Subgroups — #16812758

Order 3488.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#89137	C₂	1	2	yes	maximal, complemented
2	C₂×D₄₃₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₁₀₉	C₄	1	1	yes	characteristic, complemented
4	C₂²×D₁₀₉	C₂²	1	1	yes	characteristic
5	C₂×#89137	—	2	2	no	—
6	C₂×C₄×C₁₀₉	C₄	1	1	yes	characteristic, complemented
7	D₄₃₆	—	2	2	no	—
8	C₂²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	C₂×D₁₀₉	—	2	1	no	—
10	C₂×D₁₀₉	—	4	1	no	—
11	C₂×D₁₀₉	—	4	1	no	—
12	C₂×D₁₀₉	D₄	1	2	yes	—
13	#89137	—	4	2	no	—
14	C₄×C₁₀₉	—	2	1	no	—
15	C₂×C₁₀₉	—	2	1	no	—
16	C₂×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
17	D₁₀₉	—	2	2	no	—
18	D₁₀₉	—	4	1	no	—
19	C₁₀₉	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	109	1	no	maximal, Sylow
21	C₂×D₄	—	109	1	no	—
22	C₂²⋊C₄	—	109	2	no	—
23	C₂³	—	109	1	no	—
24	C₂³	—	109	1	no	—
25	D₄	—	218	2	no	—
26	C₂×C₄	—	218	2	no	—
27	C₂×C₄	#89137	1	1	yes	characteristic, complemented
28	C₂²	—	109	2	no	—
29	C₂²	—	436	1	no	—
30	C₂²	—	436	1	no	—
31	C₂²	—	218	1	no	—
32	C₂²	C₂×#89137	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	436	2	no	—
35	C₂	—	2	1	no	—
36	C₂	—	436	1	no	—
37	C₂	—	218	2	no	—
38	C₂	C₂²⋊#89137	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.