Finite Group Databasebeta

← #7518610

Subgroups — #7518610

Order 512.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3377C211yesmaximal, characteristic, complemented
2C22×#462C211yesmaximal, characteristic, complemented
3#59134C211yesmaximal, characteristic
4#36435C211yesmaximal, characteristic, complemented
5#31175C211yesmaximal, characteristic, complemented
6#31151C211yesmaximal, characteristic, complemented
7#30904C211yesmaximal, characteristic, complemented
8#30888C211yesmaximal, characteristic, complemented
9#28427C211yesmaximal, characteristic, complemented
10#27266C211yesmaximal, characteristic
11#27260C211yesmaximal, characteristic
12#26183C211yesmaximal, characteristic, complemented
13#26171C211yesmaximal, characteristic, complemented
14#25963C211yesmaximal, characteristic, complemented
15#25957C211yesmaximal, characteristic, complemented
16#25943C211yesmaximal, characteristic, complemented
17#25861C211yesmaximal, characteristic, complemented
18#25333C211yesmaximal, characteristic, complemented
19#25306C211yesmaximal, characteristic, complemented
20#24839C211yesmaximal, characteristic
21#24743C211yesmaximal, characteristic, complemented
22#24741C211yesmaximal, characteristic, complemented
23#24736C211yesmaximal, characteristic, complemented
24#24361C211yesmaximal, characteristic
25#24361C211yesmaximal, characteristic
26#24201C211yesmaximal, characteristic, complemented
27#23014C211yesmaximal, characteristic, complemented
28#22954C211yesmaximal, characteristic, complemented
29C22⋊C4×Q16C211yesmaximal, characteristic, complemented
30#22440C211yesmaximal, characteristic, complemented
31#21454C211yesmaximal, characteristic
32C23×Q16C2211yescharacteristic
33C23×Q16C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#3377—28no—
39C2×#491C2211yescharacteristic
40C2×#491C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#477C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#464C2211yescharacteristic
47C2×#464C2211yescharacteristic
48C2×#464C2211yescharacteristic
49C2×#464C2211yescharacteristic
50C2×#462—28no—
51C2×#462C2211yescharacteristic
52C2×#462C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#462C2211yescharacteristic
55C2×#462C2211yescharacteristic
56C2×#462C2211yescharacteristic
57C2×#462C2211yescharacteristic
58C2×#462C2211yescharacteristic
59C2×#448C2211yescharacteristic
60C2×#446C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#441C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66C2×C4×Q16C2211yescharacteristic
67C22×C4⋊C8C2211yescharacteristic
68C22×#103C2211yescharacteristic
69C22×#103C2211yescharacteristic
70#2851—21no—
71#2851C2211yescharacteristic
72#2716—21no—
73#2716—21no—
74#2581—21no—
75#2581C2211yescharacteristic
76#2568C2211yescharacteristic
77#2565—21no—
78#2565C2211yescharacteristic
79#2547C2211yescharacteristic
80#2545C2211yescharacteristic
81#2545C2211yescharacteristic
82#2492—21no—
83#2481—21no—
84#2481—21no—
85#2453—21no—
86#2453C2211yescharacteristic
87#2451—21no—
88#2451C2211yescharacteristic
89#2446C2211yescharacteristic
90#2446C2211yescharacteristic
91#2442—21no—
92#2442C2211yescharacteristic
93#2440—21no—
94#2440C2211yescharacteristic
95#2439—21no—
96#2436C2211yescharacteristic
97#2436C2211yescharacteristic
98#2417—21no—
99#2365C2211yescharacteristic
100#2352—21no—
101#2351C2211yescharacteristic
102#2351C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104Q8×C22⋊C4C2211yescharacteristic
105Q8×C22⋊C4C2211yescharacteristic
106Q8×C22⋊C4C2211yescharacteristic
107Q8×C22⋊C4C2211yescharacteristic
108C4×C22⋊Q8—21no—
109C4×C22⋊Q8C2211yescharacteristic
110C4×#121C2211yescharacteristic
111#2097C2211yescharacteristic
112#2095C2211yescharacteristic
113#2088C2211yescharacteristic
114#2087C2211yescharacteristic
115#2074C2211yescharacteristic
116#2072C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic
122#2065C2211yescharacteristic
123#2056C2211yescharacteristic
124#2056C2211yescharacteristic
125#2056C2211yescharacteristic
126#2056C2211yescharacteristic
127#2043C2211yescharacteristic
128#2043C2211yescharacteristic
129#2043C2211yescharacteristic
130#2043C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2042C2211yescharacteristic
135#2026C2211yescharacteristic
136#2026C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#2015C2211yescharacteristic
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#1989C2211yescharacteristic
144#1985C2211yescharacteristic
145#1971C2211yescharacteristic
146#1971C2211yescharacteristic
147#1969C2211yescharacteristic
148#1969C2211yescharacteristic
149#1960C2211yescharacteristic
150#1960C2211yescharacteristic
151#1959C2211yescharacteristic
152#1958C2211yescharacteristic
153#1949C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1933C2211yescharacteristic
160#1933C2211yescharacteristic
161#1917C2211yescharacteristic
162#1916C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1874C2211yescharacteristic
180#1865C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1771C2211yescharacteristic
200#1763C2211yescharacteristic
201#1763C2211yescharacteristic
202#1752C2211yescharacteristic
203C8×C22⋊C4C2211yescharacteristic
204#1749C2211yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C22×Q16—24no—
209C22×Q16—24no—
210C22×Q16—24no—
211C22×Q16—24no—
212C22×Q16—42no—
213C22×Q16—42no—
214C22×Q16C2311yescharacteristic
215C22×Q16C2311yescharacteristic
216C22×Q16C2311yescharacteristic
217C22×Q16C2311yescharacteristic
218C22×Q16C2311yescharacteristic
219C22×Q16C2311yescharacteristic
220C22×Q16C2311yescharacteristic
221C22×Q16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C23×C8C2311yescharacteristic
225C23×C8C2311yescharacteristic
226#557—24no—
227#557—42no—
228#556—24no—
229#556—42no—
230C2×C4⋊Q8—21no—
231C2×C4⋊Q8—24no—
232C2×C4⋊Q8—21no—
233C2×C4⋊Q8—21no—
234C2×C4⋊Q8—42no—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#126—21no—
241C2×#126—21no—
242C2×#125—21no—
243C2×#125—21no—
244C2×#125C2311yescharacteristic
245C2×#125C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8D411yescharacteristic
253C2×#121C2311yescharacteristic
254C2×C4×Q8—21no—
255C2×C4×Q8—21no—
256C2×C4×Q8—21no—
257C2×C4×Q8—24no—
258C2×C4×Q8—42no—
259C2×C4×Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4C2311yescharacteristic
274C2×#117—21no—
275C22×C4⋊C4—21no—
276C22×C4⋊C4—21no—
277C22×C4⋊C4—21no—
278C22×C4⋊C4C2311yescharacteristic
279C22×C42—21no—
280C22×C42C2311yescharacteristic
281#491—24no—
282#491—42no—
283#489—24no—
284#488—24no—
285#479—24no—
286#478—24no—
287#477—24no—
288#464—24no—
289#464—24no—
290#464—42no—
291#464—42no—
292#462—24no—
293#462—24no—
294#462—24no—
295#462—24no—
296#462—24no—
297#462—24no—
298#462—24no—
299#462D418yescomplemented
300#448—24no—
301#446—24no—
302#441—24no—
303#441—42no—
304#440—24no—
305#440—42no—
306C4×Q16—24no—
307C4×Q16—42no—
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×C4⋊C8—24no—
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×#103—24no—
324C2×#103—24no—
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×#97C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×#97C2311yescharacteristic
366C2×#97C2311yescharacteristic
367C2×C4×C8C2311yescharacteristic
368C2×C4×C8C2311yescharacteristic
369#400—21no—
370#400—21no—
371#400—21no—
372#400—21no—
373#400—21no—
374#400—21no—
375#400—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#398—21no—
381#398—21no—
382#398—21no—
383#398—21no—
384#397—21no—
385#397—21no—
386#396—21no—
387#396—21no—
388#396—21no—
389#396—21no—
390#395—21no—
391#395—21no—
392#395—21no—
393#393—21no—
394#393—21no—
395#393—21no—
396#393—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391—21no—
403#391—21no—
404#391—21no—
405#391—21no—
406#391—21no—
407#391D411yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#390C2311yescharacteristic
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389D411yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—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#387D411yescharacteristic
457#387D411yescharacteristic
458#386—21no—
459#386—21no—
460#386—21no—
461#386—21no—
462#386—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385D411yescharacteristic
468#385D411yescharacteristic
469#384—21no—
470#384C2311yescharacteristic
471#382—21no—
472#382—21no—
473#382—21no—
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#380—21no—
477#380—21no—
478#380—21no—
479#380—21no—
480#380—21no—
481#380—21no—
482#380—21no—
483#380D411yescharacteristic
484#380C2311yescharacteristic
485#380C2311yescharacteristic
486#380C2311yescharacteristic
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×C22⋊C4—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499C4×C22⋊C4—21no—
500C4×C22⋊C4C2311yescharacteristic
501C4×C22⋊C4C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#340C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521#336C2311yescharacteristic
522#336C2311yescharacteristic
523#336C2311yescharacteristic
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—22no—
537C22×Q8—41no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×Q8—41no—
541C22×Q8—41no—
542C22×Q8—41no—
543C22×Q8—41no—
544C22×Q8—41no—
545C22×Q8C2×D411yescharacteristic
546C22×Q8#4114yes—
547C22×Q8C2411yescharacteristic
548C22×Q8C2411yescharacteristic
549C22×Q8C2411yescharacteristic
550C22×Q8C2411yescharacteristic
551C22×Q8C2411yescharacteristic
552C22×Q8C2411yescharacteristic
553C22×D4—21no—
554C22×D4C2411yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—21no—
560C23×C4C2×D411yescharacteristic
561C23×C4C2×D411yescharacteristic
562C23×C4C2411yescharacteristic
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—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16—22no—
580C2×Q16—22no—
581C2×Q16—41no—
582C2×Q16—41no—
583C2×Q16—41no—
584C2×Q16—41no—
585C2×Q16—416no—
586C2×Q16—416no—
587C2×Q16C2×D414yes—
588C2×Q16C2×D414yes—
589C2×SD16—22no—
590C2×SD16—22no—
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—41no—
594C2×SD16—41no—
595C22×C8—22no—
596C22×C8—22no—
597C22×C8—22no—
598C22×C8—22no—
599C22×C8—41no—
600C22×C8—41no—
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C4⋊Q8—22no—
610C4⋊Q8—22no—
611C4⋊Q8—22no—
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614C4⋊Q8—22no—
615C4⋊Q8—41no—
616C4⋊Q8—44no—
617C4⋊Q8—44no—
618C4⋊Q8—41no—
619C4⋊Q8—41no—
620C4⋊Q8—44no—
621C4⋊Q8C2×D414yes—
622#126—44no—
623#126—44no—
624#125—22no—
625#125—22no—
626#125—22no—
627#125—41no—
628#125—44no—
629#125—44no—
630#124—22no—
631#124—22no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—41no—
637#124—41no—
638C22⋊Q8—42no—
639C22⋊Q8—44no—
640C22⋊Q8—44no—
641#121—22no—
642#121—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—22no—
647C4×Q8—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—44no—
657C4×Q8—41no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×Q8—41no—
664C4×Q8—41no—
665C4×Q8—44no—
666C4×Q8—44no—
667C4×Q8—41no—
668C4×Q8—41no—
669C4×Q8—41no—
670C4×Q8—41no—
671C4×Q8C2×D414yes—
672C4×D4—22no—
673C4×D4—22no—
674C4×D4—44no—
675#117—44no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
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—41no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4C2×D411yescharacteristic
717C2×C4⋊C4C2×D411yescharacteristic
718C2×C4⋊C4C2×D411yescharacteristic
719C2×C4⋊C4C2×D411yescharacteristic
720C2×C4⋊C4C2×D411yescharacteristic
721C2×C4⋊C4C2×D411yescharacteristic
722C2×C4⋊C4C2×D411yescharacteristic
723C2×C4⋊C4C2×D411yescharacteristic
724C2×C4⋊C4C2×D411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C42—21no—
754C2×C42—22no—
755C2×C42—22no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—44no—
769C2×C42C2×D411yescharacteristic
770C2×C42C2×D411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777#107—22no—
778#107—22no—
779#107—41no—
780#107—41no—
781#106—22no—
782#106—41no—
783C4⋊C8—22no—
784C4⋊C8—22no—
785C4⋊C8—22no—
786C4⋊C8—22no—
787C4⋊C8—22no—
788C4⋊C8—41no—
789C4⋊C8—41no—
790C4⋊C8C2×D414yes—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#103—41no—
811#103—41no—
812#103—41no—
813#103—41no—
814#103—41no—
815#103—41no—
816#103—41no—
817#103—41no—
818#103—41no—
819#103C2×D414yes—
820#103C2×D414yes—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—41no—
825#102—41no—
826#102—41no—
827C22⋊C8—22no—
828C22⋊C8—22no—
829#97—22no—
830#97—22no—
831#97—22no—
832#97—41no—
833C4×C8—22no—
834C4×C8—41no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
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#95C2×D411yescharacteristic
875#95C2×D411yescharacteristic
876#95C2×D411yescharacteristic
877#95C2×D411yescharacteristic
878#95C2×D411yescharacteristic
879#95C2×D411yescharacteristic
880#95C2×D411yescharacteristic
881#95C2×D411yescharacteristic
882#95C2×D411yescharacteristic
883#95C2×D411yescharacteristic
884C24—21no—
885C24C22×D411yescharacteristic
886C2×Q8—22no—
887C2×Q8—24no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—28no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
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—41no—
920C2×Q8—41no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—44no—
929C2×Q8—42no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—81no—
937C2×Q8—81no—
938C2×Q8—81no—
939C2×Q8—82no—
940C2×Q8—82no—
941C2×Q8—82no—
942C2×Q8—82no—
943C2×Q8C22×D412yes—
944C2×Q8C22×D412yes—
945C2×Q8C22×D412yes—
946C2×Q8C2×#4112yes—
947C2×Q8C2×#4112yes—
948C2×Q8H(5,𝔽2)12yes—
949C2×D4—21no—
950C2×D4—21no—
951C2×D4—21no—
952C2×D4—21no—
953C2×D4—21no—
954C2×D4—21no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C22×C4—22no—
959C22×C4—21no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—22no—
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—41no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C2×#4112yes—
1012C22×C42−1+412yes—
1013C22×C4C2511yescharacteristic
1014Q16—28no—
1015Q16—28no—
1016Q16—44no—
1017Q16—44no—
1018Q16—44no—
1019Q16—44no—
1020Q16—44no—
1021Q16—44no—
1022SD16—44no—
1023SD16—44no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—44no—
1047C2×C8—44no—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
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—81no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4—81no—
1111C4⋊C4C22×D412yes—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C42—22no—
1132C42—22no—
1133C42—24no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—81no—
1155C42—81no—
1156C42C22×D412yes—
1157C42H(5,𝔽2)12yes—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23#54812yes—
1170C23#57512yes—
1171C23#57812yes—
1172C23C23×D411yescharacteristic
1173Q8—22no—
1174Q8—22no—
1175Q8—22no—
1176Q8—22no—
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—22no—
1181Q8—22no—
1182Q8—48no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—82no—
1198Q8—84no—
1199Q8—84no—
1200Q8—84no—
1201Q8#54614yes—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—84no—
1207C2×C4—28no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—44no—
1255C2×C4—48no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4D4212yes—
1299C2×C4D4212yes—
1300C2×C4#54812yes—
1301C2×C4#57812yes—
1302C2×C4C23×D411yescharacteristic
1303C2×C4C22×#4111yescharacteristic
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×2−1+411yescharacteristic
1307C2×C4#58511yescharacteristic
1308C8—22no—
1309C8—22no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22#337714yescomplemented
1330C22C2×D4211yescharacteristic
1331C22C2×#54811yescharacteristic
1332C22#348811yescharacteristic
1333C22C2×#57511yescharacteristic
1334C22C2×#57811yescharacteristic
1335C22C2×#57811yescharacteristic
1336C22#358611yescharacteristic
1337C4—22no—
1338C4—24no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4C2×#54611yescharacteristic
1366C4#348911yescharacteristic
1367C4#350511yescharacteristic
1368C4#353611yescharacteristic
1369C2—24no—
1370C2—161no—
1371C2#5899611yescharacteristic
1372C2#6105311yescharacteristic
1373C2#6106811yescharacteristic
1374C2C2×#337711yescharacteristic
1375C2#6134211yescharacteristic
1376C2#6198211yescharacteristic
1377C2#6201011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3377C2semidirect
2. C22×#462C2semidirect
4. #36435C2semidirect
5. #31175C2semidirect
6. #31151C2semidirect
7. #30904C2semidirect
8. #30888C2semidirect
9. #28427C2semidirect
12. #26183C2semidirect
13. #26171C2semidirect
14. #25963C2semidirect
15. #25957C2semidirect
16. #25943C2semidirect
17. #25861C2semidirect
18. #25333C2semidirect
19. #25306C2semidirect
21. #24743C2semidirect
22. #24741C2semidirect
23. #24736C2semidirect
26. #24201C2semidirect
27. #23014C2semidirect
28. #22954C2semidirect
29. C22⋊C4×Q16C2semidirect
30. #22440C2semidirect
299. #462D4semidirect
1329. C22#3377semidirect

Maximal subgroups

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

subgroupindex
C2×#33772
C22×#4622
#591342
#364352
#311752
#311512
#309042
#308882
#284272
#272662
#272602
#261832
#261712
#259632
#259572
#259432
#258612
#253332
#253062
#248392
#247432
#247412
#247362
#243612
#242012
#230142
#229542
C22⋊C4×Q162
#224402
#214542