Finite Group Databasebeta

← #7561212

Subgroups — #7561212

Order 512.

1887 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3316C211yesmaximal, characteristic, complemented
2C2×#3178C211yesmaximal, characteristic, complemented
3#45246C211yesmaximal, characteristic, complemented
4#44989C211yesmaximal, characteristic, complemented
5#30965C211yesmaximal, characteristic, complemented
6#30799C211yesmaximal, characteristic, complemented
7#30758C211yesmaximal, characteristic, complemented
8#30465C211yesmaximal, characteristic, complemented
9#28912C211yesmaximal, characteristic, complemented
10#28560C211yesmaximal, characteristic, complemented
11#28358C211yesmaximal, characteristic, complemented
12#27785C211yesmaximal, characteristic, complemented
13#27258C211yesmaximal, characteristic, complemented
14#26980C211yesmaximal, characteristic, complemented
15#26902C211yesmaximal, characteristic, complemented
16#26844C211yesmaximal, characteristic, complemented
17#26839C211yesmaximal, characteristic, complemented
18#26625C211yesmaximal, characteristic, complemented
19#26169C211yesmaximal, characteristic, complemented
20#25545C211yesmaximal, characteristic, complemented
21#25204C211yesmaximal, characteristic, complemented
22#25079C211yesmaximal, characteristic, complemented
23#24906C211yesmaximal, characteristic, complemented
24#24425C211yesmaximal, characteristic
25#24071C211yesmaximal, characteristic, complemented
26#23947C211yesmaximal, characteristic, complemented
27#23139C211yesmaximal, characteristic, complemented
28#23004C211yesmaximal, characteristic, complemented
29#22855C211yesmaximal, characteristic, complemented
30#21568C211yesmaximal, characteristic, complemented
31#21087C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#541C2211yescharacteristic
36#3316—28no—
37#3178—28no—
38C2×#501C2211yescharacteristic
39C2×#497C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#488C2211yescharacteristic
42C2×#487C2211yescharacteristic
43C2×#484C2211yescharacteristic
44C2×#481C2211yescharacteristic
45C2×#483C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#470C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#467C2211yescharacteristic
50C2×#465C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#452C2211yescharacteristic
55C2×#449C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#448C2211yescharacteristic
58C2×#441C2211yescharacteristic
59C2×#441C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×C4×Q16C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×#435C2211yescharacteristic
64C2×#417C2211yescharacteristic
65C2×#416C2211yescharacteristic
66C22×#103C2211yescharacteristic
67C2×#405C2211yescharacteristic
68#2723—21no—
69#2720—21no—
70#2715—21no—
71#2704—21no—
72#2691—21no—
73#2690—21no—
74#2680—21no—
75#2674—21no—
76#2559—21no—
77#2551C2211yescharacteristic
78#2545C2211yescharacteristic
79#2542—21no—
80#2521—21no—
81#2519—21no—
82#2501C2211yescharacteristic
83#2490C2211yescharacteristic
84#2461—21no—
85#2460—21no—
86#2455—21no—
87#2454—21no—
88#2453C2211yescharacteristic
89#2452C2211yescharacteristic
90#2448C2211yescharacteristic
91#2448C2211yescharacteristic
92#2440C2211yescharacteristic
93#2434C2211yescharacteristic
94#2432C2211yescharacteristic
95#2426C2211yescharacteristic
96#2426C2211yescharacteristic
97#2423C2211yescharacteristic
98#2417C2211yescharacteristic
99#2414C2211yescharacteristic
100#2395C2211yescharacteristic
101#2365C2211yescharacteristic
102#2362C2211yescharacteristic
103#2361C2211yescharacteristic
104#2360C2211yescharacteristic
105Q8×C4⋊C4C2211yescharacteristic
106Q8×C22⋊C4C2211yescharacteristic
107#2317C2211yescharacteristic
108#2311C2211yescharacteristic
109#2095C2211yescharacteristic
110#2093C2211yescharacteristic
111#2086C2211yescharacteristic
112#2084C2211yescharacteristic
113#2076C2211yescharacteristic
114#2072C2211yescharacteristic
115#2067C2211yescharacteristic
116#2065C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2057C2211yescharacteristic
120#2056C2211yescharacteristic
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic
123#2043C2211yescharacteristic
124#2043C2211yescharacteristic
125#2043C2211yescharacteristic
126#2042C2211yescharacteristic
127#2036C2211yescharacteristic
128#2034C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#2023C2211yescharacteristic
132#2015C2211yescharacteristic
133#2015C2211yescharacteristic
134#2013C2211yescharacteristic
135#2012C2211yescharacteristic
136#2012C2211yescharacteristic
137#2012C2211yescharacteristic
138#2001C2211yescharacteristic
139#2000C2211yescharacteristic
140#1999C2211yescharacteristic
141#1983C2211yescharacteristic
142#1973C2211yescharacteristic
143#1970C2211yescharacteristic
144#1959C2211yescharacteristic
145#1956C2211yescharacteristic
146#1948C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1926C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1877C2211yescharacteristic
179#1874C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1852C2211yescharacteristic
192#1850C2211yescharacteristic
193#1818C2211yescharacteristic
194#1803C2211yescharacteristic
195#1787C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203#1736C2211yescharacteristic
204C2×#340C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#554—24no—
219#554—42no—
220#548—24no—
221#548—42no—
222#542—24no—
223#542—42no—
224#541—24no—
225#541—42no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#126—21no—
232C2×#126—21no—
233C2×#126—21no—
234C2×#125—21no—
235C2×#125—21no—
236C2×#125—21no—
237C2×#125C2311yescharacteristic
238C2×#124—21no—
239C2×#124—21no—
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#123—21no—
244C2×#123—21no—
245C2×#123—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×#121—21no—
258C2×#121C2311yescharacteristic
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4—21no—
270C2×C4×D4—21no—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278#501—24no—
279#497—24no—
280#489—24no—
281#488—24no—
282#487—24no—
283#484—42no—
284#483—24no—
285#481—24no—
286#475—24no—
287#470D418yescomplemented
288#468—24no—
289#467—24no—
290#465—24no—
291#465—24no—
292#464—24no—
293#462—24no—
294#452—24no—
295#451—24no—
296#449—42no—
297#448—24no—
298#441—24no—
299#441—24no—
300#440—24no—
301C4×Q16—24no—
302C4×SD16—24no—
303#435—24no—
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315#417—24no—
316#416—24no—
317C2×#103—24no—
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×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355#405—24no—
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362C2×C4×C8C2311yescharacteristic
363#400—21no—
364#400D411yescharacteristic
365#399—21no—
366#399—21no—
367#399—21no—
368#399—21no—
369#399—21no—
370#399D411yescharacteristic
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398D411yescharacteristic
376#397—21no—
377#397—21no—
378#397—21no—
379#397D411yescharacteristic
380#397D411yescharacteristic
381#397D411yescharacteristic
382#396—21no—
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395—21no—
392#395—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394—21no—
398#394—21no—
399#394D411yescharacteristic
400#394D411yescharacteristic
401#393—21no—
402#392—21no—
403#391—21no—
404#391—21no—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#390—21no—
412#390—21no—
413#390—21no—
414#390—21no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#388—21no—
436#388—21no—
437#388—21no—
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#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#386—21no—
456#386—21no—
457#386—21no—
458#386—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#385—21no—
469#384—21no—
470#384—21no—
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#382—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477#380—21no—
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C2×D411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16C2×D414yes—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—41no—
574C2×D8—41no—
575C2×D8—41no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16C2×D414yes—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—22no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601C4⋊Q8—82no—
602#126—44no—
603#126—44no—
604#126—44no—
605#125—22no—
606#125—41no—
607#125—44no—
608#125—44no—
609#125—44no—
610#124—22no—
611#124—22no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—44no—
617#124—44no—
618#123—44no—
619#123—82no—
620#123—82no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—44no—
627C22⋊Q8—44no—
628C22⋊Q8—44no—
629C22⋊Q8—44no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—82no—
634C22⋊Q8—82no—
635C22⋊Q8C2×D414yes—
636C22⋊Q8C2×D414yes—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—44no—
642#121—41no—
643#121—41no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—22no—
647C4×Q8—22no—
648C4×Q8—22no—
649C4×Q8—22no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—22no—
661C4×D4—41no—
662C4×D4—44no—
663C4×D4—44no—
664C4×D4—82no—
665#117—22no—
666#117—22no—
667#117—22no—
668#117—41no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2×D411yescharacteristic
712C2×C4⋊C4C2×D411yescharacteristic
713C2×C4⋊C4C2×D411yescharacteristic
714C2×C4⋊C4C2×D411yescharacteristic
715C2×C4⋊C4C2×D411yescharacteristic
716C2×C4⋊C4C2×D411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C22⋊C4C2×D411yescharacteristic
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782#107—22no—
783#107—22no—
784#107—41no—
785#107—41no—
786#106—22no—
787#106—22no—
788#106—22no—
789#106C2×D414yes—
790C4⋊C8—22no—
791C4⋊C8—22no—
792C4⋊C8—41no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#103—41no—
811#103—41no—
812#103C2×D414yes—
813#103C2×D414yes—
814#103#4114yes—
815#102—22no—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—41no—
823#102—41no—
824#102—41no—
825C22⋊C8—22no—
826C22⋊C8—22no—
827C22⋊C8—22no—
828C22⋊C8—22no—
829C22⋊C8—41no—
830#97—22no—
831#97—22no—
832#97—22no—
833#97—41no—
834C4×C8—22no—
835C4×C8—22no—
836C4×C8—41no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871C24—21no—
872C24—21no—
873C24C22×D411yescharacteristic
874C24C22×D411yescharacteristic
875#41—44no—
876#41—44no—
877#41—82no—
878#41—82no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—44no—
905C2×Q8—81no—
906C2×Q8—81no—
907C2×Q8—81no—
908C2×Q8—81no—
909C2×Q8—81no—
910C2×Q8—82no—
911C2×Q8—82no—
912C2×Q8—82no—
913C2×Q8C22×D412yes—
914C2×Q8C22×D412yes—
915C2×Q8C2×#4112yes—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—41no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D412yes—
997C22×C4C22×D411yescharacteristic
998C22×C4H(5,𝔽2)12yes—
999C22×C4C2511yescharacteristic
1000Q16—44no—
1001Q16—44no—
1002Q16—44no—
1003SD16—44no—
1004SD16—44no—
1005SD16—82no—
1006SD16—82no—
1007D8—82no—
1008M16—44no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—44no—
1031C2×C8—82no—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C2×#4112yes—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4C22×D412yes—
1095C4⋊C4C22×D412yes—
1096C4⋊C4C2×#4112yes—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—81no—
1156C42—81no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23D4212yes—
1184C23#57812yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—22no—
1189Q8—22no—
1190Q8—22no—
1191Q8—22no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—84no—
1203Q8—162no—
1204Q8—162no—
1205D4—44no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—162no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4D4212yes—
1309C2×C4#57712yes—
1310C2×C4C23×D411yescharacteristic
1311C2×C4C22×#4111yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4#58511yescharacteristic
1314C2×C4#58511yescharacteristic
1315C2×C4#58511yescharacteristic
1316C8—22no—
1317C8—22no—
1318C8—22no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22C2×D4211yescharacteristic
1353C22D4×#4111yescharacteristic
1354C22#350011yescharacteristic
1355C22C2×#57711yescharacteristic
1356C22C2×#57811yescharacteristic
1357C22#358511yescharacteristic
1358C22#358611yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—42no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4D4×#4111yescharacteristic
1386C4#348511yescharacteristic
1387C4#349411yescharacteristic
1388C4#356011yescharacteristic
1389C2—42no—
1390C2—42no—
1391C2—161no—
1392C2—161no—
1393C2#5912211yescharacteristic
1394C2#6107611yescharacteristic
1395C2#6109511yescharacteristic
1396C2#6152411yescharacteristic
1397C2#6152611yescharacteristic
1398C2#6255311yescharacteristic
1399C2#6256711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24425C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3316C2semidirect
2. C2×#3178C2semidirect
3. #45246C2semidirect
4. #44989C2semidirect
5. #30965C2semidirect
6. #30799C2semidirect
7. #30758C2semidirect
8. #30465C2semidirect
9. #28912C2semidirect
10. #28560C2semidirect
11. #28358C2semidirect
12. #27785C2semidirect
13. #27258C2semidirect
14. #26980C2semidirect
15. #26902C2semidirect
16. #26844C2semidirect
17. #26839C2semidirect
18. #26625C2semidirect
19. #26169C2semidirect
20. #25545C2semidirect
21. #25204C2semidirect
22. #25079C2semidirect
23. #24906C2semidirect
25. #24071C2semidirect
26. #23947C2semidirect
27. #23139C2semidirect
28. #23004C2semidirect
29. #22855C2semidirect
30. #21568C2semidirect
31. #21087C2semidirect
287. #470D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33162
C2×#31782
#452462
#449892
#309652
#307992
#307582
#304652
#289122
#285602
#283582
#277852
#272582
#269802
#269022
#268442
#268392
#266252
#261692
#255452
#252042
#250792
#249062
#244252
#240712
#239472
#231392
#230042
#228552
#215682
#210872