Finite Group Databasebeta

← #7548948

Subgroups — #7548948

Order 512.

1813 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59019C211yesmaximal, characteristic, complemented
2#36235C211yesmaximal, characteristic, complemented
3#32061C211yesmaximal, characteristic, complemented
4#32023C211yesmaximal, characteristic, complemented
5#31959C211yesmaximal, characteristic, complemented
6#31780C211yesmaximal, characteristic, complemented
7#28774C211yesmaximal, characteristic, complemented
8#27720C211yesmaximal, characteristic, complemented
9#27357C211yesmaximal, characteristic, complemented
10#27168C211yesmaximal, characteristic, complemented
11#26421C211yesmaximal, characteristic, complemented
12#26355C211yesmaximal, characteristic, complemented
13#26199C211yesmaximal, characteristic, complemented
14#26156C211yesmaximal, characteristic, complemented
15#25959C211yesmaximal, characteristic, complemented
16#25560C211yesmaximal, characteristic, complemented
17#25554C211yesmaximal, characteristic, complemented
18#25218C211yesmaximal, characteristic, complemented
19#25125C211yesmaximal, characteristic, complemented
20#24870C211yesmaximal, characteristic, complemented
21#24792C211yesmaximal, characteristic, complemented
22#24555C211yesmaximal, characteristic, complemented
23#24388C211yesmaximal, characteristic, complemented
24#24121C211yesmaximal, characteristic, complemented
25#23034C211yesmaximal, characteristic, complemented
26#22877C211yesmaximal, characteristic, complemented
27#22848C211yesmaximal, characteristic, complemented
28#22712C211yesmaximal, characteristic, complemented
29#22499C211yesmaximal, characteristic, complemented
30#20908C211yesmaximal, characteristic, complemented
31#20845C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#477C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#469C2211yescharacteristic, complemented
41C2×#468C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#436C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C2×#416C2211yescharacteristic
50C2×#407C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52#2850—21no—
53#2847C2211yescharacteristic
54#2685—21no—
55#2678—21no—
56#2610—21no—
57#2609—21no—
58#2558—21no—
59#2538C2211yescharacteristic
60#2500C2211yescharacteristic
61#2500C2211yescharacteristic
62#2490C2211yescharacteristic
63#2485C2211yescharacteristic
64#2476—21no—
65#2474—21no—
66#2472—21no—
67#2471—21no—
68#2466—21no—
69#2460—21no—
70#2457—21no—
71#2441C2211yescharacteristic
72#2440C2211yescharacteristic
73#2439C2211yescharacteristic
74#2424—21no—
75#2421C2211yescharacteristic
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2414C2211yescharacteristic
79#2414C2211yescharacteristic
80#2407C2211yescharacteristic
81#2363—21no—
82#2363C2211yescharacteristic
83#2362C2211yescharacteristic
84#2361C2211yescharacteristic
85#2354C2211yescharacteristic
86#2352C2211yescharacteristic
87#2352C2211yescharacteristic
88#2346C2211yescharacteristic
89#2341C2211yescharacteristic
90C4×#120C2211yescharacteristic
91#2290—21no—
92#2280C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2054C2211yescharacteristic, complemented
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic, complemented
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic, complemented
119#2033C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic, complemented
124#1999C2211yescharacteristic
125#1991C2211yescharacteristic, complemented
126#1990C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1973C2211yescharacteristic, complemented
129#1970C2211yescharacteristic, complemented
130#1954C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1947C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1928C2211yescharacteristic, complemented
138#1926C2211yescharacteristic, complemented
139#1926C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1924C2211yescharacteristic
142#1923C2211yescharacteristic
143#1918C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1895C2211yescharacteristic
146#1894C2211yescharacteristic
147#1894C2211yescharacteristic, complemented
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1880C2211yescharacteristic, complemented
151#1879C2211yescharacteristic, complemented
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1874C2211yescharacteristic
157#1874C2211yescharacteristic
158#1874C2211yescharacteristic, complemented
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic, complemented
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1870C2211yescharacteristic
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1836C2211yescharacteristic, complemented
186#1825C2211yescharacteristic
187#1824C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196#1753C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—42no—
213#555—42no—
214#552—24no—
215#552—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222#525—24no—
223#525—42no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120D411yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117—21no—
255C2×#117—21no—
256C2×#117—42no—
257C2×#117—42no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C22⋊C4—21no—
270C22×C42—21no—
271#482—42no—
272#482—42no—
273#477—42no—
274#469—42no—
275#469—42no—
276#468—24no—
277#449—24no—
278C4×SD16—42no—
279#436—42no—
280#435—24no—
281#428—42no—
282#428—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300#416—42no—
301#416—42no—
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322#407—24no—
323C2×C22⋊C8—42no—
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#399—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—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#394—21no—
361#394—21no—
362#393—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#391—21no—
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
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#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—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#386—21no—
424#386—21no—
425#386D411yescharacteristic
426#386D411yescharacteristic
427#386D411yescharacteristic
428#385—21no—
429#385—21no—
430#385—21no—
431#385D411yescharacteristic
432#385D411yescharacteristic
433#385D411yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379D411yescharacteristic
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#376—21no—
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#340C2311yescharacteristic
495#340C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25C2×D411yescharacteristic
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573#126—44no—
574#125—22no—
575#125—41no—
576#125—44no—
577#124—44no—
578#124—44no—
579#123—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—82no—
587C22⋊Q8#4114yes—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—44no—
602#121—41no—
603#121—41no—
604#121—82no—
605#120—42no—
606#120—44no—
607#120—82no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—44no—
621C4×D4—44no—
622C4×D4—44no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—22no—
631#117—44no—
632#117—44no—
633#117—44no—
634#117—44no—
635#117—41no—
636#117—41no—
637#117—41no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
642#117—41no—
643C2×C4⋊C4—21no—
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—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
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⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—44no—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—22no—
757#107—22no—
758#107—41no—
759#107—41no—
760#107—41no—
761#107—41no—
762#106—22no—
763#106—22no—
764#106—41no—
765#106—41no—
766#106—41no—
767#106—41no—
768#106—41no—
769C4⋊C8—22no—
770C4⋊C8—41no—
771C4⋊C8—41no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—41no—
777#103—41no—
778#103—41no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8#4114yes—
803#97—22no—
804C4×C8—41no—
805C4×C8—41no—
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—22no—
838C24—22no—
839C24—21no—
840C24—21no—
841C24—41no—
842C24—41no—
843C24—41no—
844C24—41no—
845C24—41no—
846C24C22×D411yescharacteristic
847C24C22×D411yescharacteristic
848C24C22×D411yescharacteristic
849C24C22×D411yescharacteristic
850#41—44no—
851#41—44no—
852#41—82no—
853#41—82no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—42no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8C2×#4112yes—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
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—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
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—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—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
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—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—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
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—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
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×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C2×#4112yes—
981C22×C4C2×#4112yes—
982C22×C4H(5,𝔽2)12yes—
983C22×C42−1+412yes—
984C22×C4C2511yescharacteristic
985SD16—44no—
986D8—82no—
987M16—44no—
988M16—44no—
989M16—82no—
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—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—82no—
1013C2×C8—82no—
1014C2×C8C2×#4112yes—
1015C2×C8C2×#4112yes—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
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—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—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4C2×#4112yes—
1064C4⋊C4H(5,𝔽2)12yes—
1065C4⋊C4H(5,𝔽2)12yes—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
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—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—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C42—24no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C23—21no—
1137C23—21no—
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—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—44no—
1163C23—44no—
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—
1178C23—82no—
1179C23—82no—
1180C23—82no—
1181C23—82no—
1182C23—82no—
1183C23#54612yes—
1184C23#54712yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—41no—
1189Q8—41no—
1190Q8—162no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—82no—
1200D4—82no—
1201D4—82no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—162no—
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—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—44no—
1250C2×C4—44no—
1251C2×C4—44no—
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—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4#54612yes—
1304C2×C4#54712yes—
1305C2×C4#57512yes—
1306C2×C4C22×#4111yescharacteristic
1307C2×C4C22×#4111yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4C2×2−1+411yescharacteristic
1312C8—22no—
1313C8—22no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—88no—
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—
1363C22C2×#54611yescharacteristic
1364C22C2×#54711yescharacteristic
1365C22#348411yescharacteristic
1366C22C2×#57511yescharacteristic
1367C22#358411yescharacteristic
1368C22#358411yescharacteristic
1369C22#358511yescharacteristic
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—41no—
1374C4—41no—
1375C4—42no—
1376C4—41no—
1377C4—42no—
1378C4—41no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—42no—
1383C4—41no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4#348111yescharacteristic
1395C4#351911yescharacteristic
1396C4#352011yescharacteristic
1397C4#353611yescharacteristic
1398C2—42no—
1399C2—42no—
1400C2—81no—
1401C2—81no—
1402C2—161no—
1403C2—161no—
1404C2#5909011yescharacteristic
1405C2#6116611yescharacteristic
1406C2#6117011yescharacteristic
1407C2#6125111yescharacteristic
1408C2#6127611yescharacteristic
1409C2#6160611yescharacteristic
1410C2#6162811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59019C2semidirect
2. #36235C2semidirect
3. #32061C2semidirect
4. #32023C2semidirect
5. #31959C2semidirect
6. #31780C2semidirect
7. #28774C2semidirect
8. #27720C2semidirect
9. #27357C2semidirect
10. #27168C2semidirect
11. #26421C2semidirect
12. #26355C2semidirect
13. #26199C2semidirect
14. #26156C2semidirect
15. #25959C2semidirect
16. #25560C2semidirect
17. #25554C2semidirect
18. #25218C2semidirect
19. #25125C2semidirect
20. #24870C2semidirect
21. #24792C2semidirect
22. #24555C2semidirect
23. #24388C2semidirect
24. #24121C2semidirect
25. #23034C2semidirect
26. #22877C2semidirect
27. #22848C2semidirect
28. #22712C2semidirect
29. #22499C2semidirect
30. #20908C2semidirect
31. #20845C2semidirect
37. C2×#482C22semidirect
38. C2×#477C22semidirect
40. C2×#469C22semidirect
43. C2×C4×SD16C22semidirect
93. #2101C22semidirect
94. #2100C22semidirect
95. #2096C22semidirect
96. #2092C22semidirect
97. #2088C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
101. #2077C22semidirect
103. #2073C22semidirect
104. #2071C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2066C22semidirect
108. #2065C22semidirect
109. #2059C22semidirect
110. #2058C22semidirect
111. #2054C22semidirect
113. #2035C22semidirect
115. #2034C22semidirect
118. #2033C22semidirect
119. #2033C22semidirect
120. #2025C22semidirect
121. #2023C22semidirect
123. #2000C22semidirect
125. #1991C22semidirect
126. #1990C22semidirect
127. #1989C22semidirect
128. #1973C22semidirect
129. #1970C22semidirect
131. #1949C22semidirect
132. #1947C22semidirect
133. #1942C22semidirect
134. #1941C22semidirect
135. #1936C22semidirect
136. #1934C22semidirect
137. #1928C22semidirect
138. #1926C22semidirect
139. #1926C22semidirect
140. #1926C22semidirect
143. #1918C22semidirect
144. #1918C22semidirect
147. #1894C22semidirect
150. #1880C22semidirect
151. #1879C22semidirect
158. #1874C22semidirect
161. #1873C22semidirect
167. #1865C22semidirect
168. #1863C22semidirect
169. #1863C22semidirect
170. #1862C22semidirect
181. #1854C22semidirect
182. #1852C22semidirect
185. #1836C22semidirect
187. #1824C22semidirect
188. #1809C22semidirect
191. #1805C22semidirect
192. #1802C22semidirect
194. #1776C22semidirect
195. C4×#103C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#590192
#362352
#320612
#320232
#319592
#317802
#287742
#277202
#273572
#271682
#264212
#263552
#261992
#261562
#259592
#255602
#255542
#252182
#251252
#248702
#247922
#245552
#243882
#241212
#230342
#228772
#228482
#227122
#224992
#209082
#208452