Subgroups — #99×C₁₉₇ #20263186

Order 6304.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₉₇	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₄×C₁₉₇	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₉₇	C₄	1	1	yes	characteristic, complemented
4	C₂³×C₁₉₇	C₂²	1	1	yes	characteristic
5	D₄×C₁₉₇	—	2	2	no	—
6	C₂×C₄×C₁₉₇	—	2	2	no	—
7	C₂×C₄×C₁₉₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₁₉₇	—	2	1	no	—
9	C₂²×C₁₉₇	—	4	1	no	—
10	C₂²×C₁₉₇	—	4	1	no	—
11	C₂²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₁₉₇	D₄	1	2	yes	—
13	C₄×C₁₉₇	—	2	1	no	—
14	C₄×C₁₉₇	—	4	2	no	—
15	C₂×C₁₉₇	—	2	2	no	—
16	C₂×C₁₉₇	—	2	1	no	—
17	C₂×C₁₉₇	—	4	1	no	—
18	C₂×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₁₉₇	#99	1	1	yes	characteristic, direct product factor, Sylow
20	#99	C₁₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×D₄	C₂×C₁₉₇	1	1	yes	characteristic
22	C₂²⋊C₄	C₂×C₁₉₇	1	2	yes	complemented
23	C₂³	C₄×C₁₉₇	1	1	yes	characteristic, complemented
24	C₂³	C₂²×C₁₉₇	1	1	yes	characteristic
25	D₄	—	2	2	no	—
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	C₄×C₁₉₇	1	1	yes	characteristic, complemented
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×C₄×C₁₉₇	1	1	yes	characteristic
32	C₂²	D₄×C₁₉₇	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	C₂²⋊C₄×C₁₉₇	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.