Finite Group Databasebeta

← #7000026

Subgroups — #7000026

Order 512.

1679 conjugacy classes of subgroups.

The subgroup lattice has 1417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45106C211yesmaximal, characteristic, complemented
2#42532C211yesmaximal, characteristic, complemented
3#32051C211yesmaximal, characteristic, complemented
4#31850C211yesmaximal, characteristic, complemented
5#31665C211yesmaximal, characteristic, complemented
6#31432C211yesmaximal, characteristic, complemented
7#31396C211yesmaximal, characteristic, complemented
8#31016C211yesmaximal, characteristic, complemented
9#30835C211yesmaximal, characteristic, complemented
10#30444C211yesmaximal, characteristic, complemented
11#29340C211yesmaximal, characteristic, complemented
12#29096C211yesmaximal, characteristic, complemented
13#29051C211yesmaximal, characteristic, complemented
14#28975C211yesmaximal, characteristic, complemented
15#27814C211yesmaximal, characteristic, complemented
16#27560C211yesmaximal, characteristic, complemented
17#27264C211yesmaximal, characteristic, complemented
18#26926C211yesmaximal, characteristic, complemented
19#26888C211yesmaximal, characteristic, complemented
20#26737C211yesmaximal, characteristic, complemented
21#26737C211yesmaximal, characteristic, complemented
22#26254C211yesmaximal, characteristic, complemented
23#25608C211yesmaximal, characteristic, complemented
24#24913C211yesmaximal, characteristic, complemented
25#24124C211yesmaximal, characteristic, complemented
26#23963C211yesmaximal, characteristic, complemented
27#23580C211yesmaximal, characteristic, complemented
28#23299C211yesmaximal, characteristic, complemented
29#23008C211yesmaximal, characteristic, complemented
30#22870C211yesmaximal, characteristic, complemented
31#22093C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#540C2211yescharacteristic, complemented
34C2×#493C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#478C2211yescharacteristic, complemented
38C2×#459C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic, complemented
44C22×#102C2211yescharacteristic
45#2824—21no—
46#2756—21no—
47#2718—21no—
48#2708—21no—
49#2703—21no—
50#2695—21no—
51#2684—21no—
52#2671—21no—
53#2670—21no—
54#2631—21no—
55#2619C2211yescharacteristic
56#2617—21no—
57#2563C2211yescharacteristic
58#2552C2211yescharacteristic, complemented
59#2537—21no—
60#2535C2211yescharacteristic
61#2513C2211yescharacteristic
62#2500C2211yescharacteristic, complemented
63#2495C2211yescharacteristic
64#2491C2211yescharacteristic
65#2491C2211yescharacteristic
66#2455—21no—
67#2454C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2445C2211yescharacteristic, complemented
70#2442C2211yescharacteristic
71#2433C2211yescharacteristic
72#2428C2211yescharacteristic
73#2428C2211yescharacteristic
74#2425—21no—
75#2425—21no—
76#2422C2211yescharacteristic
77#2418—21no—
78#2416C2211yescharacteristic
79#2408C2211yescharacteristic
80#2395C2211yescharacteristic
81#2366C2211yescharacteristic
82#2361C2211yescharacteristic
83#2361C2211yescharacteristic, complemented
84#2349C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2324C2211yescharacteristic
87#2316C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2086C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic, complemented
99#2067C2211yescharacteristic
100#2059C2211yescharacteristic, complemented
101#2054C2211yescharacteristic
102#2054C2211yescharacteristic
103#2054C2211yescharacteristic
104#2054C2211yescharacteristic, complemented
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic, complemented
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic, complemented
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2023C2211yescharacteristic, complemented
117#2023C2211yescharacteristic, complemented
118#2011C2211yescharacteristic
119#2011C2211yescharacteristic
120#1999C2211yescharacteristic
121#1999C2211yescharacteristic
122#1999C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic, complemented
127#1999C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1991C2211yescharacteristic, complemented
130#1990C2211yescharacteristic, complemented
131#1987C2211yescharacteristic, complemented
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic, complemented
137#1954C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1942C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic, complemented
145#1936C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1926C2211yescharacteristic, complemented
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic, complemented
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic, complemented
173#1879C2211yescharacteristic, complemented
174#1879C2211yescharacteristic, complemented
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1874C2211yescharacteristic, complemented
181#1869C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic, complemented
187#1852C2211yescharacteristic
188#1824C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—42no—
212#553—42no—
213#540—42no—
214#540—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4—21no—
264#493—42no—
265#490—42no—
266#480—24no—
267#478—42no—
268#459—24no—
269#447—24no—
270#447—42no—
271#442—42no—
272C4×D8—42no—
273C4×D8—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#102—42no—
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400—21no—
328#400D411yescharacteristic
329#399—21no—
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398—21no—
334#398D411yescharacteristic
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397D411yescharacteristic
341#397D411yescharacteristic
342#397D411yescharacteristic
343#396—21no—
344#396—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394D411yescharacteristic
361#394D411yescharacteristic
362#393—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—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#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384—21no—
432#384C2311yescharacteristic
433#383—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C2×#95—21no—
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#127—22no—
565#127—22no—
566#127—41no—
567#127—41no—
568#127—41no—
569#127—41no—
570#126—44no—
571#125—22no—
572#125—22no—
573#125—41no—
574#125—41no—
575#124—82no—
576#124—82no—
577#123—44no—
578#123—44no—
579#123—44no—
580#123—82no—
581#123—82no—
582#123—82no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—44no—
594#121—44no—
595#121—44no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—82no—
603#121—82no—
604#121—82no—
605#120—82no—
606#120—82no—
607#120—82no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—44no—
625C4×D4—82no—
626C4×D4—82no—
627C4×D4—82no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—41no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
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—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
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⋊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—82no—
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—22no—
737#107—22no—
738#107—41no—
739#106—41no—
740#106—41no—
741C4⋊C8—22no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102#4114yes—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—41no—
780#97—41no—
781#97—41no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
785C4×C8—41no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×D4—24no—
835C2×D4—22no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
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×D4—81no—
913C2×D4—81no—
914C2×D4C2×#4112yes—
915C2×D4H(5,𝔽2)12yes—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
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—21no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C2511yescharacteristic
979D8—44no—
980D8—44no—
981D8—44no—
982D8—82no—
983D8—82no—
984D8—82no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—82no—
1009C2×C8C2×#4112yes—
1010C4⋊C4—22no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4C2×#4112yes—
1055C4⋊C4H(5,𝔽2)12yes—
1056C22⋊C4—24no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—81no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
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—84no—
1173C23—84no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23#57612yes—
1180C23C23×D411yescharacteristic
1181Q8—162no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—82no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
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—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
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—41no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4#57612yes—
1304C2×C4C22×#4111yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4#58511yescharacteristic
1308C2×C4#58511yescharacteristic
1309C2×C4#58511yescharacteristic
1310C8—22no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—42no—
1328C22—41no—
1329C22—42no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—41no—
1334C22—42no—
1335C22—41no—
1336C22—42no—
1337C22—41no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
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—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—168no—
1368C22D4×#4111yescharacteristic
1369C22#348411yescharacteristic
1370C22#350011yescharacteristic
1371C22C2×#57611yescharacteristic
1372C22C2×#57611yescharacteristic
1373C22#358411yescharacteristic
1374C22#358511yescharacteristic
1375C4—22no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—42no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—42no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4#350611yescharacteristic
1399C4#351311yescharacteristic
1400C4#356011yescharacteristic
1401C4#356211yescharacteristic
1402C2—42no—
1403C2—81no—
1404C2—82no—
1405C2—82no—
1406C2—161no—
1407C2—161no—
1408C2—161no—
1409C2#4301111yescharacteristic
1410C2#6148011yescharacteristic
1411C2#6154711yescharacteristic
1412C2#6163911yescharacteristic
1413C2#6167911yescharacteristic
1414C2#6255811yescharacteristic
1415C2#6259811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45106C2semidirect
2. #42532C2semidirect
3. #32051C2semidirect
4. #31850C2semidirect
5. #31665C2semidirect
6. #31432C2semidirect
7. #31396C2semidirect
8. #31016C2semidirect
9. #30835C2semidirect
10. #30444C2semidirect
11. #29340C2semidirect
12. #29096C2semidirect
13. #29051C2semidirect
14. #28975C2semidirect
15. #27814C2semidirect
16. #27560C2semidirect
17. #27264C2semidirect
18. #26926C2semidirect
19. #26888C2semidirect
20. #26737C2semidirect
21. #26737C2semidirect
22. #26254C2semidirect
23. #25608C2semidirect
24. #24913C2semidirect
25. #24124C2semidirect
26. #23963C2semidirect
27. #23580C2semidirect
28. #23299C2semidirect
29. #23008C2semidirect
30. #22870C2semidirect
31. #22093C2semidirect
33. C2×#540C22semidirect
37. C2×#478C22semidirect
43. C2×C4×D8C22semidirect
58. #2552C22semidirect
62. #2500C22semidirect
67. #2454C22semidirect
69. #2445C22semidirect
83. #2361C22semidirect
84. #2349C22semidirect
87. #2316C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
93. #2086C22semidirect
97. #2073C22semidirect
98. #2071C22semidirect
100. #2059C22semidirect
104. #2054C22semidirect
108. #2041C22semidirect
110. #2034C22semidirect
112. #2033C22semidirect
116. #2023C22semidirect
117. #2023C22semidirect
126. #1999C22semidirect
127. #1999C22semidirect
128. #1991C22semidirect
129. #1991C22semidirect
130. #1990C22semidirect
131. #1987C22semidirect
134. #1970C22semidirect
136. #1961C22semidirect
138. #1949C22semidirect
139. #1943C22semidirect
140. #1942C22semidirect
144. #1936C22semidirect
145. #1936C22semidirect
149. #1934C22semidirect
150. #1926C22semidirect
152. #1925C22semidirect
154. #1924C22semidirect
156. #1923C22semidirect
157. #1921C22semidirect
158. #1921C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
172. #1879C22semidirect
173. #1879C22semidirect
174. #1879C22semidirect
177. #1875C22semidirect
180. #1874C22semidirect
183. #1864C22semidirect
185. #1862C22semidirect
186. #1854C22semidirect
189. #1824C22semidirect
190. #1804C22semidirect
193. #1771C22semidirect
194. C8×C4⋊C4C22semidirect
195. #1762C22semidirect
196. #1762C22semidirect
198. C4×#102C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#451062
#425322
#320512
#318502
#316652
#314322
#313962
#310162
#308352
#304442
#293402
#290962
#290512
#289752
#278142
#275602
#272642
#269262
#268882
#267372
#262542
#256082
#249132
#241242
#239632
#235802
#232992
#230082
#228702
#220932