Subgroups — C₂×C₁₁×C₇⋊#3874 #37528571

Order 23100.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₇⋊#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₁×D₃₅	—	3	1	no	maximal, Hall
4	C₇×C₁₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₁×D₃₅	—	3	2	no	—
6	C₂×C₅²×C₇×C₁₁	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₁×#3874	—	7	1	no	maximal, Hall
8	C₂×C₇⋊#3874	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅²×C₇×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₅²⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₁₁×#3874	—	7	2	no	—
12	C₂×C₁₁×D₃₅	—	3	1	no	—
13	C₂×C₅×C₁₁×D₇	—	15	1	no	—
14	C₂×C₅×D₅×C₁₁	—	21	1	no	Hall
15	C₂×C₇×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₇⋊#3874	C₂×C₁₁	1	2	yes	direct product factor
17	C₂×C₁₁×D₂₁	—	25	1	no	maximal, Hall
18	C₁₁×C₅²⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₇×C₁₁	—	3	1	no	—
20	C₂×C₅×C₇×C₁₁	—	3	1	no	—
21	C₁₁×D₃₅	—	3	2	no	—
22	C₅×C₁₁×D₇	—	15	2	no	—
23	C₂×C₅×D₃₅	—	3	1	no	Hall
24	C₂×C₅²×C₁₁	D₂₁	1	1	yes	characteristic, complemented
25	C₅×D₅×C₁₁	—	21	2	no	—
26	C₇×C₅²⋊C₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₇×C₁₁	—	25	1	no	—
28	C₁₁×D₂₁	—	25	2	no	—
29	C₅×C₇×C₁₁	—	3	1	no	—
30	C₅×C₇×C₁₁	—	3	1	no	—
31	C₂×C₅²×C₇	D₃×C₁₁	1	1	yes	characteristic, complemented
32	C₅×D₃₅	—	3	2	no	—
33	C₂×C₁₁×D₇	—	15	1	no	Hall
34	C₂×#3874	—	7	1	no	Hall
35	C₅²×C₁₁	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
36	C₃×C₇×C₁₁	—	25	1	no	Hall
37	C₂²×C₅×C₁₁	—	105	1	no	—
38	C₂×D₅×C₁₁	—	21	1	no	—
39	C₅²×C₇	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇×C₁₁	#3874	1	1	yes	characteristic, complemented
41	C₁₁×D₇	—	15	2	no	—
42	C₂×C₅²⋊C₃	C₁₁×D₇	1	1	yes	characteristic, complemented
43	#3874	—	7	2	no	—
44	C₂×D₃₅	—	3	1	no	—
45	C₂×C₅×D₇	—	15	1	no	—
46	C₂×D₃×C₁₁	—	175	1	no	Hall
47	C₂×C₅×C₁₁	—	3	1	no	—
48	C₂×C₅×C₁₁	—	3	1	no	—
49	C₂×C₅×C₁₁	—	105	2	no	—
50	D₅×C₁₁	—	21	2	no	—
51	C₂×C₅×D₅	—	21	1	no	Hall
52	C₂×D₂₁	—	25	1	no	Hall
53	C₇×C₁₁	C₂×#3874	1	1	yes	characteristic, complemented, Hall
54	C₅²⋊C₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
55	C₂×C₅×C₇	—	3	1	no	—
56	C₂×C₅×C₇	—	3	1	no	—
57	D₃₅	—	3	2	no	—
58	C₅×D₇	—	15	2	no	—
59	C₂×C₃×C₁₁	—	25	1	no	—
60	D₃×C₁₁	—	175	2	no	—
61	C₅×C₁₁	—	3	1	no	—
62	C₅×C₁₁	—	3	1	no	—
63	C₂×C₅²	C₁₁×D₂₁	1	1	yes	characteristic, complemented
64	C₅×D₅	—	21	2	no	—
65	C₂²×C₁₁	—	105	1	no	Hall
66	C₂×C₃×C₇	—	25	1	no	—
67	D₂₁	—	25	2	no	—
68	C₅×C₇	—	3	1	no	—
69	C₅×C₇	—	3	1	no	—
70	C₃×C₁₁	—	25	1	no	Hall
71	C₂×D₇	—	15	1	no	Hall
72	C₅²	C₂×C₁₁×D₂₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₁₁	—	105	2	no	—
74	C₂×C₁₁	C₇⋊#3874	1	1	yes	characteristic, direct product factor
75	C₃×C₇	—	25	1	no	Hall
76	C₂²×C₅	—	105	1	no	—
77	C₂×D₅	—	21	1	no	—
78	C₂×C₇	C₁₁×#3874	1	1	yes	characteristic, complemented
79	D₇	—	15	2	no	—
80	C₂×D₃	—	175	1	no	Hall
81	C₁₁	C₂×C₇⋊#3874	1	1	yes	characteristic, direct product factor, Sylow
82	C₂×C₅	—	3	1	no	—
83	C₂×C₅	—	3	1	no	—
84	C₂×C₅	—	105	2	no	—
85	D₅	—	21	2	no	—
86	C₇	C₂×C₁₁×#3874	1	1	yes	characteristic, complemented, Sylow
87	C₂×C₃	—	25	1	no	—
88	D₃	—	175	2	no	—
89	C₅	—	3	1	no	—
90	C₅	—	3	1	no	—
91	C₂²	—	105	1	no	Sylow
92	C₃	—	25	1	no	Sylow
93	C₂	—	105	2	no	—
94	C₂	C₁₁×C₇⋊#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₇⋊#3874
commutator, cosocle, hypocenter	C₇×C₅²⋊C₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₁	D₃
LCS	G ▷ C₇×C₅²⋊C₃
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₁×C₅²⋊C₃	C₂	semidirect
2. C₁₁×C₇⋊#3874	C₂	direct (N × H)
4. C₇×C₁₁×C₅²⋊C₃	C₂²	semidirect
6. C₂×C₅²×C₇×C₁₁	D₃	semidirect
8. C₂×C₇⋊#3874	C₁₁	direct (N × H)
9. C₅²×C₇×C₁₁	C₂×D₃	semidirect
10. C₂×C₁₁×C₅²⋊C₃	D₇	semidirect
15. C₂×C₇×C₅²⋊C₃	C₂×C₁₁	semidirect
16. C₇⋊#3874	C₂×C₁₁	direct (N × H)
18. C₁₁×C₅²⋊C₃	C₂×D₇	semidirect
24. C₂×C₅²×C₁₁	D₂₁	semidirect
26. C₇×C₅²⋊C₃	C₂²×C₁₁	semidirect
31. C₂×C₅²×C₇	D₃×C₁₁	semidirect
35. C₅²×C₁₁	C₂×D₂₁	semidirect
39. C₅²×C₇	C₂×D₃×C₁₁	semidirect
40. C₂×C₇×C₁₁	#3874	semidirect
42. C₂×C₅²⋊C₃	C₁₁×D₇	semidirect
53. C₇×C₁₁	C₂×#3874	semidirect
54. C₅²⋊C₃	C₂×C₁₁×D₇	semidirect
63. C₂×C₅²	C₁₁×D₂₁	semidirect
72. C₅²	C₂×C₁₁×D₂₁	semidirect
74. C₂×C₁₁	C₇⋊#3874	direct (N × H)
78. C₂×C₇	C₁₁×#3874	semidirect
81. C₁₁	C₂×C₇⋊#3874	direct (N × H)
86. C₇	C₂×C₁₁×#3874	semidirect
94. C₂	C₁₁×C₇⋊#3874	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×C₇×C₁₁×C₅²⋊C₃	2
C₁₁×C₇⋊#3874	2
C₂×C₅×C₁₁×D₃₅	3
C₂×C₁₁×#3874	7
C₂×C₇⋊#3874	11
C₂×C₁₁×D₂₁	25

Subgroups — C2×C11×C7⋊#3874 #37528571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₇⋊#3874 #37528571