Finite Group Databasebeta

← #6715080

Subgroups — #6715080

Order 512.

1341 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39370C211yesmaximal, characteristic
2#36285C211yesmaximal, characteristic, complemented
3#33073C211yesmaximal, characteristic, complemented
4#32591C211yesmaximal, characteristic, complemented
5#32566C211yesmaximal, characteristic, complemented
6#32561C211yesmaximal, characteristic
7#32546C211yesmaximal, characteristic
8#32340C211yesmaximal, characteristic, complemented
9#32317C211yesmaximal, characteristic, complemented
10#31482C211yesmaximal, characteristic
11#31459C211yesmaximal, characteristic
12#30235C211yesmaximal, characteristic, complemented
13#29870C211yesmaximal, characteristic
14#27827C211yesmaximal, characteristic, complemented
15#27741C211yesmaximal, characteristic, complemented
16#27446C211yesmaximal, characteristic
17#27435C211yesmaximal, characteristic
18#27382C211yesmaximal, characteristic, complemented
19#27371C211yesmaximal, characteristic, complemented
20#26524C211yesmaximal, characteristic, complemented
21#26458C211yesmaximal, characteristic, complemented
22#26294C211yesmaximal, characteristic, complemented
23#26276C211yesmaximal, characteristic, complemented
24#25007C211yesmaximal, characteristic
25#24990C211yesmaximal, characteristic
26#24825C211yesmaximal, characteristic
27#24690C211yesmaximal, characteristic
28#23076C211yesmaximal, characteristic
29#22978C211yesmaximal, characteristic
30#22315C211yesmaximal, characteristic, complemented
31#21124C211yesmaximal, characteristic
32C2×#544—21no—
33C2×#478C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#440C2211yescharacteristic
36#2863—21no—
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2729—21no—
40#2729—21no—
41#2704—21no—
42#2704—21no—
43#2629—21no—
44#2606—21no—
45#2606—21no—
46#2590—21no—
47#2590—21no—
48#2582C2211yescharacteristic
49#2582C2211yescharacteristic
50#2570C2211yescharacteristic
51#2570C2211yescharacteristic
52#2565C2211yescharacteristic
53#2565C2211yescharacteristic
54#2552C2211yescharacteristic
55#2551C2211yescharacteristic
56#2546C2211yescharacteristic
57#2546C2211yescharacteristic
58#2538C2211yescharacteristic
59#2538C2211yescharacteristic
60#2507—21no—
61#2506C2211yescharacteristic
62#2506C2211yescharacteristic
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2446—21no—
66#2442—21no—
67#2439—21no—
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2356C2211yescharacteristic
71#2356C2211yescharacteristic
72#2355C2211yescharacteristic
73#2354C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77#2295—21no—
78#2293C2211yescharacteristic
79C42×Q8C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic
113#2066C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1992C2211yescharacteristic
124#1992C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1985C2211yescharacteristic
131#1985C2211yescharacteristic
132#1984C2211yescharacteristic
133#1984C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1947C2211yescharacteristic
140#1943C2211yescharacteristic
141#1941C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1836C2211yescharacteristic
187#1834C2211yescharacteristic
188#1831C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1745C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204#544—48no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8D411yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C22×C4⋊C4—21no—
233#478—24no—
234#478—24no—
235#440—24no—
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×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#396—21no—
299#396—21no—
300#396—21no—
301#395—21no—
302#395—21no—
303#393—21no—
304#393—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391D411yescharacteristic
311#391D411yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
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#389D411yescharacteristic
336#389D411yescharacteristic
337#389D411yescharacteristic
338#389D411yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#384D411yescharacteristic
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#383—21no—
393#383—21no—
394#382—21no—
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424#376—21no—
425#376—21no—
426C43—21no—
427C43C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C4⋊Q8—24no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—44no—
508C4⋊Q8—44no—
509C4⋊Q8—44no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—22no—
514#125—44no—
515#125—44no—
516#125—44no—
517#125—44no—
518C22⋊Q8—44no—
519C22⋊Q8—44no—
520C22⋊Q8—44no—
521C22⋊Q8—44no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—44no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4#4114yes—
539#117—44no—
540#117—44no—
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—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—44no—
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⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
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×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×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—22no—
649#107—22no—
650#107—22no—
651#107—22no—
652#106—22no—
653#106—22no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—41no—
668#103—41no—
669#103—41no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#97—22no—
678#97—22no—
679#97—41no—
680#97—41no—
681C4×C8—41no—
682C4×C8—41no—
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#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733C24—21no—
734C2×Q8—22no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—41no—
741C2×Q8—41no—
742C2×Q8—41no—
743C2×Q8—41no—
744C2×Q8—42no—
745C2×Q8—42no—
746C2×Q8—81no—
747C2×Q8—81no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8AGL(1,ℤ/8)14yes—
751C2×Q82−1+412yes—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4C2×#4112yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
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—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—81no—
779C22×C4—81no—
780C22×C4—81no—
781C22×C4—81no—
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
797SD16—44no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
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—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
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—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
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—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—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⋊C4C2×#4112yes—
904C4⋊C42−1+412yes—
905C22⋊C4—24no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C42—24no—
917C42—22no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—42no—
934C42—42no—
935C42—42no—
936C42—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42—42no—
941C42—81no—
942C42—81no—
943C42—81no—
944C42—81no—
945C42C2×#4112yes—
946C422−1+412yes—
947C23—22no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23C23×D411yescharacteristic
955Q8—22no—
956Q8—22no—
957Q8—44no—
958Q8—41no—
959Q8—41no—
960Q8—82no—
961Q8—162no—
962Q8—162no—
963D4—22no—
964D4—22no—
965D4—41no—
966D4—41no—
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—21no—
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—22no—
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—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—48no—
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—162no—
1051C2×C4—162no—
1052C2×C4#54812yes—
1053C2×C4#54812yes—
1054C2×C4C2×AGL(1,ℤ/8)12yes—
1055C2×C4C2×AGL(1,ℤ/8)12yes—
1056C2×C4C2×AGL(1,ℤ/8)12yes—
1057C2×C4C22×#4111yescharacteristic
1058C2×C4C2×2−1+411yescharacteristic
1059C2×C4C2×2−1+411yescharacteristic
1060C2×C4C2×2−1+411yescharacteristic
1061C2×C4#58511yescharacteristic
1062C2×C4#58511yescharacteristic
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C8—41no—
1069C8—41no—
1070C8—41no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×#54811yescharacteristic
1079C22#348511yescharacteristic
1080C22#348611yescharacteristic
1081C22C22×AGL(1,ℤ/8)11yescharacteristic
1082C22#358411yescharacteristic
1083C22#358611yescharacteristic
1084C22#358611yescharacteristic
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—42no—
1098C4—42no—
1099C4—41no—
1100C4—42no—
1101C4—41no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4#346111yescharacteristic
1115C4#349511yescharacteristic
1116C4#355511yescharacteristic
1117C4#356311yescharacteristic
1118C2—82no—
1119C2#3775711yescharacteristic
1120C2#6131711yescharacteristic
1121C2#6135011yescharacteristic
1122C2#6170411yescharacteristic
1123C2#6181411yescharacteristic
1124C2#6184011yescharacteristic
1125C2#6187511yescharacteristic
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
2. #36285C2semidirect
3. #33073C2semidirect
4. #32591C2semidirect
5. #32566C2semidirect
8. #32340C2semidirect
9. #32317C2semidirect
12. #30235C2semidirect
14. #27827C2semidirect
15. #27741C2semidirect
18. #27382C2semidirect
19. #27371C2semidirect
20. #26524C2semidirect
21. #26458C2semidirect
22. #26294C2semidirect
23. #26276C2semidirect
30. #22315C2semidirect

Maximal subgroups

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

subgroupindex
#393702
#362852
#330732
#325912
#325662
#325612
#325462
#323402
#323172
#314822
#314592
#302352
#298702
#278272
#277412
#274462
#274352
#273822
#273712
#265242
#264582
#262942
#262762
#250072
#249902
#248252
#246902
#230762
#229782
#223152
#211242