Subgroups — #11858503

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#63488	C₂	1	2	yes	maximal
3	#10588805	C₂	1	8	yes	maximal, complemented
4	#10588787	C₂	1	4	yes	maximal, complemented
5	#83752	—	3	1	no	maximal
6	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₉×M₁₆	C₄	1	8	yes	complemented
8	C₂×C₉×M₁₆	C₂²	1	4	yes	—
9	C₂²×C₈×C₉	C₂²	1	2	yes	—
10	C₂×#3676	—	2	2	no	—
11	#63488	—	2	2	no	—
12	#63488	—	2	2	no	—
13	#63488	C₂²	1	4	yes	—
14	#63488	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₉	—	2	2	no	—
17	#63378	C₂²	1	8	yes	complemented
18	#63377	C₂²	1	8	yes	complemented
19	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic
20	C₂×#926	—	3	2	no	—
21	#5121	—	3	8	no	—
22	#5106	—	3	4	no	—
23	C₂⁴×C₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	D₄	1	2	yes	—
27	C₂²×C₄×C₉	Q₈	1	4	yes	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₉	C₂³	1	2	yes	—
30	C₂²×Dic₉	—	2	4	no	—
31	C₉×M₁₆	C₂×C₄	1	16	yes	complemented
32	C₂×C₈×C₉	C₂×C₄	1	8	yes	complemented
33	C₂×C₈×C₉	C₂³	1	4	yes	—
34	#3676	—	2	4	no	—
35	#3676	—	2	4	no	—
36	C₄⋊Dic₉	—	2	4	no	—
37	C₄⋊Dic₉	C₂³	1	8	yes	—
38	C₄×Dic₉	—	2	4	no	—
39	C₄×Dic₉	—	2	4	no	—
40	#2911	—	9	1	no	Sylow
41	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃×M₁₆	Dic₃	1	8	yes	—
43	C₂×C₃×M₁₆	C₂×D₃	1	4	yes	—
44	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
45	C₂×#217	—	6	2	no	—
46	#926	—	3	4	no	—
47	#926	—	3	4	no	—
48	#926	—	6	2	no	—
49	#926	—	6	2	no	—
50	C₂×C₄⋊Dic₃	—	3	4	no	—
51	C₂×C₄×Dic₃	—	6	2	no	—
52	#818	—	3	8	no	—
53	#817	—	3	8	no	—
54	C₂³×C₉	—	4	2	no	—
55	C₂³×C₉	C₄⋊C₄	1	4	yes	—
56	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
57	C₂³×C₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
59	C₂×C₄×C₉	C₄⋊C₄	1	8	yes	—
60	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
61	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
62	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
65	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
66	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
67	C₂×Dic₉	—	2	8	no	—
68	C₂×Dic₉	—	4	8	no	—
69	C₈×C₉	C₂²×C₄	1	8	yes	—
70	C₂²×M₁₆	D₉	1	1	yes	characteristic
71	C₂×#117	—	9	2	no	—
72	#428	—	9	8	no	—
73	#427	—	9	4	no	—
74	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
75	C₂²×C₃×C₄	Dic₆	1	4	yes	—
76	C₂²×C₃×C₄	D₁₂	1	2	yes	—
77	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
79	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
80	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
81	C₂²×Dic₃	—	6	4	no	—
82	C₃×M₁₆	C₂×Dic₃	1	16	yes	—
83	C₂×C₃×C₈	C₂×Dic₃	1	8	yes	—
84	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
85	#217	—	6	4	no	—
86	#217	—	6	4	no	—
87	C₄⋊Dic₃	—	3	8	no	—
88	C₄⋊Dic₃	—	6	4	no	—
89	C₄×Dic₃	—	6	4	no	—
90	C₄×Dic₃	—	6	4	no	—
91	C₂²×C₉	—	2	4	no	—
92	C₂²×C₉	—	2	2	no	—
93	C₂²×C₉	—	4	4	no	—
94	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
95	C₂²×C₉	C₂×C₄⋊C₄	1	4	yes	—
96	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
97	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
98	C₄×C₉	C₂×C₄⋊C₄	1	4	yes	—
99	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
100	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
101	Dic₉	—	4	8	no	—
102	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
103	C₂×M₁₆	Dic₉	1	8	yes	complemented
104	C₂×M₁₆	C₂×D₉	1	4	yes	—
105	C₂²×C₈	C₂×D₉	1	2	yes	—
106	#117	—	9	4	no	—
107	#117	—	9	4	no	—
108	#117	—	18	2	no	—
109	#117	—	18	2	no	—
110	C₂×C₄⋊C₄	—	9	4	no	—
111	C₂×C₂²⋊C₄	—	18	2	no	—
112	C₂×C₄²	—	18	2	no	—
113	#107	—	9	8	no	—
114	#106	—	9	8	no	—
115	C₂³×C₃	—	4	2	no	—
116	C₂³×C₃	C₄⋊Dic₃	1	4	yes	—
117	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
118	C₂³×C₃	C₂×D₁₂	1	2	yes	—
119	C₂×C₃×C₄	C₄⋊Dic₃	1	8	yes	—
120	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
121	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
122	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
123	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
124	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
125	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
126	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
127	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
128	C₂×Dic₃	—	6	8	no	—
129	C₂×Dic₃	—	12	8	no	—
130	C₃×C₈	C₂²×Dic₃	1	8	yes	—
131	C₂×C₉	—	2	4	no	—
132	C₂×C₉	—	2	2	no	—
133	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₉	#575	1	2	yes	—
135	C₂⁴	D₃₆	1	1	yes	characteristic
136	C₂²×C₄	—	18	4	no	—
137	C₂²×C₄	Dic₁₈	1	4	yes	—
138	C₂²×C₄	D₃₆	1	1	yes	characteristic
139	C₂²×C₄	D₃₆	1	2	yes	—
140	C₂²×C₄	C₂×Dic₉	1	4	yes	—
141	C₂²×C₄	C₂²×D₉	1	2	yes	—
142	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
143	M₁₆	C₂×Dic₉	1	16	yes	complemented
144	C₂×C₈	C₂×Dic₉	1	8	yes	complemented
145	C₂×C₈	C₂²×D₉	1	4	yes	—
146	C₄⋊C₄	—	9	8	no	—
147	C₄⋊C₄	—	18	4	no	—
148	C₂²⋊C₄	—	18	4	no	—
149	C₂²⋊C₄	—	18	4	no	—
150	C₄²	—	18	4	no	—
151	C₄²	—	18	4	no	—
152	C₂²×C₃	—	2	4	no	—
153	C₂²×C₃	—	2	2	no	—
154	C₂²×C₃	—	4	4	no	—
155	C₂²×C₃	C₂×C₄⋊Dic₃	1	2	yes	—
156	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
157	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
158	C₃×C₄	C₂×C₄⋊Dic₃	1	4	yes	—
159	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
160	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
161	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
162	Dic₃	—	12	8	no	—
163	C₉	#2911	1	1	yes	characteristic, complemented, Sylow
164	C₂³	—	4	2	no	—
165	C₂³	C₄⋊Dic₉	1	4	yes	—
166	C₂³	C₂×D₃₆	1	1	yes	characteristic
167	C₂³	C₂×D₃₆	1	2	yes	—
168	C₂×C₄	—	18	8	no	—
169	C₂×C₄	—	36	8	no	—
170	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
171	C₂×C₄	C₄⋊Dic₉	1	8	yes	—
172	C₂×C₄	C₂×Dic₁₈	1	4	yes	—
173	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
174	C₂×C₄	C₂×D₃₆	1	2	yes	—
175	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
176	C₂×C₄	C₂²×Dic₉	1	2	yes	—
177	C₂×C₄	C₂²×Dic₉	1	4	yes	—
178	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
179	C₈	C₂²×Dic₉	1	8	yes	—
180	C₂×C₃	—	2	4	no	—
181	C₂×C₃	—	2	2	no	—
182	C₂×C₃	#5748	1	2	yes	—
183	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
184	C₂²	—	2	4	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	4	4	no	—
187	C₂²	C₂×C₄⋊Dic₉	1	2	yes	—
188	C₂²	C₂×C₄⋊Dic₉	1	4	yes	—
189	C₂²	C₂²×D₃₆	1	1	yes	characteristic
190	C₄	—	36	8	no	—
191	C₄	C₂×C₄⋊Dic₉	1	4	yes	—
192	C₄	C₂×C₄⋊Dic₉	1	2	yes	—
193	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
194	C₄	C₂³×Dic₉	1	1	yes	characteristic
195	C₃	#83752	1	1	yes	characteristic
196	C₂	—	2	4	no	—
197	C₂	—	2	2	no	—
198	C₂	#10589850	1	2	yes	—
199	C₂	C₂²×C₄⋊Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₆
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₉×M₁₆	C₂
socle	C₂²×C₃	C₂²×D₁₂
prime radical	C₂⁴×C₃	D₁₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×M₁₆	D₉
hypocenter	C₉	#2911
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #10588805	C₂	semidirect
4. #10588787	C₂	semidirect
7. C₂×C₉×M₁₆	C₄	semidirect
17. #63378	C₂²	semidirect
18. #63377	C₂²	semidirect
31. C₉×M₁₆	C₂×C₄	semidirect
32. C₂×C₈×C₉	C₂×C₄	semidirect
103. C₂×M₁₆	Dic₉	semidirect
143. M₁₆	C₂×Dic₉	semidirect
144. C₂×C₈	C₂×Dic₉	semidirect
163. C₉	#2911	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×M₁₆	2
C₂×#63488	2
#10588805	2
#10588787	2
#83752	3