Subgroups — C₂×#11757429 #14516601

Order 1944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757429	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉⋊(C₂²⋊C₉)	C₃	1	1	yes	maximal, characteristic
4	C₂×#66353	C₃	1	2	yes	maximal
5	C₂×#6875	—	4	1	no	maximal
6	C₂²×C₂₇⋊C₃	—	3	1	no	—
7	C₂²×C₂₇⋊C₃	—	3	1	no	—
8	C₂²×C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
9	C₉⋊(C₂²⋊C₉)	C₂×C₃	1	1	yes	characteristic
10	#66353	C₂×C₃	1	2	yes	—
11	#6875	—	4	1	no	Sylow
12	C₂³×C₃×C₉	C₃²	1	1	yes	characteristic
13	C₂×C₃×C₂²⋊C₉	—	3	1	no	—
14	C₂³×C₂₇	C₉	1	3	yes	complemented
15	C₂×C₂²⋊C₂₇	—	3	2	no	—
16	C₂×C₂₇⋊C₃	—	3	1	no	—
17	C₂×C₂₇⋊C₃	—	3	1	no	—
18	C₂×C₂₇⋊C₃	—	4	2	no	—
19	C₂×C₂₇⋊C₃	A₄	1	1	yes	characteristic
20	C₂×C₉⋊C₉	—	4	1	no	—
21	C₂²×C₃×C₉	—	3	1	no	—
22	C₂²×C₃×C₉	—	3	1	no	—
23	C₂²×C₃×C₉	C₂×C₃²	1	1	yes	characteristic
24	C₃×C₂²⋊C₉	—	3	1	no	—
25	C₂²×C₂₇	—	3	3	no	—
26	C₂²×C₂₇	—	3	3	no	—
27	C₂²×C₂₇	C₂×C₉	1	3	yes	complemented
28	C₂²⋊C₂₇	—	3	2	no	—
29	C₂₇⋊C₃	—	4	2	no	—
30	C₂₇⋊C₃	C₂×A₄	1	1	yes	characteristic
31	C₉⋊C₉	—	4	1	no	—
32	C₂³×C₃²	3₋¹⁺²	1	1	yes	characteristic
33	C₂³×C₉	C₃×C₉	1	1	yes	characteristic
34	C₂³×C₉	3₋¹⁺²	1	2	yes	—
35	C₂×C₂²⋊C₉	—	9	1	no	—
36	C₂×C₃×C₉	—	3	1	no	—
37	C₂×C₃×C₉	—	3	1	no	—
38	C₂×C₃×C₉	—	12	1	no	—
39	C₂×C₃×C₉	C₃×A₄	1	1	yes	characteristic
40	C₂×C₂₇	—	3	3	no	—
41	C₂×C₂₇	—	3	3	no	—
42	C₂×C₂₇	—	12	2	no	—
43	C₂×C₂₇	C₂²⋊C₉	1	3	yes	complemented
44	C₂²×C₃²	—	3	1	no	—
45	C₂²×C₃²	—	3	1	no	—
46	C₂²×C₃²	C₂×3₋¹⁺²	1	1	yes	characteristic
47	C₂²×C₉	—	3	1	no	—
48	C₂²×C₉	—	3	2	no	—
49	C₂²×C₉	—	3	2	no	—
50	C₂²×C₉	—	3	1	no	—
51	C₂²×C₉	C₂×C₃×C₉	1	1	yes	characteristic
52	C₂²×C₉	C₂×3₋¹⁺²	1	2	yes	—
53	C₂²⋊C₉	—	9	1	no	—
54	C₃×C₉	—	12	1	no	—
55	C₃×C₉	C₂×C₃×A₄	1	1	yes	characteristic
56	C₂₇	—	12	2	no	—
57	C₂₇	C₂×C₂²⋊C₉	1	3	yes	complemented
58	C₂³×C₃	—	3	1	no	—
59	C₂³×C₃	C₉⋊C₉	1	1	yes	characteristic
60	C₂×C₃²	—	3	1	no	—
61	C₂×C₃²	—	3	1	no	—
62	C₂×C₃²	C₉⋊A₄	1	1	yes	characteristic
63	C₂×C₉	—	3	2	no	—
64	C₂×C₉	—	3	2	no	—
65	C₂×C₉	—	3	1	no	—
66	C₂×C₉	—	3	1	no	—
67	C₂×C₉	—	36	1	no	—
68	C₂×C₉	C₉⋊A₄	1	2	yes	—
69	C₂×C₉	C₃×C₂²⋊C₉	1	1	yes	characteristic
70	C₂²×C₃	—	3	1	no	—
71	C₂²×C₃	—	3	1	no	—
72	C₂²×C₃	—	3	1	no	—
73	C₂²×C₃	—	9	1	no	—
74	C₂²×C₃	—	9	1	no	—
75	C₂²×C₃	C₂×C₉⋊C₉	1	1	yes	characteristic
76	C₃²	C₂×C₉⋊A₄	1	1	yes	characteristic
77	C₉	—	36	1	no	—
78	C₉	C₂×C₉⋊A₄	1	2	yes	—
79	C₉	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic
80	C₂³	#6875	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	3	1	no	—
82	C₂×C₃	—	3	1	no	—
83	C₂×C₃	—	3	1	no	—
84	C₂×C₃	—	9	1	no	—
85	C₂×C₃	—	9	1	no	—
86	C₂×C₃	C₉⋊(C₂²⋊C₉)	1	1	yes	characteristic
87	C₂²	—	3	1	no	—
88	C₂²	—	3	1	no	—
89	C₂²	C₂×#6875	1	1	yes	characteristic, complemented
90	C₃	—	3	1	no	—
91	C₃	C₂×C₉⋊(C₂²⋊C₉)	1	1	yes	characteristic
92	C₂	—	3	1	no	—
93	C₂	—	3	1	no	—
94	C₂	#11757429	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₃	C₉⋊(C₂²⋊C₉)
commutator	C₂²×C₉	C₂×C₃×C₉
Frattini	C₃×C₉	C₂×C₃×A₄
Fitting	C₂³×C₂₇⋊C₃	C₃
socle	C₂³×C₃	C₉⋊C₉
prime radical	C₂³×C₃²	3₋¹⁺²
cosocle	C₂²×C₃×C₉	C₂×C₃²
hypercenter	C₂×C₂₇⋊C₃	A₄
hypocenter	C₂²	C₂×#6875
LCS	G ▷ C₂²×C₉ ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₉ ◁ C₂×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
1. #11757429	C₂	direct (N × H)
14. C₂³×C₂₇	C₉	semidirect
27. C₂²×C₂₇	C₂×C₉	semidirect
43. C₂×C₂₇	C₂²⋊C₉	semidirect
57. C₂₇	C₂×C₂²⋊C₉	semidirect
80. C₂³	#6875	semidirect
89. C₂²	C₂×#6875	semidirect
94. C₂	#11757429	direct (N × H)

Maximal subgroups

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

subgroup	index
#11757429	2
C₂³×C₂₇⋊C₃	3
C₂×C₉⋊(C₂²⋊C₉)	3
C₂×#66353	3
C₂×#6875	4

Subgroups — C2×#11757429 #14516601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757429 #14516601