Subgroups — C₂×C₃⋊(D₇⋊(C₁₁²⋊C₃)) #44479158

Order 30492.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇⋊(C₁₁²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₇⋊(C₁₁²⋊C₃))	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁²×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇⋊(C₁₁²⋊C₃)	—	3	1	no	maximal
5	C₃×C₇⋊(C₁₁²⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁²×D₂₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₇⋊(C₁₁²⋊C₃)	—	2	1	no	—
8	C₂×C₇⋊(C₁₁²⋊C₃)	D₃	1	1	yes	characteristic, complemented
9	D₇⋊(C₁₁²⋊C₃)	—	3	2	no	—
10	C₂×C₃×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₃×C₁₁²⋊C₃	—	7	1	no	maximal, Hall
12	C₂×C₁₁²×D₇	—	3	1	no	Hall
13	C₇⋊(C₁₁²⋊C₃)	—	2	1	no	—
14	C₇⋊(C₁₁²⋊C₃)	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇×C₁₁²	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₁²⋊C₃	—	14	1	no	—
17	D₃×C₁₁²⋊C₃	—	7	2	no	—
18	C₂×C₇×C₁₁²	C₃×D₃	1	1	yes	characteristic, complemented
19	C₁₁²×D₇	—	3	2	no	—
20	C₂×D₃×C₁₁²	—	7	1	no	—
21	C₂²×C₁₁²⋊C₃	—	21	1	no	—
22	C₃×C₁₁²⋊C₃	—	14	1	no	Hall
23	C₂×C₁₁×D₂₁	—	3	4	no	—
24	C₇×C₁₁²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₁²	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
26	D₃×C₁₁²	—	7	2	no	—
27	C₂×C₁₁²⋊C₃	—	14	1	no	—
28	C₂×C₁₁²⋊C₃	—	14	1	no	—
29	C₂×C₁₁²⋊C₃	—	21	2	no	—
30	C₂²×C₁₁²	—	21	1	no	Hall
31	C₂×C₃×C₇×C₁₁	—	3	4	no	—
32	C₁₁×D₂₁	—	3	8	no	—
33	C₃×C₁₁²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
34	C₁₁²⋊C₃	—	14	1	no	—
35	C₁₁²⋊C₃	—	14	1	no	—
36	C₂×C₁₁×D₇	—	9	4	no	—
37	C₂×C₃⋊AGL(1,𝔽₇)	—	121	1	no	maximal, Hall
38	C₂×C₁₁²	—	21	2	no	—
39	C₂×C₁₁²	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
40	C₃×C₇×C₁₁	—	3	4	no	—
41	C₂×C₇×C₁₁	—	3	4	no	—
42	C₁₁×D₇	—	9	8	no	—
43	C₂×D₃×C₁₁	—	21	4	no	—
44	C₂×C₃×ΓL(1,𝔽₈)	—	121	1	no	—
45	C₃⋊AGL(1,𝔽₇)	—	121	2	no	—
46	C₁₁²	C₂×C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₂₁	C₁₁²⋊C₃	1	1	yes	characteristic, complemented
48	C₂×AGL(1,𝔽₇)	—	363	1	no	—
49	C₇×C₁₁	—	3	4	no	—
50	C₂×C₃×C₁₁	—	3	4	no	—
51	D₃×C₁₁	—	21	8	no	—
52	C₃×ΓL(1,𝔽₈)	—	121	1	no	Hall
53	C₂²×C₁₁	—	63	4	no	—
54	C₂×C₃×C₇	C₂×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
55	D₂₁	C₂×C₁₁²⋊C₃	1	2	yes	complemented
56	C₂×ΓL(1,𝔽₈)	—	121	1	no	—
57	C₂×ΓL(1,𝔽₈)	—	242	1	no	—
58	AGL(1,𝔽₇)	—	363	2	no	—
59	C₂×C₃×D₃	—	847	1	no	Hall
60	C₃×C₁₁	—	3	4	no	—
61	C₂×D₇	—	3	1	no	Hall
62	C₂×C₁₁	—	3	4	no	—
63	C₂×C₁₁	—	63	8	no	—
64	C₃×C₇	C₂²×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
65	ΓL(1,𝔽₈)	—	121	1	no	—
66	ΓL(1,𝔽₈)	—	242	1	no	—
67	C₂×C₃²	—	1694	1	no	—
68	C₃×D₃	—	847	2	no	—
69	C₂×C₇	D₃×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
70	D₇	—	3	2	no	—
71	C₂²×C₃	—	2541	1	no	—
72	C₂×D₃	—	7	1	no	—
73	C₁₁	—	3	4	no	—
74	C₃²	—	1694	1	no	Sylow
75	C₇	C₂×D₃×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	1694	1	no	—
77	C₂×C₃	—	1694	1	no	—
78	C₂×C₃	—	2541	2	no	—
79	C₂×C₃	D₇⋊(C₁₁²⋊C₃)	1	1	yes	characteristic, complemented
80	D₃	—	7	2	no	—
81	C₂²	—	21	1	no	Sylow
82	C₃	—	1694	1	no	—
83	C₃	—	1694	1	no	—
84	C₃	C₂×D₇⋊(C₁₁²⋊C₃)	1	1	yes	characteristic, complemented
85	C₂	—	21	2	no	—
86	C₂	C₃⋊(D₇⋊(C₁₁²⋊C₃))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(D₇⋊(C₁₁²⋊C₃))
commutator, cosocle, hypocenter	C₃×C₇×C₁₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁²	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₁²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₇⋊(C₁₁²⋊C₃)	C₂	semidirect
2. C₃⋊(D₇⋊(C₁₁²⋊C₃))	C₂	direct (N × H)
3. C₂×C₁₁²×D₂₁	C₃	semidirect
5. C₃×C₇⋊(C₁₁²⋊C₃)	C₂²	semidirect
6. C₁₁²×D₂₁	C₂×C₃	semidirect
8. C₂×C₇⋊(C₁₁²⋊C₃)	D₃	semidirect
10. C₂×C₃×C₇×C₁₁²	C₂×C₃	semidirect
14. C₇⋊(C₁₁²⋊C₃)	C₂×D₃	semidirect
15. C₃×C₇×C₁₁²	C₂²×C₃	semidirect
18. C₂×C₇×C₁₁²	C₃×D₃	semidirect
24. C₇×C₁₁²	C₂×C₃×D₃	semidirect
25. C₂×C₃×C₁₁²	AGL(1,𝔽₇)	semidirect
33. C₃×C₁₁²	C₂×AGL(1,𝔽₇)	semidirect
39. C₂×C₁₁²	C₃⋊AGL(1,𝔽₇)	semidirect
46. C₁₁²	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
47. C₂×D₂₁	C₁₁²⋊C₃	semidirect
54. C₂×C₃×C₇	C₂×C₁₁²⋊C₃	semidirect
55. D₂₁	C₂×C₁₁²⋊C₃	semidirect
64. C₃×C₇	C₂²×C₁₁²⋊C₃	semidirect
69. C₂×C₇	D₃×C₁₁²⋊C₃	semidirect
75. C₇	C₂×D₃×C₁₁²⋊C₃	semidirect
79. C₂×C₃	D₇⋊(C₁₁²⋊C₃)	semidirect
84. C₃	C₂×D₇⋊(C₁₁²⋊C₃)	semidirect
86. C₂	C₃⋊(D₇⋊(C₁₁²⋊C₃))	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇⋊(C₁₁²⋊C₃)	2
C₃⋊(D₇⋊(C₁₁²⋊C₃))	2
C₂×C₁₁²×D₂₁	3
C₂×D₇⋊(C₁₁²⋊C₃)	3
C₂×D₃×C₁₁²⋊C₃	7
C₂×C₃⋊AGL(1,𝔽₇)	121

Subgroups — C2×C3⋊(D7⋊(C112⋊C3)) #44479158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(D₇⋊(C₁₁²⋊C₃)) #44479158