Finite Group Databasebeta

← #6697521

Subgroups — #6697521

Order 512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40105C211yesmaximal, characteristic
2#36475C211yesmaximal, characteristic, complemented
3#33083C211yesmaximal, characteristic, complemented
4#32509C211yesmaximal, characteristic, complemented
5#32379C211yesmaximal, characteristic
6#32345C211yesmaximal, characteristic, complemented
7#32099C211yesmaximal, characteristic
8#31992C211yesmaximal, characteristic
9#31600C211yesmaximal, characteristic, complemented
10#31580C211yesmaximal, characteristic
11#31473C211yesmaximal, characteristic, complemented
12#30380C211yesmaximal, characteristic, complemented
13#30081C211yesmaximal, characteristic
14#29008C211yesmaximal, characteristic
15#28960C211yesmaximal, characteristic
16#27578C211yesmaximal, characteristic
17#27319C211yesmaximal, characteristic, complemented
18#27297C211yesmaximal, characteristic, complemented
19#26758C211yesmaximal, characteristic, complemented
20#26383C211yesmaximal, characteristic, complemented
21#26375C211yesmaximal, characteristic
22#26189C211yesmaximal, characteristic
23#26169C211yesmaximal, characteristic
24#26167C211yesmaximal, characteristic, complemented
25#26161C211yesmaximal, characteristic
26#24826C211yesmaximal, characteristic, complemented
27#24736C211yesmaximal, characteristic
28#23014C211yesmaximal, characteristic, complemented
29C4⋊C4×Q16C211yesmaximal, characteristic, complemented
30#22377C211yesmaximal, characteristic, complemented
31C4×#464C211yesmaximal, characteristic
32C2×#479C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#464C2211yescharacteristic
35C2×#462C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×C4×Q16C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41#2864—21no—
42#2864C2211yescharacteristic
43#2863C2211yescharacteristic
44#2793—21no—
45#2783—21no—
46#2773—21no—
47#2721—21no—
48#2667—21no—
49#2577—21no—
50#2573—21no—
51#2570—21no—
52#2570—21no—
53#2570C2211yescharacteristic
54#2570C2211yescharacteristic
55#2565C2211yescharacteristic
56#2545C2211yescharacteristic
57#2512C2211yescharacteristic
58#2509—21no—
59#2509C2211yescharacteristic
60#2508—21no—
61#2508C2211yescharacteristic
62#2508C2211yescharacteristic
63#2507—21no—
64#2507C2211yescharacteristic
65#2506—21no—
66#2506C2211yescharacteristic
67#2454C2211yescharacteristic
68#2453C2211yescharacteristic
69#2448C2211yescharacteristic
70#2448C2211yescharacteristic
71#2447C2211yescharacteristic
72#2446C2211yescharacteristic
73#2365C2211yescharacteristic
74#2351C2211yescharacteristic
75#2351C2211yescharacteristic
76#2351C2211yescharacteristic
77#2351C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81#2334—21no—
82C4×#125—21no—
83C4×#125C2211yescharacteristic
84C4×#124C2211yescharacteristic
85C42×Q8C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2096C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2084C2211yescharacteristic
106#2074C2211yescharacteristic
107#2074C2211yescharacteristic
108#2073C2211yescharacteristic
109#2072C2211yescharacteristic
110#2071C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#1992C2211yescharacteristic
127#1983C2211yescharacteristic
128#1960C2211yescharacteristic
129#1958C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1944C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1940C2211yescharacteristic
138#1939C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1925C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1862C2211yescharacteristic
190#1845C2211yescharacteristic
191#1839C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#125—21no—
209C2×#125D411yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225#479—42no—
226#464—24no—
227#464—42no—
228#462—24no—
229#441—42no—
230C4×Q16—24no—
231C4×Q16—42no—
232C4×Q16—42no—
233C4×SD16—42no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
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#399—21no—
295#399—21no—
296#399—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389D411yescharacteristic
346#389D411yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—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#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#385—21no—
402#385—21no—
403#384—21no—
404#384—21no—
405#384—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#383—21no—
410#382—21no—
411#382—21no—
412#382—21no—
413#382—21no—
414#382—21no—
415#382—21no—
416#382D411yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#380—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C43—21no—
448C43C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
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×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16#4114yes—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—22no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511#126—44no—
512#125—41no—
513#125—41no—
514#125—42no—
515#125—44no—
516#124—22no—
517#124—41no—
518#124—41no—
519#124—41no—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×D4—41no—
543C4×D4—41no—
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—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⋊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⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
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×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—22no—
647#107—22no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#102—22no—
685#102—22no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#97—41no—
692#97—41no—
693C4×C8—22no—
694C4×C8—41no—
695C4×C8—41no—
696C4×C8—41no—
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#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753C24—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8C2×#4112yes—
769C2×Q8C2×#4112yes—
770C2×Q8H(5,𝔽2)12yes—
771C2×Q82−1+412yes—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—42no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C2511yescharacteristic
811Q16—28no—
812Q16—44no—
813SD16—44no—
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×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8C2×#4112yes—
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
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—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
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⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C42−1+412yes—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C42—24no—
927C42—22no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—42no—
946C42—42no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23C23×D411yescharacteristic
967Q8—22no—
968Q8—22no—
969Q8—22no—
970Q8—22no—
971Q8—22no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978Q8#53914yes—
979D4—41no—
980D4—41no—
981D4—41no—
982D4—41no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
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—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
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—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—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—162no—
1069C2×C4#57512yes—
1070C2×C4#57812yes—
1071C2×C4C22×#4111yescharacteristic
1072C2×C4C2×H(5,𝔽2)11yescharacteristic
1073C2×C4C2×2−1+411yescharacteristic
1074C2×C4C2×2−1+411yescharacteristic
1075C2×C4#58511yescharacteristic
1076C2×C4#58511yescharacteristic
1077C8—22no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C8—41no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22D4×#4111yescharacteristic
1093C22#348611yescharacteristic
1094C22#348811yescharacteristic
1095C22C2×#57511yescharacteristic
1096C22C2×#57811yescharacteristic
1097C22#358411yescharacteristic
1098C22#358411yescharacteristic
1099C4—22no—
1100C4—24no—
1101C4—22no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—42no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—42no—
1115C4—41no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4C2×#53911yescharacteristic
1129C4#351511yescharacteristic
1130C4#355311yescharacteristic
1131C4#355911yescharacteristic
1132C2—161no—
1133C2#3771711yescharacteristic
1134C2#6144611yescharacteristic
1135C2#6148811yescharacteristic
1136C2#6184511yescharacteristic
1137C2#6186611yescharacteristic
1138C2#6199411yescharacteristic
1139C2#6206511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36475C2semidirect
3. #33083C2semidirect
4. #32509C2semidirect
6. #32345C2semidirect
9. #31600C2semidirect
11. #31473C2semidirect
12. #30380C2semidirect
17. #27319C2semidirect
18. #27297C2semidirect
19. #26758C2semidirect
20. #26383C2semidirect
24. #26167C2semidirect
26. #24826C2semidirect
28. #23014C2semidirect
29. C4⋊C4×Q16C2semidirect
30. #22377C2semidirect

Maximal subgroups

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

subgroupindex
#401052
#364752
#330832
#325092
#323792
#323452
#320992
#319922
#316002
#315802
#314732
#303802
#300812
#290082
#289602
#275782
#273192
#272972
#267582
#263832
#263752
#261892
#261692
#261672
#261612
#248262
#247362
#230142
C4⋊C4×Q162
#223772
C4×#4642