Finite Group Databasebeta

← #7033329

Subgroups — #7033329

Order 512.

1625 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44871C211yesmaximal, characteristic
2#42654C211yesmaximal, characteristic, complemented
3#32206C211yesmaximal, characteristic, complemented
4#31765C211yesmaximal, characteristic, complemented
5#31672C211yesmaximal, characteristic, complemented
6#31553C211yesmaximal, characteristic, complemented
7#31447C211yesmaximal, characteristic, complemented
8#31401C211yesmaximal, characteristic, complemented
9#31336C211yesmaximal, characteristic, complemented
10#30424C211yesmaximal, characteristic, complemented
11#28998C211yesmaximal, characteristic, complemented
12#28870C211yesmaximal, characteristic, complemented
13#28559C211yesmaximal, characteristic, complemented
14#27703C211yesmaximal, characteristic, complemented
15#27536C211yesmaximal, characteristic, complemented
16#27245C211yesmaximal, characteristic, complemented
17#26341C211yesmaximal, characteristic, complemented
18#26228C211yesmaximal, characteristic, complemented
19#25547C211yesmaximal, characteristic, complemented
20#25350C211yesmaximal, characteristic, complemented
21#25210C211yesmaximal, characteristic, complemented
22#24975C211yesmaximal, characteristic, complemented
23#24957C211yesmaximal, characteristic, complemented
24#24786C211yesmaximal, characteristic, complemented
25#24564C211yesmaximal, characteristic, complemented
26#24394C211yesmaximal, characteristic, complemented
27#23641C211yesmaximal, characteristic, complemented
28#23142C211yesmaximal, characteristic, complemented
29#22845C211yesmaximal, characteristic, complemented
30#22495C211yesmaximal, characteristic, complemented
31#21770C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#484C2211yescharacteristic, complemented
35C2×#474C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#435C2211yescharacteristic, complemented
41C2×#435C2211yescharacteristic, complemented
42C2×#427C2211yescharacteristic, complemented
43C2×#408C2211yescharacteristic
44C2×#408C2211yescharacteristic
45#2824—21no—
46#2808—21no—
47#2803—21no—
48#2774—21no—
49#2759—21no—
50#2709—21no—
51#2700—21no—
52#2697—21no—
53#2678—21no—
54#2653—21no—
55#2648—21no—
56#2616C2211yescharacteristic
57#2563C2211yescharacteristic, complemented
58#2557—21no—
59#2536C2211yescharacteristic
60#2535C2211yescharacteristic
61#2518—21no—
62#2504C2211yescharacteristic
63#2495C2211yescharacteristic, complemented
64#2494C2211yescharacteristic
65#2492C2211yescharacteristic
66#2491C2211yescharacteristic
67#2485C2211yescharacteristic
68#2472—21no—
69#2439C2211yescharacteristic
70#2439C2211yescharacteristic, complemented
71#2431—21no—
72#2421C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2416C2211yescharacteristic
75#2415C2211yescharacteristic, complemented
76#2415C2211yescharacteristic, complemented
77#2414C2211yescharacteristic
78#2408C2211yescharacteristic
79#2404—21no—
80#2388C2211yescharacteristic
81#2363C2211yescharacteristic
82#2360C2211yescharacteristic, complemented
83#2352C2211yescharacteristic
84#2352C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2311C2211yescharacteristic
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2087C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2058C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1993C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1954C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1924C2211yescharacteristic
144#1921C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1918C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1894C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1870C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1850C2211yescharacteristic, complemented
179#1850C2211yescharacteristic, complemented
180#1835C2211yescharacteristic, complemented
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1804C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#547—24no—
214#547—42no—
215#535—24no—
216#535—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253#484—42no—
254#474—42no—
255#468—24no—
256#468—42no—
257#465—42no—
258#450—42no—
259#435—42no—
260#435—42no—
261#427—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295#408—42no—
296#408—42no—
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#401—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#395—21no—
330#395D411yescharacteristic
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394D411yescharacteristic
344#394D411yescharacteristic
345#394D411yescharacteristic
346#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393D411yescharacteristic
353#392—21no—
354#392—21no—
355#392—21no—
356#392D411yescharacteristic
357#392D411yescharacteristic
358#392D411yescharacteristic
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391—21no—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#383—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
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#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—44no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2×D411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570#127—44no—
571#124—44no—
572#124—82no—
573#123—44no—
574#123—44no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—44no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—82no—
596#121#4114yes—
597#120—44no—
598#120—44no—
599#120—82no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612#117—22no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
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—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
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—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—22no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#102—22no—
740#102—22no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—41no—
765#97—41no—
766C4×C8—41no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
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#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821#41—82no—
822#41—82no—
823#41—82no—
824#41—82no—
825#41—816no—
826C2×Q8—22no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—21no—
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—41no—
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—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4C2×#4112yes—
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—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C2×#4112yes—
958C22×C4H(5,𝔽2)12yes—
959C22×C4C2511yescharacteristic
960SD16—82no—
961SD16—82no—
962M16—82no—
963M16—82no—
964M16—82no—
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—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—44no—
989C2×C8—82no—
990C2×C8H(5,𝔽2)12yes—
991C4⋊C4—22no—
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—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
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—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4C2×#4112yes—
1036C22⋊C4—22no—
1037C22⋊C4—24no—
1038C22⋊C4—22no—
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—41no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
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—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—42no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
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—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—84no—
1142C23—84no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23#54612yes—
1149C23C23×D411yescharacteristic
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—82no—
1155Q8—84no—
1156Q8—162no—
1157D4—22no—
1158D4—22no—
1159D4—44no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—82no—
1167D4—82no—
1168D4—82no—
1169D4—84no—
1170D4—82no—
1171D4—82no—
1172D4—84no—
1173D4—84no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
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—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
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—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4#54612yes—
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—22no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—168no—
1328C22C2×#54611yescharacteristic
1329C22#348511yescharacteristic
1330C22#349611yescharacteristic
1331C22#358411yescharacteristic
1332C22#358511yescharacteristic
1333C22#358511yescharacteristic
1334C22#358611yescharacteristic
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4#351411yescharacteristic
1360C4#352111yescharacteristic
1361C4#353411yescharacteristic
1362C4#356011yescharacteristic
1363C2—42no—
1364C2—81no—
1365C2—81no—
1366C2—81no—
1367C2—82no—
1368C2—161no—
1369C2#4348911yescharacteristic
1370C2#6117511yescharacteristic
1371C2#6120711yescharacteristic
1372C2#6176211yescharacteristic
1373C2#6179611yescharacteristic
1374C2#6228511yescharacteristic
1375C2#6235111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44871C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42654C2semidirect
3. #32206C2semidirect
4. #31765C2semidirect
5. #31672C2semidirect
6. #31553C2semidirect
7. #31447C2semidirect
8. #31401C2semidirect
9. #31336C2semidirect
10. #30424C2semidirect
11. #28998C2semidirect
12. #28870C2semidirect
13. #28559C2semidirect
14. #27703C2semidirect
15. #27536C2semidirect
16. #27245C2semidirect
17. #26341C2semidirect
18. #26228C2semidirect
19. #25547C2semidirect
20. #25350C2semidirect
21. #25210C2semidirect
22. #24975C2semidirect
23. #24957C2semidirect
24. #24786C2semidirect
25. #24564C2semidirect
26. #24394C2semidirect
27. #23641C2semidirect
28. #23142C2semidirect
29. #22845C2semidirect
30. #22495C2semidirect
31. #21770C2semidirect
34. C2×#484C22semidirect
40. C2×#435C22semidirect
41. C2×#435C22semidirect
42. C2×#427C22semidirect
57. #2563C22semidirect
63. #2495C22semidirect
70. #2439C22semidirect
72. #2421C22semidirect
75. #2415C22semidirect
76. #2415C22semidirect
82. #2360C22semidirect
84. #2352C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
92. #2087C22semidirect
93. #2085C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
100. #2076C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
105. #2074C22semidirect
109. #2066C22semidirect
112. #2058C22semidirect
113. #2057C22semidirect
117. #2035C22semidirect
123. #2024C22semidirect
128. #1993C22semidirect
129. #1993C22semidirect
130. #1987C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1943C22semidirect
137. #1935C22semidirect
144. #1921C22semidirect
145. #1919C22semidirect
146. #1918C22semidirect
147. #1918C22semidirect
152. #1894C22semidirect
156. #1892C22semidirect
168. #1873C22semidirect
169. #1872C22semidirect
171. #1870C22semidirect
172. #1870C22semidirect
176. #1854C22semidirect
177. #1852C22semidirect
178. #1850C22semidirect
179. #1850C22semidirect
180. #1835C22semidirect
183. #1825C22semidirect
184. #1824C22semidirect
185. #1823C22semidirect
186. #1809C22semidirect
187. #1809C22semidirect
188. #1808C22semidirect
189. #1805C22semidirect
196. C4×#103C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#448712
#426542
#322062
#317652
#316722
#315532
#314472
#314012
#313362
#304242
#289982
#288702
#285592
#277032
#275362
#272452
#263412
#262282
#255472
#253502
#252102
#249752
#249572
#247862
#245642
#243942
#236412
#231422
#228452
#224952
#217702