Finite Group Databasebeta

← #6818366

Subgroups — #6818366

Order 512.

1231 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42981C211yesmaximal, characteristic
2#42489C211yesmaximal, characteristic
3#33219C211yesmaximal, characteristic
4#32692C211yesmaximal, characteristic, complemented
5#32691C211yesmaximal, characteristic, complemented
6#32521C211yesmaximal, characteristic, complemented
7#32520C211yesmaximal, characteristic, complemented
8#32143C211yesmaximal, characteristic, complemented
9#32139C211yesmaximal, characteristic, complemented
10#32133C211yesmaximal, characteristic, complemented
11#32131C211yesmaximal, characteristic, complemented
12#29979C211yesmaximal, characteristic
13#29975C211yesmaximal, characteristic
14#28822C211yesmaximal, characteristic, complemented
15#28820C211yesmaximal, characteristic, complemented
16#28679C211yesmaximal, characteristic, complemented
17#28678C211yesmaximal, characteristic, complemented
18#28009C211yesmaximal, characteristic, complemented
19#28007C211yesmaximal, characteristic, complemented
20#27998C211yesmaximal, characteristic, complemented
21#27996C211yesmaximal, characteristic, complemented
22#26075C211yesmaximal, characteristic
23#26073C211yesmaximal, characteristic
24#26003C211yesmaximal, characteristic
25#26002C211yesmaximal, characteristic
26#26001C211yesmaximal, characteristic
27#25998C211yesmaximal, characteristic
28#22624C211yesmaximal, characteristic
29#22621C211yesmaximal, characteristic
30#21602C211yesmaximal, characteristic
31#21160C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×C8×Q8C2211yescharacteristic
36C2×#428C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#405C2211yescharacteristic
39#2844—21no—
40#2841—21no—
41#2807—21no—
42#2802—21no—
43#2792—21no—
44#2791—21no—
45#2788—21no—
46#2788—21no—
47#2742—21no—
48#2726—21no—
49#2667—21no—
50#2647—21no—
51#2647—21no—
52#2629—21no—
53#2629C2211yescharacteristic
54#2628C2211yescharacteristic
55#2612—21no—
56#2584C2211yescharacteristic
57#2584C2211yescharacteristic
58#2584C2211yescharacteristic
59#2584C2211yescharacteristic
60#2552C2211yescharacteristic
61#2552C2211yescharacteristic
62#2550C2211yescharacteristic
63#2550C2211yescharacteristic
64#2509C2211yescharacteristic
65#2509C2211yescharacteristic
66#2509C2211yescharacteristic
67#2509C2211yescharacteristic
68#2507C2211yescharacteristic
69#2507C2211yescharacteristic
70#2506C2211yescharacteristic
71#2506C2211yescharacteristic
72#2442C2211yescharacteristic
73#2442C2211yescharacteristic
74#2441—21no—
75#2441C2211yescharacteristic
76#2441C2211yescharacteristic
77#2396C2211yescharacteristic
78#2346C2211yescharacteristic
79#2346C2211yescharacteristic
80#2345C2211yescharacteristic
81#2344C2211yescharacteristic
82#2317C2211yescharacteristic
83#2316C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2087C2211yescharacteristic
101#2087C2211yescharacteristic
102#2087C2211yescharacteristic
103#2087C2211yescharacteristic
104#2086C2211yescharacteristic
105#2086C2211yescharacteristic
106#2086C2211yescharacteristic
107#2086C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2084C2211yescharacteristic
111#2083C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2058C2211yescharacteristic
123#2057C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1985C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1943C2211yescharacteristic
144#1943C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1941C2211yescharacteristic
151#1941C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1940C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic
186#1823C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1798C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×#117—21no—
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220#501—42no—
221#499—42no—
222#499—42no—
223C8×Q8—42no—
224#428—42no—
225#428Q818yescomplemented
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258#405—42no—
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
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#400—21no—
280#400D411yescharacteristic
281#399—21no—
282#399—21no—
283#399—21no—
284#399D411yescharacteristic
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#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398D411yescharacteristic
306#398D411yescharacteristic
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396D411yescharacteristic
312#396D411yescharacteristic
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#395D411yescharacteristic
321#393—21no—
322#393D411yescharacteristic
323#391—21no—
324#391—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
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#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—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#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384—21no—
398#384—21no—
399#384—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#382—21no—
404#382—21no—
405#382—21no—
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
430C4×C22⋊C4—21no—
431C4×C22⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433#376—21no—
434#376—21no—
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8C2×D411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2411yescharacteristic
490C2×M16—22no—
491C2×M16—22no—
492C2×M16C2×Q814yes—
493C22×C8—22no—
494C22×C8—22no—
495C22×C8—41no—
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506#125—41no—
507#125—41no—
508#125—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—41no—
513#125—41no—
514#125—41no—
515#125—41no—
516#125—82no—
517#125—82no—
518C4×Q8—41no—
519C4×Q8—41no—
520#117—22no—
521#117—41no—
522#117—41no—
523#117—41no—
524#117—41no—
525#117—82no—
526#117C2×Q814yes—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—22no—
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—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—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×Q814yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—22no—
634#107—22no—
635#107—22no—
636#107—22no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107C2×Q814yes—
644#107C2×Q814yes—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106C2×Q814yes—
656#106C2×Q814yes—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C22⋊C8—22no—
664C22⋊C8—22no—
665#97—22no—
666#97—22no—
667#97—22no—
668#97—41no—
669C4×C8—22no—
670C4×C8—22no—
671C4×C8—22no—
672C4×C8—41no—
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#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#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C24C22×D411yescharacteristic
730C2×Q8—41no—
731C2×Q8—41no—
732C2×Q8—41no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—24no—
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—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—81no—
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×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×Q812yes—
776C22×C42−1+412yes—
777C22×C4C2511yescharacteristic
778M16—28no—
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×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—44no—
799C2×C8C22×Q812yes—
800C2×C8C22×Q812yes—
801C2×C8H(5,𝔽2)12yes—
802C2×C82−1+412yes—
803C2×C82−1+412yes—
804C4⋊C4—24no—
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—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—41no—
834C4⋊C4—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
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⋊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⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4C22×Q812yes—
891C4⋊C4C22×Q812yes—
892C4⋊C4C22×Q812yes—
893C4⋊C4C22×Q812yes—
894C22⋊C4—24no—
895C22⋊C4—41no—
896C22⋊C4—41no—
897C22⋊C4—41no—
898C22⋊C4—41no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C42—24no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23D4×Q812yes—
935C23C23×D411yescharacteristic
936Q8—44no—
937Q8—162no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
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—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—84no—
1029C2×C4—162no—
1030C2×C4D4×Q812yes—
1031C2×C4C23×Q811yescharacteristic
1032C2×C4C2×H(5,𝔽2)11yescharacteristic
1033C2×C4C2×2−1+411yescharacteristic
1034C2×C4C2×2−1+411yescharacteristic
1035C2×C4C2×2−1+411yescharacteristic
1036C2×C4#58511yescharacteristic
1037C8—22no—
1038C8—22no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8#54414yes—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22C2×D4×Q811yescharacteristic
1053C22#349611yescharacteristic
1054C22#349911yescharacteristic
1055C22#358411yescharacteristic
1056C22#358411yescharacteristic
1057C22#358511yescharacteristic
1058C22#358611yescharacteristic
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—41no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4C2×#54411yescharacteristic
1089C4#350211yescharacteristic
1090C4#353811yescharacteristic
1091C4#356311yescharacteristic
1092C2—42no—
1093C2#3936811yescharacteristic
1094C2#6138511yescharacteristic
1095C2#6138611yescharacteristic
1096C2#6228211yescharacteristic
1097C2#6233811yescharacteristic
1098C2#6252311yescharacteristic
1099C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32692C2semidirect
5. #32691C2semidirect
6. #32521C2semidirect
7. #32520C2semidirect
8. #32143C2semidirect
9. #32139C2semidirect
10. #32133C2semidirect
11. #32131C2semidirect
14. #28822C2semidirect
15. #28820C2semidirect
16. #28679C2semidirect
17. #28678C2semidirect
18. #28009C2semidirect
19. #28007C2semidirect
20. #27998C2semidirect
21. #27996C2semidirect
225. #428Q8semidirect

Maximal subgroups

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

subgroupindex
#429812
#424892
#332192
#326922
#326912
#325212
#325202
#321432
#321392
#321332
#321312
#299792
#299752
#288222
#288202
#286792
#286782
#280092
#280072
#279982
#279962
#260752
#260732
#260032
#260022
#260012
#259982
#226242
#226212
#216022
#211602