Finite Group Databasebeta

← #7124448

Subgroups — #7124448

Order 512.

1713 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3337C211yesmaximal, characteristic
2C2×#3243C211yesmaximal, characteristic, complemented
3#45107C211yesmaximal, characteristic
4#42978C211yesmaximal, characteristic, complemented
5#31249C211yesmaximal, characteristic, complemented
6#31080C211yesmaximal, characteristic, complemented
7#30972C211yesmaximal, characteristic, complemented
8#30961C211yesmaximal, characteristic, complemented
9#30831C211yesmaximal, characteristic, complemented
10#30779C211yesmaximal, characteristic, complemented
11#30665C211yesmaximal, characteristic, complemented
12#30637C211yesmaximal, characteristic, complemented
13#28929C211yesmaximal, characteristic, complemented
14#28812C211yesmaximal, characteristic, complemented
15#27943C211yesmaximal, characteristic, complemented
16#26817C211yesmaximal, characteristic, complemented
17#26790C211yesmaximal, characteristic, complemented
18#26374C211yesmaximal, characteristic, complemented
19#26346C211yesmaximal, characteristic, complemented
20#26068C211yesmaximal, characteristic, complemented
21#26052C211yesmaximal, characteristic, complemented
22#25562C211yesmaximal, characteristic, complemented
23#25509C211yesmaximal, characteristic, complemented
24#25234C211yesmaximal, characteristic, complemented
25#25212C211yesmaximal, characteristic, complemented
26#24613C211yesmaximal, characteristic, complemented
27#24586C211yesmaximal, characteristic, complemented
28#24102C211yesmaximal, characteristic
29#23557C211yesmaximal, characteristic, complemented
30#22946C211yesmaximal, characteristic, complemented
31#22909C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#542C2211yescharacteristic
36#3337—28no—
37#3243—28no—
38C2×#501C2211yescharacteristic
39C2×#500C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#484C2211yescharacteristic
44C2×#484C2211yescharacteristic
45C2×#485C2211yescharacteristic
46C2×#485C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#480C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#479C2211yescharacteristic
52C2×#477C2211yescharacteristic
53C2×#478C2211yescharacteristic
54C2×#478C2211yescharacteristic
55C2×#474C2211yescharacteristic
56C2×#470C2211yescharacteristic
57C2×#465C2211yescharacteristic
58C2×#465C2211yescharacteristic
59C2×C4×SD16C2211yescharacteristic
60C2×C8×D4C2211yescharacteristic
61C2×#433C2211yescharacteristic
62C2×#428C2211yescharacteristic
63C2×#427C2211yescharacteristic
64C22×#106C2211yescharacteristic
65#2822—21no—
66#2722—21no—
67#2717—21no—
68#2708—21no—
69#2689—21no—
70#2689—21no—
71#2689—21no—
72#2687—21no—
73#2687—21no—
74#2642—21no—
75#2628—21no—
76#2625C2211yescharacteristic
77#2611—21no—
78#2550C2211yescharacteristic
79#2550C2211yescharacteristic
80#2550C2211yescharacteristic
81#2503C2211yescharacteristic
82#2499C2211yescharacteristic
83#2492C2211yescharacteristic
84#2492C2211yescharacteristic
85#2487C2211yescharacteristic
86#2486—21no—
87#2466—21no—
88#2453C2211yescharacteristic
89#2453C2211yescharacteristic
90#2453C2211yescharacteristic
91#2449—21no—
92#2447C2211yescharacteristic
93#2442C2211yescharacteristic
94#2442C2211yescharacteristic
95#2440C2211yescharacteristic
96#2427—21no—
97#2427C2211yescharacteristic
98#2420C2211yescharacteristic
99#2417C2211yescharacteristic
100#2395C2211yescharacteristic
101#2361C2211yescharacteristic
102#2360C2211yescharacteristic
103D4×C4⋊C4C2211yescharacteristic
104#2346C2211yescharacteristic
105#2316C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2097C2211yescharacteristic
109#2095C2211yescharacteristic
110#2088C2211yescharacteristic
111#2087C2211yescharacteristic
112#2086C2211yescharacteristic
113#2085C2211yescharacteristic
114#2085C2211yescharacteristic
115#2084C2211yescharacteristic
116#2076C2211yescharacteristic
117#2073C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2068C2211yescharacteristic
123#2066C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2059C2211yescharacteristic
131#2058C2211yescharacteristic
132#2058C2211yescharacteristic
133#2058C2211yescharacteristic
134#2057C2211yescharacteristic
135#2057C2211yescharacteristic
136#2055C2211yescharacteristic
137#2042C2211yescharacteristic
138#2036C2211yescharacteristic
139#2036C2211yescharacteristic
140#2034C2211yescharacteristic
141#2034C2211yescharacteristic
142#2026C2211yescharacteristic
143#2024C2211yescharacteristic
144#2015C2211yescharacteristic
145#2001C2211yescharacteristic
146#1971C2211yescharacteristic
147#1969C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1947C2211yescharacteristic
151#1944C2211yescharacteristic
152#1943C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1940C2211yescharacteristic
156#1935C2211yescharacteristic
157#1934C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1925C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1895C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1872C2211yescharacteristic
178#1872C2211yescharacteristic
179#1870C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1847C2211yescharacteristic
193#1846C2211yescharacteristic
194#1825C2211yescharacteristic
195#1808C2211yescharacteristic
196#1804C2211yescharacteristic
197C4×#107C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic
202#1736C2211yescharacteristic
203C2×#340C2211yescharacteristic
204#1729C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#553—24no—
211#553—42no—
212#552—24no—
213#552—42no—
214#544—24no—
215#544—42no—
216#542—24no—
217#542—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264#501—24no—
265#500—24no—
266#499—24no—
267#489—24no—
268#488—24no—
269#485—24no—
270#485—24no—
271#484—24no—
272#484—24no—
273#482D418yes—
274#480—24no—
275#480—24no—
276#479—24no—
277#479—24no—
278#478—24no—
279#478—24no—
280#477—24no—
281#474—24no—
282#470—42no—
283#465—24no—
284#465—24no—
285C4×SD16—24no—
286C8×D4—24no—
287#433—24no—
288#428—42no—
289#427—24no—
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#106—24no—
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#400—21no—
353#400—21no—
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#400—21no—
359#400D411yescharacteristic
360#399—21no—
361#399D411yescharacteristic
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398D411yescharacteristic
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397D411yescharacteristic
383#397D411yescharacteristic
384#397D411yescharacteristic
385#396—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#394—21no—
391#394—21no—
392#394D411yescharacteristic
393#394D411yescharacteristic
394#393—21no—
395#393—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#390C2311yescharacteristic
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#389—21no—
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#384C2311yescharacteristic
456#382—21no—
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#381—21no—
461#381—21no—
462#381—21no—
463#381—21no—
464#380—21no—
465#380—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484#376—21no—
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—21no—
521C22×D4—21no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—44no—
563#126—44no—
564#126—44no—
565#126—44no—
566#125—22no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—44no—
575#125—44no—
576#124—22no—
577#124—41no—
578#124—44no—
579#123—44no—
580#123—44no—
581#123—44no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—82no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—44no—
598#121C2×D414yes—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—44no—
612C4×D4—82no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—44no—
619#117C2×D414yes—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—82no—
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—41no—
735#107—41no—
736#107—41no—
737#107C2×D414yes—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106C2×D414yes—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—41no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102C2×D414yes—
771#102C2×D414yes—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—41no—
776C22⋊C8C2×D414yes—
777#97—22no—
778#97—41no—
779C4×C8—22no—
780C4×C8—22no—
781C4×C8—22no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—42no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4C22×D412yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D412yes—
929C22×C4H(5,𝔽2)12yes—
930C22×C4C2511yescharacteristic
931Q16—82no—
932SD16—44no—
933M16—44no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—44no—
955C2×C8—44no—
956C2×C8C22×D412yes—
957C2×C8C22×D412yes—
958C2×C82−1+412yes—
959C2×C82−1+412yes—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4C22×D412yes—
1025C4⋊C4C22×D412yes—
1026C4⋊C4C22×D412yes—
1027C4⋊C42−1+412yes—
1028C22⋊C4—24no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—24no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C42—24no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23D4212yes—
1094C23#57812yes—
1095C23C23×D411yescharacteristic
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—162no—
1105Q8—162no—
1106Q8—162no—
1107D4—22no—
1108D4—22no—
1109D4—44no—
1110D4—41no—
1111D4—41no—
1112D4—84no—
1113D4—84no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4D4212yes—
1210C2×C4C23×D411yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4C2×2−1+411yescharacteristic
1213C2×C4C2×2−1+411yescharacteristic
1214C2×C4C2×2−1+411yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—22no—
1217C8—22no—
1218C8—22no—
1219C8—22no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22C2×D4211yescharacteristic
1246C22#348911yescharacteristic
1247C22#349911yescharacteristic
1248C22C2×#57811yescharacteristic
1249C22#358411yescharacteristic
1250C22#358411yescharacteristic
1251C22#358511yescharacteristic
1252C4—22no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—42no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4#348911yescharacteristic
1280C4#349911yescharacteristic
1281C4#353511yescharacteristic
1282C4#354411yescharacteristic
1283C2—42no—
1284C2—42no—
1285C2—82no—
1286C2#4475811yescharacteristic
1287C2#6105711yescharacteristic
1288C2#6109211yescharacteristic
1289C2#6217611yescharacteristic
1290C2#6221411yescharacteristic
1291C2#6248911yescharacteristic
1292C2#6251611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#553C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3243C2semidirect
4. #42978C2semidirect
5. #31249C2semidirect
6. #31080C2semidirect
7. #30972C2semidirect
8. #30961C2semidirect
9. #30831C2semidirect
10. #30779C2semidirect
11. #30665C2semidirect
12. #30637C2semidirect
13. #28929C2semidirect
14. #28812C2semidirect
15. #27943C2semidirect
16. #26817C2semidirect
17. #26790C2semidirect
18. #26374C2semidirect
19. #26346C2semidirect
20. #26068C2semidirect
21. #26052C2semidirect
22. #25562C2semidirect
23. #25509C2semidirect
24. #25234C2semidirect
25. #25212C2semidirect
26. #24613C2semidirect
27. #24586C2semidirect
29. #23557C2semidirect
30. #22946C2semidirect
31. #22909C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33372
C2×#32432
#451072
#429782
#312492
#310802
#309722
#309612
#308312
#307792
#306652
#306372
#289292
#288122
#279432
#268172
#267902
#263742
#263462
#260682
#260522
#255622
#255092
#252342
#252122
#246132
#245862
#241022
#235572
#229462
#229092