Finite Group Databasebeta

← #6816756

Subgroups — #6816756

Order 512.

1839 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3226C211yesmaximal, characteristic, complemented
3#37764C211yesmaximal, characteristic
4#37686C211yesmaximal, characteristic, complemented
5#33319C211yesmaximal, characteristic, complemented
6#31104C211yesmaximal, characteristic, complemented
7#31102C211yesmaximal, characteristic, complemented
8#31100C211yesmaximal, characteristic, complemented
9#31096C211yesmaximal, characteristic, complemented
10#31082C211yesmaximal, characteristic, complemented
11#31080C211yesmaximal, characteristic, complemented
12#31078C211yesmaximal, characteristic, complemented
13#31078C211yesmaximal, characteristic, complemented
14#29880C211yesmaximal, characteristic, complemented
15#29879C211yesmaximal, characteristic, complemented
16#28728C211yesmaximal, characteristic, complemented
17#28697C211yesmaximal, characteristic, complemented
18#26058C211yesmaximal, characteristic, complemented
19#26052C211yesmaximal, characteristic, complemented
20#26049C211yesmaximal, characteristic, complemented
21#26040C211yesmaximal, characteristic, complemented
22#25821C211yesmaximal, characteristic, complemented
23#25816C211yesmaximal, characteristic, complemented
24#25685C211yesmaximal, characteristic, complemented
25#25676C211yesmaximal, characteristic, complemented
26#25027C211yesmaximal, characteristic, complemented
27#25022C211yesmaximal, characteristic, complemented
28#25019C211yesmaximal, characteristic, complemented
29#25010C211yesmaximal, characteristic, complemented
30#21644C211yesmaximal, characteristic, complemented
31#21272C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36#3241—28no—
37#3226—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#500C2211yescharacteristic
42C2×#500C2211yescharacteristic
43C2×#499C2211yescharacteristic
44C2×#490C2211yescharacteristic
45C2×#486C2211yescharacteristic
46C2×#486C2211yescharacteristic
47C2×#481C2211yescharacteristic
48C2×#482C2211yescharacteristic
49C2×#482C2211yescharacteristic
50C2×#480C2211yescharacteristic
51C2×#480C2211yescharacteristic
52C2×#480C2211yescharacteristic
53C2×#480C2211yescharacteristic
54C2×#480C2211yescharacteristic
55C2×#478C2211yescharacteristic
56C2×#478C2211yescharacteristic
57C2×#476C2211yescharacteristic
58C2×#474C2211yescharacteristic
59C2×#474C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#474C2211yescharacteristic
62C2×#474C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#431C2211yescharacteristic
65#2851C2211yescharacteristic
66#2851C2211yescharacteristic
67#2734—21no—
68#2729—21no—
69#2717—21no—
70#2713—21no—
71#2708—21no—
72#2686—21no—
73#2677—21no—
74#2671—21no—
75#2660C2211yescharacteristic
76#2660C2211yescharacteristic
77#2628C2211yescharacteristic
78#2628C2211yescharacteristic
79#2551C2211yescharacteristic
80#2550C2211yescharacteristic
81#2537C2211yescharacteristic
82#2535C2211yescharacteristic
83#2473—21no—
84#2449—21no—
85#2443—21no—
86#2442C2211yescharacteristic
87#2440C2211yescharacteristic
88#2440C2211yescharacteristic
89#2439C2211yescharacteristic
90#2434—21no—
91#2430—21no—
92#2422C2211yescharacteristic
93#2422C2211yescharacteristic
94#2420C2211yescharacteristic
95#2420C2211yescharacteristic
96#2419—21no—
97#2409—21no—
98#2406—21no—
99#2352C2211yescharacteristic
100#2349C2211yescharacteristic
101D4×C4⋊C4C2211yescharacteristic
102D4×C4⋊C4C2211yescharacteristic
103#2331C2211yescharacteristic
104#2328C2211yescharacteristic
105#2290C2211yescharacteristic
106#2088C2211yescharacteristic
107#2088C2211yescharacteristic
108#2087C2211yescharacteristic
109#2087C2211yescharacteristic
110#2087C2211yescharacteristic
111#2086C2211yescharacteristic
112#2086C2211yescharacteristic
113#2086C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2083C2211yescharacteristic
117#2083C2211yescharacteristic
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2076C2211yescharacteristic
122#2076C2211yescharacteristic
123#2075C2211yescharacteristic
124#2075C2211yescharacteristic
125#2075C2211yescharacteristic
126#2073C2211yescharacteristic
127#2073C2211yescharacteristic
128#2071C2211yescharacteristic
129#2071C2211yescharacteristic
130#2059C2211yescharacteristic
131#2059C2211yescharacteristic
132#2058C2211yescharacteristic
133#2058C2211yescharacteristic
134#2057C2211yescharacteristic
135#2057C2211yescharacteristic
136#2057C2211yescharacteristic
137#2057C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2034C2211yescharacteristic
142#2033C2211yescharacteristic
143#2033C2211yescharacteristic
144#2033C2211yescharacteristic
145#2033C2211yescharacteristic
146#1993C2211yescharacteristic
147#1993C2211yescharacteristic
148#1993C2211yescharacteristic
149#1991C2211yescharacteristic
150#1991C2211yescharacteristic
151#1961C2211yescharacteristic
152#1955C2211yescharacteristic
153#1954C2211yescharacteristic
154#1949C2211yescharacteristic
155#1949C2211yescharacteristic
156#1947C2211yescharacteristic
157#1947C2211yescharacteristic
158#1940C2211yescharacteristic
159#1939C2211yescharacteristic
160#1936C2211yescharacteristic
161#1936C2211yescharacteristic
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1846C2211yescharacteristic
189#1846C2211yescharacteristic
190#1845C2211yescharacteristic
191#1845C2211yescharacteristic
192#1835C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1768C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203#1749C2211yescharacteristic
204#1726C2211yescharacteristic
205C22×#41—21no—
206C23×Q8—21no—
207#544—24no—
208#544—42no—
209#540—24no—
210#540—42no—
211#532—24no—
212#532—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—24no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—21no—
259C22×C4⋊C4—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#501—24no—
265#501—42no—
266#501—42no—
267#500—24no—
268#500—24no—
269#499—24no—
270#490—24no—
271#486—24no—
272#486D418yescomplemented
273#482—24no—
274#482—24no—
275#481—24no—
276#480—24no—
277#480—24no—
278#480—24no—
279#480—24no—
280#480—24no—
281#478—24no—
282#478—24no—
283#476—24no—
284#474—24no—
285#474—24no—
286#474—24no—
287#474—24no—
288#474—24no—
289#433—24no—
290#431—24no—
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×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353#400—21no—
354#400—21no—
355#400—21no—
356#399—21no—
357#399—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#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#396—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#393—21no—
390#393—21no—
391#393—21no—
392#392—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389—21no—
401#389—21no—
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#388—21no—
413#388D411yescharacteristic
414#388D411yescharacteristic
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387D411yescharacteristic
424#387D411yescharacteristic
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386D411yescharacteristic
435#386D411yescharacteristic
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385D411yescharacteristic
452#385D411yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#381—21no—
464#381—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483#376C2311yescharacteristic
484C2×#95—21no—
485#340C2311yescharacteristic
486#340C2311yescharacteristic
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#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C2×#41—44no—
516C2×#41—82no—
517C2×#41—82no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—44no—
525C22×Q8—82no—
526C22×Q8—82no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C2×D411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570C4⋊Q8—44no—
571C4⋊Q8—82no—
572C4⋊Q8C2×D414yes—
573#127—22no—
574#127C2×D414yes—
575#125—22no—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125—41no—
581#125—44no—
582#124—44no—
583#123—44no—
584#123—44no—
585#123—82no—
586#123—82no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—82no—
590C22⋊Q8—82no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—44no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—44no—
602#121—82no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—44no—
618C4×D4—82no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—41no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
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—44no—
663C2×C4⋊C4—82no—
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
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⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
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—41no—
739#107—41no—
740#107—41no—
741#107—41no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—41no—
747#106—41no—
748#106—41no—
749#106—41no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102C2×D414yes—
769#102C2×D414yes—
770#102C2×D414yes—
771#102C2×D414yes—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780#97—22no—
781#97—22no—
782#97—22no—
783#97—22no—
784C4×C8—22no—
785C4×C8—22no—
786C4×C8—22no—
787C4×C8C2×D414yes—
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#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—816no—
835C2×Q8—24no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—42no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—816no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—41no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C22×D412yes—
886C2×D4C22×D412yes—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C2511yescharacteristic
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8C22×D412yes—
980C2×C8C22×D412yes—
981C2×C82−1+412yes—
982C2×C82−1+412yes—
983C4⋊C4—22no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4C22×D412yes—
1048C4⋊C4C22×D412yes—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C42—22no—
1081C42—22no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42C22×D412yes—
1092C42H(5,𝔽2)12yes—
1093C422−1+412yes—
1094C422−1+412yes—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23#57612yes—
1123C23C23×D411yescharacteristic
1124Q8—84no—
1125Q8—84no—
1126Q8—84no—
1127Q8—84no—
1128Q8—84no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—44no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—84no—
1143D4—162no—
1144D4—162no—
1145C2×C4—28no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—44no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#53612yes—
1238C2×C4#53612yes—
1239C2×C4D4212yes—
1240C2×C4D4212yes—
1241C2×C4#57612yes—
1242C2×C4C23×D411yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×2−1+411yescharacteristic
1245C2×C4C2×2−1+411yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4C2×2−1+411yescharacteristic
1248C8—22no—
1249C8—22no—
1250C8—22no—
1251C8—22no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22C2×#53611yescharacteristic
1285C22C2×D4211yescharacteristic
1286C22#349911yescharacteristic
1287C22C2×#57611yescharacteristic
1288C22C2×#57611yescharacteristic
1289C22#358611yescharacteristic
1290C22#358611yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4#349911yescharacteristic
1318C4#349911yescharacteristic
1319C4#355211yescharacteristic
1320C4#355211yescharacteristic
1321C2—42no—
1322C2—81no—
1323C2—82no—
1324C2—82no—
1325C2#3936011yescharacteristic
1326C2#6087111yescharacteristic
1327C2#6088811yescharacteristic
1328C2#6104911yescharacteristic
1329C2#6106011yescharacteristic
1330C2#6251511yescharacteristic
1331C2#6252011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37764C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3241C2semidirect
2. C2×#3226C2semidirect
4. #37686C2semidirect
5. #33319C2semidirect
6. #31104C2semidirect
7. #31102C2semidirect
8. #31100C2semidirect
9. #31096C2semidirect
10. #31082C2semidirect
11. #31080C2semidirect
12. #31078C2semidirect
13. #31078C2semidirect
14. #29880C2semidirect
15. #29879C2semidirect
16. #28728C2semidirect
17. #28697C2semidirect
18. #26058C2semidirect
19. #26052C2semidirect
20. #26049C2semidirect
21. #26040C2semidirect
22. #25821C2semidirect
23. #25816C2semidirect
24. #25685C2semidirect
25. #25676C2semidirect
26. #25027C2semidirect
27. #25022C2semidirect
28. #25019C2semidirect
29. #25010C2semidirect
30. #21644C2semidirect
31. #21272C2semidirect
272. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#32262
#377642
#376862
#333192
#311042
#311022
#311002
#310962
#310822
#310802
#310782
#298802
#298792
#287282
#286972
#260582
#260522
#260492
#260402
#258212
#258162
#256852
#256762
#250272
#250222
#250192
#250102
#216442
#212722