Finite Group Databasebeta

← #6805846

Subgroups — #6805846

Order 512.

1281 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39811C211yesmaximal, characteristic
2#39622C211yesmaximal, characteristic, complemented
3#33229C211yesmaximal, characteristic
4#30834C211yesmaximal, characteristic, complemented
5#30831C211yesmaximal, characteristic
6#30830C211yesmaximal, characteristic
7#30828C211yesmaximal, characteristic, complemented
8#30820C211yesmaximal, characteristic
9#30819C211yesmaximal, characteristic
10#30814C211yesmaximal, characteristic, complemented
11#30806C211yesmaximal, characteristic, complemented
12#30211C211yesmaximal, characteristic
13#30206C211yesmaximal, characteristic, complemented
14#29217C211yesmaximal, characteristic, complemented
15#28760C211yesmaximal, characteristic
16#28668C211yesmaximal, characteristic
17#28660C211yesmaximal, characteristic, complemented
18#28526C211yesmaximal, characteristic, complemented
19#28517C211yesmaximal, characteristic
20#26477C211yesmaximal, characteristic
21#26474C211yesmaximal, characteristic, complemented
22#26470C211yesmaximal, characteristic
23#26461C211yesmaximal, characteristic, complemented
24#26335C211yesmaximal, characteristic, complemented
25#26331C211yesmaximal, characteristic
26#26325C211yesmaximal, characteristic
27#26319C211yesmaximal, characteristic, complemented
28#22231C211yesmaximal, characteristic, complemented
29#22222C211yesmaximal, characteristic
30#21730C211yesmaximal, characteristic, complemented
31#21347C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#491C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#488C2211yescharacteristic
38C2×#487C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#477C2211yescharacteristic
44C2×#475C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#478C2211yescharacteristic
47#2862C2211yescharacteristic
48#2859C2211yescharacteristic
49#2806—21no—
50#2806—21no—
51#2798—21no—
52#2792—21no—
53#2792—21no—
54#2773—21no—
55#2754—21no—
56#2754—21no—
57#2660C2211yescharacteristic
58#2660C2211yescharacteristic
59#2658C2211yescharacteristic
60#2640C2211yescharacteristic
61#2607—21no—
62#2592C2211yescharacteristic
63#2589—21no—
64#2586—21no—
65#2586—21no—
66#2575—21no—
67#2568C2211yescharacteristic
68#2552C2211yescharacteristic
69#2552C2211yescharacteristic
70#2550C2211yescharacteristic
71#2550C2211yescharacteristic
72#2550C2211yescharacteristic
73#2550C2211yescharacteristic
74#2517—21no—
75#2507—21no—
76#2507—21no—
77#2448C2211yescharacteristic
78#2447C2211yescharacteristic
79#2446C2211yescharacteristic
80#2446C2211yescharacteristic
81#2367C2211yescharacteristic
82#2365C2211yescharacteristic
83#2355C2211yescharacteristic
84#2355C2211yescharacteristic
85#2331C2211yescharacteristic
86#2330C2211yescharacteristic
87#2330C2211yescharacteristic
88#2327C2211yescharacteristic
89C4×#125C2211yescharacteristic
90C4×#124C2211yescharacteristic
91#2295C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2074C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2073C2211yescharacteristic
106#2072C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2026C2211yescharacteristic
125#2026C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic
131#2023C2211yescharacteristic
132#1993C2211yescharacteristic
133#1991C2211yescharacteristic
134#1990C2211yescharacteristic
135#1990C2211yescharacteristic
136#1985C2211yescharacteristic
137#1984C2211yescharacteristic
138#1983C2211yescharacteristic
139#1983C2211yescharacteristic
140#1981C2211yescharacteristic
141#1981C2211yescharacteristic
142#1960C2211yescharacteristic
143#1960C2211yescharacteristic
144#1959C2211yescharacteristic
145#1959C2211yescharacteristic
146#1959C2211yescharacteristic
147#1958C2211yescharacteristic
148#1958C2211yescharacteristic
149#1956C2211yescharacteristic
150#1956C2211yescharacteristic
151#1956C2211yescharacteristic
152#1949C2211yescharacteristic
153#1949C2211yescharacteristic
154#1948C2211yescharacteristic
155#1947C2211yescharacteristic
156#1944C2211yescharacteristic
157#1943C2211yescharacteristic
158#1942C2211yescharacteristic
159#1941C2211yescharacteristic
160#1940C2211yescharacteristic
161#1939C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1927C2211yescharacteristic
171#1927C2211yescharacteristic
172#1927C2211yescharacteristic
173#1927C2211yescharacteristic
174#1926C2211yescharacteristic
175#1926C2211yescharacteristic
176#1925C2211yescharacteristic
177#1925C2211yescharacteristic
178#1917C2211yescharacteristic
179#1917C2211yescharacteristic
180#1916C2211yescharacteristic
181#1916C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1862C2211yescharacteristic
190#1847C2211yescharacteristic
191#1847C2211yescharacteristic
192#1846C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199#1767C2211yescharacteristic
200#1746C2211yescharacteristic
201#1744C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222#501—24no—
223#491—24no—
224#491—42no—
225#489—42no—
226#488—24no—
227#488—42no—
228#487—42no—
229#479—42no—
230#479—42no—
231#479—42no—
232#479—42no—
233#478—42no—
234#478—42no—
235#477—42no—
236#475—42no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
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#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#393—21no—
337#393—21no—
338#393—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391D411yescharacteristic
351#391D411yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389D411yescharacteristic
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—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#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387D411yescharacteristic
420#387D411yescharacteristic
421#387D411yescharacteristic
422#387D411yescharacteristic
423#385—21no—
424#385—21no—
425#384—21no—
426#384—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382—21no—
433#382—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460#376C2311yescharacteristic
461#376C2311yescharacteristic
462C43C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522#125—22no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—41no—
530#125—41no—
531#125#4114yes—
532#124—22no—
533#124—22no—
534#124—22no—
535#124—22no—
536#124—41no—
537#124—41no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×D4—41no—
547C4×D4—41no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642#107—22no—
643#107—22no—
644#107—22no—
645#107—22no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#97—22no—
697#97—22no—
698#97—22no—
699#97—22no—
700C4×C8—22no—
701C4×C8—22no—
702C4×C8—22no—
703C4×C8—22no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
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#95—21no—
749#95—21no—
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
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
764C24—21no—
765C2×Q8—22no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—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—41no—
785C2×Q8—41no—
786C2×Q8—42no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—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—42no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C2511yescharacteristic
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
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×C8H(5,𝔽2)12yes—
857C2×C8H(5,𝔽2)12yes—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
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—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
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⋊C4C2×#4112yes—
928C4⋊C4C2×#4112yes—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—41no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42C2×#4112yes—
968C422−1+412yes—
969C422−1+412yes—
970C422−1+412yes—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23C23×D411yescharacteristic
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—82no—
992Q8—162no—
993Q8—162no—
994Q8—162no—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—41no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
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—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
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—162no—
1083C2×C4#53612yes—
1084C2×C4#53612yes—
1085C2×C4#54812yes—
1086C2×C4#54812yes—
1087C2×C4C22×#4111yescharacteristic
1088C2×C4C2×H(5,𝔽2)11yescharacteristic
1089C2×C4C2×H(5,𝔽2)11yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C8—22no—
1094C8—22no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×#53611yescharacteristic
1109C22C2×#54811yescharacteristic
1110C22#349811yescharacteristic
1111C22#358411yescharacteristic
1112C22#358411yescharacteristic
1113C22#358611yescharacteristic
1114C22#358611yescharacteristic
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—42no—
1123C4—42no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4#352211yescharacteristic
1145C4#352211yescharacteristic
1146C4#355011yescharacteristic
1147C4#355011yescharacteristic
1148C2—161no—
1149C2#3916811yescharacteristic
1150C2#6087611yescharacteristic
1151C2#6089111yescharacteristic
1152C2#6133111yescharacteristic
1153C2#6133811yescharacteristic
1154C2#6246211yescharacteristic
1155C2#6246711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39622C2semidirect
4. #30834C2semidirect
7. #30828C2semidirect
10. #30814C2semidirect
11. #30806C2semidirect
13. #30206C2semidirect
14. #29217C2semidirect
17. #28660C2semidirect
18. #28526C2semidirect
21. #26474C2semidirect
23. #26461C2semidirect
24. #26335C2semidirect
27. #26319C2semidirect
28. #22231C2semidirect
30. #21730C2semidirect
31. #21347C2semidirect

Maximal subgroups

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

subgroupindex
#398112
#396222
#332292
#308342
#308312
#308302
#308282
#308202
#308192
#308142
#308062
#302112
#302062
#292172
#287602
#286682
#286602
#285262
#285172
#264772
#264742
#264702
#264612
#263352
#263312
#263252
#263192
#222312
#222222
#217302
#213472