Finite Group Databasebeta

← #7563002

Subgroups — #7563002

Order 512.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3371C211yesmaximal, characteristic, complemented
2C2×#3371C211yesmaximal, characteristic, complemented
3#45421C211yesmaximal, characteristic
4#35957C211yesmaximal, characteristic, complemented
5#30835C211yesmaximal, characteristic, complemented
6#30833C211yesmaximal, characteristic, complemented
7#30822C211yesmaximal, characteristic, complemented
8#30818C211yesmaximal, characteristic, complemented
9#28730C211yesmaximal, characteristic, complemented
10#28525C211yesmaximal, characteristic, complemented
11#27786C211yesmaximal, characteristic, complemented
12#27775C211yesmaximal, characteristic
13#26189C211yesmaximal, characteristic, complemented
14#26185C211yesmaximal, characteristic, complemented
15#26179C211yesmaximal, characteristic, complemented
16#26159C211yesmaximal, characteristic, complemented
17#26057C211yesmaximal, characteristic, complemented
18#26051C211yesmaximal, characteristic, complemented
19#25660C211yesmaximal, characteristic, complemented
20#25653C211yesmaximal, characteristic, complemented
21#25482C211yesmaximal, characteristic, complemented
22#25477C211yesmaximal, characteristic, complemented
23#24742C211yesmaximal, characteristic
24#24733C211yesmaximal, characteristic, complemented
25#24346C211yesmaximal, characteristic, complemented
26#24328C211yesmaximal, characteristic, complemented
27#23155C211yesmaximal, characteristic, complemented
28#22678C211yesmaximal, characteristic, complemented
29#22675C211yesmaximal, characteristic, complemented
30#21515C211yesmaximal, characteristic, complemented
31#21512C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#559C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#3371—28no—
37#3371—28no—
38C2×#490C2211yescharacteristic
39C2×#490C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#476C2211yescharacteristic
50C2×#476C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#460C2211yescharacteristic
56C2×#460C2211yescharacteristic
57C2×#460C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×SD16C2211yescharacteristic
67C2×C4×SD16C2211yescharacteristic
68#2706—21no—
69#2706—21no—
70#2672—21no—
71#2672—21no—
72#2660—21no—
73#2660C2211yescharacteristic
74#2584—21no—
75#2584C2211yescharacteristic
76#2567—21no—
77#2567C2211yescharacteristic
78#2552—21no—
79#2552—21no—
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2550—21no—
83#2550—21no—
84#2550C2211yescharacteristic
85#2550C2211yescharacteristic
86#2548C2211yescharacteristic
87#2541C2211yescharacteristic
88#2538C2211yescharacteristic
89#2538C2211yescharacteristic
90#2461—21no—
91#2461—21no—
92#2448C2211yescharacteristic
93#2448C2211yescharacteristic
94#2445C2211yescharacteristic
95#2445C2211yescharacteristic
96#2425—21no—
97#2425—21no—
98#2399—21no—
99#2399C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102#2351C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104Q8×C4⋊C4C2211yescharacteristic
105#2349C2211yescharacteristic
106#2328C2211yescharacteristic
107#2326C2211yescharacteristic
108#2276C2211yescharacteristic
109#2094C2211yescharacteristic
110#2093C2211yescharacteristic
111#2092C2211yescharacteristic
112#2092C2211yescharacteristic
113#2088C2211yescharacteristic
114#2088C2211yescharacteristic
115#2088C2211yescharacteristic
116#2087C2211yescharacteristic
117#2074C2211yescharacteristic
118#2073C2211yescharacteristic
119#2072C2211yescharacteristic
120#2071C2211yescharacteristic
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2067C2211yescharacteristic
124#2067C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2057C2211yescharacteristic
129#2042C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2041C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2041C2211yescharacteristic
137#2025C2211yescharacteristic
138#2025C2211yescharacteristic
139#2025C2211yescharacteristic
140#2023C2211yescharacteristic
141#1992C2211yescharacteristic
142#1990C2211yescharacteristic
143#1985C2211yescharacteristic
144#1984C2211yescharacteristic
145#1983C2211yescharacteristic
146#1982C2211yescharacteristic
147#1961C2211yescharacteristic
148#1957C2211yescharacteristic
149#1949C2211yescharacteristic
150#1947C2211yescharacteristic
151#1943C2211yescharacteristic
152#1943C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1936C2211yescharacteristic
158#1936C2211yescharacteristic
159#1936C2211yescharacteristic
160#1934C2211yescharacteristic
161#1928C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1916C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1878C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1847C2211yescharacteristic
190#1846C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1802C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#102C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#559—24no—
210#559—24no—
211#559—42no—
212#559—42no—
213#557—24no—
214#557—24no—
215#557—42no—
216#557—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#124—21no—
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8—21no—
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×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268#490—24no—
269#490—24no—
270#489—24no—
271#489—24no—
272#488—24no—
273#488—24no—
274#479—24no—
275#479—24no—
276#478—24no—
277#478—24no—
278#478—42no—
279#476—24no—
280#476—24no—
281#474—42no—
282#464—24no—
283#464—24no—
284#464D418yescomplemented
285#460—24no—
286#460—24no—
287#460—24no—
288#446—24no—
289#446—24no—
290#441—24no—
291#441—24no—
292#440—24no—
293#440—24no—
294#440—24no—
295C4×Q16—24no—
296C4×SD16—24no—
297C4×SD16—24no—
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358#399—21no—
359#399—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#398—21no—
369#398D411yescharacteristic
370#398D411yescharacteristic
371#398D411yescharacteristic
372#398D411yescharacteristic
373#397—21no—
374#397—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#395D411yescharacteristic
387#395D411yescharacteristic
388#395D411yescharacteristic
389#395D411yescharacteristic
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#392—21no—
397#392—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391C2311yescharacteristic
402#390—21no—
403#390—21no—
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
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#389—21no—
426#389—21no—
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#384—21no—
456#384—21no—
457#384—21no—
458#384—21no—
459#384—21no—
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#382—21no—
464#382—21no—
465#382—21no—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#380—21no—
470#380—21no—
471#380—21no—
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⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487#376—21no—
488#376C2311yescharacteristic
489C2×#95—21no—
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×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16C2×D414yes—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16C2×D414yes—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—41no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564#127—22no—
565#127—22no—
566#127—22no—
567#127—22no—
568#127—41no—
569#127—41no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—41no—
576#125—41no—
577#125—41no—
578#125—44no—
579#125—44no—
580#125—44no—
581#125—44no—
582#124—22no—
583#124—22no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—44no—
588#124—44no—
589#124C2×D414yes—
590#123—44no—
591#123—44no—
592#123—44no—
593#123—44no—
594#123—82no—
595#123—82no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598#121—82no—
599#121—82no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—44no—
623C4×Q8—44no—
624C4×Q8C2×D414yes—
625C4×Q8#4114yes—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—44no—
637C4×D4—44no—
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⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#107—22no—
747#107—22no—
748#107—22no—
749#107—22no—
750#107—41no—
751#107—41no—
752#107—41no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—22no—
757#106—41no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—22no—
765C4⋊C8C2×D414yes—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103C2×D414yes—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102C2×D414yes—
798#97—22no—
799#97—22no—
800#97—22no—
801#97—22no—
802#97—22no—
803C4×C8—22no—
804C4×C8—22no—
805C4×C8—22no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841C24—21no—
842C24—21no—
843C24—21no—
844C2×Q8—22no—
845C2×Q8—22no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×Q8—42no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8C22×D412yes—
865C2×Q8C22×D412yes—
866C2×Q8C2×#4112yes—
867C2×Q82−1+412yes—
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—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4C22×D412yes—
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—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2511yescharacteristic
947Q16—28no—
948SD16—28no—
949SD16—44no—
950SD16—44no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
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×C8C22×D412yes—
974C2×C8C22×D412yes—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—24no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
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—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
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—81no—
1031C4⋊C4—81no—
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⋊C4C22×D412yes—
1047C4⋊C4C2×#4112yes—
1048C4⋊C42−1+412yes—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C42—24no—
1075C42—24no—
1076C42—24no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42C22×D412yes—
1098C42C2×#4112yes—
1099C42H(5,𝔽2)12yes—
1100C422−1+412yes—
1101C23—22no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23C23×D411yescharacteristic
1123Q8—22no—
1124Q8—22no—
1125Q8—22no—
1126Q8—22no—
1127Q8—22no—
1128Q8—41no—
1129Q8—41no—
1130Q8—82no—
1131Q8—82no—
1132Q8—84no—
1133Q8—84no—
1134Q8#54714yes—
1135D4—22no—
1136D4—22no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—84no—
1148D4—84no—
1149D4—162no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
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—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
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—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
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—41no—
1229C2×C4—41no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4D4212yes—
1236C2×C4D4212yes—
1237C2×C4#54812yes—
1238C2×C4#54812yes—
1239C2×C4C23×D411yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4C2×2−1+411yescharacteristic
1244C2×C4C2×2−1+411yescharacteristic
1245C8—22no—
1246C8—22no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22C2×D4211yescharacteristic
1275C22C2×#54811yescharacteristic
1276C22#348611yescharacteristic
1277C22#358411yescharacteristic
1278C22#358511yescharacteristic
1279C22#358511yescharacteristic
1280C22#358611yescharacteristic
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—24no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—42no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4C2×#54711yescharacteristic
1309C4#349911yescharacteristic
1310C4#351111yescharacteristic
1311C4#355211yescharacteristic
1312C2—82no—
1313C2—161no—
1314C2—161no—
1315C2#5912511yescharacteristic
1316C2#6106211yescharacteristic
1317C2#6107711yescharacteristic
1318C2#6133711yescharacteristic
1319C2#6134411yescharacteristic
1320C2#6186111yescharacteristic
1321C2#6187411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2541C22
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×#3371C2semidirect
2. C2×#3371C2semidirect
4. #35957C2semidirect
5. #30835C2semidirect
6. #30833C2semidirect
7. #30822C2semidirect
8. #30818C2semidirect
9. #28730C2semidirect
10. #28525C2semidirect
11. #27786C2semidirect
13. #26189C2semidirect
14. #26185C2semidirect
15. #26179C2semidirect
16. #26159C2semidirect
17. #26057C2semidirect
18. #26051C2semidirect
19. #25660C2semidirect
20. #25653C2semidirect
21. #25482C2semidirect
22. #25477C2semidirect
24. #24733C2semidirect
25. #24346C2semidirect
26. #24328C2semidirect
27. #23155C2semidirect
28. #22678C2semidirect
29. #22675C2semidirect
30. #21515C2semidirect
31. #21512C2semidirect
284. #464D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33712
#454212
#359572
#308352
#308332
#308222
#308182
#287302
#285252
#277862
#277752
#261892
#261852
#261792
#261592
#260572
#260512
#256602
#256532
#254822
#254772
#247422
#247332
#243462
#243282
#231552
#226782
#226752
#215152
#215122