Finite Group Databasebeta

← #6583311

Subgroups — #6583311

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3164C211yesmaximal, characteristic, complemented
2C2×#3163C211yesmaximal, characteristic, complemented
3#39366C211yesmaximal, characteristic
4#39365C211yesmaximal, characteristic
5#33317C211yesmaximal, characteristic, complemented
6#33219C211yesmaximal, characteristic, complemented
7#33219C211yesmaximal, characteristic, complemented
8#28818C211yesmaximal, characteristic, complemented
9#28815C211yesmaximal, characteristic, complemented
10#28812C211yesmaximal, characteristic, complemented
11#28810C211yesmaximal, characteristic, complemented
12#28690C211yesmaximal, characteristic, complemented
13#28688C211yesmaximal, characteristic, complemented
14#26075C211yesmaximal, characteristic, complemented
15#26074C211yesmaximal, characteristic, complemented
16#26073C211yesmaximal, characteristic, complemented
17#26072C211yesmaximal, characteristic, complemented
18#26071C211yesmaximal, characteristic, complemented
19#26070C211yesmaximal, characteristic, complemented
20#26069C211yesmaximal, characteristic, complemented
21#26068C211yesmaximal, characteristic, complemented
22#25822C211yesmaximal, characteristic, complemented
23#25822C211yesmaximal, characteristic, complemented
24#25821C211yesmaximal, characteristic, complemented
25#25820C211yesmaximal, characteristic, complemented
26#22666C211yesmaximal, characteristic
27#22664C211yesmaximal, characteristic
28#22656C211yesmaximal, characteristic
29#22654C211yesmaximal, characteristic
30C4×#501C211yesmaximal, characteristic, complemented
31#20495C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#544C2211yescharacteristic
36#3164—28no—
37#3163—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#501C2211yescharacteristic
42C2×#501C2211yescharacteristic
43C2×#501C2211yescharacteristic
44C2×#501C2211yescharacteristic
45C2×#501C2211yescharacteristic
46C2×#501C2211yescharacteristic
47C2×#500C2211yescharacteristic
48C2×#500C2211yescharacteristic
49C2×#499C2211yescharacteristic
50C2×#499C2211yescharacteristic
51C2×#499C2211yescharacteristic
52C2×#499C2211yescharacteristic
53C2×#498C2211yescharacteristic
54C2×#498C2211yescharacteristic
55C2×#436C2211yescharacteristic
56C2×C8×D4C2211yescharacteristic
57C2×#428C2211yescharacteristic
58C2×#428C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C2×#427C2211yescharacteristic
62C2×#427C2211yescharacteristic
63C22×#107C2211yescharacteristic
64C22×#106C2211yescharacteristic
65C2×#405C2211yescharacteristic
66C2×#405C2211yescharacteristic
67#2862C2211yescharacteristic
68#2859C2211yescharacteristic
69#2734—21no—
70#2732—21no—
71#2726—21no—
72#2713—21no—
73#2713—21no—
74#2692—21no—
75#2692—21no—
76#2683—21no—
77#2629C2211yescharacteristic
78#2629C2211yescharacteristic
79#2628C2211yescharacteristic
80#2628C2211yescharacteristic
81#2556—21no—
82#2556—21no—
83#2556—21no—
84#2556—21no—
85#2550C2211yescharacteristic
86#2550C2211yescharacteristic
87#2550C2211yescharacteristic
88#2550C2211yescharacteristic
89#2492—21no—
90#2492—21no—
91#2442C2211yescharacteristic
92#2442C2211yescharacteristic
93#2441C2211yescharacteristic
94#2441C2211yescharacteristic
95#2440C2211yescharacteristic
96#2440C2211yescharacteristic
97#2439C2211yescharacteristic
98#2439C2211yescharacteristic
99#2429—21no—
100#2429—21no—
101#2352C2211yescharacteristic
102#2352C2211yescharacteristic
103#2352C2211yescharacteristic
104#2352C2211yescharacteristic
105C4×C4⋊Q8C2211yescharacteristic
106C4×#125C2211yescharacteristic
107#2293C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2084C2211yescharacteristic
113#2084C2211yescharacteristic
114#2083C2211yescharacteristic
115#2083C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2058C2211yescharacteristic
125#2058C2211yescharacteristic
126#2058C2211yescharacteristic
127#2058C2211yescharacteristic
128#2057C2211yescharacteristic
129#2057C2211yescharacteristic
130#2057C2211yescharacteristic
131#2057C2211yescharacteristic
132#1993C2211yescharacteristic
133#1992C2211yescharacteristic
134#1991C2211yescharacteristic
135#1991C2211yescharacteristic
136#1990C2211yescharacteristic
137#1990C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1944C2211yescharacteristic
147#1944C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1943C2211yescharacteristic
152#1943C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1942C2211yescharacteristic
156#1941C2211yescharacteristic
157#1941C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1853C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1852C2211yescharacteristic
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1846C2211yescharacteristic
180#1846C2211yescharacteristic
181#1846C2211yescharacteristic
182#1846C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195#1770C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C4×C4⋊C8C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1750C2211yescharacteristic
203#1750C2211yescharacteristic
204C4×#97C2211yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#544—24no—
210#544—24no—
211#544—24no—
212#544—24no—
213#544—42no—
214#544—42no—
215#544—42no—
216#544—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#125—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#125—21no—
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261#501—24no—
262#501—24no—
263#501—24no—
264#501—24no—
265#501—24no—
266#501—24no—
267#501—42no—
268#501—42no—
269#501D418yescomplemented
270#500—24no—
271#500—24no—
272#499—24no—
273#499—24no—
274#499—24no—
275#499—24no—
276#498—24no—
277#498—24no—
278#436Q818yescomplemented
279C8×D4Q818yescomplemented
280#428—24no—
281#428—24no—
282#428—24no—
283#428—24no—
284#427—24no—
285#427—24no—
286C2×#107—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#106—24no—
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×#106C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323C2×#106C2311yescharacteristic
324C2×#106C2311yescharacteristic
325C2×#106C2311yescharacteristic
326C2×#106C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334#405—24no—
335#405—24no—
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#399—21no—
353#399—21no—
354#399—21no—
355#399—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#393—21no—
385#393—21no—
386#393—21no—
387#393—21no—
388#391—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#390D411yescharacteristic
400#390D411yescharacteristic
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389D411yescharacteristic
413#389D411yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388D411yescharacteristic
431#388D411yescharacteristic
432#388D411yescharacteristic
433#388D411yescharacteristic
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#380—21no—
463#380—21no—
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486C43C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×D4C2×D411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16C2×Q814yes—
536C2×M16C2×Q814yes—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8C2×Q814yes—
542C22×C8C2×Q814yes—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566C4⋊Q8—44no—
567C4⋊Q8—44no—
568C4⋊Q8C2×D414yes—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—22no—
576#125—22no—
577#125—22no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—44no—
583#125—44no—
584#125—44no—
585#125—44no—
586#125C2×D414yes—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—44no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597C4×Q8—82no—
598C4×D4C2×Q814yes—
599C4×D4C2×Q814yes—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—41no—
740#107—41no—
741#107—41no—
742#107—41no—
743#107C2×D414yes—
744#107C2×D414yes—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—22no—
757#106—22no—
758#106—22no—
759#106—41no—
760#106—41no—
761#106—41no—
762#106—41no—
763#106C2×D414yes—
764#106C2×D414yes—
765C4⋊C8C2×Q814yes—
766C4⋊C8C2×Q814yes—
767C22⋊C8C2×Q814yes—
768C22⋊C8C2×Q814yes—
769C22⋊C8C2×Q814yes—
770C22⋊C8C2×Q814yes—
771#97—22no—
772#97—22no—
773#97—22no—
774#97—22no—
775#97—22no—
776#97C2×D414yes—
777C4×C8—22no—
778C4×C8—22no—
779C4×C8—22no—
780C4×C8—22no—
781C4×C8C2×Q814yes—
782C4×C8C2×Q814yes—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829C2×Q8—24no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4C4⋊Q814yes—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×Q812yes—
902C22×C4C22×Q812yes—
903C22×C4C22×Q812yes—
904C22×C4C22×Q812yes—
905C22×C4C2511yescharacteristic
906M16—28no—
907M16—28no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—28no—
921C2×C8—28no—
922C2×C8C22×D412yes—
923C2×C8C22×D412yes—
924C2×C8C22×Q812yes—
925C2×C8C22×Q812yes—
926C2×C8C22×Q812yes—
927C2×C8C22×Q812yes—
928C2×C8C22×Q812yes—
929C2×C8C22×Q812yes—
930C2×C8C22×Q812yes—
931C2×C8C22×Q812yes—
932C2×C82−1+412yes—
933C2×C82−1+412yes—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4C4⋊Q814yes—
1012C4⋊C4C22×D412yes—
1013C4⋊C4C22×D412yes—
1014C4⋊C4C22×D412yes—
1015C4⋊C4C22×D412yes—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4C4⋊Q814yes—
1037C22⋊C4C4⋊Q814yes—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—41no—
1045C42—41no—
1046C42—41no—
1047C42—41no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42C22×D412yes—
1057C42C22×Q812yes—
1058C42C22×Q812yes—
1059C42H(5,𝔽2)12yes—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23C2×C4⋊Q812yes—
1073C23C2×C4⋊Q812yes—
1074C23C23×D411yescharacteristic
1075Q8—84no—
1076Q8—162no—
1077Q8—162no—
1078Q8—162no—
1079Q8—162no—
1080Q8—162no—
1081Q8—162no—
1082D4—44no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—162no—
1170C2×C4—162no—
1171C2×C4—162no—
1172C2×C4—162no—
1173C2×C4C2×C4⋊Q812yes—
1174C2×C4C2×C4⋊Q812yes—
1175C2×C4C2×C4⋊Q812yes—
1176C2×C4C2×C4⋊Q812yes—
1177C2×C4D4212yes—
1178C2×C4D4212yes—
1179C2×C4C23×D411yescharacteristic
1180C2×C4C23×Q811yescharacteristic
1181C2×C4C23×Q811yescharacteristic
1182C2×C4C2×H(5,𝔽2)11yescharacteristic
1183C2×C4C2×2−1+411yescharacteristic
1184C2×C4C2×2−1+411yescharacteristic
1185C8—22no—
1186C8—22no—
1187C8—22no—
1188C8—22no—
1189C8—22no—
1190C8—22no—
1191C8D4×Q814yes—
1192C8D4×Q814yes—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22C22×C4⋊Q811yescharacteristic
1208C22C2×D4211yescharacteristic
1209C22#349911yescharacteristic
1210C22#358411yescharacteristic
1211C22#358411yescharacteristic
1212C22#358511yescharacteristic
1213C22#358611yescharacteristic
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4C2×D4×Q811yescharacteristic
1243C4C2×D4×Q811yescharacteristic
1244C4#350311yescharacteristic
1245C4#350311yescharacteristic
1246C2—42no—
1247C2—42no—
1248C2D4×C4⋊Q811yescharacteristic
1249C2#6066011yescharacteristic
1250C2#6066811yescharacteristic
1251C2#6109211yescharacteristic
1252C2#6109611yescharacteristic
1253C2#6252311yescharacteristic
1254C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3164C2semidirect
2. C2×#3163C2semidirect
5. #33317C2semidirect
6. #33219C2semidirect
7. #33219C2semidirect
8. #28818C2semidirect
9. #28815C2semidirect
10. #28812C2semidirect
11. #28810C2semidirect
12. #28690C2semidirect
13. #28688C2semidirect
14. #26075C2semidirect
15. #26074C2semidirect
16. #26073C2semidirect
17. #26072C2semidirect
18. #26071C2semidirect
19. #26070C2semidirect
20. #26069C2semidirect
21. #26068C2semidirect
22. #25822C2semidirect
23. #25822C2semidirect
24. #25821C2semidirect
25. #25820C2semidirect
30. C4×#501C2semidirect
269. #501D4semidirect
278. #436Q8semidirect
279. C8×D4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#31642
C2×#31632
#393662
#393652
#333172
#332192
#288182
#288152
#288122
#288102
#286902
#286882
#260752
#260742
#260732
#260722
#260712
#260702
#260692
#260682
#258222
#258212
#258202
#226662
#226642
#226562
#226542
C4×#5012
#204952