Finite Group Databasebeta

← #6812179

Subgroups — #6812179

Order 512.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39605C211yesmaximal, characteristic, complemented
2#38938C211yesmaximal, characteristic
3#32935C211yesmaximal, characteristic, complemented
4#32420C211yesmaximal, characteristic, complemented
5#32418C211yesmaximal, characteristic, complemented
6#32277C211yesmaximal, characteristic, complemented
7#32268C211yesmaximal, characteristic, complemented
8#30692C211yesmaximal, characteristic, complemented
9#30685C211yesmaximal, characteristic, complemented
10#30588C211yesmaximal, characteristic, complemented
11#30573C211yesmaximal, characteristic, complemented
12#29894C211yesmaximal, characteristic, complemented
13#29890C211yesmaximal, characteristic, complemented
14#28859C211yesmaximal, characteristic, complemented
15#28858C211yesmaximal, characteristic, complemented
16#28769C211yesmaximal, characteristic, complemented
17#28565C211yesmaximal, characteristic, complemented
18#28091C211yesmaximal, characteristic, complemented
19#28088C211yesmaximal, characteristic, complemented
20#26342C211yesmaximal, characteristic, complemented
21#26338C211yesmaximal, characteristic, complemented
22#26138C211yesmaximal, characteristic, complemented
23#26126C211yesmaximal, characteristic, complemented
24#25349C211yesmaximal, characteristic, complemented
25#25346C211yesmaximal, characteristic, complemented
26#25261C211yesmaximal, characteristic, complemented
27#25258C211yesmaximal, characteristic, complemented
28#23126C211yesmaximal, characteristic, complemented
29#22709C211yesmaximal, characteristic, complemented
30#21441C211yesmaximal, characteristic, complemented
31C2×#1809C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#485C2211yescharacteristic, complemented
34C2×#480C2211yescharacteristic, complemented
35C2×#477C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C22×#107C2211yescharacteristic
44C22×#106C2211yescharacteristic
45#2848C2211yescharacteristic
46#2847C2211yescharacteristic
47#2788—21no—
48#2784—21no—
49#2784—21no—
50#2781—21no—
51#2780—21no—
52#2768—21no—
53#2756—21no—
54#2686—21no—
55#2639—21no—
56#2626—21no—
57#2563C2211yescharacteristic
58#2563C2211yescharacteristic
59#2538C2211yescharacteristic
60#2537C2211yescharacteristic
61#2505—21no—
62#2497C2211yescharacteristic
63#2497C2211yescharacteristic
64#2497C2211yescharacteristic
65#2495C2211yescharacteristic
66#2492C2211yescharacteristic
67#2491C2211yescharacteristic
68#2487C2211yescharacteristic
69#2485C2211yescharacteristic
70#2472—21no—
71#2450—21no—
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic
74#2424—21no—
75#2423C2211yescharacteristic
76#2420C2211yescharacteristic
77#2417C2211yescharacteristic
78#2417C2211yescharacteristic
79#2416C2211yescharacteristic
80#2414C2211yescharacteristic
81#2361C2211yescharacteristic
82#2360C2211yescharacteristic
83#2352C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic
85#2321—21no—
86#2318—21no—
87C4×#120C2211yescharacteristic
88C2×#380C2211yescharacteristic
89C2×#380C2211yescharacteristic
90#2097C2211yescharacteristic, complemented
91#2095C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic, complemented
104#2077C2211yescharacteristic, complemented
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2075C2211yescharacteristic
109#2075C2211yescharacteristic
110#2075C2211yescharacteristic
111#2075C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2065C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2057C2211yescharacteristic, complemented
117#2057C2211yescharacteristic, complemented
118#2055C2211yescharacteristic, complemented
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic, complemented
129#2000C2211yescharacteristic, complemented
130#1990C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1947C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1936C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1925C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1918C2211yescharacteristic, complemented
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic, complemented
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1880C2211yescharacteristic, complemented
159#1877C2211yescharacteristic, complemented
160#1874C2211yescharacteristic
161#1874C2211yescharacteristic
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1870C2211yescharacteristic
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1864C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1854C2211yescharacteristic, complemented
170#1854C2211yescharacteristic, complemented
171#1853C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic, complemented
176#1852C2211yescharacteristic, complemented
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1850C2211yescharacteristic
180#1836C2211yescharacteristic, complemented
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic, complemented
192#1808C2211yescharacteristic
193#1779C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16—24no—
206C22×M16—42no—
207C22×M16—42no—
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#124—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120D411yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247#485—42no—
248#480—42no—
249#477—42no—
250#476—42no—
251#468—42no—
252#468—42no—
253#465—24no—
254#436—42no—
255#436—42no—
256#435—24no—
257C2×#107—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106—42no—
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#392—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386D411yescharacteristic
396#386D411yescharacteristic
397#386D411yescharacteristic
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385D411yescharacteristic
409#385D411yescharacteristic
410#385D411yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#381—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
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#380C2311yescharacteristic
444#379—21no—
445#379D411yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
456C2×#95—21no—
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
493C25C2×D411yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—416no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8#4114yes—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561#124—82no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—82no—
571C22⋊Q8—82no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—82no—
581#121—82no—
582#120—24no—
583#120—82no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—82no—
596#117—41no—
597#117—41no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
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—82no—
684C2×C22⋊C4—82no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—22no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—22no—
719#106—22no—
720#106—22no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751#97—22no—
752C4×C8—41no—
753C4×C8—41no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
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#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796C24—22no—
797C24—22no—
798C24—22no—
799C24—21no—
800C24—41no—
801C24—41no—
802C24—41no—
803C24—41no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2×#4112yes—
926C22×C42−1+412yes—
927C22×C4C2511yescharacteristic
928SD16—82no—
929M16—44no—
930M16—44no—
931M16—44no—
932M16—44no—
933M16—82no—
934C2×C8—28no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—44no—
956C2×C8C2×#4112yes—
957C2×C8C2×#4112yes—
958C2×C8H(5,𝔽2)12yes—
959C2×C8H(5,𝔽2)12yes—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4#13714yes—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—42no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—44no—
1099C23—44no—
1100C23—44no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—82no—
1109C23—82no—
1110C23—82no—
1111C23—82no—
1112C23#54712yes—
1113C23C2×#13712yes—
1114C23#57612yes—
1115C23C23×D411yescharacteristic
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—162no—
1121Q8—162no—
1122D4—44no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—82no—
1128D4—82no—
1129D4—84no—
1130D4—162no—
1131D4—162no—
1132D4—162no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—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—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4#54712yes—
1231C2×C4C2×#13712yes—
1232C2×C4C2×#13712yes—
1233C2×C4C22×#4111yescharacteristic
1234C2×C4C2×H(5,𝔽2)11yescharacteristic
1235C2×C4C2×H(5,𝔽2)11yescharacteristic
1236C2×C4C2×2−1+411yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—88no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22#335714yes—
1283C22C2×#54711yescharacteristic
1284C22#349611yescharacteristic
1285C22#349611yescharacteristic
1286C22C22×#13711yescharacteristic
1287C22C2×#57611yescharacteristic
1288C22#358511yescharacteristic
1289C22#358611yescharacteristic
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4#345511yescharacteristic
1316C4#349011yescharacteristic
1317C4#354111yescharacteristic
1318C4#354111yescharacteristic
1319C2—24no—
1320C2—81no—
1321C2—81no—
1322C2—81no—
1323C2—161no—
1324C2#3934411yescharacteristic
1325C2C2×#335711yescharacteristic
1326C2#6126611yescharacteristic
1327C2#6229611yescharacteristic
1328C2#6230011yescharacteristic
1329C2#6231111yescharacteristic
1330C2#6231511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38938C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39605C2semidirect
3. #32935C2semidirect
4. #32420C2semidirect
5. #32418C2semidirect
6. #32277C2semidirect
7. #32268C2semidirect
8. #30692C2semidirect
9. #30685C2semidirect
10. #30588C2semidirect
11. #30573C2semidirect
12. #29894C2semidirect
13. #29890C2semidirect
14. #28859C2semidirect
15. #28858C2semidirect
16. #28769C2semidirect
17. #28565C2semidirect
18. #28091C2semidirect
19. #28088C2semidirect
20. #26342C2semidirect
21. #26338C2semidirect
22. #26138C2semidirect
23. #26126C2semidirect
24. #25349C2semidirect
25. #25346C2semidirect
26. #25261C2semidirect
27. #25258C2semidirect
28. #23126C2semidirect
29. #22709C2semidirect
30. #21441C2semidirect
31. C2×#1809C2semidirect
33. C2×#485C22semidirect
34. C2×#480C22semidirect
35. C2×#477C22semidirect
36. C2×#476C22semidirect
90. #2097C22semidirect
91. #2095C22semidirect
92. #2094C22semidirect
93. #2093C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2085C22semidirect
98. #2083C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
103. #2077C22semidirect
104. #2077C22semidirect
111. #2075C22semidirect
112. #2068C22semidirect
113. #2065C22semidirect
114. #2058C22semidirect
115. #2057C22semidirect
116. #2057C22semidirect
117. #2057C22semidirect
118. #2055C22semidirect
123. #2035C22semidirect
128. #2033C22semidirect
129. #2000C22semidirect
130. #1990C22semidirect
131. #1990C22semidirect
132. #1949C22semidirect
133. #1948C22semidirect
134. #1947C22semidirect
135. #1947C22semidirect
136. #1942C22semidirect
137. #1942C22semidirect
138. #1936C22semidirect
139. #1935C22semidirect
140. #1934C22semidirect
141. #1933C22semidirect
142. #1927C22semidirect
143. #1925C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1919C22semidirect
149. #1918C22semidirect
152. #1895C22semidirect
155. #1894C22semidirect
158. #1880C22semidirect
159. #1877C22semidirect
167. #1864C22semidirect
168. #1863C22semidirect
169. #1854C22semidirect
170. #1854C22semidirect
175. #1852C22semidirect
176. #1852C22semidirect
180. #1836C22semidirect
191. #1809C22semidirect
194. #1776C22semidirect
195. C4×#103C22semidirect
196. C4×#102C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#396052
#389382
#329352
#324202
#324182
#322772
#322682
#306922
#306852
#305882
#305732
#298942
#298902
#288592
#288582
#287692
#285652
#280912
#280882
#263422
#263382
#261382
#261262
#253492
#253462
#252612
#252582
#231262
#227092
#214412
C2×#18092