Subgroups — #11783501

Order 1152.

360 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63375	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₉	C₂	1	1	yes	maximal, characteristic
3	#10588612	C₂	1	1	yes	maximal, characteristic
4	C₉×#336	C₂	1	1	yes	maximal, characteristic
5	#10588228	C₂	1	1	yes	maximal, characteristic
6	#10588228	C₂	1	1	yes	maximal, characteristic
7	#10588200	C₂	1	1	yes	maximal, characteristic
8	#68598	—	3	1	no	maximal
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₉⋊#95	C₄	1	2	yes	—
17	C₉⋊#95	C₄	1	2	yes	—
18	#63375	C₄	1	4	yes	complemented
19	C₈×Dic₉	C₄	1	4	yes	complemented
20	C₂×#815	—	3	1	no	—
21	C₂×C₈×Dic₃	—	3	1	no	—
22	#4932	—	3	1	no	—
23	C₃×#336	D₃	1	1	yes	characteristic
24	#4550	—	3	1	no	—
25	#4550	—	3	1	no	—
26	#4524	—	3	1	no	—
27	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₉	C₂×C₄	1	2	yes	—
30	C₂²×Dic₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Dic₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₉	—	2	1	no	—
33	C₂×C₈×C₉	—	2	1	no	—
34	C₂×C₈×C₉	—	2	1	no	—
35	C₂×C₈×C₉	—	2	1	no	—
36	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
37	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
38	C₄²×C₉	—	2	1	no	—
39	C₄²×C₉	—	2	1	no	—
40	C₄×Dic₉	—	2	1	no	—
41	C₄×Dic₉	—	2	1	no	—
42	C₄×Dic₉	C₂×C₄	1	2	yes	—
43	C₄×Dic₉	C₂×C₄	1	2	yes	—
44	C₂×C₉⋊C₈	—	2	1	no	—
45	C₂×C₉⋊C₈	—	2	1	no	—
46	C₂×C₉⋊C₈	—	2	1	no	—
47	C₂×C₉⋊C₈	—	2	1	no	—
48	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
49	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
50	#1746	—	9	1	no	Sylow
51	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
52	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
53	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
54	C₂×C₄×Dic₃	—	3	1	no	—
55	C₂×C₄×Dic₃	—	3	1	no	—
56	C₂²×C₃⋊C₈	—	3	1	no	—
57	C₂²×C₃⋊C₈	—	3	1	no	—
58	C₃⋊#95	—	3	2	no	—
59	C₃⋊#95	—	3	2	no	—
60	#815	—	3	4	no	—
61	C₈×Dic₃	—	3	4	no	—
62	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₉	—	2	2	no	—
64	C₂×C₄×C₉	—	2	2	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₉	#41	1	1	yes	characteristic
69	C₂×C₄×C₉	#41	1	1	yes	characteristic
70	C₂×C₄×C₉	#41	1	1	yes	characteristic
71	C₂×C₄×C₉	#41	1	1	yes	characteristic
72	C₂×Dic₉	—	2	2	no	—
73	C₂×Dic₉	—	2	2	no	—
74	C₂×Dic₉	—	2	2	no	—
75	C₂×Dic₉	—	2	2	no	—
76	C₂×Dic₉	—	2	2	no	—
77	C₂×Dic₉	C₄²	1	2	yes	—
78	C₂×Dic₉	C₄²	1	2	yes	—
79	C₈×C₉	—	2	2	no	—
80	C₈×C₉	—	2	2	no	—
81	C₉⋊C₈	—	2	2	no	—
82	C₉⋊C₈	—	2	2	no	—
83	C₂×#97	—	9	1	no	—
84	C₂×C₄×C₈	—	9	1	no	—
85	#376	—	9	1	no	—
86	#336	—	9	1	no	—
87	#336	—	9	1	no	—
88	#336	—	9	1	no	—
89	#336	D₉	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
91	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
92	C₂²×Dic₃	—	3	1	no	—
93	C₂²×Dic₃	—	3	1	no	—
94	C₂²×Dic₃	—	3	2	no	—
95	C₂×C₃×C₈	—	2	1	no	—
96	C₂×C₃×C₈	—	2	1	no	—
97	C₂×C₃×C₈	—	2	1	no	—
98	C₂×C₃×C₈	—	2	1	no	—
99	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
100	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
101	C₃×C₄²	—	2	1	no	—
102	C₃×C₄²	—	2	1	no	—
103	C₄×Dic₃	—	3	2	no	—
104	C₄×Dic₃	—	3	2	no	—
105	C₄×Dic₃	—	6	1	no	—
106	C₄×Dic₃	—	6	1	no	—
107	C₂×C₃⋊C₈	—	3	2	no	—
108	C₂×C₃⋊C₈	—	3	2	no	—
109	C₂×C₃⋊C₈	—	6	1	no	—
110	C₂×C₃⋊C₈	—	6	1	no	—
111	C₂×C₃⋊C₈	—	6	1	no	—
112	C₂×C₃⋊C₈	—	6	1	no	—
113	C₂²×C₉	C₂×C₄²	1	1	yes	characteristic
114	C₂²×C₉	#117	1	1	yes	characteristic
115	C₂²×C₉	#117	1	1	yes	characteristic
116	C₂²×C₉	#131	1	2	yes	—
117	C₂²×C₉	#131	1	2	yes	—
118	C₄×C₉	—	4	2	no	—
119	C₄×C₉	#117	1	1	yes	characteristic
120	C₄×C₉	#117	1	1	yes	characteristic
121	C₄×C₉	#117	1	1	yes	characteristic
122	C₄×C₉	#117	1	1	yes	characteristic
123	Dic₉	—	2	2	no	—
124	Dic₉	—	2	2	no	—
125	Dic₉	—	4	2	no	—
126	C₂²×C₈	—	9	1	no	—
127	C₂²×C₈	—	9	1	no	—
128	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
129	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
130	C₂×C₄²	—	9	1	no	—
131	C₂×C₄²	—	9	1	no	—
132	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
133	#97	—	9	4	no	—
134	C₄×C₈	—	9	4	no	—
135	#95	—	9	2	no	—
136	#95	—	9	2	no	—
137	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
142	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
143	C₂×C₃×C₄	#237	1	1	yes	characteristic
144	C₂×C₃×C₄	#237	1	1	yes	characteristic
145	C₂×C₃×C₄	#237	1	1	yes	characteristic
146	C₂×C₃×C₄	#239	1	1	yes	characteristic
147	C₂×Dic₃	—	3	2	no	—
148	C₂×Dic₃	—	3	2	no	—
149	C₂×Dic₃	—	6	2	no	—
150	C₂×Dic₃	—	6	2	no	—
151	C₂×Dic₃	—	6	2	no	—
152	C₂×Dic₃	—	6	2	no	—
153	C₂×Dic₃	—	6	2	no	—
154	C₃×C₈	—	2	2	no	—
155	C₃×C₈	—	2	2	no	—
156	C₃⋊C₈	—	6	2	no	—
157	C₃⋊C₈	—	6	2	no	—
158	C₂×C₉	#376	1	1	yes	characteristic
159	C₂×C₉	#405	1	1	yes	characteristic
160	C₂×C₉	#405	1	1	yes	characteristic
161	C₂×C₉	#433	1	2	yes	—
162	C₂×C₉	#433	1	2	yes	—
163	C₂²×C₄	—	9	1	no	—
164	C₂²×C₄	—	9	1	no	—
165	C₂²×C₄	—	9	2	no	—
166	C₂²×C₄	C₄×D₉	1	2	yes	—
167	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	2	1	no	—
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	9	2	no	—
173	C₂×C₈	—	9	2	no	—
174	C₂×C₈	—	18	1	no	—
175	C₂×C₈	—	18	1	no	—
176	C₂×C₈	—	18	1	no	—
177	C₂×C₈	—	18	1	no	—
178	C₂×C₈	C₄×D₉	1	2	yes	—
179	C₂×C₈	C₄×D₉	1	2	yes	—
180	C₄²	—	2	1	no	—
181	C₄²	—	2	1	no	—
182	C₄²	—	9	2	no	—
183	C₄²	—	9	2	no	—
184	C₄²	—	18	1	no	—
185	C₄²	—	18	1	no	—
186	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
187	C₂²×C₃	#877	1	1	yes	characteristic
188	C₂²×C₃	#892	1	1	yes	characteristic
189	C₂²×C₃	#901	1	2	yes	—
190	C₂²×C₃	#907	1	2	yes	—
191	C₃×C₄	—	4	2	no	—
192	C₃×C₄	#877	1	1	yes	characteristic
193	C₃×C₄	#877	1	1	yes	characteristic
194	C₃×C₄	#892	1	1	yes	characteristic
195	C₃×C₄	#892	1	1	yes	characteristic
196	Dic₃	—	6	2	no	—
197	Dic₃	—	6	2	no	—
198	Dic₃	—	12	2	no	—
199	C₉	#1746	1	1	yes	characteristic, complemented, Sylow
200	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	9	2	no	—
205	C₂×C₄	—	9	2	no	—
206	C₂×C₄	—	18	2	no	—
207	C₂×C₄	—	18	2	no	—
208	C₂×C₄	—	18	2	no	—
209	C₂×C₄	—	18	2	no	—
210	C₂×C₄	—	18	2	no	—
211	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
212	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
213	C₂×C₄	#3699	1	1	yes	characteristic
214	C₂×C₄	#3699	1	1	yes	characteristic
215	C₂×C₄	#3699	1	1	yes	characteristic
216	C₂×C₄	#3701	1	1	yes	characteristic
217	C₈	—	2	2	no	—
218	C₈	—	2	2	no	—
219	C₈	—	18	2	no	—
220	C₈	—	18	2	no	—
221	C₂×C₃	#4648	1	1	yes	characteristic
222	C₂×C₃	#4689	1	1	yes	characteristic
223	C₂×C₃	#4708	1	1	yes	characteristic
224	C₂×C₃	#4720	1	2	yes	—
225	C₂×C₃	#4840	1	2	yes	—
226	C₂²	C₄²×D₉	1	1	yes	characteristic
227	C₂²	#63439	1	1	yes	characteristic
228	C₂²	#63454	1	1	yes	characteristic
229	C₂²	#63464	1	2	yes	—
230	C₂²	#63469	1	2	yes	—
231	C₄	—	4	2	no	—
232	C₄	—	18	2	no	—
233	C₄	—	18	2	no	—
234	C₄	—	36	2	no	—
235	C₄	#63439	1	1	yes	characteristic
236	C₄	#63439	1	1	yes	characteristic
237	C₄	#63454	1	1	yes	characteristic
238	C₄	#63454	1	1	yes	characteristic
239	C₃	#68598	1	1	yes	characteristic
240	C₂	#10588328	1	1	yes	characteristic
241	C₂	#10588371	1	1	yes	characteristic
242	C₂	#10588389	1	1	yes	characteristic
243	C₂	#10588400	1	2	yes	—
244	C₂	#10588524	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂×C₄²
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#336	C₂
socle, prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#336	D₉
hypocenter	C₉	#1746
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

Complements

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

N	H ≅ G/N	type
18. #63375	C₄	semidirect
19. C₈×Dic₉	C₄	semidirect
199. C₉	#1746	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63375	2
C₂×C₈×Dic₉	2
#10588612	2
C₉×#336	2
#10588228	2
#10588200	2
#68598	3