Subgroups — D₂₇₇₈₄ #72291111

Order 55568.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₈₉₂	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₃×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₄₇₃	—	2	2	no	—
4	C₄×C₂₃×C₁₅₁	C₂²	1	1	yes	characteristic
5	C₂×C₂₃×C₁₅₁	D₄	1	1	yes	characteristic
6	D₃₄₇₃	—	4	2	no	—
7	C₂₃×C₁₅₁	D₈	1	1	yes	characteristic, complemented, Hall
8	D₁₂₀₈	—	23	1	no	maximal, Hall
9	D₆₀₄	—	23	2	no	—
10	C₈×C₁₅₁	D₂₃	1	1	yes	characteristic, complemented
11	C₂×D₁₅₁	—	46	2	no	—
12	C₄×C₁₅₁	C₂×D₂₃	1	1	yes	characteristic
13	D₁₈₄	—	151	1	no	maximal, Hall
14	C₂×C₁₅₁	D₉₂	1	1	yes	characteristic
15	D₁₅₁	—	92	2	no	—
16	D₉₂	—	151	2	no	—
17	C₈×C₂₃	D₁₅₁	1	1	yes	characteristic, complemented
18	C₁₅₁	D₁₈₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₂₃	—	302	2	no	—
20	C₄×C₂₃	C₂×D₁₅₁	1	1	yes	characteristic
21	C₂×C₂₃	D₆₀₄	1	1	yes	characteristic
22	D₂₃	—	604	2	no	—
23	C₂₃	D₁₂₀₈	1	1	yes	characteristic, complemented, Sylow
24	D₈	—	3473	1	no	Sylow
25	D₄	—	3473	2	no	—
26	C₈	D₃₄₇₃	1	1	yes	characteristic, complemented
27	C₂²	—	6946	2	no	—
28	C₄	C₂×D₃₄₇₃	1	1	yes	characteristic
29	C₂	—	13892	2	no	—
30	C₂	D₁₃₈₉₂	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.