Finite Group Databasebeta

← #6436806

Subgroups — #6436806

Order 512.

1825 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3178C211yesmaximal, characteristic, complemented
2C2×#2924C211yesmaximal, characteristic, complemented
3#35310C211yesmaximal, characteristic, complemented
4#35260C211yesmaximal, characteristic
5#29885C211yesmaximal, characteristic, complemented
6#29884C211yesmaximal, characteristic, complemented
7#29849C211yesmaximal, characteristic, complemented
8#29848C211yesmaximal, characteristic, complemented
9#29846C211yesmaximal, characteristic, complemented
10#29844C211yesmaximal, characteristic, complemented
11#29817C211yesmaximal, characteristic, complemented
12#29815C211yesmaximal, characteristic, complemented
13#29787C211yesmaximal, characteristic, complemented
14#29786C211yesmaximal, characteristic, complemented
15#29780C211yesmaximal, characteristic, complemented
16#29779C211yesmaximal, characteristic, complemented
17#29744C211yesmaximal, characteristic
18#29743C211yesmaximal, characteristic, complemented
19#29735C211yesmaximal, characteristic
20#29731C211yesmaximal, characteristic, complemented
21#23715C211yesmaximal, characteristic, complemented
22#23713C211yesmaximal, characteristic, complemented
23#23711C211yesmaximal, characteristic, complemented
24#23709C211yesmaximal, characteristic, complemented
25#23706C211yesmaximal, characteristic, complemented
26#23705C211yesmaximal, characteristic, complemented
27#23701C211yesmaximal, characteristic, complemented
28#23698C211yesmaximal, characteristic, complemented
29#21413C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#20821C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#3178—28no—
36C2×#501C2211yescharacteristic, complemented
37C2×#497C2211yescharacteristic, complemented
38C2×#488C2211yescharacteristic, complemented
39C2×#487C2211yescharacteristic, complemented
40C2×#470C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#441C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic, complemented
46C2×C4×Q16C2211yescharacteristic, complemented
47C2×C4×SD16C2211yescharacteristic, complemented
48#2924—28no—
49C2×#433C2211yescharacteristic
50C2×#433C2211yescharacteristic
51C2×#433C2211yescharacteristic
52C2×#433C2211yescharacteristic
53C2×#432C2211yescharacteristic
54C2×#432C2211yescharacteristic
55C2×#431C2211yescharacteristic
56C2×#431C2211yescharacteristic
57C2×#424C2211yescharacteristic
58C2×#424C2211yescharacteristic
59C2×#407C2211yescharacteristic
60C22×C22⋊C8C2211yescharacteristic
61C2×#405C2211yescharacteristic
62C2×#405C2211yescharacteristic
63#2857C2211yescharacteristic
64#2857C2211yescharacteristic
65#2851C2211yescharacteristic
66#2850C2211yescharacteristic
67#2848C2211yescharacteristic
68#2848C2211yescharacteristic
69#2848C2211yescharacteristic
70#2847C2211yescharacteristic
71#2629C2211yescharacteristic
72#2628C2211yescharacteristic
73#2625C2211yescharacteristic
74#2625C2211yescharacteristic
75#2625C2211yescharacteristic
76#2624C2211yescharacteristic
77#2621C2211yescharacteristic
78#2620C2211yescharacteristic
79#2481—21no—
80#2480—21no—
81#2480—21no—
82#2479—21no—
83#2478—21no—
84#2478—21no—
85#2477—21no—
86#2475—21no—
87#2475—21no—
88#2474—21no—
89#2473—21no—
90#2473—21no—
91#2472—21no—
92#2470—21no—
93#2449—21no—
94#2418—21no—
95#2324C2211yescharacteristic
96#2323C2211yescharacteristic
97#2323C2211yescharacteristic
98#2323C2211yescharacteristic
99#2314C2211yescharacteristic
100#2314C2211yescharacteristic
101C4×C22⋊Q8C2211yescharacteristic
102C4×C22⋊Q8C2211yescharacteristic
103C4×C22⋊Q8C2211yescharacteristic
104C4×#121C2211yescharacteristic
105#2088C2211yescharacteristic, complemented
106#2088C2211yescharacteristic, complemented
107#2088C2211yescharacteristic, complemented
108#2088C2211yescharacteristic, complemented
109#2087C2211yescharacteristic, complemented
110#2086C2211yescharacteristic, complemented
111#2086C2211yescharacteristic, complemented
112#2086C2211yescharacteristic, complemented
113#2077C2211yescharacteristic
114#2077C2211yescharacteristic
115#2077C2211yescharacteristic
116#2077C2211yescharacteristic
117#2076C2211yescharacteristic
118#2076C2211yescharacteristic
119#2076C2211yescharacteristic
120#2075C2211yescharacteristic
121#2068C2211yescharacteristic, complemented
122#2068C2211yescharacteristic, complemented
123#2068C2211yescharacteristic, complemented
124#2068C2211yescharacteristic, complemented
125#2068C2211yescharacteristic, complemented
126#2068C2211yescharacteristic, complemented
127#2068C2211yescharacteristic, complemented
128#2068C2211yescharacteristic, complemented
129#2068C2211yescharacteristic, complemented
130#2067C2211yescharacteristic, complemented
131#2067C2211yescharacteristic, complemented
132#2067C2211yescharacteristic, complemented
133#2066C2211yescharacteristic, complemented
134#2066C2211yescharacteristic, complemented
135#2066C2211yescharacteristic, complemented
136#2065C2211yescharacteristic, complemented
137#2056C2211yescharacteristic, complemented
138#2056C2211yescharacteristic, complemented
139#2056C2211yescharacteristic, complemented
140#2056C2211yescharacteristic, complemented
141#2055C2211yescharacteristic, complemented
142#2055C2211yescharacteristic, complemented
143#2055C2211yescharacteristic, complemented
144#2055C2211yescharacteristic, complemented
145#2036C2211yescharacteristic
146#2036C2211yescharacteristic
147#2036C2211yescharacteristic
148#2036C2211yescharacteristic
149#2036C2211yescharacteristic
150#2036C2211yescharacteristic
151#2036C2211yescharacteristic
152#2036C2211yescharacteristic
153#2036C2211yescharacteristic
154#2035C2211yescharacteristic
155#2035C2211yescharacteristic
156#2035C2211yescharacteristic
157#2034C2211yescharacteristic
158#2033C2211yescharacteristic
159#2033C2211yescharacteristic
160#2033C2211yescharacteristic
161#2001C2211yescharacteristic
162#2001C2211yescharacteristic
163#2001C2211yescharacteristic
164#2001C2211yescharacteristic
165#2000C2211yescharacteristic
166#2000C2211yescharacteristic
167#2000C2211yescharacteristic
168#2000C2211yescharacteristic
169#1993C2211yescharacteristic, complemented
170#1992C2211yescharacteristic, complemented
171#1991C2211yescharacteristic, complemented
172#1990C2211yescharacteristic, complemented
173#1960C2211yescharacteristic, complemented
174#1959C2211yescharacteristic, complemented
175#1958C2211yescharacteristic, complemented
176#1956C2211yescharacteristic, complemented
177#1895C2211yescharacteristic
178#1894C2211yescharacteristic
179#1894C2211yescharacteristic
180#1894C2211yescharacteristic
181#1893C2211yescharacteristic
182#1892C2211yescharacteristic
183#1892C2211yescharacteristic
184#1892C2211yescharacteristic
185#1846C2211yescharacteristic, complemented
186#1845C2211yescharacteristic, complemented
187#1836C2211yescharacteristic, complemented
188#1836C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1808C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196C4×#107C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202C4×#103C2211yescharacteristic, complemented
203C4×#103C2211yescharacteristic, complemented
204C4×#102C2211yescharacteristic, complemented
205C24×C4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#542—24no—
215#542—24no—
216#541—24no—
217#541—24no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×#117—24no—
250C2×#117—24no—
251C2×#117D411yescharacteristic
252C2×#117D411yescharacteristic
253C2×#117D411yescharacteristic
254C2×#117D411yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4D411yescharacteristic
260C22×C4⋊C4D411yescharacteristic
261C22×C22⋊C4D411yescharacteristic
262C22×C22⋊C4D411yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265#501—24no—
266#497—24no—
267#488—24no—
268#487—24no—
269#470—24no—
270#468—24no—
271#467—24no—
272#465—24no—
273#441—24no—
274#440—24no—
275C4×Q16—24no—
276C4×SD16—24no—
277#433—24no—
278#433—24no—
279#433—24no—
280#433—24no—
281#432—24no—
282#432—24no—
283#431—24no—
284#431—24no—
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297#424—24no—
298#424—24no—
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331#407—24no—
332C2×C22⋊C8—24no—
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341#405—24no—
342#405D418yescomplemented
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351#400—21no—
352#400—21no—
353#400—21no—
354#400—21no—
355#399—21no—
356#399—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#395—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#393—21no—
383#391—21no—
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#379—21no—
475#379—21no—
476#379—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
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#340C2311yescharacteristic
511#340C2311yescharacteristic
512C25C2×D411yescharacteristic
513C22×Q8—21no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4C2411yescharacteristic
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—21no—
524C23×C4—41no—
525C23×C4—41no—
526C23×C4—41no—
527C23×C4—41no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16C2×D414yes—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2×D414yes—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C4⋊Q8—22no—
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574#126—44no—
575#126—44no—
576#126—44no—
577#125—22no—
578#125—22no—
579#125—44no—
580#125—44no—
581#124—22no—
582#124—22no—
583#124—44no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—44no—
604C22⋊Q8—82no—
605#121—22no—
606#121—22no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#120—82no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—82no—
621#117—22no—
622#117—22no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—22no—
631#117C2×D414yes—
632#117#4114yes—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
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⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C22⋊C4—24no—
685C2×C22⋊C4—24no—
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—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⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107—41no—
751#107—41no—
752#106—22no—
753#106—22no—
754#106—41no—
755#106—41no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#102—22no—
783#102—22no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796#97—22no—
797#97—22no—
798#97C2×D414yes—
799#97C2×D414yes—
800C4×C8—22no—
801C4×C8—22no—
802C4×C8C2×D414yes—
803C4×C8C2×D414yes—
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#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—
844C24—22no—
845C24—22no—
846C24—21no—
847C24—41no—
848C24—41no—
849C24—41no—
850C24—41no—
851C24—41no—
852C24C22×D411yescharacteristic
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—42no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
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—22no—
915C22×C4—22no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—42no—
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×D411yescharacteristic
961C22×C4C22×D412yes—
962C22×C4C2×#4112yes—
963C22×C4C2511yescharacteristic
964Q16—44no—
965Q16—44no—
966SD16—44no—
967SD16—44no—
968M16—44no—
969M16—44no—
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×C8C22×D412yes—
995C2×C8C22×D412yes—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
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—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
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—81no—
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⋊C4—81no—
1055C4⋊C4#12114yes—
1056C4⋊C4#12114yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
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—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4#12114yes—
1095C22⋊C4#12114yes—
1096C42—22no—
1097C42—22no—
1098C42—22no—
1099C42—22no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42C22×D412yes—
1112C42C22×D412yes—
1113C42C2×#4112yes—
1114C42C2×#4112yes—
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—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—44no—
1135C23—44no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—82no—
1144C23—82no—
1145C23—82no—
1146C23—82no—
1147C23—82no—
1148C23C2×#12112yes—
1149C23#57812yes—
1150C23C23×D411yescharacteristic
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—162no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—162no—
1170D4—162no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
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—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—44no—
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—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—82no—
1262C2×C4—82no—
1263C2×C4—162no—
1264C2×C4C2×#12112yes—
1265C2×C4C2×#12112yes—
1266C2×C4C2×#12112yes—
1267C2×C4C2×#12112yes—
1268C2×C4C2×#12112yes—
1269C2×C4C23×D411yescharacteristic
1270C2×C4C22×#4111yescharacteristic
1271C2×C4#58511yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—22no—
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—88no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22C22×#12111yescharacteristic
1313C22#344911yescharacteristic
1314C22#344911yescharacteristic
1315C22C2×#57811yescharacteristic
1316C22#358411yescharacteristic
1317C22#358511yescharacteristic
1318C22#358611yescharacteristic
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4#344911yescharacteristic
1346C4#344911yescharacteristic
1347C4#345511yescharacteristic
1348C4#345511yescharacteristic
1349C2—42no—
1350C2—42no—
1351C2—81no—
1352C2—161no—
1353C2#3463311yescharacteristic
1354C2#6045911yescharacteristic
1355C2#6046011yescharacteristic
1356C2#6098111yescharacteristic
1357C2#6098311yescharacteristic
1358C2#6098411yescharacteristic
1359C2#6098611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3178C2semidirect
2. C2×#2924C2semidirect
3. #35310C2semidirect
5. #29885C2semidirect
6. #29884C2semidirect
7. #29849C2semidirect
8. #29848C2semidirect
9. #29846C2semidirect
10. #29844C2semidirect
11. #29817C2semidirect
12. #29815C2semidirect
13. #29787C2semidirect
14. #29786C2semidirect
15. #29780C2semidirect
16. #29779C2semidirect
18. #29743C2semidirect
20. #29731C2semidirect
21. #23715C2semidirect
22. #23713C2semidirect
23. #23711C2semidirect
24. #23709C2semidirect
25. #23706C2semidirect
26. #23705C2semidirect
27. #23701C2semidirect
28. #23698C2semidirect
29. #21413C2semidirect
30. #21412C2semidirect
31. #20821C2semidirect
36. C2×#501C22semidirect
37. C2×#497C22semidirect
38. C2×#488C22semidirect
39. C2×#487C22semidirect
44. C2×#441C22semidirect
45. C2×#440C22semidirect
46. C2×C4×Q16C22semidirect
47. C2×C4×SD16C22semidirect
105. #2088C22semidirect
106. #2088C22semidirect
107. #2088C22semidirect
108. #2088C22semidirect
109. #2087C22semidirect
110. #2086C22semidirect
111. #2086C22semidirect
112. #2086C22semidirect
121. #2068C22semidirect
122. #2068C22semidirect
123. #2068C22semidirect
124. #2068C22semidirect
125. #2068C22semidirect
126. #2068C22semidirect
127. #2068C22semidirect
128. #2068C22semidirect
129. #2068C22semidirect
130. #2067C22semidirect
131. #2067C22semidirect
132. #2067C22semidirect
133. #2066C22semidirect
134. #2066C22semidirect
135. #2066C22semidirect
136. #2065C22semidirect
137. #2056C22semidirect
138. #2056C22semidirect
139. #2056C22semidirect
140. #2056C22semidirect
141. #2055C22semidirect
142. #2055C22semidirect
143. #2055C22semidirect
144. #2055C22semidirect
169. #1993C22semidirect
170. #1992C22semidirect
171. #1991C22semidirect
172. #1990C22semidirect
173. #1960C22semidirect
174. #1959C22semidirect
175. #1958C22semidirect
176. #1956C22semidirect
185. #1846C22semidirect
186. #1845C22semidirect
187. #1836C22semidirect
188. #1836C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect
196. C4×#107C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
200. #1762C22semidirect
201. C4×#103C22semidirect
202. C4×#103C22semidirect
203. C4×#103C22semidirect
204. C4×#102C22semidirect
342. #405D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31782
C2×#29242
#353102
#352602
#298852
#298842
#298492
#298482
#298462
#298442
#298172
#298152
#297872
#297862
#297802
#297792
#297442
#297432
#297352
#297312
#237152
#237132
#237112
#237092
#237062
#237052
#237012
#236982
#214132
#214122
#208212