Finite Group Databasebeta

← #7503410

Subgroups — #7503410

Order 512.

1971 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3091C211yesmaximal, characteristic
2C2×#3076C211yesmaximal, characteristic, complemented
3#34742C211yesmaximal, characteristic
4#34739C211yesmaximal, characteristic, complemented
5#31109C211yesmaximal, characteristic, complemented
6#31108C211yesmaximal, characteristic, complemented
7#31107C211yesmaximal, characteristic, complemented
8#31106C211yesmaximal, characteristic, complemented
9#31105C211yesmaximal, characteristic, complemented
10#31104C211yesmaximal, characteristic, complemented
11#31103C211yesmaximal, characteristic, complemented
12#31102C211yesmaximal, characteristic, complemented
13#31101C211yesmaximal, characteristic, complemented
14#31100C211yesmaximal, characteristic, complemented
15#31099C211yesmaximal, characteristic, complemented
16#31098C211yesmaximal, characteristic, complemented
17#31097C211yesmaximal, characteristic, complemented
18#31096C211yesmaximal, characteristic, complemented
19#31095C211yesmaximal, characteristic, complemented
20#31094C211yesmaximal, characteristic, complemented
21#23666C211yesmaximal, characteristic, complemented
22#23656C211yesmaximal, characteristic, complemented
23#23638C211yesmaximal, characteristic, complemented
24#23627C211yesmaximal, characteristic, complemented
25#23551C211yesmaximal, characteristic, complemented
26#23479C211yesmaximal, characteristic
27#21086C211yesmaximal, characteristic, complemented
28C2×#1924C211yesmaximal, characteristic, complemented
29#20872C211yesmaximal, characteristic, complemented
30#20843C211yesmaximal, characteristic, complemented
31#20799C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×#117C2211yescharacteristic
36#3091—28no—
37C2×#484C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#482C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#483C2211yescharacteristic
44C2×#480C2211yescharacteristic
45#3076—28no—
46C2×#479C2211yescharacteristic, complemented
47C2×#479C2211yescharacteristic, complemented
48C2×#477C2211yescharacteristic, complemented
49C2×#475C2211yescharacteristic, complemented
50C2×#478C2211yescharacteristic, complemented
51C2×#478C2211yescharacteristic, complemented
52C2×#476C2211yescharacteristic, complemented
53C2×#474C2211yescharacteristic, complemented
54C2×#427C2211yescharacteristic
55C2×#427C2211yescharacteristic
56C2×#427C2211yescharacteristic
57C2×#427C2211yescharacteristic
58C2×#427C2211yescharacteristic
59C2×#427C2211yescharacteristic
60C22×C4⋊C8C2211yescharacteristic
61C2×#416C2211yescharacteristic
62C2×#416C2211yescharacteristic
63C2×#416C2211yescharacteristic
64C2×#416C2211yescharacteristic
65C22×C22⋊C8C2211yescharacteristic
66C22×C22⋊C8C2211yescharacteristic
67C22×#97C2211yescharacteristic
68#2442C2211yescharacteristic
69#2442C2211yescharacteristic
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic
74#2439C2211yescharacteristic
75#2439C2211yescharacteristic
76#2438—21no—
77#2438—21no—
78#2437—21no—
79#2437—21no—
80#2423C2211yescharacteristic
81#2423C2211yescharacteristic
82#2422C2211yescharacteristic
83#2422C2211yescharacteristic
84#2421C2211yescharacteristic
85#2421C2211yescharacteristic
86#2420C2211yescharacteristic
87#2420C2211yescharacteristic
88#2419—21no—
89#2419—21no—
90#2418—21no—
91#2418—21no—
92#2396—21no—
93#2396—21no—
94#2395—21no—
95#2395—21no—
96C4×C22⋊Q8—21no—
97C4×C22⋊Q8—21no—
98C4×#123—21no—
99C4×#123—21no—
100#2297C2211yescharacteristic
101#2296C2211yescharacteristic
102#2296C2211yescharacteristic
103#2296C2211yescharacteristic
104#2285C2211yescharacteristic
105#2285C2211yescharacteristic
106#2280C2211yescharacteristic
107#2280C2211yescharacteristic
108C2×C4×C22⋊C4C2211yescharacteristic
109#2088C2211yescharacteristic, complemented
110#2088C2211yescharacteristic, complemented
111#2088C2211yescharacteristic, complemented
112#2088C2211yescharacteristic, complemented
113#2087C2211yescharacteristic, complemented
114#2087C2211yescharacteristic, complemented
115#2086C2211yescharacteristic, complemented
116#2086C2211yescharacteristic, complemented
117#2085C2211yescharacteristic, complemented
118#2085C2211yescharacteristic, complemented
119#2085C2211yescharacteristic, complemented
120#2085C2211yescharacteristic, complemented
121#2084C2211yescharacteristic, complemented
122#2084C2211yescharacteristic, complemented
123#2083C2211yescharacteristic, complemented
124#2083C2211yescharacteristic, complemented
125#2077C2211yescharacteristic
126#2077C2211yescharacteristic
127#2077C2211yescharacteristic
128#2077C2211yescharacteristic
129#2076C2211yescharacteristic
130#2076C2211yescharacteristic
131#2075C2211yescharacteristic
132#2075C2211yescharacteristic
133#2074C2211yescharacteristic, complemented
134#2074C2211yescharacteristic, complemented
135#2073C2211yescharacteristic, complemented
136#2073C2211yescharacteristic, complemented
137#2072C2211yescharacteristic, complemented
138#2072C2211yescharacteristic, complemented
139#2071C2211yescharacteristic, complemented
140#2071C2211yescharacteristic, complemented
141#2059C2211yescharacteristic, complemented
142#2059C2211yescharacteristic, complemented
143#2059C2211yescharacteristic, complemented
144#2059C2211yescharacteristic, complemented
145#2058C2211yescharacteristic, complemented
146#2058C2211yescharacteristic, complemented
147#2057C2211yescharacteristic, complemented
148#2057C2211yescharacteristic, complemented
149#2036C2211yescharacteristic
150#2036C2211yescharacteristic
151#2035C2211yescharacteristic
152#2035C2211yescharacteristic
153#2034C2211yescharacteristic
154#2034C2211yescharacteristic
155#2033C2211yescharacteristic
156#2033C2211yescharacteristic
157#1936C2211yescharacteristic, complemented
158#1936C2211yescharacteristic, complemented
159#1936C2211yescharacteristic, complemented
160#1936C2211yescharacteristic, complemented
161#1935C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1935C2211yescharacteristic, complemented
164#1935C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic
170#1924C2211yescharacteristic
171#1924C2211yescharacteristic
172#1924C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1847C2211yescharacteristic, complemented
190#1847C2211yescharacteristic, complemented
191#1847C2211yescharacteristic, complemented
192#1847C2211yescharacteristic, complemented
193#1847C2211yescharacteristic, complemented
194#1847C2211yescharacteristic, complemented
195#1847C2211yescharacteristic, complemented
196#1847C2211yescharacteristic, complemented
197#1735C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C2×#336C2211yescharacteristic
204C2×#336C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#533—24no—
212#533—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217#525—24no—
218#525—42no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C4×#41—24no—
232C4×#41—42no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—24no—
247C2×#117—42no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4D411yescharacteristic
261C22×C22⋊C4D411yescharacteristic
262C22×C42—21no—
263C22×C42—21no—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266#485—24no—
267#485—24no—
268#484—24no—
269#483—24no—
270#482—24no—
271#482—24no—
272#481—24no—
273#480—24no—
274#479—24no—
275#479—24no—
276#478—24no—
277#478—24no—
278#477—24no—
279#476—24no—
280#475—24no—
281#474—24no—
282#427—24no—
283#427—24no—
284#427—24no—
285#427—24no—
286#427—42no—
287#427—42no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×C4⋊C8—24no—
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317#416—24no—
318#416—24no—
319#416—24no—
320#416D418yes—
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⋊C8—24no—
338C2×C22⋊C8—24no—
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×#97—24no—
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352#400—21no—
353#400—21no—
354#400—21no—
355#400—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#399—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—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#396—21no—
375#396—21no—
376#395—21no—
377#395—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#393—21no—
383#393—21no—
384#391—21no—
385#391—21no—
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#381—21no—
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4D411yescharacteristic
477C4×C22⋊C4D411yescharacteristic
478C4×C22⋊C4D411yescharacteristic
479C4×C22⋊C4D411yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484C2×#95D411yescharacteristic
485C2×#95D411yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25C2×D411yescharacteristic
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41C2×D414yes—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8C2411yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4C2411yescharacteristic
532C23×C4—22no—
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2×D411yescharacteristic
548C23×C4C2×D411yescharacteristic
549C23×C4C2×D411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—22no—
563C22×C8C2×D414yes—
564C22×C8#4114yes—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#125—22no—
578#125—22no—
579#125—41no—
580#125—41no—
581#123—44no—
582#123—44no—
583#123—44no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#120—44no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—44no—
608C4×D4—44no—
609C4×D4—44no—
610C4×D4—44no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—44no—
627#117—44no—
628#117—44no—
629#117—41no—
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—21no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—42no—
710C2×C22⋊C4—42no—
711C2×C22⋊C4—44no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—22no—
721C2×C42—21no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—44no—
736C2×C42—44no—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—22no—
746#107—22no—
747#107—22no—
748#107—22no—
749#107—22no—
750#107—22no—
751#107—22no—
752#107—22no—
753#107—41no—
754#107—41no—
755#107—41no—
756#107—41no—
757#106—22no—
758#106—22no—
759#106—22no—
760#106—22no—
761#106—22no—
762#106—22no—
763#106—22no—
764#106—22no—
765#106—41no—
766#106—41no—
767#106—41no—
768#106—41no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103C2×D414yes—
780#103C2×D414yes—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102C2×D414yes—
788#102C2×D414yes—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797#97—22no—
798#97—22no—
799#97—22no—
800#97—22no—
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#95—21no—
832#95—21no—
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—22no—
842C24—21no—
843C24—22no—
844C24—22no—
845C24—22no—
846C24—41no—
847C24—41no—
848C24—41no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—28no—
853#41—28no—
854#41—44no—
855#41—44no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8C22×D412yes—
868C2×D4—24no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4C22×D412yes—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—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—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—44no—
938C22×C4—42no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D412yes—
961C22×C4C22×D411yescharacteristic
962C22×C4C2×#4112yes—
963C22×C4H(5,𝔽2)12yes—
964C22×C42−1+412yes—
965C22×C42−1+412yes—
966C22×C42−1+412yes—
967C22×C4C2511yescharacteristic
968C2×C8—28no—
969C2×C8—28no—
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—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—44no—
991C2×C8—44no—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C2×C8C2×#4112yes—
995C2×C8C2×#4112yes—
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—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
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—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4C22×D412yes—
1055C4⋊C4C22×D412yes—
1056C22⋊C4—24no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C42—22no—
1092C42—22no—
1093C42—24no—
1094C42—22no—
1095C42—22no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—44no—
1133C23—44no—
1134C23—44no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—44no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—82no—
1143C23—82no—
1144C23—82no—
1145C23#53612yes—
1146C23D4212yes—
1147C23#54712yes—
1148C23#57512yes—
1149C23C23×D411yescharacteristic
1150Q8—22no—
1151Q8—22no—
1152Q8—41no—
1153Q8—41no—
1154Q8—84no—
1155Q8—84no—
1156D4—22no—
1157D4—22no—
1158D4—48no—
1159D4—41no—
1160D4—41no—
1161D4—84no—
1162D4—84no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—44no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—44no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—48no—
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—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—84no—
1251C2×C4—82no—
1252C2×C4—82no—
1253C2×C4—82no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4#53614yes—
1258C2×C4#53612yes—
1259C2×C4#53914yes—
1260C2×C4D4212yes—
1261C2×C4#54712yes—
1262C2×C4#54714yes—
1263C2×C4#56314yes—
1264C2×C4#57512yes—
1265C2×C4C23×D411yescharacteristic
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×2−1+411yescharacteristic
1269C2×C4C2×2−1+411yescharacteristic
1270C2×C4C2×2−1+411yescharacteristic
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—22no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—42no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—88no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22#268014yes—
1308C22C2×#53611yescharacteristic
1309C22C2×D4211yescharacteristic
1310C22C2×#54711yescharacteristic
1311C22C2×#57511yescharacteristic
1312C22C2×#57511yescharacteristic
1313C22#358411yescharacteristic
1314C22#358411yescharacteristic
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—42no—
1325C4—41no—
1326C4—41no—
1327C4—42no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4#268014yes—
1341C4C2×#53611yescharacteristic
1342C4C2×#53911yescharacteristic
1343C4C2×#54711yescharacteristic
1344C4C2×#56311yescharacteristic
1345C2—24no—
1346C2—42no—
1347C2—81no—
1348C2—82no—
1349C2C2×#268011yescharacteristic
1350C2#6085411yescharacteristic
1351C2#6085911yescharacteristic
1352C2#6103011yescharacteristic
1353C2#6103011yescharacteristic
1354C2#6124311yescharacteristic
1355C2#6125111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3076C2semidirect
4. #34739C2semidirect
5. #31109C2semidirect
6. #31108C2semidirect
7. #31107C2semidirect
8. #31106C2semidirect
9. #31105C2semidirect
10. #31104C2semidirect
11. #31103C2semidirect
12. #31102C2semidirect
13. #31101C2semidirect
14. #31100C2semidirect
15. #31099C2semidirect
16. #31098C2semidirect
17. #31097C2semidirect
18. #31096C2semidirect
19. #31095C2semidirect
20. #31094C2semidirect
21. #23666C2semidirect
22. #23656C2semidirect
23. #23638C2semidirect
24. #23627C2semidirect
25. #23551C2semidirect
27. #21086C2semidirect
28. C2×#1924C2semidirect
29. #20872C2semidirect
30. #20843C2semidirect
31. #20799C2semidirect
46. C2×#479C22semidirect
47. C2×#479C22semidirect
48. C2×#477C22semidirect
49. C2×#475C22semidirect
50. C2×#478C22semidirect
51. C2×#478C22semidirect
52. C2×#476C22semidirect
53. C2×#474C22semidirect
109. #2088C22semidirect
110. #2088C22semidirect
111. #2088C22semidirect
112. #2088C22semidirect
113. #2087C22semidirect
114. #2087C22semidirect
115. #2086C22semidirect
116. #2086C22semidirect
117. #2085C22semidirect
118. #2085C22semidirect
119. #2085C22semidirect
120. #2085C22semidirect
121. #2084C22semidirect
122. #2084C22semidirect
123. #2083C22semidirect
124. #2083C22semidirect
133. #2074C22semidirect
134. #2074C22semidirect
135. #2073C22semidirect
136. #2073C22semidirect
137. #2072C22semidirect
138. #2072C22semidirect
139. #2071C22semidirect
140. #2071C22semidirect
141. #2059C22semidirect
142. #2059C22semidirect
143. #2059C22semidirect
144. #2059C22semidirect
145. #2058C22semidirect
146. #2058C22semidirect
147. #2057C22semidirect
148. #2057C22semidirect
157. #1936C22semidirect
158. #1936C22semidirect
159. #1936C22semidirect
160. #1936C22semidirect
161. #1935C22semidirect
162. #1935C22semidirect
163. #1935C22semidirect
164. #1935C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
189. #1847C22semidirect
190. #1847C22semidirect
191. #1847C22semidirect
192. #1847C22semidirect
193. #1847C22semidirect
194. #1847C22semidirect
195. #1847C22semidirect
196. #1847C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30912
C2×#30762
#347422
#347392
#311092
#311082
#311072
#311062
#311052
#311042
#311032
#311022
#311012
#311002
#310992
#310982
#310972
#310962
#310952
#310942
#236662
#236562
#236382
#236272
#235512
#234792
#210862
C2×#19242
#208722
#208432
#207992