Subgroups — #27163085

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₈₈	C₂	1	1	yes	maximal, characteristic
2	#20263708	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₉₇	C₂²	1	2	yes	—
6	D₁₅₈₈	—	2	2	no	—
7	C₂×Dic₃₉₇	C₂²	1	2	yes	—
8	Q₈×C₃₉₇	—	2	2	no	—
9	C₂×C₄×C₃₉₇	C₂²	1	2	yes	—
10	C₂×C₄×C₃₉₇	C₂²	1	1	yes	characteristic
11	C₂²×C₃₉₇	C₂³	1	1	yes	characteristic
12	C₂×D₃₉₇	—	2	2	no	—
13	C₂×D₃₉₇	—	2	4	no	—
14	C₄×C₃₉₇	—	2	2	no	—
15	C₄×C₃₉₇	D₄	1	2	yes	—
16	Dic₃₉₇	—	2	2	no	—
17	C₂×C₃₉₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₃₉₇	#41	1	2	yes	—
19	D₃₉₇	—	4	2	no	—
20	C₃₉₇	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	397	1	no	maximal, Sylow
22	C₂×Q₈	D₃₉₇	1	1	yes	characteristic, complemented
23	C₂×D₄	—	397	1	no	—
24	C₂²⋊C₄	—	397	4	no	—
25	C₄²	—	397	1	no	—
26	C₂³	—	397	2	no	—
27	Q₈	—	2	2	no	—
28	D₄	—	794	2	no	—
29	C₂×C₄	—	397	2	no	—
30	C₂×C₄	C₂×D₃₉₇	1	2	yes	—
31	C₂×C₄	C₂×D₃₉₇	1	1	yes	characteristic
32	C₂²	—	794	2	no	—
33	C₂²	—	794	4	no	—
34	C₂²	C₂²×D₃₉₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	794	2	no	—
37	C₄	C₂²⋊D₃₉₇	1	2	yes	—
38	C₂	—	1588	2	no	—
39	C₂	C₂×C₂²⋊D₃₉₇	1	1	yes	characteristic
40	C₂	#20263732	1	2	yes	—

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.