Finite Group Databasebeta

← #6809635

Subgroups — #6809635

Order 512.

1669 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic
2C2×#3242C211yesmaximal, characteristic, complemented
3#39347C211yesmaximal, characteristic
4#35167C211yesmaximal, characteristic, complemented
5#33110C211yesmaximal, characteristic
6#30969C211yesmaximal, characteristic, complemented
7#30963C211yesmaximal, characteristic, complemented
8#30958C211yesmaximal, characteristic, complemented
9#30956C211yesmaximal, characteristic, complemented
10#30828C211yesmaximal, characteristic, complemented
11#30822C211yesmaximal, characteristic, complemented
12#30820C211yesmaximal, characteristic, complemented
13#30814C211yesmaximal, characteristic, complemented
14#29649C211yesmaximal, characteristic, complemented
15#29647C211yesmaximal, characteristic
16#28820C211yesmaximal, characteristic, complemented
17#28819C211yesmaximal, characteristic, complemented
18#27915C211yesmaximal, characteristic
19#27785C211yesmaximal, characteristic, complemented
20#27781C211yesmaximal, characteristic, complemented
21#27649C211yesmaximal, characteristic, complemented
22#26477C211yesmaximal, characteristic, complemented
23#26476C211yesmaximal, characteristic, complemented
24#26057C211yesmaximal, characteristic, complemented
25#26056C211yesmaximal, characteristic, complemented
26#24615C211yesmaximal, characteristic
27#24613C211yesmaximal, characteristic, complemented
28#24075C211yesmaximal, characteristic
29#24072C211yesmaximal, characteristic, complemented
30#22602C211yesmaximal, characteristic, complemented
31#21579C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#541C2211yescharacteristic
36#3244—28no—
37#3242—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#498C2211yescharacteristic
42C2×#491C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#487C2211yescharacteristic
46C2×#484C2211yescharacteristic
47C2×#481C2211yescharacteristic
48C2×#485C2211yescharacteristic
49C2×#485C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#479C2211yescharacteristic
56C2×#479C2211yescharacteristic
57C2×#479C2211yescharacteristic
58C2×#477C2211yescharacteristic
59C2×#475C2211yescharacteristic
60C2×#475C2211yescharacteristic
61C2×#478C2211yescharacteristic
62C2×#476C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#433C2211yescharacteristic
65#2857—21no—
66#2857—21no—
67#2850C2211yescharacteristic
68#2721—21no—
69#2720—21no—
70#2715—21no—
71#2695—21no—
72#2659—21no—
73#2659—21no—
74#2625C2211yescharacteristic
75#2624C2211yescharacteristic
76#2553—21no—
77#2552—21no—
78#2552C2211yescharacteristic
79#2552C2211yescharacteristic
80#2551—21no—
81#2551C2211yescharacteristic
82#2551C2211yescharacteristic
83#2550—21no—
84#2550—21no—
85#2550C2211yescharacteristic
86#2550C2211yescharacteristic
87#2550C2211yescharacteristic
88#2550C2211yescharacteristic
89#2550C2211yescharacteristic
90#2545C2211yescharacteristic
91#2521—21no—
92#2519—21no—
93#2489—21no—
94#2454C2211yescharacteristic
95#2451C2211yescharacteristic
96#2448C2211yescharacteristic
97#2446C2211yescharacteristic
98#2367C2211yescharacteristic
99#2351C2211yescharacteristic
100#2316C2211yescharacteristic
101#2316C2211yescharacteristic
102C4×C22⋊Q8C2211yescharacteristic
103#2285C2211yescharacteristic
104#2285C2211yescharacteristic
105C2×C4×C4⋊C4C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2088C2211yescharacteristic
112#2087C2211yescharacteristic
113#2086C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2074C2211yescharacteristic
117#2074C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2057C2211yescharacteristic
133#2057C2211yescharacteristic
134#2043C2211yescharacteristic
135#2043C2211yescharacteristic
136#2042C2211yescharacteristic
137#2042C2211yescharacteristic
138#2026C2211yescharacteristic
139#2026C2211yescharacteristic
140#2025C2211yescharacteristic
141#2025C2211yescharacteristic
142#2024C2211yescharacteristic
143#2024C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic
150#1949C2211yescharacteristic
151#1949C2211yescharacteristic
152#1948C2211yescharacteristic
153#1947C2211yescharacteristic
154#1943C2211yescharacteristic
155#1943C2211yescharacteristic
156#1942C2211yescharacteristic
157#1942C2211yescharacteristic
158#1940C2211yescharacteristic
159#1940C2211yescharacteristic
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic
162#1934C2211yescharacteristic
163#1933C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1874C2211yescharacteristic
177#1872C2211yescharacteristic
178#1872C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1862C2211yescharacteristic
187#1852C2211yescharacteristic
188#1847C2211yescharacteristic
189#1847C2211yescharacteristic
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1823C2211yescharacteristic
193#1818C2211yescharacteristic
194#1818C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1797C2211yescharacteristic
198#1776C2211yescharacteristic
199#1776C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202#1763C2211yescharacteristic
203#1763C2211yescharacteristic
204#1749C2211yescharacteristic
205#544—24no—
206#544—24no—
207#544—42no—
208#544—42no—
209#542—24no—
210#542—42no—
211#541—24no—
212#541—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#126—21no—
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×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C42—21no—
259C22×C42C2311yescharacteristic
260#501—24no—
261#501—24no—
262#499—24no—
263#498—24no—
264#491—24no—
265#489—24no—
266#488—24no—
267#487—24no—
268#485—24no—
269#485—24no—
270#485—24no—
271#485—42no—
272#484—24no—
273#483D418yes—
274#482—24no—
275#482—42no—
276#481—24no—
277#479—24no—
278#479—24no—
279#479—24no—
280#478—24no—
281#477—24no—
282#476—24no—
283#475—24no—
284#475—24no—
285#433—24no—
286#433—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
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×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
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×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
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×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347#400—21no—
348#400—21no—
349#399—21no—
350#399—21no—
351#399—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#394—21no—
382#394—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
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#389—21no—
410#389—21no—
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
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#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#384—21no—
442#384—21no—
443#384D411yescharacteristic
444#384D411yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382—21no—
448#382D411yescharacteristic
449#382D411yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380D411yescharacteristic
461#380D411yescharacteristic
462#380D411yescharacteristic
463#380D411yescharacteristic
464#380C2311yescharacteristic
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C2×#95—21no—
483#340C2311yescharacteristic
484#340C2311yescharacteristic
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#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×Q8—21no—
519C22×Q8—21no—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—82no—
553C4⋊Q8—82no—
554#126—44no—
555#126—44no—
556#126—44no—
557#125—22no—
558#125—22no—
559#125—22no—
560#125—22no—
561#125—22no—
562#125—41no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—44no—
568#125—44no—
569#125—44no—
570#125—44no—
571#124—22no—
572#124—22no—
573#124—22no—
574#124—41no—
575#124—44no—
576#123—44no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8C2×D414yes—
586#121—22no—
587#121—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—41no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—22no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D414yes—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
678C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C42—22no—
699C2×C42—22no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—82no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—22no—
723#107—22no—
724#107—22no—
725#107—22no—
726#107—22no—
727#107—22no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106C2×D414yes—
739#106C2×D414yes—
740C4⋊C8—22no—
741C4⋊C8—22no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—41no—
759#103—41no—
760#103C2×D414yes—
761#103C2×D414yes—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8C2×D414yes—
774#97—22no—
775#97—22no—
776#97—22no—
777#97—22no—
778C4×C8—22no—
779C4×C8—22no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
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#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24C22×D411yescharacteristic
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8C22×D412yes—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—42no—
857C2×D4—81no—
858C2×D4—81no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D412yes—
907C22×C4H(5,𝔽2)12yes—
908C22×C4C2511yescharacteristic
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8C22×D412yes—
932C2×C8C22×D412yes—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
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—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4C22×D412yes—
1009C4⋊C4C22×D412yes—
1010C4⋊C4C22×D412yes—
1011C4⋊C42−1+412yes—
1012C4⋊C42−1+412yes—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C42—22no—
1035C42—22no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C422−1+412yes—
1058C422−1+412yes—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23D4212yes—
1073C23C23×D411yescharacteristic
1074Q8—22no—
1075Q8—22no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—162no—
1083Q8—162no—
1084Q8—162no—
1085Q8—162no—
1086Q8—162no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—162no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
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—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—44no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
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—82no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—162no—
1182C2×C4#53612yes—
1183C2×C4#53612yes—
1184C2×C4D4212yes—
1185C2×C4C23×D411yescharacteristic
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C2×C4C2×2−1+411yescharacteristic
1188C2×C4C2×2−1+411yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4C2×2−1+411yescharacteristic
1191C8—22no—
1192C8—22no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22C2×#53611yescharacteristic
1214C22C2×D4211yescharacteristic
1215C22#348611yescharacteristic
1216C22#358411yescharacteristic
1217C22#358511yescharacteristic
1218C22#358611yescharacteristic
1219C22#358611yescharacteristic
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—42no—
1229C4—42no—
1230C4—42no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—42no—
1236C4—42no—
1237C4—41no—
1238C4—41no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4#349911yescharacteristic
1249C4#349911yescharacteristic
1250C4#354411yescharacteristic
1251C4#354411yescharacteristic
1252C2—42no—
1253C2—161no—
1254C2#3933711yescharacteristic
1255C2#6086711yescharacteristic
1256C2#6087611yescharacteristic
1257C2#6108011yescharacteristic
1258C2#6109611yescharacteristic
1259C2#6185511yescharacteristic
1260C2#6187511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3242C2semidirect
4. #35167C2semidirect
6. #30969C2semidirect
7. #30963C2semidirect
8. #30958C2semidirect
9. #30956C2semidirect
10. #30828C2semidirect
11. #30822C2semidirect
12. #30820C2semidirect
13. #30814C2semidirect
14. #29649C2semidirect
16. #28820C2semidirect
17. #28819C2semidirect
19. #27785C2semidirect
20. #27781C2semidirect
21. #27649C2semidirect
22. #26477C2semidirect
23. #26476C2semidirect
24. #26057C2semidirect
25. #26056C2semidirect
27. #24613C2semidirect
29. #24072C2semidirect
30. #22602C2semidirect
31. #21579C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32442
C2×#32422
#393472
#351672
#331102
#309692
#309632
#309582
#309562
#308282
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