Subgroups — #11861388

Order 1152.

522 conjugacy classes of subgroups.

The subgroup lattice has 192 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	#10588701	C₂	1	8	yes	maximal, complemented
3	#10588677	C₂	1	2	yes	maximal
4	#10588675	C₂	1	2	yes	maximal
5	#10588604	C₂	1	1	yes	maximal, characteristic
6	C₂×#63362	C₂	1	1	yes	maximal, characteristic
7	#83329	—	3	1	no	maximal
8	C₉×C₄⋊Q₈	C₄	1	2	yes	—
9	C₉×#125	C₄	1	2	yes	—
10	C₉×C₂²⋊Q₈	C₄	1	4	yes	—
11	C₄×Q₈×C₉	C₂²	1	4	yes	—
12	C₉×#117	C₂²	1	2	yes	—
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₂×#3667	C₂²	1	2	yes	—
15	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊(C₉⋊C₈)	C₂²	1	8	yes	—
18	C₄⋊(C₉⋊C₈)	C₂²	1	4	yes	—
19	#63362	C₂²	1	4	yes	—
20	#63362	C₂²	1	4	yes	—
21	C₄×C₉⋊C₈	C₂²	1	4	yes	—
22	C₃×#533	D₃	1	1	yes	characteristic
23	#5024	—	3	8	no	—
24	#4999	—	3	2	no	—
25	#4997	—	3	2	no	—
26	#4924	—	3	1	no	—
27	C₂×#803	—	3	1	no	—
28	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
29	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
33	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
34	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
35	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₉	C₂³	1	2	yes	—
38	C₄²×C₉	C₂³	1	4	yes	—
39	#3667	—	2	4	no	—
40	C₂×C₉⋊C₈	—	2	2	no	—
41	C₂×C₉⋊C₈	Q₈	1	4	yes	complemented
42	C₂×C₉⋊C₈	C₂³	1	4	yes	—
43	C₂×C₉⋊C₈	C₂³	1	2	yes	—
44	C₂×C₉⋊C₈	C₂³	1	2	yes	—
45	#2961	—	9	1	no	Sylow
46	C₃×C₄⋊Q₈	Dic₃	1	2	yes	—
47	C₃×#125	Dic₃	1	2	yes	—
48	C₃×C₂²⋊Q₈	Dic₃	1	4	yes	—
49	C₃×C₄×Q₈	C₂×D₃	1	4	yes	—
50	C₃×#117	C₂×D₃	1	2	yes	—
51	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	C₂×#208	—	3	2	no	—
53	C₂²×C₃⋊C₈	—	3	1	no	—
54	C₂²×C₃⋊C₈	—	3	1	no	—
55	C₄⋊(C₃⋊C₈)	—	3	4	no	—
56	C₄⋊(C₃⋊C₈)	—	3	8	no	—
57	#803	—	3	4	no	—
58	#803	—	3	4	no	—
59	C₄×C₃⋊C₈	—	3	4	no	—
60	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
61	Q₈×C₉	—	4	4	no	—
62	C₂×C₄×C₉	—	4	2	no	—
63	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
66	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
68	C₂×C₄×C₉	#41	1	2	yes	—
69	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
70	C₉⋊C₈	—	2	2	no	—
71	C₉⋊C₈	—	2	4	no	—
72	C₉⋊C₈	C₂×Q₈	1	4	yes	—
73	#533	D₉	1	1	yes	characteristic
74	#446	—	9	8	no	—
75	#424	—	9	2	no	—
76	#423	—	9	1	no	—
77	#405	—	9	2	no	—
78	C₂×#97	—	9	1	no	—
79	C₂×C₃×Q₈	C₂×Dic₃	1	4	yes	—
80	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
81	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
82	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
83	C₃×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
84	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
85	C₃×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
86	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
87	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
88	C₃×C₄²	C₂²×D₃	1	4	yes	—
89	C₃×C₄²	C₂²×D₃	1	2	yes	—
90	#208	—	6	4	no	—
91	C₂×C₃⋊C₈	—	3	4	no	—
92	C₂×C₃⋊C₈	—	3	2	no	—
93	C₂×C₃⋊C₈	—	3	4	no	—
94	C₂×C₃⋊C₈	—	3	2	no	—
95	C₂×C₃⋊C₈	—	6	2	no	—
96	C₂²×C₉	—	2	2	no	—
97	C₂²×C₉	C₄×Q₈	1	2	yes	—
98	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
99	C₄×C₉	—	2	2	no	—
100	C₄×C₉	—	2	2	no	—
101	C₄×C₉	—	2	8	no	—
102	C₄×C₉	C₄×Q₈	1	2	yes	—
103	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
104	C₄×C₉	C₂×#41	1	1	yes	characteristic
105	C₂×M₁₆	—	9	2	no	—
106	C₂²×C₈	—	9	1	no	—
107	C₂²×C₈	—	9	1	no	—
108	C₄⋊Q₈	Dic₉	1	2	yes	—
109	#125	Dic₉	1	2	yes	—
110	C₂²⋊Q₈	Dic₉	1	4	yes	—
111	C₄×Q₈	C₂×D₉	1	4	yes	—
112	#117	C₂×D₉	1	2	yes	—
113	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
114	C₄⋊C₈	—	9	4	no	—
115	C₄⋊C₈	—	9	8	no	—
116	#97	—	9	4	no	—
117	#97	—	9	4	no	—
118	C₄×C₈	—	9	4	no	—
119	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
120	C₃×Q₈	—	4	4	no	—
121	C₂×C₃×C₄	—	4	2	no	—
122	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
123	C₂×C₃×C₄	#239	1	2	yes	—
124	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
125	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
126	C₂×C₃×C₄	C₂²×Dic₃	1	8	yes	—
127	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
128	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
129	C₃⋊C₈	—	3	4	no	—
130	C₃⋊C₈	—	6	2	no	—
131	C₃⋊C₈	—	6	4	no	—
132	C₂×C₉	—	2	2	no	—
133	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
134	C₂×C₉	#568	1	2	yes	—
135	C₂×Q₈	C₂×Dic₉	1	4	yes	—
136	C₂²×C₄	C₂×Dic₉	1	2	yes	—
137	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
138	M₁₆	—	18	4	no	—
139	C₂×C₈	—	9	4	no	—
140	C₂×C₈	—	9	2	no	—
141	C₂×C₈	—	9	4	no	—
142	C₂×C₈	—	9	2	no	—
143	C₂×C₈	—	18	2	no	—
144	C₄⋊C₄	C₂×Dic₉	1	4	yes	—
145	C₄⋊C₄	C₂×Dic₉	1	8	yes	—
146	C₄⋊C₄	C₂×Dic₉	1	4	yes	—
147	C₂²⋊C₄	C₂×Dic₉	1	4	yes	—
148	C₄²	C₂×Dic₉	1	1	yes	characteristic
149	C₄²	C₂×Dic₉	1	1	yes	characteristic
150	C₄²	C₂²×D₉	1	4	yes	—
151	C₄²	C₂²×D₉	1	2	yes	—
152	C₂²×C₃	—	2	2	no	—
153	C₂²×C₃	Q₈×Dic₃	1	2	yes	—
154	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
155	C₃×C₄	—	2	2	no	—
156	C₃×C₄	—	2	2	no	—
157	C₃×C₄	—	2	8	no	—
158	C₃×C₄	Q₈×Dic₃	1	2	yes	—
159	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
160	C₃×C₄	C₂×#239	1	1	yes	characteristic
161	C₉	#2961	1	1	yes	characteristic, complemented, Sylow
162	C₂³	C₂²×Dic₉	1	1	yes	characteristic
163	Q₈	—	4	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	Q₈×D₉	1	2	yes	—
166	C₂×C₄	#3701	1	2	yes	—
167	C₂×C₄	C₂²×Dic₉	1	2	yes	—
168	C₂×C₄	C₂²×Dic₉	1	2	yes	—
169	C₂×C₄	C₂²×Dic₉	1	8	yes	—
170	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
171	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
172	C₈	—	9	4	no	—
173	C₈	—	18	2	no	—
174	C₈	—	18	4	no	—
175	C₂×C₃	—	2	2	no	—
176	C₂×C₃	C₂×Q₈×Dic₃	1	1	yes	characteristic
177	C₂×C₃	#5819	1	2	yes	—
178	C₂²	—	2	2	no	—
179	C₂²	Q₈×Dic₉	1	2	yes	—
180	C₂²	C₂³×Dic₉	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	2	no	—
183	C₄	—	2	8	no	—
184	C₄	Q₈×Dic₉	1	2	yes	—
185	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
186	C₄	C₂×#3701	1	1	yes	characteristic
187	C₃	#83329	1	1	yes	characteristic
188	C₂	—	2	2	no	—
189	C₂	C₂×Q₈×Dic₉	1	1	yes	characteristic
190	C₂	#10589921	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#533	C₂
socle	C₂²×C₃	C₂³×Dic₃
prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#533	D₉
hypocenter	C₉	#2961
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
2. #10588701	C₂	semidirect
41. C₂×C₉⋊C₈	Q₈	semidirect
161. C₉	#2961	semidirect

Maximal subgroups

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

subgroup	index
C₉×#533	2
#10588701	2
#10588677	2
#10588675	2
#10588604	2
C₂×#63362	2
#83329	3