Subgroups — C₂×#13095500 #15690825

Order 3104.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃₈₈	C₂	1	1	yes	maximal, characteristic
3	#13095500	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₉₇	—	2	1	no	—
6	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₉₇	—	2	1	no	—
8	D₃₈₈	—	2	1	no	—
9	D₃₈₈	C₂²	1	2	yes	—
10	Dic₁₉₄	—	2	1	no	—
11	Dic₁₉₄	C₂²	1	2	yes	complemented
12	C₈×C₉₇	C₂²	1	2	yes	complemented
13	C₂²×C₉₇	D₄	1	1	yes	characteristic
14	C₂×D₉₇	—	2	2	no	—
15	C₂×D₉₇	—	4	2	no	—
16	C₄×C₉₇	D₄	1	1	yes	characteristic
17	C₄×C₉₇	C₂³	1	1	yes	characteristic
18	Dic₉₇	—	2	2	no	—
19	C₂×C₉₇	SD₁₆	1	2	yes	complemented
20	C₂×C₉₇	C₂×D₄	1	1	yes	characteristic
21	D₉₇	—	4	2	no	—
22	C₉₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	97	1	no	maximal, Sylow
24	C₂×Q₈	—	97	1	no	—
25	C₂×D₄	—	97	1	no	—
26	SD₁₆	—	97	4	no	—
27	C₂×C₈	D₉₇	1	1	yes	characteristic, complemented
28	C₂³	—	194	1	no	—
29	Q₈	—	97	2	no	—
30	Q₈	—	194	1	no	—
31	D₄	—	97	2	no	—
32	D₄	—	194	1	no	—
33	C₂×C₄	—	194	1	no	—
34	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
35	C₈	C₂×D₉₇	1	2	yes	complemented
36	C₂²	—	388	2	no	—
37	C₂²	—	194	2	no	—
38	C₂²	D₃₈₈	1	1	yes	characteristic
39	C₄	—	194	2	no	—
40	C₄	D₃₈₈	1	1	yes	characteristic
41	C₄	C₂²×D₉₇	1	1	yes	characteristic
42	C₂	—	388	2	no	—
43	C₂	#13095500	1	2	yes	direct product factor
44	C₂	C₂×D₃₈₈	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.