Subgroups — C₂×C₃⋊C₈² #11773500

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₃⋊C₈²	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₃⋊C₈	—	3	2	no	maximal
5	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
6	C₂²×C₃⋊(C₃⋊C₈)	C₄	1	2	yes	—
7	C₂²×C₃×C₃⋊C₈	C₄	1	4	yes	—
8	C₄×C₃⋊(C₃⋊C₈)	C₄	1	2	yes	—
9	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
10	C₃×C₄×C₃⋊C₈	C₄	1	4	yes	—
11	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	—
12	C₂×C₃×C₄×C₈	—	3	2	no	—
13	C₂×C₄×C₃⋊C₈	—	3	2	no	—
14	C₂×C₄×C₃⋊C₈	—	6	1	no	—
15	C₂×C₄×C₃⋊C₈	D₃	1	2	yes	—
16	C₈×C₃⋊C₈	—	3	8	no	—
17	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
19	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
20	C₃²×C₄²	C₂×C₄	1	2	yes	—
21	C₃²×C₄²	C₂³	1	1	yes	characteristic
22	C₂×C₃⋊(C₃⋊C₈)	C₈	1	8	yes	complemented
23	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
24	C₂×C₃×C₃⋊C₈	C₈	1	16	yes	complemented
25	C₂×C₃×C₃⋊C₈	C₂×C₄	1	8	yes	—
26	C₂×C₈²	—	9	1	no	Sylow
27	C₂²×C₃×C₈	—	3	4	no	—
28	C₂×C₃×C₄²	—	2	1	no	—
29	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
30	C₂²×C₃⋊C₈	—	3	4	no	—
31	C₂²×C₃⋊C₈	—	6	2	no	—
32	C₂²×C₃⋊C₈	Dic₃	1	4	yes	—
33	C₃×C₄×C₈	—	3	4	no	—
34	C₃×C₄×C₈	—	3	4	no	—
35	C₄×C₃⋊C₈	—	3	4	no	—
36	C₄×C₃⋊C₈	—	3	4	no	—
37	C₄×C₃⋊C₈	—	6	2	no	—
38	C₄×C₃⋊C₈	—	6	2	no	—
39	C₄×C₃⋊C₈	Dic₃	1	4	yes	—
40	C₄×C₃⋊C₈	C₂×D₃	1	4	yes	—
41	C₂³×C₃²	C₄²	1	1	yes	characteristic
42	C₂×C₃²×C₄	C₄²	1	2	yes	—
43	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
44	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
45	C₂×C₃²×C₄	C₂×C₈	1	8	yes	—
46	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
48	C₃⋊(C₃⋊C₈)	C₂×C₈	1	8	yes	complemented
49	C₃×C₃⋊C₈	C₂×C₈	1	16	yes	complemented
50	C₂×C₄×C₈	—	3	2	no	—
51	C₂×C₄×C₈	—	9	1	no	—
52	C₈²	—	9	4	no	—
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	C₄×D₃	1	2	yes	—
57	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
58	C₂×C₃×C₈	—	3	16	no	—
59	C₂×C₃×C₈	—	3	8	no	—
60	C₃×C₄²	—	2	2	no	—
61	C₃×C₄²	—	2	1	no	—
62	C₃×C₄²	—	2	1	no	—
63	C₃×C₄²	C₄×D₃	1	2	yes	—
64	C₃×C₄²	C₄×D₃	1	2	yes	—
65	C₃×C₄²	C₂×Dic₃	1	2	yes	—
66	C₃×C₄²	C₂²×D₃	1	2	yes	—
67	C₂×C₃⋊C₈	—	3	16	no	—
68	C₂×C₃⋊C₈	—	3	8	no	—
69	C₂×C₃⋊C₈	—	6	4	no	—
70	C₂×C₃⋊C₈	—	6	8	no	—
71	C₂×C₃⋊C₈	C₃⋊C₈	1	16	yes	direct product factor
72	C₂×C₃⋊C₈	C₂×Dic₃	1	8	yes	—
73	C₂²×C₃²	C₄×C₈	1	4	yes	—
74	C₂²×C₃²	C₄×C₈	1	2	yes	—
75	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
76	C₃²×C₄	C₄×C₈	1	4	yes	—
77	C₃²×C₄	C₄×C₈	1	2	yes	—
78	C₃²×C₄	C₂²×C₈	1	2	yes	—
79	C₃²×C₄	C₂²×C₈	1	4	yes	—
80	C₂²×C₈	—	3	4	no	—
81	C₂²×C₈	—	9	2	no	—
82	C₂×C₄²	D₃²	1	1	yes	characteristic
83	C₄×C₈	—	3	4	no	—
84	C₄×C₈	—	3	4	no	—
85	C₄×C₈	—	9	2	no	—
86	C₄×C₈	—	9	2	no	—
87	C₂³×C₃	—	2	1	no	—
88	C₂³×C₃	C₄×Dic₃	1	2	yes	—
89	C₂×C₃×C₄	—	2	8	no	—
90	C₂×C₃×C₄	—	2	4	no	—
91	C₂×C₃×C₄	—	2	2	no	—
92	C₂×C₃×C₄	—	2	1	no	—
93	C₂×C₃×C₄	—	2	2	no	—
94	C₂×C₃×C₄	—	2	1	no	—
95	C₂×C₃×C₄	D₃×C₈	1	8	yes	—
96	C₂×C₃×C₄	D₃×C₈	1	8	yes	—
97	C₂×C₃×C₄	C₂×C₃⋊C₈	1	8	yes	—
98	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
99	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
100	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
101	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
102	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
103	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
104	C₃×C₈	—	3	16	no	—
105	C₃⋊C₈	—	3	16	no	—
106	C₃⋊C₈	—	6	8	no	—
107	C₃⋊C₈	C₂×C₃⋊C₈	1	16	yes	direct product factor
108	C₂×C₃²	C₈²	1	4	yes	complemented
109	C₂×C₃²	C₂×C₄×C₈	1	2	yes	—
110	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
111	C₂²×C₄	D₃×Dic₃	1	2	yes	—
112	C₂²×C₄	#624	1	1	yes	characteristic
113	C₂×C₈	—	3	16	no	—
114	C₂×C₈	—	3	8	no	—
115	C₂×C₈	—	9	8	no	—
116	C₂×C₈	—	9	4	no	—
117	C₄²	D₃×Dic₃	1	2	yes	—
118	C₄²	#624	1	1	yes	characteristic
119	C₄²	C₂×D₃²	1	1	yes	characteristic
120	C₂²×C₃	—	2	4	no	—
121	C₂²×C₃	—	2	2	no	—
122	C₂²×C₃	—	2	1	no	—
123	C₂²×C₃	C₄×C₃⋊C₈	1	4	yes	—
124	C₂²×C₃	C₈×Dic₃	1	4	yes	—
125	C₂²×C₃	C₈×Dic₃	1	4	yes	—
126	C₂²×C₃	C₂×C₄×Dic₃	1	2	yes	—
127	C₃×C₄	—	2	4	no	—
128	C₃×C₄	—	2	2	no	—
129	C₃×C₄	—	2	4	no	—
130	C₃×C₄	—	2	2	no	—
131	C₃×C₄	C₄×C₃⋊C₈	1	4	yes	—
132	C₃×C₄	C₈×Dic₃	1	4	yes	—
133	C₃×C₄	C₈×Dic₃	1	4	yes	—
134	C₃×C₄	C₂×D₃×C₈	1	4	yes	—
135	C₃×C₄	C₂×D₃×C₈	1	4	yes	—
136	C₃×C₄	C₂²×C₃⋊C₈	1	4	yes	—
137	C₃²	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
138	C₂³	Dic₃²	1	1	yes	characteristic
139	C₂×C₄	D₃×C₃⋊C₈	1	8	yes	—
140	C₂×C₄	#3710	1	4	yes	—
141	C₂×C₄	Dic₃²	1	2	yes	—
142	C₂×C₄	Dic₃²	1	1	yes	characteristic
143	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
144	C₂×C₄	C₂×#624	1	1	yes	characteristic
145	C₈	—	3	16	no	—
146	C₈	—	9	8	no	—
147	C₂×C₃	—	2	2	no	—
148	C₂×C₃	—	2	1	no	—
149	C₂×C₃	—	2	4	no	—
150	C₂×C₃	C₈×C₃⋊C₈	1	8	yes	complemented
151	C₂×C₃	C₂×C₄×C₃⋊C₈	1	2	yes	—
152	C₂×C₃	C₂×C₈×Dic₃	1	2	yes	—
153	C₂×C₃	C₂×C₈×Dic₃	1	2	yes	—
154	C₂²	Dic₃×C₃⋊C₈	1	4	yes	—
155	C₂²	#63553	1	2	yes	—
156	C₂²	C₂×Dic₃²	1	1	yes	characteristic
157	C₄	Dic₃×C₃⋊C₈	1	4	yes	—
158	C₄	#63553	1	2	yes	—
159	C₄	C₂×D₃×C₃⋊C₈	1	4	yes	—
160	C₄	C₂×#3710	1	2	yes	—
161	C₃	—	2	1	no	—
162	C₃	C₂×C₈×C₃⋊C₈	1	2	yes	complemented
163	C₂	C₃⋊C₈²	1	4	yes	direct product factor
164	C₂	C₂×Dic₃×C₃⋊C₈	1	2	yes	—
165	C₂	C₂×#63553	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₃²
commutator, hypocenter	C₃²	C₂×C₈²
Frattini	C₄²	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₄²
cosocle	C₃²×C₄²	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃⋊C₈²	C₂	direct (N × H)
22. C₂×C₃⋊(C₃⋊C₈)	C₈	semidirect
24. C₂×C₃×C₃⋊C₈	C₈	semidirect
48. C₃⋊(C₃⋊C₈)	C₂×C₈	semidirect
49. C₃×C₃⋊C₈	C₂×C₈	semidirect
71. C₂×C₃⋊C₈	C₃⋊C₈	direct (N × H)
107. C₃⋊C₈	C₂×C₃⋊C₈	direct (N × H)
108. C₂×C₃²	C₈²	semidirect
137. C₃²	C₂×C₈²	semidirect
150. C₂×C₃	C₈×C₃⋊C₈	semidirect
162. C₃	C₂×C₈×C₃⋊C₈	semidirect
163. C₂	C₃⋊C₈²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₃⋊(C₃⋊C₈)	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃⋊C₈²	2
C₂×C₈×C₃⋊C₈	3

Subgroups — C2×C3⋊C82 #11773500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊C₈² #11773500