Subgroups — C₂×Q₈×D₃₉₇ #27163135

Order 12704.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₉₄	C₂	1	3	yes	maximal, complemented
2	Q₈×D₃₉₇	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₃₉₇	C₂	1	3	yes	maximal
4	C₂×Q₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₉₇	C₂²	1	1	yes	characteristic
6	Dic₇₉₄	C₂²	1	12	yes	complemented
7	C₂×Dic₃₉₇	C₂²	1	3	yes	—
8	C₄×D₃₉₇	C₂²	1	12	yes	—
9	Q₈×C₃₉₇	C₂²	1	4	yes	complemented
10	C₂×C₄×C₃₉₇	C₂²	1	3	yes	—
11	C₂²×C₃₉₇	C₂³	1	1	yes	characteristic
12	C₂×D₃₉₇	Q₈	1	4	yes	direct product factor
13	C₂×D₃₉₇	C₂³	1	2	yes	—
14	C₄×C₃₉₇	C₂³	1	6	yes	—
15	Dic₃₉₇	C₂³	1	6	yes	—
16	C₂×C₃₉₇	C₂×Q₈	1	2	yes	complemented
17	C₂×C₃₉₇	C₂⁴	1	1	yes	characteristic
18	D₃₉₇	C₂×Q₈	1	4	yes	direct product factor
19	C₃₉₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×Q₈	—	397	1	no	maximal, Sylow
21	C₂×Q₈	—	397	8	no	—
22	C₂×Q₈	—	397	3	no	—
23	C₂×Q₈	D₃₉₇	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	397	3	no	—
25	C₂³	—	397	1	no	—
26	Q₈	—	397	12	no	—
27	Q₈	C₂×D₃₉₇	1	4	yes	direct product factor
28	C₂×C₄	—	397	3	no	—
29	C₂×C₄	—	397	12	no	—
30	C₂×C₄	C₂×D₃₉₇	1	3	yes	—
31	C₂²	—	397	4	no	—
32	C₂²	—	397	2	no	—
33	C₂²	C₂²×D₃₉₇	1	1	yes	characteristic
34	C₄	—	397	6	no	—
35	C₄	C₂²×D₃₉₇	1	6	yes	—
36	C₂	—	397	4	no	—
37	C₂	Q₈×D₃₉₇	1	2	yes	direct product factor
38	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.