Subgroups — #11797122

Order 1152.

216 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#10588787	C₂	1	1	yes	maximal, characteristic
3	C₂×#63372	C₂	1	1	yes	maximal, characteristic
4	#10588190	C₂	1	4	yes	maximal, complemented
5	#71427	—	3	1	no	maximal
6	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
7	#63488	—	2	1	no	—
8	C₂×#3667	—	2	1	no	—
9	C₉×M₃₂	C₄	1	2	yes	complemented
10	C₉×M₃₂	C₂²	1	2	yes	—
11	C₂×C₉×C₁₆	C₄	1	2	yes	complemented
12	#63378	—	2	1	no	—
13	#63377	C₂²	1	2	yes	—
14	#63372	—	2	1	no	—
15	#63372	C₂²	1	2	yes	—
16	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic
17	C₂×#819	—	3	1	no	—
18	#5106	—	3	1	no	—
19	#4513	—	3	4	no	—
20	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
25	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
27	#3676	—	4	1	no	—
28	C₄⋊Dic₉	—	2	2	no	—
29	C₄×Dic₉	—	4	1	no	—
30	#3667	—	2	2	no	—
31	#3667	—	4	1	no	—
32	C₂×C₉⋊C₈	—	4	1	no	—
33	C₉×C₁₆	C₂×C₄	1	4	yes	—
34	#2155	—	9	1	no	Sylow
35	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
36	#926	—	6	1	no	—
37	C₂×#208	—	6	1	no	—
38	C₃×M₃₂	Dic₃	1	2	yes	—
39	C₃×M₃₂	C₂×D₃	1	2	yes	—
40	C₂×C₃×C₁₆	Dic₃	1	2	yes	—
41	#819	—	3	2	no	—
42	#819	—	6	1	no	—
43	#818	—	6	1	no	—
44	#817	—	3	2	no	—
45	C₂³×C₉	SD₁₆	1	1	yes	characteristic
46	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₉	SD₁₆	1	1	yes	characteristic
49	C₂×C₄×C₉	SD₁₆	1	1	yes	characteristic
50	C₂×C₄×C₉	SD₁₆	1	1	yes	characteristic
51	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₉	—	4	2	no	—
53	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
54	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
55	C₈×C₉	C₂²×C₄	1	1	yes	characteristic
56	C₈×C₉	C₂×Q₈	1	1	yes	characteristic
57	C₉⋊C₈	—	4	2	no	—
58	C₂×M₃₂	D₉	1	1	yes	characteristic
59	C₂×#108	—	9	1	no	—
60	#427	—	9	1	no	—
61	#365	—	9	4	no	—
62	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
63	C₂×C₃×C₈	Dic₆	1	1	yes	characteristic
64	C₂×C₃×C₈	Dic₆	1	1	yes	characteristic
65	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
66	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
67	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
68	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
69	#217	—	12	1	no	—
70	C₄⋊Dic₃	—	6	2	no	—
71	C₄×Dic₃	—	12	1	no	—
72	#208	—	6	2	no	—
73	#208	—	12	1	no	—
74	C₂×C₃⋊C₈	—	12	1	no	—
75	C₃×C₁₆	C₂×Dic₃	1	4	yes	—
76	C₂²×C₉	—	4	1	no	—
77	C₂²×C₉	#106	1	1	yes	characteristic
78	C₂²×C₉	#106	1	1	yes	characteristic
79	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₄×C₉	#106	1	1	yes	characteristic
81	C₄×C₉	#106	1	1	yes	characteristic
82	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₄×C₉	C₂×SD₁₆	1	1	yes	characteristic
84	Dic₉	—	8	2	no	—
85	C₂×M₁₆	—	18	1	no	—
86	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
87	#117	—	18	1	no	—
88	M₃₂	Dic₉	1	2	yes	complemented
89	M₃₂	C₂×D₉	1	2	yes	—
90	C₂×C₁₆	Dic₉	1	2	yes	complemented
91	#108	—	9	2	no	—
92	#108	—	18	1	no	—
93	#107	—	18	1	no	—
94	#106	—	9	2	no	—
95	C₂³×C₃	#204	1	1	yes	characteristic
96	C₂×C₃×C₄	#204	1	1	yes	characteristic
97	C₂×C₃×C₄	#204	1	1	yes	characteristic
98	C₂×C₃×C₄	#204	1	1	yes	characteristic
99	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
100	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
101	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
102	C₂×Dic₃	—	12	2	no	—
103	C₃×C₈	C₄⋊Dic₃	1	1	yes	characteristic
104	C₃×C₈	C₄⋊Dic₃	1	1	yes	characteristic
105	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
106	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
107	C₃⋊C₈	—	12	2	no	—
108	C₂×C₉	—	2	1	no	—
109	C₂×C₉	—	2	1	no	—
110	C₂×C₉	—	2	1	no	—
111	C₂×C₉	C₂×#106	1	1	yes	characteristic
112	C₂²×C₄	D₃₆	1	1	yes	characteristic
113	M₁₆	—	18	2	no	—
114	M₁₆	—	36	1	no	—
115	C₂×C₈	—	36	1	no	—
116	C₂×C₈	Dic₁₈	1	1	yes	characteristic
117	C₂×C₈	Dic₁₈	1	1	yes	characteristic
118	C₂×C₈	D₃₆	1	1	yes	characteristic
119	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
120	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
121	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
122	C₄⋊C₄	—	18	2	no	—
123	C₂²⋊C₄	—	36	1	no	—
124	C₄²	—	36	1	no	—
125	C₁₆	C₂×Dic₉	1	4	yes	—
126	C₂²×C₃	—	4	1	no	—
127	C₂²×C₃	#817	1	1	yes	characteristic
128	C₂²×C₃	#817	1	1	yes	characteristic
129	C₂²×C₃	C₂×#204	1	1	yes	characteristic
130	C₃×C₄	#817	1	1	yes	characteristic
131	C₃×C₄	#817	1	1	yes	characteristic
132	C₃×C₄	C₂×#204	1	1	yes	characteristic
133	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
134	Dic₃	—	24	2	no	—
135	C₉	#2155	1	1	yes	characteristic, complemented, Sylow
136	C₂³	#3664	1	1	yes	characteristic
137	C₂×C₄	—	36	2	no	—
138	C₂×C₄	#3664	1	1	yes	characteristic
139	C₂×C₄	#3664	1	1	yes	characteristic
140	C₂×C₄	#3664	1	1	yes	characteristic
141	C₂×C₄	C₄⋊Dic₉	1	1	yes	characteristic
142	C₂×C₄	C₄⋊Dic₉	1	1	yes	characteristic
143	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
144	C₈	—	36	2	no	—
145	C₈	C₄⋊Dic₉	1	1	yes	characteristic
146	C₈	C₄⋊Dic₉	1	1	yes	characteristic
147	C₈	C₂×Dic₁₈	1	1	yes	characteristic
148	C₈	C₂²×Dic₉	1	1	yes	characteristic
149	C₂×C₃	—	2	1	no	—
150	C₂×C₃	—	2	1	no	—
151	C₂×C₃	—	2	1	no	—
152	C₂×C₃	C₂×#817	1	1	yes	characteristic
153	C₂²	—	4	1	no	—
154	C₂²	#63377	1	1	yes	characteristic
155	C₂²	#63377	1	1	yes	characteristic
156	C₂²	C₂×#3664	1	1	yes	characteristic
157	C₄	—	72	2	no	—
158	C₄	#63377	1	1	yes	characteristic
159	C₄	#63377	1	1	yes	characteristic
160	C₄	C₂×#3664	1	1	yes	characteristic
161	C₄	C₂×C₄⋊Dic₉	1	1	yes	characteristic
162	C₃	#71427	1	1	yes	characteristic
163	C₂	—	2	1	no	—
164	C₂	—	2	1	no	—
165	C₂	—	2	1	no	—
166	C₂	C₂×#63377	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#63377
commutator	C₈×C₉	C₂²×C₄
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₂×C₉×M₃₂	C₂
socle	C₂×C₃	C₂×#817
prime radical	C₂³×C₃	#204
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₂×M₃₂	D₉
hypocenter	C₉	#2155
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
4. #10588190	C₂	semidirect
9. C₉×M₃₂	C₄	semidirect
11. C₂×C₉×C₁₆	C₄	semidirect
88. M₃₂	Dic₉	semidirect
90. C₂×C₁₆	Dic₉	semidirect
135. C₉	#2155	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×M₃₂	2
#10588787	2
C₂×#63372	2
#10588190	2
#71427	3