Finite Group Databasebeta

← #6578261

Subgroups — #6578261

Order 512.

2025 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3127C211yesmaximal, characteristic, complemented
2C2×#3120C211yesmaximal, characteristic, complemented
3#39385C211yesmaximal, characteristic, complemented
4#34312C211yesmaximal, characteristic
5#33163C211yesmaximal, characteristic, complemented
6#32916C211yesmaximal, characteristic, complemented
7#32915C211yesmaximal, characteristic, complemented
8#28449C211yesmaximal, characteristic, complemented
9#28285C211yesmaximal, characteristic, complemented
10#26642C211yesmaximal, characteristic, complemented
11#26636C211yesmaximal, characteristic, complemented
12#26627C211yesmaximal, characteristic, complemented
13#26621C211yesmaximal, characteristic, complemented
14#26249C211yesmaximal, characteristic, complemented
15#26247C211yesmaximal, characteristic, complemented
16#25767C211yesmaximal, characteristic
17#25767C211yesmaximal, characteristic
18#25173C211yesmaximal, characteristic, complemented
19#25171C211yesmaximal, characteristic, complemented
20#25161C211yesmaximal, characteristic, complemented
21#25151C211yesmaximal, characteristic, complemented
22#24666C211yesmaximal, characteristic, complemented
23#24664C211yesmaximal, characteristic, complemented
24#24165C211yesmaximal, characteristic, complemented
25#24163C211yesmaximal, characteristic, complemented
26#23194C211yesmaximal, characteristic, complemented
27#23192C211yesmaximal, characteristic, complemented
28#23014C211yesmaximal, characteristic, complemented
29#23014C211yesmaximal, characteristic, complemented
30#22798C211yesmaximal, characteristic, complemented
31#21618C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#541C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#497C2211yescharacteristic
38C2×#497C2211yescharacteristic
39#3127—28no—
40#3120—28no—
41C2×#484C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#483C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#462C2211yescharacteristic
49C2×#462C2211yescharacteristic
50C2×#462C2211yescharacteristic
51C2×#462C2211yescharacteristic
52C2×#462C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#462C2211yescharacteristic
55C2×#462C2211yescharacteristic
56C2×#461C2211yescharacteristic
57C2×#461C2211yescharacteristic
58C2×#452C2211yescharacteristic
59C2×#452C2211yescharacteristic
60C2×#452C2211yescharacteristic
61C2×#452C2211yescharacteristic
62C2×#451C2211yescharacteristic
63C2×#451C2211yescharacteristic
64C2×#451C2211yescharacteristic
65C2×#451C2211yescharacteristic
66C2×#441C2211yescharacteristic
67C2×#441C2211yescharacteristic
68C2×#441C2211yescharacteristic
69C2×#440C2211yescharacteristic
70C2×C4×Q16C2211yescharacteristic
71C2×C4×Q16C2211yescharacteristic
72C2×C4×Q16C2211yescharacteristic
73C2×C4×SD16C2211yescharacteristic
74C2×#433C2211yescharacteristic
75C2×#433C2211yescharacteristic
76#2868C2211yescharacteristic
77#2721—21no—
78#2721—21no—
79#2721—21no—
80#2721—21no—
81#2621C2211yescharacteristic
82#2621C2211yescharacteristic
83#2552—21no—
84#2552—21no—
85#2542C2211yescharacteristic
86#2542C2211yescharacteristic
87#2512—21no—
88#2512—21no—
89#2429C2211yescharacteristic
90#2429C2211yescharacteristic
91#2429C2211yescharacteristic
92#2429C2211yescharacteristic
93#2367—21no—
94#2367C2211yescharacteristic
95#2365C2211yescharacteristic
96#2365C2211yescharacteristic
97#2363—21no—
98#2363C2211yescharacteristic
99#2360—21no—
100#2360C2211yescharacteristic
101#2352—21no—
102#2352C2211yescharacteristic
103#2351C2211yescharacteristic
104#2341C2211yescharacteristic
105Q8×C22⋊C4C2211yescharacteristic
106#2324—21no—
107#2324C2211yescharacteristic
108#2323—21no—
109#2323C2211yescharacteristic
110C4×#125C2211yescharacteristic
111C4×#124—21no—
112C4×#124C2211yescharacteristic
113#2293—21no—
114#2293C2211yescharacteristic
115C42×Q8C2211yescharacteristic
116#2068C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic
119#2065C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2035C2211yescharacteristic
128#2016C2211yescharacteristic
129#2016C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#1989C2211yescharacteristic
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1981C2211yescharacteristic
144#1981C2211yescharacteristic
145#1981C2211yescharacteristic
146#1981C2211yescharacteristic
147#1981C2211yescharacteristic
148#1981C2211yescharacteristic
149#1973C2211yescharacteristic
150#1971C2211yescharacteristic
151#1969C2211yescharacteristic
152#1968C2211yescharacteristic
153#1960C2211yescharacteristic
154#1960C2211yescharacteristic
155#1955C2211yescharacteristic
156#1955C2211yescharacteristic
157#1949C2211yescharacteristic
158#1949C2211yescharacteristic
159#1949C2211yescharacteristic
160#1935C2211yescharacteristic
161#1935C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1921C2211yescharacteristic
169#1919C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1873C2211yescharacteristic
183#1873C2211yescharacteristic
184#1872C2211yescharacteristic
185#1872C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1865C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1863C2211yescharacteristic
192#1842C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1804C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1776C2211yescharacteristic
199#1776C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202#1767C2211yescharacteristic
203#1763C2211yescharacteristic
204#1763C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219#548—24no—
220#548—24no—
221#541—24no—
222#541—24no—
223#541—42no—
224#541—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#126—21no—
232C2×#126—21no—
233C2×#126—21no—
234C2×#126—21no—
235C2×#125—21no—
236C2×#125—21no—
237C2×#125—21no—
238C2×#125—21no—
239C2×#125C2311yescharacteristic
240C2×#124—21no—
241C2×#124C2311yescharacteristic
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121—21no—
253C2×#121C2311yescharacteristic
254#520—24no—
255#520—42no—
256#519—24no—
257#519—42no—
258C2×C4×Q8—21no—
259C2×C4×Q8—21no—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4—21no—
272C2×C4×D4—21no—
273C2×C4×D4—21no—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117—21no—
279C2×#117—21no—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4—21no—
284C22×C4⋊C4C2311yescharacteristic
285#497—24no—
286#497—24no—
287#485—24no—
288#485—24no—
289#484—24no—
290#483—24no—
291#479—24no—
292#479D418yescomplemented
293#478—24no—
294#462—24no—
295#462—24no—
296#462—24no—
297#462—24no—
298#462—24no—
299#462—42no—
300#462—42no—
301#462—42no—
302#461—24no—
303#461—42no—
304#452—24no—
305#452—24no—
306#452—42no—
307#452—42no—
308#451—24no—
309#451—24no—
310#451—42no—
311#451—42no—
312#441—24no—
313#441—24no—
314#441—24no—
315#440—24no—
316C4×Q16—24no—
317C4×Q16—24no—
318C4×Q16—24no—
319C4×SD16—24no—
320#433—24no—
321#433—24no—
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#106C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×#106C2311yescharacteristic
329C2×#106C2311yescharacteristic
330C2×C4⋊C8C2311yescharacteristic
331C2×C4⋊C8C2311yescharacteristic
332C2×C4⋊C8C2311yescharacteristic
333C2×C4⋊C8C2311yescharacteristic
334C2×C4⋊C8C2311yescharacteristic
335C2×C4⋊C8C2311yescharacteristic
336C2×C4⋊C8C2311yescharacteristic
337C2×C4⋊C8C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×C22⋊C8C2311yescharacteristic
371C2×C22⋊C8C2311yescharacteristic
372C2×C22⋊C8C2311yescharacteristic
373C2×C22⋊C8C2311yescharacteristic
374C2×C22⋊C8C2311yescharacteristic
375C2×C22⋊C8C2311yescharacteristic
376C2×C22⋊C8C2311yescharacteristic
377C2×C22⋊C8C2311yescharacteristic
378C2×#97C2311yescharacteristic
379C2×#97C2311yescharacteristic
380C2×#97C2311yescharacteristic
381C2×#97C2311yescharacteristic
382C2×C4×C8C2311yescharacteristic
383C2×C4×C8C2311yescharacteristic
384#399—21no—
385#399—21no—
386#399—21no—
387#399—21no—
388#398—21no—
389#398—21no—
390#398—21no—
391#398—21no—
392#398—21no—
393#398—21no—
394#398—21no—
395#398—21no—
396#397—21no—
397#397—21no—
398#397—21no—
399#397—21no—
400#396—21no—
401#396—21no—
402#396—21no—
403#396—21no—
404#391—21no—
405#391—21no—
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#390—21no—
413#390—21no—
414#390—21no—
415#390—21no—
416#390—21no—
417#390—21no—
418#390D411yescharacteristic
419#390D411yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389—21no—
430#389—21no—
431#389—21no—
432#389D411yescharacteristic
433#389D411yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#388—21no—
450#388—21no—
451#388D411yescharacteristic
452#388D411yescharacteristic
453#388D411yescharacteristic
454#388D411yescharacteristic
455#387—21no—
456#387—21no—
457#387—21no—
458#387—21no—
459#387—21no—
460#387—21no—
461#387—21no—
462#387—21no—
463#387—21no—
464#386—21no—
465#386—21no—
466#386—21no—
467#385—21no—
468#385—21no—
469#385—21no—
470#384—21no—
471#384—21no—
472#384—21no—
473#384—21no—
474#384—21no—
475#384—21no—
476#382—21no—
477#382C2311yescharacteristic
478#382C2311yescharacteristic
479#380—21no—
480#380—21no—
481#380C2311yescharacteristic
482#380C2311yescharacteristic
483C4×C4⋊C4—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4—21no—
486C4×C4⋊C4—21no—
487C4×C4⋊C4—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4—21no—
490C4×C4⋊C4—21no—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499C4×C22⋊C4—21no—
500C4×C22⋊C4—21no—
501C4×C22⋊C4—21no—
502C4×C22⋊C4—21no—
503C4×C22⋊C4—21no—
504C4×C22⋊C4—21no—
505C4×C22⋊C4C2311yescharacteristic
506C4×C22⋊C4C2311yescharacteristic
507C43—21no—
508C43C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518#340C2311yescharacteristic
519#340C2311yescharacteristic
520#340C2311yescharacteristic
521#336C2311yescharacteristic
522#336C2311yescharacteristic
523#336C2311yescharacteristic
524#336C2311yescharacteristic
525#336C2311yescharacteristic
526#336C2311yescharacteristic
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—21no—
536C22×Q8—22no—
537C22×Q8—22no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×Q8C2411yescharacteristic
541C22×Q8C2411yescharacteristic
542C22×Q8C2411yescharacteristic
543C22×Q8C2411yescharacteristic
544C22×Q8C2411yescharacteristic
545C22×Q8C2411yescharacteristic
546C22×D4—21no—
547C22×D4—21no—
548C22×D4C2×D411yescharacteristic
549C22×D4C2411yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—21no—
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C2×Q16—22no—
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—22no—
564C2×Q16—22no—
565C2×Q16—22no—
566C2×Q16—22no—
567C2×Q16—22no—
568C2×Q16—22no—
569C2×Q16—22no—
570C2×Q16—22no—
571C2×Q16—22no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—41no—
576C2×Q16—41no—
577C2×Q16—41no—
578C2×Q16—41no—
579C2×Q16—41no—
580C2×Q16—41no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—22no—
586C2×SD16—22no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C4⋊Q8—22no—
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—22no—
605C4⋊Q8—22no—
606C4⋊Q8—22no—
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609C4⋊Q8—41no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612C4⋊Q8—41no—
613#126—44no—
614#126—44no—
615#126—44no—
616#126—44no—
617#125—22no—
618#125—44no—
619#125—44no—
620#125—44no—
621#125—44no—
622#125C2×D414yes—
623#124—28no—
624#124—22no—
625#124#4114yes—
626C22⋊Q8—28no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—22no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648C4×Q8—22no—
649C4×Q8—22no—
650C4×Q8—22no—
651C4×Q8—22no—
652C4×Q8—22no—
653C4×Q8—22no—
654C4×Q8—22no—
655C4×Q8—22no—
656C4×Q8—22no—
657C4×Q8—22no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×Q8—41no—
664C4×Q8—41no—
665C4×Q8—41no—
666C4×Q8—41no—
667C4×Q8—41no—
668C4×Q8—44no—
669C4×Q8—44no—
670C4×Q8C2×D414yes—
671C4×Q8#4114yes—
672C4×D4—28no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—44no—
679C4×D4—41no—
680C4×D4—44no—
681#117—22no—
682#117—22no—
683#117—22no—
684#117—22no—
685#117—22no—
686#117—44no—
687#117—44no—
688#117—44no—
689#117—41no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2×D411yescharacteristic
733C2×C4⋊C4C2×D411yescharacteristic
734C2×C4⋊C4C2×D411yescharacteristic
735C2×C4⋊C4C2×D411yescharacteristic
736C2×C4⋊C4C2×D411yescharacteristic
737C2×C4⋊C4C2×D411yescharacteristic
738C2×C4⋊C4C2×D411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—21no—
762C2×C22⋊C4—21no—
763C2×C22⋊C4—21no—
764C2×C22⋊C4—21no—
765C2×C22⋊C4—21no—
766C2×C22⋊C4—21no—
767C2×C22⋊C4—21no—
768C2×C22⋊C4—21no—
769C2×C22⋊C4C2×D411yescharacteristic
770C2×C22⋊C4C2×D411yescharacteristic
771C2×C22⋊C4C2×D411yescharacteristic
772C2×C22⋊C4C2×D411yescharacteristic
773C2×C22⋊C4C2×D411yescharacteristic
774C2×C22⋊C4C2×D411yescharacteristic
775C2×C22⋊C4C2×D411yescharacteristic
776C2×C22⋊C4C2×D411yescharacteristic
777C2×C22⋊C4C2×D411yescharacteristic
778C2×C22⋊C4C2×D411yescharacteristic
779C2×C42—21no—
780C2×C42—21no—
781C2×C42—21no—
782C2×C42—21no—
783C2×C42—21no—
784C2×C42—21no—
785C2×C42—21no—
786C2×C42—21no—
787C2×C42—21no—
788C2×C42—21no—
789C2×C42—21no—
790C2×C42—21no—
791C2×C42—21no—
792C2×C42—21no—
793C2×C42—21no—
794C2×C42—21no—
795C2×C42—21no—
796C2×C42C2×D411yescharacteristic
797C2×C42C2×D411yescharacteristic
798C2×C42C2×D411yescharacteristic
799C2×C42C2×D411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805#107—22no—
806#107—22no—
807#107—41no—
808#107C2×D414yes—
809#106—22no—
810#106—22no—
811#106—41no—
812#106C2×D414yes—
813C4⋊C8—22no—
814C4⋊C8—22no—
815C4⋊C8—22no—
816C4⋊C8—22no—
817C4⋊C8—22no—
818C4⋊C8—41no—
819C4⋊C8—41no—
820C4⋊C8C2×D414yes—
821#103—22no—
822#103—22no—
823#103—22no—
824#103—22no—
825#103—22no—
826#103—22no—
827#103—22no—
828#103—22no—
829#103—22no—
830#103—22no—
831#103—22no—
832#103—22no—
833#103—22no—
834#103—22no—
835#103—22no—
836#103—22no—
837#103—41no—
838#103—41no—
839#103—41no—
840#103—41no—
841#103—41no—
842#103—41no—
843#103—41no—
844#103—41no—
845#103—41no—
846#103—41no—
847#103C2×D414yes—
848#103C2×D414yes—
849#102—22no—
850#102—22no—
851#102—41no—
852#102—41no—
853C22⋊C8—22no—
854C22⋊C8—22no—
855C22⋊C8—22no—
856C22⋊C8—22no—
857C22⋊C8—41no—
858C22⋊C8—41no—
859C22⋊C8—41no—
860C22⋊C8—41no—
861#97—22no—
862#97—22no—
863#97—22no—
864#97—22no—
865C4×C8—22no—
866C4×C8—22no—
867#95—21no—
868#95—21no—
869#95—21no—
870#95—21no—
871#95—21no—
872#95—21no—
873#95—21no—
874#95—21no—
875#95—21no—
876#95—21no—
877#95—21no—
878#95—21no—
879#95—21no—
880#95—21no—
881#95—21no—
882#95—21no—
883#95—21no—
884#95—21no—
885#95—21no—
886#95—21no—
887#95—21no—
888#95—21no—
889#95—21no—
890#95—21no—
891#95—21no—
892#95—21no—
893#95—21no—
894#95C2×D411yescharacteristic
895#95C2×D411yescharacteristic
896#95C2×D411yescharacteristic
897#95C2×D411yescharacteristic
898#95C2×D411yescharacteristic
899#95C2×D411yescharacteristic
900C24—21no—
901C24C22×D411yescharacteristic
902C24C22×D411yescharacteristic
903#41—44no—
904#41—44no—
905#41—44no—
906#41—44no—
907C2×Q8—24no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—21no—
917C2×Q8—21no—
918C2×Q8—21no—
919C2×Q8—21no—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—21no—
923C2×Q8—21no—
924C2×Q8—21no—
925C2×Q8—21no—
926C2×Q8—21no—
927C2×Q8—21no—
928C2×Q8—21no—
929C2×Q8—21no—
930C2×Q8—21no—
931C2×Q8—21no—
932C2×Q8—21no—
933C2×Q8—21no—
934C2×Q8—21no—
935C2×Q8—21no—
936C2×Q8—21no—
937C2×Q8—21no—
938C2×Q8—21no—
939C2×Q8—21no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—44no—
945C2×Q8—44no—
946C2×Q8C22×D412yes—
947C2×Q8C2×#4112yes—
948C2×Q8C2×#4112yes—
949C2×Q8H(5,𝔽2)12yes—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—21no—
954C2×D4—21no—
955C2×D4—21no—
956C2×D4—21no—
957C2×D4—21no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—81no—
963C2×D4—81no—
964C2×D4C2×#4112yes—
965C22×C4—21no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4—81no—
1006C22×C4—81no—
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C2511yescharacteristic
1020Q16—44no—
1021Q16—44no—
1022Q16—44no—
1023Q16—44no—
1024Q16—44no—
1025Q16—44no—
1026Q16—82no—
1027Q16—82no—
1028SD16—44no—
1029SD16—44no—
1030SD16—82no—
1031SD16—82no—
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—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8C22×D412yes—
1055C2×C8C22×D412yes—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4—81no—
1111C4⋊C4—81no—
1112C4⋊C4—81no—
1113C4⋊C4—81no—
1114C4⋊C4—81no—
1115C4⋊C4—81no—
1116C4⋊C4C22×D412yes—
1117C4⋊C4C22×D412yes—
1118C4⋊C4C22×D412yes—
1119C4⋊C4C2×#4112yes—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C22⋊C4—81no—
1151C42—24no—
1152C42—24no—
1153C42—22no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—41no—
1161C42—41no—
1162C42—41no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—42no—
1175C42—81no—
1176C42—81no—
1177C42—81no—
1178C42C22×D412yes—
1179C42C2×#4112yes—
1180C42C2×#4112yes—
1181C42H(5,𝔽2)12yes—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—22no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23C23×D411yescharacteristic
1204Q8—22no—
1205Q8—22no—
1206Q8—22no—
1207Q8—22no—
1208Q8—22no—
1209Q8—48no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8#55014yes—
1229D4—22no—
1230D4—22no—
1231D4—48no—
1232D4—41no—
1233D4—41no—
1234D4—82no—
1235D4—84no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—48no—
1276C2×C4—48no—
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—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4#52512yes—
1326C2×C4#52512yes—
1327C2×C4D4212yes—
1328C2×C4D4212yes—
1329C2×C4#57812yes—
1330C2×C4C23×D411yescharacteristic
1331C2×C4C22×#4111yescharacteristic
1332C2×C4C22×#4111yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4#58511yescharacteristic
1336C8—22no—
1337C8—22no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—42no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22C2×#52511yescharacteristic
1366C22C2×D4211yescharacteristic
1367C22#348811yescharacteristic
1368C22C2×#57811yescharacteristic
1369C22#358611yescharacteristic
1370C22#358611yescharacteristic
1371C22#358611yescharacteristic
1372C4—24no—
1373C4—22no—
1374C4—22no—
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—41no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—42no—
1383C4—41no—
1384C4—41no—
1385C4—42no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—42no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4C2×#55011yescharacteristic
1400C4D4×#4111yescharacteristic
1401C4#350611yescharacteristic
1402C4#351911yescharacteristic
1403C2—81no—
1404C2—81no—
1405C2—82no—
1406C2#3610111yescharacteristic
1407C2#6056911yescharacteristic
1408C2#6059411yescharacteristic
1409C2#6108311yescharacteristic
1410C2#6109711yescharacteristic
1411C2#6201011yescharacteristic
1412C2#6208211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3127C2semidirect
2. C2×#3120C2semidirect
3. #39385C2semidirect
5. #33163C2semidirect
6. #32916C2semidirect
7. #32915C2semidirect
8. #28449C2semidirect
9. #28285C2semidirect
10. #26642C2semidirect
11. #26636C2semidirect
12. #26627C2semidirect
13. #26621C2semidirect
14. #26249C2semidirect
15. #26247C2semidirect
18. #25173C2semidirect
19. #25171C2semidirect
20. #25161C2semidirect
21. #25151C2semidirect
22. #24666C2semidirect
23. #24664C2semidirect
24. #24165C2semidirect
25. #24163C2semidirect
26. #23194C2semidirect
27. #23192C2semidirect
28. #23014C2semidirect
29. #23014C2semidirect
30. #22798C2semidirect
31. #21618C2semidirect
292. #479D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31272
C2×#31202
#393852
#343122
#331632
#329162
#329152
#284492
#282852
#266422
#266362
#266272
#266212
#262492
#262472
#257672
#251732
#251712
#251612
#251512
#246662
#246642
#241652
#241632
#231942
#231922
#230142
#227982
#216182