Subgroups — #11795066

Order 1152.

345 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×#63366	C₂	1	2	yes	maximal
3	#10588615	C₂	1	1	yes	maximal, characteristic
4	#10588206	C₂	1	2	yes	maximal
5	#10588200	C₂	1	1	yes	maximal, characteristic
6	#69607	—	3	1	no	maximal
7	C₂×C₉×C₄⋊C₄	—	2	1	no	—
8	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₉	—	2	1	no	—
12	C₂×C₄⋊Dic₉	—	2	1	no	—
13	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
14	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
15	C₉×#95	—	2	1	no	—
16	#63366	—	2	4	no	—
17	C₃×#389	D₃	1	1	yes	characteristic
18	C₂×#807	—	3	2	no	—
19	#4935	—	3	1	no	—
20	#4529	—	3	2	no	—
21	#4524	—	3	1	no	—
22	C₂²×C₄×C₉	—	2	1	no	—
23	C₂²×C₄×C₉	—	2	1	no	—
24	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₉	—	2	2	no	—
28	C₉×C₄⋊C₄	—	2	1	no	—
29	C₉×C₄⋊C₄	—	2	2	no	—
30	C₉×C₄⋊C₄	—	4	2	no	—
31	C₉×C₄⋊C₄	D₄	1	2	yes	—
32	C₄²×C₉	—	2	2	no	—
33	C₄⋊Dic₉	—	2	2	no	—
34	C₄⋊Dic₉	—	2	2	no	—
35	C₄⋊Dic₉	—	4	2	no	—
36	C₄⋊Dic₉	—	4	2	no	—
37	C₂×C₉⋊C₈	—	2	2	no	—
38	C₂×C₉⋊C₈	—	2	2	no	—
39	C₂×C₉⋊C₈	Q₈	1	4	yes	—
40	#2083	—	9	1	no	Sylow
41	C₂×C₃×C₄⋊C₄	—	2	1	no	—
42	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
43	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
44	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
45	C₂×C₄⋊Dic₃	—	3	2	no	—
46	C₂×C₄⋊Dic₃	—	6	1	no	—
47	C₂×C₄⋊Dic₃	—	6	1	no	—
48	C₂²×C₃⋊C₈	—	3	2	no	—
49	C₃×#95	—	2	1	no	—
50	#807	—	6	4	no	—
51	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₉	—	2	1	no	—
53	C₂×C₄×C₉	—	2	1	no	—
54	C₂×C₄×C₉	—	2	1	no	—
55	C₂×C₄×C₉	—	2	1	no	—
56	C₂×C₄×C₉	—	2	2	no	—
57	C₂×C₄×C₉	—	4	1	no	—
58	C₂×C₄×C₉	—	4	1	no	—
59	C₂×C₄×C₉	—	4	1	no	—
60	C₂×C₄×C₉	—	4	1	no	—
61	C₂×C₄×C₉	—	4	1	no	—
62	C₂×C₄×C₉	D₈	1	2	yes	—
63	C₂×C₄×C₉	Q₁₆	1	2	yes	—
64	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
66	C₂×C₄×C₉	#41	1	1	yes	characteristic
67	C₂×C₄×C₉	#41	1	2	yes	—
68	C₂×Dic₉	—	4	2	no	—
69	C₂×Dic₉	—	4	2	no	—
70	C₂×Dic₉	—	4	2	no	—
71	C₉⋊C₈	—	2	4	no	—
72	C₂×#107	—	9	2	no	—
73	#389	D₉	1	1	yes	characteristic
74	#384	—	9	1	no	—
75	#340	—	9	2	no	—
76	#336	—	9	1	no	—
77	C₂²×C₃×C₄	—	2	1	no	—
78	C₂²×C₃×C₄	—	2	1	no	—
79	C₂²×C₃×C₄	#67	1	1	yes	characteristic
80	C₂²×C₃×C₄	#67	1	1	yes	characteristic
81	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
82	C₂²×Dic₃	—	6	2	no	—
83	C₃×C₄⋊C₄	—	2	1	no	—
84	C₃×C₄⋊C₄	—	2	2	no	—
85	C₃×C₄⋊C₄	—	4	2	no	—
86	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
87	C₃×C₄²	—	2	2	no	—
88	C₄⋊Dic₃	—	6	2	no	—
89	C₄⋊Dic₃	—	6	2	no	—
90	C₄⋊Dic₃	—	12	2	no	—
91	C₄⋊Dic₃	—	12	2	no	—
92	C₂×C₃⋊C₈	—	3	4	no	—
93	C₂×C₃⋊C₈	—	6	2	no	—
94	C₂×C₃⋊C₈	—	6	2	no	—
95	C₂²×C₉	#121	1	1	yes	characteristic
96	C₂²×C₉	#123	1	1	yes	characteristic
97	C₂²×C₉	C₄⋊Q₈	1	1	yes	characteristic
98	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
99	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
100	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂²×C₉	#137	1	1	yes	characteristic
102	C₄×C₉	—	2	2	no	—
103	C₄×C₉	—	2	2	no	—
104	C₄×C₉	—	4	2	no	—
105	C₄×C₉	—	8	1	no	—
106	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
107	C₄×C₉	#125	1	2	yes	—
108	Dic₉	—	8	2	no	—
109	C₂²×C₈	—	9	2	no	—
110	C₂×C₄⋊C₄	—	2	1	no	—
111	C₂×C₄⋊C₄	—	9	2	no	—
112	C₂×C₄⋊C₄	—	18	1	no	—
113	C₂×C₄⋊C₄	—	18	1	no	—
114	C₂×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
115	C₂×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
116	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
117	#107	—	18	4	no	—
118	#95	—	2	1	no	—
119	C₂³×C₃	C₂×#67	1	1	yes	characteristic
120	C₂×C₃×C₄	—	2	1	no	—
121	C₂×C₃×C₄	—	2	1	no	—
122	C₂×C₃×C₄	—	2	1	no	—
123	C₂×C₃×C₄	—	2	1	no	—
124	C₂×C₃×C₄	—	2	2	no	—
125	C₂×C₃×C₄	—	4	1	no	—
126	C₂×C₃×C₄	—	4	1	no	—
127	C₂×C₃×C₄	—	4	1	no	—
128	C₂×C₃×C₄	—	4	1	no	—
129	C₂×C₃×C₄	—	4	1	no	—
130	C₂×C₃×C₄	#213	1	2	yes	—
131	C₂×C₃×C₄	#216	1	2	yes	—
132	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
133	C₂×C₃×C₄	#235	1	1	yes	characteristic
134	C₂×C₃×C₄	#237	1	2	yes	—
135	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
136	C₂×Dic₃	—	12	2	no	—
137	C₂×Dic₃	—	12	2	no	—
138	C₂×Dic₃	—	12	2	no	—
139	C₃⋊C₈	—	6	4	no	—
140	C₂×C₉	#398	1	1	yes	characteristic
141	C₂×C₉	#459	1	1	yes	characteristic
142	C₂×C₉	#462	1	1	yes	characteristic
143	C₂×C₉	#480	1	1	yes	characteristic
144	C₂×C₉	#484	1	1	yes	characteristic
145	C₂×C₉	#500	1	1	yes	characteristic
146	C₂×C₉	#501	1	1	yes	characteristic
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	18	2	no	—
150	C₂²×C₄	#611	1	1	yes	characteristic
151	C₂²×C₄	#611	1	1	yes	characteristic
152	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
153	C₂×C₈	—	9	4	no	—
154	C₂×C₈	—	18	2	no	—
155	C₂×C₈	—	18	2	no	—
156	C₄⋊C₄	—	2	1	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	18	2	no	—
160	C₄⋊C₄	—	18	2	no	—
161	C₄⋊C₄	—	36	2	no	—
162	C₄⋊C₄	—	36	2	no	—
163	C₄⋊C₄	D₃₆	1	2	yes	—
164	C₄²	—	2	2	no	—
165	C₂²×C₃	#930	1	1	yes	characteristic
166	C₂²×C₃	C₂×#213	1	1	yes	characteristic
167	C₂²×C₃	#935	1	1	yes	characteristic
168	C₂²×C₃	C₂×#216	1	1	yes	characteristic
169	C₂²×C₃	#944	1	1	yes	characteristic
170	C₂²×C₃	#949	1	1	yes	characteristic
171	C₂²×C₃	#951	1	1	yes	characteristic
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	—	2	2	no	—
174	C₃×C₄	—	4	2	no	—
175	C₃×C₄	—	8	1	no	—
176	C₃×C₄	#889	1	2	yes	—
177	C₃×C₄	#897	1	2	yes	—
178	Dic₃	—	24	2	no	—
179	C₉	#2083	1	1	yes	characteristic, complemented, Sylow
180	C₂³	C₂×#611	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	36	2	no	—
192	C₂×C₄	—	36	2	no	—
193	C₂×C₄	—	36	2	no	—
194	C₂×C₄	#3673	1	2	yes	—
195	C₂×C₄	#3674	1	2	yes	—
196	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
197	C₂×C₄	#3697	1	1	yes	characteristic
198	C₂×C₄	#3699	1	2	yes	—
199	C₂×C₄	Q₈×D₉	1	2	yes	—
200	C₈	—	18	4	no	—
201	C₂×C₃	#4981	1	1	yes	characteristic
202	C₂×C₃	#5015	1	1	yes	characteristic
203	C₂×C₃	#5031	1	1	yes	characteristic
204	C₂×C₃	#5033	1	1	yes	characteristic
205	C₂×C₃	#5044	1	1	yes	characteristic
206	C₂×C₃	#5064	1	1	yes	characteristic
207	C₂×C₃	#5078	1	1	yes	characteristic
208	C₂²	#63492	1	1	yes	characteristic
209	C₂²	C₂×#3673	1	1	yes	characteristic
210	C₂²	#63497	1	1	yes	characteristic
211	C₂²	C₂×#3674	1	1	yes	characteristic
212	C₂²	#63506	1	1	yes	characteristic
213	C₂²	#63511	1	1	yes	characteristic
214	C₂²	#63512	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	—	4	2	no	—
218	C₄	—	8	1	no	—
219	C₄	—	72	2	no	—
220	C₄	#63451	1	2	yes	—
221	C₄	#63459	1	2	yes	—
222	C₃	#69607	1	1	yes	characteristic
223	C₂	#10588661	1	1	yes	characteristic
224	C₂	#10588698	1	1	yes	characteristic
225	C₂	#10588707	1	1	yes	characteristic
226	C₂	#10588713	1	1	yes	characteristic
227	C₂	#10588724	1	1	yes	characteristic
228	C₂	#10588743	1	1	yes	characteristic
229	C₂	#10588758	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#611
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#389	C₂
socle, prime radical	C₂³×C₃	C₂×#67
hypercenter	#389	D₉
hypocenter	C₉	#2083
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

Complements

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

N	H ≅ G/N	type
179. C₉	#2083	semidirect

Maximal subgroups

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

subgroup	index
C₉×#389	2
C₂×#63366	2
#10588615	2
#10588206	2
#10588200	2
#69607	3