Finite Group Databasebeta

← #6569159

Subgroups — #6569159

Order 512.

1303 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36601C211yesmaximal, characteristic
2#36313C211yesmaximal, characteristic, complemented
3#30347C211yesmaximal, characteristic
4#30341C211yesmaximal, characteristic
5#30214C211yesmaximal, characteristic, complemented
6#29563C211yesmaximal, characteristic
7#29557C211yesmaximal, characteristic
8#29522C211yesmaximal, characteristic, complemented
9#29517C211yesmaximal, characteristic, complemented
10#29214C211yesmaximal, characteristic, complemented
11#29094C211yesmaximal, characteristic
12#29090C211yesmaximal, characteristic, complemented
13#29086C211yesmaximal, characteristic
14#29082C211yesmaximal, characteristic, complemented
15#28384C211yesmaximal, characteristic
16#28028C211yesmaximal, characteristic, complemented
17#28026C211yesmaximal, characteristic
18#28019C211yesmaximal, characteristic
19#28016C211yesmaximal, characteristic, complemented
20#25485C211yesmaximal, characteristic
21#25483C211yesmaximal, characteristic, complemented
22#25308C211yesmaximal, characteristic
23#25306C211yesmaximal, characteristic, complemented
24#23826C211yesmaximal, characteristic
25#23785C211yesmaximal, characteristic, complemented
26#23779C211yesmaximal, characteristic, complemented
27#23112C211yesmaximal, characteristic
28#23110C211yesmaximal, characteristic, complemented
29#23075C211yesmaximal, characteristic
30#23073C211yesmaximal, characteristic, complemented
31#20570C211yesmaximal, characteristic, complemented
32C2×#477C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×#462C2211yescharacteristic
35C2×#461C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#446C2211yescharacteristic
38#2863C2211yescharacteristic
39#2863C2211yescharacteristic
40#2862C2211yescharacteristic
41#2861C2211yescharacteristic
42#2861C2211yescharacteristic
43#2859C2211yescharacteristic
44#2596—21no—
45#2596—21no—
46#2581C2211yescharacteristic
47#2580C2211yescharacteristic
48#2573—21no—
49#2573—21no—
50#2568C2211yescharacteristic
51#2546C2211yescharacteristic
52#2528—21no—
53#2528—21no—
54#2524—21no—
55#2524—21no—
56#2514—21no—
57#2514C2211yescharacteristic
58#2514C2211yescharacteristic
59#2512C2211yescharacteristic
60#2512C2211yescharacteristic
61#2511C2211yescharacteristic
62#2511C2211yescharacteristic
63#2469—21no—
64#2469—21no—
65#2453C2211yescharacteristic
66#2453C2211yescharacteristic
67#2446—21no—
68#2373—21no—
69#2373—21no—
70#2365—21no—
71#2365C2211yescharacteristic
72#2365C2211yescharacteristic
73#2357C2211yescharacteristic
74#2356—21no—
75#2356C2211yescharacteristic
76C4×#125C2211yescharacteristic
77C4×#125C2211yescharacteristic
78C4×#125C2211yescharacteristic
79C4×#124C2211yescharacteristic
80#2295C2211yescharacteristic
81#2295C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2074C2211yescharacteristic
92#2073C2211yescharacteristic
93#2072C2211yescharacteristic
94#2072C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2026C2211yescharacteristic
119#2026C2211yescharacteristic
120#2025C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#1993C2211yescharacteristic
124#1993C2211yescharacteristic
125#1992C2211yescharacteristic
126#1992C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1971C2211yescharacteristic
132#1971C2211yescharacteristic
133#1971C2211yescharacteristic
134#1971C2211yescharacteristic
135#1969C2211yescharacteristic
136#1969C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1960C2211yescharacteristic
140#1960C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1944C2211yescharacteristic
146#1943C2211yescharacteristic
147#1942C2211yescharacteristic
148#1941C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1920C2211yescharacteristic
171#1919C2211yescharacteristic
172#1918C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181C4×#107C2211yescharacteristic
182C4×#106C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1771C2211yescharacteristic
186#1771C2211yescharacteristic
187#1770C2211yescharacteristic
188#1770C2211yescharacteristic
189#1767C2211yescharacteristic
190#1767C2211yescharacteristic
191C4×C4⋊C8C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1745C2211yescharacteristic
201#1745C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×Q8D411yescharacteristic
218C2×C4×Q8D411yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224#477—24no—
225#476—24no—
226#462—24no—
227#461—24no—
228#446—24no—
229#446—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#401—21no—
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#399—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#397—21no—
303#397—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#393—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
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#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
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#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#383—21no—
403#383—21no—
404#383—21no—
405#383—21no—
406#383—21no—
407#382—21no—
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4D411yescharacteristic
429C4×C4⋊C4D411yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444#376—21no—
445#376—21no—
446#376—21no—
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2311yescharacteristic
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16—41no—
502C2×SD16—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—44no—
516#126—44no—
517#126—44no—
518#125—22no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#124—41no—
525#124—41no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—42no—
533C4×Q8—42no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—44no—
537C4×D4—22no—
538C4×D4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631#107—22no—
632#107—22no—
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#106—22no—
638#106—22no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643C4⋊C8—22no—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8#4114yes—
648C4⋊C8#4114yes—
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—41no—
671#102—41no—
672#102—41no—
673#97—22no—
674#97—22no—
675#97—22no—
676#97—22no—
677#97—41no—
678#97—41no—
679#97—41no—
680#97—41no—
681C4×C8—22no—
682C4×C8—22no—
683C4×C8—41no—
684C4×C8—41no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
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#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—42no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C2511yescharacteristic
813Q16—82no—
814Q16—82no—
815SD16—82no—
816SD16—82no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8C2×#4112yes—
838C2×C8C2×#4112yes—
839C2×C8C2×#4112yes—
840C2×C8C2×#4112yes—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C42−1+412yes—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C42—22no—
916C42—22no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—41no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—41no—
934C42—41no—
935C42—41no—
936C42—41no—
937C42—41no—
938C42—41no—
939C42—42no—
940C42—42no—
941C42—42no—
942C42—42no—
943C42—42no—
944C42—42no—
945C42—42no—
946C42—42no—
947C42—42no—
948C42—81no—
949C42—81no—
950C42C2×#4112yes—
951C42C2×#4112yes—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23C23×D411yescharacteristic
960Q8—44no—
961Q8—41no—
962Q8—41no—
963Q8—41no—
964Q8—41no—
965Q8—41no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971Q8—41no—
972Q8—41no—
973Q8—84no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
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—22no—
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—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
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—162no—
1062C2×C4#53212yes—
1063C2×C4#53212yes—
1064C2×C4#57512yes—
1065C2×C4#57512yes—
1066C2×C4C22×#4111yescharacteristic
1067C2×C4C22×#4111yescharacteristic
1068C2×C4C2×2−1+411yescharacteristic
1069C2×C4#58511yescharacteristic
1070C2×C4#58511yescharacteristic
1071C2×C4#58511yescharacteristic
1072C8—22no—
1073C8—22no—
1074C8—22no—
1075C8—22no—
1076C8—41no—
1077C8—41no—
1078C8—41no—
1079C8—41no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22C2×#53211yescharacteristic
1088C22#348711yescharacteristic
1089C22#348911yescharacteristic
1090C22C2×#57511yescharacteristic
1091C22C2×#57511yescharacteristic
1092C22#358611yescharacteristic
1093C22#358611yescharacteristic
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—42no—
1107C4—41no—
1108C4—41no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4#351811yescharacteristic
1124C4#351811yescharacteristic
1125C4#352111yescharacteristic
1126C4#352111yescharacteristic
1127C2—161no—
1128C2#3604811yescharacteristic
1129C2#6070211yescharacteristic
1130C2#6072011yescharacteristic
1131C2#6189711yescharacteristic
1132C2#6189711yescharacteristic
1133C2#6212011yescharacteristic
1134C2#6212111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36313C2semidirect
5. #30214C2semidirect
8. #29522C2semidirect
9. #29517C2semidirect
10. #29214C2semidirect
12. #29090C2semidirect
14. #29082C2semidirect
16. #28028C2semidirect
19. #28016C2semidirect
21. #25483C2semidirect
23. #25306C2semidirect
25. #23785C2semidirect
26. #23779C2semidirect
28. #23110C2semidirect
30. #23073C2semidirect
31. #20570C2semidirect

Maximal subgroups

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

subgroupindex
#366012
#363132
#303472
#303412
#302142
#295632
#295572
#295222
#295172
#292142
#290942
#290902
#290862
#290822
#283842
#280282
#280262
#280192
#280162
#254852
#254832
#253082
#253062
#238262
#237852
#237792
#231122
#231102
#230752
#230732
#205702