Subgroups — #11861376

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	#10589572	C₂	1	1	yes	maximal, characteristic
2	C₉×#423	C₂	1	1	yes	maximal, characteristic
3	#10588803	C₂	1	2	yes	maximal
4	#10588797	C₂	1	2	yes	maximal
5	C₂×#63362	C₂	1	1	yes	maximal, characteristic
6	#10588510	C₂	1	8	yes	maximal, complemented
7	#79045	—	3	1	no	maximal
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	#63488	C₂²	1	2	yes	—
11	#63486	C₄	1	4	yes	—
12	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
14	#63432	C₄	1	2	yes	—
15	#63431	C₄	1	2	yes	—
16	C₄×Dic₁₈	C₂²	1	4	yes	—
17	C₉×C₄⋊C₈	C₂²	1	4	yes	—
18	#63375	C₂²	1	4	yes	—
19	Dic₉⋊C₈	C₂²	1	8	yes	—
20	C₈×Dic₉	C₂²	1	4	yes	—
21	#63362	C₂²	1	4	yes	—
22	#5470	—	3	1	no	—
23	C₃×#423	D₃	1	1	yes	characteristic
24	#5122	—	3	2	no	—
25	#5119	—	3	2	no	—
26	C₂×#803	—	3	1	no	—
27	#4828	—	3	8	no	—
28	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₁₈	C₂×C₄	1	4	yes	—
31	C₉×M₁₆	—	2	4	no	—
32	C₂×C₈×C₉	C₂³	1	4	yes	—
33	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
34	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₉	C₂³	1	2	yes	—
36	#3676	C₂×C₄	1	4	yes	—
37	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
38	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
39	Dic₉⋊C₄	C₂×C₄	1	8	yes	—
40	C₄×Dic₉	C₂³	1	4	yes	—
41	C₂×C₉⋊C₈	—	2	2	no	—
42	C₂×C₉⋊C₈	Q₈	1	4	yes	complemented
43	C₂×C₉⋊C₈	C₂³	1	2	yes	—
44	C₂×C₉⋊C₈	C₂³	1	2	yes	—
45	#2961	—	9	1	no	Sylow
46	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
47	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
48	#926	—	3	2	no	—
49	#924	—	3	4	no	—
50	C₂²×C₃⋊C₈	—	3	1	no	—
51	C₂²×C₃⋊C₈	—	3	1	no	—
52	#870	—	3	2	no	—
53	#869	—	3	2	no	—
54	C₄×Dic₆	—	3	4	no	—
55	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
56	#815	—	3	4	no	—
57	Dic₃⋊C₈	—	3	8	no	—
58	C₈×Dic₃	—	3	4	no	—
59	#803	—	3	4	no	—
60	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
66	C₂×C₄×C₉	#41	1	2	yes	—
67	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
68	C₂×Dic₉	C₂²×C₄	1	8	yes	—
69	Dic₁₈	—	4	4	no	—
70	C₈×C₉	—	2	4	no	—
71	C₉⋊C₈	—	2	2	no	—
72	C₉⋊C₈	C₂×Q₈	1	4	yes	—
73	#533	—	9	1	no	—
74	#446	—	9	8	no	—
75	#424	—	9	2	no	—
76	#423	D₉	1	1	yes	characteristic
77	#405	—	9	2	no	—
78	C₂×#97	—	9	1	no	—
79	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
80	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
81	C₂×Dic₆	—	3	4	no	—
82	C₃×M₁₆	—	2	4	no	—
83	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
84	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
85	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
86	C₃×C₄²	C₂²×D₃	1	2	yes	—
87	#217	—	3	4	no	—
88	C₄⋊Dic₃	—	3	4	no	—
89	C₄⋊Dic₃	—	3	4	no	—
90	Dic₃⋊C₄	—	3	8	no	—
91	C₄×Dic₃	—	3	4	no	—
92	C₂×C₃⋊C₈	—	3	4	no	—
93	C₂×C₃⋊C₈	—	3	2	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	C₄×Q₈	1	2	yes	—
102	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
103	C₄×C₉	C₂×#41	1	1	yes	characteristic
104	Dic₉	—	2	8	no	—
105	C₂×M₁₆	C₂×D₉	1	2	yes	—
106	C₂²×C₈	—	9	1	no	—
107	C₂²×C₈	—	9	1	no	—
108	C₄⋊Q₈	—	9	2	no	—
109	#125	—	9	2	no	—
110	C₂²⋊Q₈	—	9	4	no	—
111	C₄×Q₈	—	9	4	no	—
112	#117	—	9	2	no	—
113	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
114	C₄⋊C₈	—	9	8	no	—
115	C₄⋊C₈	C₂×D₉	1	4	yes	—
116	#97	—	9	4	no	—
117	#97	—	9	4	no	—
118	C₄×C₈	—	9	4	no	—
119	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
120	C₂×C₃×C₄	—	4	2	no	—
121	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
122	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
123	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
124	C₂×C₃×C₄	#237	1	2	yes	—
125	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
126	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
127	C₂×Dic₃	—	3	8	no	—
128	Dic₆	—	12	4	no	—
129	C₃×C₈	—	2	4	no	—
130	C₃⋊C₈	—	3	4	no	—
131	C₃⋊C₈	—	6	2	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	—	9	4	no	—
136	C₂²×C₄	C₄×D₉	1	2	yes	—
137	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
138	M₁₆	—	2	4	no	—
139	C₂×C₈	—	9	4	no	—
140	C₂×C₈	—	9	2	no	—
141	C₂×C₈	—	9	2	no	—
142	C₂×C₈	—	18	2	no	—
143	C₂×C₈	C₂²×D₉	1	4	yes	—
144	C₄⋊C₄	—	9	4	no	—
145	C₄⋊C₄	—	9	8	no	—
146	C₄⋊C₄	—	9	4	no	—
147	C₂²⋊C₄	—	9	4	no	—
148	C₄²	—	9	4	no	—
149	C₄²	C₄×D₉	1	1	yes	characteristic
150	C₄²	C₄×D₉	1	1	yes	characteristic
151	C₄²	C₂²×D₉	1	2	yes	—
152	C₂²×C₃	—	2	2	no	—
153	C₂²×C₃	#887	1	2	yes	—
154	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
155	C₃×C₄	—	2	2	no	—
156	C₃×C₄	—	2	2	no	—
157	C₃×C₄	#887	1	2	yes	—
158	C₃×C₄	C₂×#237	1	1	yes	characteristic
159	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
160	Dic₃	—	6	8	no	—
161	C₉	#2961	1	1	yes	characteristic, complemented, Sylow
162	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
163	Q₈	—	36	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	9	8	no	—
166	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
167	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
168	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
169	C₂×C₄	#3699	1	2	yes	—
170	C₂×C₄	Q₈×D₉	1	2	yes	—
171	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
172	C₈	—	2	4	no	—
173	C₈	—	9	4	no	—
174	C₈	—	18	2	no	—
175	C₂×C₃	—	2	2	no	—
176	C₂×C₃	C₂×#887	1	1	yes	characteristic
177	C₂×C₃	#5745	1	2	yes	—
178	C₂²	—	2	2	no	—
179	C₂²	#63449	1	2	yes	—
180	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	2	no	—
183	C₄	—	18	8	no	—
184	C₄	#63449	1	2	yes	—
185	C₄	C₂×#3699	1	1	yes	characteristic
186	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
187	C₃	#79045	1	1	yes	characteristic
188	C₂	—	2	2	no	—
189	C₂	C₂×#63449	1	1	yes	characteristic
190	C₂	#10589847	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#423	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#423	D₉
hypocenter	C₉	#2961
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
6. #10588510	C₂	semidirect
42. 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
#10589572	2
C₉×#423	2
#10588803	2
#10588797	2
C₂×#63362	2
#10588510	2
#79045	3