Finite Group Databasebeta

← #6440228

Subgroups — #6440228

Order 512.

2172 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3120C211yesmaximal, characteristic, complemented
2C2×#2947C211yesmaximal, characteristic, complemented
3#35671C211yesmaximal, characteristic, complemented
4#34308C211yesmaximal, characteristic
5#26895C211yesmaximal, characteristic, complemented
6#26621C211yesmaximal, characteristic, complemented
7#26607C211yesmaximal, characteristic, complemented
8#26574C211yesmaximal, characteristic, complemented
9#26398C211yesmaximal, characteristic, complemented
10#26360C211yesmaximal, characteristic, complemented
11#26166C211yesmaximal, characteristic, complemented
12#26148C211yesmaximal, characteristic, complemented
13#25964C211yesmaximal, characteristic, complemented
14#25166C211yesmaximal, characteristic, complemented
15#25082C211yesmaximal, characteristic, complemented
16#24907C211yesmaximal, characteristic, complemented
17#24863C211yesmaximal, characteristic, complemented
18#24430C211yesmaximal, characteristic
19#24376C211yesmaximal, characteristic, complemented
20#23865C211yesmaximal, characteristic
21#23805C211yesmaximal, characteristic, complemented
22#23713C211yesmaximal, characteristic, complemented
23#23679C211yesmaximal, characteristic, complemented
24#23586C211yesmaximal, characteristic, complemented
25#21530C211yesmaximal, characteristic, complemented
26C4×#461C211yesmaximal, characteristic, complemented
27#21463C211yesmaximal, characteristic, complemented
28#21461C211yesmaximal, characteristic, complemented
29#21461C211yesmaximal, characteristic, complemented
30#21121C211yesmaximal, characteristic, complemented
31#21111C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#541C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#3120—28no—
39C2×#484C2211yescharacteristic
40C2×#483C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#478C2211yescharacteristic
43C2×#467C2211yescharacteristic
44C2×#462C2211yescharacteristic
45C2×#461C2211yescharacteristic
46C2×#461C2211yescharacteristic
47C2×#452C2211yescharacteristic
48C2×#452C2211yescharacteristic
49C2×#452C2211yescharacteristic
50C2×#452C2211yescharacteristic
51C2×#451C2211yescharacteristic
52#2947—28no—
53C2×#441C2211yescharacteristic
54C2×#441C2211yescharacteristic
55C2×#441C2211yescharacteristic
56C2×#441C2211yescharacteristic
57C2×#441C2211yescharacteristic
58C2×#440C2211yescharacteristic
59C2×#440C2211yescharacteristic
60C2×C4×Q16C2211yescharacteristic
61C2×C4×Q16C2211yescharacteristic
62C2×C4×Q16C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×C4×SD16C2211yescharacteristic
65C2×C4×SD16C2211yescharacteristic
66C2×#433C2211yescharacteristic
67C2×#428C2211yescharacteristic
68C2×#416C2211yescharacteristic
69C22×#103C2211yescharacteristic
70C2×#405C2211yescharacteristic
71#2611—21no—
72#2604—21no—
73#2601—21no—
74#2584—21no—
75#2479—21no—
76#2475—21no—
77#2469—21no—
78#2462—21no—
79#2453C2211yescharacteristic
80#2446C2211yescharacteristic
81#2441C2211yescharacteristic
82#2434C2211yescharacteristic
83#2429C2211yescharacteristic
84#2423C2211yescharacteristic
85#2415C2211yescharacteristic
86#2409C2211yescharacteristic
87#2365C2211yescharacteristic
88#2361—21no—
89#2360C2211yescharacteristic
90#2360C2211yescharacteristic
91#2359—21no—
92#2359—21no—
93D4×C4⋊C4C2211yescharacteristic
94D4×C4⋊C4C2211yescharacteristic
95#2344—21no—
96#2339C2211yescharacteristic
97#2339C2211yescharacteristic
98#2323C2211yescharacteristic
99#2323C2211yescharacteristic
100#2323C2211yescharacteristic
101#2323C2211yescharacteristic
102#2322—21no—
103#2322—21no—
104C4×C4⋊Q8C2211yescharacteristic
105C4×C4⋊Q8C2211yescharacteristic
106C4×#121—21no—
107#2295C2211yescharacteristic
108#2293C2211yescharacteristic
109C2×#389—21no—
110C42×D4C2211yescharacteristic
111#2096C2211yescharacteristic
112#2096C2211yescharacteristic
113#2096C2211yescharacteristic
114#2096C2211yescharacteristic
115#2088C2211yescharacteristic
116#2083C2211yescharacteristic
117#2077C2211yescharacteristic
118#2072C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2066C2211yescharacteristic
123#2059C2211yescharacteristic
124#2056C2211yescharacteristic
125#2056C2211yescharacteristic
126#2056C2211yescharacteristic
127#2043C2211yescharacteristic
128#2043C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2035C2211yescharacteristic
132#2035C2211yescharacteristic
133#2026C2211yescharacteristic
134#2016C2211yescharacteristic
135#2016C2211yescharacteristic
136#2016C2211yescharacteristic
137#2016C2211yescharacteristic
138#2016C2211yescharacteristic
139#2016C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#1981C2211yescharacteristic
144#1971C2211yescharacteristic
145#1948C2211yescharacteristic
146#1943C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1921C2211yescharacteristic
156#1918C2211yescharacteristic
157#1917C2211yescharacteristic
158#1916C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1851C2211yescharacteristic
188#1850C2211yescharacteristic
189#1807C2211yescharacteristic
190#1802C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1787C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×C4⋊C8C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1750C2211yescharacteristic
203#1750C2211yescharacteristic
204#1745C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C2×#137—24no—
209C2×#137—24no—
210C2×#137—24no—
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×Q16C2311yescharacteristic
216C22×Q16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×M16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#547—24no—
223#547—24no—
224#541—24no—
225#541—42no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#126—21no—
230C2×#126—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243#520—24no—
244#520—24no—
245#520—42no—
246#520—42no—
247#519—24no—
248#519—42no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—21no—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×#117—21no—
272C2×#117—21no—
273C2×#117—21no—
274C2×#117—21no—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C22×C4⋊C4—21no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4—21no—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C42—21no—
285#484—24no—
286#483—24no—
287#479—24no—
288#478—24no—
289#467—24no—
290#462—24no—
291#461—24no—
292#461—24no—
293#452—24no—
294#452—24no—
295#452—24no—
296#452—24no—
297#451—24no—
298#441—24no—
299#441—24no—
300#441—24no—
301#441—42no—
302#441—42no—
303#440—24no—
304#440D418yescomplemented
305C4×Q16—24no—
306C4×Q16—24no—
307C4×Q16—24no—
308C4×SD16—24no—
309C4×SD16—24no—
310C4×SD16—24no—
311#433—24no—
312#428—24no—
313C2×#107C2311yescharacteristic
314C2×#107C2311yescharacteristic
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×#106C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323C2×#106C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328#416—24no—
329C2×#103—24no—
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×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×C22⋊C8C2311yescharacteristic
365C2×C22⋊C8C2311yescharacteristic
366#405—24no—
367C2×#97C2311yescharacteristic
368C2×#97C2311yescharacteristic
369C2×#97C2311yescharacteristic
370C2×C4×C8C2311yescharacteristic
371C2×C4×C8C2311yescharacteristic
372C2×C4×C8C2311yescharacteristic
373#400—21no—
374#400—21no—
375#399—21no—
376#399—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#398—21no—
381#397—21no—
382#396—21no—
383#396—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#394—21no—
388#393—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390D411yescharacteristic
400#390D411yescharacteristic
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389D411yescharacteristic
418#389D411yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388D411yescharacteristic
437#388D411yescharacteristic
438#388D411yescharacteristic
439#388D411yescharacteristic
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#386—21no—
456#386—21no—
457#386—21no—
458#386—21no—
459#386—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#385—21no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#381—21no—
472#381—21no—
473#380—21no—
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4—21no—
492C4×C22⋊C4—21no—
493C4×C22⋊C4—21no—
494C4×C22⋊C4C2311yescharacteristic
495C4×C22⋊C4C2311yescharacteristic
496#376—21no—
497C2×#95—21no—
498C2×#95—21no—
499C43C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
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
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41#4114yes—
536C22×Q8—21no—
537C22×Q8—22no—
538C22×Q8—22no—
539C22×Q8—22no—
540C22×Q8—22no—
541C22×Q8—41no—
542C22×Q8—41no—
543C22×Q8C2411yescharacteristic
544C22×Q8C2411yescharacteristic
545C22×Q8C2411yescharacteristic
546C22×Q8C2411yescharacteristic
547C22×Q8C2411yescharacteristic
548C22×D4—21no—
549C22×D4—21no—
550C22×D4C2×D411yescharacteristic
551C22×D4C2411yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—21no—
561C23×C4—21no—
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564#137—232no—
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—41no—
579C2×Q16—41no—
580C2×Q16—41no—
581C2×Q16—41no—
582C2×Q16—41no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—22no—
586C2×SD16—22no—
587C2×SD16—22no—
588C2×SD16—22no—
589C2×SD16—22no—
590C2×SD16C2×D414yes—
591C2×SD16#4114yes—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—22no—
595C22×C8—22no—
596C22×C8—22no—
597C22×C8—41no—
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C4⋊Q8—22no—
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609C4⋊Q8—22no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612#126—44no—
613#126—44no—
614#125—22no—
615#125—41no—
616#125—44no—
617#125—44no—
618#123—28no—
619#123—28no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8#4114yes—
632#121—28no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×Q8—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—44no—
651C4×Q8—44no—
652C4×Q8C2×D414yes—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—22no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—44no—
665C4×D4—44no—
666C4×D4—44no—
667C4×D4—44no—
668C4×D4—82no—
669C4×D4C2×D414yes—
670#117—22no—
671#117—22no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—44no—
676#117—44no—
677#117—44no—
678#117—44no—
679#117—41no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
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—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—41no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4—82no—
723C2×C4⋊C4C2×D411yescharacteristic
724C2×C4⋊C4C2×D411yescharacteristic
725C2×C4⋊C4C2×D411yescharacteristic
726C2×C4⋊C4C2×D411yescharacteristic
727C2×C4⋊C4C2×D411yescharacteristic
728C2×C4⋊C4C2×D411yescharacteristic
729C2×C4⋊C4C2×D411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C22⋊C4C2×D411yescharacteristic
763C2×C22⋊C4C2×D411yescharacteristic
764C2×C22⋊C4C2×D411yescharacteristic
765C2×C22⋊C4C2×D411yescharacteristic
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—21no—
779C2×C42—21no—
780C2×C42—82no—
781C2×C42C2×D411yescharacteristic
782C2×C42C2×D411yescharacteristic
783C2×C42C2×D411yescharacteristic
784C2×C42C2×D411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790#107—22no—
791#107—22no—
792#107—22no—
793#107C2×D414yes—
794#106—22no—
795#106—22no—
796#106—22no—
797#106—22no—
798#106—41no—
799#106—41no—
800#106—41no—
801C4⋊C8—22no—
802C4⋊C8—22no—
803C4⋊C8—22no—
804C4⋊C8—41no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
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—41no—
824#103—41no—
825#103—41no—
826#103—41no—
827#103—41no—
828#103—41no—
829#103C2×D414yes—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834#102C2×D414yes—
835C22⋊C8—22no—
836C22⋊C8—22no—
837C22⋊C8—22no—
838C22⋊C8—22no—
839C22⋊C8—22no—
840C22⋊C8—41no—
841#97—22no—
842#97—22no—
843#97C2×D414yes—
844C4×C8—22no—
845C4×C8—22no—
846C4×C8—22no—
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#95—21no—
875#95—21no—
876#95—21no—
877#95—21no—
878#95—21no—
879#95—21no—
880#95—21no—
881#95C2×D411yescharacteristic
882#95C2×D411yescharacteristic
883#95C2×D411yescharacteristic
884#95C2×D411yescharacteristic
885#95C2×D411yescharacteristic
886#95C2×D411yescharacteristic
887C24—21no—
888C24C22×D411yescharacteristic
889C24C22×D411yescharacteristic
890#41—28no—
891#41—44no—
892#41—44no—
893#41—44no—
894#41—44no—
895#41—44no—
896#41—44no—
897#41—44no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—28no—
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—21no—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—21no—
923C2×Q8—21no—
924C2×Q8—21no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—44no—
928C2×Q8—44no—
929C2×Q8—44no—
930C2×Q8—42no—
931C2×Q8C22×D412yes—
932C2×Q8C2×#4112yes—
933C2×Q8C2×#4112yes—
934C2×Q8C2×#4112yes—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—24no—
938C2×D4—22no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—41no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4C22×D412yes—
948C2×D4C2×#4112yes—
949C2×D4C2×#4112yes—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—24no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—24no—
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—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
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—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
1018C22×C4C2×#4112yes—
1019C22×C4C2511yescharacteristic
1020Q16—28no—
1021Q16—28no—
1022Q16—44no—
1023Q16—44no—
1024Q16—44no—
1025Q16—44no—
1026SD16—28no—
1027SD16—28no—
1028SD16—44no—
1029M16—28no—
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—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—44no—
1052C2×C8C22×D412yes—
1053C2×C8C22×D412yes—
1054C2×C8C2×#4112yes—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—22no—
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—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—41no—
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—42no—
1107C4⋊C4—42no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4—81no—
1111C4⋊C4—81no—
1112C4⋊C4—81no—
1113C4⋊C4—81no—
1114C4⋊C4C22×D412yes—
1115C4⋊C4C22×D412yes—
1116C4⋊C4C2×#4112yes—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—24no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C42—24no—
1144C42—22no—
1145C42—22no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—41no—
1155C42—41no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—81no—
1167C42—81no—
1168C42—81no—
1169C42C22×D412yes—
1170C42H(5,𝔽2)12yes—
1171C23—21no—
1172C23—21no—
1173C23—22no—
1174C23—21no—
1175C23—22no—
1176C23—22no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23#52512yes—
1192C23C23×D411yescharacteristic
1193Q8—22no—
1194Q8—22no—
1195Q8—22no—
1196Q8—22no—
1197Q8—22no—
1198Q8—22no—
1199Q8—22no—
1200Q8—22no—
1201Q8—48no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214D4—22no—
1215D4—22no—
1216D4—22no—
1217D4—44no—
1218D4—48no—
1219D4—48no—
1220D4#52514yes—
1221C2×C4—21no—
1222C2×C4—21no—
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—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
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—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—48no—
1264C2×C4—48no—
1265C2×C4—48no—
1266C2×C4—48no—
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—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—84no—
1310C2×C4—84no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4#52512yes—
1316C2×C4D4212yes—
1317C2×C4D4212yes—
1318C2×C4#57712yes—
1319C2×C4#57812yes—
1320C2×C4C23×D411yescharacteristic
1321C2×C4C22×#4111yescharacteristic
1322C2×C4C22×#4111yescharacteristic
1323C2×C4C22×#4111yescharacteristic
1324C2×C4C2×H(5,𝔽2)11yescharacteristic
1325C2×C4#58511yescharacteristic
1326C8—22no—
1327C8—22no—
1328C8—22no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C22—22no—
1335C22—24no—
1336C22—22no—
1337C22—22no—
1338C22—42no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—42no—
1343C22—41no—
1344C22—42no—
1345C22—41no—
1346C22—42no—
1347C22—42no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22C2×#52511yescharacteristic
1356C22C2×D4211yescharacteristic
1357C22D4×#4111yescharacteristic
1358C22C2×#57711yescharacteristic
1359C22C2×#57811yescharacteristic
1360C22#358611yescharacteristic
1361C22#358611yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—22no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4C2×#52511yescharacteristic
1390C4#345911yescharacteristic
1391C4D4×#4111yescharacteristic
1392C4#348111yescharacteristic
1393C2—42no—
1394C2—44no—
1395C2—81no—
1396C2#3465511yescharacteristic
1397C2#6058511yescharacteristic
1398C2#6059411yescharacteristic
1399C2#6109411yescharacteristic
1400C2#6109711yescharacteristic
1401C2#6149711yescharacteristic
1402C2#6151711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
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×#3120C2semidirect
2. C2×#2947C2semidirect
3. #35671C2semidirect
5. #26895C2semidirect
6. #26621C2semidirect
7. #26607C2semidirect
8. #26574C2semidirect
9. #26398C2semidirect
10. #26360C2semidirect
11. #26166C2semidirect
12. #26148C2semidirect
13. #25964C2semidirect
14. #25166C2semidirect
15. #25082C2semidirect
16. #24907C2semidirect
17. #24863C2semidirect
19. #24376C2semidirect
21. #23805C2semidirect
22. #23713C2semidirect
23. #23679C2semidirect
24. #23586C2semidirect
25. #21530C2semidirect
26. C4×#461C2semidirect
27. #21463C2semidirect
28. #21461C2semidirect
29. #21461C2semidirect
30. #21121C2semidirect
31. #21111C2semidirect
304. #440D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31202
C2×#29472
#356712
#343082
#268952
#266212
#266072
#265742
#263982
#263602
#261662
#261482
#259642
#251662
#250822
#249072
#248632
#244302
#243762
#238652
#238052
#237132
#236792
#235862
#215302
C4×#4612
#214632
#214612
#211212
#211112