Subgroups — C₂×Dic₇₇₆ #20261163

Order 6208.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₈	C₂	1	2	yes	maximal
2	Dic₇₇₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉₄	—	2	2	no	—
5	Dic₃₈₈	—	2	2	no	—
6	Dic₃₈₈	C₂²	1	4	yes	—
7	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₉₇	C₂²	1	2	yes	—
9	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
10	C₂×Dic₉₇	—	4	2	no	—
11	Dic₁₉₄	—	2	4	no	—
12	Dic₁₉₄	—	4	2	no	—
13	C₈×C₉₇	D₄	1	1	yes	characteristic
14	C₈×C₉₇	C₂³	1	1	yes	characteristic
15	C₂²×C₉₇	D₈	1	1	yes	characteristic
16	C₄×C₉₇	D₈	1	1	yes	characteristic
17	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
18	Dic₉₇	—	4	4	no	—
19	C₂×C₉₇	Q₃₂	1	2	yes	complemented
20	C₂×C₉₇	C₂×D₈	1	1	yes	characteristic
21	C₉₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₃₂	—	97	1	no	maximal, Sylow
23	C₂×Q₁₆	—	97	2	no	—
24	Q₃₂	—	97	4	no	—
25	C₂×C₁₆	D₉₇	1	1	yes	characteristic
26	C₂×Q₈	—	194	2	no	—
27	Q₁₆	—	97	4	no	—
28	Q₁₆	—	194	2	no	—
29	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
30	C₁₆	C₂×D₉₇	1	2	yes	—
31	Q₈	—	388	2	no	—
32	Q₈	—	194	4	no	—
33	C₂×C₄	—	388	2	no	—
34	C₂×C₄	D₃₈₈	1	1	yes	characteristic
35	C₈	D₃₈₈	1	1	yes	characteristic
36	C₈	C₂²×D₉₇	1	1	yes	characteristic
37	C₂²	D₇₇₆	1	1	yes	characteristic
38	C₄	—	388	4	no	—
39	C₄	D₇₇₆	1	1	yes	characteristic
40	C₄	C₂×D₃₈₈	1	1	yes	characteristic
41	C₂	Dic₇₇₆	1	2	yes	direct product factor
42	C₂	C₂×D₇₇₆	1	1	yes	characteristic

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