Subgroups — C₃×#69074 #11797355

Order 1152.

303 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#4689	C₂	1	1	yes	maximal, characteristic
2	C₃²×#346	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₂×D₃)⋊C₁₆	C₂	1	2	yes	maximal
4	C₃×Dic₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2164	—	3	1	no	maximal
7	#69074	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
9	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
10	C₃×#872	C₄	1	1	yes	characteristic
11	C₂×C₃²×C₁₆	C₂²	1	2	yes	—
12	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
13	C₃×#815	C₄	1	1	yes	characteristic
14	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
16	C₃×#803	C₄	1	1	yes	characteristic
17	C₃×#405	—	3	1	no	—
18	#4689	C₂×C₃	1	1	yes	characteristic
19	C₃×C₄⋊C₁₆	—	3	2	no	—
20	C₃×C₂²⋊C₁₆	—	3	2	no	—
21	C₃×#346	—	2	1	no	—
22	C₃×#346	D₃	1	1	yes	characteristic, complemented
23	C₃×#346	C₂×C₃	1	1	yes	characteristic, complemented
24	C₃×C₄×C₁₆	—	3	1	no	—
25	(C₂×D₃)⋊C₁₆	C₂×C₃	1	2	yes	—
26	Dic₃⋊C₁₆	C₂×C₃	1	2	yes	complemented
27	C₄×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
31	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
32	C₃×(C₂×D₃)⋊C₄	C₈	1	2	yes	—
33	C₃×Dic₃⋊C₄	C₈	1	2	yes	—
34	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
38	C₃×D₃×C₈	—	2	2	no	—
39	C₃²×C₁₆	—	2	2	no	—
40	C₃×C₃⋊C₁₆	—	2	2	no	—
41	#2164	—	3	1	no	Sylow
42	C₂×C₃×M₁₆	—	3	1	no	—
43	C₂²×C₃×C₈	—	3	1	no	—
44	C₃×#117	—	3	1	no	—
45	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	1	yes	characteristic
46	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
47	#872	C₃×C₄	1	1	yes	characteristic
48	C₂×C₃×C₁₆	—	2	2	no	—
49	C₂×C₃×C₁₆	—	3	2	no	—
50	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
51	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	—
52	C₃×#97	—	3	1	no	—
53	C₃×#97	—	3	1	no	—
54	C₃×C₄×C₈	—	2	1	no	—
55	C₃×C₄×C₈	—	3	1	no	—
56	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
57	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
58	#815	C₃×C₄	1	1	yes	characteristic
59	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	—
61	#803	C₃×C₄	1	1	yes	characteristic
62	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
63	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
64	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃×Dic₃	C₂×C₈	1	2	yes	—
66	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
67	C₃×C₄×D₃	—	2	1	no	—
68	C₃×C₄×D₃	—	2	1	no	—
69	C₃²×C₈	M₁₆	1	2	yes	—
70	C₃²×C₈	#41	1	2	yes	—
71	C₃×C₃⋊C₈	—	2	1	no	—
72	C₃×C₃⋊C₈	—	2	1	no	—
73	#405	—	3	1	no	—
74	C₄⋊C₁₆	—	3	2	no	—
75	C₂²⋊C₁₆	—	3	2	no	—
76	#346	C₃×D₃	1	1	yes	characteristic, complemented
77	C₄×C₁₆	—	3	1	no	—
78	C₂²×C₃×C₄	—	3	1	no	—
79	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
80	C₃×M₁₆	—	6	2	no	—
81	C₂×C₃×C₈	—	2	1	no	—
82	C₂×C₃×C₈	—	2	1	no	—
83	C₂×C₃×C₈	—	3	1	no	—
84	C₂×C₃×C₈	—	3	1	no	—
85	C₂×C₃×C₈	—	6	2	no	—
86	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
87	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
88	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
89	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
90	C₃×C₄⋊C₄	—	3	2	no	—
91	C₃×C₂²⋊C₄	—	3	2	no	—
92	C₃×C₄²	—	2	1	no	—
93	C₃×C₄²	—	3	1	no	—
94	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
95	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
96	(C₂×D₃)⋊C₄	C₃×C₈	1	2	yes	—
97	Dic₃⋊C₄	C₃×C₈	1	2	yes	—
98	C₄×Dic₃	C₂×C₃×C₄	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	ΓL(1,𝔽₂₅)	—	2	2	no	—
102	D₃×C₈	—	2	2	no	—
103	C₃×C₁₆	—	2	4	no	—
104	C₃×C₁₆	—	2	2	no	—
105	C₃×C₁₆	—	2	2	no	—
106	C₃×C₁₆	—	6	2	no	—
107	C₃⋊C₁₆	—	2	2	no	—
108	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
109	C₂×C₃×D₃	—	2	1	no	—
110	C₂×C₃×D₃	—	2	2	no	—
111	C₃²×C₄	—	2	2	no	—
112	C₃²×C₄	#117	1	1	yes	characteristic
113	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
114	C₃×Dic₃	—	2	1	no	—
115	C₃×Dic₃	—	2	2	no	—
116	C₂×M₁₆	—	3	1	no	—
117	C₂²×C₈	—	3	1	no	—
118	#117	—	3	1	no	—
119	C₂×C₁₆	—	3	2	no	—
120	C₂×C₁₆	C₂×C₃×D₃	1	2	yes	—
121	#97	—	3	1	no	—
122	#97	—	3	1	no	—
123	C₄×C₈	—	3	1	no	—
124	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
125	C₂³×C₃	—	3	1	no	—
126	C₂²×D₃	C₂×C₃×C₈	1	1	yes	characteristic
127	C₂×C₃×C₄	—	2	2	no	—
128	C₂×C₃×C₄	—	2	1	no	—
129	C₂×C₃×C₄	—	3	2	no	—
130	C₂×C₃×C₄	—	3	1	no	—
131	C₂×C₃×C₄	—	6	1	no	—
132	C₂×C₃×C₄	—	6	1	no	—
133	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
134	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
135	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
137	C₂×Dic₃	C₂×C₃×C₈	1	2	yes	—
138	C₂×Dic₃	C₂×C₃×C₈	1	1	yes	characteristic
139	C₄×D₃	—	2	1	no	—
140	C₄×D₃	—	2	1	no	—
141	C₃×C₈	—	2	2	no	—
142	C₃×C₈	—	2	2	no	—
143	C₃×C₈	—	6	1	no	—
144	C₃×C₈	—	6	1	no	—
145	C₃×C₈	ΓL(1,𝔽₂₅)	1	2	yes	—
146	C₃×C₈	C₃×M₁₆	1	2	yes	—
147	C₃×C₈	#235	1	2	yes	—
148	C₃×C₈	C₃×#41	1	2	yes	—
149	C₃⋊C₈	—	2	1	no	—
150	C₃⋊C₈	—	2	1	no	—
151	C₂×C₃²	#431	1	1	yes	characteristic
152	C₂×C₃²	#504	1	2	yes	—
153	C₃×D₃	—	4	1	no	—
154	C₂²×C₄	—	3	1	no	—
155	M₁₆	—	6	2	no	—
156	C₂×C₈	—	3	1	no	—
157	C₂×C₈	—	3	1	no	—
158	C₂×C₈	—	6	2	no	—
159	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
160	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
161	C₄⋊C₄	—	3	2	no	—
162	C₂²⋊C₄	—	3	2	no	—
163	C₄²	—	3	1	no	—
164	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
165	C₁₆	—	2	2	no	—
166	C₁₆	—	6	2	no	—
167	C₂²×C₃	—	2	1	no	—
168	C₂²×C₃	—	6	2	no	—
169	C₂²×C₃	—	6	1	no	—
170	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
171	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
172	C₂×D₃	—	2	2	no	—
173	C₂×D₃	—	2	1	no	—
174	C₃×C₄	—	2	2	no	—
175	C₃×C₄	—	2	2	no	—
176	C₃×C₄	—	2	1	no	—
177	C₃×C₄	—	2	1	no	—
178	C₃×C₄	—	4	2	no	—
179	C₃×C₄	—	6	2	no	—
180	C₃×C₄	—	6	1	no	—
181	C₃×C₄	#872	1	1	yes	characteristic
182	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
183	C₃×C₄	C₃×#117	1	1	yes	characteristic
184	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
185	Dic₃	—	2	2	no	—
186	Dic₃	—	2	1	no	—
187	C₃²	#2164	1	1	yes	characteristic, complemented, Sylow
188	C₂³	—	3	1	no	—
189	C₂×C₄	—	3	2	no	—
190	C₂×C₄	—	3	1	no	—
191	C₂×C₄	—	6	1	no	—
192	C₂×C₄	—	6	1	no	—
193	C₂×C₄	C₃×D₃×C₈	1	2	yes	—
194	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
195	C₈	—	6	1	no	—
196	C₈	—	6	1	no	—
197	C₈	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
198	C₈	C₃×#235	1	2	yes	—
199	C₂×C₃	—	2	2	no	—
200	C₂×C₃	—	2	1	no	—
201	C₂×C₃	—	12	1	no	—
202	C₂×C₃	#4685	1	1	yes	characteristic
203	C₂×C₃	#4907	1	2	yes	—
204	C₂×C₃	C₃×#431	1	1	yes	characteristic
205	C₂×C₃	C₃×#504	1	2	yes	—
206	D₃	—	4	1	no	—
207	C₂²	—	6	2	no	—
208	C₂²	—	6	1	no	—
209	C₂²	C₂×C₃×D₃×C₈	1	1	yes	characteristic
210	C₄	—	2	2	no	—
211	C₄	—	6	2	no	—
212	C₄	—	6	1	no	—
213	C₄	C₃×#872	1	1	yes	characteristic
214	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
215	C₃	—	2	1	no	—
216	C₃	#69074	1	1	yes	characteristic, direct product factor
217	C₃	C₃×#2164	1	1	yes	characteristic, complemented
218	C₂	—	12	1	no	—
219	C₂	C₃×#4685	1	1	yes	characteristic
220	C₂	C₃×#4907	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×#346	C₂
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂²×C₃×D₃	C₂×C₈
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₃×#346	D₃
hypocenter	C₃	C₃×#2164
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×#346

Complements

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

N	H ≅ G/N	type
2. C₃²×#346	C₂	semidirect
4. C₃×Dic₃⋊C₁₆	C₂	semidirect
5. C₃×C₄×C₃⋊C₁₆	C₂	semidirect
7. #69074	C₃	direct (N × H)
22. C₃×#346	D₃	semidirect
23. C₃×#346	C₂×C₃	semidirect
26. Dic₃⋊C₁₆	C₂×C₃	semidirect
27. C₄×C₃⋊C₁₆	C₂×C₃	semidirect
76. #346	C₃×D₃	semidirect
187. C₃²	#2164	semidirect
216. C₃	#69074	direct (N × H)
217. 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
C₃×#4689	2
C₃²×#346	2
C₃×(C₂×D₃)⋊C₁₆	2
C₃×Dic₃⋊C₁₆	2
C₃×C₄×C₃⋊C₁₆	2
C₃×#2164	3
#69074	3

Subgroups — C3×#69074 #11797355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69074 #11797355