Finite Group Databasebeta

← #7563035

Subgroups — #7563035

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3377C211yesmaximal, characteristic, complemented
2C2×#3364C211yesmaximal, characteristic, complemented
3#45266C211yesmaximal, characteristic
4#35957C211yesmaximal, characteristic, complemented
5#30830C211yesmaximal, characteristic, complemented
6#30820C211yesmaximal, characteristic, complemented
7#30818C211yesmaximal, characteristic, complemented
8#30810C211yesmaximal, characteristic, complemented
9#28729C211yesmaximal, characteristic, complemented
10#28525C211yesmaximal, characteristic
11#27786C211yesmaximal, characteristic
12#27770C211yesmaximal, characteristic
13#26185C211yesmaximal, characteristic, complemented
14#26173C211yesmaximal, characteristic, complemented
15#26173C211yesmaximal, characteristic, complemented
16#26169C211yesmaximal, characteristic, complemented
17#26057C211yesmaximal, characteristic, complemented
18#26050C211yesmaximal, characteristic, complemented
19#25656C211yesmaximal, characteristic, complemented
20#25646C211yesmaximal, characteristic, complemented
21#25481C211yesmaximal, characteristic, complemented
22#25473C211yesmaximal, characteristic, complemented
23#24747C211yesmaximal, characteristic
24#24733C211yesmaximal, characteristic
25#24340C211yesmaximal, characteristic, complemented
26#24334C211yesmaximal, characteristic, complemented
27#23154C211yesmaximal, characteristic, complemented
28#22685C211yesmaximal, characteristic, complemented
29#22679C211yesmaximal, characteristic, complemented
30#21516C211yesmaximal, characteristic, complemented
31#21515C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#556C2211yescharacteristic
36#3377—28no—
37#3364—28no—
38C2×#491C2211yescharacteristic
39C2×#489C2211yescharacteristic
40C2×#488C2211yescharacteristic
41C2×#488C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#487C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#477C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#476C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#462C2211yescharacteristic
57C2×#460C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×C8×Q8C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic
64C2×C4×Q16C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×Q16C2211yescharacteristic
67C2×C4×SD16C2211yescharacteristic
68#2723—21no—
69#2723—21no—
70#2723—21no—
71#2723—21no—
72#2660—21no—
73#2660C2211yescharacteristic
74#2584—21no—
75#2584C2211yescharacteristic
76#2580C2211yescharacteristic
77#2580C2211yescharacteristic
78#2567—21no—
79#2567C2211yescharacteristic
80#2552—21no—
81#2552—21no—
82#2552C2211yescharacteristic
83#2552C2211yescharacteristic
84#2550—21no—
85#2550—21no—
86#2550C2211yescharacteristic
87#2550C2211yescharacteristic
88#2548C2211yescharacteristic
89#2548C2211yescharacteristic
90#2479—21no—
91#2479—21no—
92#2479—21no—
93#2479—21no—
94#2448C2211yescharacteristic
95#2448C2211yescharacteristic
96#2448C2211yescharacteristic
97#2448C2211yescharacteristic
98#2399—21no—
99#2399C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102#2351C2211yescharacteristic
103#2351C2211yescharacteristic
104Q8×C4⋊C4C2211yescharacteristic
105Q8×C4⋊C4C2211yescharacteristic
106#2328C2211yescharacteristic
107#2327C2211yescharacteristic
108#2276C2211yescharacteristic
109#2094C2211yescharacteristic
110#2093C2211yescharacteristic
111#2092C2211yescharacteristic
112#2092C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2087C2211yescharacteristic
116#2086C2211yescharacteristic
117#2074C2211yescharacteristic
118#2074C2211yescharacteristic
119#2072C2211yescharacteristic
120#2072C2211yescharacteristic
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2042C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2042C2211yescharacteristic
135#2042C2211yescharacteristic
136#2042C2211yescharacteristic
137#2025C2211yescharacteristic
138#2025C2211yescharacteristic
139#2025C2211yescharacteristic
140#2023C2211yescharacteristic
141#1993C2211yescharacteristic
142#1991C2211yescharacteristic
143#1985C2211yescharacteristic
144#1984C2211yescharacteristic
145#1982C2211yescharacteristic
146#1981C2211yescharacteristic
147#1961C2211yescharacteristic
148#1957C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1944C2211yescharacteristic
152#1942C2211yescharacteristic
153#1942C2211yescharacteristic
154#1941C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1936C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1847C2211yescharacteristic
190#1846C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#557—24no—
210#557—24no—
211#557—42no—
212#557—42no—
213#556—24no—
214#556—24no—
215#556—42no—
216#556—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117—21no—
262#491—24no—
263#489—24no—
264#488—24no—
265#488—24no—
266#488—24no—
267#487—24no—
268#479—24no—
269#479—24no—
270#479—24no—
271#478—24no—
272#478—42no—
273#477—24no—
274#476—42no—
275#474—24no—
276#464—24no—
277#464—24no—
278#464—24no—
279#464—24no—
280#462D418yescomplemented
281#460—24no—
282#446—24no—
283C8×Q8—24no—
284#441—24no—
285#441—24no—
286#440—24no—
287C4×Q16—24no—
288C4×Q16—24no—
289C4×Q16—24no—
290C4×Q16—24no—
291C4×SD16—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×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352#399—21no—
353#399—21no—
354#399—21no—
355#399—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#398—21no—
367#398D411yescharacteristic
368#398D411yescharacteristic
369#398D411yescharacteristic
370#398D411yescharacteristic
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395D411yescharacteristic
383#395D411yescharacteristic
384#395D411yescharacteristic
385#395D411yescharacteristic
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#393—21no—
391#393—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#390—21no—
398#390—21no—
399#390—21no—
400#390—21no—
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#389—21no—
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#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#384—21no—
458#384—21no—
459#384—21no—
460#384—21no—
461#384—21no—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#382—21no—
465#382—21no—
466#382—21no—
467#382—21no—
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488#376—21no—
489#376C2311yescharacteristic
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#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8C2×D411yescharacteristic
521C22×Q8C2×D411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16C2×D414yes—
536C2×Q16C2×D414yes—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
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—41no—
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558C4⋊Q8C2×D414yes—
559#127—22no—
560#127—22no—
561#126—44no—
562#126—44no—
563#126—44no—
564#126—44no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—44no—
574#125—44no—
575#125—44no—
576#125—44no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—22no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—44no—
616C4×Q8—44no—
617C4×Q8C2×D414yes—
618C4×Q8#4114yes—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623#117—44no—
624#117—44no—
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—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
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×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#107—41no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747#106—41no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8C2×D414yes—
756#103—22no—
757#103—22no—
758#103—22no—
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—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103C2×D414yes—
773#103C2×D414yes—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#97—22no—
789#97—22no—
790#97—22no—
791C4×C8—22no—
792C4×C8—22no—
793C4×C8—22no—
794C4×C8—22no—
795C4×C8—22no—
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#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
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
834#95C2×D411yescharacteristic
835C24—21no—
836C24—21no—
837C2×Q8—22no—
838C2×Q8—22no—
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—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—41no—
853C2×Q8—41no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8C22×D412yes—
863C2×Q8C22×D412yes—
864C2×Q8C22×D412yes—
865C2×Q8C2×#4112yes—
866C2×Q82−1+412yes—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
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—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C2511yescharacteristic
920Q16—28no—
921Q16—28no—
922SD16—44no—
923SD16—44no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
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×C8C22×D412yes—
947C2×C8C22×D412yes—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—24no—
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—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—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
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—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—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
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⋊C4C22×D412yes—
1023C4⋊C4C2×#4112yes—
1024C4⋊C42−1+412yes—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C42—24no—
1048C42—24no—
1049C42—24no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42C22×D412yes—
1074C42C2×#4112yes—
1075C42H(5,𝔽2)12yes—
1076C422−1+412yes—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23C23×D411yescharacteristic
1092Q8—22no—
1093Q8—22no—
1094Q8—22no—
1095Q8—22no—
1096Q8—22no—
1097Q8—22no—
1098Q8—22no—
1099Q8—44no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—82no—
1105Q8—84no—
1106Q8—84no—
1107Q8#54714yes—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—162no—
1117D4—162no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
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—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—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
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—84no—
1199C2×C4—84no—
1200C2×C4D4212yes—
1201C2×C4D4212yes—
1202C2×C4#54812yes—
1203C2×C4#54812yes—
1204C2×C4C23×D411yescharacteristic
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4C2×2−1+411yescharacteristic
1208C2×C4C2×2−1+411yescharacteristic
1209C2×C4C2×2−1+411yescharacteristic
1210C8—22no—
1211C8—22no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22C2×D4211yescharacteristic
1233C22C2×#54811yescharacteristic
1234C22#348611yescharacteristic
1235C22#358411yescharacteristic
1236C22#358411yescharacteristic
1237C22#358411yescharacteristic
1238C22#358611yescharacteristic
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—24no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—42no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4C2×#54711yescharacteristic
1268C4#349911yescharacteristic
1269C4#351111yescharacteristic
1270C4#355211yescharacteristic
1271C2—161no—
1272C2—161no—
1273C2#5912511yescharacteristic
1274C2#6105411yescharacteristic
1275C2#6107811yescharacteristic
1276C2#6133111yescharacteristic
1277C2#6134411yescharacteristic
1278C2#6185611yescharacteristic
1279C2#6186711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3377C2semidirect
2. C2×#3364C2semidirect
4. #35957C2semidirect
5. #30830C2semidirect
6. #30820C2semidirect
7. #30818C2semidirect
8. #30810C2semidirect
9. #28729C2semidirect
13. #26185C2semidirect
14. #26173C2semidirect
15. #26173C2semidirect
16. #26169C2semidirect
17. #26057C2semidirect
18. #26050C2semidirect
19. #25656C2semidirect
20. #25646C2semidirect
21. #25481C2semidirect
22. #25473C2semidirect
25. #24340C2semidirect
26. #24334C2semidirect
27. #23154C2semidirect
28. #22685C2semidirect
29. #22679C2semidirect
30. #21516C2semidirect
280. #462D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33772
C2×#33642
#452662
#359572
#308302
#308202
#308182
#308102
#287292
#285252
#277862
#277702
#261852
#261732
#261692
#260572
#260502
#256562
#256462
#254812
#254732
#247472
#247332
#243402
#243342
#231542
#226852
#226792
#215162
#215152