Subgroups — Dic₁₃₆₂₂ #72289776

Order 54488.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₉₄₆	—	7	1	no	maximal
2	Dic₆₈₁₁	C₂	1	2	yes	maximal
3	C₄×C₄₉×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₉×C₁₃₉	C₂²	1	1	yes	characteristic
5	C₄₉×C₁₃₉	Q₈	1	1	yes	characteristic, complemented, Hall
6	Dic₉₇₃	—	7	2	no	—
7	C₄×C₇×C₁₃₉	D₇	1	1	yes	characteristic
8	C₂×C₇×C₁₃₉	C₂×D₇	1	1	yes	characteristic
9	Dic₂₇₈	—	49	1	no	Hall
10	C₇×C₁₃₉	Dic₁₄	1	1	yes	characteristic
11	C₄×C₁₃₉	D₄₉	1	1	yes	characteristic
12	Dic₁₃₉	—	49	2	no	—
13	Dic₉₈	—	139	1	no	maximal, Hall
14	C₂×C₁₃₉	C₂×D₄₉	1	1	yes	characteristic
15	C₄×C₄₉	D₁₃₉	1	1	yes	characteristic
16	Dic₄₉	—	139	2	no	—
17	C₁₃₉	Dic₉₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄₉	C₂×D₁₃₉	1	1	yes	characteristic
19	Dic₁₄	—	973	1	no	—
20	C₄₉	Dic₂₇₈	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₇	D₉₇₃	1	1	yes	characteristic
22	Dic₇	—	973	2	no	—
23	C₂×C₇	C₂×D₉₇₃	1	1	yes	characteristic
24	Q₈	—	6811	1	no	Sylow
25	C₇	Dic₁₉₄₆	1	1	yes	characteristic
26	C₄	—	6811	2	no	—
27	C₄	D₆₈₁₁	1	1	yes	characteristic
28	C₂	C₂×D₆₈₁₁	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.