Finite Group Databasebeta

← #7490354

Subgroups — #7490354

Order 512.

1228 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46344C211yesmaximal, characteristic, complemented
2#39498C211yesmaximal, characteristic
3#32658C211yesmaximal, characteristic
4#32641C211yesmaximal, characteristic, complemented
5#32592C211yesmaximal, characteristic
6#32590C211yesmaximal, characteristic, complemented
7#32512C211yesmaximal, characteristic, complemented
8#32325C211yesmaximal, characteristic, complemented
9#32251C211yesmaximal, characteristic, complemented
10#31873C211yesmaximal, characteristic, complemented
11#31807C211yesmaximal, characteristic
12#31599C211yesmaximal, characteristic, complemented
13#31157C211yesmaximal, characteristic
14#30960C211yesmaximal, characteristic, complemented
15#30385C211yesmaximal, characteristic, complemented
16#30377C211yesmaximal, characteristic, complemented
17#29448C211yesmaximal, characteristic
18#29433C211yesmaximal, characteristic
19#29021C211yesmaximal, characteristic, complemented
20#28951C211yesmaximal, characteristic
21#28681C211yesmaximal, characteristic, complemented
22#28192C211yesmaximal, characteristic
23#28035C211yesmaximal, characteristic, complemented
24#27488C211yesmaximal, characteristic
25#27440C211yesmaximal, characteristic
26#27310C211yesmaximal, characteristic
27#26481C211yesmaximal, characteristic
28#26166C211yesmaximal, characteristic
29#25488C211yesmaximal, characteristic, complemented
30#25308C211yesmaximal, characteristic
31#23151C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#461C2211yescharacteristic
35C2×#446C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38#2863C2211yescharacteristic
39#2863C2211yescharacteristic
40#2859C2211yescharacteristic
41#2839—21no—
42#2807—21no—
43#2807—21no—
44#2791—21no—
45#2788—21no—
46#2788—21no—
47#2776—21no—
48#2769—21no—
49#2762—21no—
50#2758—21no—
51#2713—21no—
52#2628—21no—
53#2584C2211yescharacteristic
54#2584C2211yescharacteristic
55#2584C2211yescharacteristic
56#2582C2211yescharacteristic
57#2581C2211yescharacteristic
58#2580C2211yescharacteristic
59#2580C2211yescharacteristic
60#2571C2211yescharacteristic
61#2568C2211yescharacteristic
62#2552C2211yescharacteristic
63#2514C2211yescharacteristic
64#2511C2211yescharacteristic
65#2509C2211yescharacteristic
66#2509C2211yescharacteristic
67#2508C2211yescharacteristic
68#2506C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2453C2211yescharacteristic
72#2453C2211yescharacteristic
73#2446C2211yescharacteristic
74#2446C2211yescharacteristic
75#2442—21no—
76#2441—21no—
77#2382—21no—
78#2354C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2317—21no—
81C4×C4⋊Q8C2211yescharacteristic
82#2293C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2094C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2087C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2083C2211yescharacteristic
106#2083C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic
123#2055C2211yescharacteristic
124#2055C2211yescharacteristic
125#2043C2211yescharacteristic
126#2043C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2026C2211yescharacteristic
130#2025C2211yescharacteristic
131#1992C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1985C2211yescharacteristic
135#1985C2211yescharacteristic
136#1973C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1960C2211yescharacteristic
140#1949C2211yescharacteristic
141#1948C2211yescharacteristic
142#1944C2211yescharacteristic
143#1944C2211yescharacteristic
144#1944C2211yescharacteristic
145#1944C2211yescharacteristic
146#1944C2211yescharacteristic
147#1942C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1941C2211yescharacteristic
151#1939C2211yescharacteristic
152#1939C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1934C2211yescharacteristic
160#1933C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1926C2211yescharacteristic
171#1921C2211yescharacteristic
172#1921C2211yescharacteristic
173#1921C2211yescharacteristic
174#1919C2211yescharacteristic
175#1919C2211yescharacteristic
176#1918C2211yescharacteristic
177#1917C2211yescharacteristic
178#1917C2211yescharacteristic
179#1916C2211yescharacteristic
180#1916C2211yescharacteristic
181#1880C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1865C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1862C2211yescharacteristic
193#1835C2211yescharacteristic
194#1805C2211yescharacteristic
195#1804C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1770C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1767C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C2×C4⋊Q8D411yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220C2×#117—21no—
221C22×C4⋊C4—21no—
222#499—42no—
223#479—42no—
224#461—42no—
225#446—42no—
226#446—42no—
227C4×SD16—42no—
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#401—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#393—21no—
321#393—21no—
322#391—21no—
323#391—21no—
324#391D411yescharacteristic
325#391D411yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389D411yescharacteristic
358#389D411yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—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#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#384—21no—
415#384D411yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#383—21no—
421#383—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C43C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—41no—
496C2×SD16—41no—
497C2×SD16—41no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—42no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—41no—
513#125—41no—
514#125—41no—
515#125—44no—
516#125—82no—
517C4×Q8—41no—
518C4×Q8—41no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—41no—
529C4×D4—41no—
530C4×D4—41no—
531#117—44no—
532#117—82no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
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—82no—
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
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×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—41no—
630#107—41no—
631#107—41no—
632#107—41no—
633#107—41no—
634#106—22no—
635#106—22no—
636#106—22no—
637#106—22no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642C4⋊C8—22no—
643C4⋊C8—22no—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—41no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649C4⋊C8—41no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#102—22no—
665#102—22no—
666#102—22no—
667#102—41no—
668#102—41no—
669#102—41no—
670#97—41no—
671#97—41no—
672#97—41no—
673#97—41no—
674C4×C8—22no—
675C4×C8—22no—
676C4×C8—41no—
677C4×C8—41no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
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#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—41no—
755C2×Q8—41no—
756C2×Q8—41no—
757C2×Q8—41no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D42−1+412yes—
764C22×C4—24no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4—81no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C2511yescharacteristic
803SD16—44no—
804SD16—82no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8H(5,𝔽2)12yes—
828C2×C82−1+412yes—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C42−1+412yes—
907C22⋊C4—24no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C42—22no—
919C42—22no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—41no—
935C42—41no—
936C42—42no—
937C42—42no—
938C42—81no—
939C42—81no—
940C42—81no—
941C42—81no—
942C42—81no—
943C23—22no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23C23×D411yescharacteristic
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—41no—
955Q8—41no—
956Q8—41no—
957Q8—41no—
958Q8—41no—
959Q8—82no—
960Q8—82no—
961D4—22no—
962D4—22no—
963D4—41no—
964D4—41no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—48no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
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—162no—
1052C2×C4—162no—
1053C2×C4#57512yes—
1054C2×C4#57712yes—
1055C2×C4C2×H(5,𝔽2)11yescharacteristic
1056C2×C4C2×2−1+411yescharacteristic
1057C2×C4C2×2−1+411yescharacteristic
1058C2×C4C2×2−1+411yescharacteristic
1059C2×C4#58511yescharacteristic
1060C2×C4#58511yescharacteristic
1061C8—22no—
1062C8—22no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22#348611yescharacteristic
1077C22#349611yescharacteristic
1078C22#349711yescharacteristic
1079C22C2×#57511yescharacteristic
1080C22C2×#57711yescharacteristic
1081C22#358411yescharacteristic
1082C22#358611yescharacteristic
1083C4—22no—
1084C4—22no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4#353511yescharacteristic
1113C4#355211yescharacteristic
1114C4#356311yescharacteristic
1115C4#356511yescharacteristic
1116C2—82no—
1117C2#5201411yescharacteristic
1118C2#6184111yescharacteristic
1119C2#6186211yescharacteristic
1120C2#6230311yescharacteristic
1121C2#6232311yescharacteristic
1122C2#6236711yescharacteristic
1123C2#6240211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46344C2semidirect
4. #32641C2semidirect
6. #32590C2semidirect
7. #32512C2semidirect
8. #32325C2semidirect
9. #32251C2semidirect
10. #31873C2semidirect
12. #31599C2semidirect
14. #30960C2semidirect
15. #30385C2semidirect
16. #30377C2semidirect
19. #29021C2semidirect
21. #28681C2semidirect
23. #28035C2semidirect
29. #25488C2semidirect
31. #23151C2semidirect

Maximal subgroups

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

subgroupindex
#463442
#394982
#326582
#326412
#325922
#325902
#325122
#323252
#322512
#318732
#318072
#315992
#311572
#309602
#303852
#303772
#294482
#294332
#290212
#289512
#286812
#281922
#280352
#274882
#274402
#273102
#264812
#261662
#254882
#253082
#231512