Finite Group Databasebeta

← #6834091

Subgroups — #6834091

Order 512.

1209 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42527C211yesmaximal, characteristic, complemented
2#42500C211yesmaximal, characteristic
3#33292C211yesmaximal, characteristic, complemented
4#32435C211yesmaximal, characteristic
5#32433C211yesmaximal, characteristic
6#32325C211yesmaximal, characteristic, complemented
7#32314C211yesmaximal, characteristic, complemented
8#32254C211yesmaximal, characteristic, complemented
9#32245C211yesmaximal, characteristic, complemented
10#31478C211yesmaximal, characteristic
11#31474C211yesmaximal, characteristic
12#29992C211yesmaximal, characteristic, complemented
13#29874C211yesmaximal, characteristic
14#29100C211yesmaximal, characteristic
15#29075C211yesmaximal, characteristic
16#28802C211yesmaximal, characteristic, complemented
17#28794C211yesmaximal, characteristic, complemented
18#28057C211yesmaximal, characteristic, complemented
19#28042C211yesmaximal, characteristic, complemented
20#27832C211yesmaximal, characteristic, complemented
21#27745C211yesmaximal, characteristic, complemented
22#27743C211yesmaximal, characteristic
23#27735C211yesmaximal, characteristic
24#26509C211yesmaximal, characteristic, complemented
25#26450C211yesmaximal, characteristic, complemented
26#24815C211yesmaximal, characteristic
27#24686C211yesmaximal, characteristic
28#23075C211yesmaximal, characteristic
29#22974C211yesmaximal, characteristic
30#21678C211yesmaximal, characteristic, complemented
31#21280C211yesmaximal, characteristic
32C2×#478C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2841—21no—
36#2833—21no—
37#2788—21no—
38#2776—21no—
39#2769—21no—
40#2768—21no—
41#2766—21no—
42#2763—21no—
43#2719—21no—
44#2704—21no—
45#2666—21no—
46#2665—21no—
47#2660C2211yescharacteristic
48#2660C2211yescharacteristic
49#2634—21no—
50#2627—21no—
51#2571C2211yescharacteristic
52#2571C2211yescharacteristic
53#2570C2211yescharacteristic
54#2567C2211yescharacteristic
55#2566C2211yescharacteristic
56#2565C2211yescharacteristic
57#2563C2211yescharacteristic
58#2552C2211yescharacteristic
59#2552C2211yescharacteristic
60#2550C2211yescharacteristic
61#2550C2211yescharacteristic
62#2550C2211yescharacteristic
63#2514C2211yescharacteristic
64#2514C2211yescharacteristic
65#2511C2211yescharacteristic
66#2511C2211yescharacteristic
67#2508C2211yescharacteristic
68#2506C2211yescharacteristic
69#2462—21no—
70#2454C2211yescharacteristic
71#2452C2211yescharacteristic
72#2442—21no—
73#2402C2211yescharacteristic
74#2370C2211yescharacteristic
75#2365C2211yescharacteristic
76#2357C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2320C2211yescharacteristic
79#2319C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2097C2211yescharacteristic
89#2095C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2057C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1993C2211yescharacteristic
122#1992C2211yescharacteristic
123#1992C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1991C2211yescharacteristic
127#1990C2211yescharacteristic
128#1990C2211yescharacteristic
129#1990C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1988C2211yescharacteristic
133#1987C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1947C2211yescharacteristic
142#1944C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1939C2211yescharacteristic
147#1939C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1928C2211yescharacteristic
159#1927C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1920C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1836C2211yescharacteristic
181#1835C2211yescharacteristic
182#1835C2211yescharacteristic
183#1834C2211yescharacteristic
184#1832C2211yescharacteristic
185#1805C2211yescharacteristic
186#1803C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1776C2211yescharacteristic
190C4×#106C2211yescharacteristic
191C4×#106C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C4×Q8—21no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C22×C4⋊C4—21no—
220#478—24no—
221#476—24no—
222C4×SD16—24no—
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264#401—21no—
265#401—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400D411yescharacteristic
280#400D411yescharacteristic
281#400D411yescharacteristic
282#400D411yescharacteristic
283#399—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398D411yescharacteristic
301#398D411yescharacteristic
302#398D411yescharacteristic
303#398D411yescharacteristic
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—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#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#383—21no—
394#383—21no—
395#383—21no—
396#382—21no—
397#382—21no—
398#382—21no—
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4—21no—
430#376C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C2×SD16—22no—
490C2×SD16—22no—
491C2×SD16—41no—
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506#125—22no—
507#125—22no—
508#125—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—82no—
513#125—82no—
514#125—82no—
515C22⋊Q8—82no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8—82no—
519C4×D4—22no—
520C4×D4—41no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4#4114yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
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—82no—
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
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×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617#107—22no—
618#107—41no—
619#107—41no—
620#107—41no—
621#106—22no—
622#106—22no—
623#106—22no—
624#106—22no—
625#106—22no—
626#106—41no—
627#106—41no—
628C4⋊C8—22no—
629C4⋊C8—22no—
630C4⋊C8—22no—
631C4⋊C8—22no—
632C4⋊C8—41no—
633C4⋊C8—41no—
634#103—22no—
635#103—22no—
636#103—41no—
637#103—41no—
638#103—41no—
639#103—41no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—22no—
646#102—22no—
647#102—41no—
648#97—22no—
649#97—22no—
650#97—22no—
651#97—41no—
652#97—41no—
653C4×C8—22no—
654C4×C8—22no—
655C4×C8—22no—
656C4×C8—41no—
657C4×C8—41no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
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#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—42no—
730C2×Q8—81no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4C2×#4112yes—
744C22×C4—21no—
745C22×C4—24no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—42no—
761C22×C4—81no—
762C22×C4—81no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C2511yescharacteristic
783SD16—44no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C82−1+412yes—
807C2×C82−1+412yes—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4C2×#4112yes—
886C22⋊C4—24no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C22⋊C4—81no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C22⋊C4—81no—
894C22⋊C4—81no—
895C22⋊C4—81no—
896C22⋊C4—81no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—42no—
910C42—42no—
911C42—42no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42C2×#4112yes—
919C422−1+412yes—
920C23—22no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23C23×D411yescharacteristic
928Q8—41no—
929Q8—41no—
930Q8—41no—
931Q8—41no—
932Q8—84no—
933Q8—162no—
934Q8—162no—
935D4—22no—
936D4—22no—
937D4—41no—
938D4—41no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—84no—
1024C2×C4—162no—
1025C2×C4—162no—
1026C2×C4#54812yes—
1027C2×C4#54812yes—
1028C2×C4#57712yes—
1029C2×C4C22×#4111yescharacteristic
1030C2×C4C2×2−1+411yescharacteristic
1031C2×C4C2×2−1+411yescharacteristic
1032C2×C4C2×2−1+411yescharacteristic
1033C2×C4#58511yescharacteristic
1034C2×C4#58511yescharacteristic
1035C8—22no—
1036C8—22no—
1037C8—41no—
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22C2×#54811yescharacteristic
1051C22#349911yescharacteristic
1052C22#350011yescharacteristic
1053C22C2×#57711yescharacteristic
1054C22#358411yescharacteristic
1055C22#358511yescharacteristic
1056C22#358611yescharacteristic
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—42no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4#346111yescharacteristic
1087C4#349511yescharacteristic
1088C4#355511yescharacteristic
1089C4#356311yescharacteristic
1090C2—82no—
1091C2#3942711yescharacteristic
1092C2#6134011yescharacteristic
1093C2#6134911yescharacteristic
1094C2#6249411yescharacteristic
1095C2#6249711yescharacteristic
1096C2#6260211yescharacteristic
1097C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42527C2semidirect
3. #33292C2semidirect
6. #32325C2semidirect
7. #32314C2semidirect
8. #32254C2semidirect
9. #32245C2semidirect
12. #29992C2semidirect
16. #28802C2semidirect
17. #28794C2semidirect
18. #28057C2semidirect
19. #28042C2semidirect
20. #27832C2semidirect
21. #27745C2semidirect
24. #26509C2semidirect
25. #26450C2semidirect
30. #21678C2semidirect

Maximal subgroups

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

subgroupindex
#425272
#425002
#332922
#324352
#324332
#323252
#323142
#322542
#322452
#314782
#314742
#299922
#298742
#291002
#290752
#288022
#287942
#280572
#280422
#278322
#277452
#277432
#277352
#265092
#264502
#248152
#246862
#230752
#229742
#216782
#212802