Finite Group Databasebeta

← #6720339

Subgroups — #6720339

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42942C211yesmaximal, characteristic
2#35688C211yesmaximal, characteristic, complemented
3#32987C211yesmaximal, characteristic, complemented
4#31999C211yesmaximal, characteristic, complemented
5#31938C211yesmaximal, characteristic, complemented
6#31861C211yesmaximal, characteristic, complemented
7#31676C211yesmaximal, characteristic, complemented
8#31390C211yesmaximal, characteristic, complemented
9#31374C211yesmaximal, characteristic, complemented
10#31134C211yesmaximal, characteristic, complemented
11#31024C211yesmaximal, characteristic, complemented
12#29741C211yesmaximal, characteristic, complemented
13#29608C211yesmaximal, characteristic, complemented
14#27703C211yesmaximal, characteristic, complemented
15#27397C211yesmaximal, characteristic, complemented
16#27174C211yesmaximal, characteristic, complemented
17#26681C211yesmaximal, characteristic, complemented
18#26638C211yesmaximal, characteristic, complemented
19#25951C211yesmaximal, characteristic, complemented
20#25242C211yesmaximal, characteristic, complemented
21#25210C211yesmaximal, characteristic, complemented
22#24975C211yesmaximal, characteristic, complemented
23#24937C211yesmaximal, characteristic, complemented
24#24869C211yesmaximal, characteristic, complemented
25#24436C211yesmaximal, characteristic, complemented
26#24134C211yesmaximal, characteristic, complemented
27#23969C211yesmaximal, characteristic, complemented
28#22867C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic, complemented
30#22037C211yesmaximal, characteristic, complemented
31#20915C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#537C2211yescharacteristic
35C2×#520C2211yescharacteristic, complemented
36C2×#484C2211yescharacteristic, complemented
37C2×#481C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#475C2211yescharacteristic, complemented
40C2×#465C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C2×#408C2211yescharacteristic, complemented
49#2814—21no—
50#2699—21no—
51#2699—21no—
52#2678—21no—
53#2678—21no—
54#2661—21no—
55#2638—21no—
56#2617—21no—
57#2616C2211yescharacteristic, complemented
58#2615C2211yescharacteristic
59#2600—21no—
60#2561—21no—
61#2536C2211yescharacteristic
62#2536C2211yescharacteristic
63#2504C2211yescharacteristic
64#2499C2211yescharacteristic, complemented
65#2486C2211yescharacteristic
66#2485C2211yescharacteristic
67#2465—21no—
68#2463—21no—
69#2462—21no—
70#2460—21no—
71#2440C2211yescharacteristic, complemented
72#2439C2211yescharacteristic, complemented
73#2426C2211yescharacteristic
74#2426C2211yescharacteristic
75#2420C2211yescharacteristic
76#2420C2211yescharacteristic
77#2417C2211yescharacteristic
78#2415—21no—
79#2415C2211yescharacteristic
80#2408C2211yescharacteristic
81#2408C2211yescharacteristic
82#2392—21no—
83#2388C2211yescharacteristic
84#2362C2211yescharacteristic, complemented
85#2360C2211yescharacteristic, complemented
86#2352C2211yescharacteristic
87D4×C4⋊C4C2211yescharacteristic
88#2344C2211yescharacteristic, complemented
89#2341C2211yescharacteristic
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2055C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic, complemented
111#2036C2211yescharacteristic, complemented
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic, complemented
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2015C2211yescharacteristic
123#2001C2211yescharacteristic
124#2001C2211yescharacteristic, complemented
125#2001C2211yescharacteristic, complemented
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1968C2211yescharacteristic
133#1959C2211yescharacteristic
134#1955C2211yescharacteristic
135#1954C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic, complemented
141#1934C2211yescharacteristic
142#1926C2211yescharacteristic
143#1925C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1924C2211yescharacteristic, complemented
146#1924C2211yescharacteristic, complemented
147#1923C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1895C2211yescharacteristic
151#1894C2211yescharacteristic, complemented
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1878C2211yescharacteristic, complemented
157#1877C2211yescharacteristic
158#1875C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic, complemented
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic, complemented
170#1872C2211yescharacteristic, complemented
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
182#1853C2211yescharacteristic, complemented
183#1850C2211yescharacteristic, complemented
184#1835C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1823C2211yescharacteristic, complemented
188#1823C2211yescharacteristic, complemented
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1780C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#554—42no—
213#554—42no—
214#546—24no—
215#546—42no—
216#537—24no—
217#537—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125—21no—
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×#120—21no—
246#520—42no—
247#520—42no—
248C2×C4×Q8—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C22⋊C4—21no—
271#484—42no—
272#482—42no—
273#481—42no—
274#475—42no—
275#465—42no—
276#452—24no—
277#450—42no—
278#441—42no—
279#435—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292#417—42no—
293#416—42no—
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#102—42no—
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×#102C2311yescharacteristic
321#408—42no—
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×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#395—21no—
357#395—21no—
358#395D411yescharacteristic
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#394—21no—
372#394D411yescharacteristic
373#394D411yescharacteristic
374#394D411yescharacteristic
375#393—21no—
376#393—21no—
377#393D411yescharacteristic
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392D411yescharacteristic
384#392D411yescharacteristic
385#392D411yescharacteristic
386#391—21no—
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#389—21no—
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#381—21no—
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41#4114yes—
512C22×Q8—21no—
513C22×Q8C2×D411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2×D411yescharacteristic
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×M16—22no—
558C2×M16—41no—
559C2×M16—41no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576#125—44no—
577#124—22no—
578#124—41no—
579#123—44no—
580#123—82no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—44no—
596C22⋊Q8—44no—
597C22⋊Q8—44no—
598C22⋊Q8—82no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—44no—
604#121—41no—
605#121—41no—
606#121—44no—
607#121—44no—
608#121—44no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#120—44no—
614#120—82no—
615#120—82no—
616C4×Q8—22no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—44no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—44no—
632C4×D4—44no—
633C4×D4—44no—
634C4×D4—44no—
635C4×D4—82no—
636#117—22no—
637#117—22no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
642#117—82no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
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—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107—41no—
753#107—41no—
754#107—41no—
755#106—22no—
756#106—22no—
757#106—41no—
758#106—41no—
759#106—41no—
760#106—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
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—22no—
791C22⋊C8—22no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803#97—41no—
804#97—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#95—21no—
832#95—21no—
833#95—21no—
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—21no—
841C24—21no—
842C24—42no—
843C24—42no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852C24C22×D411yescharacteristic
853#41—44no—
854#41—44no—
855#41—44no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—82no—
860#41—82no—
861C2×Q8—22no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—41no—
874C2×Q8—41no—
875C2×Q8—42no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8C2×#4112yes—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—24no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—42no—
910C2×D4—44no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—82no—
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×D4C2×#4112yes—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—24no—
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—24no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C2×#4112yes—
1002C22×C4H(5,𝔽2)12yes—
1003C22×C4C2511yescharacteristic
1004Q16—44no—
1005SD16—82no—
1006SD16—82no—
1007M16—82no—
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—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—82no—
1033C2×C8—82no—
1034C4⋊C4—24no—
1035C4⋊C4—22no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4H(5,𝔽2)12yes—
1084C4⋊C4H(5,𝔽2)12yes—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
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—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—42no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
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—21no—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
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—84no—
1188C23—84no—
1189C23—162no—
1190C23—162no—
1191C23—162no—
1192C23—162no—
1193C23—162no—
1194C23#54612yes—
1195C23#57712yes—
1196C23C23×D411yescharacteristic
1197Q8—22no—
1198Q8—22no—
1199Q8—44no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—162no—
1207D4—22no—
1208D4—22no—
1209D4—44no—
1210D4—44no—
1211D4—44no—
1212D4—44no—
1213D4—44no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—82no—
1221D4—84no—
1222D4—84no—
1223D4—162no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
1227D4—162no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
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—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—84no—
1316C2×C4—84no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4#54612yes—
1323C2×C4C22×#4111yescharacteristic
1324C2×C4C2×H(5,𝔽2)11yescharacteristic
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4C2×H(5,𝔽2)11yescharacteristic
1327C2×C4#58511yescharacteristic
1328C2×C4#58511yescharacteristic
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—42no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—168no—
1380C22C2×#54611yescharacteristic
1381C22#348411yescharacteristic
1382C22#348511yescharacteristic
1383C22C2×#57711yescharacteristic
1384C22#358411yescharacteristic
1385C22#358511yescharacteristic
1386C22#358611yescharacteristic
1387C4—22no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—42no—
1396C4—41no—
1397C4—41no—
1398C4—42no—
1399C4—42no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4#345911yescharacteristic
1412C4#350511yescharacteristic
1413C4#354211yescharacteristic
1414C4#354211yescharacteristic
1415C2—42no—
1416C2—42no—
1417C2—81no—
1418C2—81no—
1419C2—82no—
1420C2—161no—
1421C2#3777611yescharacteristic
1422C2#6119211yescharacteristic
1423C2#6120711yescharacteristic
1424C2#6161111yescharacteristic
1425C2#6167811yescharacteristic
1426C2#6177011yescharacteristic
1427C2#6179911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42942C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35688C2semidirect
3. #32987C2semidirect
4. #31999C2semidirect
5. #31938C2semidirect
6. #31861C2semidirect
7. #31676C2semidirect
8. #31390C2semidirect
9. #31374C2semidirect
10. #31134C2semidirect
11. #31024C2semidirect
12. #29741C2semidirect
13. #29608C2semidirect
14. #27703C2semidirect
15. #27397C2semidirect
16. #27174C2semidirect
17. #26681C2semidirect
18. #26638C2semidirect
19. #25951C2semidirect
20. #25242C2semidirect
21. #25210C2semidirect
22. #24975C2semidirect
23. #24937C2semidirect
24. #24869C2semidirect
25. #24436C2semidirect
26. #24134C2semidirect
27. #23969C2semidirect
28. #22867C2semidirect
29. #22419C2semidirect
30. #22037C2semidirect
31. #20915C2semidirect
35. C2×#520C22semidirect
36. C2×#484C22semidirect
39. C2×#475C22semidirect
43. C2×#441C22semidirect
48. C2×#408C22semidirect
57. #2616C22semidirect
64. #2499C22semidirect
71. #2440C22semidirect
72. #2439C22semidirect
84. #2362C22semidirect
85. #2360C22semidirect
88. #2344C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
94. #2087C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
102. #2074C22semidirect
104. #2068C22semidirect
110. #2036C22semidirect
111. #2036C22semidirect
114. #2035C22semidirect
115. #2035C22semidirect
124. #2001C22semidirect
125. #2001C22semidirect
130. #1993C22semidirect
136. #1949C22semidirect
137. #1944C22semidirect
140. #1935C22semidirect
144. #1924C22semidirect
145. #1924C22semidirect
146. #1924C22semidirect
147. #1923C22semidirect
148. #1919C22semidirect
149. #1919C22semidirect
151. #1894C22semidirect
156. #1878C22semidirect
166. #1873C22semidirect
167. #1873C22semidirect
169. #1872C22semidirect
170. #1872C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
177. #1863C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
181. #1853C22semidirect
182. #1853C22semidirect
183. #1850C22semidirect
184. #1835C22semidirect
185. #1825C22semidirect
187. #1823C22semidirect
188. #1823C22semidirect
190. #1807C22semidirect
191. #1805C22semidirect
192. #1805C22semidirect
197. #1780C22semidirect
199. C4×#103C22semidirect
200. #1753C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#429422
#356882
#329872
#319992
#319382
#318612
#316762
#313902
#313742
#311342
#310242
#297412
#296082
#277032
#273972
#271742
#266812
#266382
#259512
#252422
#252102
#249752
#249372
#248692
#244362
#241342
#239692
#228672
#224192
#220372
#209152