Subgroups — C₂×D₃₉₇⋊C₈ #27163179

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₇⋊C₈	C₂	1	4	yes	maximal, direct product factor
2	C₂×#15691794	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	#15691794	C₂²	1	4	yes	complemented
5	C₂²×D₃₉₇	C₄	1	1	yes	characteristic
6	C₂×Dic₃₉₇	C₂²	1	1	yes	characteristic
7	C₄×D₃₉₇	C₄	1	2	yes	—
8	C₄×D₃₉₇	C₂²	1	2	yes	—
9	C₂×C₄×C₃₉₇	C₄	1	1	yes	characteristic
10	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₉₇	C₈	1	4	yes	complemented
12	C₂×D₃₉₇	C₂×C₄	1	2	yes	—
13	C₄×C₃₉₇	C₂×C₄	1	2	yes	—
14	Dic₃₉₇	C₂×C₄	1	1	yes	characteristic
15	Dic₃₉₇	C₂³	1	1	yes	characteristic
16	C₂×C₃₉₇	C₂×C₈	1	2	yes	complemented
17	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
18	D₃₉₇	C₂×C₈	1	4	yes	complemented
19	C₃₉₇	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₈	—	397	1	no	maximal, Sylow
21	C₂²×C₄	—	397	1	no	—
22	C₂×C₈	—	397	2	no	—
23	C₂×C₈	—	397	4	no	—
24	C₂³	—	397	1	no	—
25	C₂×C₄	—	397	1	no	—
26	C₂×C₄	—	397	2	no	—
27	C₂×C₄	—	397	2	no	—
28	C₂×C₄	#13097544	1	1	yes	characteristic
29	C₈	—	397	4	no	—
30	C₂²	—	397	4	no	—
31	C₂²	—	397	2	no	—
32	C₂²	C₂×#13097544	1	1	yes	characteristic
33	C₄	—	397	1	no	—
34	C₄	—	397	1	no	—
35	C₄	C₂×#13097544	1	2	yes	—
36	C₂	—	397	4	no	—
37	C₂	D₃₉₇⋊C₈	1	2	yes	direct product factor
38	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.