Finite Group Databasebeta

← #6802450

Subgroups — #6802450

Order 512.

1285 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39802C211yesmaximal, characteristic, complemented
2#35206C211yesmaximal, characteristic
3#33026C211yesmaximal, characteristic
4#32661C211yesmaximal, characteristic
5#32649C211yesmaximal, characteristic
6#32625C211yesmaximal, characteristic, complemented
7#32608C211yesmaximal, characteristic, complemented
8#32392C211yesmaximal, characteristic, complemented
9#32376C211yesmaximal, characteristic, complemented
10#32187C211yesmaximal, characteristic
11#32171C211yesmaximal, characteristic
12#29873C211yesmaximal, characteristic, complemented
13#29837C211yesmaximal, characteristic, complemented
14#28901C211yesmaximal, characteristic
15#28886C211yesmaximal, characteristic
16#28524C211yesmaximal, characteristic
17#28390C211yesmaximal, characteristic
18#28385C211yesmaximal, characteristic, complemented
19#28289C211yesmaximal, characteristic
20#28209C211yesmaximal, characteristic, complemented
21#28168C211yesmaximal, characteristic
22#28028C211yesmaximal, characteristic, complemented
23#28020C211yesmaximal, characteristic, complemented
24#27512C211yesmaximal, characteristic, complemented
25#27505C211yesmaximal, characteristic, complemented
26#27219C211yesmaximal, characteristic
27#27210C211yesmaximal, characteristic
28#22827C211yesmaximal, characteristic, complemented
29#22164C211yesmaximal, characteristic, complemented
30#22129C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic
32C2×#479C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#462C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#461C2211yescharacteristic
41#2862C2211yescharacteristic
42#2855—21no—
43#2851—21no—
44#2789—21no—
45#2767—21no—
46#2762—21no—
47#2758—21no—
48#2660C2211yescharacteristic
49#2652—21no—
50#2652—21no—
51#2642C2211yescharacteristic
52#2605—21no—
53#2588—21no—
54#2582C2211yescharacteristic
55#2581C2211yescharacteristic
56#2568C2211yescharacteristic
57#2552C2211yescharacteristic
58#2547C2211yescharacteristic
59#2538C2211yescharacteristic
60#2528—21no—
61#2524—21no—
62#2515—21no—
63#2515—21no—
64#2514C2211yescharacteristic
65#2514C2211yescharacteristic
66#2511C2211yescharacteristic
67#2511C2211yescharacteristic
68#2511C2211yescharacteristic
69#2511C2211yescharacteristic
70#2495—21no—
71#2489—21no—
72#2447C2211yescharacteristic
73#2447C2211yescharacteristic
74#2356C2211yescharacteristic
75#2355C2211yescharacteristic
76#2331C2211yescharacteristic
77#2327C2211yescharacteristic
78#2326C2211yescharacteristic
79#2326C2211yescharacteristic
80#2320C2211yescharacteristic
81#2320C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic
83C4×#125C2211yescharacteristic
84#2295C2211yescharacteristic
85C42×D4C2211yescharacteristic
86#2097C2211yescharacteristic
87#2096C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2095C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2056C2211yescharacteristic
115#2056C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2043C2211yescharacteristic
119#2043C2211yescharacteristic
120#2016C2211yescharacteristic
121#2016C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#1989C2211yescharacteristic
127#1987C2211yescharacteristic
128#1985C2211yescharacteristic
129#1984C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1981C2211yescharacteristic
133#1973C2211yescharacteristic
134#1971C2211yescharacteristic
135#1971C2211yescharacteristic
136#1971C2211yescharacteristic
137#1971C2211yescharacteristic
138#1971C2211yescharacteristic
139#1971C2211yescharacteristic
140#1969C2211yescharacteristic
141#1969C2211yescharacteristic
142#1968C2211yescharacteristic
143#1959C2211yescharacteristic
144#1958C2211yescharacteristic
145#1949C2211yescharacteristic
146#1948C2211yescharacteristic
147#1948C2211yescharacteristic
148#1944C2211yescharacteristic
149#1941C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1919C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1916C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1865C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1847C2211yescharacteristic
187#1844C2211yescharacteristic
188#1843C2211yescharacteristic
189#1832C2211yescharacteristic
190#1831C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1804C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1768C2211yescharacteristic
199#1768C2211yescharacteristic
200#1767C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C22×C42—21no—
226#479—42no—
227#479—42no—
228#478—24no—
229#476—42no—
230#475—24no—
231#475—42no—
232#462—24no—
233#462—42no—
234#461—42no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#401—21no—
292#401—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391D411yescharacteristic
334#391D411yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389D411yescharacteristic
360#389D411yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—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#387D411yescharacteristic
402#387D411yescharacteristic
403#387D411yescharacteristic
404#387D411yescharacteristic
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#383—21no—
417#383—21no—
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453#376—21no—
454#376C2311yescharacteristic
455#376C2311yescharacteristic
456C43C2311yescharacteristic
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#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C2×Q16—22no—
498C2×Q16—22no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529#125—22no—
530#125—22no—
531#125—82no—
532#124—22no—
533#124—22no—
534#124—41no—
535#124—41no—
536C22⋊Q8—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—82no—
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636#107—22no—
637#107—41no—
638#107—41no—
639#107—41no—
640#106—22no—
641#106—22no—
642#106—22no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650C4⋊C8—22no—
651C4⋊C8—22no—
652C4⋊C8—22no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8#4114yes—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#102—22no—
681#102—22no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
686#97—41no—
687#97—41no—
688#97—41no—
689#97—41no—
690C4×C8—41no—
691C4×C8—41no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
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#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C2×Q8—22no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
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—41no—
790C2×Q8—41no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D42−1+412yes—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C2511yescharacteristic
839Q16—82no—
840Q16—82no—
841Q16—82no—
842Q16—82no—
843SD16—82no—
844SD16—82no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
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×C8C2×#4112yes—
868C2×C8C2×#4112yes—
869C4⋊C4—22no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
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—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C42—22no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42C2×#4112yes—
968C42H(5,𝔽2)12yes—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C23×D411yescharacteristic
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—82no—
994Q8—162no—
995D4—22no—
996D4—22no—
997D4—41no—
998D4—41no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
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—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
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—84no—
1084C2×C4—84no—
1085C2×C4—84no—
1086C2×C4#55012yes—
1087C2×C4#55012yes—
1088C2×C4#57712yes—
1089C2×C4C22×#4111yescharacteristic
1090C2×C4C2×H(5,𝔽2)11yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C2×C4#58511yescharacteristic
1095C8—22no—
1096C8—22no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22#344911yescharacteristic
1111C22C2×#55011yescharacteristic
1112C22#348911yescharacteristic
1113C22C2×#57711yescharacteristic
1114C22#358611yescharacteristic
1115C22#358611yescharacteristic
1116C22#358611yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4#351611yescharacteristic
1147C4#352111yescharacteristic
1148C4#356111yescharacteristic
1149C4#356211yescharacteristic
1150C2—82no—
1151C2#3913111yescharacteristic
1152C2#6097511yescharacteristic
1153C2#6097711yescharacteristic
1154C2#6141811yescharacteristic
1155C2#6142011yescharacteristic
1156C2#6218911yescharacteristic
1157C2#6223711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39802C2semidirect
6. #32625C2semidirect
7. #32608C2semidirect
8. #32392C2semidirect
9. #32376C2semidirect
12. #29873C2semidirect
13. #29837C2semidirect
18. #28385C2semidirect
20. #28209C2semidirect
22. #28028C2semidirect
23. #28020C2semidirect
24. #27512C2semidirect
25. #27505C2semidirect
28. #22827C2semidirect
29. #22164C2semidirect
30. #22129C2semidirect

Maximal subgroups

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

subgroupindex
#398022
#352062
#330262
#326612
#326492
#326252
#326082
#323922
#323762
#321872
#321712
#298732
#298372
#289012
#288862
#285242
#283902
#283852
#282892
#282092
#281682
#280282
#280202
#275122
#275052
#272192
#272102
#228272
#221642
#221292
#216172