Finite Group Databasebeta

← #7330051

Subgroups — #7330051

Order 512.

1540 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53062C211yesmaximal, characteristic, complemented
2#45303C211yesmaximal, characteristic, complemented
3#32346C211yesmaximal, characteristic, complemented
4#32276C211yesmaximal, characteristic, complemented
5#32003C211yesmaximal, characteristic, complemented
6#31552C211yesmaximal, characteristic, complemented
7#31534C211yesmaximal, characteristic, complemented
8#31369C211yesmaximal, characteristic, complemented
9#31331C211yesmaximal, characteristic, complemented
10#31265C211yesmaximal, characteristic, complemented
11#31091C211yesmaximal, characteristic, complemented
12#30679C211yesmaximal, characteristic, complemented
13#30570C211yesmaximal, characteristic, complemented
14#30399C211yesmaximal, characteristic, complemented
15#30035C211yesmaximal, characteristic, complemented
16#29702C211yesmaximal, characteristic, complemented
17#29173C211yesmaximal, characteristic, complemented
18#28231C211yesmaximal, characteristic, complemented
19#28112C211yesmaximal, characteristic, complemented
20#27244C211yesmaximal, characteristic, complemented
21#26891C211yesmaximal, characteristic, complemented
22#26780C211yesmaximal, characteristic, complemented
23#25981C211yesmaximal, characteristic, complemented
24#25964C211yesmaximal, characteristic, complemented
25#25513C211yesmaximal, characteristic, complemented
26#25357C211yesmaximal, characteristic, complemented
27#25125C211yesmaximal, characteristic, complemented
28#24899C211yesmaximal, characteristic, complemented
29#24455C211yesmaximal, characteristic, complemented
30#24040C211yesmaximal, characteristic, complemented
31#22175C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#469C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#416C2211yescharacteristic
48#2837—21no—
49#2829—21no—
50#2829—21no—
51#2813—21no—
52#2800—21no—
53#2747—21no—
54#2715—21no—
55#2711—21no—
56#2710—21no—
57#2700—21no—
58#2694—21no—
59#2672—21no—
60#2629C2211yescharacteristic
61#2624C2211yescharacteristic
62#2567C2211yescharacteristic
63#2562C2211yescharacteristic
64#2555—21no—
65#2549—21no—
66#2547C2211yescharacteristic
67#2538C2211yescharacteristic
68#2537C2211yescharacteristic
69#2537C2211yescharacteristic
70#2506C2211yescharacteristic
71#2490C2211yescharacteristic
72#2485C2211yescharacteristic
73#2485C2211yescharacteristic
74#2466—21no—
75#2454C2211yescharacteristic
76#2441C2211yescharacteristic
77#2441C2211yescharacteristic
78#2425—21no—
79#2423C2211yescharacteristic
80#2422C2211yescharacteristic
81#2422C2211yescharacteristic
82#2414C2211yescharacteristic
83#2414C2211yescharacteristic
84#2409C2211yescharacteristic
85#2407C2211yescharacteristic
86#2392C2211yescharacteristic
87#2367C2211yescharacteristic
88Q8×C22⋊C4C2211yescharacteristic
89#2339C2211yescharacteristic
90#2323C2211yescharacteristic
91#2100C2211yescharacteristic
92#2099C2211yescharacteristic
93#2096C2211yescharacteristic
94#2095C2211yescharacteristic
95#2093C2211yescharacteristic
96#2088C2211yescharacteristic
97#2084C2211yescharacteristic
98#2083C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic
132#2026C2211yescharacteristic
133#2026C2211yescharacteristic
134#2025C2211yescharacteristic
135#2023C2211yescharacteristic
136#2012C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1992C2211yescharacteristic
140#1973C2211yescharacteristic
141#1948C2211yescharacteristic
142#1936C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1916C2211yescharacteristic
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1879C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1870C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1862C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1844C2211yescharacteristic
186#1825C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1808C2211yescharacteristic
191#1807C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1787C2211yescharacteristic
200#1787C2211yescharacteristic
201#1763C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#548—42no—
213#548—42no—
214#542—42no—
215#542—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254#485—42no—
255#479—42no—
256#479—42no—
257#478—42no—
258#469—42no—
259#469—42no—
260#465—42no—
261#449—42no—
262#448—42no—
263C4×D8—42no—
264#436—42no—
265#435—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#419—42no—
284#416—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398D411yescharacteristic
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397D411yescharacteristic
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396D411yescharacteristic
350#396D411yescharacteristic
351#395—21no—
352#395—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394D411yescharacteristic
370#394D411yescharacteristic
371#394D411yescharacteristic
372#393—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392D411yescharacteristic
377#391—21no—
378#391—21no—
379#391—21no—
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C2×#95—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#126—44no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—82no—
568#124—22no—
569#124—22no—
570#124—44no—
571#124—44no—
572#124—82no—
573#123—44no—
574#123—82no—
575#123—82no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—82no—
596#121—82no—
597C4×Q8—22no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—41no—
778C4×C8—22no—
779#95—21no—
780#95—21no—
781#95—21no—
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#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—82no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—44no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—82no—
842C2×Q8—82no—
843C2×Q8—82no—
844C2×Q8H(5,𝔽2)12yes—
845C2×Q82−1+412yes—
846C2×D4—22no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4H(5,𝔽2)12yes—
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—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
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—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
944SD16—82no—
945SD16—82no—
946D8—44no—
947M16—82no—
948M16—82no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
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—82no—
973C2×C8—82no—
974C2×C8H(5,𝔽2)12yes—
975C4⋊C4—22no—
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—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
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—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
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⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
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—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—42no—
1089C42—42no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23C23×D411yescharacteristic
1131Q8—22no—
1132Q8—22no—
1133Q8—22no—
1134Q8—22no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—84no—
1140Q8—162no—
1141D4—22no—
1142D4—22no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—82no—
1150D4—82no—
1151D4—82no—
1152D4—84no—
1153D4—84no—
1154D4—162no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
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—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
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—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4#57712yes—
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4C2×H(5,𝔽2)11yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4C2×2−1+411yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C8—22no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—42no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22#348411yescharacteristic
1300C22#348911yescharacteristic
1301C22#349611yescharacteristic
1302C22C2×#57711yescharacteristic
1303C22#358411yescharacteristic
1304C22#358511yescharacteristic
1305C22#358611yescharacteristic
1306C4—22no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4#353411yescharacteristic
1332C4#353511yescharacteristic
1333C4#353611yescharacteristic
1334C4#354511yescharacteristic
1335C2—81no—
1336C2—81no—
1337C2—81no—
1338C2—82no—
1339C2—161no—
1340C2#4793811yescharacteristic
1341C2#6162811yescharacteristic
1342C2#6169211yescharacteristic
1343C2#6221911yescharacteristic
1344C2#6222611yescharacteristic
1345C2#6231911yescharacteristic
1346C2#6232211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53062C2semidirect
2. #45303C2semidirect
3. #32346C2semidirect
4. #32276C2semidirect
5. #32003C2semidirect
6. #31552C2semidirect
7. #31534C2semidirect
8. #31369C2semidirect
9. #31331C2semidirect
10. #31265C2semidirect
11. #31091C2semidirect
12. #30679C2semidirect
13. #30570C2semidirect
14. #30399C2semidirect
15. #30035C2semidirect
16. #29702C2semidirect
17. #29173C2semidirect
18. #28231C2semidirect
19. #28112C2semidirect
20. #27244C2semidirect
21. #26891C2semidirect
22. #26780C2semidirect
23. #25981C2semidirect
24. #25964C2semidirect
25. #25513C2semidirect
26. #25357C2semidirect
27. #25125C2semidirect
28. #24899C2semidirect
29. #24455C2semidirect
30. #24040C2semidirect
31. #22175C2semidirect

Maximal subgroups

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

subgroupindex
#530622
#453032
#323462
#322762
#320032
#315522
#315342
#313692
#313312
#312652
#310912
#306792
#305702
#303992
#300352
#297022
#291732
#282312
#281122
#272442
#268912
#267802
#259812
#259642
#255132
#253572
#251252
#248992
#244552
#240402
#221752