Subgroups — #27163144

Order 12704.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263732	C₂	1	4	yes	maximal, complemented
2	#20263731	C₂	1	6	yes	maximal, complemented
3	Q₈×D₃₉₇	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₇₉₄	C₂²	1	6	yes	—
6	D₁₅₈₈	C₂²	1	6	yes	—
7	C₂²⋊D₃₉₇	C₂²	1	4	yes	—
8	C₄×D₃₉₇	C₂²	1	12	yes	—
9	Q₈×C₃₉₇	C₂²	1	4	yes	—
10	C₂×C₄×C₃₉₇	C₂²	1	3	yes	—
11	C₂²×C₃₉₇	C₂³	1	1	yes	characteristic
12	C₂×D₃₉₇	C₂³	1	4	yes	—
13	C₄×C₃₉₇	C₂³	1	6	yes	—
14	Dic₃₉₇	C₂³	1	4	yes	—
15	C₂×C₃₉₇	—	2	1	no	—
16	C₂×C₃₉₇	C₂⁴	1	1	yes	characteristic
17	D₃₉₇	—	2	4	no	—
18	C₃₉₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
19	2₋¹⁺⁴	—	397	1	no	maximal, Sylow
20	#41	—	397	4	no	—
21	#41	—	397	6	no	—
22	C₂×Q₈	—	397	4	no	—
23	C₂×Q₈	D₃₉₇	1	1	yes	characteristic, complemented
24	Q₈	—	397	6	no	—
25	Q₈	C₂×D₃₉₇	1	4	yes	—
26	D₄	—	397	4	no	—
27	D₄	—	397	6	no	—
28	C₂×C₄	—	397	12	no	—
29	C₂×C₄	C₂×D₃₉₇	1	3	yes	—
30	C₂²	—	397	4	no	—
31	C₂²	C₂²×D₃₉₇	1	1	yes	characteristic
32	C₄	—	397	4	no	—
33	C₄	C₂²×D₃₉₇	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	794	4	no	—
36	C₂	C₂³×D₃₉₇	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.