Subgroups — #11858307

Order 1152.

726 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	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3667	C₂	1	2	yes	maximal
3	#10588677	C₂	1	8	yes	maximal, complemented
4	#10588604	C₂	1	4	yes	maximal, complemented
5	#82204	—	3	1	no	maximal
6	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₉×#117	C₄	1	4	yes	—
8	C₉×#117	C₂²	1	4	yes	—
9	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₉×C₂²⋊C₄	C₄	1	2	yes	—
11	C₂×C₄²×C₉	C₂²	1	2	yes	—
12	C₂×#3667	—	2	8	no	—
13	C₂×#3667	C₂²	1	4	yes	—
14	C₂×#3667	C₂²	1	4	yes	—
15	C₂²×C₉⋊C₈	C₂²	1	4	yes	—
16	C₄⋊(C₉⋊C₈)	C₂²	1	16	yes	complemented
17	C₂×C₃×#117	D₃	1	1	yes	characteristic
18	C₂²×#208	—	3	2	no	—
19	#4999	—	3	8	no	—
20	#4924	—	3	4	no	—
21	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₉	D₄	1	4	yes	—
26	C₂²×C₄×C₉	Q₈	1	4	yes	—
27	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	2	yes	—
29	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
30	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
31	C₄²×C₉	C₂×C₄	1	4	yes	—
32	C₄²×C₉	C₂³	1	4	yes	—
33	#3667	—	2	8	no	—
34	#3667	—	2	8	no	—
35	C₂×C₉⋊C₈	—	2	8	no	—
36	C₂×C₉⋊C₈	C₂³	1	8	yes	—
37	#2905	—	9	1	no	Sylow
38	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
39	C₃×#117	Dic₃	1	4	yes	—
40	C₃×#117	C₂×D₃	1	4	yes	—
41	C₂×C₃×C₄⋊C₄	Dic₃	1	2	yes	—
42	C₂×C₃×C₂²⋊C₄	Dic₃	1	2	yes	—
43	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
44	C₂×#208	—	3	4	no	—
45	C₂×#208	—	3	4	no	—
46	C₂×#208	—	6	8	no	—
47	C₂²×C₃⋊C₈	—	3	4	no	—
48	C₄⋊(C₃⋊C₈)	—	3	16	no	—
49	C₂³×C₉	—	4	2	no	—
50	C₂³×C₉	C₄⋊C₄	1	4	yes	—
51	C₂³×C₉	C₂²×C₄	1	2	yes	—
52	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₉	—	4	4	no	—
54	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
55	C₂×C₄×C₉	C₄⋊C₄	1	8	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
57	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
60	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
62	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
63	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
64	C₉⋊C₈	—	2	8	no	—
65	C₂²×M₁₆	—	9	2	no	—
66	C₂×#117	D₉	1	1	yes	characteristic
67	#424	—	9	8	no	—
68	#423	—	9	4	no	—
69	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
70	C₂²×C₃×C₄	Dic₆	1	4	yes	—
71	C₂²×C₃×C₄	D₁₂	1	4	yes	—
72	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
73	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
74	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
75	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
76	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
77	C₃×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
78	C₃×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
79	C₃×C₄²	C₂×Dic₃	1	4	yes	—
80	C₃×C₄²	C₂²×D₃	1	4	yes	—
81	#208	—	6	8	no	—
82	#208	—	6	8	no	—
83	C₂×C₃⋊C₈	—	3	8	no	—
84	C₂×C₃⋊C₈	—	6	8	no	—
85	C₂²×C₉	—	2	2	no	—
86	C₂²×C₉	—	2	4	no	—
87	C₂²×C₉	—	4	4	no	—
88	C₂²×C₉	C₂×C₄⋊C₄	1	4	yes	—
89	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
90	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
91	C₄×C₉	—	2	8	no	—
92	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
93	C₄×C₉	C₂×C₄⋊C₄	1	4	yes	—
94	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
95	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
96	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
97	C₂×M₁₆	—	9	4	no	—
98	C₂×M₁₆	—	9	4	no	—
99	C₂×M₁₆	—	18	8	no	—
100	C₂²×C₈	—	9	4	no	—
101	#117	Dic₉	1	4	yes	—
102	#117	C₂×D₉	1	4	yes	—
103	C₂×C₄⋊C₄	Dic₉	1	2	yes	—
104	C₂×C₂²⋊C₄	Dic₉	1	2	yes	—
105	C₂×C₄²	C₂×D₉	1	2	yes	—
106	C₄⋊C₈	—	9	16	no	—
107	C₂³×C₃	—	4	2	no	—
108	C₂³×C₃	C₄⋊Dic₃	1	4	yes	—
109	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
110	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
111	C₂×C₃×C₄	—	4	4	no	—
112	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
113	C₂×C₃×C₄	C₄⋊Dic₃	1	8	yes	—
114	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
115	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
116	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
117	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
118	C₂×C₃×C₄	C₂²×Dic₃	1	8	yes	—
119	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
120	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
121	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
122	C₃⋊C₈	—	6	8	no	—
123	C₂×C₉	—	2	2	no	—
124	C₂×C₉	—	2	4	no	—
125	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₉	#568	1	2	yes	—
127	C₂⁴	C₂×Dic₉	1	1	yes	characteristic
128	C₂²×C₄	Dic₁₈	1	4	yes	—
129	C₂²×C₄	D₃₆	1	4	yes	—
130	C₂²×C₄	C₂×Dic₉	1	4	yes	—
131	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
132	C₂²×C₄	C₂×Dic₉	1	2	yes	—
133	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₉	1	2	yes	—
135	M₁₆	—	18	8	no	—
136	M₁₆	—	18	8	no	—
137	C₂×C₈	—	9	8	no	—
138	C₂×C₈	—	18	8	no	—
139	C₄⋊C₄	C₂×Dic₉	1	8	yes	—
140	C₂²⋊C₄	C₂×Dic₉	1	8	yes	—
141	C₄²	C₂×Dic₉	1	4	yes	—
142	C₄²	C₂²×D₉	1	4	yes	—
143	C₂²×C₃	—	2	2	no	—
144	C₂²×C₃	—	2	4	no	—
145	C₂²×C₃	—	4	4	no	—
146	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
147	C₂²×C₃	C₂×C₄⋊Dic₃	1	2	yes	—
148	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
149	C₃×C₄	—	2	8	no	—
150	C₃×C₄	C₂×C₄⋊Dic₃	1	4	yes	—
151	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
152	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
153	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
154	C₉	#2905	1	1	yes	characteristic, complemented, Sylow
155	C₂³	—	4	2	no	—
156	C₂³	C₄⋊Dic₉	1	4	yes	—
157	C₂³	C₂²×Dic₉	1	2	yes	—
158	C₂³	C₂²×Dic₉	1	1	yes	characteristic
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
161	C₂×C₄	C₄⋊Dic₉	1	8	yes	—
162	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
163	C₂×C₄	C₂×Dic₁₈	1	4	yes	—
164	C₂×C₄	C₂×D₃₆	1	4	yes	—
165	C₂×C₄	C₂×D₃₆	1	2	yes	—
166	C₂×C₄	C₂²×Dic₉	1	8	yes	—
167	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
168	C₂×C₄	C₂²×Dic₉	1	2	yes	—
169	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
170	C₈	—	18	8	no	—
171	C₂×C₃	—	2	2	no	—
172	C₂×C₃	—	2	4	no	—
173	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
174	C₂×C₃	#5819	1	2	yes	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	4	4	no	—
178	C₂²	C₂×C₄⋊Dic₉	1	4	yes	—
179	C₂²	C₂×C₄⋊Dic₉	1	2	yes	—
180	C₂²	C₂³×Dic₉	1	1	yes	characteristic
181	C₄	—	2	8	no	—
182	C₄	C₂×C₄⋊Dic₉	1	4	yes	—
183	C₄	C₂×C₄⋊Dic₉	1	2	yes	—
184	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
185	C₄	C₂²×D₃₆	1	1	yes	characteristic
186	C₃	#82204	1	1	yes	characteristic
187	C₂	—	2	2	no	—
188	C₂	—	2	4	no	—
189	C₂	C₂²×C₄⋊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	C₂×C₉×#117	C₂
socle	C₂²×C₃	C₂³×Dic₃
prime radical	C₂⁴×C₃	C₂×Dic₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×#117	D₉
hypocenter	C₉	#2905
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
3. #10588677	C₂	semidirect
4. #10588604	C₂	semidirect
16. C₄⋊(C₉⋊C₈)	C₂²	semidirect
154. C₉	#2905	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#117	2
C₂²×#3667	2
#10588677	2
#10588604	2
#82204	3