Finite Group Databasebeta

← #7081679

Subgroups — #7081679

Order 512.

1669 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59094C211yesmaximal, characteristic
2#39476C211yesmaximal, characteristic, complemented
3#32085C211yesmaximal, characteristic, complemented
4#32053C211yesmaximal, characteristic, complemented
5#31908C211yesmaximal, characteristic, complemented
6#31580C211yesmaximal, characteristic, complemented
7#31519C211yesmaximal, characteristic, complemented
8#31287C211yesmaximal, characteristic, complemented
9#30642C211yesmaximal, characteristic, complemented
10#30602C211yesmaximal, characteristic, complemented
11#28943C211yesmaximal, characteristic, complemented
12#28407C211yesmaximal, characteristic, complemented
13#28338C211yesmaximal, characteristic, complemented
14#28065C211yesmaximal, characteristic, complemented
15#27256C211yesmaximal, characteristic, complemented
16#27073C211yesmaximal, characteristic, complemented
17#26536C211yesmaximal, characteristic, complemented
18#26344C211yesmaximal, characteristic, complemented
19#26134C211yesmaximal, characteristic, complemented
20#25961C211yesmaximal, characteristic, complemented
21#25498C211yesmaximal, characteristic, complemented
22#25084C211yesmaximal, characteristic, complemented
23#24904C211yesmaximal, characteristic, complemented
24#24781C211yesmaximal, characteristic, complemented
25#24501C211yesmaximal, characteristic, complemented
26#24426C211yesmaximal, characteristic
27C2×#2093C211yesmaximal, characteristic, complemented
28#23024C211yesmaximal, characteristic, complemented
29#22900C211yesmaximal, characteristic, complemented
30#22414C211yesmaximal, characteristic
31#21860C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic, complemented
40C2×#464C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×C8×D4C2211yescharacteristic
45C2×#431C2211yescharacteristic
46C22×#107C2211yescharacteristic
47C22×#107C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2855C2211yescharacteristic
52#2794—21no—
53#2793—21no—
54#2791—21no—
55#2721—21no—
56#2711—21no—
57#2707—21no—
58#2623—21no—
59#2570C2211yescharacteristic, complemented
60#2565C2211yescharacteristic, complemented
61#2545C2211yescharacteristic
62#2511C2211yescharacteristic, complemented
63#2506C2211yescharacteristic, complemented
64#2499C2211yescharacteristic, complemented
65#2496C2211yescharacteristic, complemented
66#2491C2211yescharacteristic
67#2481—21no—
68#2473—21no—
69#2472—21no—
70#2458—21no—
71#2452C2211yescharacteristic
72#2448C2211yescharacteristic
73#2442C2211yescharacteristic
74#2441C2211yescharacteristic, complemented
75#2437—21no—
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2426—21no—
79#2426C2211yescharacteristic
80#2423C2211yescharacteristic, complemented
81#2417C2211yescharacteristic
82#2417C2211yescharacteristic
83#2411—21no—
84#2367C2211yescharacteristic
85#2360C2211yescharacteristic
86#2360C2211yescharacteristic
87#2352C2211yescharacteristic
88#2342—21no—
89#2341C2211yescharacteristic
90#2313—21no—
91C4×#123C2211yescharacteristic
92C2×#390C2211yescharacteristic
93C2×#384C2211yescharacteristic
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic
103#2093C2211yescharacteristic
104#2086C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2075C2211yescharacteristic, complemented
107#2073C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2068C2211yescharacteristic, complemented
111#2067C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2059C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2043C2211yescharacteristic, complemented
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2036C2211yescharacteristic, complemented
125#2036C2211yescharacteristic, complemented
126#2036C2211yescharacteristic, complemented
127#2033C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2016C2211yescharacteristic, complemented
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2000C2211yescharacteristic
134#1990C2211yescharacteristic, complemented
135#1990C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1969C2211yescharacteristic, complemented
139#1969C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1958C2211yescharacteristic
143#1958C2211yescharacteristic
144#1956C2211yescharacteristic, complemented
145#1956C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1923C2211yescharacteristic, complemented
159#1923C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1877C2211yescharacteristic
171#1875C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic, complemented
185#1853C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#107C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#533—24no—
215#533—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#488—42no—
257#485—42no—
258#479—42no—
259#467—24no—
260#467—42no—
261#467—42no—
262#464—42no—
263#452—42no—
264#450—42no—
265C4×Q16—42no—
266C8×D4—42no—
267#431—42no—
268C2×#107—42no—
269C2×#107—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#416—42no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
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×#102—42no—
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
321C2×#102C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#393—21no—
367#393—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
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#388D411yescharacteristic
407#388D411yescharacteristic
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—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#387D411yescharacteristic
426#387D411yescharacteristic
427#386—21no—
428#386—21no—
429#386—21no—
430#386D411yescharacteristic
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385D411yescharacteristic
440#384—21no—
441#384—21no—
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#381—21no—
449#381D411yescharacteristic
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#126—82no—
565#125—41no—
566#125—41no—
567#125—44no—
568#125—82no—
569#124—22no—
570#124—22no—
571#124—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—82no—
576#123—24no—
577#123—44no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—82no—
589C22⋊Q8#4114yes—
590#121—22no—
591#121—44no—
592#121—41no—
593#120—44no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—44no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—41no—
607#117—44no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—82no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C4×C8—22no—
780C4×C8—41no—
781C4×C8—41no—
782C4×C8—41no—
783C4×C8—41no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836#41—44no—
837#41—82no—
838#41—82no—
839#41—82no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×Q8C2×#4112yes—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
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—44no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D42−1+412yes—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
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—21no—
917C22×C4—41no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4#13514yes—
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2×#4112yes—
947C22×C4H(5,𝔽2)12yes—
948C22×C4C2511yescharacteristic
949Q16—44no—
950Q16—82no—
951SD16—82no—
952SD16—82no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—44no—
976C2×C8—44no—
977C2×C8—82no—
978C2×C8H(5,𝔽2)12yes—
979C2×C8H(5,𝔽2)12yes—
980C4⋊C4—24no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—41no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4C2×#4112yes—
1040C22⋊C4—24no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C42—22no—
1079C42—22no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—42no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23#54612yes—
1131C23C2×#13512yes—
1132C23#57812yes—
1133C23C23×D411yescharacteristic
1134Q8—22no—
1135Q8—22no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—84no—
1147D4—22no—
1148D4—22no—
1149D4—44no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—84no—
1157D4—84no—
1158D4—162no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—28no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—44no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—84no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4#54612yes—
1249C2×C4C2×#13512yes—
1250C2×C4C2×#13512yes—
1251C2×C4#57612yes—
1252C2×C4C22×#4111yescharacteristic
1253C2×C4C2×H(5,𝔽2)11yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×2−1+411yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—22no—
1259C8—22no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—168no—
1294C22#330014yes—
1295C22C2×#54611yescharacteristic
1296C22#348911yescharacteristic
1297C22#349811yescharacteristic
1298C22C22×#13511yescharacteristic
1299C22C2×#57611yescharacteristic
1300C22C2×#57811yescharacteristic
1301C22#358611yescharacteristic
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—41no—
1315C4—41no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4#351311yescharacteristic
1329C4#352011yescharacteristic
1330C4#353411yescharacteristic
1331C4#353611yescharacteristic
1332C2—24no—
1333C2—81no—
1334C2—82no—
1335C2—161no—
1336C2#4402211yescharacteristic
1337C2C2×#330011yescharacteristic
1338C2#6119111yescharacteristic
1339C2#6209711yescharacteristic
1340C2#6220111yescharacteristic
1341C2#6241711yescharacteristic
1342C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39476C2semidirect
3. #32085C2semidirect
4. #32053C2semidirect
5. #31908C2semidirect
6. #31580C2semidirect
7. #31519C2semidirect
8. #31287C2semidirect
9. #30642C2semidirect
10. #30602C2semidirect
11. #28943C2semidirect
12. #28407C2semidirect
13. #28338C2semidirect
14. #28065C2semidirect
15. #27256C2semidirect
16. #27073C2semidirect
17. #26536C2semidirect
18. #26344C2semidirect
19. #26134C2semidirect
20. #25961C2semidirect
21. #25498C2semidirect
22. #25084C2semidirect
23. #24904C2semidirect
24. #24781C2semidirect
25. #24501C2semidirect
27. C2×#2093C2semidirect
28. #23024C2semidirect
29. #22900C2semidirect
31. #21860C2semidirect
35. C2×#485C22semidirect
36. C2×#479C22semidirect
39. C2×#467C22semidirect
43. C2×C4×Q16C22semidirect
59. #2570C22semidirect
60. #2565C22semidirect
62. #2511C22semidirect
63. #2506C22semidirect
64. #2499C22semidirect
65. #2496C22semidirect
74. #2441C22semidirect
80. #2423C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
104. #2086C22semidirect
105. #2085C22semidirect
106. #2075C22semidirect
108. #2068C22semidirect
109. #2068C22semidirect
110. #2068C22semidirect
114. #2059C22semidirect
115. #2057C22semidirect
119. #2043C22semidirect
124. #2036C22semidirect
125. #2036C22semidirect
126. #2036C22semidirect
129. #2024C22semidirect
130. #2016C22semidirect
134. #1990C22semidirect
135. #1990C22semidirect
138. #1969C22semidirect
139. #1969C22semidirect
144. #1956C22semidirect
145. #1956C22semidirect
146. #1949C22semidirect
147. #1942C22semidirect
148. #1942C22semidirect
149. #1939C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
158. #1923C22semidirect
159. #1923C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1916C22semidirect
163. #1916C22semidirect
168. #1878C22semidirect
169. #1878C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
184. #1854C22semidirect
187. #1850C22semidirect
188. #1808C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
193. #1803C22semidirect
197. C4×#107C22semidirect
198. C8×C4⋊C4C22semidirect
201. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#590942
#394762
#320852
#320532
#319082
#315802
#315192
#312872
#306422
#306022
#289432
#284072
#283382
#280652
#272562
#270732
#265362
#263442
#261342
#259612
#254982
#250842
#249042
#247812
#245012
#244262
C2×#20932
#230242
#229002
#224142
#218602