Subgroups — C₃×#69883 #11797352

Order 1152.

341 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	C₃²×#405	C₂	1	1	yes	maximal, characteristic
2	C₃×#4549	C₂	1	2	yes	maximal
3	C₃×C₄⋊(C₃⋊C₁₆)	C₂	1	2	yes	maximal, complemented
4	C₃×#4461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2164	—	3	1	no	maximal
7	#69883	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	1	yes	characteristic
12	C₃²×#97	C₄	1	1	yes	characteristic
13	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
14	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
17	C₃×#405	—	2	1	no	—
18	C₃×#405	D₃	1	1	yes	characteristic
19	C₃×#405	C₂×C₃	1	1	yes	characteristic
20	C₃×C₄⋊C₁₆	—	3	2	no	—
21	C₃×C₂²⋊C₁₆	—	3	2	no	—
22	C₃×#346	—	3	1	no	—
23	C₃×C₄×C₁₆	—	3	1	no	—
24	#4549	C₂×C₃	1	2	yes	—
25	C₄⋊(C₃⋊C₁₆)	C₂×C₃	1	2	yes	complemented
26	#4461	C₂×C₃	1	1	yes	characteristic, complemented
27	C₄×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
29	C₃²×M₁₆	—	2	2	no	—
30	C₂×C₃²×C₈	—	2	2	no	—
31	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
35	C₃²×C₄⋊C₄	C₈	1	2	yes	—
36	C₃²×C₂²⋊C₄	C₈	1	2	yes	—
37	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
38	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
39	C₃×C₃⋊C₁₆	—	2	2	no	—
40	C₃×C₃⋊C₁₆	—	2	2	no	—
41	#2164	—	3	1	no	Sylow
42	C₂×C₃×M₁₆	—	2	1	no	—
43	C₂×C₃×M₁₆	Dic₃	1	1	yes	characteristic
44	C₂×C₃×M₁₆	C₃×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
47	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₃×#117	—	2	1	no	—
49	C₃×#117	Dic₃	1	1	yes	characteristic
50	C₃×#117	C₃×C₄	1	1	yes	characteristic
51	C₂×C₃×C₁₆	—	3	2	no	—
52	C₂×C₃×C₁₆	—	3	2	no	—
53	C₃×#97	—	2	1	no	—
54	C₃×#97	—	2	1	no	—
55	C₃×#97	Dic₃	1	1	yes	characteristic
56	C₃×#97	Dic₃	1	1	yes	characteristic
57	C₃×#97	C₃×C₄	1	1	yes	characteristic
58	C₃×#97	C₃×C₄	1	1	yes	characteristic
59	C₃×C₄×C₈	—	2	1	no	—
60	C₃×C₄×C₈	—	2	1	no	—
61	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
62	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
63	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	—
66	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	—
67	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
68	C₂×C₃²×C₄	—	2	1	no	—
69	C₂×C₃²×C₄	—	2	1	no	—
70	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
71	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
72	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
73	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
74	C₃²×C₈	—	2	1	no	—
75	C₃²×C₈	—	2	1	no	—
76	C₃²×C₈	M₁₆	1	2	yes	—
77	C₃²×C₈	#41	1	2	yes	—
78	#405	C₃×D₃	1	1	yes	characteristic
79	C₄⋊C₁₆	—	3	2	no	—
80	C₂²⋊C₁₆	—	3	2	no	—
81	#346	—	3	1	no	—
82	C₄×C₁₆	—	3	1	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	—	2	2	no	—
88	C₃×M₁₆	—	2	2	no	—
89	C₂×C₃×C₈	—	2	4	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	—	2	1	no	—
95	C₂×C₃×C₈	—	2	1	no	—
96	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
97	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
98	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
99	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
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	1	no	—
111	C₃×C₄²	—	2	1	no	—
112	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
113	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
114	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
115	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
116	C₃×C₁₆	—	6	2	no	—
117	C₃×C₁₆	—	6	2	no	—
118	C₃⋊C₁₆	—	2	2	no	—
119	C₃⋊C₁₆	—	2	2	no	—
120	C₂²×C₃²	—	2	1	no	—
121	C₂²×C₃²	—	2	2	no	—
122	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
123	C₃²×C₄	—	2	1	no	—
124	C₃²×C₄	—	2	2	no	—
125	C₃²×C₄	—	2	2	no	—
126	C₃²×C₄	#117	1	1	yes	characteristic
127	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
128	C₂×M₁₆	C₃×Dic₃	1	1	yes	characteristic
129	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
130	#117	C₃×Dic₃	1	1	yes	characteristic
131	C₂×C₁₆	—	3	2	no	—
132	C₂×C₁₆	—	3	2	no	—
133	#97	C₃×Dic₃	1	1	yes	characteristic
134	#97	C₃×Dic₃	1	1	yes	characteristic
135	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
136	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
137	C₂³×C₃	—	2	1	no	—
138	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
139	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	1	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	2	2	no	—
148	C₂×C₃×C₄	—	2	2	no	—
149	C₂×C₃×C₄	—	2	1	no	—
150	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
151	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
152	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
153	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
154	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
155	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
156	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
157	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
158	C₃×C₈	—	2	2	no	—
159	C₃×C₈	—	2	2	no	—
160	C₃×C₈	—	2	1	no	—
161	C₃×C₈	—	2	1	no	—
162	C₃×C₈	—	2	1	no	—
163	C₃×C₈	—	2	1	no	—
164	C₃×C₈	—	2	2	no	—
165	C₃×C₈	—	2	2	no	—
166	C₃×C₈	#208	1	2	yes	—
167	C₃×C₈	C₃×M₁₆	1	2	yes	—
168	C₃×C₈	#235	1	2	yes	—
169	C₃×C₈	C₃×#41	1	2	yes	—
170	C₂×C₃²	—	4	1	no	—
171	C₂×C₃²	#431	1	1	yes	characteristic
172	C₂×C₃²	#504	1	2	yes	—
173	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
174	M₁₆	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
177	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
178	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
179	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
180	C₄⋊C₄	C₃×C₃⋊C₈	1	2	yes	—
181	C₂²⋊C₄	C₃×C₃⋊C₈	1	2	yes	—
182	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
183	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
184	C₁₆	—	6	2	no	—
185	C₁₆	—	6	2	no	—
186	C₂²×C₃	—	2	2	no	—
187	C₂²×C₃	—	2	2	no	—
188	C₂²×C₃	—	2	2	no	—
189	C₂²×C₃	—	2	1	no	—
190	C₂²×C₃	—	2	1	no	—
191	C₂²×C₃	—	2	1	no	—
192	C₂²×C₃	—	4	2	no	—
193	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
194	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
195	C₃×C₄	—	2	2	no	—
196	C₃×C₄	—	2	2	no	—
197	C₃×C₄	—	2	2	no	—
198	C₃×C₄	—	2	2	no	—
199	C₃×C₄	—	2	2	no	—
200	C₃×C₄	—	2	1	no	—
201	C₃×C₄	—	2	1	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	1	no	—
204	C₃×C₄	—	4	2	no	—
205	C₃×C₄	—	4	2	no	—
206	C₃×C₄	C₂×#208	1	1	yes	characteristic
207	C₃×C₄	#926	1	1	yes	characteristic
208	C₃×C₄	C₃×#117	1	1	yes	characteristic
209	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
210	C₃²	#2164	1	1	yes	characteristic, complemented, Sylow
211	C₂³	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	C₂×C₃×C₃⋊C₈	1	2	yes	—
215	C₂×C₄	C₂×C₃×C₃⋊C₈	1	2	yes	—
216	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
217	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	C₃×#208	1	2	yes	—
221	C₈	C₃×#235	1	2	yes	—
222	C₂×C₃	—	2	1	no	—
223	C₂×C₃	—	2	2	no	—
224	C₂×C₃	—	4	2	no	—
225	C₂×C₃	—	4	1	no	—
226	C₂×C₃	—	4	1	no	—
227	C₂×C₃	#4925	1	1	yes	characteristic
228	C₂×C₃	#5140	1	2	yes	—
229	C₂×C₃	C₃×#431	1	1	yes	characteristic
230	C₂×C₃	C₃×#504	1	2	yes	—
231	C₂²	—	2	1	no	—
232	C₂²	—	2	2	no	—
233	C₂²	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
234	C₄	—	2	1	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	2	no	—
237	C₄	C₂×C₃×#208	1	1	yes	characteristic
238	C₄	C₃×#926	1	1	yes	characteristic
239	C₃	—	2	1	no	—
240	C₃	#69883	1	1	yes	characteristic, direct product factor
241	C₃	C₃×#2164	1	1	yes	characteristic, complemented
242	C₂	—	4	1	no	—
243	C₂	C₃×#4925	1	1	yes	characteristic
244	C₂	C₃×#5140	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃×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×#2164
LCS	G ▷ C₂²×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
3. C₃×C₄⋊(C₃⋊C₁₆)	C₂	semidirect
4. C₃×#4461	C₂	semidirect
5. C₃×C₄×C₃⋊C₁₆	C₂	semidirect
7. #69883	C₃	direct (N × H)
25. C₄⋊(C₃⋊C₁₆)	C₂×C₃	semidirect
26. #4461	C₂×C₃	semidirect
27. C₄×C₃⋊C₁₆	C₂×C₃	semidirect
210. C₃²	#2164	semidirect
240. C₃	#69883	direct (N × H)
241. C₃	C₃×#2164	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
C₃×#4549	2
C₃×C₄⋊(C₃⋊C₁₆)	2
C₃×#4461	2
C₃×C₄×C₃⋊C₁₆	2
C₃×#2164	3
#69883	3

Subgroups — C3×#69883 #11797352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69883 #11797352