Finite Group Databasebeta

← #7065192

Subgroups — #7065192

Order 512.

1883 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3314C211yesmaximal, characteristic
2C2×#3258C211yesmaximal, characteristic, complemented
3#45177C211yesmaximal, characteristic, complemented
4#45108C211yesmaximal, characteristic
5#31252C211yesmaximal, characteristic, complemented
6#31215C211yesmaximal, characteristic, complemented
7#31146C211yesmaximal, characteristic, complemented
8#30996C211yesmaximal, characteristic, complemented
9#30901C211yesmaximal, characteristic, complemented
10#30853C211yesmaximal, characteristic, complemented
11#30831C211yesmaximal, characteristic, complemented
12#30668C211yesmaximal, characteristic, complemented
13#28356C211yesmaximal, characteristic, complemented
14#26790C211yesmaximal, characteristic, complemented
15#26610C211yesmaximal, characteristic, complemented
16#26471C211yesmaximal, characteristic, complemented
17#26385C211yesmaximal, characteristic, complemented
18#25960C211yesmaximal, characteristic, complemented
19#25545C211yesmaximal, characteristic, complemented
20#25212C211yesmaximal, characteristic, complemented
21#25176C211yesmaximal, characteristic, complemented
22#25084C211yesmaximal, characteristic, complemented
23#25079C211yesmaximal, characteristic, complemented
24#24791C211yesmaximal, characteristic, complemented
25#24743C211yesmaximal, characteristic, complemented
26#24436C211yesmaximal, characteristic
27#24073C211yesmaximal, characteristic, complemented
28#23944C211yesmaximal, characteristic, complemented
29#23616C211yesmaximal, characteristic, complemented
30#23040C211yesmaximal, characteristic, complemented
31#22072C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#541C2211yescharacteristic, complemented
36#3314—28no—
37#3258—28no—
38C2×#489C2211yescharacteristic
39C2×#484C2211yescharacteristic
40C2×#484C2211yescharacteristic, complemented
41C2×#480C2211yescharacteristic
42C2×#479C2211yescharacteristic, complemented
43C2×#477C2211yescharacteristic, complemented
44C2×#475C2211yescharacteristic, complemented
45C2×#478C2211yescharacteristic
46C2×#474C2211yescharacteristic
47C2×#470C2211yescharacteristic, complemented
48C2×#468C2211yescharacteristic
49C2×#467C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#467C2211yescharacteristic, complemented
52C2×#465C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#462C2211yescharacteristic, complemented
57C2×#462C2211yescharacteristic, complemented
58C2×#461C2211yescharacteristic
59C2×#452C2211yescharacteristic
60C2×#452C2211yescharacteristic
61C2×#450C2211yescharacteristic
62C2×#450C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×#435C2211yescharacteristic
66C2×#428C2211yescharacteristic, complemented
67C2×#424C2211yescharacteristic, complemented
68C2×#417C2211yescharacteristic
69C2×#416C2211yescharacteristic
70C22×#102C2211yescharacteristic
71#2720—21no—
72#2719—21no—
73#2708—21no—
74#2698—21no—
75#2695—21no—
76#2689—21no—
77#2687—21no—
78#2684—21no—
79#2550C2211yescharacteristic, complemented
80#2547C2211yescharacteristic
81#2534—21no—
82#2506—21no—
83#2503C2211yescharacteristic, complemented
84#2492C2211yescharacteristic
85#2489—21no—
86#2480—21no—
87#2468—21no—
88#2466—21no—
89#2452C2211yescharacteristic
90#2451C2211yescharacteristic, complemented
91#2447C2211yescharacteristic
92#2446C2211yescharacteristic, complemented
93#2442C2211yescharacteristic
94#2437—21no—
95#2435C2211yescharacteristic
96#2432C2211yescharacteristic
97#2429C2211yescharacteristic
98#2429C2211yescharacteristic
99#2427—21no—
100#2421C2211yescharacteristic
101#2417C2211yescharacteristic
102#2415C2211yescharacteristic
103#2395C2211yescharacteristic
104#2367C2211yescharacteristic
105#2362C2211yescharacteristic, complemented
106#2361C2211yescharacteristic
107#2360C2211yescharacteristic
108#2351C2211yescharacteristic, complemented
109D4×C22⋊C4C2211yescharacteristic
110#2317C2211yescharacteristic, complemented
111#2311C2211yescharacteristic
112#2097C2211yescharacteristic, complemented
113#2092C2211yescharacteristic
114#2085C2211yescharacteristic, complemented
115#2073C2211yescharacteristic
116#2068C2211yescharacteristic, complemented
117#2068C2211yescharacteristic, complemented
118#2068C2211yescharacteristic, complemented
119#2068C2211yescharacteristic, complemented
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2066C2211yescharacteristic, complemented
124#2066C2211yescharacteristic, complemented
125#2066C2211yescharacteristic, complemented
126#2065C2211yescharacteristic
127#2065C2211yescharacteristic
128#2057C2211yescharacteristic, complemented
129#2057C2211yescharacteristic, complemented
130#2057C2211yescharacteristic, complemented
131#2056C2211yescharacteristic, complemented
132#2055C2211yescharacteristic
133#2043C2211yescharacteristic, complemented
134#2042C2211yescharacteristic
135#2042C2211yescharacteristic
136#2042C2211yescharacteristic
137#2036C2211yescharacteristic
138#2036C2211yescharacteristic
139#2035C2211yescharacteristic
140#2035C2211yescharacteristic
141#2026C2211yescharacteristic, complemented
142#2025C2211yescharacteristic
143#2024C2211yescharacteristic, complemented
144#2016C2211yescharacteristic, complemented
145#2016C2211yescharacteristic, complemented
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2013C2211yescharacteristic
150#2001C2211yescharacteristic
151#2001C2211yescharacteristic
152#1983C2211yescharacteristic
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic, complemented
155#1969C2211yescharacteristic, complemented
156#1968C2211yescharacteristic
157#1960C2211yescharacteristic, complemented
158#1958C2211yescharacteristic
159#1949C2211yescharacteristic, complemented
160#1943C2211yescharacteristic, complemented
161#1943C2211yescharacteristic, complemented
162#1940C2211yescharacteristic, complemented
163#1939C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1927C2211yescharacteristic, complemented
167#1925C2211yescharacteristic
168#1924C2211yescharacteristic
169#1923C2211yescharacteristic
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1875C2211yescharacteristic
181#1873C2211yescharacteristic, complemented
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic, complemented
184#1872C2211yescharacteristic, complemented
185#1869C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1863C2211yescharacteristic, complemented
190#1863C2211yescharacteristic, complemented
191#1863C2211yescharacteristic, complemented
192#1862C2211yescharacteristic
193#1862C2211yescharacteristic
194#1852C2211yescharacteristic
195#1850C2211yescharacteristic
196#1850C2211yescharacteristic
197#1850C2211yescharacteristic, complemented
198#1818C2211yescharacteristic, complemented
199#1807C2211yescharacteristic
200#1804C2211yescharacteristic
201#1786C2211yescharacteristic
202C4×#107C2211yescharacteristic, complemented
203#1753C2211yescharacteristic, complemented
204C2×#340C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#554—24no—
219#554—42no—
220#546—24no—
221#546—42no—
222#542—24no—
223#542—42no—
224#541—24no—
225#541—42no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×#126—21no—
231C2×#126—21no—
232C2×#126—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#124—21no—
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×#121—21no—
255C2×#121C2311yescharacteristic
256C2×#120—21no—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C22⋊C4—21no—
274C22×C22⋊C4—21no—
275#489—24no—
276#484—24no—
277#484—42no—
278#480—24no—
279#479—24no—
280#478—24no—
281#477—24no—
282#475—24no—
283#474—24no—
284#470—24no—
285#468D418yes—
286#467—24no—
287#467—24no—
288#467—42no—
289#465—24no—
290#464—24no—
291#464—24no—
292#464—24no—
293#462—24no—
294#462—42no—
295#461—24no—
296#452—24no—
297#452—42no—
298#450—24no—
299#450—42no—
300#440—24no—
301#440—42no—
302#435—24no—
303#428—42no—
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316#424—24no—
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324#417—24no—
325#416—42no—
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#102—24no—
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×C22⋊C8C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×#97C2311yescharacteristic
366C2×C4×C8C2311yescharacteristic
367#400—21no—
368#400—21no—
369#400—21no—
370#400—21no—
371#400—21no—
372#400—21no—
373#400D411yescharacteristic
374#399D411yescharacteristic
375#398—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#398—21no—
381#398—21no—
382#398D411yescharacteristic
383#397—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#397—21no—
389#397D411yescharacteristic
390#397D411yescharacteristic
391#397D411yescharacteristic
392#396—21no—
393#396—21no—
394#396—21no—
395#396—21no—
396#395—21no—
397#395—21no—
398#394—21no—
399#394—21no—
400#394—21no—
401#394—21no—
402#394—21no—
403#394D411yescharacteristic
404#394D411yescharacteristic
405#393—21no—
406#393—21no—
407#391—21no—
408#391—21no—
409#391—21no—
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#386—21no—
454#386—21no—
455#386—21no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#385—21no—
469#384—21no—
470#382—21no—
471#382—21no—
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381—21no—
475#381—21no—
476#381—21no—
477#380—21no—
478#380—21no—
479#380—21no—
480#380—21no—
481#380—21no—
482#380—21no—
483#380C2311yescharacteristic
484#380C2311yescharacteristic
485#379—21no—
486#379—21no—
487#379—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4—21no—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C22⋊C4—21no—
495C4×C22⋊C4—21no—
496C4×C22⋊C4C2311yescharacteristic
497C4×C22⋊C4C2311yescharacteristic
498C4×C22⋊C4C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C25—21no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4C2×D411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16C2×D414yes—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16C2×D414yes—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C4⋊Q8—22no—
597C4⋊Q8—22no—
598C4⋊Q8—22no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601C4⋊Q8—41no—
602C4⋊Q8—41no—
603C4⋊Q8—41no—
604#126—44no—
605#126—44no—
606#126—44no—
607#125—22no—
608#125—41no—
609#125—44no—
610#125—44no—
611#125—44no—
612#124—22no—
613#124—22no—
614#124—22no—
615#124—41no—
616#124—41no—
617#124—41no—
618#124—44no—
619#123—44no—
620#123—44no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—44no—
630C22⋊Q8—44no—
631C22⋊Q8—44no—
632C22⋊Q8—41no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—82no—
638C22⋊Q8C2×D414yes—
639#121—22no—
640#121—44no—
641#121C2×D414yes—
642#120—44no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—22no—
647C4×Q8—22no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—44no—
662C4×D4—82no—
663#117—22no—
664#117—22no—
665#117—22no—
666#117—41no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—41no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
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—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—44no—
750C2×C22⋊C4—82no—
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774#107—22no—
775#107—22no—
776#107—22no—
777#107—22no—
778#107—22no—
779#107—41no—
780#107—41no—
781#107C2×D414yes—
782#106—22no—
783#106—22no—
784#106—41no—
785#106—41no—
786C4⋊C8—22no—
787C4⋊C8—22no—
788C4⋊C8—22no—
789C4⋊C8—22no—
790C4⋊C8—22no—
791C4⋊C8—41no—
792C4⋊C8—41no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—41no—
804#103—41no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#103—41no—
811#103—41no—
812#103C2×D414yes—
813#102—22no—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—41no—
822#102—41no—
823#102—41no—
824#102C2×D414yes—
825C22⋊C8—22no—
826C22⋊C8—22no—
827C22⋊C8—22no—
828C22⋊C8—41no—
829C22⋊C8—41no—
830#97—22no—
831#97—41no—
832C4×C8—41no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871#95C2×D411yescharacteristic
872#95C2×D411yescharacteristic
873#95C2×D411yescharacteristic
874#95C2×D411yescharacteristic
875C24—21no—
876C24—21no—
877C24—42no—
878C24—42no—
879C24—42no—
880C24—81no—
881C24—81no—
882C24—81no—
883C24—81no—
884C24C22×D411yescharacteristic
885C24C22×D411yescharacteristic
886#41—44no—
887#41—44no—
888#41—82no—
889#41—82no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—81no—
916C2×Q8—81no—
917C2×Q8—81no—
918C2×Q8—81no—
919C2×Q8C22×D412yes—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—24no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—41no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—81no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4C22×D412yes—
947C2×D42−1+412yes—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—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—42no—
978C22×C4—42no—
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×C4—81no—
992C22×C4—81no—
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×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D412yes—
1006C22×C4H(5,𝔽2)12yes—
1007C22×C4C2511yescharacteristic
1008Q16—82no—
1009Q16—82no—
1010Q16—82no—
1011Q16—82no—
1012SD16—44no—
1013SD16—44no—
1014SD16—82no—
1015SD16—82no—
1016M16—44no—
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—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—82no—
1040C2×C8—82no—
1041C2×C8C22×D412yes—
1042C2×C8C22×D412yes—
1043C4⋊C4—24no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
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—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
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—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C4⋊C4C22×D412yes—
1099C4⋊C4C22×D412yes—
1100C4⋊C4H(5,𝔽2)12yes—
1101C22⋊C4—24no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—24no—
1108C22⋊C4—22no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—81no—
1156C42—81no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—22no—
1170C23—22no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—84no—
1184C23—84no—
1185C23—84no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23D4212yes—
1191C23#57812yes—
1192C23C23×D411yescharacteristic
1193Q8—22no—
1194Q8—22no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—162no—
1210Q8—162no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—22no—
1215D4—44no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—84no—
1221D4—84no—
1222D4—84no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—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—84no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4D4212yes—
1316C2×C4C23×D411yescharacteristic
1317C2×C4C2×H(5,𝔽2)11yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×2−1+411yescharacteristic
1320C2×C4#58511yescharacteristic
1321C2×C4#58511yescharacteristic
1322C8—22no—
1323C8—22no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—168no—
1359C22C2×D4211yescharacteristic
1360C22#348811yescharacteristic
1361C22#348911yescharacteristic
1362C22C2×#57811yescharacteristic
1363C22#358411yescharacteristic
1364C22#358511yescharacteristic
1365C22#358611yescharacteristic
1366C4—22no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—41no—
1371C4—42no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—42no—
1379C4—42no—
1380C4—41no—
1381C4—41no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4#348911yescharacteristic
1393C4#349611yescharacteristic
1394C4#353611yescharacteristic
1395C4#356011yescharacteristic
1396C2—42no—
1397C2—42no—
1398C2—82no—
1399C2—82no—
1400C2#4390711yescharacteristic
1401C2#6107611yescharacteristic
1402C2#6109211yescharacteristic
1403C2#6206511yescharacteristic
1404C2#6208911yescharacteristic
1405C2#6216511yescharacteristic
1406C2#6217211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3258C2semidirect
3. #45177C2semidirect
5. #31252C2semidirect
6. #31215C2semidirect
7. #31146C2semidirect
8. #30996C2semidirect
9. #30901C2semidirect
10. #30853C2semidirect
11. #30831C2semidirect
12. #30668C2semidirect
13. #28356C2semidirect
14. #26790C2semidirect
15. #26610C2semidirect
16. #26471C2semidirect
17. #26385C2semidirect
18. #25960C2semidirect
19. #25545C2semidirect
20. #25212C2semidirect
21. #25176C2semidirect
22. #25084C2semidirect
23. #25079C2semidirect
24. #24791C2semidirect
25. #24743C2semidirect
27. #24073C2semidirect
28. #23944C2semidirect
29. #23616C2semidirect
30. #23040C2semidirect
31. #22072C2semidirect
35. C2×#541C22semidirect
40. C2×#484C22semidirect
42. C2×#479C22semidirect
43. C2×#477C22semidirect
44. C2×#475C22semidirect
47. C2×#470C22semidirect
51. C2×#467C22semidirect
56. C2×#462C22semidirect
57. C2×#462C22semidirect
66. C2×#428C22semidirect
67. C2×#424C22semidirect
79. #2550C22semidirect
83. #2503C22semidirect
90. #2451C22semidirect
92. #2446C22semidirect
105. #2362C22semidirect
108. #2351C22semidirect
110. #2317C22semidirect
112. #2097C22semidirect
114. #2085C22semidirect
116. #2068C22semidirect
117. #2068C22semidirect
118. #2068C22semidirect
119. #2068C22semidirect
123. #2066C22semidirect
124. #2066C22semidirect
125. #2066C22semidirect
128. #2057C22semidirect
129. #2057C22semidirect
130. #2057C22semidirect
131. #2056C22semidirect
133. #2043C22semidirect
141. #2026C22semidirect
143. #2024C22semidirect
144. #2016C22semidirect
145. #2016C22semidirect
154. #1971C22semidirect
155. #1969C22semidirect
157. #1960C22semidirect
159. #1949C22semidirect
160. #1943C22semidirect
161. #1943C22semidirect
162. #1940C22semidirect
163. #1939C22semidirect
164. #1928C22semidirect
165. #1928C22semidirect
166. #1927C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
181. #1873C22semidirect
183. #1872C22semidirect
184. #1872C22semidirect
188. #1863C22semidirect
189. #1863C22semidirect
190. #1863C22semidirect
191. #1863C22semidirect
197. #1850C22semidirect
198. #1818C22semidirect
202. C4×#107C22semidirect
203. #1753C22semidirect
204. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33142
C2×#32582
#451772
#451082
#312522
#312152
#311462
#309962
#309012
#308532
#308312
#306682
#283562
#267902
#266102
#264712
#263852
#259602
#255452
#252122
#251762
#250842
#250792
#247912
#247432
#244362
#240732
#239442
#236162
#230402
#220722