Subgroups — #11783251

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 261 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	C₂×#63488	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10588206	C₂	1	4	yes	maximal, complemented
5	#71580	—	3	1	no	maximal
6	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₉×#117	—	2	2	no	—
8	C₉×#117	C₄	1	4	yes	complemented
9	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
11	C₂×C₄²×C₉	—	2	1	no	—
12	C₂×#3676	—	2	1	no	—
13	#63488	—	2	2	no	—
14	#63488	C₄	1	4	yes	complemented
15	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₉	—	2	1	no	—
17	C₂²×C₉⋊C₈	—	2	2	no	—
18	C₂²×C₉⋊C₈	—	2	2	no	—
19	C₂²×C₉⋊C₈	C₄	1	4	yes	complemented
20	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
21	C₂×C₃×#117	D₃	1	1	yes	characteristic
22	C₂×#926	—	3	1	no	—
23	C₂³×C₃⋊C₈	—	3	1	no	—
24	#4529	—	3	4	no	—
25	C₂⁴×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	—	2	2	no	—
27	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₉	D₄	1	2	yes	—
32	C₂²×C₄×C₉	D₄	1	2	yes	—
33	C₂²×C₄×C₉	Q₈	1	2	yes	—
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₉	—	2	2	no	—
36	C₉×C₄⋊C₄	—	2	2	no	—
37	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
38	C₉×C₂²⋊C₄	—	2	4	no	—
39	C₄²×C₉	—	2	4	no	—
40	#3676	—	2	4	no	—
41	C₄⋊Dic₉	—	2	2	no	—
42	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
43	C₄×Dic₉	—	2	4	no	—
44	C₂×C₉⋊C₈	—	2	8	no	—
45	C₂×C₉⋊C₈	—	2	2	no	—
46	C₂×C₉⋊C₈	—	2	2	no	—
47	C₂×C₉⋊C₈	C₂×C₄	1	4	yes	—
48	#1735	—	9	1	no	Sylow
49	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
50	C₃×#117	—	2	2	no	—
51	C₃×#117	Dic₃	1	4	yes	—
52	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
53	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
54	C₂×C₃×C₄²	—	2	1	no	—
55	C₂×#217	—	6	1	no	—
56	#926	—	3	4	no	—
57	#926	—	6	2	no	—
58	C₂×C₄⋊Dic₃	—	3	2	no	—
59	C₂×C₄×Dic₃	—	6	1	no	—
60	C₂²×C₃⋊C₈	—	3	4	no	—
61	C₂²×C₃⋊C₈	—	3	2	no	—
62	C₂²×C₃⋊C₈	—	6	2	no	—
63	C₂²×C₃⋊C₈	—	6	2	no	—
64	C₂³×C₉	—	2	4	no	—
65	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
66	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
67	C₂³×C₉	C₄⋊C₄	1	2	yes	—
68	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₉	—	2	4	no	—
70	C₂×C₄×C₉	—	4	4	no	—
71	C₂×C₄×C₉	C₄²	1	4	yes	—
72	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
74	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
75	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
76	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
77	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
78	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
84	C₂×Dic₉	—	2	4	no	—
85	C₂×Dic₉	—	4	4	no	—
86	C₉⋊C₈	—	2	4	no	—
87	C₂³×C₈	—	9	1	no	—
88	C₂×#117	—	9	1	no	—
89	C₂×#117	D₉	1	1	yes	characteristic
90	#340	—	9	4	no	—
91	C₂⁴×C₃	#67	1	1	yes	characteristic
92	C₂²×C₃×C₄	—	2	2	no	—
93	C₂²×C₃×C₄	Dic₆	1	2	yes	—
94	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
95	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
96	C₂²×C₃×C₄	D₁₂	1	2	yes	—
97	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
98	C₂²×C₃×C₄	#67	1	2	yes	—
99	C₂²×C₃×C₄	#67	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
101	C₂²×Dic₃	—	6	2	no	—
102	C₃×C₄⋊C₄	—	2	2	no	—
103	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
104	C₃×C₂²⋊C₄	—	2	4	no	—
105	C₃×C₄²	—	2	4	no	—
106	#217	—	6	4	no	—
107	C₄⋊Dic₃	—	3	4	no	—
108	C₄⋊Dic₃	—	6	2	no	—
109	C₄×Dic₃	—	6	4	no	—
110	C₂×C₃⋊C₈	—	3	4	no	—
111	C₂×C₃⋊C₈	—	6	8	no	—
112	C₂×C₃⋊C₈	—	6	2	no	—
113	C₂×C₃⋊C₈	—	6	2	no	—
114	C₂²×C₉	—	2	4	no	—
115	C₂²×C₉	—	2	4	no	—
116	C₂²×C₉	—	2	4	no	—
117	C₂²×C₉	#95	1	4	yes	—
118	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₉	#135	1	4	yes	—
122	C₄×C₉	—	4	4	no	—
123	C₄×C₉	#95	1	4	yes	—
124	C₄×C₉	C₂×C₄²	1	1	yes	characteristic
125	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
128	Dic₉	—	4	4	no	—
129	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
130	C₂²×C₈	—	9	4	no	—
131	C₂²×C₈	—	9	2	no	—
132	C₂²×C₈	—	18	2	no	—
133	C₂²×C₈	—	18	2	no	—
134	#117	—	2	2	no	—
135	#117	—	9	4	no	—
136	#117	—	18	2	no	—
137	#117	Dic₉	1	4	yes	complemented
138	C₂×C₄⋊C₄	—	9	2	no	—
139	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
140	C₂×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₂²⋊C₄	—	18	1	no	—
142	C₂×C₄²	—	2	1	no	—
143	C₂×C₄²	—	18	1	no	—
144	C₂³×C₃	—	2	4	no	—
145	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
146	C₂³×C₃	(C₂×D₃)⋊C₄	1	2	yes	—
147	C₂³×C₃	#217	1	2	yes	—
148	C₂³×C₃	C₂×#67	1	1	yes	characteristic
149	C₂×C₃×C₄	—	2	4	no	—
150	C₂×C₃×C₄	—	4	4	no	—
151	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
152	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
153	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
154	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
155	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
156	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
157	C₂×C₃×C₄	#217	1	2	yes	—
158	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
159	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
161	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
162	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
164	C₂×Dic₃	—	6	4	no	—
165	C₂×Dic₃	—	12	4	no	—
166	C₃⋊C₈	—	6	4	no	—
167	C₂×C₉	—	2	4	no	—
168	C₂×C₉	C₂×#95	1	1	yes	characteristic
169	C₂×C₉	#416	1	2	yes	—
170	C₂×C₉	#416	1	2	yes	—
171	C₂×C₉	#427	1	2	yes	—
172	C₂⁴	#611	1	1	yes	characteristic
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	18	2	no	—
175	C₂²×C₄	Dic₁₈	1	2	yes	—
176	C₂²×C₄	C₄×D₉	1	2	yes	—
177	C₂²×C₄	C₄×D₉	1	2	yes	—
178	C₂²×C₄	D₃₆	1	2	yes	—
179	C₂²×C₄	C₂×Dic₉	1	2	yes	—
180	C₂²×C₄	#611	1	2	yes	—
181	C₂²×C₄	#611	1	1	yes	characteristic
182	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
183	C₂×C₈	—	9	4	no	—
184	C₂×C₈	—	18	8	no	—
185	C₂×C₈	—	18	2	no	—
186	C₂×C₈	—	18	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	9	4	no	—
189	C₄⋊C₄	—	18	2	no	—
190	C₄⋊C₄	C₂×Dic₉	1	4	yes	—
191	C₂²⋊C₄	—	2	4	no	—
192	C₂²⋊C₄	—	18	4	no	—
193	C₄²	—	2	4	no	—
194	C₄²	—	18	4	no	—
195	C₂²×C₃	—	2	4	no	—
196	C₂²×C₃	—	2	4	no	—
197	C₂²×C₃	—	2	4	no	—
198	C₂²×C₃	C₃⋊#95	1	4	yes	—
199	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
200	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
201	C₂²×C₃	#950	1	4	yes	—
202	C₂²×C₃	C₂×#217	1	1	yes	characteristic
203	C₃×C₄	—	4	4	no	—
204	C₃×C₄	C₃⋊#95	1	4	yes	—
205	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
206	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
207	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
208	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
209	Dic₃	—	12	4	no	—
210	C₉	#1735	1	1	yes	characteristic, complemented, Sylow
211	C₂³	—	2	4	no	—
212	C₂³	Dic₉⋊C₄	1	2	yes	—
213	C₂³	(C₂×D₉)⋊C₄	1	2	yes	—
214	C₂³	#3676	1	2	yes	—
215	C₂³	C₂×#611	1	1	yes	characteristic
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	18	4	no	—
219	C₂×C₄	—	36	4	no	—
220	C₂×C₄	C₄×Dic₉	1	4	yes	—
221	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
222	C₂×C₄	Dic₉⋊C₄	1	4	yes	—
223	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
224	C₂×C₄	(C₂×D₉)⋊C₄	1	4	yes	—
225	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
226	C₂×C₄	#3676	1	2	yes	—
227	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
228	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
229	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
230	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
231	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
232	C₂×C₄	C₂×#611	1	1	yes	characteristic
233	C₈	—	18	4	no	—
234	C₂×C₃	—	2	4	no	—
235	C₂×C₃	#4998	1	2	yes	—
236	C₂×C₃	#5002	1	2	yes	—
237	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
238	C₂×C₃	#5233	1	2	yes	—
239	C₂²	—	2	4	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	2	4	no	—
242	C₂²	C₉⋊#95	1	4	yes	—
243	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
244	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
245	C₂²	#63513	1	4	yes	—
246	C₂²	C₂×#3676	1	1	yes	characteristic
247	C₄	—	4	4	no	—
248	C₄	—	36	4	no	—
249	C₄	C₉⋊#95	1	4	yes	—
250	C₄	C₂×C₄×Dic₉	1	1	yes	characteristic
251	C₄	C₂×Dic₉⋊C₄	1	1	yes	characteristic
252	C₄	C₂×C₄⋊Dic₉	1	1	yes	characteristic
253	C₄	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
254	C₃	#71580	1	1	yes	characteristic
255	C₂	—	2	4	no	—
256	C₂	#10588676	1	2	yes	—
257	C₂	#10588683	1	2	yes	—
258	C₂	C₂×C₉⋊#95	1	1	yes	characteristic
259	C₂	#10588917	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#611
commutator	C₄×C₉	C₂×C₄²
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#117	C₂
socle	C₂³×C₃	C₂×#67
prime radical	C₂⁴×C₃	#67
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#117	D₉
hypocenter	C₉	#1735
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
4. #10588206	C₂	semidirect
8. C₉×#117	C₄	semidirect
14. #63488	C₄	semidirect
19. C₂²×C₉⋊C₈	C₄	semidirect
137. #117	Dic₉	semidirect
210. C₉	#1735	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
C₂×#63488	2
C₂³×C₉⋊C₈	2
#10588206	2
#71580	3