Subgroups — C₃×#69791 #11786093

Order 1152.

457 conjugacy classes of subgroups.

The subgroup lattice has 187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#4924	C₂	1	2	yes	maximal
3	C₃×#4552	C₂	1	4	yes	maximal
4	C₃×#1837	—	3	1	no	maximal
5	#69791	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×C₈	C₂²	1	2	yes	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₃×#208	C₂²	1	4	yes	—
9	C₃²×C₄×C₈	C₄	1	2	yes	—
10	C₃²×C₄×C₈	C₄	1	2	yes	—
11	C₃×C₄⋊(C₃⋊C₈)	—	2	4	no	—
12	C₃×#423	—	3	2	no	—
13	C₂×C₃×C₄×C₈	—	2	1	no	—
14	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
15	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
16	#4924	C₂×C₃	1	2	yes	—
17	C₃×#341	—	3	4	no	—
18	#4552	C₂×C₃	1	4	yes	—
19	C₂²×C₃²×C₄	Q₈	1	2	yes	—
20	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
21	C₂×C₃²×C₈	—	2	4	no	—
22	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
23	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
24	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
25	C₃²×C₄²	D₄	1	2	yes	—
26	C₃×#208	—	2	8	no	—
27	C₂×C₃×C₃⋊C₈	—	2	4	no	—
28	#1837	—	3	1	no	Sylow
29	C₂×C₃×M₁₆	—	3	4	no	—
30	C₂²×C₃×C₈	—	2	2	no	—
31	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
32	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
33	C₂×C₃×C₄²	—	2	1	no	—
34	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
35	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₂×#208	C₂²×C₃	1	4	yes	—
37	C₃×C₄⋊C₈	—	6	4	no	—
38	C₃×C₄×C₈	—	2	2	no	—
39	C₃×C₄×C₈	—	2	2	no	—
40	C₃×C₄×C₈	Dic₃	1	2	yes	—
41	C₃×C₄×C₈	Dic₃	1	2	yes	—
42	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
43	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
44	C₄⋊(C₃⋊C₈)	—	2	4	no	—
45	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₃²×C₄	—	2	4	no	—
47	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
48	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
49	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
51	C₂×C₃²×C₄	#41	1	4	yes	—
52	C₃²×C₈	—	2	4	no	—
53	C₃×C₃⋊C₈	—	4	4	no	—
54	#423	—	3	2	no	—
55	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic
56	#341	—	3	4	no	—
57	C₂²×C₃×C₄	—	2	2	no	—
58	C₂²×C₃×C₄	—	2	1	no	—
59	C₂²×C₃×C₄	Dic₆	1	2	yes	—
60	C₂²×C₃×C₄	C₃×Q₈	1	2	yes	—
61	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
63	C₃×M₁₆	—	6	8	no	—
64	C₂×C₃×C₈	—	2	8	no	—
65	C₂×C₃×C₈	—	2	4	no	—
66	C₂×C₃×C₈	—	2	4	no	—
67	C₂×C₃×C₈	—	2	4	no	—
68	C₂×C₃×C₈	—	6	4	no	—
69	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
70	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
71	C₃×C₄²	—	2	2	no	—
72	C₃×C₄²	—	2	1	no	—
73	C₃×C₄²	—	2	1	no	—
74	C₃×C₄²	D₁₂	1	2	yes	—
75	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
76	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
77	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
78	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
79	C₃×C₄²	C₃×D₄	1	2	yes	—
80	#208	—	2	8	no	—
81	C₂×C₃⋊C₈	—	2	4	no	—
82	C₂²×C₃²	—	2	2	no	—
83	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₃²	#125	1	2	yes	—
85	C₃²×C₄	—	2	2	no	—
86	C₃²×C₄	#108	1	4	yes	—
87	C₃²×C₄	#117	1	2	yes	—
88	C₃²×C₄	#124	1	2	yes	—
89	C₂×M₁₆	—	3	4	no	—
90	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
91	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
92	C₄⋊C₈	—	6	4	no	—
93	C₄×C₈	C₃×Dic₃	1	2	yes	—
94	C₄×C₈	C₃×Dic₃	1	2	yes	—
95	C₂³×C₃	—	2	1	no	—
96	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
97	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
98	C₂×C₃×C₄	—	2	8	no	—
99	C₂×C₃×C₄	—	2	4	no	—
100	C₂×C₃×C₄	—	2	4	no	—
101	C₂×C₃×C₄	—	2	2	no	—
102	C₂×C₃×C₄	—	2	2	no	—
103	C₂×C₃×C₄	—	2	1	no	—
104	C₂×C₃×C₄	—	2	4	no	—
105	C₂×C₃×C₄	—	2	1	no	—
106	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
107	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
108	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
109	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
110	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
111	C₂×C₃×C₄	#235	1	4	yes	—
112	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
113	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄	C₃×#41	1	4	yes	—
116	C₃×C₈	—	2	8	no	—
117	C₃×C₈	—	2	4	no	—
118	C₃×C₈	—	2	4	no	—
119	C₃×C₈	—	12	4	no	—
120	C₃⋊C₈	—	4	4	no	—
121	C₂×C₃²	—	2	2	no	—
122	C₂×C₃²	#382	1	1	yes	characteristic
123	C₂×C₃²	C₂×#108	1	2	yes	—
124	C₂²×C₄	C₃×Dic₆	1	2	yes	—
125	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
126	M₁₆	—	6	8	no	—
127	C₂×C₈	—	2	4	no	—
128	C₂×C₈	—	6	4	no	—
129	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	—
130	C₄²	C₃×D₁₂	1	2	yes	—
131	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
132	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
133	C₂²×C₃	—	2	4	no	—
134	C₂²×C₃	—	2	2	no	—
135	C₂²×C₃	—	2	2	no	—
136	C₂²×C₃	—	2	1	no	—
137	C₂²×C₃	—	2	2	no	—
138	C₂²×C₃	#870	1	2	yes	—
139	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
140	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×C₃	C₃×#125	1	2	yes	—
142	C₃×C₄	—	2	4	no	—
143	C₃×C₄	—	2	2	no	—
144	C₃×C₄	—	2	2	no	—
145	C₃×C₄	—	2	2	no	—
146	C₃×C₄	—	2	4	no	—
147	C₃×C₄	—	2	2	no	—
148	C₃×C₄	#819	1	4	yes	—
149	C₃×C₄	C₃×#108	1	4	yes	—
150	C₃×C₄	#875	1	2	yes	—
151	C₃×C₄	#926	1	2	yes	—
152	C₃×C₄	C₃×#117	1	2	yes	—
153	C₃×C₄	C₃×#124	1	2	yes	—
154	C₃²	#1837	1	1	yes	characteristic, complemented, Sylow
155	C₂³	C₂×C₃×Dic₆	1	1	yes	characteristic
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
158	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
159	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
160	C₂×C₄	C₃×#235	1	4	yes	—
161	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
162	C₈	—	2	4	no	—
163	C₈	—	12	4	no	—
164	C₂×C₃	—	2	4	no	—
165	C₂×C₃	—	2	2	no	—
166	C₂×C₃	—	2	2	no	—
167	C₂×C₃	—	2	1	no	—
168	C₂×C₃	—	2	2	no	—
169	C₂×C₃	#4936	1	1	yes	characteristic
170	C₂×C₃	C₂×#819	1	2	yes	—
171	C₂×C₃	C₃×#382	1	1	yes	characteristic
172	C₂×C₃	C₂×C₃×#108	1	2	yes	—
173	C₂²	—	2	2	no	—
174	C₂²	C₃×#870	1	2	yes	—
175	C₂²	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	C₃×#819	1	4	yes	—
178	C₄	C₃×#875	1	2	yes	—
179	C₄	C₃×#926	1	2	yes	—
180	C₃	—	2	1	no	—
181	C₃	#69791	1	1	yes	characteristic, direct product factor
182	C₃	C₃×#1837	1	1	yes	characteristic, complemented
183	C₂	—	2	2	no	—
184	C₂	C₃×#4936	1	1	yes	characteristic
185	C₂	C₂×C₃×#819	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃²	C₂×Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#1837
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #69791	C₃	direct (N × H)
154. C₃²	#1837	semidirect
181. C₃	#69791	direct (N × H)
182. C₃	C₃×#1837	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×C₈	2
C₃×#4924	2
C₃×#4552	2
C₃×#1837	3
#69791	3

Subgroups — C3×#69791 #11786093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69791 #11786093