Finite Group Databasebeta

← #6582691

Subgroups — #6582691

Order 512.

1417 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35838C211yesmaximal, characteristic
2#35818C211yesmaximal, characteristic, complemented
3#33188C211yesmaximal, characteristic
4#33121C211yesmaximal, characteristic
5#33117C211yesmaximal, characteristic, complemented
6#28837C211yesmaximal, characteristic, complemented
7#28747C211yesmaximal, characteristic, complemented
8#28018C211yesmaximal, characteristic, complemented
9#28012C211yesmaximal, characteristic, complemented
10#27946C211yesmaximal, characteristic
11#27940C211yesmaximal, characteristic, complemented
12#27517C211yesmaximal, characteristic, complemented
13#27506C211yesmaximal, characteristic, complemented
14#27505C211yesmaximal, characteristic, complemented
15#27502C211yesmaximal, characteristic, complemented
16#26535C211yesmaximal, characteristic, complemented
17#26528C211yesmaximal, characteristic, complemented
18#26324C211yesmaximal, characteristic, complemented
19#26317C211yesmaximal, characteristic, complemented
20#25208C211yesmaximal, characteristic, complemented
21#25203C211yesmaximal, characteristic
22#25202C211yesmaximal, characteristic
23#25201C211yesmaximal, characteristic, complemented
24#23192C211yesmaximal, characteristic, complemented
25#23038C211yesmaximal, characteristic, complemented
26#23034C211yesmaximal, characteristic
27#22818C211yesmaximal, characteristic, complemented
28#22805C211yesmaximal, characteristic, complemented
29#22730C211yesmaximal, characteristic, complemented
30#21606C211yesmaximal, characteristic, complemented
31#20453C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#428C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2655—21no—
48#2653—21no—
49#2621C2211yescharacteristic
50#2620C2211yescharacteristic
51#2594—21no—
52#2592C2211yescharacteristic
53#2575—21no—
54#2574—21no—
55#2573—21no—
56#2570C2211yescharacteristic
57#2568C2211yescharacteristic
58#2552C2211yescharacteristic
59#2527—21no—
60#2525—21no—
61#2524—21no—
62#2520—21no—
63#2518—21no—
64#2515—21no—
65#2514C2211yescharacteristic
66#2514C2211yescharacteristic
67#2513C2211yescharacteristic
68#2511C2211yescharacteristic
69#2503C2211yescharacteristic
70#2502C2211yescharacteristic
71#2500C2211yescharacteristic
72#2499C2211yescharacteristic
73#2475—21no—
74#2460—21no—
75#2402—21no—
76#2396C2211yescharacteristic
77#2395—21no—
78#2367C2211yescharacteristic
79#2365C2211yescharacteristic
80#2362C2211yescharacteristic
81#2362C2211yescharacteristic
82#2361C2211yescharacteristic
83#2360C2211yescharacteristic
84#2356C2211yescharacteristic
85#2355C2211yescharacteristic
86#2355C2211yescharacteristic
87#2355C2211yescharacteristic
88#2355C2211yescharacteristic
89#2354C2211yescharacteristic
90#2274C2211yescharacteristic
91#2274C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2096C2211yescharacteristic
95#2096C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2083C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2074C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2056C2211yescharacteristic
113#2056C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#1984C2211yescharacteristic
117#1983C2211yescharacteristic
118#1983C2211yescharacteristic
119#1981C2211yescharacteristic
120#1981C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1971C2211yescharacteristic
125#1971C2211yescharacteristic
126#1969C2211yescharacteristic
127#1969C2211yescharacteristic
128#1969C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1958C2211yescharacteristic
132#1956C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1944C2211yescharacteristic
142#1942C2211yescharacteristic
143#1939C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1880C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1877C2211yescharacteristic
166#1875C2211yescharacteristic
167#1873C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1862C2211yescharacteristic
174#1850C2211yescharacteristic
175#1850C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1846C2211yescharacteristic
180#1844C2211yescharacteristic
181#1805C2211yescharacteristic
182#1803C2211yescharacteristic
183#1803C2211yescharacteristic
184#1802C2211yescharacteristic
185#1798C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228#497—24no—
229#485—42no—
230#485—42no—
231#483—42no—
232#481—42no—
233#470—24no—
234#468—24no—
235#467—42no—
236#465—42no—
237#446—24no—
238#441—24no—
239C4×SD16—24no—
240#428—24no—
241#428—24no—
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#400D411yescharacteristic
315#399D411yescharacteristic
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398D411yescharacteristic
324#398D411yescharacteristic
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396D411yescharacteristic
335#396D411yescharacteristic
336#395D411yescharacteristic
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#393—21no—
342#393D411yescharacteristic
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—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#387—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#376—21no—
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×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16#4114yes—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531#125—82no—
532#124—22no—
533#124—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540#121—22no—
541#121—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×D4—22no—
551C4×D4—41no—
552C4×D4—82no—
553#117—22no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—82no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—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—41no—
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
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×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—22no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106#4114yes—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
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#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707C22⋊C8—22no—
708C22⋊C8—22no—
709#97—22no—
710#97—22no—
711#97—22no—
712#97#4114yes—
713C4×C8—22no—
714C4×C8—22no—
715C4×C8—22no—
716C4×C8—22no—
717#95—21no—
718#95—21no—
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—21no—
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—41no—
799C2×Q8—41no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—42no—
807C2×D4—81no—
808C2×D4—81no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
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—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
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×C4C22×D411yescharacteristic
850C22×C4C2×#4112yes—
851C22×C4H(5,𝔽2)12yes—
852C22×C4C2511yescharacteristic
853Q16—44no—
854Q16—82no—
855SD16—44no—
856SD16—82no—
857M16—28no—
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—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—44no—
878C2×C8C2×#4112yes—
879C2×C8C2×#4112yes—
880C2×C8C2×#4112yes—
881C2×C8C2×#4112yes—
882C2×C8C2×#4112yes—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
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—21no—
911C4⋊C4—21no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
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⋊C4C2×#4112yes—
941C4⋊C4C2×#4112yes—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—81no—
982C42—81no—
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—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23#55012yes—
1008C23C23×D411yescharacteristic
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—82no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—84no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
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—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
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—84no—
1112C2×C4—162no—
1113C2×C4—162no—
1114C2×C4#54712yes—
1115C2×C4#54712yes—
1116C2×C4#55012yes—
1117C2×C4#57712yes—
1118C2×C4C22×#4111yescharacteristic
1119C2×C4C22×#4111yescharacteristic
1120C2×C4C22×#4111yescharacteristic
1121C2×C4C2×H(5,𝔽2)11yescharacteristic
1122C2×C4C2×2−1+411yescharacteristic
1123C2×C4#58511yescharacteristic
1124C8—22no—
1125C8—22no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8#52914yes—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22C2×#54711yescharacteristic
1147C22C2×#55011yescharacteristic
1148C22D4×#4111yescharacteristic
1149C22C2×#57711yescharacteristic
1150C22#358411yescharacteristic
1151C22#358611yescharacteristic
1152C22#358611yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—41no—
1158C4—42no—
1159C4—41no—
1160C4—41no—
1161C4—42no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4C2×#52911yescharacteristic
1182C4#349411yescharacteristic
1183C4#350711yescharacteristic
1184C4#352211yescharacteristic
1185C2—42no—
1186C2—161no—
1187C2#3611711yescharacteristic
1188C2#6127511yescharacteristic
1189C2#6128111yescharacteristic
1190C2#6142011yescharacteristic
1191C2#6142311yescharacteristic
1192C2#6149011yescharacteristic
1193C2#6151711yescharacteristic
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
2. #35818C2semidirect
5. #33117C2semidirect
6. #28837C2semidirect
7. #28747C2semidirect
8. #28018C2semidirect
9. #28012C2semidirect
11. #27940C2semidirect
12. #27517C2semidirect
13. #27506C2semidirect
14. #27505C2semidirect
15. #27502C2semidirect
16. #26535C2semidirect
17. #26528C2semidirect
18. #26324C2semidirect
19. #26317C2semidirect
20. #25208C2semidirect
23. #25201C2semidirect
24. #23192C2semidirect
25. #23038C2semidirect
27. #22818C2semidirect
28. #22805C2semidirect
29. #22730C2semidirect
30. #21606C2semidirect
31. #20453C2semidirect

Maximal subgroups

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

subgroupindex
#358382
#358182
#331882
#331212
#331172
#288372
#287472
#280182
#280122
#279462
#279402
#275172
#275062
#275052
#275022
#265352
#265282
#263242
#263172
#252082
#252032
#252022
#252012
#231922
#230382
#230342
#228182
#228052
#227302
#216062
#204532