Subgroups — #26044261

Order 11744.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₃₄	C₂	1	2	yes	maximal
2	C₄⋊Dic₃₆₇	C₂	1	4	yes	maximal
3	C₄²×C₃₆₇	C₂	1	1	yes	maximal, characteristic
4	Dic₇₃₄	—	2	4	no	—
5	C₂×Dic₃₆₇	C₂²	1	4	yes	—
6	C₂×C₄×C₃₆₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₃₆₇	C₂²	1	2	yes	—
8	C₂²×C₃₆₇	C₂³	1	1	yes	characteristic
9	C₄×C₃₆₇	D₄	1	2	yes	—
10	C₄×C₃₆₇	Q₈	1	4	yes	complemented
11	Dic₃₆₇	—	2	4	no	—
12	C₂×C₃₆₇	C₂×D₄	1	1	yes	characteristic
13	C₂×C₃₆₇	C₂×Q₈	1	2	yes	—
14	C₃₆₇	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	367	1	no	maximal, Sylow
16	C₂×Q₈	—	367	2	no	—
17	C₄⋊C₄	—	367	4	no	—
18	C₄²	D₃₆₇	1	1	yes	characteristic
19	Q₈	—	734	4	no	—
20	C₂×C₄	—	367	4	no	—
21	C₂×C₄	C₂×D₃₆₇	1	1	yes	characteristic
22	C₂×C₄	C₂×D₃₆₇	1	2	yes	—
23	C₂²	C₂²×D₃₆₇	1	1	yes	characteristic
24	C₄	—	734	4	no	—
25	C₄	D₁₄₆₈	1	2	yes	—
26	C₄	Dic₇₃₄	1	4	yes	complemented
27	C₂	C₂×D₁₄₆₈	1	1	yes	characteristic
28	C₂	C₂×Dic₇₃₄	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₆₇
commutator, socle, prime radical, cosocle	C₂²×C₃₆₇	C₂³
Fitting	C₄²×C₃₆₇	C₂
hypercenter	C₄²	D₃₆₇
hypocenter	C₃₆₇	C₄⋊Q₈
LCS	G ▷ C₂²×C₃₆₇ ▷ C₃₆₇
UCS	C₁ ◁ C₂² ◁ C₄²

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.