Finite Group Databasebeta

← #6814015

Subgroups — #6814015

Order 512.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42672C211yesmaximal, characteristic, complemented
2#42459C211yesmaximal, characteristic
3#33188C211yesmaximal, characteristic
4#32438C211yesmaximal, characteristic, complemented
5#32434C211yesmaximal, characteristic, complemented
6#32430C211yesmaximal, characteristic, complemented
7#32429C211yesmaximal, characteristic, complemented
8#30690C211yesmaximal, characteristic
9#30687C211yesmaximal, characteristic
10#30686C211yesmaximal, characteristic, complemented
11#30684C211yesmaximal, characteristic, complemented
12#29932C211yesmaximal, characteristic
13#29930C211yesmaximal, characteristic, complemented
14#28822C211yesmaximal, characteristic, complemented
15#28747C211yesmaximal, characteristic, complemented
16#28550C211yesmaximal, characteristic, complemented
17#28537C211yesmaximal, characteristic, complemented
18#28028C211yesmaximal, characteristic, complemented
19#28019C211yesmaximal, characteristic, complemented
20#27800C211yesmaximal, characteristic
21#27789C211yesmaximal, characteristic, complemented
22#26470C211yesmaximal, characteristic, complemented
23#26461C211yesmaximal, characteristic, complemented
24#26325C211yesmaximal, characteristic, complemented
25#26320C211yesmaximal, characteristic, complemented
26#25043C211yesmaximal, characteristic, complemented
27#25030C211yesmaximal, characteristic
28#23192C211yesmaximal, characteristic, complemented
29#22729C211yesmaximal, characteristic, complemented
30#21605C211yesmaximal, characteristic, complemented
31#20822C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#446C2211yescharacteristic
44C2×#441C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2838—21no—
48#2837—21no—
49#2800—21no—
50#2790—21no—
51#2773—21no—
52#2772—21no—
53#2762—21no—
54#2759—21no—
55#2755—21no—
56#2718—21no—
57#2666—21no—
58#2655—21no—
59#2652—21no—
60#2637—21no—
61#2621C2211yescharacteristic
62#2620C2211yescharacteristic
63#2592C2211yescharacteristic
64#2568C2211yescharacteristic
65#2567C2211yescharacteristic
66#2566C2211yescharacteristic
67#2565C2211yescharacteristic
68#2565C2211yescharacteristic
69#2552C2211yescharacteristic
70#2550C2211yescharacteristic
71#2525—21no—
72#2514C2211yescharacteristic
73#2514C2211yescharacteristic
74#2512C2211yescharacteristic
75#2511C2211yescharacteristic
76#2492C2211yescharacteristic
77#2490C2211yescharacteristic
78#2489C2211yescharacteristic
79#2489C2211yescharacteristic
80#2458—21no—
81#2423C2211yescharacteristic
82#2423C2211yescharacteristic
83#2422C2211yescharacteristic
84#2421C2211yescharacteristic
85#2396C2211yescharacteristic
86#2367C2211yescharacteristic
87#2365C2211yescharacteristic
88#2355C2211yescharacteristic
89Q8×C4⋊C4C2211yescharacteristic
90#2314C2211yescharacteristic
91#2314C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2096C2211yescharacteristic
95#2096C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2094C2211yescharacteristic
99#2092C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2072C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2026C2211yescharacteristic
129#2026C2211yescharacteristic
130#2026C2211yescharacteristic
131#2023C2211yescharacteristic
132#1984C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1981C2211yescharacteristic
136#1981C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1971C2211yescharacteristic
141#1971C2211yescharacteristic
142#1969C2211yescharacteristic
143#1969C2211yescharacteristic
144#1969C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1958C2211yescharacteristic
148#1956C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1949C2211yescharacteristic
152#1948C2211yescharacteristic
153#1948C2211yescharacteristic
154#1948C2211yescharacteristic
155#1948C2211yescharacteristic
156#1947C2211yescharacteristic
157#1944C2211yescharacteristic
158#1941C2211yescharacteristic
159#1939C2211yescharacteristic
160#1928C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1880C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1877C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1851C2211yescharacteristic
179#1851C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1844C2211yescharacteristic
185#1835C2211yescharacteristic
186#1834C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1798C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1770C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117C2311yescharacteristic
228#501—42no—
229#499—42no—
230#497—24no—
231#479—42no—
232#479—42no—
233#478—42no—
234#475—42no—
235#470—42no—
236#468—42no—
237#467—42no—
238#465—42no—
239#446—24no—
240#441—42no—
241C4×SD16—42no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294#405—24no—
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#401—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400D411yescharacteristic
316#399—21no—
317#399—21no—
318#399D411yescharacteristic
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398D411yescharacteristic
331#398D411yescharacteristic
332#397—21no—
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#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396D411yescharacteristic
347#396D411yescharacteristic
348#395—21no—
349#395—21no—
350#395—21no—
351#395D411yescharacteristic
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393D411yescharacteristic
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#383—21no—
439#383—21no—
440#382—21no—
441#382—21no—
442#382—21no—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4C2411yescharacteristic
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532#126—82no—
533#125—41no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—41no—
539#124—22no—
540#124—22no—
541#123—82no—
542C22⋊Q8—41no—
543C22⋊Q8—41no—
544C22⋊Q8—41no—
545C22⋊Q8—41no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548#121—41no—
549#121—41no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—82no—
559C4×D4—41no—
560C4×D4—41no—
561#117—22no—
562#117—22no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#102—22no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711#97—22no—
712#97—22no—
713#97—22no—
714#97#4114yes—
715C4×C8—22no—
716C4×C8—22no—
717C4×C8—22no—
718C4×C8—22no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
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#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777C24—21no—
778C24C22×D411yescharacteristic
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—41no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C2511yescharacteristic
850Q16—44no—
851Q16—82no—
852SD16—44no—
853SD16—82no—
854M16—44no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—44no—
875C2×C8C2×#4112yes—
876C2×C8C2×#4112yes—
877C2×C8H(5,𝔽2)12yes—
878C2×C8H(5,𝔽2)12yes—
879C2×C82−1+412yes—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—42no—
982C42—42no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42C2×#4112yes—
993C422−1+412yes—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23C23×D411yescharacteristic
1009Q8—44no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—162no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—162no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—162no—
1114C2×C4#54712yes—
1115C2×C4#54712yes—
1116C2×C4#57712yes—
1117C2×C4C22×#4111yescharacteristic
1118C2×C4C2×H(5,𝔽2)11yescharacteristic
1119C2×C4C2×H(5,𝔽2)11yescharacteristic
1120C2×C4C2×2−1+411yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C2×C4#58511yescharacteristic
1123C8—22no—
1124C8—22no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8#54214yes—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22C2×#54711yescharacteristic
1146C22#349711yescharacteristic
1147C22#349811yescharacteristic
1148C22C2×#57711yescharacteristic
1149C22#358411yescharacteristic
1150C22#358611yescharacteristic
1151C22#358611yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4C2×#54211yescharacteristic
1181C4#349411yescharacteristic
1182C4#355011yescharacteristic
1183C4#355411yescharacteristic
1184C2—81no—
1185C2—161no—
1186C2#3935111yescharacteristic
1187C2#6127111yescharacteristic
1188C2#6128011yescharacteristic
1189C2#6238611yescharacteristic
1190C2#6239111yescharacteristic
1191C2#6246211yescharacteristic
1192C2#6246611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42672C2semidirect
4. #32438C2semidirect
5. #32434C2semidirect
6. #32430C2semidirect
7. #32429C2semidirect
10. #30686C2semidirect
11. #30684C2semidirect
13. #29930C2semidirect
14. #28822C2semidirect
15. #28747C2semidirect
16. #28550C2semidirect
17. #28537C2semidirect
18. #28028C2semidirect
19. #28019C2semidirect
21. #27789C2semidirect
22. #26470C2semidirect
23. #26461C2semidirect
24. #26325C2semidirect
25. #26320C2semidirect
26. #25043C2semidirect
28. #23192C2semidirect
29. #22729C2semidirect
30. #21605C2semidirect
31. #20822C2semidirect

Maximal subgroups

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

subgroupindex
#426722
#424592
#331882
#324382
#324342
#324302
#324292
#306902
#306872
#306862
#306842
#299322
#299302
#288222
#287472
#285502
#285372
#280282
#280192
#278002
#277892
#264702
#264612
#263252
#263202
#250432
#250302
#231922
#227292
#216052
#208222