Subgroups — C₂×C₉×#382 #11767002

Order 1152.

1068 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
2	C₂²×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#382	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#95	C₂	1	4	yes	maximal
5	C₂×C₃×#382	C₃	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₉	C₂²	1	4	yes	—
7	C₂³×C₄×C₉	C₂²	1	2	yes	—
8	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×C₄⋊C₄	—	2	8	no	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	8	yes	—
11	C₂×C₄²×C₉	C₄	1	8	yes	complemented
12	C₂×C₄²×C₉	C₂²	1	4	yes	—
13	C₉×#95	C₂²	1	16	yes	—
14	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
15	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
16	C₃×#382	C₂×C₃	1	8	yes	—
17	C₂×C₃×#95	C₂×C₃	1	4	yes	—
18	C₂⁴×C₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₉	—	2	8	no	—
20	C₂²×C₄×C₉	—	2	8	no	—
21	C₂²×C₄×C₉	—	2	16	no	—
22	C₂²×C₄×C₉	C₂×C₄	1	8	yes	—
23	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₉	D₄	1	4	yes	—
25	C₂²×C₄×C₉	Q₈	1	4	yes	—
26	C₂²×C₄×C₉	C₂³	1	8	yes	—
27	C₂²×C₄×C₉	C₂³	1	4	yes	—
28	C₂²×C₄×C₉	C₂³	1	2	yes	—
29	C₉×C₄⋊C₄	—	2	16	no	—
30	C₄²×C₉	C₂×C₄	1	16	yes	complemented
31	C₂×#382	C₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
33	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
34	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
35	C₂×C₃×C₄⋊C₄	—	2	8	no	—
36	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
37	C₂×C₃×C₄²	C₃×C₄	1	8	yes	—
38	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
39	C₃×#95	C₂²×C₃	1	16	yes	—
40	C₂³×C₉	C₂²×C₄	1	2	yes	—
41	C₂³×C₉	C₂×D₄	1	2	yes	—
42	C₂³×C₉	C₂×Q₈	1	2	yes	—
43	C₂³×C₉	#41	1	8	yes	—
44	C₂³×C₉	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₉	—	2	16	no	—
46	C₂×C₄×C₉	—	2	8	no	—
47	C₂×C₄×C₉	—	2	8	no	—
48	C₂×C₄×C₉	—	2	16	no	—
49	C₂×C₄×C₉	—	4	16	no	—
50	C₂×C₄×C₉	C₄⋊C₄	1	16	yes	—
51	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
52	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
53	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
54	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
55	C₂²×C₄⋊C₄	C₂×C₉	1	2	yes	—
56	C₂²×C₄²	C₂×C₉	1	1	yes	characteristic
57	#382	C₂×C₉	1	8	yes	direct product factor
58	C₂×#95	C₂×C₉	1	4	yes	—
59	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
60	C₂²×C₃×C₄	—	2	8	no	—
61	C₂²×C₃×C₄	—	2	8	no	—
62	C₂²×C₃×C₄	—	2	16	no	—
63	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
64	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
65	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
66	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
67	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
69	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
70	C₃×C₄⋊C₄	—	2	16	no	—
71	C₃×C₄²	C₂×C₃×C₄	1	16	yes	—
72	C₂²×C₉	C₂×C₄⋊C₄	1	4	yes	—
73	C₂²×C₉	#117	1	8	yes	—
74	C₂²×C₉	#124	1	8	yes	—
75	C₂²×C₉	#125	1	8	yes	—
76	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
77	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
78	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
79	C₂²×C₉	C₂×#41	1	4	yes	—
80	C₄×C₉	—	2	8	no	—
81	C₄×C₉	—	4	8	no	—
82	C₄×C₉	C₂×C₄⋊C₄	1	8	yes	—
83	C₂³×C₄	C₂²×C₉	1	4	yes	—
84	C₂³×C₄	C₂²×C₉	1	2	yes	—
85	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	—	2	8	no	—
87	C₂×C₄⋊C₄	C₂²×C₉	1	8	yes	—
88	C₂×C₄²	C₄×C₉	1	8	yes	complemented
89	C₂×C₄²	C₂²×C₉	1	4	yes	—
90	#95	C₂²×C₉	1	16	yes	—
91	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
92	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
93	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
94	C₂³×C₃	C₃×#41	1	8	yes	—
95	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄	—	2	16	no	—
97	C₂×C₃×C₄	—	2	8	no	—
98	C₂×C₃×C₄	—	2	8	no	—
99	C₂×C₃×C₄	—	2	16	no	—
100	C₂×C₃×C₄	—	4	16	no	—
101	C₂×C₃×C₄	C₃×C₄⋊C₄	1	16	yes	—
102	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
103	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
104	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
105	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
106	C₂×C₉	#382	1	8	yes	direct product factor
107	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₉	C₂×#117	1	2	yes	—
109	C₂×C₉	C₂×#124	1	2	yes	—
110	C₂×C₉	C₂×#125	1	2	yes	—
111	C₂⁴	C₂³×C₉	1	1	yes	characteristic
112	C₂²×C₄	—	2	8	no	—
113	C₂²×C₄	—	2	8	no	—
114	C₂²×C₄	—	2	16	no	—
115	C₂²×C₄	C₂×C₄×C₉	1	8	yes	—
116	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
117	C₂²×C₄	D₄×C₉	1	4	yes	—
118	C₂²×C₄	Q₈×C₉	1	4	yes	—
119	C₂²×C₄	C₂³×C₉	1	8	yes	—
120	C₂²×C₄	C₂³×C₉	1	4	yes	—
121	C₂²×C₄	C₂³×C₉	1	2	yes	—
122	C₄⋊C₄	—	2	16	no	—
123	C₄²	C₂×C₄×C₉	1	16	yes	complemented
124	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
125	C₂²×C₃	C₃×#117	1	8	yes	—
126	C₂²×C₃	C₃×#124	1	8	yes	—
127	C₂²×C₃	C₃×#125	1	8	yes	—
128	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
129	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
130	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
131	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
132	C₃×C₄	—	2	8	no	—
133	C₃×C₄	—	4	8	no	—
134	C₃×C₄	C₂×C₃×C₄⋊C₄	1	8	yes	—
135	C₉	C₂×#382	1	1	yes	characteristic, direct product factor, Sylow
136	C₂³	C₂²×C₄×C₉	1	2	yes	—
137	C₂³	C₂×D₄×C₉	1	2	yes	—
138	C₂³	C₂×Q₈×C₉	1	2	yes	—
139	C₂³	C₉×#41	1	8	yes	—
140	C₂³	C₂⁴×C₉	1	1	yes	characteristic
141	C₂×C₄	—	2	16	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	2	8	no	—
144	C₂×C₄	—	2	16	no	—
145	C₂×C₄	—	4	16	no	—
146	C₂×C₄	C₉×C₄⋊C₄	1	16	yes	—
147	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
148	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
149	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
150	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
151	C₂×C₃	C₃×#382	1	8	yes	—
152	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₃	C₂×C₃×#117	1	2	yes	—
154	C₂×C₃	C₂×C₃×#124	1	2	yes	—
155	C₂×C₃	C₂×C₃×#125	1	2	yes	—
156	C₂²	C₂×C₉×C₄⋊C₄	1	4	yes	—
157	C₂²	C₉×#117	1	8	yes	—
158	C₂²	C₉×#124	1	8	yes	—
159	C₂²	C₉×#125	1	8	yes	—
160	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
161	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
162	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
163	C₂²	C₂×C₉×#41	1	4	yes	—
164	C₄	—	2	8	no	—
165	C₄	—	4	8	no	—
166	C₄	C₂×C₉×C₄⋊C₄	1	8	yes	—
167	C₃	C₂×C₃×#382	1	1	yes	characteristic
168	C₂	C₉×#382	1	8	yes	direct product factor
169	C₂	C₂²×C₉×C₄⋊C₄	1	1	yes	characteristic
170	C₂	C₂×C₉×#117	1	2	yes	—
171	C₂	C₂×C₉×#124	1	2	yes	—
172	C₂	C₂×C₉×#125	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#382	C₂	direct (N × H)
11. C₂×C₄²×C₉	C₄	semidirect
30. C₄²×C₉	C₂×C₄	semidirect
31. C₂×#382	C₉	direct (N × H)
57. #382	C₂×C₉	direct (N × H)
88. C₂×C₄²	C₄×C₉	semidirect
106. C₂×C₉	#382	direct (N × H)
123. C₄²	C₂×C₄×C₉	semidirect
135. C₉	C₂×#382	direct (N × H)
168. C₂	C₉×#382	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×C₄⋊C₄	2
C₂²×C₄²×C₉	2
C₉×#382	2
C₂×C₉×#95	2
C₂×C₃×#382	3

Subgroups — C2×C9×#382 #11767002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#382 #11767002