Finite Group Databasebeta

← #6669803

Subgroups — #6669803

Order 512.

1791 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3313C211yesmaximal, characteristic
2C2×#3078C211yesmaximal, characteristic, complemented
3#39867C211yesmaximal, characteristic, complemented
4#36578C211yesmaximal, characteristic
5#33008C211yesmaximal, characteristic, complemented
6#31169C211yesmaximal, characteristic, complemented
7#31161C211yesmaximal, characteristic, complemented
8#31109C211yesmaximal, characteristic, complemented
9#31085C211yesmaximal, characteristic, complemented
10#30830C211yesmaximal, characteristic, complemented
11#30824C211yesmaximal, characteristic, complemented
12#30670C211yesmaximal, characteristic, complemented
13#30668C211yesmaximal, characteristic, complemented
14#29784C211yesmaximal, characteristic, complemented
15#29644C211yesmaximal, characteristic, complemented
16#27947C211yesmaximal, characteristic, complemented
17#27668C211yesmaximal, characteristic, complemented
18#27247C211yesmaximal, characteristic, complemented
19#27233C211yesmaximal, characteristic, complemented
20#26393C211yesmaximal, characteristic, complemented
21#26391C211yesmaximal, characteristic, complemented
22#26056C211yesmaximal, characteristic, complemented
23#26050C211yesmaximal, characteristic, complemented
24#25959C211yesmaximal, characteristic, complemented
25#25953C211yesmaximal, characteristic, complemented
26#24599C211yesmaximal, characteristic, complemented
27#24540C211yesmaximal, characteristic, complemented
28#24108C211yesmaximal, characteristic, complemented
29#24047C211yesmaximal, characteristic
30#22585C211yesmaximal, characteristic, complemented
31#22071C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#3313—28no—
37C2×#489C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#482C2211yescharacteristic
41C2×#483C2211yescharacteristic
42#3078—28no—
43C2×#479C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#477C2211yescharacteristic
48C2×#477C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#475C2211yescharacteristic
51C2×#475C2211yescharacteristic
52C2×#468C2211yescharacteristic
53C2×#467C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#441C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C2×#423C2211yescharacteristic
62C2×#419C2211yescharacteristic
63C2×#419C2211yescharacteristic
64C2×#416C2211yescharacteristic
65#2855C2211yescharacteristic
66#2854—21no—
67#2854C2211yescharacteristic
68#2700—21no—
69#2698—21no—
70#2689—21no—
71#2674—21no—
72#2637—21no—
73#2604—21no—
74#2581—21no—
75#2551C2211yescharacteristic
76#2550C2211yescharacteristic
77#2504—21no—
78#2504C2211yescharacteristic
79#2499C2211yescharacteristic
80#2492C2211yescharacteristic
81#2489C2211yescharacteristic
82#2487—21no—
83#2487C2211yescharacteristic
84#2485C2211yescharacteristic
85#2453C2211yescharacteristic
86#2451C2211yescharacteristic
87#2448—21no—
88#2448—21no—
89#2448C2211yescharacteristic
90#2448C2211yescharacteristic
91#2441C2211yescharacteristic
92#2439C2211yescharacteristic
93#2421—21no—
94#2421—21no—
95#2421C2211yescharacteristic
96#2421C2211yescharacteristic
97#2351C2211yescharacteristic
98#2351C2211yescharacteristic
99#2346C2211yescharacteristic
100#2341C2211yescharacteristic
101#2341C2211yescharacteristic
102Q8×C22⋊C4C2211yescharacteristic
103#2327—21no—
104C4×#123—21no—
105C4×#123C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2094C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2087C2211yescharacteristic
112#2086C2211yescharacteristic
113#2086C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2077C2211yescharacteristic
117#2076C2211yescharacteristic
118#2074C2211yescharacteristic
119#2072C2211yescharacteristic
120#2068C2211yescharacteristic
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2067C2211yescharacteristic
124#2066C2211yescharacteristic
125#2065C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2056C2211yescharacteristic
133#2056C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2042C2211yescharacteristic
137#2042C2211yescharacteristic
138#2036C2211yescharacteristic
139#2035C2211yescharacteristic
140#2035C2211yescharacteristic
141#2035C2211yescharacteristic
142#2025C2211yescharacteristic
143#2025C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1973C2211yescharacteristic
147#1968C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1944C2211yescharacteristic
151#1943C2211yescharacteristic
152#1940C2211yescharacteristic
153#1939C2211yescharacteristic
154#1935C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1924C2211yescharacteristic
161#1923C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1870C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic
189#1846C2211yescharacteristic
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1823C2211yescharacteristic
193#1817C2211yescharacteristic
194#1809C2211yescharacteristic
195#1808C2211yescharacteristic
196#1807C2211yescharacteristic
197#1805C2211yescharacteristic
198#1803C2211yescharacteristic
199#1788C2211yescharacteristic
200#1788C2211yescharacteristic
201#1787C2211yescharacteristic
202#1763C2211yescharacteristic
203C4×#103C2211yescharacteristic
204#1753C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#556—24no—
214#556—42no—
215#548—24no—
216#548—42no—
217#533—24no—
218#533—42no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123D411yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×C4×Q8—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8—21no—
245C2×C4×Q8—24no—
246C2×C4×Q8—42no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C4⋊C4C2311yescharacteristic
262C22×C42—21no—
263C22×C42C2311yescharacteristic
264#489—24no—
265#485—24no—
266#483—42no—
267#482—24no—
268#482—42no—
269#479—24no—
270#479—24no—
271#479—24no—
272#479—24no—
273#477—24no—
274#477—24no—
275#477—24no—
276#475—24no—
277#475—24no—
278#468—24no—
279#467—24no—
280#464—24no—
281#452—24no—
282#451—24no—
283#441—24no—
284#435—24no—
285#428—24no—
286#428—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304#423—24no—
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312#419—24no—
313#419D418yes—
314#416—24no—
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×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×#97C2311yescharacteristic
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#399—21no—
358#399—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#396—21no—
373#396—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#394—21no—
379#393—21no—
380#393—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
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#388—21no—
430#388—21no—
431#388—21no—
432#388D411yescharacteristic
433#388D411yescharacteristic
434#387—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#387D411yescharacteristic
446#387D411yescharacteristic
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386D411yescharacteristic
452#385—21no—
453#385—21no—
454#385D411yescharacteristic
455#384C2311yescharacteristic
456#382—21no—
457#382—21no—
458#382—21no—
459#382—21no—
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#381—21no—
464#381D411yescharacteristic
465#380—21no—
466#380—21no—
467#380—21no—
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#376—21no—
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—41no—
519C2×#41—41no—
520C2×#41—41no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8—22no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8C2×D414yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4C2×D411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×M16—22no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16C2×D414yes—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—44no—
578#126—44no—
579#126—44no—
580#125—22no—
581#125—22no—
582#125—41no—
583#125—41no—
584#124—22no—
585#124—41no—
586#124—44no—
587#124—44no—
588#123—42no—
589#123—44no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—44no—
595C22⋊Q8—44no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—44no—
599#121—22no—
600#121—22no—
601#121—44no—
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—44no—
611C4×Q8—44no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—44no—
621C4×Q8—44no—
622C4×Q8—44no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—44no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—41no—
631#117C2×D414yes—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
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—44no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
705C2×C22⋊C4—21no—
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—22no—
716C2×C42—22no—
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×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—44no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#107—22no—
742#107—22no—
743#107—41no—
744#107—41no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—41no—
751#106—41no—
752#106—41no—
753#106—41no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103C2×D414yes—
777#103C2×D414yes—
778#103C2×D414yes—
779#103C2×D414yes—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787C22⋊C8—22no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792#97—22no—
793#97—41no—
794C4×C8—41no—
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#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841C24—21no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844#41—44no—
845#41—82no—
846#41—82no—
847#41—82no—
848C2×Q8—24no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—28no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8C22×D412yes—
879C2×Q8C22×D412yes—
880C2×Q82−1+412yes—
881C2×Q82−1+412yes—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
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×C4C22×D411yescharacteristic
948C22×C4C22×D412yes—
949C22×C4C22×D411yescharacteristic
950C22×C4H(5,𝔽2)12yes—
951C22×C4C2511yescharacteristic
952Q16—44no—
953Q16—82no—
954SD16—82no—
955M16—44no—
956M16—44no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—82no—
980C2×C8C22×D412yes—
981C2×C8C22×D412yes—
982C4⋊C4—22no—
983C4⋊C4—22no—
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—41no—
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—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4C22×D412yes—
1041C4⋊C4C22×D412yes—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—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—
1072C22⋊C4—81no—
1073C42—22no—
1074C42—22no—
1075C42—24no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23D4212yes—
1119C23C23×D411yescharacteristic
1120Q8—22no—
1121Q8—22no—
1122Q8—22no—
1123Q8—22no—
1124Q8—22no—
1125Q8—48no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—84no—
1133Q8—84no—
1134Q8—84no—
1135Q8#53614yes—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4—82no—
1142D4—84no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
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—22no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—44no—
1188C2×C4—48no—
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—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—84no—
1233C2×C4—82no—
1234C2×C4—84no—
1235C2×C4D4212yes—
1236C2×C4#57512yes—
1237C2×C4C23×D411yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×2−1+411yescharacteristic
1240C2×C4C2×2−1+411yescharacteristic
1241C2×C4#58511yescharacteristic
1242C2×C4#58511yescharacteristic
1243C8—22no—
1244C8—22no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22C2×D4211yescharacteristic
1273C22#348911yescharacteristic
1274C22#348911yescharacteristic
1275C22C2×#57511yescharacteristic
1276C22#358411yescharacteristic
1277C22#358611yescharacteristic
1278C22#358611yescharacteristic
1279C4—22no—
1280C4—24no—
1281C4—22no—
1282C4—41no—
1283C4—42no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—42no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4C2×#53611yescharacteristic
1307C4#348511yescharacteristic
1308C4#353511yescharacteristic
1309C4#353511yescharacteristic
1310C2—42no—
1311C2—81no—
1312C2—161no—
1313C2#3764711yescharacteristic
1314C2#6106811yescharacteristic
1315C2#6107811yescharacteristic
1316C2#6211811yescharacteristic
1317C2#6214211yescharacteristic
1318C2#6217811yescharacteristic
1319C2#6223411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3078C2semidirect
3. #39867C2semidirect
5. #33008C2semidirect
6. #31169C2semidirect
7. #31161C2semidirect
8. #31109C2semidirect
9. #31085C2semidirect
10. #30830C2semidirect
11. #30824C2semidirect
12. #30670C2semidirect
13. #30668C2semidirect
14. #29784C2semidirect
15. #29644C2semidirect
16. #27947C2semidirect
17. #27668C2semidirect
18. #27247C2semidirect
19. #27233C2semidirect
20. #26393C2semidirect
21. #26391C2semidirect
22. #26056C2semidirect
23. #26050C2semidirect
24. #25959C2semidirect
25. #25953C2semidirect
26. #24599C2semidirect
27. #24540C2semidirect
28. #24108C2semidirect
30. #22585C2semidirect
31. #22071C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33132
C2×#30782
#398672
#365782
#330082
#311692
#311612
#311092
#310852
#308302
#308242
#306702
#306682
#297842
#296442
#279472
#276682
#272472
#272332
#263932
#263912
#260562
#260502
#259592
#259532
#245992
#245402
#241082
#240472
#225852
#220712