Finite Group Databasebeta

← #7204557

Subgroups — #7204557

Order 512.

1675 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53102C211yesmaximal, characteristic, complemented
2#35763C211yesmaximal, characteristic, complemented
3#33012C211yesmaximal, characteristic, complemented
4#32913C211yesmaximal, characteristic, complemented
5#32782C211yesmaximal, characteristic, complemented
6#32754C211yesmaximal, characteristic, complemented
7#32456C211yesmaximal, characteristic, complemented
8#31961C211yesmaximal, characteristic, complemented
9#31637C211yesmaximal, characteristic, complemented
10#31625C211yesmaximal, characteristic, complemented
11#31063C211yesmaximal, characteristic, complemented
12#31021C211yesmaximal, characteristic, complemented
13#30984C211yesmaximal, characteristic, complemented
14#30605C211yesmaximal, characteristic, complemented
15#30588C211yesmaximal, characteristic, complemented
16#30515C211yesmaximal, characteristic, complemented
17#30420C211yesmaximal, characteristic, complemented
18#30417C211yesmaximal, characteristic, complemented
19#27486C211yesmaximal, characteristic, complemented
20#27211C211yesmaximal, characteristic, complemented
21#27102C211yesmaximal, characteristic, complemented
22#26947C211yesmaximal, characteristic, complemented
23#26230C211yesmaximal, characteristic, complemented
24#26218C211yesmaximal, characteristic, complemented
25#25553C211yesmaximal, characteristic, complemented
26#25224C211yesmaximal, characteristic, complemented
27#25093C211yesmaximal, characteristic, complemented
28#24981C211yesmaximal, characteristic, complemented
29#24882C211yesmaximal, characteristic, complemented
30#23973C211yesmaximal, characteristic, complemented
31#23332C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#520C2211yescharacteristic, complemented
34C2×#485C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#480C2211yescharacteristic, complemented
37C2×#469C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#449C2211yescharacteristic, complemented
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2828—21no—
49#2818—21no—
50#2813—21no—
51#2812—21no—
52#2756—21no—
53#2685—21no—
54#2678—21no—
55#2669—21no—
56#2630—21no—
57#2629C2211yescharacteristic, complemented
58#2624C2211yescharacteristic
59#2619C2211yescharacteristic
60#2579—21no—
61#2565C2211yescharacteristic, complemented
62#2541C2211yescharacteristic
63#2538C2211yescharacteristic
64#2537C2211yescharacteristic
65#2512C2211yescharacteristic
66#2500C2211yescharacteristic
67#2495C2211yescharacteristic
68#2478—21no—
69#2476—21no—
70#2466—21no—
71#2456—21no—
72#2445C2211yescharacteristic
73#2433C2211yescharacteristic
74#2428C2211yescharacteristic
75#2422C2211yescharacteristic
76#2420C2211yescharacteristic, complemented
77#2414C2211yescharacteristic
78#2414C2211yescharacteristic
79#2413—21no—
80#2408C2211yescharacteristic
81#2408C2211yescharacteristic
82#2407C2211yescharacteristic
83#2407C2211yescharacteristic, complemented
84#2392—21no—
85#2392C2211yescharacteristic
86#2362C2211yescharacteristic
87#2360C2211yescharacteristic, complemented
88#2354C2211yescharacteristic, complemented
89#2352C2211yescharacteristic
90D4×C4⋊C4C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic, complemented
127#2033C2211yescharacteristic, complemented
128#2033C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2025C2211yescharacteristic, complemented
132#2014C2211yescharacteristic
133#2011C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic, complemented
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1982C2211yescharacteristic
140#1973C2211yescharacteristic
141#1972C2211yescharacteristic
142#1970C2211yescharacteristic
143#1957C2211yescharacteristic
144#1955C2211yescharacteristic
145#1954C2211yescharacteristic, complemented
146#1947C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1933C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1923C2211yescharacteristic
156#1920C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic, complemented
169#1879C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic, complemented
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1874C2211yescharacteristic
176#1874C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1870C2211yescharacteristic
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic, complemented
189#1836C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1824C2211yescharacteristic, complemented
192#1818C2211yescharacteristic, complemented
193#1809C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1804C2211yescharacteristic, complemented
196#1804C2211yescharacteristic, complemented
197#1798C2211yescharacteristic, complemented
198#1788C2211yescharacteristic, complemented
199#1786C2211yescharacteristic
200C4×#107C2211yescharacteristic, complemented
201#1762C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#553—42no—
214#553—42no—
215C2×#127—21no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242#520—42no—
243#520—42no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4—21no—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264#485—42no—
265#480—42no—
266#480—42no—
267#469—42no—
268#468—42no—
269#468—42no—
270#460—42no—
271#459—42no—
272#450—42no—
273#449—42no—
274#449—42no—
275#449—42no—
276#447—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#418—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398D411yescharacteristic
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396D411yescharacteristic
351#396D411yescharacteristic
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#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394D411yescharacteristic
372#394D411yescharacteristic
373#394D411yescharacteristic
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#392—21no—
386#392—21no—
387#392D411yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#383—21no—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573#127—41no—
574#127—41no—
575#127—41no—
576#127—41no—
577#127—82no—
578#126—44no—
579#126—82no—
580#125—41no—
581#125—41no—
582#123—44no—
583#123—82no—
584#123—82no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589#121—22no—
590#121—22no—
591#121—44no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—82no—
609#121—82no—
610#120—82no—
611#120—82no—
612#120—82no—
613#120—82no—
614C4×Q8—22no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—44no—
631C4×D4—44no—
632C4×D4—44no—
633C4×D4—82no—
634#117—22no—
635#117—41no—
636#117—41no—
637#117—44no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—82no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
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—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—44no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—41no—
750#107—41no—
751#107—41no—
752#107—41no—
753#107—41no—
754#107—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
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—
788#102—41no—
789#102—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800#97—41no—
801C4×C8—41no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—44no—
846#41—44no—
847#41—44no—
848#41—44no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8H(5,𝔽2)12yes—
855C2×D4—22no—
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—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—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—42no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—81no—
897C2×D4—81no—
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—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4H(5,𝔽2)12yes—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—24no—
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—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
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×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
997SD16—82no—
998SD16—82no—
999SD16—82no—
1000D8—82no—
1001D8—82no—
1002D8—82no—
1003M16—82no—
1004M16—82no—
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—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
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—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
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—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4H(5,𝔽2)12yes—
1077C22⋊C4—24no—
1078C22⋊C4—22no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
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—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
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—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—81no—
1144C42—81no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—84no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23C23×D411yescharacteristic
1202Q8—22no—
1203Q8—22no—
1204Q8—41no—
1205Q8—41no—
1206D4—22no—
1207D4—22no—
1208D4—44no—
1209D4—48no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—82no—
1225D4—82no—
1226D4—84no—
1227D4—84no—
1228D4—162no—
1229D4—162no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233D4—162no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238D4—162no—
1239D4—162no—
1240C2×C4—21no—
1241C2×C4—21no—
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—21no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—48no—
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—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—84no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4—162no—
1326C2×C4#57612yes—
1327C2×C4C2×H(5,𝔽2)11yescharacteristic
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4C2×H(5,𝔽2)11yescharacteristic
1330C2×C4#58511yescharacteristic
1331C2×C4#58511yescharacteristic
1332C2×C4#58511yescharacteristic
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—42no—
1360C22—41no—
1361C22—42no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—168no—
1391C22#348411yescharacteristic
1392C22#348511yescharacteristic
1393C22#348811yescharacteristic
1394C22C2×#57611yescharacteristic
1395C22#358511yescharacteristic
1396C22#358511yescharacteristic
1397C22#358611yescharacteristic
1398C4—22no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—42no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—42no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4#352911yescharacteristic
1422C4#353311yescharacteristic
1423C4#353411yescharacteristic
1424C4#354211yescharacteristic
1425C2—81no—
1426C2—81no—
1427C2—81no—
1428C2—82no—
1429C2—161no—
1430C2—161no—
1431C2—161no—
1432C2#4544811yescharacteristic
1433C2#6165611yescharacteristic
1434C2#6167911yescharacteristic
1435C2#6174411yescharacteristic
1436C2#6177811yescharacteristic
1437C2#6203711yescharacteristic
1438C2#6208511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53102C2semidirect
2. #35763C2semidirect
3. #33012C2semidirect
4. #32913C2semidirect
5. #32782C2semidirect
6. #32754C2semidirect
7. #32456C2semidirect
8. #31961C2semidirect
9. #31637C2semidirect
10. #31625C2semidirect
11. #31063C2semidirect
12. #31021C2semidirect
13. #30984C2semidirect
14. #30605C2semidirect
15. #30588C2semidirect
16. #30515C2semidirect
17. #30420C2semidirect
18. #30417C2semidirect
19. #27486C2semidirect
20. #27211C2semidirect
21. #27102C2semidirect
22. #26947C2semidirect
23. #26230C2semidirect
24. #26218C2semidirect
25. #25553C2semidirect
26. #25224C2semidirect
27. #25093C2semidirect
28. #24981C2semidirect
29. #24882C2semidirect
30. #23973C2semidirect
31. #23332C2semidirect
33. C2×#520C22semidirect
34. C2×#485C22semidirect
36. C2×#480C22semidirect
37. C2×#469C22semidirect
44. C2×#449C22semidirect
57. #2629C22semidirect
61. #2565C22semidirect
76. #2420C22semidirect
83. #2407C22semidirect
87. #2360C22semidirect
88. #2354C22semidirect
90. D4×C4⋊C4C22semidirect
91. #2099C22semidirect
92. #2094C22semidirect
94. #2093C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
100. #2083C22semidirect
102. #2076C22semidirect
103. #2075C22semidirect
105. #2072C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
126. #2033C22semidirect
127. #2033C22semidirect
128. #2033C22semidirect
131. #2025C22semidirect
135. #2000C22semidirect
145. #1954C22semidirect
146. #1947C22semidirect
147. #1947C22semidirect
148. #1933C22semidirect
149. #1927C22semidirect
153. #1925C22semidirect
154. #1924C22semidirect
156. #1920C22semidirect
157. #1917C22semidirect
158. #1916C22semidirect
164. #1880C22semidirect
168. #1879C22semidirect
169. #1879C22semidirect
170. #1877C22semidirect
172. #1875C22semidirect
176. #1874C22semidirect
180. #1870C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
186. #1854C22semidirect
188. #1851C22semidirect
189. #1836C22semidirect
191. #1824C22semidirect
192. #1818C22semidirect
194. #1805C22semidirect
195. #1804C22semidirect
196. #1804C22semidirect
197. #1798C22semidirect
198. #1788C22semidirect
200. C4×#107C22semidirect
201. #1762C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#531022
#357632
#330122
#329132
#327822
#327542
#324562
#319612
#316372
#316252
#310632
#310212
#309842
#306052
#305882
#305152
#304202
#304172
#274862
#272112
#271022
#269472
#262302
#262182
#255532
#252242
#250932
#249812
#248822
#239732
#233322