Subgroups — C₂²×D₁₆₇₆ #27211756

Order 13408.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄₁₉	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₆₇₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×C₄₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄₁₉	—	2	8	no	—
5	C₂²×D₄₁₉	C₂²	1	12	yes	complemented
6	D₁₆₇₆	C₂²	1	16	yes	direct product factor
7	C₂³×C₄₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₄₁₉	C₂²	1	6	yes	complemented
9	C₂²×C₄₁₉	D₄	1	4	yes	complemented
10	C₂²×C₄₁₉	C₂³	1	3	yes	—
11	C₂×D₄₁₉	—	2	24	no	—
12	C₂×D₄₁₉	C₂³	1	8	yes	complemented
13	C₄×C₄₁₉	C₂³	1	4	yes	complemented
14	C₂×C₄₁₉	C₂×D₄	1	6	yes	complemented
15	C₂×C₄₁₉	C₂⁴	1	1	yes	characteristic
16	D₄₁₉	—	2	8	no	—
17	C₄₁₉	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×D₄	—	419	1	no	maximal, Sylow
19	C₂⁴	—	419	2	no	—
20	C₂×D₄	—	419	12	no	—
21	C₂²×C₄	D₄₁₉	1	1	yes	characteristic, complemented
22	C₂³	—	838	8	no	—
23	C₂³	—	419	12	no	—
24	C₂³	C₂×D₄₁₉	1	1	yes	characteristic
25	D₄	—	419	16	no	—
26	C₂×C₄	C₂×D₄₁₉	1	6	yes	complemented
27	C₂²	—	838	24	no	—
28	C₂²	—	419	8	no	—
29	C₂²	D₁₆₇₆	1	4	yes	direct product factor
30	C₂²	C₂²×D₄₁₉	1	3	yes	—
31	C₄	C₂²×D₄₁₉	1	4	yes	complemented
32	C₂	—	838	8	no	—
33	C₂	C₂×D₁₆₇₆	1	6	yes	direct product factor
34	C₂	C₂³×D₄₁₉	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.