Finite Group Databasebeta

← #6875546

Subgroups — #6875546

Order 512.

1178 conjugacy classes of subgroups.

The subgroup lattice has 1083 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38927C211yesmaximal, characteristic
2#35213C211yesmaximal, characteristic
3#33152C211yesmaximal, characteristic
4#31695C211yesmaximal, characteristic
5#31687C211yesmaximal, characteristic
6#31451C211yesmaximal, characteristic
7#31439C211yesmaximal, characteristic
8#31363C211yesmaximal, characteristic
9#31351C211yesmaximal, characteristic
10#31109C211yesmaximal, characteristic
11#31107C211yesmaximal, characteristic
12#30103C211yesmaximal, characteristic, complemented
13#30100C211yesmaximal, characteristic, complemented
14#29407C211yesmaximal, characteristic, complemented
15#29403C211yesmaximal, characteristic, complemented
16#29189C211yesmaximal, characteristic, complemented
17#29188C211yesmaximal, characteristic, complemented
18#28833C211yesmaximal, characteristic, complemented
19#28794C211yesmaximal, characteristic, complemented
20#27879C211yesmaximal, characteristic
21#27820C211yesmaximal, characteristic, complemented
22#27732C211yesmaximal, characteristic, complemented
23#27634C211yesmaximal, characteristic
24#26515C211yesmaximal, characteristic, complemented
25#26450C211yesmaximal, characteristic, complemented
26#26116C211yesmaximal, characteristic, complemented
27#26048C211yesmaximal, characteristic, complemented
28#22640C211yesmaximal, characteristic
29#22129C211yesmaximal, characteristic, complemented
30#22124C211yesmaximal, characteristic, complemented
31C4×#485C211yesmaximal, characteristic
32C2×#485C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#475C2211yescharacteristic
35#2863—21no—
36#2863—21no—
37#2851C2211yescharacteristic
38#2770—21no—
39#2769—21no—
40#2768—21no—
41#2767—21no—
42#2667—21no—
43#2665—21no—
44#2647C2211yescharacteristic
45#2647C2211yescharacteristic
46#2612—21no—
47#2612—21no—
48#2608—21no—
49#2607—21no—
50#2575—21no—
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2565C2211yescharacteristic
55#2550C2211yescharacteristic
56#2550C2211yescharacteristic
57#2524—21no—
58#2524—21no—
59#2515—21no—
60#2497C2211yescharacteristic
61#2495C2211yescharacteristic
62#2441C2211yescharacteristic
63#2441C2211yescharacteristic
64#2439C2211yescharacteristic
65#2439C2211yescharacteristic
66#2423C2211yescharacteristic
67#2421C2211yescharacteristic
68#2370C2211yescharacteristic
69#2351C2211yescharacteristic
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2330C2211yescharacteristic
73#2330C2211yescharacteristic
74#2320C2211yescharacteristic
75#2320C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77#2283C2211yescharacteristic
78#2283C2211yescharacteristic
79C4×#117C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2074C2211yescharacteristic
109#2072C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2057C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2026C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1992C2211yescharacteristic
122#1991C2211yescharacteristic
123#1991C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1987C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1947C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1942C2211yescharacteristic
139#1941C2211yescharacteristic
140#1939C2211yescharacteristic
141#1939C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1873C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1846C2211yescharacteristic
181#1840C2211yescharacteristic
182#1840C2211yescharacteristic
183#1835C2211yescharacteristic
184#1835C2211yescharacteristic
185#1834C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1805C2211yescharacteristic
192#1803C2211yescharacteristic
193#1797C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1768C2211yescharacteristic
199#1768C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#125C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×C22⋊Q8C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C22×C42C2311yescharacteristic
215#485—24no—
216#479—24no—
217#475—24no—
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
248C2×C22⋊C8C2311yescharacteristic
249C2×C22⋊C8C2311yescharacteristic
250C2×C22⋊C8C2311yescharacteristic
251C2×C22⋊C8C2311yescharacteristic
252C2×#97C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258#400—21no—
259#400—21no—
260#400—21no—
261#400—21no—
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#399—21no—
269#399—21no—
270#399—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#397—21no—
284#397—21no—
285#396—21no—
286#396—21no—
287#396—21no—
288#396—21no—
289#396—21no—
290#395—21no—
291#395—21no—
292#393—21no—
293#393—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391C2311yescharacteristic
303#391C2311yescharacteristic
304#391C2311yescharacteristic
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#387—21no—
338#387—21no—
339#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#383—21no—
377#383—21no—
378#383—21no—
379#383—21no—
380#383D411yescharacteristic
381#383D411yescharacteristic
382#382—21no—
383#382—21no—
384#382—21no—
385#382D411yescharacteristic
386#382D411yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#381—21no—
395#381D411yescharacteristic
396#381D411yescharacteristic
397#380D411yescharacteristic
398#380D411yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C22⋊C4—21no—
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2311yescharacteristic
424#376—21no—
425#376—21no—
426#376C2311yescharacteristic
427#376C2311yescharacteristic
428C43—21no—
429#340C2311yescharacteristic
430#340C2311yescharacteristic
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×Q8C2411yescharacteristic
484C23×C4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C4⋊Q8—22no—
496C4⋊Q8—22no—
497C4⋊Q8—41no—
498C4⋊Q8—41no—
499#125—22no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125—41no—
504#125—41no—
505C22⋊Q8—22no—
506C22⋊Q8—41no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—41no—
512C4×Q8—41no—
513#117—22no—
514#117—22no—
515#117—41no—
516#117—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4C2×D411yescharacteristic
582C2×C22⋊C4C2×D411yescharacteristic
583C2×C22⋊C4C2×D411yescharacteristic
584C2×C22⋊C4C2×D411yescharacteristic
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609#107—22no—
610#107—22no—
611#107—41no—
612#107—41no—
613#107—41no—
614#107—41no—
615#107—41no—
616#107—41no—
617#106—22no—
618#106—22no—
619#106—22no—
620#106—22no—
621#106—22no—
622#106—41no—
623#106—41no—
624#106—41no—
625C4⋊C8—22no—
626C4⋊C8—22no—
627C4⋊C8—22no—
628C4⋊C8—22no—
629C4⋊C8—41no—
630C4⋊C8—41no—
631#103—22no—
632#103—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103#4114yes—
639C22⋊C8—22no—
640C22⋊C8—41no—
641C22⋊C8—41no—
642C22⋊C8—41no—
643#97—41no—
644#97—41no—
645C4×C8—22no—
646C4×C8—22no—
647C4×C8—41no—
648C4×C8—41no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
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#95C2×D411yescharacteristic
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
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
716C24C22×D411yescharacteristic
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8—21no—
720C2×Q8—21no—
721C2×Q8—21no—
722C2×Q8—42no—
723C2×Q8—42no—
724C2×Q8—81no—
725C2×Q8—81no—
726C2×Q8—81no—
727C2×Q8—81no—
728C2×Q8C2×#4112yes—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C2511yescharacteristic
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
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×C8C2×#4112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
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—41no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—41no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—81no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
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⋊C4C2×#4112yes—
865C4⋊C42−1+412yes—
866C22⋊C4—41no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—41no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—81no—
875C22⋊C4—81no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C42—22no—
879C42—22no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—42no—
895C42—81no—
896C42—81no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C422−1+412yes—
905C422−1+412yes—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23C23×D411yescharacteristic
914Q8—22no—
915Q8—22no—
916Q8—41no—
917Q8—41no—
918Q8—162no—
919Q8—162no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
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—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
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—82no—
1010C2×C4—82no—
1011C2×C4#53612yes—
1012C2×C4#53612yes—
1013C2×C4C22×#4111yescharacteristic
1014C2×C4C2×2−1+411yescharacteristic
1015C2×C4C2×2−1+411yescharacteristic
1016C2×C4C2×2−1+411yescharacteristic
1017C2×C4#58511yescharacteristic
1018C2×C4#58511yescharacteristic
1019C8—22no—
1020C8—41no—
1021C8—41no—
1022C8—41no—
1023C8—41no—
1024C8—41no—
1025C8—41no—
1026C8—41no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22C2×#53611yescharacteristic
1035C22D4×#4111yescharacteristic
1036C22#348911yescharacteristic
1037C22#358411yescharacteristic
1038C22#358411yescharacteristic
1039C22#358411yescharacteristic
1040C22#358611yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—42no—
1050C4—41no—
1051C4—41no—
1052C4—41no—
1053C4—42no—
1054C4—41no—
1055C4—41no—
1056C4—42no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—81no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4—81no—
1068C4—81no—
1069C4—81no—
1070C4#350911yescharacteristic
1071C4#351511yescharacteristic
1072C4#355511yescharacteristic
1073C4#356511yescharacteristic
1074C2—81no—
1075C2#3989011yescharacteristic
1076C2#6085911yescharacteristic
1077C2#6087611yescharacteristic
1078C2#6150211yescharacteristic
1079C2#6153811yescharacteristic
1080C2#6219611yescharacteristic
1081C2#6220911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #30103C2semidirect
13. #30100C2semidirect
14. #29407C2semidirect
15. #29403C2semidirect
16. #29189C2semidirect
17. #29188C2semidirect
18. #28833C2semidirect
19. #28794C2semidirect
21. #27820C2semidirect
22. #27732C2semidirect
24. #26515C2semidirect
25. #26450C2semidirect
26. #26116C2semidirect
27. #26048C2semidirect
29. #22129C2semidirect
30. #22124C2semidirect

Maximal subgroups

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

subgroupindex
#389272
#352132
#331522
#316952
#316872
#314512
#314392
#313632
#313512
#311092
#311072
#301032
#301002
#294072
#294032
#291892
#291882
#288332
#287942
#278792
#278202
#277322
#276342
#265152
#264502
#261162
#260482
#226402
#221292
#221242
C4×#4852