Subgroups — C₇⋊#19128972 #49176366

Order 37548.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₄₄₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×D₄₄₇	—	6	2	no	—
4	#19128972	—	7	1	no	maximal, Hall
5	C₇⋊#10597010	—	9	1	no	maximal, Hall
6	C₃×C₇×C₁₄₉	—	2	2	no	—
7	C₃⋊D₄₄₇	D₇	1	1	yes	characteristic
8	C₇×D₁₄₉	—	9	1	no	—
9	C₃²×C₁₄₉	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₄₉	#157	1	1	yes	characteristic, complemented, Hall
11	D₄₄₇	—	6	2	no	—
12	#10597010	—	63	1	no	Hall
13	C₃×C₁₄₉	—	2	2	no	—
14	D₁₄₉	—	9	1	no	—
15	C₇⋊#157	—	149	1	no	maximal, Hall
16	C₁₄₉	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
17	C₇×C₃⋊D₃	—	149	1	no	—
18	C₃²×C₇	#10597010	1	1	yes	characteristic, complemented, Hall
19	D₃×C₇	—	894	2	no	—
20	#157	—	1043	1	no	Hall
21	Dic₇	—	1341	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	—	149	1	no	—
24	C₂×C₇	—	1341	1	no	—
25	C₃²	C₇⋊#10597010	1	1	yes	characteristic, complemented, Sylow
26	C₇	#19128972	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	894	2	no	—
28	C₄	—	9387	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	1341	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₁₄₉	C₄
prime radical, cosocle	C₇×C₃⋊D₄₄₇	C₂
LCS	G ▷ C₃²×C₇×C₁₄₉
UCS	C₁

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.