Finite Group Databasebeta

← #6763687

Subgroups — #6763687

Order 512.

1374 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37879C211yesmaximal, characteristic, complemented
2#37711C211yesmaximal, characteristic
3#33044C211yesmaximal, characteristic, complemented
4#31753C211yesmaximal, characteristic, complemented
5#31750C211yesmaximal, characteristic, complemented
6#31748C211yesmaximal, characteristic, complemented
7#31747C211yesmaximal, characteristic, complemented
8#31468C211yesmaximal, characteristic, complemented
9#31467C211yesmaximal, characteristic, complemented
10#31465C211yesmaximal, characteristic, complemented
11#31462C211yesmaximal, characteristic, complemented
12#30211C211yesmaximal, characteristic, complemented
13#29885C211yesmaximal, characteristic, complemented
14#29229C211yesmaximal, characteristic, complemented
15#28668C211yesmaximal, characteristic, complemented
16#27979C211yesmaximal, characteristic, complemented
17#27971C211yesmaximal, characteristic, complemented
18#26421C211yesmaximal, characteristic, complemented
19#26419C211yesmaximal, characteristic, complemented
20#26413C211yesmaximal, characteristic, complemented
21#26411C211yesmaximal, characteristic, complemented
22#26213C211yesmaximal, characteristic
23#26207C211yesmaximal, characteristic, complemented
24#26205C211yesmaximal, characteristic, complemented
25#26199C211yesmaximal, characteristic
26#25817C211yesmaximal, characteristic, complemented
27#25684C211yesmaximal, characteristic, complemented
28#22255C211yesmaximal, characteristic, complemented
29#21871C211yesmaximal, characteristic, complemented
30#21318C211yesmaximal, characteristic, complemented
31#21103C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#433C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic
39#2851C2211yescharacteristic
40#2850C2211yescharacteristic
41#2788—21no—
42#2784—21no—
43#2780—21no—
44#2768—21no—
45#2730—21no—
46#2728—21no—
47#2723—21no—
48#2696—21no—
49#2660C2211yescharacteristic
50#2640C2211yescharacteristic
51#2629C2211yescharacteristic
52#2628C2211yescharacteristic
53#2588—21no—
54#2587—21no—
55#2585—21no—
56#2574—21no—
57#2571C2211yescharacteristic
58#2570C2211yescharacteristic
59#2490C2211yescharacteristic
60#2489C2211yescharacteristic
61#2469—21no—
62#2458—21no—
63#2454C2211yescharacteristic
64#2453C2211yescharacteristic
65#2448—21no—
66#2442C2211yescharacteristic
67#2441C2211yescharacteristic
68#2439C2211yescharacteristic
69#2439C2211yescharacteristic
70#2421—21no—
71#2415C2211yescharacteristic
72#2414C2211yescharacteristic
73#2363C2211yescharacteristic
74#2362C2211yescharacteristic
75#2354C2211yescharacteristic
76#2352C2211yescharacteristic
77#2331C2211yescharacteristic
78#2330C2211yescharacteristic
79#2317C2211yescharacteristic
80#2290C2211yescharacteristic
81#2285C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2026C2211yescharacteristic
119#2025C2211yescharacteristic
120#2024C2211yescharacteristic
121#2023C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1991C2211yescharacteristic
125#1991C2211yescharacteristic
126#1991C2211yescharacteristic
127#1991C2211yescharacteristic
128#1991C2211yescharacteristic
129#1990C2211yescharacteristic
130#1990C2211yescharacteristic
131#1990C2211yescharacteristic
132#1990C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1988C2211yescharacteristic
136#1987C2211yescharacteristic
137#1959C2211yescharacteristic
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1923C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1875C2211yescharacteristic
167#1874C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1872C2211yescharacteristic
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1835C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic
191#1805C2211yescharacteristic
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic
194#1802C2211yescharacteristic
195#1768C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1746C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#542—24no—
206#542—42no—
207#533—24no—
208#533—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C42C2311yescharacteristic
240#501—24no—
241#501—42no—
242#488—42no—
243#433—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8—42no—
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#400—21no—
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#399—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#393—21no—
324#392—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
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#388—21no—
368#388—21no—
369#388D411yescharacteristic
370#388D411yescharacteristic
371#387—21no—
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#387—21no—
385#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386D411yescharacteristic
392#386D411yescharacteristic
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385D411yescharacteristic
400#385D411yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8#4114yes—
521#126—44no—
522#125—22no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—41no—
530#124—22no—
531#124—22no—
532#124—44no—
533#123—44no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—41no—
538C22⋊Q8—44no—
539C22⋊Q8—44no—
540C22⋊Q8—44no—
541#121—22no—
542#121—22no—
543#121—22no—
544#121—41no—
545C4×Q8—22no—
546C4×Q8—41no—
547C4×Q8—44no—
548C4×Q8—44no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—41no—
553#117—22no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C42—22no—
652C2×C42—22no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#107—22no—
671#107—22no—
672#107—41no—
673#107—41no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698C22⋊C8—22no—
699C22⋊C8—22no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704#97—22no—
705#97—22no—
706C4×C8—22no—
707C4×C8—22no—
708C4×C8—41no—
709C4×C8—41no—
710#95—21no—
711#95—21no—
712#95—21no—
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#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24C22×D411yescharacteristic
760C24C22×D411yescharacteristic
761C2×Q8—24no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—42no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
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—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—42no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C42−1+412yes—
841C22×C42−1+412yes—
842C22×C4C2511yescharacteristic
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—44no—
868C2×C8—44no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
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—41no—
900C4⋊C4—41no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4C2×#4112yes—
934C4⋊C4C2×#4112yes—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
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—
967C42—22no—
968C42—22no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42C2×#4112yes—
988C42H(5,𝔽2)12yes—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23#53612yes—
1010C23C23×D411yescharacteristic
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—84no—
1016Q8—84no—
1017Q8—162no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—82no—
1023D4—162no—
1024D4—162no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
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—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—162no—
1114C2×C4—162no—
1115C2×C4#53612yes—
1116C2×C4#54612yes—
1117C2×C4#54612yes—
1118C2×C4C22×#4111yescharacteristic
1119C2×C4C2×H(5,𝔽2)11yescharacteristic
1120C2×C4C2×2−1+411yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C2×C4#58511yescharacteristic
1123C2×C4#58511yescharacteristic
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22C2×#53611yescharacteristic
1154C22C2×#54611yescharacteristic
1155C22#350011yescharacteristic
1156C22#358411yescharacteristic
1157C22#358411yescharacteristic
1158C22#358411yescharacteristic
1159C22#358411yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—42no—
1171C4—42no—
1172C4—41no—
1173C4—41no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4#351611yescharacteristic
1188C4#351611yescharacteristic
1189C4#354111yescharacteristic
1190C4#354111yescharacteristic
1191C2—42no—
1192C2—81no—
1193C2—161no—
1194C2#3808311yescharacteristic
1195C2#6085911yescharacteristic
1196C2#6087911yescharacteristic
1197C2#6116911yescharacteristic
1198C2#6117011yescharacteristic
1199C2#6255511yescharacteristic
1200C2#6255511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2414C22
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
1. #37879C2semidirect
3. #33044C2semidirect
4. #31753C2semidirect
5. #31750C2semidirect
6. #31748C2semidirect
7. #31747C2semidirect
8. #31468C2semidirect
9. #31467C2semidirect
10. #31465C2semidirect
11. #31462C2semidirect
12. #30211C2semidirect
13. #29885C2semidirect
14. #29229C2semidirect
15. #28668C2semidirect
16. #27979C2semidirect
17. #27971C2semidirect
18. #26421C2semidirect
19. #26419C2semidirect
20. #26413C2semidirect
21. #26411C2semidirect
23. #26207C2semidirect
24. #26205C2semidirect
26. #25817C2semidirect
27. #25684C2semidirect
28. #22255C2semidirect
29. #21871C2semidirect
30. #21318C2semidirect
31. #21103C2semidirect

Maximal subgroups

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

subgroupindex
#378792
#377112
#330442
#317532
#317502
#317482
#317472
#314682
#314672
#314652
#314622
#302112
#298852
#292292
#286682
#279792
#279712
#264212
#264192
#264132
#264112
#262132
#262072
#262052
#261992
#258172
#256842
#222552
#218712
#213182
#211032