C22#358411yescharacteristic
1173C4—22no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4#353811yescharacteristic
1201C4#353811yescharacteristic
1202C4#356111yescharacteristic
1203C4#356111yescharacteristic
1204C2—42no—
1205C2—81no—
1206C2—82no—
1207C2#4059511yescharacteristic
1208C2#6085911yescharacteristic
1209C2#6088211yescharacteristic
1210C2#6163611yescharacteristic
1211C2#6163711yescharacteristic
1212C2#6220711yescharacteristic
1213C2#6220711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37691C2semidirect
3. #32847C2semidirect
4. #32753C2semidirect
5. #32238C2semidirect
6. #32235C2semidirect
7. #31364C2semidirect
8. #31361C2semidirect
9. #30959C2semidirect
10. #30950C2semidirect
11. #30785C2semidirect
12. #30782C2semidirect
13. #30292C2semidirect
14. #30179C2semidirect
15. #30159C2semidirect
16. #29991C2semidirect
17. #29648C2semidirect
18. #29400C2semidirect
19. #29108C2semidirect
20. #25997C2semidirect
21. #25991C2semidirect
22. #25964C2semidirect
23. #25954C2semidirect
24. #25814C2semidirect
25. #24946C2semidirect
26. #24934C2semidirect
29. #24308C2semidirect
30. #23451C2semidirect
31. #21997C2semidirect

Maximal subgroups

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

subgroupindex
#381182
#376912
#328472
#327532
#322382
#322352
#313642
#313612
#309592
#309502
#307852
#307822
#302922
#301792
#301592
#299912
#296482
#294002
#291082
#259972
#259912
#259642
#259542
#258142
#249462
#249342
#248722
#248682
#243082
#234512
#219972