Finite Group Databasebeta

← #6672133

Subgroups — #6672133

Order 512.

1715 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3390C211yesmaximal, characteristic, complemented
2C2×#3120C211yesmaximal, characteristic
3#42801C211yesmaximal, characteristic, complemented
4#35816C211yesmaximal, characteristic
5#32968C211yesmaximal, characteristic
6#31167C211yesmaximal, characteristic, complemented
7#31165C211yesmaximal, characteristic, complemented
8#31097C211yesmaximal, characteristic, complemented
9#31095C211yesmaximal, characteristic, complemented
10#30975C211yesmaximal, characteristic, complemented
11#30971C211yesmaximal, characteristic, complemented
12#30803C211yesmaximal, characteristic, complemented
13#30795C211yesmaximal, characteristic, complemented
14#29882C211yesmaximal, characteristic, complemented
15#29701C211yesmaximal, characteristic, complemented
16#28537C211yesmaximal, characteristic, complemented
17#28195C211yesmaximal, characteristic, complemented
18#27252C211yesmaximal, characteristic
19#27247C211yesmaximal, characteristic
20#26187C211yesmaximal, characteristic, complemented
21#26183C211yesmaximal, characteristic, complemented
22#26057C211yesmaximal, characteristic, complemented
23#26055C211yesmaximal, characteristic, complemented
24#24924C211yesmaximal, characteristic
25#24920C211yesmaximal, characteristic
26#24826C211yesmaximal, characteristic, complemented
27#24689C211yesmaximal, characteristic, complemented
28#24348C211yesmaximal, characteristic, complemented
29#24346C211yesmaximal, characteristic, complemented
30#22763C211yesmaximal, characteristic, complemented
31#22105C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#541C2211yescharacteristic
35C2×#520C2211yescharacteristic
36#3390—28no—
37C2×#501C2211yescharacteristic
38C2×#501C2211yescharacteristic
39C2×#499C2211yescharacteristic
40#3120—28no—
41C2×#484C2211yescharacteristic
42C2×#483C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#477C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#461C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#452C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×#441C2211yescharacteristic
59C2×#441C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×C4×Q16C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×#433C2211yescharacteristic
65#2822—21no—
66#2721—21no—
67#2719—21no—
68#2716—21no—
69#2713—21no—
70#2664—21no—
71#2637—21no—
72#2629—21no—
73#2629C2211yescharacteristic
74#2629C2211yescharacteristic
75#2582C2211yescharacteristic
76#2566—21no—
77#2566C2211yescharacteristic
78#2565—21no—
79#2565C2211yescharacteristic
80#2552C2211yescharacteristic
81#2550C2211yescharacteristic
82#2538—21no—
83#2538C2211yescharacteristic
84#2492C2211yescharacteristic
85#2489C2211yescharacteristic
86#2454—21no—
87#2454C2211yescharacteristic
88#2452—21no—
89#2452C2211yescharacteristic
90#2446C2211yescharacteristic
91#2446C2211yescharacteristic
92#2442—21no—
93#2442C2211yescharacteristic
94#2440—21no—
95#2440C2211yescharacteristic
96#2423C2211yescharacteristic
97#2421C2211yescharacteristic
98#2396—21no—
99#2396C2211yescharacteristic
100#2355C2211yescharacteristic
101#2351C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2341C2211yescharacteristic
105#2341C2211yescharacteristic
106#2097C2211yescharacteristic
107#2096C2211yescharacteristic
108#2094C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2088C2211yescharacteristic
112#2088C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2086C2211yescharacteristic
116#2085C2211yescharacteristic
117#2084C2211yescharacteristic
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2075C2211yescharacteristic
122#2074C2211yescharacteristic
123#2072C2211yescharacteristic
124#2068C2211yescharacteristic
125#2066C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2043C2211yescharacteristic
137#2043C2211yescharacteristic
138#2036C2211yescharacteristic
139#2036C2211yescharacteristic
140#2035C2211yescharacteristic
141#2035C2211yescharacteristic
142#2026C2211yescharacteristic
143#2025C2211yescharacteristic
144#2024C2211yescharacteristic
145#2023C2211yescharacteristic
146#1992C2211yescharacteristic
147#1992C2211yescharacteristic
148#1985C2211yescharacteristic
149#1973C2211yescharacteristic
150#1973C2211yescharacteristic
151#1949C2211yescharacteristic
152#1947C2211yescharacteristic
153#1940C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1935C2211yescharacteristic
159#1935C2211yescharacteristic
160#1935C2211yescharacteristic
161#1935C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1862C2211yescharacteristic
188#1853C2211yescharacteristic
189#1852C2211yescharacteristic
190#1847C2211yescharacteristic
191#1847C2211yescharacteristic
192#1834C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1803C2211yescharacteristic
198#1802C2211yescharacteristic
199#1798C2211yescharacteristic
200#1788C2211yescharacteristic
201#1788C2211yescharacteristic
202#1770C2211yescharacteristic
203#1763C2211yescharacteristic
204#1763C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210#557—24no—
211#557—24no—
212#557—42no—
213#557—42no—
214#541—24no—
215#541—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239#520—24no—
240#520—42no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C4⋊C4C2311yescharacteristic
262#501—24no—
263#501—24no—
264#499—24no—
265#484—24no—
266#483—24no—
267#479—24no—
268#479—24no—
269#479—24no—
270#479—24no—
271#479—24no—
272#479—42no—
273#478—24no—
274#478—42no—
275#477—24no—
276#477—24no—
277#462—24no—
278#461—24no—
279#452—24no—
280#452—24no—
281#446—24no—
282#441—24no—
283#441—24no—
284#441—24no—
285#440—24no—
286C4×Q16D418yes—
287C4×SD16—24no—
288#433—24no—
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347#400—21no—
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#400—21no—
353#400D411yescharacteristic
354#399—21no—
355#399—21no—
356#399D411yescharacteristic
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398D411yescharacteristic
374#398D411yescharacteristic
375#397—21no—
376#397—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396D411yescharacteristic
388#396D411yescharacteristic
389#395—21no—
390#395—21no—
391#395D411yescharacteristic
392#393—21no—
393#393—21no—
394#393D411yescharacteristic
395#391—21no—
396#391—21no—
397#391—21no—
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390—21no—
405#390—21no—
406#390—21no—
407#390—21no—
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#384—21no—
452#384—21no—
453#384—21no—
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382—21no—
459#382—21no—
460#382—21no—
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#380—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8C2×D411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16C2×D414yes—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562#126—44no—
563#126—44no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—22no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—44no—
575#125—44no—
576#125—44no—
577#125—44no—
578#125—44no—
579#125—44no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—82no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—44no—
608C4×Q8—44no—
609C4×Q8C2×D414yes—
610C4×Q8C2×D414yes—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—44no—
615C4×D4—41no—
616C4×D4—44no—
617#117—22no—
618#117—22no—
619#117—44no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—22no—
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—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—44no—
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—41no—
737#107—41no—
738#107C2×D414yes—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103C2×D414yes—
772#103C2×D414yes—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—41no—
778#102—41no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—22no—
784#97—22no—
785#97—22no—
786#97—41no—
787#97—41no—
788C4×C8C2×D414yes—
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#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24C22×D411yescharacteristic
833#41—44no—
834#41—44no—
835#41—44no—
836#41—44no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
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—41no—
853C2×Q8—41no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8C22×D412yes—
861C2×Q8C22×D412yes—
862C2×Q82−1+412yes—
863C2×Q82−1+412yes—
864C2×D4—24no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D42−1+412yes—
873C22×C4—21no—
874C22×C4—24no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C2511yescharacteristic
920Q16—28no—
921Q16—44no—
922SD16—44no—
923SD16—44no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8C22×D412yes—
947C2×C8C22×D412yes—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4C22×D412yes—
1027C4⋊C4C22×D412yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C42—24no—
1051C42—24no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42C22×D412yes—
1073C42H(5,𝔽2)12yes—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—22no—
1081C23—21no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23C23×D411yescharacteristic
1089Q8—22no—
1090Q8—22no—
1091Q8—22no—
1092Q8—22no—
1093Q8—22no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—82no—
1101Q8—84no—
1102Q8—84no—
1103Q8#53614yes—
1104D4—22no—
1105D4—22no—
1106D4—48no—
1107D4—41no—
1108D4—41no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—48no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4—162no—
1199C2×C4D4212yes—
1200C2×C4D4212yes—
1201C2×C4C23×D411yescharacteristic
1202C2×C4C2×H(5,𝔽2)11yescharacteristic
1203C2×C4C2×2−1+411yescharacteristic
1204C2×C4C2×2−1+411yescharacteristic
1205C2×C4C2×2−1+411yescharacteristic
1206C2×C4#58511yescharacteristic
1207C8—22no—
1208C8—22no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—42no—
1223C22—41no—
1224C22—42no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22C2×D4211yescharacteristic
1230C22#348611yescharacteristic
1231C22#348911yescharacteristic
1232C22#358511yescharacteristic
1233C22#358611yescharacteristic
1234C22#358611yescharacteristic
1235C22#358611yescharacteristic
1236C4—24no—
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—42no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4C2×#53611yescharacteristic
1265C4#348911yescharacteristic
1266C4#353811yescharacteristic
1267C4#354111yescharacteristic
1268C2—81no—
1269C2—82no—
1270C2#3765111yescharacteristic
1271C2#6106211yescharacteristic
1272C2#6108111yescharacteristic
1273C2#6187711yescharacteristic
1274C2#6187911yescharacteristic
1275C2#6223411yescharacteristic
1276C2#6224111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3390C2semidirect
3. #42801C2semidirect
6. #31167C2semidirect
7. #31165C2semidirect
8. #31097C2semidirect
9. #31095C2semidirect
10. #30975C2semidirect
11. #30971C2semidirect
12. #30803C2semidirect
13. #30795C2semidirect
14. #29882C2semidirect
15. #29701C2semidirect
16. #28537C2semidirect
17. #28195C2semidirect
20. #26187C2semidirect
21. #26183C2semidirect
22. #26057C2semidirect
23. #26055C2semidirect
26. #24826C2semidirect
27. #24689C2semidirect
28. #24348C2semidirect
29. #24346C2semidirect
30. #22763C2semidirect
31. #22105C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33902
C2×#31202
#428012
#358162
#329682
#311672
#311652
#310972
#310952
#309752
#309712
#308032
#307952
#298822
#297012
#285372
#281952
#272522
#272472
#261872
#261832
#260572
#260552
#249242
#249202
#248262
#246892
#243482
#243462
#227632
#221052