Subgroups — C₂×#10588864 #11860104

Order 1152.

720 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₉	C₂	1	2	yes	maximal
3	C₂×#63395	C₂	1	2	yes	maximal
4	#10588864	C₂	1	8	yes	maximal, direct product factor
5	C₂×#63377	C₂	1	1	yes	maximal, characteristic
6	C₂×#63375	C₂	1	1	yes	maximal, characteristic
7	C₂×#5184	—	3	1	no	maximal
8	C₂²×Q₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×Q₁₆	C₄	1	8	yes	complemented
10	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	Q₈×Dic₉	—	2	4	no	—
13	Q₈×Dic₉	C₂²	1	8	yes	—
14	C₂×C₄⋊Dic₉	—	2	2	no	—
15	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₉	—	2	2	no	—
17	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
18	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
19	#63395	C₂²	1	8	yes	—
20	#63377	C₂²	1	4	yes	—
21	#63375	C₂²	1	4	yes	—
22	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic
23	C₂×Q₈×Dic₃	—	3	2	no	—
24	C₂×#835	—	3	2	no	—
25	#5184	—	3	8	no	—
26	C₂×#817	—	3	1	no	—
27	C₂×#815	—	3	1	no	—
28	C₂×Q₈×C₉	—	2	2	no	—
29	C₂×Q₈×C₉	—	2	4	no	—
30	C₂×Q₈×C₉	C₂×C₄	1	8	yes	—
31	C₂×Q₈×C₉	C₂³	1	4	yes	—
32	C₂²×C₄×C₉	—	2	2	no	—
33	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₉	—	2	2	no	—
35	C₂²×Dic₉	D₄	1	2	yes	—
36	C₉×Q₁₆	C₂×C₄	1	16	yes	complemented
37	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
38	C₂×C₈×C₉	C₂³	1	2	yes	—
39	C₄⋊Dic₉	—	2	2	no	—
40	C₄⋊Dic₉	—	2	8	no	—
41	C₄⋊Dic₉	C₂³	1	4	yes	—
42	C₄×Dic₉	—	2	8	no	—
43	C₄×Dic₉	D₄	1	2	yes	—
44	C₄×Dic₉	C₂³	1	2	yes	—
45	C₂×C₉⋊C₈	—	2	2	no	—
46	C₂×C₉⋊C₈	C₂³	1	2	yes	—
47	C₂×#441	—	9	1	no	Sylow
48	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
49	C₂×C₃×Q₁₆	Dic₃	1	8	yes	—
50	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	—
51	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
52	Q₈×Dic₃	—	3	8	no	—
53	Q₈×Dic₃	—	6	4	no	—
54	C₂×C₄⋊Dic₃	—	3	2	no	—
55	C₂×C₄⋊Dic₃	—	6	2	no	—
56	C₂×C₄×Dic₃	—	3	1	no	—
57	C₂×C₄×Dic₃	—	6	2	no	—
58	C₂²×C₃⋊C₈	—	3	1	no	—
59	#835	—	3	8	no	—
60	#817	—	3	4	no	—
61	#815	—	3	4	no	—
62	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
63	Q₈×C₉	—	2	8	no	—
64	Q₈×C₉	—	2	4	no	—
65	Q₈×C₉	C₂²×C₄	1	8	yes	—
66	C₂×C₄×C₉	—	2	8	no	—
67	C₂×C₄×C₉	—	2	4	no	—
68	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₉	#41	1	2	yes	—
71	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
72	C₂×Dic₉	—	2	4	no	—
73	C₂×Dic₉	—	2	4	no	—
74	C₂×Dic₉	—	4	4	no	—
75	C₂×Dic₉	C₂×D₄	1	4	yes	—
76	C₈×C₉	C₂²×C₄	1	4	yes	—
77	C₉⋊C₈	—	2	2	no	—
78	C₂²×Q₁₆	D₉	1	1	yes	characteristic
79	C₂×C₄×Q₈	—	9	2	no	—
80	#441	—	9	8	no	—
81	C₂×#106	—	9	1	no	—
82	C₂×#103	—	9	2	no	—
83	C₂×#97	—	9	1	no	—
84	C₂×C₃×Q₈	—	2	2	no	—
85	C₂×C₃×Q₈	—	2	4	no	—
86	C₂×C₃×Q₈	C₂×Dic₃	1	8	yes	—
87	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
88	C₂²×C₃×C₄	—	2	2	no	—
89	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
90	C₂²×Dic₃	—	3	2	no	—
91	C₂²×Dic₃	—	6	2	no	—
92	C₃×Q₁₆	C₂×Dic₃	1	16	yes	—
93	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
94	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
95	C₄⋊Dic₃	—	3	4	no	—
96	C₄⋊Dic₃	—	6	8	no	—
97	C₄⋊Dic₃	—	6	2	no	—
98	C₄×Dic₃	—	3	2	no	—
99	C₄×Dic₃	—	3	2	no	—
100	C₄×Dic₃	—	6	8	no	—
101	C₂×C₃⋊C₈	—	3	2	no	—
102	C₂×C₃⋊C₈	—	6	2	no	—
103	C₂²×C₉	C₄×D₄	1	2	yes	—
104	C₂²×C₉	#137	1	4	yes	—
105	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₉	—	2	8	no	—
107	C₄×C₉	C₄×D₄	1	2	yes	—
108	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
109	C₄×C₉	C₂×#41	1	1	yes	characteristic
110	Dic₉	—	2	4	no	—
111	Dic₉	—	4	4	no	—
112	C₂²×Q₈	C₂×D₉	1	2	yes	—
113	C₂×Q₁₆	Dic₉	1	8	yes	complemented
114	C₂×Q₁₆	C₂×D₉	1	4	yes	—
115	C₂²×C₈	—	9	1	no	—
116	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
117	C₄×Q₈	—	9	8	no	—
118	C₄×Q₈	—	18	4	no	—
119	C₂×C₄⋊C₄	—	9	2	no	—
120	C₂×C₄⋊C₄	—	18	2	no	—
121	C₂×C₄²	—	9	1	no	—
122	C₂×C₄²	—	18	2	no	—
123	#106	—	9	4	no	—
124	#103	—	9	8	no	—
125	#97	—	9	4	no	—
126	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
127	C₃×Q₈	—	2	8	no	—
128	C₃×Q₈	—	2	4	no	—
129	C₃×Q₈	C₂²×Dic₃	1	8	yes	—
130	C₂×C₃×C₄	—	2	8	no	—
131	C₂×C₃×C₄	—	2	4	no	—
132	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄	#237	1	2	yes	—
134	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
135	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
136	C₂×Dic₃	—	3	4	no	—
137	C₂×Dic₃	—	6	4	no	—
138	C₂×Dic₃	—	6	4	no	—
139	C₂×Dic₃	—	12	4	no	—
140	C₃×C₈	C₂²×Dic₃	1	4	yes	—
141	C₃⋊C₈	—	6	2	no	—
142	C₂×C₉	#441	1	4	yes	complemented
143	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂×C₉	C₂×#137	1	2	yes	—
145	C₂×Q₈	—	2	2	no	—
146	C₂×Q₈	—	2	4	no	—
147	C₂×Q₈	C₂×Dic₉	1	8	yes	—
148	C₂×Q₈	C₂²×D₉	1	4	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	9	2	no	—
151	C₂²×C₄	—	18	2	no	—
152	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
153	Q₁₆	C₂×Dic₉	1	16	yes	complemented
154	C₂×C₈	—	9	2	no	—
155	C₂×C₈	—	18	2	no	—
156	C₂×C₈	C₂×Dic₉	1	4	yes	—
157	C₂×C₈	C₂²×D₉	1	2	yes	—
158	C₄⋊C₄	—	9	4	no	—
159	C₄⋊C₄	—	18	8	no	—
160	C₄⋊C₄	—	18	2	no	—
161	C₄²	—	9	2	no	—
162	C₄²	—	9	2	no	—
163	C₄²	—	18	8	no	—
164	C₂²×C₃	#918	1	4	yes	—
165	C₂²×C₃	D₄×Dic₃	1	2	yes	—
166	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
167	C₃×C₄	—	2	8	no	—
168	C₃×C₄	D₄×Dic₃	1	2	yes	—
169	C₃×C₄	C₂×#237	1	1	yes	characteristic
170	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
171	Dic₃	—	6	4	no	—
172	Dic₃	—	12	4	no	—
173	C₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
174	C₂³	D₄×D₉	1	1	yes	characteristic
175	Q₈	—	2	8	no	—
176	Q₈	—	2	4	no	—
177	Q₈	C₂²×Dic₉	1	8	yes	—
178	C₂×C₄	—	2	8	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	9	4	no	—
181	C₂×C₄	—	18	4	no	—
182	C₂×C₄	—	18	4	no	—
183	C₂×C₄	—	36	4	no	—
184	C₂×C₄	D₄×D₉	1	1	yes	characteristic
185	C₂×C₄	#3699	1	2	yes	—
186	C₂×C₄	C₂²×Dic₉	1	2	yes	—
187	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
188	C₈	—	18	2	no	—
189	C₈	C₂²×Dic₉	1	4	yes	—
190	C₂×C₃	#5184	1	4	yes	—
191	C₂×C₃	C₂×#918	1	2	yes	—
192	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
193	C₂²	#63480	1	4	yes	—
194	C₂²	D₄×Dic₉	1	2	yes	—
195	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
196	C₄	—	2	8	no	—
197	C₄	—	18	4	no	—
198	C₄	—	36	4	no	—
199	C₄	D₄×Dic₉	1	2	yes	—
200	C₄	C₂×#3699	1	1	yes	characteristic
201	C₄	C₂³×Dic₉	1	1	yes	characteristic
202	C₃	C₂×#5184	1	1	yes	characteristic
203	C₂	#10588864	1	4	yes	direct product factor
204	C₂	C₂×#63480	1	2	yes	—
205	C₂	C₂×D₄×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₉
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₉×Q₁₆	C₂
socle, prime radical	C₂³×C₃	D₃×D₄
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×Q₁₆	D₉
hypocenter	C₉	C₂×#441
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #10588864	C₂	direct (N × H)
9. C₂×C₉×Q₁₆	C₄	semidirect
36. C₉×Q₁₆	C₂×C₄	semidirect
113. C₂×Q₁₆	Dic₉	semidirect
142. C₂×C₉	#441	semidirect
153. Q₁₆	C₂×Dic₉	semidirect
173. C₉	C₂×#441	semidirect
203. C₂	#10588864	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×Q₁₆	2
C₂×Q₈×Dic₉	2
C₂×#63395	2
#10588864	2
C₂×#63377	2
C₂×#63375	2
C₂×#5184	3

Subgroups — C2×#10588864 #11860104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588864 #11860104