Subgroups — C₉×#1994 #11766715

Order 1152.

426 conjugacy classes of subgroups.

The subgroup lattice has 177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#339	C₂	1	4	yes	maximal
5	C₃×#1994	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×M₁₆	C₂²	1	2	yes	—
7	C₉×C₄⋊Q₈	C₄	1	2	yes	complemented
8	C₉×#125	C₄	1	2	yes	complemented
9	C₉×C₂²⋊Q₈	—	2	2	no	—
10	C₄×Q₈×C₉	—	2	2	no	—
11	C₉×#117	C₂²	1	2	yes	—
12	C₂×C₄²×C₉	—	2	2	no	—
13	C₂×C₄²×C₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₉×C₄⋊C₈	—	2	2	no	—
16	C₃×#533	C₂×C₃	1	1	yes	characteristic
17	C₃×#423	C₂×C₃	1	1	yes	characteristic
18	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
19	C₃×#339	C₂×C₃	1	4	yes	—
20	C₂×Q₈×C₉	—	2	2	no	—
21	C₂²×C₄×C₉	—	2	2	no	—
22	C₂²×C₄×C₉	D₄	1	2	yes	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₉×M₁₆	—	2	4	no	—
25	C₂×C₈×C₉	—	2	2	no	—
26	C₉×C₄⋊C₄	—	2	4	no	—
27	C₉×C₄⋊C₄	—	2	2	no	—
28	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
29	C₉×C₂²⋊C₄	—	2	2	no	—
30	C₄²×C₉	—	2	8	no	—
31	C₄²×C₉	—	2	2	no	—
32	C₄²×C₉	—	2	2	no	—
33	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
34	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₉	D₄	1	2	yes	—
36	C₄²×C₉	Q₈	1	4	yes	complemented
37	#1994	C₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
39	C₃×C₄⋊Q₈	C₃×C₄	1	2	yes	—
40	C₃×#125	C₃×C₄	1	2	yes	—
41	C₃×C₂²⋊Q₈	—	2	2	no	—
42	C₃×C₄×Q₈	—	2	2	no	—
43	C₃×#117	C₂²×C₃	1	2	yes	—
44	C₂×C₃×C₄²	—	2	2	no	—
45	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
46	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
47	C₃×C₄⋊C₈	—	2	2	no	—
48	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
49	Q₈×C₉	—	4	4	no	—
50	C₂×C₄×C₉	—	2	8	no	—
51	C₂×C₄×C₉	—	2	4	no	—
52	C₂×C₄×C₉	—	2	4	no	—
53	C₂×C₄×C₉	—	2	4	no	—
54	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
59	C₂×C₄×C₉	#41	1	2	yes	—
60	C₈×C₉	—	4	2	no	—
61	#533	C₂×C₉	1	1	yes	characteristic
62	#423	C₂×C₉	1	1	yes	characteristic
63	C₄³	C₂×C₉	1	1	yes	characteristic
64	#339	C₂×C₉	1	4	yes	—
65	C₂×C₃×Q₈	—	2	2	no	—
66	C₂²×C₃×C₄	—	2	2	no	—
67	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₃×M₁₆	—	2	4	no	—
70	C₂×C₃×C₈	—	2	2	no	—
71	C₃×C₄⋊C₄	—	2	4	no	—
72	C₃×C₄⋊C₄	—	2	2	no	—
73	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
74	C₃×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₄²	—	2	8	no	—
76	C₃×C₄²	—	2	2	no	—
77	C₃×C₄²	—	2	2	no	—
78	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
79	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
80	C₃×C₄²	C₃×D₄	1	2	yes	—
81	C₃×C₄²	C₃×Q₈	1	4	yes	—
82	C₂²×C₉	—	2	2	no	—
83	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
85	C₄×C₉	—	2	8	no	—
86	C₄×C₉	—	2	2	no	—
87	C₄×C₉	—	4	4	no	—
88	C₄×C₉	#104	1	4	yes	—
89	C₄×C₉	C₄×Q₈	1	2	yes	—
90	C₄×C₉	#124	1	1	yes	characteristic
91	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
92	C₂×M₁₆	C₂²×C₉	1	2	yes	—
93	C₄⋊Q₈	C₄×C₉	1	2	yes	complemented
94	#125	C₄×C₉	1	2	yes	complemented
95	C₂²⋊Q₈	—	2	2	no	—
96	C₄×Q₈	—	2	2	no	—
97	#117	C₂²×C₉	1	2	yes	—
98	C₂×C₄²	—	2	2	no	—
99	C₂×C₄²	C₂²×C₉	1	2	yes	—
100	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
101	C₄⋊C₈	—	2	2	no	—
102	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
103	C₃×Q₈	—	4	4	no	—
104	C₂×C₃×C₄	—	2	8	no	—
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	4	no	—
107	C₂×C₃×C₄	—	2	4	no	—
108	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
109	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
110	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
113	C₂×C₃×C₄	C₃×#41	1	2	yes	—
114	C₃×C₈	—	4	2	no	—
115	C₂×C₉	—	2	2	no	—
116	C₂×C₉	#391	1	1	yes	characteristic
117	C₂×C₉	C₂×#104	1	2	yes	—
118	C₂×Q₈	—	2	2	no	—
119	C₂²×C₄	—	2	2	no	—
120	C₂²×C₄	D₄×C₉	1	2	yes	—
121	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
122	M₁₆	—	2	4	no	—
123	C₂×C₈	—	2	2	no	—
124	C₄⋊C₄	—	2	4	no	—
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
127	C₂²⋊C₄	—	2	2	no	—
128	C₄²	—	2	8	no	—
129	C₄²	—	2	2	no	—
130	C₄²	—	2	2	no	—
131	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
132	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
133	C₄²	D₄×C₉	1	2	yes	—
134	C₄²	Q₈×C₉	1	4	yes	complemented
135	C₂²×C₃	—	2	2	no	—
136	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
138	C₃×C₄	—	2	8	no	—
139	C₃×C₄	—	2	2	no	—
140	C₃×C₄	—	4	4	no	—
141	C₃×C₄	C₃×#104	1	4	yes	—
142	C₃×C₄	C₃×C₄×Q₈	1	2	yes	—
143	C₃×C₄	C₃×#124	1	1	yes	characteristic
144	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
145	C₉	#1994	1	1	yes	characteristic, direct product factor, Sylow
146	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
147	Q₈	—	4	4	no	—
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
155	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
156	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
157	C₂×C₄	C₉×#41	1	2	yes	—
158	C₈	—	4	2	no	—
159	C₂×C₃	—	2	2	no	—
160	C₂×C₃	C₃×#391	1	1	yes	characteristic
161	C₂×C₃	C₂×C₃×#104	1	2	yes	—
162	C₂²	—	2	2	no	—
163	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²	C₉×C₂²⋊Q₈	1	2	yes	—
165	C₄	—	2	8	no	—
166	C₄	—	2	2	no	—
167	C₄	—	4	4	no	—
168	C₄	C₉×#104	1	4	yes	—
169	C₄	C₄×Q₈×C₉	1	2	yes	—
170	C₄	C₉×#124	1	1	yes	characteristic
171	C₄	C₉×C₄⋊Q₈	1	1	yes	characteristic
172	C₃	C₃×#1994	1	1	yes	characteristic
173	C₂	—	2	2	no	—
174	C₂	C₉×#391	1	1	yes	characteristic
175	C₂	C₂×C₉×#104	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₂²⋊C₄
prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₉×C₄⋊Q₈	C₄	semidirect
8. C₉×#125	C₄	semidirect
36. C₄²×C₉	Q₈	semidirect
37. #1994	C₉	direct (N × H)
93. C₄⋊Q₈	C₄×C₉	semidirect
94. #125	C₄×C₉	semidirect
134. C₄²	Q₈×C₉	semidirect
145. C₉	#1994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#533	2
C₉×#423	2
C₄³×C₉	2
C₉×#339	2
C₃×#1994	3

Subgroups — C9×#1994 #11766715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1994 #11766715