Subgroups — #11790490

Order 1152.

294 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#108	C₂	1	1	yes	maximal, characteristic
2	#10588805	C₂	1	2	yes	maximal
3	C₂×#63378	C₂	1	1	yes	maximal, characteristic
4	#10588782	C₂	1	1	yes	maximal, characteristic
5	#10588234	C₂	1	2	yes	maximal
6	#70701	—	3	1	no	maximal
7	C₂×C₉×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	#63488	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×#3667	C₂²	1	1	yes	characteristic
12	C₉×#108	C₄	1	4	yes	complemented
13	#63378	—	2	1	no	—
14	#63378	—	2	1	no	—
15	#63378	—	2	2	no	—
16	#63377	—	2	2	no	—
17	#63375	—	2	1	no	—
18	C₈×Dic₉	—	2	1	no	—
19	C₂×C₃×#108	D₃	1	1	yes	characteristic
20	#5121	—	3	2	no	—
21	C₂×#818	—	3	1	no	—
22	#5101	—	3	1	no	—
23	#4554	—	3	2	no	—
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₉	—	2	2	no	—
26	C₉×M₁₆	—	2	2	no	—
27	C₉×M₁₆	C₂×C₄	1	4	yes	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₉	D₄	1	1	yes	characteristic
31	C₂×C₈×C₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₉	Q₈	1	2	yes	—
33	#3676	—	2	1	no	—
34	C₄⋊Dic₉	—	2	2	no	—
35	C₄⋊Dic₉	—	2	2	no	—
36	C₄⋊Dic₉	D₄	1	1	yes	characteristic
37	C₄⋊Dic₉	D₄	1	1	yes	characteristic
38	C₄×Dic₉	—	2	1	no	—
39	#3667	—	2	1	no	—
40	#3667	Q₈	1	2	yes	—
41	C₂×C₉⋊C₈	—	2	1	no	—
42	#1952	—	9	1	no	Sylow
43	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
44	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
45	#926	—	3	1	no	—
46	C₂×C₄⋊Dic₃	—	3	2	no	—
47	C₂×#208	—	3	1	no	—
48	C₃×#108	Dic₃	1	4	yes	—
49	#818	—	6	2	no	—
50	#818	—	6	1	no	—
51	#818	—	6	1	no	—
52	#817	—	6	2	no	—
53	#815	—	6	1	no	—
54	C₈×Dic₃	—	6	1	no	—
55	C₂³×C₉	#41	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
59	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₉	#41	1	1	yes	characteristic
62	C₂×Dic₉	—	2	1	no	—
63	C₂×Dic₉	—	2	1	no	—
64	C₂×Dic₉	—	4	2	no	—
65	C₂×Dic₉	—	8	2	no	—
66	C₈×C₉	—	2	4	no	—
67	C₈×C₉	C₄⋊C₄	1	2	yes	—
68	C₈×C₉	C₄⋊C₄	1	2	yes	—
69	C₉⋊C₈	—	2	2	no	—
70	C₂×#108	D₉	1	1	yes	characteristic
71	#428	—	9	2	no	—
72	C₂×#107	—	9	1	no	—
73	#405	—	9	1	no	—
74	#343	—	9	2	no	—
75	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₂²×Dic₃	—	6	2	no	—
77	C₃×M₁₆	—	2	2	no	—
78	C₃×M₁₆	C₂×Dic₃	1	4	yes	—
79	C₂×C₃×C₈	—	2	2	no	—
80	C₂×C₃×C₈	Dic₆	1	2	yes	—
81	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
82	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
83	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
84	#217	—	6	1	no	—
85	C₄⋊Dic₃	—	3	1	no	—
86	C₄⋊Dic₃	—	3	1	no	—
87	C₄⋊Dic₃	—	6	2	no	—
88	C₄⋊Dic₃	—	6	2	no	—
89	C₄×Dic₃	—	6	1	no	—
90	#208	—	3	2	no	—
91	#208	—	6	1	no	—
92	C₂×C₃⋊C₈	—	6	1	no	—
93	C₂²×C₉	—	2	1	no	—
94	C₂²×C₉	—	2	1	no	—
95	C₂²×C₉	C₄×Q₈	1	1	yes	characteristic
96	C₂²×C₉	#121	1	1	yes	characteristic
97	C₂²×C₉	#125	1	1	yes	characteristic
98	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₄×C₉	C₄×D₄	1	1	yes	characteristic
100	C₄×C₉	C₂²⋊Q₈	1	1	yes	characteristic
101	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
102	Dic₉	—	4	1	no	—
103	Dic₉	—	4	1	no	—
104	Dic₉	—	8	2	no	—
105	C₂×M₁₆	—	9	1	no	—
106	C₂×M₁₆	C₂×D₉	1	2	yes	—
107	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
108	#117	—	9	1	no	—
109	C₂×C₄⋊C₄	—	9	2	no	—
110	#108	Dic₉	1	4	yes	complemented
111	#107	—	18	2	no	—
112	#107	—	18	1	no	—
113	#107	—	18	1	no	—
114	#106	—	18	2	no	—
115	#97	—	18	1	no	—
116	C₄×C₈	—	18	1	no	—
117	C₂³×C₃	#239	1	1	yes	characteristic
118	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
119	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
120	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄	#237	1	1	yes	characteristic
122	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
123	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
124	C₂×Dic₃	—	6	1	no	—
125	C₂×Dic₃	—	6	1	no	—
126	C₂×Dic₃	—	12	2	no	—
127	C₂×Dic₃	—	24	2	no	—
128	C₃×C₈	—	2	4	no	—
129	C₃×C₈	C₄⋊Dic₃	1	2	yes	—
130	C₃×C₈	C₄⋊Dic₃	1	2	yes	—
131	C₃⋊C₈	—	6	2	no	—
132	C₂×C₉	—	2	1	no	—
133	C₂×C₉	—	2	1	no	—
134	C₂×C₉	#389	1	1	yes	characteristic
135	C₂×C₉	#472	1	1	yes	characteristic
136	C₂×C₉	#473	1	1	yes	characteristic
137	C₂²×C₄	—	18	2	no	—
138	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
139	M₁₆	—	2	2	no	—
140	M₁₆	—	9	2	no	—
141	M₁₆	—	18	1	no	—
142	M₁₆	C₂×Dic₉	1	4	yes	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	18	1	no	—
145	C₂×C₈	Dic₁₈	1	2	yes	—
146	C₂×C₈	D₃₆	1	1	yes	characteristic
147	C₂×C₈	D₃₆	1	1	yes	characteristic
148	C₂×C₈	C₂×Dic₉	1	2	yes	—
149	C₄⋊C₄	—	9	1	no	—
150	C₄⋊C₄	—	9	1	no	—
151	C₄⋊C₄	—	18	2	no	—
152	C₄⋊C₄	—	18	2	no	—
153	C₂²⋊C₄	—	18	1	no	—
154	C₄²	—	18	1	no	—
155	C₂²×C₃	—	2	1	no	—
156	C₂²×C₃	—	2	1	no	—
157	C₂²×C₃	#890	1	1	yes	characteristic
158	C₂²×C₃	#895	1	1	yes	characteristic
159	C₂²×C₃	Q₈×Dic₃	1	1	yes	characteristic
160	C₃×C₄	#888	1	1	yes	characteristic
161	C₃×C₄	#897	1	1	yes	characteristic
162	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
163	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
164	Dic₃	—	12	1	no	—
165	Dic₃	—	12	1	no	—
166	Dic₃	—	24	2	no	—
167	C₉	#1952	1	1	yes	characteristic, complemented, Sylow
168	C₂³	#3701	1	1	yes	characteristic
169	C₂×C₄	—	18	1	no	—
170	C₂×C₄	—	18	1	no	—
171	C₂×C₄	—	36	2	no	—
172	C₂×C₄	—	72	2	no	—
173	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
174	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
175	C₂×C₄	D₄×D₉	1	1	yes	characteristic
176	C₂×C₄	#3699	1	1	yes	characteristic
177	C₂×C₄	Q₈×D₉	1	1	yes	characteristic
178	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
179	C₈	—	2	4	no	—
180	C₈	—	18	2	no	—
181	C₈	C₄⋊Dic₉	1	2	yes	—
182	C₈	C₄⋊Dic₉	1	2	yes	—
183	C₂×C₃	—	2	1	no	—
184	C₂×C₃	—	2	1	no	—
185	C₂×C₃	#4896	1	1	yes	characteristic
186	C₂×C₃	#4897	1	1	yes	characteristic
187	C₂×C₃	#4984	1	1	yes	characteristic
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	#63452	1	1	yes	characteristic
191	C₂²	#63457	1	1	yes	characteristic
192	C₂²	Q₈×Dic₉	1	1	yes	characteristic
193	C₄	—	36	1	no	—
194	C₄	—	36	1	no	—
195	C₄	—	72	2	no	—
196	C₄	#63450	1	1	yes	characteristic
197	C₄	#63459	1	1	yes	characteristic
198	C₄	C₂×C₄⋊Dic₉	1	1	yes	characteristic
199	C₄	D₄×Dic₉	1	1	yes	characteristic
200	C₃	#70701	1	1	yes	characteristic
201	C₂	—	2	1	no	—
202	C₂	—	2	1	no	—
203	C₂	#10588576	1	1	yes	characteristic
204	C₂	#10588577	1	1	yes	characteristic
205	C₂	#10588664	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63457
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#108	C₂
socle	C₂²×C₃	#895
prime radical	C₂³×C₃	#239
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#108	D₉
hypocenter	C₉	#1952
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
12. C₉×#108	C₄	semidirect
110. #108	Dic₉	semidirect
167. C₉	#1952	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#108	2
#10588805	2
C₂×#63378	2
#10588782	2
#10588234	2
#70701	3