Subgroups — C₃×#69881 #11795880

Order 1152.

433 conjugacy classes of subgroups.

The subgroup lattice has 237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#4461	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	C₃×#2108	—	3	1	no	maximal
7	#69881	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×M₁₆	C₄	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₃²×#117	C₄	1	1	yes	characteristic
11	C₃²×#97	C₄	1	2	yes	—
12	C₃²×C₄×C₈	C₂²	1	2	yes	—
13	C₃×#812	C₄	1	4	yes	complemented
14	C₂×C₃×C₃⋊C₁₆	C₄	1	4	yes	complemented
15	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×M₃₂	—	3	1	no	—
19	C₂²×C₃×C₁₆	—	3	1	no	—
20	C₃×#405	—	2	1	no	—
21	C₃×#405	D₃	1	1	yes	characteristic
22	C₃×#405	C₂×C₃	1	1	yes	characteristic
23	C₂×#812	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic
25	C₃×#346	—	3	2	no	—
26	C₃×C₄×C₁₆	—	3	2	no	—
27	#4461	C₂×C₃	1	2	yes	complemented
28	C₄×C₃⋊C₁₆	C₂×C₃	1	2	yes	complemented
29	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
30	C₃²×M₁₆	C₈	1	4	yes	—
31	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
33	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
34	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
35	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
36	C₃²×C₄⋊C₄	C₈	1	2	yes	—
37	C₃²×C₂²⋊C₄	C₈	1	2	yes	—
38	C₃²×C₄²	C₂×C₄	1	2	yes	—
39	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
40	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
41	C₃×C₃⋊C₁₆	C₂×C₄	1	4	yes	—
42	#2108	—	3	1	no	Sylow
43	C₂×C₃×M₁₆	—	2	1	no	—
44	C₂×C₃×M₁₆	Dic₃	1	1	yes	characteristic
45	C₂×C₃×M₁₆	C₃×C₄	1	1	yes	characteristic
46	C₂²×C₃×C₈	—	2	1	no	—
47	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
48	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
49	C₃×#117	—	2	1	no	—
50	C₃×#117	Dic₃	1	1	yes	characteristic
51	C₃×#117	C₃×C₄	1	1	yes	characteristic
52	C₃×M₃₂	—	3	4	no	—
53	C₂×C₃×C₁₆	—	3	4	no	—
54	C₂×C₃×C₁₆	—	3	1	no	—
55	C₂×C₃×C₁₆	—	3	1	no	—
56	C₂×C₃×C₁₆	—	3	2	no	—
57	C₃×#97	—	2	2	no	—
58	C₃×#97	Dic₃	1	2	yes	—
59	C₃×#97	C₃×C₄	1	2	yes	—
60	C₃×C₄×C₈	—	2	2	no	—
61	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
62	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
63	#812	C₃×C₄	1	4	yes	complemented
64	C₂×C₃⋊C₁₆	C₃×C₄	1	4	yes	complemented
65	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	—
67	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
69	C₂×C₃²×C₄	C₄²	1	2	yes	—
70	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
71	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
72	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
73	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
74	C₃²×C₈	C₄²	1	2	yes	—
75	C₃²×C₈	C₂×C₈	1	4	yes	—
76	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
77	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
78	C₂×M₃₂	—	3	1	no	—
79	C₂²×C₁₆	—	3	1	no	—
80	#405	C₃×D₃	1	1	yes	characteristic
81	#346	—	3	2	no	—
82	C₄×C₁₆	—	3	2	no	—
83	C₂²×C₃×C₄	—	2	1	no	—
84	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
85	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
86	C₃×M₁₆	—	2	4	no	—
87	C₃×M₁₆	C₃⋊C₈	1	4	yes	—
88	C₃×M₁₆	C₃×C₈	1	4	yes	—
89	C₂×C₃×C₈	—	2	2	no	—
90	C₂×C₃×C₈	—	2	2	no	—
91	C₂×C₃×C₈	—	2	2	no	—
92	C₂×C₃×C₈	—	2	1	no	—
93	C₂×C₃×C₈	—	2	1	no	—
94	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
95	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
96	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
97	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
98	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
99	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
100	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
102	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
103	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
104	C₃×C₄⋊C₄	—	2	2	no	—
105	C₃×C₄⋊C₄	C₃⋊C₈	1	2	yes	—
106	C₃×C₄⋊C₄	C₃×C₈	1	2	yes	—
107	C₃×C₂²⋊C₄	—	2	2	no	—
108	C₃×C₂²⋊C₄	C₃⋊C₈	1	2	yes	—
109	C₃×C₂²⋊C₄	C₃×C₈	1	2	yes	—
110	C₃×C₄²	—	2	2	no	—
111	C₃×C₄²	C₂×Dic₃	1	2	yes	—
112	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
113	C₃×C₁₆	—	3	2	no	—
114	C₃×C₁₆	—	3	2	no	—
115	C₃×C₁₆	—	3	4	no	—
116	C₃⋊C₁₆	C₂×C₃×C₄	1	2	yes	—
117	C₃⋊C₁₆	C₂×C₃×C₄	1	2	yes	—
118	C₃⋊C₁₆	C₂×C₃×C₄	1	4	yes	—
119	C₂²×C₃²	—	2	2	no	—
120	C₂²×C₃²	C₄×C₈	1	2	yes	—
121	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
122	C₃²×C₄	—	2	4	no	—
123	C₃²×C₄	C₄×C₈	1	2	yes	—
124	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
125	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
126	C₂×M₁₆	C₃×Dic₃	1	1	yes	characteristic
127	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
128	#117	C₃×Dic₃	1	1	yes	characteristic
129	M₃₂	—	3	4	no	—
130	C₂×C₁₆	—	3	4	no	—
131	C₂×C₁₆	—	3	1	no	—
132	C₂×C₁₆	—	3	2	no	—
133	C₂×C₁₆	—	3	1	no	—
134	#97	C₃×Dic₃	1	2	yes	—
135	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
136	C₂³×C₃	—	2	1	no	—
137	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
138	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
139	C₂×C₃×C₄	—	2	1	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	2	4	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	C₂×C₃⋊C₈	1	4	yes	—
145	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
146	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
147	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
148	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
149	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	—
150	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
151	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
152	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
153	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
154	C₃×C₈	—	2	4	no	—
155	C₃×C₈	—	2	2	no	—
156	C₃×C₈	—	2	1	no	—
157	C₃×C₈	—	2	1	no	—
158	C₃×C₈	C₂×C₃⋊C₈	1	4	yes	—
159	C₃×C₈	C₄×Dic₃	1	2	yes	—
160	C₃×C₈	C₃×C₄²	1	2	yes	—
161	C₃×C₈	C₂×C₃×C₈	1	4	yes	—
162	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
163	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
164	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
165	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
166	C₂×C₃²	—	2	2	no	—
167	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
168	C₂×C₃²	#504	1	2	yes	—
169	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
170	M₁₆	C₃×C₃⋊C₈	1	4	yes	—
171	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
172	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
173	C₂×C₈	C₂×C₃×Dic₃	1	2	yes	—
174	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
175	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
176	C₄⋊C₄	C₃×C₃⋊C₈	1	2	yes	—
177	C₂²⋊C₄	C₃×C₃⋊C₈	1	2	yes	—
178	C₄²	C₂×C₃×Dic₃	1	2	yes	—
179	C₁₆	—	3	2	no	—
180	C₁₆	—	3	2	no	—
181	C₁₆	—	3	4	no	—
182	C₂²×C₃	—	2	2	no	—
183	C₂²×C₃	—	2	2	no	—
184	C₂²×C₃	—	2	1	no	—
185	C₂²×C₃	—	2	2	no	—
186	C₂²×C₃	—	4	2	no	—
187	C₂²×C₃	C₄×C₃⋊C₈	1	2	yes	—
188	C₂²×C₃	C₃×C₄×C₈	1	2	yes	—
189	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
190	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
191	C₃×C₄	—	2	4	no	—
192	C₃×C₄	—	2	4	no	—
193	C₃×C₄	—	2	1	no	—
194	C₃×C₄	—	2	1	no	—
195	C₃×C₄	—	2	2	no	—
196	C₃×C₄	—	4	4	no	—
197	C₃×C₄	C₄×C₃⋊C₈	1	2	yes	—
198	C₃×C₄	C₃×C₄×C₈	1	2	yes	—
199	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
200	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
201	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
202	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
203	C₃²	#2108	1	1	yes	characteristic, complemented, Sylow
204	C₂³	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
205	C₂×C₄	C₂×C₃×C₃⋊C₈	1	4	yes	—
206	C₂×C₄	C₂×C₃×C₃⋊C₈	1	2	yes	—
207	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
208	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
209	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
210	C₈	C₂×C₃×C₃⋊C₈	1	4	yes	—
211	C₈	C₃×C₄×Dic₃	1	2	yes	—
212	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
213	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
214	C₂×C₃	—	2	2	no	—
215	C₂×C₃	—	2	2	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	2	2	no	—
218	C₂×C₃	—	4	2	no	—
219	C₂×C₃	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
220	C₂×C₃	#5140	1	2	yes	—
221	C₂×C₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
222	C₂×C₃	C₃×#504	1	2	yes	—
223	C₂²	—	2	2	no	—
224	C₂²	C₃×C₄×C₃⋊C₈	1	2	yes	—
225	C₂²	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
226	C₄	—	2	4	no	—
227	C₄	C₃×C₄×C₃⋊C₈	1	2	yes	—
228	C₄	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
229	C₄	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
230	C₃	—	2	1	no	—
231	C₃	#69881	1	1	yes	characteristic, direct product factor
232	C₃	C₃×#2108	1	1	yes	characteristic, complemented
233	C₂	—	2	2	no	—
234	C₂	C₂×C₃×C₄×C₃⋊C₈	1	1	yes	characteristic
235	C₂	C₃×#5140	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂×C₃	C₂×C₃×C₄×C₈
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂³×C₃²	C₂×C₈
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2108
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
4. C₃×#4461	C₂	semidirect
5. C₃×C₄×C₃⋊C₁₆	C₂	semidirect
7. #69881	C₃	direct (N × H)
13. C₃×#812	C₄	semidirect
14. C₂×C₃×C₃⋊C₁₆	C₄	semidirect
27. #4461	C₂×C₃	semidirect
28. C₄×C₃⋊C₁₆	C₂×C₃	semidirect
63. #812	C₃×C₄	semidirect
64. C₂×C₃⋊C₁₆	C₃×C₄	semidirect
203. C₃²	#2108	semidirect
231. C₃	#69881	direct (N × H)
232. C₃	C₃×#2108	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#405	2
C₂×C₃×#812	2
C₂²×C₃×C₃⋊C₁₆	2
C₃×#4461	2
C₃×C₄×C₃⋊C₁₆	2
C₃×#2108	3
#69881	3

Subgroups — C3×#69881 #11795880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69881 #11795880