Finite Group Databasebeta

← #7183773

Subgroups — #7183773

Order 512.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3383C211yesmaximal, characteristic, complemented
2C2×#3370C211yesmaximal, characteristic
3#45424C211yesmaximal, characteristic, complemented
4#42886C211yesmaximal, characteristic, complemented
5#31244C211yesmaximal, characteristic, complemented
6#31235C211yesmaximal, characteristic, complemented
7#31177C211yesmaximal, characteristic, complemented
8#31153C211yesmaximal, characteristic, complemented
9#30951C211yesmaximal, characteristic, complemented
10#30946C211yesmaximal, characteristic, complemented
11#30824C211yesmaximal, characteristic, complemented
12#30818C211yesmaximal, characteristic, complemented
13#28665C211yesmaximal, characteristic, complemented
14#28389C211yesmaximal, characteristic
15#26907C211yesmaximal, characteristic, complemented
16#26891C211yesmaximal, characteristic, complemented
17#26830C211yesmaximal, characteristic, complemented
18#26823C211yesmaximal, characteristic, complemented
19#26598C211yesmaximal, characteristic, complemented
20#26598C211yesmaximal, characteristic, complemented
21#26492C211yesmaximal, characteristic, complemented
22#26484C211yesmaximal, characteristic, complemented
23#25944C211yesmaximal, characteristic, complemented
24#25843C211yesmaximal, characteristic, complemented
25#25484C211yesmaximal, characteristic, complemented
26#25292C211yesmaximal, characteristic
27#24346C211yesmaximal, characteristic, complemented
28#24190C211yesmaximal, characteristic, complemented
29#23695C211yesmaximal, characteristic, complemented
30#23154C211yesmaximal, characteristic, complemented
31#22124C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#554C2211yescharacteristic
36#3383—28no—
37#3370—28no—
38C2×#500C2211yescharacteristic
39C2×#499C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#490C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#475C2211yescharacteristic
49C2×#475C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#460C2211yescharacteristic
54C2×#463C2211yescharacteristic
55C2×#463C2211yescharacteristic
56C2×#459C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×C8×Q8C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×C4×Q16C2211yescharacteristic
62C2×C4×Q16C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic
64C2×C4×D8C2211yescharacteristic
65#2820—21no—
66#2720—21no—
67#2704—21no—
68#2704—21no—
69#2694—21no—
70#2694—21no—
71#2677—21no—
72#2674—21no—
73#2674—21no—
74#2641C2211yescharacteristic
75#2633—21no—
76#2632—21no—
77#2584C2211yescharacteristic
78#2582C2211yescharacteristic
79#2552C2211yescharacteristic
80#2551C2211yescharacteristic
81#2548C2211yescharacteristic
82#2538C2211yescharacteristic
83#2536—21no—
84#2473—21no—
85#2465—21no—
86#2454C2211yescharacteristic
87#2454C2211yescharacteristic
88#2454C2211yescharacteristic
89#2453C2211yescharacteristic
90#2452C2211yescharacteristic
91#2452C2211yescharacteristic
92#2452C2211yescharacteristic
93#2451C2211yescharacteristic
94#2448C2211yescharacteristic
95#2448C2211yescharacteristic
96#2448C2211yescharacteristic
97#2448C2211yescharacteristic
98#2440—21no—
99#2429—21no—
100#2399C2211yescharacteristic
101#2367C2211yescharacteristic
102#2367C2211yescharacteristic
103#2330C2211yescharacteristic
104#2326C2211yescharacteristic
105#2320C2211yescharacteristic
106#2094C2211yescharacteristic
107#2093C2211yescharacteristic
108#2088C2211yescharacteristic
109#2086C2211yescharacteristic
110#2083C2211yescharacteristic
111#2072C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2058C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2056C2211yescharacteristic
129#2055C2211yescharacteristic
130#2054C2211yescharacteristic
131#2054C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2042C2211yescharacteristic
135#2025C2211yescharacteristic
136#2025C2211yescharacteristic
137#2025C2211yescharacteristic
138#2023C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2012C2211yescharacteristic
145#2012C2211yescharacteristic
146#1992C2211yescharacteristic
147#1989C2211yescharacteristic
148#1985C2211yescharacteristic
149#1984C2211yescharacteristic
150#1973C2211yescharacteristic
151#1972C2211yescharacteristic
152#1970C2211yescharacteristic
153#1970C2211yescharacteristic
154#1970C2211yescharacteristic
155#1968C2211yescharacteristic
156#1957C2211yescharacteristic
157#1947C2211yescharacteristic
158#1944C2211yescharacteristic
159#1943C2211yescharacteristic
160#1942C2211yescharacteristic
161#1942C2211yescharacteristic
162#1940C2211yescharacteristic
163#1939C2211yescharacteristic
164#1935C2211yescharacteristic
165#1935C2211yescharacteristic
166#1934C2211yescharacteristic
167#1934C2211yescharacteristic
168#1933C2211yescharacteristic
169#1933C2211yescharacteristic
170#1928C2211yescharacteristic
171#1928C2211yescharacteristic
172#1926C2211yescharacteristic
173#1926C2211yescharacteristic
174#1925C2211yescharacteristic
175#1925C2211yescharacteristic
176#1920C2211yescharacteristic
177#1918C2211yescharacteristic
178#1917C2211yescharacteristic
179#1916C2211yescharacteristic
180#1916C2211yescharacteristic
181#1916C2211yescharacteristic
182#1880C2211yescharacteristic
183#1880C2211yescharacteristic
184#1880C2211yescharacteristic
185#1880C2211yescharacteristic
186#1880C2211yescharacteristic
187#1880C2211yescharacteristic
188#1877C2211yescharacteristic
189#1877C2211yescharacteristic
190#1865C2211yescharacteristic
191#1864C2211yescharacteristic
192#1864C2211yescharacteristic
193#1863C2211yescharacteristic
194#1862C2211yescharacteristic
195#1862C2211yescharacteristic
196#1862C2211yescharacteristic
197#1862C2211yescharacteristic
198#1803C2211yescharacteristic
199#1771C2211yescharacteristic
200C8×C4⋊C4C2211yescharacteristic
201#1768C2211yescharacteristic
202#1768C2211yescharacteristic
203#1763C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211#559—24no—
212#559—42no—
213#557—24no—
214#557—24no—
215#557—42no—
216#557—42no—
217#554—24no—
218#554—42no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#125—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#124—21no—
236C2×#124—21no—
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#123—21no—
241C2×#123—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C22×C4⋊C4—21no—
266#500—24no—
267#499—24no—
268#499—24no—
269#490—24no—
270#489—24no—
271#488—24no—
272#479—24no—
273#479—24no—
274#479—24no—
275#479D418yes—
276#478—24no—
277#478—42no—
278#475—24no—
279#475—24no—
280#474—24no—
281#463—24no—
282#463—24no—
283#460—42no—
284#459—24no—
285#446—24no—
286C8×Q8—24no—
287#442—24no—
288#440—24no—
289C4×Q16—24no—
290C4×Q16—24no—
291C4×Q16—24no—
292C4×D8—24no—
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351#400—21no—
352#399—21no—
353#399—21no—
354#399—21no—
355#399—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398D411yescharacteristic
367#398D411yescharacteristic
368#398D411yescharacteristic
369#398D411yescharacteristic
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#396—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#395D411yescharacteristic
387#395D411yescharacteristic
388#395D411yescharacteristic
389#395D411yescharacteristic
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#393—21no—
397#393—21no—
398#393—21no—
399#391—21no—
400#391—21no—
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390—21no—
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
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#388—21no—
448#388—21no—
449#388—21no—
450#388—21no—
451#388—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#385—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#384—21no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#383—21no—
472#382—21no—
473#380—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486#376C2311yescharacteristic
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#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2×D411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—41no—
549C2×D8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566C4⋊Q8—82no—
567#127—22no—
568#127—22no—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—41no—
576#125—41no—
577#125—41no—
578#125—44no—
579#125—44no—
580#125—44no—
581#125—44no—
582#125C2×D414yes—
583#124—22no—
584#124—22no—
585#124—22no—
586#124—22no—
587#124—41no—
588#124—41no—
589#124—44no—
590#124—82no—
591#123—44no—
592#123—44no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595C22⋊Q8—44no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598C22⋊Q8—82no—
599C22⋊Q8—82no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—44no—
616C4×Q8—44no—
617C4×Q8C2×D414yes—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—44no—
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—44no—
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—22no—
740#107—22no—
741#107—22no—
742#107—22no—
743#107—22no—
744#107—41no—
745#107—41no—
746#107—41no—
747#107C2×D414yes—
748#106—22no—
749#106—22no—
750#106—22no—
751#106—41no—
752#106C2×D414yes—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760C4⋊C8C2×D414yes—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103C2×D414yes—
771#103C2×D414yes—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#97—22no—
790#97—22no—
791#97—41no—
792C4×C8—22no—
793C4×C8—22no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—41no—
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#95—21no—
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
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—21no—
836C24—21no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8—22no—
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—41no—
851C2×Q8—41no—
852C2×Q8—41no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8C22×D412yes—
863C2×Q82−1+412yes—
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—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D42−1+412yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2511yescharacteristic
931Q16—28no—
932SD16—44no—
933SD16—82no—
934SD16—82no—
935D8—44no—
936D8—44no—
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×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8C22×D412yes—
959C2×C8C22×D412yes—
960C2×C82−1+412yes—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
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—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
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⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4C22×D412yes—
1030C4⋊C4C22×D412yes—
1031C4⋊C4C22×D412yes—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C42—24no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42C22×D412yes—
1087C42H(5,𝔽2)12yes—
1088C23—22no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23C23×D411yescharacteristic
1110Q8—22no—
1111Q8—22no—
1112Q8—22no—
1113Q8—22no—
1114Q8—44no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—82no—
1120Q8—84no—
1121Q8—84no—
1122Q8—162no—
1123D4—22no—
1124D4—22no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—84no—
1136D4—162no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
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—41no—
1197C2×C4—41no—
1198C2×C4—41no—
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—84no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4D4212yes—
1221C2×C4D4212yes—
1222C2×C4#57612yes—
1223C2×C4C23×D411yescharacteristic
1224C2×C4C2×H(5,𝔽2)11yescharacteristic
1225C2×C4C2×2−1+411yescharacteristic
1226C2×C4C2×2−1+411yescharacteristic
1227C2×C4C2×2−1+411yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—22no—
1230C8—22no—
1231C8—22no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×D4211yescharacteristic
1259C22#348611yescharacteristic
1260C22#349711yescharacteristic
1261C22C2×#57611yescharacteristic
1262C22#358411yescharacteristic
1263C22#358411yescharacteristic
1264C22#358611yescharacteristic
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—42no—
1282C4—42no—
1283C4—41no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4#348611yescharacteristic
1293C4#348911yescharacteristic
1294C4#355211yescharacteristic
1295C4#356111yescharacteristic
1296C2—82no—
1297C2—161no—
1298C2—161no—
1299C2#4524811yescharacteristic
1300C2#6105611yescharacteristic
1301C2#6107811yescharacteristic
1302C2#6185711yescharacteristic
1303C2#6186711yescharacteristic
1304C2#6237911yescharacteristic
1305C2#6240911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3383C2semidirect
3. #45424C2semidirect
4. #42886C2semidirect
5. #31244C2semidirect
6. #31235C2semidirect
7. #31177C2semidirect
8. #31153C2semidirect
9. #30951C2semidirect
10. #30946C2semidirect
11. #30824C2semidirect
12. #30818C2semidirect
13. #28665C2semidirect
15. #26907C2semidirect
16. #26891C2semidirect
17. #26830C2semidirect
18. #26823C2semidirect
19. #26598C2semidirect
20. #26598C2semidirect
21. #26492C2semidirect
22. #26484C2semidirect
23. #25944C2semidirect
24. #25843C2semidirect
25. #25484C2semidirect
27. #24346C2semidirect
28. #24190C2semidirect
29. #23695C2semidirect
30. #23154C2semidirect
31. #22124C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33832
C2×#33702
#454242
#428862
#312442
#312352
#311772
#311532
#309512
#309462
#308242
#308182
#286652
#283892
#269072
#268912
#268302
#268232
#265982
#264922
#264842
#259442
#258432
#254842
#252922
#243462
#241902
#236952
#231542
#221242