Subgroups — C₃×#67661 #11770822

Order 1152.

377 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₃×#4925	C₂	1	2	yes	maximal
3	C₃×#1281	—	3	1	no	maximal
4	#67661	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃²×C₈	C₄	1	2	yes	—
6	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
7	C₃²×#97	—	2	2	no	—
8	C₃×#830	C₄	1	4	yes	—
9	C₃×C₄⋊(C₃⋊C₈)	—	2	2	no	—
10	C₃×C₄×C₃⋊C₈	—	2	2	no	—
11	C₃×#431	—	3	2	no	—
12	C₂×C₃×#97	—	2	1	no	—
13	C₂×C₃×#97	D₃	1	1	yes	characteristic
14	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
15	#4925	C₂×C₃	1	2	yes	—
16	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
17	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₈	—	2	2	no	—
19	C₂×C₃²×C₈	—	2	2	no	—
20	C₂×C₃²×C₈	C₈	1	4	yes	complemented
21	C₃²×C₄²	D₄	1	1	yes	characteristic
22	C₃²×C₄²	D₄	1	2	yes	—
23	C₃²×C₄²	Q₈	1	1	yes	characteristic
24	C₂×C₃×C₃⋊C₈	—	2	4	no	—
25	#1281	—	3	1	no	Sylow
26	C₂²×C₃×C₈	—	2	2	no	—
27	C₂²×C₃×C₈	Dic₃	1	2	yes	—
28	C₂²×C₃×C₈	C₃×C₄	1	2	yes	—
29	C₂×C₃×C₄²	—	2	1	no	—
30	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
32	C₃×C₄⋊C₈	—	6	2	no	—
33	C₃×C₂²⋊C₈	—	3	4	no	—
34	C₃×#97	—	2	4	no	—
35	C₃×#97	—	2	2	no	—
36	C₃×#97	—	2	2	no	—
37	C₃×C₄×C₈	—	6	2	no	—
38	#830	C₃×C₄	1	4	yes	—
39	C₄⋊(C₃⋊C₈)	—	2	2	no	—
40	C₄×C₃⋊C₈	—	2	2	no	—
41	C₂³×C₃²	C₄²	1	1	yes	characteristic
42	C₂×C₃²×C₄	—	4	2	no	—
43	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
44	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
46	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
48	C₂×C₃²×C₄	M₁₆	1	2	yes	—
49	C₃²×C₈	—	2	4	no	—
50	C₃×C₃⋊C₈	—	4	4	no	—
51	#431	—	3	2	no	—
52	C₂×#97	C₃×D₃	1	1	yes	characteristic
53	C₂²×C₃×C₄	—	2	2	no	—
54	C₂²×C₃×C₄	—	2	1	no	—
55	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
56	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
57	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
58	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
59	C₂×C₃×C₈	—	2	4	no	—
60	C₂×C₃×C₈	—	2	4	no	—
61	C₂×C₃×C₈	—	2	2	no	—
62	C₂×C₃×C₈	—	2	2	no	—
63	C₂×C₃×C₈	—	2	2	no	—
64	C₂×C₃×C₈	—	2	2	no	—
65	C₂×C₃×C₈	—	2	4	no	—
66	C₂×C₃×C₈	—	6	4	no	—
67	C₂×C₃×C₈	C₃⋊C₈	1	4	yes	complemented
68	C₂×C₃×C₈	C₃×C₈	1	4	yes	complemented
69	C₃×C₄²	—	2	1	no	—
70	C₃×C₄²	—	2	1	no	—
71	C₃×C₄²	—	2	2	no	—
72	C₃×C₄²	Dic₆	1	1	yes	characteristic
73	C₃×C₄²	D₁₂	1	1	yes	characteristic
74	C₃×C₄²	#67	1	2	yes	—
75	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
76	C₃×C₄²	C₃×D₄	1	2	yes	—
77	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
78	C₂×C₃⋊C₈	—	2	4	no	—
79	C₂²×C₃²	—	2	2	no	—
80	C₂²×C₃²	#95	1	1	yes	characteristic
81	C₂²×C₃²	C₄×C₈	1	1	yes	characteristic
82	C₂²×C₃²	#97	1	1	yes	characteristic
83	C₃²×C₄	—	2	2	no	—
84	C₃²×C₄	—	2	2	no	—
85	C₃²×C₄	C₂²⋊C₈	1	2	yes	—
86	C₃²×C₄	C₄⋊C₈	1	2	yes	—
87	C₂²×C₈	C₃×Dic₃	1	2	yes	—
88	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
89	C₄⋊C₈	—	6	2	no	—
90	C₂²⋊C₈	—	3	4	no	—
91	#97	—	2	2	no	—
92	C₄×C₈	—	6	2	no	—
93	C₂³×C₃	—	2	1	no	—
94	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
95	C₂³×C₃	C₃×C₄²	1	1	yes	characteristic
96	C₂×C₃×C₄	—	2	2	no	—
97	C₂×C₃×C₄	—	2	2	no	—
98	C₂×C₃×C₄	—	2	2	no	—
99	C₂×C₃×C₄	—	2	1	no	—
100	C₂×C₃×C₄	—	2	2	no	—
101	C₂×C₃×C₄	—	2	1	no	—
102	C₂×C₃×C₄	—	4	2	no	—
103	C₂×C₃×C₄	—	4	2	no	—
104	C₂×C₃×C₄	—	4	4	no	—
105	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
106	C₂×C₃×C₄	#208	1	2	yes	—
107	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
108	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
109	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
110	C₂×C₃×C₄	#217	1	1	yes	characteristic
111	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
112	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
114	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
116	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
117	C₃×C₈	—	2	8	no	—
118	C₃×C₈	—	2	4	no	—
119	C₃×C₈	—	2	4	no	—
120	C₃×C₈	—	12	4	no	—
121	C₃⋊C₈	—	4	4	no	—
122	C₂×C₃²	—	2	1	no	—
123	C₂×C₃²	—	2	1	no	—
124	C₂×C₃²	#336	1	1	yes	characteristic
125	C₂×C₃²	#344	1	2	yes	—
126	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
127	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	6	4	no	—
131	C₂×C₈	C₃×C₃⋊C₈	1	4	yes	complemented
132	C₄²	C₃×Dic₆	1	1	yes	characteristic
133	C₄²	C₃×D₁₂	1	1	yes	characteristic
134	C₄²	C₃×#67	1	2	yes	—
135	C₂²×C₃	—	2	4	no	—
136	C₂²×C₃	—	2	2	no	—
137	C₂²×C₃	—	2	2	no	—
138	C₂²×C₃	—	2	1	no	—
139	C₂²×C₃	—	2	1	no	—
140	C₂²×C₃	—	2	1	no	—
141	C₂²×C₃	C₄×C₃⋊C₈	1	1	yes	characteristic
142	C₂²×C₃	#803	1	1	yes	characteristic
143	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
144	C₂²×C₃	C₃×#95	1	1	yes	characteristic
145	C₂²×C₃	C₃×C₄×C₈	1	1	yes	characteristic
146	C₂²×C₃	C₃×#97	1	1	yes	characteristic
147	C₃×C₄	—	2	2	no	—
148	C₃×C₄	—	2	2	no	—
149	C₃×C₄	—	2	2	no	—
150	C₃×C₄	—	2	2	no	—
151	C₃×C₄	—	2	2	no	—
152	C₃×C₄	—	2	2	no	—
153	C₃×C₄	—	4	2	no	—
154	C₃×C₄	—	4	2	no	—
155	C₃×C₄	C₄⋊(C₃⋊C₈)	1	2	yes	—
156	C₃×C₄	#830	1	2	yes	—
157	C₃×C₄	C₃×C₂²⋊C₈	1	2	yes	—
158	C₃×C₄	C₃×C₄⋊C₈	1	2	yes	—
159	C₃²	#1281	1	1	yes	characteristic, complemented, Sylow
160	C₂³	C₃×C₄×Dic₃	1	1	yes	characteristic
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	C₂×C₃×C₃⋊C₈	1	2	yes	—
163	C₂×C₄	C₃×#208	1	2	yes	—
164	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
165	C₂×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
166	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
167	C₂×C₄	C₃×#217	1	1	yes	characteristic
168	C₈	—	2	4	no	—
169	C₈	—	12	4	no	—
170	C₂×C₃	—	2	2	no	—
171	C₂×C₃	—	2	2	no	—
172	C₂×C₃	—	2	1	no	—
173	C₂×C₃	—	2	1	no	—
174	C₂×C₃	—	2	1	no	—
175	C₂×C₃	—	2	1	no	—
176	C₂×C₃	—	2	1	no	—
177	C₂×C₃	—	2	2	no	—
178	C₂×C₃	#4524	1	1	yes	characteristic
179	C₂×C₃	#4556	1	2	yes	—
180	C₂×C₃	C₃×#336	1	1	yes	characteristic
181	C₂×C₃	C₃×#344	1	2	yes	—
182	C₂²	—	2	2	no	—
183	C₂²	C₃×C₄×C₃⋊C₈	1	1	yes	characteristic
184	C₂²	C₃×#803	1	1	yes	characteristic
185	C₂²	C₃×C₃⋊#95	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	C₃×C₄⋊(C₃⋊C₈)	1	2	yes	—
189	C₄	C₃×#830	1	2	yes	—
190	C₃	—	2	1	no	—
191	C₃	#67661	1	1	yes	characteristic, direct product factor
192	C₃	C₃×#1281	1	1	yes	characteristic, complemented
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	C₃×#4524	1	1	yes	characteristic
196	C₂	C₃×#4556	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	#217
commutator	C₂²×C₃	C₃×C₄×C₈
Frattini	C₂×C₄²	C₂×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄²
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₃×#1281
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
4. #67661	C₃	direct (N × H)
20. C₂×C₃²×C₈	C₈	semidirect
67. C₂×C₃×C₈	C₃⋊C₈	semidirect
68. C₂×C₃×C₈	C₃×C₈	semidirect
131. C₂×C₈	C₃×C₃⋊C₈	semidirect
159. C₃²	#1281	semidirect
191. C₃	#67661	direct (N × H)
192. C₃	C₃×#1281	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#97	2
C₃×#4925	2
C₃×#1281	3
#67661	3

Subgroups — C3×#67661 #11770822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67661 #11770822