Subgroups — D₁₁²×C₇⋊C₉ #44478928

Order 30492.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₁₁×C₇⋊C₉	C₂	1	2	yes	maximal, complemented
3	C₃×C₇×D₁₁²	C₃	1	1	yes	maximal, characteristic
4	C₁₁²×C₇⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇×C₁₁×D₁₁	C₂×C₃	1	2	yes	—
7	C₉×D₁₁²	—	7	1	no	maximal, Hall
8	C₇×D₁₁²	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×D₁₁×C₇⋊C₉	—	11	2	no	maximal
10	C₃×C₇×C₁₁²	C₂²×C₃	1	1	yes	characteristic
11	C₉×C₁₁⋊D₁₁	—	7	1	no	—
12	C₉×C₁₁×D₁₁	—	7	2	no	—
13	C₇×C₁₁⋊D₁₁	C₂×C₉	1	1	yes	characteristic, complemented
14	C₇×C₁₁×D₁₁	C₂×C₉	1	2	yes	complemented
15	C₃×D₁₁²	ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₂×C₁₁×C₇⋊C₉	—	11	2	no	—
17	D₁₁×C₇⋊C₉	—	11	2	no	—
18	D₁₁×C₇⋊C₉	—	22	5	no	—
19	D₁₁×C₇⋊C₉	D₁₁	1	2	yes	direct product factor
20	C₉×C₁₁²	—	7	1	no	Hall
21	C₂×C₃×C₇×D₁₁	—	11	2	no	—
22	C₇×C₁₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₁⋊D₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₃×C₁₁×D₁₁	C₂×ΓL(1,𝔽₈)	1	2	yes	—
25	C₁₁×C₇⋊C₉	—	2	5	no	—
26	C₁₁×C₇⋊C₉	C₂×D₁₁	1	2	yes	complemented
27	D₁₁²	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₇×C₁₁	—	11	2	no	—
29	C₃×C₇×D₁₁	—	11	2	no	—
30	C₃×C₇×D₁₁	—	22	5	no	—
31	C₃×C₇×D₁₁	C₃×D₁₁	1	2	yes	—
32	C₂×C₉×D₁₁	—	77	2	no	—
33	C₃×C₁₁²	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
34	C₂×C₇×D₁₁	—	11	2	no	—
35	C₂²×C₇⋊C₉	—	121	1	no	Hall
36	C₁₁⋊D₁₁	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
37	C₁₁×D₁₁	C₂×C₇⋊C₉	1	2	yes	complemented
38	C₃×C₇×C₁₁	—	2	5	no	—
39	C₃×C₇×C₁₁	C₂×C₃×D₁₁	1	2	yes	—
40	C₂×C₉×C₁₁	—	77	2	no	—
41	C₉×D₁₁	—	7	2	no	—
42	C₉×D₁₁	—	77	2	no	—
43	C₉×D₁₁	—	154	5	no	—
44	C₂×C₇×C₁₁	—	11	2	no	—
45	C₇×D₁₁	—	11	2	no	—
46	C₇×D₁₁	—	22	5	no	—
47	C₇×D₁₁	C₉×D₁₁	1	2	yes	complemented
48	C₂×C₃×D₁₁	—	11	2	no	—
49	C₂×C₇⋊C₉	—	11	2	no	—
50	C₂×C₇⋊C₉	—	121	1	no	—
51	C₁₁²	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
52	C₉×C₁₁	—	7	2	no	—
53	C₉×C₁₁	—	14	5	no	—
54	C₂²×C₃×C₇	—	121	1	no	—
55	C₇×C₁₁	—	2	5	no	—
56	C₇×C₁₁	C₂×C₉×D₁₁	1	2	yes	complemented
57	C₂×C₃×C₁₁	—	11	2	no	—
58	C₃×D₁₁	—	11	2	no	—
59	C₃×D₁₁	—	22	5	no	—
60	C₃×D₁₁	ΓL(1,𝔽₈)×D₁₁	1	2	yes	—
61	C₇⋊C₉	D₁₁²	1	1	yes	characteristic, direct product factor, Hall
62	C₂×D₁₁	—	11	2	no	—
63	C₂×C₃×C₇	—	11	2	no	—
64	C₂×C₃×C₇	—	121	1	no	—
65	C₂²×C₉	—	847	1	no	Hall
66	C₃×C₁₁	—	2	5	no	—
67	C₃×C₁₁	C₂×ΓL(1,𝔽₈)×D₁₁	1	2	yes	—
68	C₂²×C₇	—	121	1	no	Hall
69	C₂×C₁₁	—	11	2	no	—
70	D₁₁	—	11	2	no	—
71	D₁₁	—	22	5	no	—
72	D₁₁	D₁₁×C₇⋊C₉	1	2	yes	direct product factor
73	C₃×C₇	C₃×D₁₁²	1	1	yes	characteristic
74	C₂×C₉	—	77	2	no	—
75	C₂×C₉	—	847	1	no	—
76	C₂×C₇	—	11	2	no	—
77	C₂×C₇	—	121	1	no	—
78	C₂²×C₃	—	121	1	no	—
79	C₁₁	—	2	5	no	—
80	C₁₁	C₂×D₁₁×C₇⋊C₉	1	2	yes	complemented
81	C₉	—	7	1	no	Sylow
82	C₇	C₉×D₁₁²	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₃	—	11	2	no	—
84	C₂×C₃	—	121	1	no	—
85	C₂²	—	121	1	no	Sylow
86	C₃	ΓL(1,𝔽₈)×D₁₁²	1	1	yes	characteristic
87	C₂	—	11	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₁₁²
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₁²	C₂²×C₃
prime radical	C₃×C₇×D₁₁²	C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₇⋊C₉×C₁₁⋊D₁₁	C₂	semidirect
2. C₁₁×D₁₁×C₇⋊C₉	C₂	semidirect
4. C₁₁²×C₇⋊C₉	C₂²	semidirect
8. C₇×D₁₁²	C₉	semidirect
13. C₇×C₁₁⋊D₁₁	C₂×C₉	semidirect
14. C₇×C₁₁×D₁₁	C₂×C₉	semidirect
19. D₁₁×C₇⋊C₉	D₁₁	direct (N × H)
22. C₇×C₁₁²	C₂²×C₉	semidirect
26. C₁₁×C₇⋊C₉	C₂×D₁₁	semidirect
27. D₁₁²	C₇⋊C₉	direct (N × H)
36. C₁₁⋊D₁₁	C₂×C₇⋊C₉	semidirect
37. C₁₁×D₁₁	C₂×C₇⋊C₉	semidirect
47. C₇×D₁₁	C₉×D₁₁	semidirect
51. C₁₁²	C₂²×C₇⋊C₉	semidirect
56. C₇×C₁₁	C₂×C₉×D₁₁	semidirect
61. C₇⋊C₉	D₁₁²	direct (N × H)
72. D₁₁	D₁₁×C₇⋊C₉	direct (N × H)
80. C₁₁	C₂×D₁₁×C₇⋊C₉	semidirect
82. C₇	C₉×D₁₁²	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊C₉×C₁₁⋊D₁₁	2
C₁₁×D₁₁×C₇⋊C₉	2
C₃×C₇×D₁₁²	3
C₉×D₁₁²	7
C₂×D₁₁×C₇⋊C₉	11

Subgroups — D112×C7⋊C9 #44478928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁²×C₇⋊C₉ #44478928