Subgroups — #97×C₃⋊Dic₃ #11783017

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 174 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	C₂×#63642	C₂	1	2	yes	maximal
3	C₂×C₈×C₃⋊Dic₃	C₂	1	2	yes	maximal
4	C₄²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#63630	C₂	1	1	yes	maximal, characteristic
6	Dic₃×#97	—	3	4	no	maximal
7	C₂²×C₃²×C₈	C₂²	1	2	yes	—
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₃⋊Dic₃	C₄	1	4	yes	—
10	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
13	C₃²×#97	C₄	1	4	yes	complemented
14	#63642	C₄	1	8	yes	complemented
15	C₈×C₃⋊Dic₃	C₄	1	8	yes	complemented
16	#63630	C₄	1	4	yes	complemented
17	C₂×C₃×#97	D₃	1	4	yes	—
18	C₂×#815	—	3	8	no	—
19	C₂×C₈×Dic₃	—	3	8	no	—
20	C₄²×Dic₃	—	3	4	no	—
21	C₂×#803	—	3	4	no	—
22	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
23	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
24	C₂²×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
25	C₂²×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
26	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
27	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
28	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
29	C₃²×C₄²	C₂×C₄	1	2	yes	—
30	C₃²×C₄²	C₂×C₄	1	2	yes	—
31	C₄×C₃⋊Dic₃	—	2	8	no	—
32	C₄×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
33	C₄×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
34	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
35	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
36	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
37	C₄×#97	—	9	1	no	Sylow
38	C₂²×C₃×C₈	C₂×D₃	1	8	yes	—
39	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
40	C₂×C₄×Dic₃	—	3	4	no	—
41	C₂×C₄×Dic₃	—	3	4	no	—
42	C₂×C₄×Dic₃	—	3	16	no	—
43	C₂²×C₃⋊C₈	—	3	8	no	—
44	C₃×#97	Dic₃	1	16	yes	complemented
45	#815	—	3	32	no	—
46	C₈×Dic₃	—	3	32	no	—
47	#803	—	3	16	no	—
48	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₃²×C₄	—	2	4	no	—
50	C₂×C₃²×C₄	C₄²	1	4	yes	—
51	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
53	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
54	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃⋊Dic₃	—	2	4	no	—
56	C₂×C₃⋊Dic₃	C₄²	1	4	yes	—
57	C₂×C₃⋊Dic₃	C₄²	1	4	yes	—
58	C₂×C₃⋊Dic₃	M₁₆	1	8	yes	—
59	C₃²×C₈	C₄²	1	8	yes	complemented
60	C₃⋊(C₃⋊C₈)	C₄²	1	8	yes	complemented
61	C₂×#97	—	9	2	no	—
62	C₂×#97	—	9	1	no	—
63	C₂×#97	C₃⋊D₃	1	1	yes	characteristic
64	C₂×C₄×C₈	—	9	2	no	—
65	C₄³	—	9	1	no	—
66	C₂²×C₃×C₄	C₄×D₃	1	8	yes	—
67	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
68	C₂²×Dic₃	—	3	8	no	—
69	C₂²×Dic₃	—	3	8	no	—
70	C₂×C₃×C₈	C₄×D₃	1	16	yes	—
71	C₂×C₃×C₈	C₄×D₃	1	16	yes	—
72	C₂×C₃×C₈	C₂×Dic₃	1	16	yes	—
73	C₃×C₄²	C₄×D₃	1	8	yes	—
74	C₃×C₄²	C₂×Dic₃	1	8	yes	—
75	C₄×Dic₃	—	3	16	no	—
76	C₄×Dic₃	—	3	16	no	—
77	C₄×Dic₃	—	6	32	no	—
78	C₂×C₃⋊C₈	—	3	16	no	—
79	C₂×C₃⋊C₈	—	3	16	no	—
80	C₂×C₃⋊C₈	—	3	16	no	—
81	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
82	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
83	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
84	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
85	C₃²×C₄	—	2	4	no	—
86	C₃²×C₄	C₂×C₄²	1	2	yes	—
87	C₃²×C₄	C₂×C₄²	1	2	yes	—
88	C₃⋊Dic₃	—	2	4	no	—
89	C₃⋊Dic₃	#97	1	8	yes	direct product factor
90	C₂²×C₈	—	9	2	no	—
91	C₂²×C₈	C₂×C₃⋊D₃	1	2	yes	—
92	C₂×C₄²	—	9	1	no	—
93	C₂×C₄²	—	9	1	no	—
94	C₂×C₄²	—	9	4	no	—
95	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
96	#97	—	9	8	no	—
97	#97	—	9	4	no	—
98	#97	C₃⋊Dic₃	1	4	yes	direct product factor
99	C₄×C₈	—	9	8	no	—
100	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
101	C₂×C₃×C₄	—	2	16	no	—
102	C₂×C₃×C₄	C₄×Dic₃	1	16	yes	—
103	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
104	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
105	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
106	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
107	C₂×Dic₃	—	3	16	no	—
108	C₂×Dic₃	—	3	32	no	—
109	C₂×Dic₃	—	3	16	no	—
110	C₂×Dic₃	—	6	16	no	—
111	C₃×C₈	C₄×Dic₃	1	32	yes	complemented
112	C₃⋊C₈	—	3	32	no	—
113	C₂×C₃²	C₄³	1	1	yes	characteristic
114	C₂×C₃²	C₂×#97	1	2	yes	—
115	C₂×C₃²	C₄×M₁₆	1	2	yes	—
116	C₂×C₃²	C₄×M₁₆	1	2	yes	—
117	C₂²×C₄	—	9	2	no	—
118	C₂²×C₄	—	9	2	no	—
119	C₂²×C₄	C₄×C₃⋊D₃	1	2	yes	—
120	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
121	C₂×C₈	—	9	4	no	—
122	C₂×C₈	—	9	4	no	—
123	C₂×C₈	—	9	4	no	—
124	C₂×C₈	C₄×C₃⋊D₃	1	4	yes	—
125	C₂×C₈	C₄×C₃⋊D₃	1	4	yes	—
126	C₂×C₈	C₂×C₃⋊Dic₃	1	4	yes	—
127	C₄²	—	9	4	no	—
128	C₄²	—	9	4	no	—
129	C₄²	—	18	8	no	—
130	C₄²	C₄×C₃⋊D₃	1	2	yes	—
131	C₄²	C₂×C₃⋊Dic₃	1	2	yes	—
132	C₂²×C₃	C₄²×D₃	1	4	yes	—
133	C₂²×C₃	C₄²×D₃	1	4	yes	—
134	C₂²×C₃	D₃×M₁₆	1	16	yes	—
135	C₂²×C₃	C₂×C₄×Dic₃	1	4	yes	—
136	C₃×C₄	—	2	16	no	—
137	C₃×C₄	C₄²×D₃	1	8	yes	—
138	C₃×C₄	C₂×C₄×Dic₃	1	8	yes	—
139	Dic₃	—	3	32	no	—
140	Dic₃	—	6	16	no	—
141	C₃²	C₄×#97	1	1	yes	characteristic, complemented, Sylow
142	C₂³	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	9	4	no	—
145	C₂×C₄	—	9	8	no	—
146	C₂×C₄	—	9	4	no	—
147	C₂×C₄	—	18	4	no	—
148	C₂×C₄	C₄×C₃⋊Dic₃	1	4	yes	—
149	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
150	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
151	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
152	C₂×C₄	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
153	C₈	—	9	8	no	—
154	C₈	C₄×C₃⋊Dic₃	1	8	yes	complemented
155	C₂×C₃	D₃×#97	1	8	yes	—
156	C₂×C₃	#4707	1	8	yes	—
157	C₂×C₃	C₄²×Dic₃	1	4	yes	—
158	C₂×C₃	Dic₃×M₁₆	1	8	yes	—
159	C₂²	C₄²×C₃⋊D₃	1	1	yes	characteristic
160	C₂²	C₄²×C₃⋊D₃	1	1	yes	characteristic
161	C₂²	M₁₆×C₃⋊D₃	1	4	yes	—
162	C₂²	C₂×C₄×C₃⋊Dic₃	1	1	yes	characteristic
163	C₄	—	2	4	no	—
164	C₄	—	9	8	no	—
165	C₄	—	18	4	no	—
166	C₄	C₄²×C₃⋊D₃	1	2	yes	—
167	C₄	C₂×C₄×C₃⋊Dic₃	1	2	yes	—
168	C₃	Dic₃×#97	1	4	yes	complemented
169	C₂	C₃⋊D₃×#97	1	2	yes	—
170	C₂	#10592406	1	2	yes	—
171	C₂	C₄²×C₃⋊Dic₃	1	1	yes	characteristic
172	C₂	M₁₆×C₃⋊Dic₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₄³
Fitting	C₂×C₃²×#97	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×#97	C₃⋊D₃
hypocenter	C₃²	C₄×#97
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
13. C₃²×#97	C₄	semidirect
14. #63642	C₄	semidirect
15. C₈×C₃⋊Dic₃	C₄	semidirect
16. #63630	C₄	semidirect
44. C₃×#97	Dic₃	semidirect
59. C₃²×C₈	C₄²	semidirect
60. C₃⋊(C₃⋊C₈)	C₄²	semidirect
89. C₃⋊Dic₃	#97	direct (N × H)
98. #97	C₃⋊Dic₃	direct (N × H)
111. C₃×C₈	C₄×Dic₃	semidirect
141. C₃²	C₄×#97	semidirect
154. C₈	C₄×C₃⋊Dic₃	semidirect
168. C₃	Dic₃×#97	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
C₂×#63642	2
C₂×C₈×C₃⋊Dic₃	2
C₄²×C₃⋊Dic₃	2
C₂×#63630	2
Dic₃×#97	3

Subgroups — #97×C3⋊Dic3 #11783017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #97×C₃⋊Dic₃ #11783017