Finite Group Databasebeta

← #6812005

Subgroups — #6812005

Order 512.

1721 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic, complemented
2C2×#3231C211yesmaximal, characteristic, complemented
3#37690C211yesmaximal, characteristic, complemented
4#35573C211yesmaximal, characteristic
5#33204C211yesmaximal, characteristic, complemented
6#30792C211yesmaximal, characteristic, complemented
7#30778C211yesmaximal, characteristic, complemented
8#30775C211yesmaximal, characteristic, complemented
9#30774C211yesmaximal, characteristic, complemented
10#30658C211yesmaximal, characteristic, complemented
11#30644C211yesmaximal, characteristic, complemented
12#30636C211yesmaximal, characteristic, complemented
13#30633C211yesmaximal, characteristic, complemented
14#29702C211yesmaximal, characteristic, complemented
15#29688C211yesmaximal, characteristic, complemented
16#28821C211yesmaximal, characteristic, complemented
17#28809C211yesmaximal, characteristic, complemented
18#28524C211yesmaximal, characteristic, complemented
19#28293C211yesmaximal, characteristic, complemented
20#27785C211yesmaximal, characteristic, complemented
21#27772C211yesmaximal, characteristic, complemented
22#26245C211yesmaximal, characteristic
23#26240C211yesmaximal, characteristic
24#25029C211yesmaximal, characteristic, complemented
25#25015C211yesmaximal, characteristic, complemented
26#24719C211yesmaximal, characteristic, complemented
27#24701C211yesmaximal, characteristic, complemented
28#24310C211yesmaximal, characteristic, complemented
29#24304C211yesmaximal, characteristic, complemented
30#22800C211yesmaximal, characteristic, complemented
31#21622C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#533C2211yescharacteristic
36#3244—28no—
37#3231—28no—
38C2×#501C2211yescharacteristic
39C2×#500C2211yescharacteristic
40C2×#498C2211yescharacteristic
41C2×#498C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#487C2211yescharacteristic
45C2×#487C2211yescharacteristic
46C2×#481C2211yescharacteristic
47C2×#485C2211yescharacteristic
48C2×#485C2211yescharacteristic
49C2×#485C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#483C2211yescharacteristic
54C2×#479C2211yescharacteristic
55C2×#479C2211yescharacteristic
56C2×#479C2211yescharacteristic
57C2×#479C2211yescharacteristic
58C2×#475C2211yescharacteristic
59C2×#475C2211yescharacteristic
60C2×#478C2211yescharacteristic
61C2×#478C2211yescharacteristic
62C2×#476C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#431C2211yescharacteristic
65#2857C2211yescharacteristic
66#2704—21no—
67#2692—21no—
68#2683—21no—
69#2677—21no—
70#2660C2211yescharacteristic
71#2629C2211yescharacteristic
72#2610—21no—
73#2604—21no—
74#2601—21no—
75#2558—21no—
76#2556—21no—
77#2551C2211yescharacteristic
78#2551C2211yescharacteristic
79#2550C2211yescharacteristic
80#2545—21no—
81#2545C2211yescharacteristic
82#2540C2211yescharacteristic
83#2538C2211yescharacteristic
84#2492C2211yescharacteristic
85#2491C2211yescharacteristic
86#2465—21no—
87#2462—21no—
88#2461—21no—
89#2452—21no—
90#2451—21no—
91#2441C2211yescharacteristic
92#2440C2211yescharacteristic
93#2439C2211yescharacteristic
94#2439C2211yescharacteristic
95#2429—21no—
96#2429C2211yescharacteristic
97#2426C2211yescharacteristic
98#2354C2211yescharacteristic
99#2352C2211yescharacteristic
100#2330C2211yescharacteristic
101#2326C2211yescharacteristic
102#2323C2211yescharacteristic
103C4×#121C2211yescharacteristic
104#2290C2211yescharacteristic
105#2276C2211yescharacteristic
106#2097C2211yescharacteristic
107#2096C2211yescharacteristic
108#2094C2211yescharacteristic
109#2092C2211yescharacteristic
110#2077C2211yescharacteristic
111#2077C2211yescharacteristic
112#2077C2211yescharacteristic
113#2076C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2043C2211yescharacteristic
127#2043C2211yescharacteristic
128#2042C2211yescharacteristic
129#2042C2211yescharacteristic
130#2036C2211yescharacteristic
131#2035C2211yescharacteristic
132#2035C2211yescharacteristic
133#2035C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2035C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2026C2211yescharacteristic
143#2024C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1987C2211yescharacteristic
149#1983C2211yescharacteristic
150#1983C2211yescharacteristic
151#1959C2211yescharacteristic
152#1958C2211yescharacteristic
153#1955C2211yescharacteristic
154#1954C2211yescharacteristic
155#1949C2211yescharacteristic
156#1949C2211yescharacteristic
157#1948C2211yescharacteristic
158#1948C2211yescharacteristic
159#1948C2211yescharacteristic
160#1948C2211yescharacteristic
161#1947C2211yescharacteristic
162#1944C2211yescharacteristic
163#1941C2211yescharacteristic
164#1941C2211yescharacteristic
165#1941C2211yescharacteristic
166#1935C2211yescharacteristic
167#1934C2211yescharacteristic
168#1934C2211yescharacteristic
169#1933C2211yescharacteristic
170#1924C2211yescharacteristic
171#1923C2211yescharacteristic
172#1923C2211yescharacteristic
173#1923C2211yescharacteristic
174#1921C2211yescharacteristic
175#1920C2211yescharacteristic
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1873C2211yescharacteristic
179#1872C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1847C2211yescharacteristic
187#1844C2211yescharacteristic
188#1843C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1797C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1771C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202#1768C2211yescharacteristic
203#1763C2211yescharacteristic
204C4×#103C2211yescharacteristic
205#544—24no—
206#544—42no—
207#542—24no—
208#542—42no—
209#533—24no—
210#533—24no—
211#533—42no—
212#533—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C42C2311yescharacteristic
265#501—24no—
266#500—24no—
267#498—24no—
268#498—24no—
269#489—24no—
270#488—24no—
271#487—24no—
272#487—24no—
273#485—24no—
274#485—24no—
275#485—24no—
276#485—24no—
277#485—24no—
278#483—24no—
279#482—24no—
280#481—24no—
281#479—24no—
282#479—24no—
283#479—24no—
284#479D418yescomplemented
285#478—24no—
286#478—42no—
287#476—24no—
288#475—24no—
289#475—42no—
290#433—24no—
291#431—24no—
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358#400—21no—
359#399—21no—
360#399—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#396—21no—
377#396—21no—
378#396—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#394—21no—
388#394—21no—
389#393—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#392—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#390—21no—
402#390—21no—
403#390—21no—
404#390—21no—
405#390—21no—
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
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#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388D411yescharacteristic
441#388D411yescharacteristic
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387D411yescharacteristic
450#387D411yescharacteristic
451#386—21no—
452#386—21no—
453#386D411yescharacteristic
454#386D411yescharacteristic
455#385—21no—
456#385—21no—
457#385—21no—
458#385D411yescharacteristic
459#385D411yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#380—21no—
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487#376—21no—
488#376C2311yescharacteristic
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
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—44no—
556C4⋊Q8—82no—
557C4⋊Q8—82no—
558#126—44no—
559#125—22no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—41no—
564#125—44no—
565#125—44no—
566#125C2×D414yes—
567#124—22no—
568#124—22no—
569#124—22no—
570#124—44no—
571#124—41no—
572#124—82no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—82no—
589C22⋊Q8—82no—
590#121—22no—
591#121—22no—
592#121—41no—
593#121—41no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—44no—
601C4×Q8—41no—
602C4×Q8—44no—
603C4×Q8—44no—
604C4×Q8C2×D414yes—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—82no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—44no—
616#117—41no—
617#117—41no—
618#117—41no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—21no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—41no—
736#107C2×D414yes—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—41no—
748#106—41no—
749#106—41no—
750#106C2×D414yes—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8C2×D414yes—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103C2×D414yes—
774#103C2×D414yes—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791#97—22no—
792#97—22no—
793C4×C8—22no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—22no—
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#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8C22×D412yes—
867C2×D4—22no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—21no—
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—41no—
914C22×C4—41no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2511yescharacteristic
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8C22×D412yes—
957C2×C8C22×D412yes—
958C4⋊C4—22no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
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—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4C22×D412yes—
1025C4⋊C4C22×D412yes—
1026C4⋊C4C22×D412yes—
1027C4⋊C42−1+412yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C42—22no—
1061C42—22no—
1062C42—24no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42C22×D412yes—
1081C42H(5,𝔽2)12yes—
1082C422−1+412yes—
1083C422−1+412yes—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23C23×D411yescharacteristic
1106Q8—22no—
1107Q8—22no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—84no—
1115Q8—84no—
1116Q8—84no—
1117Q8—162no—
1118Q8—162no—
1119Q8—162no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—82no—
1125D4—84no—
1126D4—162no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—44no—
1163C2×C4—44no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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—162no—
1213C2×C4—162no—
1214C2×C4#53612yes—
1215C2×C4#53612yes—
1216C2×C4D4212yes—
1217C2×C4D4212yes—
1218C2×C4#57712yes—
1219C2×C4#57712yes—
1220C2×C4C23×D411yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C2×C4C2×2−1+411yescharacteristic
1224C2×C4C2×2−1+411yescharacteristic
1225C2×C4#58511yescharacteristic
1226C8—22no—
1227C8—22no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22C2×#53611yescharacteristic
1256C22C2×D4211yescharacteristic
1257C22#348911yescharacteristic
1258C22C2×#57711yescharacteristic
1259C22C2×#57711yescharacteristic
1260C22#358411yescharacteristic
1261C22#358611yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—41no—
1269C4—41no—
1270C4—42no—
1271C4—42no—
1272C4—41no—
1273C4—42no—
1274C4—41no—
1275C4—41no—
1276C4—42no—
1277C4—41no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#349711yescharacteristic
1290C4#349911yescharacteristic
1291C4#354711yescharacteristic
1292C4#355011yescharacteristic
1293C2—81no—
1294C2—81no—
1295C2—161no—
1296C2#3934311yescharacteristic
1297C2#6087611yescharacteristic
1298C2#6088111yescharacteristic
1299C2#6105511yescharacteristic
1300C2#6107511yescharacteristic
1301C2#6218911yescharacteristic
1302C2#6221911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
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×#3244C2semidirect
2. C2×#3231C2semidirect
3. #37690C2semidirect
5. #33204C2semidirect
6. #30792C2semidirect
7. #30778C2semidirect
8. #30775C2semidirect
9. #30774C2semidirect
10. #30658C2semidirect
11. #30644C2semidirect
12. #30636C2semidirect
13. #30633C2semidirect
14. #29702C2semidirect
15. #29688C2semidirect
16. #28821C2semidirect
17. #28809C2semidirect
18. #28524C2semidirect
19. #28293C2semidirect
20. #27785C2semidirect
21. #27772C2semidirect
24. #25029C2semidirect
25. #25015C2semidirect
26. #24719C2semidirect
27. #24701C2semidirect
28. #24310C2semidirect
29. #24304C2semidirect
30. #22800C2semidirect
31. #21622C2semidirect
284. #479D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32442
C2×#32312
#376902
#355732
#332042
#307922
#307782
#307752
#307742
#306582
#306442
#306362
#306332
#297022
#296882
#288212
#288092
#285242
#282932
#277852
#277722
#262452
#262402
#250292
#250152
#247192
#247012
#243102
#243042
#228002
#216222