Subgroups — #27163183

Order 12704.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263741	C₂	1	1	yes	maximal, characteristic, complemented
2	#20263740	C₂	1	2	yes	maximal, complemented
3	D₃₉₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15691794	C₂	1	2	yes	maximal, complemented
5	#20263730	C₂	1	1	yes	maximal, characteristic
6	#15691794	C₂²	1	1	yes	characteristic
7	#15691794	C₂²	1	2	yes	—
8	#15691794	C₂²	1	1	yes	characteristic
9	Dic₇₉₄	C₄	1	1	yes	characteristic
10	C₂²⋊D₃₉₇	C₄	1	2	yes	—
11	C₂×Dic₃₉₇	C₂²	1	2	yes	—
12	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
13	D₄×C₃₉₇	C₄	1	1	yes	characteristic
14	C₂²×C₃₉₇	C₂×C₄	1	2	yes	—
15	C₂×D₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
17	Dic₃₉₇	C₂×C₄	1	2	yes	—
18	Dic₃₉₇	C₂³	1	1	yes	characteristic
19	C₂×C₃₉₇	—	2	2	no	—
20	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
21	D₃₉₇	—	2	1	no	—
22	C₃₉₇	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	397	1	no	maximal, Sylow
24	#41	—	397	1	no	—
25	M₁₆	—	397	2	no	—
26	M₁₆	—	397	1	no	—
27	C₂×C₈	—	397	2	no	—
28	C₂×C₈	—	397	1	no	—
29	Q₈	—	397	1	no	—
30	D₄	—	397	2	no	—
31	D₄	#13097544	1	1	yes	characteristic
32	C₂×C₄	—	397	2	no	—
33	C₂×C₄	—	397	1	no	—
34	C₈	—	397	1	no	—
35	C₈	—	397	2	no	—
36	C₈	—	397	1	no	—
37	C₂²	—	397	1	no	—
38	C₂²	C₂×#13097544	1	2	yes	—
39	C₄	—	397	1	no	—
40	C₄	—	397	2	no	—
41	C₄	C₂×#13097544	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	794	1	no	—
44	C₂	C₂²×#13097544	1	1	yes	characteristic

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

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