Finite Group Databasebeta

← #7143323

Subgroups — #7143323

Order 512.

1901 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59318C211yesmaximal, characteristic, complemented
2#39340C211yesmaximal, characteristic, complemented
3#32012C211yesmaximal, characteristic, complemented
4#31996C211yesmaximal, characteristic, complemented
5#31800C211yesmaximal, characteristic, complemented
6#31774C211yesmaximal, characteristic, complemented
7#31376C211yesmaximal, characteristic, complemented
8#31374C211yesmaximal, characteristic, complemented
9#31145C211yesmaximal, characteristic, complemented
10#31140C211yesmaximal, characteristic, complemented
11#28782C211yesmaximal, characteristic, complemented
12#28776C211yesmaximal, characteristic, complemented
13#28237C211yesmaximal, characteristic, complemented
14#27956C211yesmaximal, characteristic, complemented
15#27830C211yesmaximal, characteristic, complemented
16#26977C211yesmaximal, characteristic, complemented
17#26968C211yesmaximal, characteristic, complemented
18#26052C211yesmaximal, characteristic, complemented
19#25550C211yesmaximal, characteristic, complemented
20#25533C211yesmaximal, characteristic, complemented
21#25027C211yesmaximal, characteristic, complemented
22#24829C211yesmaximal, characteristic, complemented
23#24708C211yesmaximal, characteristic, complemented
24#24136C211yesmaximal, characteristic, complemented
25#24128C211yesmaximal, characteristic, complemented
26#24116C211yesmaximal, characteristic, complemented
27#23573C211yesmaximal, characteristic, complemented
28#23086C211yesmaximal, characteristic, complemented
29#22676C211yesmaximal, characteristic, complemented
30#22495C211yesmaximal, characteristic, complemented
31#21865C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#537—21no—
36C2×#532C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#469C2211yescharacteristic
43C2×#466C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×#442C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#432C2211yescharacteristic
50#2857C2211yescharacteristic
51#2706—21no—
52#2698—21no—
53#2672—21no—
54#2672—21no—
55#2671—21no—
56#2671—21no—
57#2616—21no—
58#2553—21no—
59#2550C2211yescharacteristic
60#2542C2211yescharacteristic
61#2537C2211yescharacteristic
62#2537C2211yescharacteristic
63#2537C2211yescharacteristic
64#2535C2211yescharacteristic
65#2488—21no—
66#2487C2211yescharacteristic
67#2486C2211yescharacteristic
68#2442C2211yescharacteristic
69#2440C2211yescharacteristic
70#2440C2211yescharacteristic
71#2439C2211yescharacteristic
72#2430—21no—
73#2428C2211yescharacteristic
74#2428C2211yescharacteristic
75#2425—21no—
76#2420C2211yescharacteristic
77#2420C2211yescharacteristic
78#2419—21no—
79#2417—21no—
80#2416C2211yescharacteristic
81#2416C2211yescharacteristic
82#2407—21no—
83#2352C2211yescharacteristic
84#2349C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic
86#2339—21no—
87C4×#121C2211yescharacteristic
88C4×#121C2211yescharacteristic
89C2×#382C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2041C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2011C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1999C2211yescharacteristic
129#1999C2211yescharacteristic
130#1993C2211yescharacteristic
131#1993C2211yescharacteristic
132#1993C2211yescharacteristic
133#1993C2211yescharacteristic
134#1992C2211yescharacteristic
135#1990C2211yescharacteristic
136#1987C2211yescharacteristic
137#1961C2211yescharacteristic
138#1961C2211yescharacteristic
139#1955C2211yescharacteristic
140#1955C2211yescharacteristic
141#1954C2211yescharacteristic
142#1947C2211yescharacteristic
143#1944C2211yescharacteristic
144#1943C2211yescharacteristic
145#1943C2211yescharacteristic
146#1941C2211yescharacteristic
147#1940C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1934C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1895C2211yescharacteristic
155#1893C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1875C2211yescharacteristic
159#1874C2211yescharacteristic
160#1874C2211yescharacteristic
161#1874C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1870C2211yescharacteristic
167#1869C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1824C2211yescharacteristic
185#1823C2211yescharacteristic
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1771C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41—21no—
204C22×#41—21no—
205C22×#41—21no—
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#553—42no—
211#553—42no—
212#547—24no—
213#547—42no—
214#547—42no—
215#547—42no—
216#537—48no—
217#532—24no—
218#532—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—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×#121—21no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121D411yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×#121C2311yescharacteristic
257C2×#121C2311yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C22×C4⋊C4—21no—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C42C2311yescharacteristic
279#482—42no—
280#480—42no—
281#478—42no—
282#476—42no—
283#474—42no—
284#469—42no—
285#466—42no—
286#442—24no—
287#442—42no—
288#442—42no—
289C4×D8—42no—
290#435—42no—
291#432—42no—
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×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346#400—21no—
347#400—21no—
348#399—21no—
349#399—21no—
350#399—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#395—21no—
364#395—21no—
365#395—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#393—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#390D411yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389D411yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#388—21no—
402#388—21no—
403#388D411yescharacteristic
404#388D411yescharacteristic
405#387—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#386D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380D411yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C2×#95—21no—
464C2×#95—21no—
465C2×#95—21no—
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C2×#41—44no—
501C2×#41—44no—
502C2×#41—44no—
503C2×#41—44no—
504C2×#41—44no—
505C2×#41—44no—
506C2×#41—82no—
507C2×#41—82no—
508C2×#41—82no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—41no—
552C2×M16—22no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#127—22no—
573#127—41no—
574#126—44no—
575#125—22no—
576#125—41no—
577#124—44no—
578#123—44no—
579#123—44no—
580#123—44no—
581#123—44no—
582#123—44no—
583#123—82no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—82no—
591#121—24no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—44no—
601#121—44no—
602#121—44no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—44no—
610#121—44no—
611#121—44no—
612#121—44no—
613#121—44no—
614#121—44no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—41no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—44no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—44no—
640C4×D4—82no—
641C4×D4#4114yescomplemented
642#117—22no—
643#117—41no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
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—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—44no—
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
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×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×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×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C42—22no—
741C2×C42—22no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750#107—22no—
751#107—22no—
752#107—41no—
753#107—41no—
754#107—41no—
755#107—41no—
756#106—22no—
757#106—41no—
758#106—41no—
759#106—41no—
760#106—41no—
761#106—41no—
762#106—41no—
763#106—41no—
764C4⋊C8—22no—
765C4⋊C8—22no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798#97—22no—
799#97—22no—
800#97—41no—
801#97—41no—
802#97—41no—
803C4×C8—41no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—21no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
843#41—816no—
844#41—816no—
845#41—816no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
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—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
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—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4AGL(1,ℤ/8)14yes—
913C2×D4C2×#4112yes—
914C2×D4H(5,𝔽2)12yes—
915C22×C4—22no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—22no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C2511yescharacteristic
1000D8—28no—
1001D8—44no—
1002M16—82no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—82no—
1026C2×C82−1+412yes—
1027C2×C82−1+412yes—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4C2×#4112yes—
1083C4⋊C4H(5,𝔽2)12yes—
1084C22⋊C4—24no—
1085C22⋊C4—22no—
1086C22⋊C4—24no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C42—22no—
1127C42—22no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—42no—
1135C42—81no—
1136C42C2×#4112yes—
1137C42H(5,𝔽2)12yes—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—21no—
1155C23—22no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23C2×AGL(1,ℤ/8)12yes—
1179C23C2×AGL(1,ℤ/8)12yes—
1180C23C23×D411yescharacteristic
1181Q8—84no—
1182Q8—84no—
1183Q8—84no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—44no—
1189D4—44no—
1190D4—48no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—82no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—44no—
1243C2×C4—48no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—82no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4#54612yes—
1306C2×C4#54612yes—
1307C2×C4C2×AGL(1,ℤ/8)12yes—
1308C2×C4C22×#4111yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4C2×H(5,𝔽2)11yescharacteristic
1312C2×C4C2×2−1+411yescharacteristic
1313C2×C4C2×2−1+411yescharacteristic
1314C8—22no—
1315C8—22no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22C2×#54611yescharacteristic
1365C22#348411yescharacteristic
1366C22#349911yescharacteristic
1367C22C22×AGL(1,ℤ/8)11yescharacteristic
1368C22#358511yescharacteristic
1369C22#358511yescharacteristic
1370C22#358611yescharacteristic
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—42no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4#349211yescharacteristic
1396C4#351111yescharacteristic
1397C4#353611yescharacteristic
1398C4#354811yescharacteristic
1399C2—42no—
1400C2—42no—
1401C2—81no—
1402C2—82no—
1403C2—82no—
1404C2—161no—
1405C2#4486911yescharacteristic
1406C2#6115511yescharacteristic
1407C2#6118211yescharacteristic
1408C2#6156911yescharacteristic
1409C2#6167711yescharacteristic
1410C2#6250111yescharacteristic
1411C2#6250311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59318C2semidirect
2. #39340C2semidirect
3. #32012C2semidirect
4. #31996C2semidirect
5. #31800C2semidirect
6. #31774C2semidirect
7. #31376C2semidirect
8. #31374C2semidirect
9. #31145C2semidirect
10. #31140C2semidirect
11. #28782C2semidirect
12. #28776C2semidirect
13. #28237C2semidirect
14. #27956C2semidirect
15. #27830C2semidirect
16. #26977C2semidirect
17. #26968C2semidirect
18. #26052C2semidirect
19. #25550C2semidirect
20. #25533C2semidirect
21. #25027C2semidirect
22. #24829C2semidirect
23. #24708C2semidirect
24. #24136C2semidirect
25. #24128C2semidirect
26. #24116C2semidirect
27. #23573C2semidirect
28. #23086C2semidirect
29. #22676C2semidirect
30. #22495C2semidirect
31. #21865C2semidirect
641. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#593182
#393402
#320122
#319962
#318002
#317742
#313762
#313742
#311452
#311402
#287822
#287762
#282372
#279562
#278302
#269772
#269682
#260522
#255502
#255332
#250272
#248292
#247082
#241362
#241282
#241162
#235732
#230862
#226762
#224952
#218652