Finite Group Databasebeta

← #6575672

Subgroups — #6575672

Order 512.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3127C211yesmaximal, characteristic, complemented
2C22×#462C211yesmaximal, characteristic, complemented
3#37695C211yesmaximal, characteristic
4#34291C211yesmaximal, characteristic
5#33041C211yesmaximal, characteristic, complemented
6#32960C211yesmaximal, characteristic, complemented
7#32915C211yesmaximal, characteristic, complemented
8#28391C211yesmaximal, characteristic, complemented
9#28170C211yesmaximal, characteristic, complemented
10#26952C211yesmaximal, characteristic, complemented
11#26937C211yesmaximal, characteristic, complemented
12#26607C211yesmaximal, characteristic, complemented
13#26590C211yesmaximal, characteristic, complemented
14#26183C211yesmaximal, characteristic, complemented
15#26167C211yesmaximal, characteristic, complemented
16#25173C211yesmaximal, characteristic, complemented
17#25161C211yesmaximal, characteristic, complemented
18#24875C211yesmaximal, characteristic
19#24871C211yesmaximal, characteristic
20#24840C211yesmaximal, characteristic, complemented
21#24664C211yesmaximal, characteristic, complemented
22#24212C211yesmaximal, characteristic, complemented
23#24165C211yesmaximal, characteristic, complemented
24#23856C211yesmaximal, characteristic
25#23856C211yesmaximal, characteristic
26#22871C211yesmaximal, characteristic, complemented
27#22859C211yesmaximal, characteristic, complemented
28#22754C211yesmaximal, characteristic
29C22⋊C4×Q16C211yesmaximal, characteristic, complemented
30#22440C211yesmaximal, characteristic, complemented
31#21516C211yesmaximal, characteristic, complemented
32C23×Q16C2211yescharacteristic
33C23×Q16C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#541C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#3127—28no—
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#462—28no—
46C2×#462C2211yescharacteristic
47C2×#462C2211yescharacteristic
48C2×#462C2211yescharacteristic
49C2×#462C2211yescharacteristic
50C2×#462C2211yescharacteristic
51C2×#462C2211yescharacteristic
52C2×#462C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#462C2211yescharacteristic
55C2×#462C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#451C2211yescharacteristic
58C2×#451C2211yescharacteristic
59C2×#451C2211yescharacteristic
60C2×#451C2211yescharacteristic
61C2×#451C2211yescharacteristic
62C2×#441C2211yescharacteristic
63C2×#441C2211yescharacteristic
64C2×#441C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×Q16C2211yescharacteristic
67C2×C4×Q16C2211yescharacteristic
68C2×#433C2211yescharacteristic
69C22×C4⋊C8C2211yescharacteristic
70C22×#103C2211yescharacteristic
71C22×#103C2211yescharacteristic
72#2851C2211yescharacteristic
73#2716—21no—
74#2716—21no—
75#2713—21no—
76#2713—21no—
77#2642C2211yescharacteristic
78#2621C2211yescharacteristic
79#2481—21no—
80#2481—21no—
81#2473—21no—
82#2473—21no—
83#2446C2211yescharacteristic
84#2446C2211yescharacteristic
85#2429C2211yescharacteristic
86#2429C2211yescharacteristic
87#2409C2211yescharacteristic
88#2409C2211yescharacteristic
89#2365—21no—
90#2365C2211yescharacteristic
91#2362—21no—
92#2362C2211yescharacteristic
93#2360—21no—
94#2360C2211yescharacteristic
95#2352—21no—
96#2352C2211yescharacteristic
97#2351C2211yescharacteristic
98Q8×C22⋊C4C2211yescharacteristic
99Q8×C22⋊C4C2211yescharacteristic
100Q8×C22⋊C4C2211yescharacteristic
101Q8×C22⋊C4C2211yescharacteristic
102#2327—21no—
103#2327C2211yescharacteristic
104#2327C2211yescharacteristic
105#2323—21no—
106#2323C2211yescharacteristic
107C4×C22⋊Q8—21no—
108C4×C22⋊Q8C2211yescharacteristic
109#2290—21no—
110#2290C2211yescharacteristic
111#2276C2211yescharacteristic
112#2097C2211yescharacteristic
113#2097C2211yescharacteristic
114#2088C2211yescharacteristic
115#2086C2211yescharacteristic
116#2074C2211yescharacteristic
117#2074C2211yescharacteristic
118#2068C2211yescharacteristic
119#2066C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2016C2211yescharacteristic
127#2016C2211yescharacteristic
128#2016C2211yescharacteristic
129#2016C2211yescharacteristic
130#2016C2211yescharacteristic
131#2016C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#1989C2211yescharacteristic
137#1981C2211yescharacteristic
138#1981C2211yescharacteristic
139#1971C2211yescharacteristic
140#1971C2211yescharacteristic
141#1971C2211yescharacteristic
142#1969C2211yescharacteristic
143#1969C2211yescharacteristic
144#1969C2211yescharacteristic
145#1949C2211yescharacteristic
146#1935C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1892C2211yescharacteristic
159#1892C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1832C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1787C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202C4×#103C2211yescharacteristic
203#1752C2211yescharacteristic
204C8×C22⋊C4C2211yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C23×Q8C2311yescharacteristic
209C22×Q16—24no—
210C22×Q16—24no—
211C22×Q16—24no—
212C22×Q16—24no—
213C22×Q16—42no—
214C22×Q16—42no—
215C22×Q16C2311yescharacteristic
216C22×Q16C2311yescharacteristic
217C22×Q16C2311yescharacteristic
218C22×Q16C2311yescharacteristic
219C22×Q16C2311yescharacteristic
220C22×Q16C2311yescharacteristic
221C22×Q16C2311yescharacteristic
222C22×Q16C2311yescharacteristic
223C22×Q16C2311yescharacteristic
224C22×Q16C2311yescharacteristic
225C22×Q16C2311yescharacteristic
226C22×Q16C2311yescharacteristic
227C23×C8C2311yescharacteristic
228C23×C8C2311yescharacteristic
229D4×Q8—24no—
230D4×Q8—24no—
231#541—24no—
232#541—42no—
233C2×C4⋊Q8—21no—
234C2×C4⋊Q8—24no—
235C2×C4⋊Q8—21no—
236C2×C4⋊Q8—21no—
237C2×C4⋊Q8—42no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×#126—21no—
244C2×#126—21no—
245C2×#125—21no—
246C2×#125—21no—
247C2×#125C2311yescharacteristic
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256#519—24no—
257#519—42no—
258C2×C4×Q8—21no—
259C2×C4×Q8—21no—
260C2×C4×Q8—21no—
261C2×C4×Q8—21no—
262C2×C4×Q8—24no—
263C2×C4×Q8—42no—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×D4—21no—
278C2×C4×D4C2311yescharacteristic
279C2×#117—21no—
280C2×#117—21no—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4—21no—
284C22×C4⋊C4—21no—
285C22×C4⋊C4—21no—
286C22×C4⋊C4C2311yescharacteristic
287C22×C42—21no—
288C22×C42C2311yescharacteristic
289#485—24no—
290#485—24no—
291#479—24no—
292#479—24no—
293#479—42no—
294#462—24no—
295#462—24no—
296#462—24no—
297#462—24no—
298#462—24no—
299#462—24no—
300#462—24no—
301#462—24no—
302#462—42no—
303#462D418yescomplemented
304#451—24no—
305#451—24no—
306#451—24no—
307#451—24no—
308#451—42no—
309#451—42no—
310#441—24no—
311#441—24no—
312#441—42no—
313C4×Q16—24no—
314C4×Q16—24no—
315C4×Q16—42no—
316#433—24no—
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323C2×#106C2311yescharacteristic
324C2×#106C2311yescharacteristic
325C2×C4⋊C8—24no—
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330C2×C4⋊C8C2311yescharacteristic
331C2×C4⋊C8C2311yescharacteristic
332C2×#103—24no—
333C2×#103—24no—
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
367C2×C22⋊C8C2311yescharacteristic
368C2×C22⋊C8C2311yescharacteristic
369C2×C22⋊C8C2311yescharacteristic
370C2×C22⋊C8C2311yescharacteristic
371C2×C22⋊C8C2311yescharacteristic
372C2×#97C2311yescharacteristic
373C2×#97C2311yescharacteristic
374C2×C4×C8C2311yescharacteristic
375C2×C4×C8C2311yescharacteristic
376#400—21no—
377#400—21no—
378#400—21no—
379#400—21no—
380#400—21no—
381#400—21no—
382#398—21no—
383#398—21no—
384#398—21no—
385#398—21no—
386#398—21no—
387#398—21no—
388#397—21no—
389#397—21no—
390#396—21no—
391#396—21no—
392#395—21no—
393#395—21no—
394#393—21no—
395#393—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391—21no—
403#391—21no—
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387D411yescharacteristic
458#387D411yescharacteristic
459#386—21no—
460#386—21no—
461#386—21no—
462#386D411yescharacteristic
463#386D411yescharacteristic
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#385—21no—
469#385—21no—
470#385D411yescharacteristic
471#385D411yescharacteristic
472#382—21no—
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#380—21no—
476#380—21no—
477#380—21no—
478#380—21no—
479#380C2311yescharacteristic
480#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C22⋊C4—21no—
495C4×C22⋊C4—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499C4×C22⋊C4—21no—
500C4×C22⋊C4—21no—
501C4×C22⋊C4C2311yescharacteristic
502C4×C22⋊C4C2311yescharacteristic
503#376—21no—
504#376C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521#336C2311yescharacteristic
522#336C2311yescharacteristic
523#336C2311yescharacteristic
524#336C2311yescharacteristic
525#336C2311yescharacteristic
526#336C2311yescharacteristic
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—22no—
537C22×Q8—22no—
538C22×Q8—22no—
539C22×Q8—22no—
540C22×Q8—22no—
541C22×Q8—22no—
542C22×Q8—22no—
543C22×Q8—22no—
544C22×Q8—41no—
545C22×Q8—41no—
546C22×Q8—41no—
547C22×Q8—41no—
548C22×Q8—41no—
549C22×Q8—41no—
550C22×Q8—41no—
551C22×Q8—41no—
552C22×Q8—41no—
553C22×Q8—41no—
554C22×Q8#4114yes—
555C22×Q8C2411yescharacteristic
556C22×Q8C2411yescharacteristic
557C22×Q8C2411yescharacteristic
558C22×Q8C2411yescharacteristic
559C22×Q8C2411yescharacteristic
560C22×Q8C2411yescharacteristic
561C22×Q8C2411yescharacteristic
562C22×D4C2×D411yescharacteristic
563C23×C4—21no—
564C23×C4—21no—
565C23×C4—21no—
566C23×C4—21no—
567C23×C4—21no—
568C23×C4C2×D411yescharacteristic
569C23×C4C2×D411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16—22no—
580C2×Q16—22no—
581C2×Q16—22no—
582C2×Q16—22no—
583C2×Q16—22no—
584C2×Q16—22no—
585C2×Q16—22no—
586C2×Q16—22no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16—22no—
593C2×Q16—22no—
594C2×Q16—22no—
595C2×Q16—22no—
596C2×Q16—41no—
597C2×Q16—41no—
598C2×Q16—41no—
599C2×Q16—41no—
600C2×Q16—41no—
601C2×Q16—41no—
602C2×Q16—41no—
603C2×Q16—41no—
604C2×Q16—41no—
605C2×Q16—41no—
606C2×Q16—416no—
607C2×Q16—416no—
608C2×Q16C2×D414yes—
609C2×Q16C2×D414yes—
610C22×C8—22no—
611C22×C8—22no—
612C22×C8—22no—
613C22×C8—22no—
614C22×C8—41no—
615C22×C8—41no—
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C22×C8C2411yescharacteristic
623C22×C8C2411yescharacteristic
624C4⋊Q8—28no—
625C4⋊Q8—22no—
626C4⋊Q8—22no—
627C4⋊Q8—22no—
628C4⋊Q8—22no—
629C4⋊Q8—22no—
630C4⋊Q8—22no—
631C4⋊Q8—22no—
632C4⋊Q8—44no—
633C4⋊Q8—44no—
634C4⋊Q8—41no—
635C4⋊Q8—41no—
636C4⋊Q8C2×D414yes—
637#126—44no—
638#126—44no—
639#125—22no—
640#125—22no—
641#125—44no—
642#125—44no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—41no—
653C22⋊Q8—41no—
654C22⋊Q8—41no—
655C22⋊Q8—41no—
656C22⋊Q8#4114yes—
657C4×Q8—22no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×Q8—22no—
669C4×Q8—22no—
670C4×Q8—22no—
671C4×Q8—44no—
672C4×Q8—41no—
673C4×Q8—41no—
674C4×Q8—41no—
675C4×Q8—41no—
676C4×Q8—41no—
677C4×Q8—41no—
678C4×Q8—41no—
679C4×Q8—44no—
680C4×Q8—44no—
681C4×Q8—41no—
682C4×Q8—41no—
683C4×Q8—41no—
684C4×Q8—41no—
685C4×Q8—44no—
686C4×Q8C2×D414yes—
687C4×D4—28no—
688C4×D4—22no—
689C4×D4—22no—
690#117—22no—
691#117—22no—
692#117—22no—
693#117—44no—
694#117—44no—
695#117—41no—
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—22no—
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—21no—
731C2×C4⋊C4—21no—
732C2×C4⋊C4—21no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—44no—
735C2×C4⋊C4—44no—
736C2×C4⋊C4—44no—
737C2×C4⋊C4C2×D411yescharacteristic
738C2×C4⋊C4C2×D411yescharacteristic
739C2×C4⋊C4C2×D411yescharacteristic
740C2×C4⋊C4C2×D411yescharacteristic
741C2×C4⋊C4C2×D411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C22⋊C4C2×D411yescharacteristic
767C2×C22⋊C4C2×D411yescharacteristic
768C2×C22⋊C4C2×D411yescharacteristic
769C2×C22⋊C4C2×D411yescharacteristic
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—22no—
773C2×C42—22no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—21no—
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—44no—
790C2×C42C2×D411yescharacteristic
791C2×C42C2×D411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797#107—22no—
798#107—22no—
799#107—41no—
800#107—41no—
801#106—22no—
802#106—22no—
803#106—41no—
804#106—41no—
805C4⋊C8—22no—
806C4⋊C8—22no—
807C4⋊C8—22no—
808C4⋊C8—22no—
809C4⋊C8—22no—
810C4⋊C8C2×D414yes—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#103—22no—
820#103—22no—
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—41no—
830#103—41no—
831#103—41no—
832#103—41no—
833#103—41no—
834#103—41no—
835#103—41no—
836#103—41no—
837#103—41no—
838#103—41no—
839#103—41no—
840#103—41no—
841#103C2×D414yes—
842#103C2×D414yes—
843C22⋊C8—22no—
844C22⋊C8—22no—
845C22⋊C8—22no—
846C22⋊C8—22no—
847C22⋊C8—41no—
848C22⋊C8—41no—
849#97—22no—
850#97—41no—
851C4×C8—22no—
852C4×C8—41no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95—21no—
864#95—21no—
865#95—21no—
866#95—21no—
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#95C2×D411yescharacteristic
893#95C2×D411yescharacteristic
894#95C2×D411yescharacteristic
895#95C2×D411yescharacteristic
896#95C2×D411yescharacteristic
897#95C2×D411yescharacteristic
898#95C2×D411yescharacteristic
899#95C2×D411yescharacteristic
900#95C2×D411yescharacteristic
901#95C2×D411yescharacteristic
902C24C22×D411yescharacteristic
903C24C22×D411yescharacteristic
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—28no—
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—21no—
941C2×Q8—21no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—42no—
948C2×Q8—44no—
949C2×Q8—44no—
950C2×Q8—44no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—81no—
962C2×Q8—81no—
963C2×Q8—82no—
964C2×Q8—82no—
965C2×Q8—82no—
966C2×Q8—82no—
967C2×Q8C22×D412yes—
968C2×Q8C22×D412yes—
969C2×Q8C22×D412yes—
970C2×Q8C2×#4112yes—
971C2×Q8C2×#4112yes—
972C2×Q8C2×#4112yes—
973C2×Q8H(5,𝔽2)12yes—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—22no—
977C22×C4—22no—
978C22×C4—21no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—22no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—22no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—41no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—81no—
1022C22×C4—81no—
1023C22×C4—81no—
1024C22×C4C22×D411yescharacteristic
1025C22×C4C22×D411yescharacteristic
1026C22×C4C22×D411yescharacteristic
1027C22×C4C22×D411yescharacteristic
1028C22×C4C22×D411yescharacteristic
1029C22×C4C22×D411yescharacteristic
1030C22×C4C22×D411yescharacteristic
1031C22×C4C22×D411yescharacteristic
1032C22×C4C22×D411yescharacteristic
1033C22×C4C22×D411yescharacteristic
1034C22×C4C22×D411yescharacteristic
1035C22×C4C22×D411yescharacteristic
1036C22×C4C2×#4112yes—
1037C22×C4C2×#4112yes—
1038C22×C4C2511yescharacteristic
1039Q16—28no—
1040Q16—28no—
1041Q16—44no—
1042Q16—44no—
1043Q16—44no—
1044Q16—44no—
1045Q16—44no—
1046Q16—44no—
1047Q16—44no—
1048Q16—44no—
1049Q16—82no—
1050Q16—82no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C2×C8—21no—
1062C2×C8—21no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8—21no—
1068C2×C8—21no—
1069C2×C8—21no—
1070C2×C8—21no—
1071C2×C8—21no—
1072C2×C8—21no—
1073C2×C8—44no—
1074C2×C8—44no—
1075C2×C8C22×D412yes—
1076C2×C8C22×D412yes—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—22no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—21no—
1090C4⋊C4—21no—
1091C4⋊C4—21no—
1092C4⋊C4—21no—
1093C4⋊C4—21no—
1094C4⋊C4—21no—
1095C4⋊C4—21no—
1096C4⋊C4—21no—
1097C4⋊C4—21no—
1098C4⋊C4—21no—
1099C4⋊C4—21no—
1100C4⋊C4—21no—
1101C4⋊C4—21no—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—81no—
1130C4⋊C4—81no—
1131C4⋊C4—81no—
1132C4⋊C4—81no—
1133C4⋊C4—81no—
1134C4⋊C4C22×D412yes—
1135C4⋊C4C2×#4112yes—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—22no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—22no—
1143C22⋊C4—22no—
1144C22⋊C4—22no—
1145C22⋊C4—41no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—81no—
1153C22⋊C4—81no—
1154C22⋊C4—81no—
1155C42—24no—
1156C42—22no—
1157C42—22no—
1158C42—24no—
1159C42—21no—
1160C42—21no—
1161C42—21no—
1162C42—21no—
1163C42—21no—
1164C42—21no—
1165C42—21no—
1166C42—21no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—42no—
1175C42—42no—
1176C42—42no—
1177C42—81no—
1178C42—81no—
1179C42—81no—
1180C42—81no—
1181C42—81no—
1182C42C22×D412yes—
1183C42H(5,𝔽2)12yes—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23#52512yes—
1196C23#57812yes—
1197C23#57812yes—
1198C23C23×D411yescharacteristic
1199Q8—22no—
1200Q8—22no—
1201Q8—22no—
1202Q8—22no—
1203Q8—22no—
1204Q8—22no—
1205Q8—22no—
1206Q8—22no—
1207Q8—22no—
1208Q8—22no—
1209Q8—22no—
1210Q8—48no—
1211Q8—48no—
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—84no—
1229Q8—84no—
1230Q8#54614yes—
1231D4—44no—
1232C2×C4—28no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—44no—
1279C2×C4—48no—
1280C2×C4—48no—
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—41no—
1323C2×C4—41no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—84no—
1327C2×C4#52512yes—
1328C2×C4D4212yes—
1329C2×C4D4212yes—
1330C2×C4#57812yes—
1331C2×C4C23×D411yescharacteristic
1332C2×C4C22×#4111yescharacteristic
1333C2×C4C22×#4111yescharacteristic
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4#58511yescharacteristic
1337C8—22no—
1338C8—22no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22#312714yescomplemented
1359C22C2×#52511yescharacteristic
1360C22C2×D4211yescharacteristic
1361C22#348811yescharacteristic
1362C22C2×#57811yescharacteristic
1363C22C2×#57811yescharacteristic
1364C22C2×#57811yescharacteristic
1365C22#358611yescharacteristic
1366C4—22no—
1367C4—24no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—41no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—42no—
1383C4—41no—
1384C4—42no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4C2×#54611yescharacteristic
1395C4D4×#4111yescharacteristic
1396C4#350511yescharacteristic
1397C4#351911yescharacteristic
1398C2—24no—
1399C2—81no—
1400C2#3609611yescharacteristic
1401C2C2×#312711yescharacteristic
1402C2#6059411yescharacteristic
1403C2#6105311yescharacteristic
1404C2#6107611yescharacteristic
1405C2#6201011yescharacteristic
1406C2#6205611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3127C2semidirect
2. C22×#462C2semidirect
5. #33041C2semidirect
6. #32960C2semidirect
7. #32915C2semidirect
8. #28391C2semidirect
9. #28170C2semidirect
10. #26952C2semidirect
11. #26937C2semidirect
12. #26607C2semidirect
13. #26590C2semidirect
14. #26183C2semidirect
15. #26167C2semidirect
16. #25173C2semidirect
17. #25161C2semidirect
20. #24840C2semidirect
21. #24664C2semidirect
22. #24212C2semidirect
23. #24165C2semidirect
26. #22871C2semidirect
27. #22859C2semidirect
29. C22⋊C4×Q16C2semidirect
30. #22440C2semidirect
31. #21516C2semidirect
303. #462D4semidirect
1358. C22#3127semidirect

Maximal subgroups

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

subgroupindex
C2×#31272
C22×#4622
#376952
#342912
#330412
#329602
#329152
#283912
#281702
#269522
#269372
#266072
#265902
#261832
#261672
#251732
#251612
#248752
#248712
#248402
#246642
#242122
#241652
#238562
#228712
#228592
#227542
C22⋊C4×Q162
#224402
#215162