Finite Group Databasebeta

← #7034943

Subgroups — #7034943

Order 512.

1815 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3346C211yesmaximal, characteristic, complemented
2C2×#3201C211yesmaximal, characteristic, complemented
3#45114C211yesmaximal, characteristic, complemented
4#45092C211yesmaximal, characteristic
5#31082C211yesmaximal, characteristic, complemented
6#31079C211yesmaximal, characteristic, complemented
7#31023C211yesmaximal, characteristic, complemented
8#31018C211yesmaximal, characteristic, complemented
9#30798C211yesmaximal, characteristic, complemented
10#30793C211yesmaximal, characteristic, complemented
11#30422C211yesmaximal, characteristic, complemented
12#30419C211yesmaximal, characteristic, complemented
13#28564C211yesmaximal, characteristic, complemented
14#27931C211yesmaximal, characteristic, complemented
15#27237C211yesmaximal, characteristic, complemented
16#27223C211yesmaximal, characteristic, complemented
17#26154C211yesmaximal, characteristic, complemented
18#26149C211yesmaximal, characteristic, complemented
19#25561C211yesmaximal, characteristic, complemented
20#25551C211yesmaximal, characteristic, complemented
21#25229C211yesmaximal, characteristic, complemented
22#25225C211yesmaximal, characteristic, complemented
23#25020C211yesmaximal, characteristic, complemented
24#25019C211yesmaximal, characteristic, complemented
25#24923C211yesmaximal, characteristic, complemented
26#24914C211yesmaximal, characteristic, complemented
27#24014C211yesmaximal, characteristic, complemented
28#24012C211yesmaximal, characteristic, complemented
29#23639C211yesmaximal, characteristic, complemented
30#23131C211yesmaximal, characteristic, complemented
31#22033C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#537C2211yescharacteristic
35C2×#536C2211yescharacteristic
36#3346—28no—
37#3201—28no—
38C2×#501C2211yescharacteristic
39C2×#484C2211yescharacteristic
40C2×#484C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#483C2211yescharacteristic
46C2×#483C2211yescharacteristic
47C2×#483C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#479C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#470C2211yescharacteristic
52C2×#468C2211yescharacteristic
53C2×#468C2211yescharacteristic
54C2×#467C2211yescharacteristic
55C2×#465C2211yescharacteristic
56C2×#452C2211yescharacteristic
57C2×#452C2211yescharacteristic
58C2×#451C2211yescharacteristic
59C2×#448C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#435C2211yescharacteristic
62C2×#428C2211yescharacteristic
63C22×#107C2211yescharacteristic
64C2×#408C2211yescharacteristic
65#2713—21no—
66#2703—21no—
67#2700—21no—
68#2699—21no—
69#2696—21no—
70#2689—21no—
71#2688—21no—
72#2687—21no—
73#2559—21no—
74#2558—21no—
75#2536C2211yescharacteristic
76#2535C2211yescharacteristic
77#2503C2211yescharacteristic
78#2503C2211yescharacteristic
79#2492—21no—
80#2492C2211yescharacteristic
81#2489C2211yescharacteristic
82#2488—21no—
83#2459—21no—
84#2457—21no—
85#2444—21no—
86#2442C2211yescharacteristic
87#2439C2211yescharacteristic
88#2421C2211yescharacteristic
89#2420—21no—
90#2420C2211yescharacteristic
91#2417C2211yescharacteristic
92#2415C2211yescharacteristic
93#2415C2211yescharacteristic
94#2415C2211yescharacteristic
95#2409C2211yescharacteristic
96#2407C2211yescharacteristic
97#2388C2211yescharacteristic
98#2363C2211yescharacteristic
99#2362C2211yescharacteristic
100#2352C2211yescharacteristic
101#2352C2211yescharacteristic
102Q8×C22⋊C4C2211yescharacteristic
103#2339C2211yescharacteristic
104#2311C2211yescharacteristic
105#2311C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2097C2211yescharacteristic
109#2097C2211yescharacteristic
110#2087C2211yescharacteristic
111#2085C2211yescharacteristic
112#2085C2211yescharacteristic
113#2076C2211yescharacteristic
114#2076C2211yescharacteristic
115#2076C2211yescharacteristic
116#2076C2211yescharacteristic
117#2076C2211yescharacteristic
118#2075C2211yescharacteristic
119#2075C2211yescharacteristic
120#2075C2211yescharacteristic
121#2075C2211yescharacteristic
122#2074C2211yescharacteristic
123#2073C2211yescharacteristic
124#2068C2211yescharacteristic
125#2066C2211yescharacteristic
126#2059C2211yescharacteristic
127#2058C2211yescharacteristic
128#2056C2211yescharacteristic
129#2056C2211yescharacteristic
130#2055C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2035C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2035C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2026C2211yescharacteristic
142#2024C2211yescharacteristic
143#2001C2211yescharacteristic
144#2001C2211yescharacteristic
145#2000C2211yescharacteristic
146#1969C2211yescharacteristic
147#1969C2211yescharacteristic
148#1954C2211yescharacteristic
149#1954C2211yescharacteristic
150#1949C2211yescharacteristic
151#1949C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1880C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1875C2211yescharacteristic
173#1873C2211yescharacteristic
174#1873C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1872C2211yescharacteristic
178#1870C2211yescharacteristic
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1851C2211yescharacteristic
190#1846C2211yescharacteristic
191#1846C2211yescharacteristic
192#1805C2211yescharacteristic
193#1804C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1780C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic
203#1736C2211yescharacteristic
204#1735C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#554—24no—
216#554—42no—
217#553—24no—
218#553—42no—
219#537—24no—
220#537—42no—
221#536—24no—
222#536—42no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#126—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268#501—24no—
269#485—24no—
270#485—24no—
271#484—24no—
272#484—24no—
273#483—24no—
274#483—42no—
275#483—42no—
276#482—24no—
277#481—24no—
278#480—24no—
279#479—24no—
280#474—24no—
281#470—24no—
282#468—24no—
283#468—24no—
284#467—24no—
285#465D418yescomplemented
286#452—24no—
287#452—24no—
288#451—24no—
289#448—24no—
290#440—24no—
291#435—24no—
292#428—24no—
293C2×#107—24no—
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337#408—24no—
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#400—21no—
359#400—21no—
360#400—21no—
361#400—21no—
362#398—21no—
363#398—21no—
364#398—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#395D411yescharacteristic
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394D411yescharacteristic
383#394D411yescharacteristic
384#394D411yescharacteristic
385#393—21no—
386#393—21no—
387#393—21no—
388#393D411yescharacteristic
389#392—21no—
390#392—21no—
391#392D411yescharacteristic
392#392D411yescharacteristic
393#392D411yescharacteristic
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#390—21no—
408#390—21no—
409#390—21no—
410#390C2311yescharacteristic
411#389—21no—
412#389—21no—
413#389—21no—
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#388—21no—
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#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—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#386—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#382—21no—
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381—21no—
460#381—21no—
461#381—21no—
462#381—21no—
463#381—21no—
464#381—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478C4×C4⋊C4—21no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488C2×#95—21no—
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#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
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—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8C2×D411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4C2×D411yescharacteristic
544C22×D4C2×D411yescharacteristic
545C22×D4C2×D411yescharacteristic
546C22×D4C2×D411yescharacteristic
547C22×D4C2×D411yescharacteristic
548C22×D4C2×D411yescharacteristic
549C22×D4C2411yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C2×Q16—22no—
563C2×Q16—22no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×SD16—22no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16C2×D414yes—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16—41no—
579C2×M16—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2×D414yes—
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C4⋊Q8—22no—
592C4⋊Q8—41no—
593C4⋊Q8—44no—
594#126—44no—
595#125—22no—
596#125—41no—
597#125—44no—
598#124—44no—
599#123—44no—
600#123—44no—
601#123—44no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—44no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8C2×D414yes—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—44no—
627#121—41no—
628#121—41no—
629#121—44no—
630#121—44no—
631#121—44no—
632#121C2×D414yes—
633C4×Q8—22no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
648C4×D4—44no—
649#117—22no—
650#117—22no—
651#117—41no—
652#117—41no—
653#117—41no—
654#117—41no—
655#117—41no—
656#117—41no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
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—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—22no—
757#107—22no—
758#107—22no—
759#107—22no—
760#107—22no—
761#107—22no—
762#107—22no—
763#106—22no—
764#106—22no—
765#106—22no—
766#106—41no—
767#106—41no—
768#106—41no—
769#106—41no—
770#106C2×D414yes—
771C4⋊C8—22no—
772C4⋊C8—41no—
773C4⋊C8—41no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103C2×D414yes—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—41no—
796#102—41no—
797#102C2×D414yes—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—22no—
801C22⋊C8—22no—
802C22⋊C8—22no—
803C22⋊C8—22no—
804C22⋊C8—22no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C22⋊C8—41no—
808C22⋊C8—41no—
809C22⋊C8—41no—
810C22⋊C8—41no—
811#97—22no—
812C4×C8—41no—
813C4×C8—41no—
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#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
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#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858C24—21no—
859C24C22×D411yescharacteristic
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862C24C22×D411yescharacteristic
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867#41—82no—
868#41—82no—
869#41—82no—
870#41—82no—
871C2×Q8—22no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
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—41no—
890C2×Q8—41no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—81no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×Q8—82no—
898C2×Q8—82no—
899C2×Q8—82no—
900C2×Q8—82no—
901C2×Q8C22×D412yes—
902C2×D4—22no—
903C2×D4—24no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—41no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—41no—
919C2×D4—41no—
920C2×D4—41no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—41no—
924C2×D4—41no—
925C2×D4—41no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4C22×D412yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
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—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D412yes—
1010C22×C4H(5,𝔽2)12yes—
1011C22×C4C2511yescharacteristic
1012Q16—82no—
1013Q16—82no—
1014SD16—44no—
1015SD16—82no—
1016M16—44no—
1017M16—82no—
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—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—44no—
1041C2×C8C22×D412yes—
1042C2×C8C22×D412yes—
1043C4⋊C4—24no—
1044C4⋊C4—22no—
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—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
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—42no—
1083C4⋊C4—42no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4C22×D412yes—
1091C4⋊C4C22×D412yes—
1092C22⋊C4—24no—
1093C22⋊C4—22no—
1094C22⋊C4—24no—
1095C22⋊C4—22no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
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—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
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—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—81no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—22no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23D4212yes—
1183C23C23×D411yescharacteristic
1184Q8—22no—
1185Q8—22no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—82no—
1197Q8—84no—
1198Q8—162no—
1199D4—22no—
1200D4—22no—
1201D4—44no—
1202D4—41no—
1203D4—41no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—84no—
1208D4—82no—
1209D4—82no—
1210D4—84no—
1211D4—162no—
1212D4—162no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
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—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
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—41no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4D4212yes—
1312C2×C4C23×D411yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4#58511yescharacteristic
1315C2×C4#58511yescharacteristic
1316C2×C4#58511yescharacteristic
1317C2×C4#58511yescharacteristic
1318C8—22no—
1319C8—22no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—41no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—42no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22C2×D4211yescharacteristic
1362C22#348511yescharacteristic
1363C22#348511yescharacteristic
1364C22#358411yescharacteristic
1365C22#358411yescharacteristic
1366C22#358611yescharacteristic
1367C22#358611yescharacteristic
1368C4—22no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—42no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4#348511yescharacteristic
1394C4#350011yescharacteristic
1395C4#356011yescharacteristic
1396C4#356011yescharacteristic
1397C2—42no—
1398C2—81no—
1399C2—81no—
1400C2—81no—
1401C2—82no—
1402C2#4349211yescharacteristic
1403C2#6106011yescharacteristic
1404C2#6109011yescharacteristic
1405C2#6174811yescharacteristic
1406C2#6176311yescharacteristic
1407C2#6180111yescharacteristic
1408C2#6181411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45092C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3346C2semidirect
2. C2×#3201C2semidirect
3. #45114C2semidirect
5. #31082C2semidirect
6. #31079C2semidirect
7. #31023C2semidirect
8. #31018C2semidirect
9. #30798C2semidirect
10. #30793C2semidirect
11. #30422C2semidirect
12. #30419C2semidirect
13. #28564C2semidirect
14. #27931C2semidirect
15. #27237C2semidirect
16. #27223C2semidirect
17. #26154C2semidirect
18. #26149C2semidirect
19. #25561C2semidirect
20. #25551C2semidirect
21. #25229C2semidirect
22. #25225C2semidirect
23. #25020C2semidirect
24. #25019C2semidirect
25. #24923C2semidirect
26. #24914C2semidirect
27. #24014C2semidirect
28. #24012C2semidirect
29. #23639C2semidirect
30. #23131C2semidirect
31. #22033C2semidirect
285. #465D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33462
C2×#32012
#451142
#450922
#310822
#310792
#310232
#310182
#307982
#307932
#304222
#304192
#285642
#279312
#272372
#272232
#261542
#261492
#255612
#255512
#252292
#252252
#250202
#250192
#249232
#249142
#240142
#240122
#236392
#231312
#220332