Subgroups — C₂×C₄⋊Dic₉₇ #15690765

Order 3104.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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