Finite Group Databasebeta

← #7182540

Subgroups — #7182540

Order 512.

1756 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3386C211yesmaximal, characteristic, complemented
2C2×#3262C211yesmaximal, characteristic
3#45102C211yesmaximal, characteristic, complemented
4#42427C211yesmaximal, characteristic, complemented
5#31176C211yesmaximal, characteristic, complemented
6#31162C211yesmaximal, characteristic, complemented
7#30973C211yesmaximal, characteristic, complemented
8#30962C211yesmaximal, characteristic, complemented
9#30933C211yesmaximal, characteristic, complemented
10#30917C211yesmaximal, characteristic, complemented
11#30687C211yesmaximal, characteristic, complemented
12#30675C211yesmaximal, characteristic
13#28432C211yesmaximal, characteristic, complemented
14#27797C211yesmaximal, characteristic, complemented
15#27795C211yesmaximal, characteristic, complemented
16#26983C211yesmaximal, characteristic, complemented
17#26975C211yesmaximal, characteristic
18#26613C211yesmaximal, characteristic, complemented
19#26604C211yesmaximal, characteristic, complemented
20#26478C211yesmaximal, characteristic, complemented
21#26466C211yesmaximal, characteristic, complemented
22#25939C211yesmaximal, characteristic, complemented
23#25681C211yesmaximal, characteristic, complemented
24#25455C211yesmaximal, characteristic, complemented
25#25299C211yesmaximal, characteristic, complemented
26#24853C211yesmaximal, characteristic, complemented
27#24636C211yesmaximal, characteristic, complemented
28#24344C211yesmaximal, characteristic, complemented
29#23581C211yesmaximal, characteristic, complemented
30#23079C211yesmaximal, characteristic, complemented
31#22961C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#542C2211yescharacteristic
36#3386—28no—
37#3262—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#500C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#477C2211yescharacteristic
43C2×#477C2211yescharacteristic
44C2×#477C2211yescharacteristic
45C2×#477C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#474C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#468C2211yescharacteristic
52C2×#468C2211yescharacteristic
53C2×#467C2211yescharacteristic
54C2×#466C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#464C2211yescharacteristic
57C2×#463C2211yescharacteristic
58C2×#463C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×#424C2211yescharacteristic
65#2817—21no—
66#2731—21no—
67#2729—21no—
68#2725—21no—
69#2707—21no—
70#2689—21no—
71#2689—21no—
72#2674—21no—
73#2674—21no—
74#2663—21no—
75#2628C2211yescharacteristic
76#2614—21no—
77#2592C2211yescharacteristic
78#2581C2211yescharacteristic
79#2567C2211yescharacteristic
80#2558—21no—
81#2551C2211yescharacteristic
82#2551C2211yescharacteristic
83#2545C2211yescharacteristic
84#2519—21no—
85#2492C2211yescharacteristic
86#2492C2211yescharacteristic
87#2490C2211yescharacteristic
88#2489C2211yescharacteristic
89#2454C2211yescharacteristic
90#2453C2211yescharacteristic
91#2448—21no—
92#2447C2211yescharacteristic
93#2447C2211yescharacteristic
94#2434—21no—
95#2429C2211yescharacteristic
96#2426C2211yescharacteristic
97#2422C2211yescharacteristic
98#2422C2211yescharacteristic
99#2421—21no—
100#2396C2211yescharacteristic
101#2369C2211yescharacteristic
102#2367C2211yescharacteristic
103#2365C2211yescharacteristic
104#2357C2211yescharacteristic
105#2323C2211yescharacteristic
106#2096C2211yescharacteristic
107#2094C2211yescharacteristic
108#2088C2211yescharacteristic
109#2088C2211yescharacteristic
110#2083C2211yescharacteristic
111#2083C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2058C2211yescharacteristic
121#2056C2211yescharacteristic
122#2055C2211yescharacteristic
123#2055C2211yescharacteristic
124#2054C2211yescharacteristic
125#2042C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2035C2211yescharacteristic
129#2034C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic
132#2026C2211yescharacteristic
133#2026C2211yescharacteristic
134#2024C2211yescharacteristic
135#2024C2211yescharacteristic
136#2024C2211yescharacteristic
137#2023C2211yescharacteristic
138#2023C2211yescharacteristic
139#2016C2211yescharacteristic
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2013C2211yescharacteristic
143#2012C2211yescharacteristic
144#2001C2211yescharacteristic
145#2000C2211yescharacteristic
146#1993C2211yescharacteristic
147#1987C2211yescharacteristic
148#1985C2211yescharacteristic
149#1983C2211yescharacteristic
150#1981C2211yescharacteristic
151#1973C2211yescharacteristic
152#1971C2211yescharacteristic
153#1971C2211yescharacteristic
154#1968C2211yescharacteristic
155#1959C2211yescharacteristic
156#1958C2211yescharacteristic
157#1956C2211yescharacteristic
158#1949C2211yescharacteristic
159#1947C2211yescharacteristic
160#1947C2211yescharacteristic
161#1940C2211yescharacteristic
162#1939C2211yescharacteristic
163#1939C2211yescharacteristic
164#1936C2211yescharacteristic
165#1936C2211yescharacteristic
166#1935C2211yescharacteristic
167#1934C2211yescharacteristic
168#1928C2211yescharacteristic
169#1928C2211yescharacteristic
170#1927C2211yescharacteristic
171#1926C2211yescharacteristic
172#1926C2211yescharacteristic
173#1925C2211yescharacteristic
174#1921C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1894C2211yescharacteristic
179#1892C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1851C2211yescharacteristic
193#1850C2211yescharacteristic
194#1809C2211yescharacteristic
195#1807C2211yescharacteristic
196#1805C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#107C2211yescharacteristic
199#1771C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1753C2211yescharacteristic
203#1752C2211yescharacteristic
204#1750C2211yescharacteristic
205C23×Q8—21no—
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#557—24no—
215#557—42no—
216D4×Q8—24no—
217D4×Q8—42no—
218#542—24no—
219#542—24no—
220#542—42no—
221#542—42no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#126—21no—
232C2×#126—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#124—21no—
238C2×#124—21no—
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#123—21no—
243C2×#123—21no—
244C2×#123—21no—
245C2×#123—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×C4×Q8—21no—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×#117C2311yescharacteristic
268#501—24no—
269#501—24no—
270#500—24no—
271#489—42no—
272#478—24no—
273#478—24no—
274#477—24no—
275#477—24no—
276#477—24no—
277#477—24no—
278#475—24no—
279#474—24no—
280#474D418yes—
281#468—24no—
282#468—24no—
283#467—24no—
284#466—24no—
285#464—24no—
286#464—24no—
287#463—24no—
288#463—24no—
289#446—24no—
290#441—42no—
291#440—24no—
292#440—24no—
293C4×SD16—24no—
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308#424—24no—
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350C2×#97C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353#400—21no—
354#400—21no—
355#400—21no—
356#400—21no—
357#400—21no—
358#400—21no—
359#400D411yescharacteristic
360#399—21no—
361#399—21no—
362#399D411yescharacteristic
363#398—21no—
364#398—21no—
365#398D411yescharacteristic
366#398D411yescharacteristic
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#396D411yescharacteristic
382#396D411yescharacteristic
383#395—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395D411yescharacteristic
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#393—21no—
397#393—21no—
398#393—21no—
399#393—21no—
400#393D411yescharacteristic
401#391—21no—
402#391—21no—
403#391—21no—
404#391—21no—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#390—21no—
414#390—21no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#389—21no—
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#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#388—21no—
450#388—21no—
451#388—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#382—21no—
467#382C2311yescharacteristic
468#381—21no—
469#381—21no—
470#381—21no—
471#380—21no—
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C22⋊C4—21no—
486C4×C22⋊C4—21no—
487C4×C22⋊C4C2311yescharacteristic
488C4×C22⋊C4C2311yescharacteristic
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×Q8—21no—
519C22×Q8—21no—
520C22×Q8—44no—
521C22×Q8—82no—
522C22×Q8—82no—
523C22×Q8C2×D411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×M16—22no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—44no—
580C4⋊Q8—82no—
581C4⋊Q8—82no—
582C4⋊Q8C2×D414yes—
583#126—44no—
584#126—44no—
585#125—22no—
586#125—22no—
587#125—41no—
588#125—41no—
589#125—44no—
590#125—44no—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—22no—
595#124—41no—
596#124—41no—
597#124—44no—
598#124—44no—
599#123—44no—
600#123—44no—
601#123—82no—
602#123—82no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—44no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614#121—22no—
615#121—22no—
616#121—41no—
617#121—41no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—44no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4C2×D414yes—
639#117—22no—
640#117—22no—
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—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#107—22no—
744#107—22no—
745#107—22no—
746#107—22no—
747#107—22no—
748#107—22no—
749#107—41no—
750#107C2×D414yes—
751#107C2×D414yes—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—41no—
756#106—41no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764C4⋊C8C2×D414yes—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102C2×D414yes—
792#102C2×D414yes—
793C22⋊C8—22no—
794C22⋊C8—41no—
795#97—22no—
796#97—22no—
797#97—22no—
798#97—41no—
799C4×C8—22no—
800C4×C8—41no—
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#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844C24—21no—
845C24—21no—
846C24C22×D411yescharacteristic
847C2×Q8—22no—
848C2×Q8—24no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—41no—
867C2×Q8—41no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×Q8—81no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—816no—
883C2×Q82−1+412yes—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4C22×D412yes—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—24no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C2511yescharacteristic
948Q16—44no—
949Q16—82no—
950SD16—28no—
951SD16—82no—
952SD16—82no—
953D8—82no—
954M16—82no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—82no—
977C2×C8C22×D412yes—
978C2×C8C22×D412yes—
979C2×C82−1+412yes—
980C4⋊C4—24no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4C22×D412yes—
1041C4⋊C4C22×D412yes—
1042C4⋊C4C22×D412yes—
1043C22⋊C4—24no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42C22×D412yes—
1098C42H(5,𝔽2)12yes—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23C23×D411yescharacteristic
1121Q8—22no—
1122Q8—22no—
1123Q8—44no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—84no—
1135Q8—84no—
1136Q8—84no—
1137Q8—84no—
1138Q8—162no—
1139D4—22no—
1140D4—22no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—162no—
1148D4—162no—
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—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
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—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4D4212yes—
1236C2×C4D4212yes—
1237C2×C4#57812yes—
1238C2×C4C23×D411yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×2−1+411yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—22no—
1245C8—22no—
1246C8—22no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—41no—
1261C22—41no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22C2×D4211yescharacteristic
1274C22#348911yescharacteristic
1275C22#349711yescharacteristic
1276C22C2×#57811yescharacteristic
1277C22#358511yescharacteristic
1278C22#358511yescharacteristic
1279C22#358611yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4#348611yescharacteristic
1308C4#350011yescharacteristic
1309C4#354111yescharacteristic
1310C4#354711yescharacteristic
1311C2—81no—
1312C2—82no—
1313C2—161no—
1314C2#4524511yescharacteristic
1315C2#6105811yescharacteristic
1316C2#6109711yescharacteristic
1317C2#6215811yescharacteristic
1318C2#6222911yescharacteristic
1319C2#6238911yescharacteristic
1320C2#6240411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#466C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3386C2semidirect
3. #45102C2semidirect
4. #42427C2semidirect
5. #31176C2semidirect
6. #31162C2semidirect
7. #30973C2semidirect
8. #30962C2semidirect
9. #30933C2semidirect
10. #30917C2semidirect
11. #30687C2semidirect
13. #28432C2semidirect
14. #27797C2semidirect
15. #27795C2semidirect
16. #26983C2semidirect
18. #26613C2semidirect
19. #26604C2semidirect
20. #26478C2semidirect
21. #26466C2semidirect
22. #25939C2semidirect
23. #25681C2semidirect
24. #25455C2semidirect
25. #25299C2semidirect
26. #24853C2semidirect
27. #24636C2semidirect
28. #24344C2semidirect
29. #23581C2semidirect
30. #23079C2semidirect
31. #22961C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33862
C2×#32622
#451022
#424272
#311762
#311622
#309732
#309622
#309332
#309172
#306872
#306752
#284322
#277972
#277952
#269832
#269752
#266132
#266042
#264782
#264662
#259392
#256812
#254552
#252992
#248532
#246362
#243442
#235812
#230792
#229612