Finite Group Databasebeta

← #6672587

Subgroups — #6672587

Order 512.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3083C211yesmaximal, characteristic, complemented
3#39366C211yesmaximal, characteristic, complemented
4#35601C211yesmaximal, characteristic
5#32965C211yesmaximal, characteristic, complemented
6#31129C211yesmaximal, characteristic, complemented
7#31126C211yesmaximal, characteristic, complemented
8#31082C211yesmaximal, characteristic, complemented
9#31080C211yesmaximal, characteristic, complemented
10#30972C211yesmaximal, characteristic, complemented
11#30961C211yesmaximal, characteristic, complemented
12#30825C211yesmaximal, characteristic, complemented
13#30807C211yesmaximal, characteristic, complemented
14#29865C211yesmaximal, characteristic, complemented
15#29698C211yesmaximal, characteristic, complemented
16#28510C211yesmaximal, characteristic, complemented
17#28208C211yesmaximal, characteristic, complemented
18#27280C211yesmaximal, characteristic, complemented
19#27257C211yesmaximal, characteristic, complemented
20#26143C211yesmaximal, characteristic, complemented
21#26140C211yesmaximal, characteristic, complemented
22#26076C211yesmaximal, characteristic, complemented
23#26067C211yesmaximal, characteristic, complemented
24#24885C211yesmaximal, characteristic, complemented
25#24866C211yesmaximal, characteristic, complemented
26#24847C211yesmaximal, characteristic, complemented
27#24714C211yesmaximal, characteristic, complemented
28#24310C211yesmaximal, characteristic, complemented
29#24309C211yesmaximal, characteristic, complemented
30#22756C211yesmaximal, characteristic, complemented
31#22114C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#520C2211yescharacteristic
36#3241—28no—
37C2×#501C2211yescharacteristic
38C2×#499C2211yescharacteristic
39C2×#490C2211yescharacteristic
40C2×#486C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#480C2211yescharacteristic
45#3083—28no—
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#477C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#475C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#478C2211yescharacteristic
54C2×#476C2211yescharacteristic
55C2×#476C2211yescharacteristic
56C2×#474C2211yescharacteristic
57C2×#474C2211yescharacteristic
58C2×#474C2211yescharacteristic
59C2×#433C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C22×#107C2211yescharacteristic
62C2×#424C2211yescharacteristic
63C2×#417C2211yescharacteristic
64C2×#416C2211yescharacteristic
65#2862C2211yescharacteristic
66#2713—21no—
67#2713—21no—
68#2692—21no—
69#2692—21no—
70#2628C2211yescharacteristic
71#2628C2211yescharacteristic
72#2602—21no—
73#2591—21no—
74#2556—21no—
75#2556—21no—
76#2550C2211yescharacteristic
77#2550C2211yescharacteristic
78#2492—21no—
79#2492—21no—
80#2476—21no—
81#2470—21no—
82#2464—21no—
83#2457—21no—
84#2453C2211yescharacteristic
85#2445C2211yescharacteristic
86#2442C2211yescharacteristic
87#2442C2211yescharacteristic
88#2442C2211yescharacteristic
89#2439C2211yescharacteristic
90#2439C2211yescharacteristic
91#2431C2211yescharacteristic
92#2426C2211yescharacteristic
93#2420C2211yescharacteristic
94#2416C2211yescharacteristic
95#2414—21no—
96#2413—21no—
97#2407C2211yescharacteristic
98#2352C2211yescharacteristic
99#2352C2211yescharacteristic
100#2324C2211yescharacteristic
101#2323C2211yescharacteristic
102C4×#125C2211yescharacteristic
103C4×#124C2211yescharacteristic
104#2293C2211yescharacteristic
105#2293C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic
110#2087C2211yescharacteristic
111#2086C2211yescharacteristic
112#2085C2211yescharacteristic
113#2085C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2085C2211yescharacteristic
117#2085C2211yescharacteristic
118#2076C2211yescharacteristic
119#2075C2211yescharacteristic
120#2073C2211yescharacteristic
121#2073C2211yescharacteristic
122#2073C2211yescharacteristic
123#2073C2211yescharacteristic
124#2067C2211yescharacteristic
125#2065C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2058C2211yescharacteristic
131#2058C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2036C2211yescharacteristic
137#2035C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2033C2211yescharacteristic
141#2033C2211yescharacteristic
142#2026C2211yescharacteristic
143#2025C2211yescharacteristic
144#2024C2211yescharacteristic
145#2023C2211yescharacteristic
146#1989C2211yescharacteristic
147#1988C2211yescharacteristic
148#1987C2211yescharacteristic
149#1958C2211yescharacteristic
150#1958C2211yescharacteristic
151#1949C2211yescharacteristic
152#1944C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1935C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1927C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1917C2211yescharacteristic
171#1916C2211yescharacteristic
172#1895C2211yescharacteristic
173#1893C2211yescharacteristic
174#1875C2211yescharacteristic
175#1874C2211yescharacteristic
176#1873C2211yescharacteristic
177#1872C2211yescharacteristic
178#1870C2211yescharacteristic
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1853C2211yescharacteristic
190#1846C2211yescharacteristic
191#1846C2211yescharacteristic
192#1831C2211yescharacteristic
193#1809C2211yescharacteristic
194#1808C2211yescharacteristic
195#1805C2211yescharacteristic
196#1804C2211yescharacteristic
197#1804C2211yescharacteristic
198#1798C2211yescharacteristic
199#1798C2211yescharacteristic
200#1788C2211yescharacteristic
201#1788C2211yescharacteristic
202C4×C4⋊C8C2211yescharacteristic
203#1753C2211yescharacteristic
204C8×C22⋊C4C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#544—24no—
209#544—24no—
210#544—42no—
211#544—42no—
212#540—24no—
213#540—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#125—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242#520—24no—
243#520—42no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262#501—24no—
263#499—24no—
264#490—24no—
265#486—24no—
266#482—24no—
267#482—24no—
268#481—24no—
269#480—24no—
270#479—24no—
271#479—24no—
272#478—24no—
273#478—24no—
274#478D418yescomplemented
275#477—24no—
276#477—24no—
277#476—24no—
278#476—42no—
279#475—42no—
280#474—24no—
281#474—24no—
282#474—24no—
283#433—24no—
284#428—24no—
285C2×#107—24no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306#424—24no—
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313#417—24no—
314#416—24no—
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349#400—21no—
350#400—21no—
351#400—21no—
352#400—21no—
353#400—21no—
354#400—21no—
355#399—21no—
356#399—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#397—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#395—21no—
369#395—21no—
370#395—21no—
371#395—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#393—21no—
379#393—21no—
380#393—21no—
381#393—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#390—21no—
396#390—21no—
397#390D411yescharacteristic
398#390D411yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389D411yescharacteristic
408#389D411yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388D411yescharacteristic
430#388D411yescharacteristic
431#388D411yescharacteristic
432#388D411yescharacteristic
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#381—21no—
462#380—21no—
463#380—21no—
464#380—21no—
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471C4×C4⋊C4—21no—
472C4×C4⋊C4—21no—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4—21no—
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484C43C2311yescharacteristic
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×Q8—21no—
524C22×Q8—21no—
525C22×Q8C2411yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—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—22no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—44no—
567C4⋊Q8—44no—
568#127—22no—
569#127—41no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—41no—
575#125—41no—
576#125—41no—
577#125—44no—
578#125—44no—
579#125C2×D414yes—
580#124—22no—
581#124—41no—
582#123—44no—
583#123—44no—
584#123—82no—
585C22⋊Q8—22no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—44no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—82no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—41no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4C2×D414yes—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—44no—
621#117—41no—
622#117—41no—
623#117—82no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
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—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—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⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—41no—
739#107C2×D414yes—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—41no—
745#106—41no—
746#106—41no—
747#106—41no—
748#106—41no—
749#106C2×D414yes—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8C2×D414yes—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102C2×D414yes—
779#102C2×D414yes—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786#97—22no—
787C4×C8—22no—
788C4×C8—41no—
789C4×C8—41no—
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#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—28no—
836#41—44no—
837#41—44no—
838#41—44no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q82−1+412yes—
857C2×D4—22no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—42no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4C22×D412yes—
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—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—24no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C42−1+412yes—
948C22×C42−1+412yes—
949C22×C4C2511yescharacteristic
950M16—44no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—44no—
974C2×C8C22×D412yes—
975C2×C8C22×D412yes—
976C4⋊C4—22no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
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—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4C22×D412yes—
1035C4⋊C4C22×D412yes—
1036C4⋊C4C22×D412yes—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—24no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—41no—
1081C42—41no—
1082C42—41no—
1083C42—41no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42C22×D412yes—
1092C42H(5,𝔽2)12yes—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—21no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23#53612yes—
1121C23C23×D411yescharacteristic
1122Q8—22no—
1123Q8—22no—
1124Q8—41no—
1125Q8—41no—
1126Q8—162no—
1127Q8—162no—
1128Q8—162no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—48no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—82no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—48no—
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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—84no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4#53612yes—
1236C2×C4D4212yes—
1237C2×C4D4212yes—
1238C2×C4C23×D411yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×2−1+411yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—22no—
1245C8—22no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#53611yescharacteristic
1281C22C2×D4211yescharacteristic
1282C22#348911yescharacteristic
1283C22#358411yescharacteristic
1284C22#358411yescharacteristic
1285C22#358411yescharacteristic
1286C22#358511yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—42no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4#348611yescharacteristic
1314C4#348911yescharacteristic
1315C4#353811yescharacteristic
1316C4#354111yescharacteristic
1317C2—42no—
1318C2—81no—
1319C2—82no—
1320C2—161no—
1321C2#3765111yescharacteristic
1322C2#6087511yescharacteristic
1323C2#6088211yescharacteristic
1324C2#6109011yescharacteristic
1325C2#6109211yescharacteristic
1326C2#6216211yescharacteristic
1327C2#6221011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35601C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3241C2semidirect
2. C2×#3083C2semidirect
3. #39366C2semidirect
5. #32965C2semidirect
6. #31129C2semidirect
7. #31126C2semidirect
8. #31082C2semidirect
9. #31080C2semidirect
10. #30972C2semidirect
11. #30961C2semidirect
12. #30825C2semidirect
13. #30807C2semidirect
14. #29865C2semidirect
15. #29698C2semidirect
16. #28510C2semidirect
17. #28208C2semidirect
18. #27280C2semidirect
19. #27257C2semidirect
20. #26143C2semidirect
21. #26140C2semidirect
22. #26076C2semidirect
23. #26067C2semidirect
24. #24885C2semidirect
25. #24866C2semidirect
26. #24847C2semidirect
27. #24714C2semidirect
28. #24310C2semidirect
29. #24309C2semidirect
30. #22756C2semidirect
31. #22114C2semidirect
274. #478D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#30832
#393662
#356012
#329652
#311292
#311262
#310822
#310802
#309722
#309612
#308252
#308072
#298652
#296982
#285102
#282082
#272802
#272572
#261432
#261402
#260762
#260672
#248852
#248662
#248472
#247142
#243102
#243092
#227562
#221142