Subgroups — C₃×#69763 #11786051

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 175 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×#4936	C₂	1	2	yes	maximal
3	C₃×#4551	C₂	1	4	yes	maximal
4	C₃×#1835	—	3	1	no	maximal
5	#69763	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×C₄⋊Dic₃	C₂²	1	4	yes	—
9	C₃²×C₄×C₈	C₄	1	4	yes	complemented
10	C₃×C₃⋊#95	—	2	4	no	—
11	C₂×C₃×C₄×C₈	—	2	1	no	—
12	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
13	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
14	C₃×#382	—	3	2	no	—
15	#4936	C₂×C₃	1	2	yes	—
16	C₃×#340	—	3	4	no	—
17	#4551	C₂×C₃	1	4	yes	—
18	C₂²×C₃²×C₄	D₄	1	2	yes	—
19	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
20	C₂²×C₃×Dic₃	—	2	4	no	—
21	C₂×C₃²×C₈	—	2	4	no	—
22	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
23	C₃²×C₄²	C₂×C₄	1	2	yes	—
24	C₃²×C₄²	Q₈	1	2	yes	—
25	C₃×C₄⋊Dic₃	—	2	8	no	—
26	#1835	—	3	1	no	Sylow
27	C₂²×C₃×C₈	—	2	2	no	—
28	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
29	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
30	C₂×C₃×C₄⋊C₄	—	3	4	no	—
31	C₂×C₃×C₄²	—	2	1	no	—
32	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
33	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
35	C₃×C₄×C₈	—	2	4	no	—
36	C₃×C₄×C₈	Dic₃	1	4	yes	complemented
37	C₃×C₄×C₈	C₃×C₄	1	4	yes	complemented
38	C₃×#95	—	6	4	no	—
39	C₃⋊#95	—	2	4	no	—
40	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃²×C₄	—	2	4	no	—
42	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
43	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₃²×C₄	#41	1	4	yes	—
46	C₂×C₃×Dic₃	—	4	4	no	—
47	C₂×C₃×Dic₃	—	4	8	no	—
48	C₃²×C₈	—	2	4	no	—
49	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic
50	#382	—	3	2	no	—
51	#340	—	3	4	no	—
52	C₂²×C₃×C₄	—	2	2	no	—
53	C₂²×C₃×C₄	—	2	1	no	—
54	C₂²×C₃×C₄	—	6	4	no	—
55	C₂²×C₃×C₄	D₁₂	1	2	yes	—
56	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
57	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
58	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
59	C₂²×Dic₃	—	2	4	no	—
60	C₂×C₃×C₈	—	2	8	no	—
61	C₂×C₃×C₈	—	2	4	no	—
62	C₂×C₃×C₈	—	2	4	no	—
63	C₂×C₃×C₈	—	2	4	no	—
64	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
65	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
66	C₃×C₄⋊C₄	—	6	8	no	—
67	C₃×C₄²	—	2	2	no	—
68	C₃×C₄²	—	2	2	no	—
69	C₃×C₄²	Dic₆	1	2	yes	—
70	C₃×C₄²	C₂×Dic₃	1	2	yes	—
71	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
72	C₃×C₄²	C₃×Q₈	1	2	yes	—
73	C₄⋊Dic₃	—	2	8	no	—
74	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₃²	#124	1	2	yes	—
76	C₂²×C₃²	#135	1	4	yes	—
77	C₃²×C₄	—	2	4	no	—
78	C₃²×C₄	#117	1	2	yes	—
79	C₃²×C₄	#125	1	2	yes	—
80	C₃×Dic₃	—	8	4	no	—
81	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
82	C₂×C₄⋊C₄	—	3	4	no	—
83	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
84	C₄×C₈	C₃×Dic₃	1	4	yes	complemented
85	#95	—	6	4	no	—
86	C₂³×C₃	—	2	1	no	—
87	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
88	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄	—	2	8	no	—
90	C₂×C₃×C₄	—	2	4	no	—
91	C₂×C₃×C₄	—	2	4	no	—
92	C₂×C₃×C₄	—	2	4	no	—
93	C₂×C₃×C₄	—	2	1	no	—
94	C₂×C₃×C₄	—	2	4	no	—
95	C₂×C₃×C₄	—	2	1	no	—
96	C₂×C₃×C₄	—	12	4	no	—
97	C₂×C₃×C₄	—	12	8	no	—
98	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
99	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
100	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
101	C₂×C₃×C₄	#235	1	4	yes	—
102	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
103	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
105	C₂×C₃×C₄	C₃×#41	1	4	yes	—
106	C₂×Dic₃	—	4	4	no	—
107	C₂×Dic₃	—	4	8	no	—
108	C₃×C₈	—	2	8	no	—
109	C₃×C₈	—	2	4	no	—
110	C₃×C₈	—	2	4	no	—
111	C₂×C₃²	#382	1	1	yes	characteristic
112	C₂×C₃²	#427	1	2	yes	—
113	C₂×C₃²	#488	1	4	yes	—
114	C₂²×C₄	—	6	4	no	—
115	C₂²×C₄	C₃×D₁₂	1	2	yes	—
116	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
117	C₂×C₈	—	2	4	no	—
118	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	—
119	C₄⋊C₄	—	6	8	no	—
120	C₄²	C₃×Dic₆	1	2	yes	—
121	C₄²	C₂×C₃×Dic₃	1	2	yes	—
122	C₂²×C₃	—	2	4	no	—
123	C₂²×C₃	—	2	1	no	—
124	C₂²×C₃	—	2	2	no	—
125	C₂²×C₃	#875	1	2	yes	—
126	C₂²×C₃	#904	1	4	yes	—
127	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
128	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
129	C₂²×C₃	C₃×#124	1	2	yes	—
130	C₂²×C₃	C₃×#135	1	4	yes	—
131	C₃×C₄	—	2	8	no	—
132	C₃×C₄	—	2	4	no	—
133	C₃×C₄	—	2	4	no	—
134	C₃×C₄	—	2	2	no	—
135	C₃×C₄	—	2	2	no	—
136	C₃×C₄	—	24	4	no	—
137	C₃×C₄	#870	1	2	yes	—
138	C₃×C₄	#926	1	2	yes	—
139	C₃×C₄	C₃×#117	1	2	yes	—
140	C₃×C₄	C₃×#125	1	2	yes	—
141	Dic₃	—	8	4	no	—
142	C₃²	#1835	1	1	yes	characteristic, complemented, Sylow
143	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	12	8	no	—
146	C₂×C₄	—	12	4	no	—
147	C₂×C₄	C₃×C₄⋊Dic₃	1	4	yes	—
148	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
149	C₂×C₄	C₃×#235	1	4	yes	—
150	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
151	C₈	—	2	4	no	—
152	C₂×C₃	—	2	1	no	—
153	C₂×C₃	—	2	4	no	—
154	C₂×C₃	—	2	2	no	—
155	C₂×C₃	#4697	1	4	yes	—
156	C₂×C₃	#4936	1	1	yes	characteristic
157	C₂×C₃	#5106	1	2	yes	—
158	C₂×C₃	C₃×#382	1	1	yes	characteristic
159	C₂×C₃	C₃×#427	1	2	yes	—
160	C₂×C₃	C₃×#488	1	4	yes	—
161	C₂²	C₃×#875	1	2	yes	—
162	C₂²	C₃×#904	1	4	yes	—
163	C₂²	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
164	C₄	—	2	4	no	—
165	C₄	—	24	4	no	—
166	C₄	C₃×#870	1	2	yes	—
167	C₄	C₃×#926	1	2	yes	—
168	C₃	—	2	1	no	—
169	C₃	#69763	1	1	yes	characteristic, direct product factor
170	C₃	C₃×#1835	1	1	yes	characteristic, complemented
171	C₂	C₃×#4697	1	4	yes	—
172	C₂	C₃×#4936	1	1	yes	characteristic
173	C₂	C₃×#5106	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#1835
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #69763	C₃	direct (N × H)
9. C₃²×C₄×C₈	C₄	semidirect
36. C₃×C₄×C₈	Dic₃	semidirect
37. C₃×C₄×C₈	C₃×C₄	semidirect
84. C₄×C₈	C₃×Dic₃	semidirect
142. C₃²	#1835	semidirect
169. C₃	#69763	direct (N × H)
170. C₃	C₃×#1835	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×#4936	2
C₃×#4551	2
C₃×#1835	3
#69763	3

Subgroups — C3×#69763 #11786051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69763 #11786051