Finite Group Databasebeta

← #6586678

Subgroups — #6586678

Order 512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36481C211yesmaximal, characteristic
2#36284C211yesmaximal, characteristic
3#33217C211yesmaximal, characteristic
4#33153C211yesmaximal, characteristic
5#33152C211yesmaximal, characteristic
6#28822C211yesmaximal, characteristic, complemented
7#28685C211yesmaximal, characteristic, complemented
8#28009C211yesmaximal, characteristic, complemented
9#28004C211yesmaximal, characteristic, complemented
10#26883C211yesmaximal, characteristic, complemented
11#26882C211yesmaximal, characteristic, complemented
12#26882C211yesmaximal, characteristic, complemented
13#26875C211yesmaximal, characteristic, complemented
14#26459C211yesmaximal, characteristic, complemented
15#26455C211yesmaximal, characteristic, complemented
16#26294C211yesmaximal, characteristic, complemented
17#26290C211yesmaximal, characteristic, complemented
18#26070C211yesmaximal, characteristic
19#26066C211yesmaximal, characteristic
20#26003C211yesmaximal, characteristic
21#26001C211yesmaximal, characteristic
22#25997C211yesmaximal, characteristic
23#25991C211yesmaximal, characteristic
24#23168C211yesmaximal, characteristic, complemented
25#23168C211yesmaximal, characteristic, complemented
26#23164C211yesmaximal, characteristic, complemented
27#22728C211yesmaximal, characteristic, complemented
28#22616C211yesmaximal, characteristic
29#22610C211yesmaximal, characteristic
30#21599C211yesmaximal, characteristic
31#20451C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#446C2211yescharacteristic
36C2×#427C2211yescharacteristic
37C2×#427C2211yescharacteristic
38C22×#97C2211yescharacteristic
39#2864—21no—
40#2863—21no—
41#2857C2211yescharacteristic
42#2851C2211yescharacteristic
43#2612—21no—
44#2612—21no—
45#2606—21no—
46#2606—21no—
47#2589—21no—
48#2587—21no—
49#2584C2211yescharacteristic
50#2552C2211yescharacteristic
51#2550C2211yescharacteristic
52#2546C2211yescharacteristic
53#2522—21no—
54#2522—21no—
55#2522—21no—
56#2509C2211yescharacteristic
57#2507C2211yescharacteristic
58#2507C2211yescharacteristic
59#2507C2211yescharacteristic
60#2465—21no—
61#2441C2211yescharacteristic
62#2441C2211yescharacteristic
63#2441C2211yescharacteristic
64#2439C2211yescharacteristic
65#2429—21no—
66#2423—21no—
67#2370C2211yescharacteristic
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2365C2211yescharacteristic
72#2365C2211yescharacteristic
73#2355C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75#2347C2211yescharacteristic
76#2347C2211yescharacteristic
77#2346C2211yescharacteristic
78#2346C2211yescharacteristic
79C4×C4⋊Q8—21no—
80C4×C22⋊Q8C2211yescharacteristic
81#2295—21no—
82C4×#117C2211yescharacteristic
83C4×#117C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#1993C2211yescharacteristic
109#1992C2211yescharacteristic
110#1989C2211yescharacteristic
111#1989C2211yescharacteristic
112#1989C2211yescharacteristic
113#1989C2211yescharacteristic
114#1989C2211yescharacteristic
115#1987C2211yescharacteristic
116#1987C2211yescharacteristic
117#1987C2211yescharacteristic
118#1985C2211yescharacteristic
119#1949C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1947C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1942C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1940C2211yescharacteristic
140#1921C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1850C2211yescharacteristic
171#1850C2211yescharacteristic
172#1847C2211yescharacteristic
173#1847C2211yescharacteristic
174#1845C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1808C2211yescharacteristic
180#1808C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1797C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8D411yescharacteristic
214C2×C4×Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#501—24no—
224#501—24no—
225#499—24no—
226#446—24no—
227#427—24no—
228#427Q818yescomplemented
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×#97—24no—
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270#400—21no—
271#400—21no—
272#399—21no—
273#399—21no—
274#399—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#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#396—21no—
288#396—21no—
289#396—21no—
290#396—21no—
291#395—21no—
292#395—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#391D411yescharacteristic
302#389—21no—
303#389—21no—
304#389—21no—
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#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389D411yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—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#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387D411yescharacteristic
375#387D411yescharacteristic
376#385—21no—
377#385—21no—
378#385D411yescharacteristic
379#385D411yescharacteristic
380#384—21no—
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#383—21no—
386#383—21no—
387#382—21no—
388#382—21no—
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#380—21no—
392#380D411yescharacteristic
393#380C2311yescharacteristic
394#380C2311yescharacteristic
395#380C2311yescharacteristic
396#380C2311yescharacteristic
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2311yescharacteristic
428C4×C22⋊C4C2311yescharacteristic
429#376—21no—
430#376—21no—
431#376—21no—
432#376—21no—
433C43—21no—
434C43—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×Q8—21no—
487C22×Q8C2×D411yescharacteristic
488C23×C4C2×D411yescharacteristic
489C23×C4C2×D411yescharacteristic
490C23×C4C2411yescharacteristic
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—22no—
495C22×C8—41no—
496C22×C8C2×Q814yes—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—41no—
509C4⋊Q8—44no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—22no—
514#125—22no—
515#125—41no—
516#125—41no—
517#125—41no—
518C22⋊Q8—42no—
519C22⋊Q8—82no—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—44no—
523C4×Q8—82no—
524C4×Q8—82no—
525#117—22no—
526#117—22no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
531#117C2×Q814yes—
532#117C2×Q814yes—
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⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
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×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638#107—22no—
639#107—22no—
640#107—22no—
641#107—22no—
642#107—22no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#107C2×Q814yes—
648#107C2×Q814yes—
649#107#4114yes—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—41no—
659#106—41no—
660#106C2×Q814yes—
661#106C2×Q814yes—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—22no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C22⋊C8—22no—
669C22⋊C8—22no—
670#97—22no—
671#97—22no—
672#97—22no—
673#97—22no—
674#97—22no—
675#97#4114yes—
676C4×C8—22no—
677C4×C8—22no—
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#95—21no—
720#95—21no—
721#95—21no—
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732C24C22×D411yescharacteristic
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—41no—
736C2×Q8—42no—
737C2×Q8—42no—
738C2×Q8—42no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—81no—
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—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
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×Q812yes—
782C22×C42−1+412yes—
783C22×C4C2511yescharacteristic
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—28no—
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—44no—
805C2×C8C22×Q812yes—
806C2×C8C22×Q812yes—
807C2×C8C2×#4112yes—
808C2×C8C2×#4112yes—
809C2×C8C2×#4112yes—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
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—21no—
839C4⋊C4—21no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—42no—
846C4⋊C4—42no—
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—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
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⋊C4C22×Q812yes—
884C4⋊C4C22×Q812yes—
885C4⋊C4C22×Q812yes—
886C4⋊C4C22×Q812yes—
887C4⋊C4C2×#4112yes—
888C4⋊C4C2×#4112yes—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—22no—
892C22⋊C4—41no—
893C22⋊C4—41no—
894C22⋊C4—41no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C42—22no—
902C42—22no—
903C42—24no—
904C42—24no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—42no—
916C42—42no—
917C42—42no—
918C42—42no—
919C42—42no—
920C42—42no—
921C42—42no—
922C42—42no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42C2×#4112yes—
934C422−1+412yes—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23D4×Q812yes—
942C23C23×D411yescharacteristic
943Q8—44no—
944Q8—84no—
945Q8—84no—
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—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
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—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—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
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—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—82no—
1034C2×C4—82no—
1035C2×C4#54712yes—
1036C2×C4#54712yes—
1037C2×C4D4×Q812yes—
1038C2×C4#57512yes—
1039C2×C4C23×Q811yescharacteristic
1040C2×C4C22×#4111yescharacteristic
1041C2×C4C22×#4111yescharacteristic
1042C2×C4C2×2−1+411yescharacteristic
1043C2×C4C2×2−1+411yescharacteristic
1044C2×C4#58511yescharacteristic
1045C8—22no—
1046C8—22no—
1047C8—41no—
1048C8—41no—
1049C8—41no—
1050C8—41no—
1051C8—41no—
1052C8#53314yes—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22C2×#54711yescharacteristic
1061C22C2×D4×Q811yescharacteristic
1062C22D4×#4111yescharacteristic
1063C22C2×#57511yescharacteristic
1064C22#358411yescharacteristic
1065C22#358511yescharacteristic
1066C22#358611yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—22no—
1071C4—41no—
1072C4—41no—
1073C4—42no—
1074C4—42no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4C2×#53311yescharacteristic
1097C4#349511yescharacteristic
1098C4#350211yescharacteristic
1099C4#352311yescharacteristic
1100C2—42no—
1101C2#3613311yescharacteristic
1102C2#6125511yescharacteristic
1103C2#6127511yescharacteristic
1104C2#6136511yescharacteristic
1105C2#6138011yescharacteristic
1106C2#6146111yescharacteristic
1107C2#6153411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #28822C2semidirect
7. #28685C2semidirect
8. #28009C2semidirect
9. #28004C2semidirect
10. #26883C2semidirect
11. #26882C2semidirect
12. #26882C2semidirect
13. #26875C2semidirect
14. #26459C2semidirect
15. #26455C2semidirect
16. #26294C2semidirect
17. #26290C2semidirect
24. #23168C2semidirect
25. #23168C2semidirect
26. #23164C2semidirect
27. #22728C2semidirect
228. #427Q8semidirect

Maximal subgroups

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

subgroupindex
#364812
#362842
#332172
#331532
#331522
#288222
#286852
#280092
#280042
#268832
#268822
#268752
#264592
#264552
#262942
#262902
#260702
#260662
#260032
#260012
#259972
#259912
#231682
#231642
#227282
#226162
#226102
#215992
#204512