Subgroups — C₇×#17983787 #44479171

Order 30492.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊(C₃⋊(C₁₁⋊D₁₁))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₃⋊(C₁₁⋊D₁₁)	—	6	2	no	—
4	#17983787	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×#92150	—	9	1	no	maximal, Hall
6	C₃×C₇×C₁₁²	—	2	2	no	—
7	C₃⋊(C₃⋊(C₁₁⋊D₁₁))	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₁⋊D₁₁	—	9	1	no	—
9	C₇×C₃⋊D₃₃	—	22	6	no	—
10	C₃²×C₁₁²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₁²	#157	1	1	yes	characteristic, complemented, Hall
12	C₃⋊(C₁₁⋊D₁₁)	—	6	2	no	—
13	C₃²×C₇×C₁₁	—	2	6	no	—
14	#92150	—	9	1	no	Hall
15	C₇×D₃₃	—	66	24	no	—
16	C₃×C₁₁²	—	2	2	no	—
17	C₇×#157	—	121	1	no	maximal, Hall
18	C₁₁⋊D₁₁	—	9	1	no	—
19	C₃×C₇×C₁₁	—	2	24	no	—
20	C₃⋊D₃₃	—	22	6	no	—
21	C₇×D₁₁	—	198	6	no	—
22	C₇×C₃⋊D₃	—	121	1	no	—
23	C₁₁²	C₇×#157	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₁₁	—	2	6	no	—
25	C₇×C₁₁	—	2	6	no	—
26	D₃₃	—	66	24	no	—
27	C₃²×C₇	#92150	1	1	yes	characteristic, complemented, Hall
28	D₃×C₇	—	726	2	no	—
29	#157	—	121	1	no	Hall
30	C₃×C₁₁	—	2	24	no	—
31	C₄×C₇	—	1089	1	no	Hall
32	D₁₁	—	198	6	no	—
33	C₃×C₇	—	2	2	no	—
34	C₃⋊D₃	—	121	1	no	—
35	C₂×C₇	—	1089	1	no	—
36	C₁₁	—	2	6	no	—
37	C₃²	C₇×#92150	1	1	yes	characteristic, complemented, Sylow
38	C₇	#17983787	1	1	yes	characteristic, direct product factor, Sylow
39	D₃	—	726	2	no	—
40	C₄	—	1089	1	no	Sylow
41	C₃	—	2	2	no	—
42	C₂	—	1089	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#17983787
commutator, hypocenter	C₃²×C₁₁²	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₄
prime radical	C₇×C₃⋊(C₃⋊(C₁₁⋊D₁₁))	C₂
cosocle	C₃⋊(C₃⋊(C₁₁⋊D₁₁))	C₂×C₇
LCS	G ▷ C₃²×C₁₁²
UCS	C₁ ◁ C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃²×C₇×C₁₁²	C₄	semidirect
4. #17983787	C₇	direct (N × H)
10. C₃²×C₁₁²	C₄×C₇	semidirect
11. C₇×C₁₁²	#157	semidirect
23. C₁₁²	C₇×#157	semidirect
27. C₃²×C₇	#92150	semidirect
37. C₃²	C₇×#92150	semidirect
38. C₇	#17983787	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×C₃⋊(C₃⋊(C₁₁⋊D₁₁))	2
#17983787	7
C₇×#92150	9
C₇×#157	121

Subgroups — C7×#17983787 #44479171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17983787 #44479171