Subgroups — C₂×#10588803 #11858273

Order 1152.

768 conjugacy classes of subgroups.

The subgroup lattice has 210 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	1	yes	maximal, characteristic
3	C₂³×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10588803	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₉⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂×#5119	—	3	1	no	maximal
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	—	2	4	no	—
9	C₂×C₉×M₁₆	C₂²	1	4	yes	—
10	C₂²×C₈×C₉	C₂²	1	2	yes	—
11	C₂×#3676	C₄	1	2	yes	—
12	#63488	C₄	1	4	yes	—
13	#63488	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₉	C₄	1	2	yes	—
15	C₂×C₄×Dic₉	C₂²	1	2	yes	—
16	C₂²×C₉⋊C₈	—	2	4	no	—
17	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
18	C₂²×C₉⋊C₈	C₂²	1	4	yes	—
19	Dic₉⋊C₈	C₂²	1	16	yes	complemented
20	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic
21	C₂×#926	—	3	1	no	—
22	C₂³×C₃⋊C₈	—	3	1	no	—
23	#5119	—	3	8	no	—
24	C₂×Dic₃⋊C₈	—	3	4	no	—
25	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₉	D₄	1	4	yes	—
29	C₂²×C₄×C₉	Q₈	1	4	yes	—
30	C₂²×C₄×C₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₉	C₂×C₄	1	4	yes	—
33	C₉×M₁₆	—	2	8	no	—
34	C₂×C₈×C₉	—	2	4	no	—
35	C₂×C₈×C₉	C₂³	1	4	yes	—
36	#3676	C₂×C₄	1	8	yes	—
37	C₄⋊Dic₉	C₂×C₄	1	8	yes	—
38	C₄×Dic₉	C₂×C₄	1	4	yes	—
39	C₄×Dic₉	C₂³	1	4	yes	—
40	C₂×C₉⋊C₈	—	2	4	no	—
41	C₂×C₉⋊C₈	—	2	8	no	—
42	C₂×C₉⋊C₈	C₂³	1	4	yes	—
43	C₂×#424	—	9	1	no	Sylow
44	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
45	C₂×C₃×M₁₆	—	2	4	no	—
46	C₂×C₃×M₁₆	C₂×D₃	1	4	yes	—
47	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
48	C₂×#217	—	3	2	no	—
49	#926	—	3	4	no	—
50	#926	—	3	4	no	—
51	C₂×C₄⋊Dic₃	—	3	2	no	—
52	C₂×C₄×Dic₃	—	3	2	no	—
53	C₂²×C₃⋊C₈	—	3	2	no	—
54	C₂²×C₃⋊C₈	—	3	4	no	—
55	C₂²×C₃⋊C₈	—	6	4	no	—
56	Dic₃⋊C₈	—	3	16	no	—
57	C₂³×C₉	—	2	4	no	—
58	C₂³×C₉	C₄⋊C₄	1	4	yes	—
59	C₂³×C₉	C₂²×C₄	1	2	yes	—
60	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₉	C₄⋊C₄	1	8	yes	—
62	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
63	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
67	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
68	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
69	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
70	C₂×Dic₉	—	2	8	no	—
71	C₂×Dic₉	C₂²×C₄	1	8	yes	—
72	C₈×C₉	—	2	4	no	—
73	C₉⋊C₈	—	2	4	no	—
74	C₂²×M₁₆	D₉	1	1	yes	characteristic
75	C₂³×C₈	—	9	1	no	—
76	C₂×#117	—	9	1	no	—
77	#424	—	9	8	no	—
78	C₂×C₄⋊C₈	—	9	4	no	—
79	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
80	C₂²×C₃×C₄	Dic₆	1	4	yes	—
81	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
82	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
83	C₂²×C₃×C₄	#67	1	4	yes	—
84	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
85	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
86	C₂²×Dic₃	—	3	4	no	—
87	C₃×M₁₆	—	2	8	no	—
88	C₂×C₃×C₈	—	2	4	no	—
89	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
90	#217	—	3	8	no	—
91	C₄⋊Dic₃	—	3	8	no	—
92	C₄×Dic₃	—	3	4	no	—
93	C₄×Dic₃	—	3	4	no	—
94	C₂×C₃⋊C₈	—	3	4	no	—
95	C₂×C₃⋊C₈	—	6	4	no	—
96	C₂×C₃⋊C₈	—	6	8	no	—
97	C₂²×C₉	—	2	4	no	—
98	C₂²×C₉	—	2	8	no	—
99	C₂²×C₉	C₂×C₄⋊C₄	1	4	yes	—
100	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
101	C₂²×C₉	#131	1	4	yes	—
102	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
103	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
104	C₄×C₉	C₂×C₄⋊C₄	1	4	yes	—
105	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
107	Dic₉	—	2	8	no	—
108	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
109	C₂×M₁₆	—	2	4	no	—
110	C₂×M₁₆	C₂×D₉	1	4	yes	—
111	C₂²×C₈	—	9	4	no	—
112	C₂²×C₈	—	9	2	no	—
113	C₂²×C₈	—	18	4	no	—
114	C₂²×C₈	C₂×D₉	1	2	yes	—
115	#117	—	9	4	no	—
116	#117	—	9	4	no	—
117	C₂×C₄⋊C₄	—	9	2	no	—
118	C₂×C₂²⋊C₄	—	9	2	no	—
119	C₂×C₄²	—	9	2	no	—
120	C₄⋊C₈	—	9	16	no	—
121	C₂³×C₃	—	2	4	no	—
122	C₂³×C₃	Dic₃⋊C₄	1	4	yes	—
123	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
124	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
125	C₂×C₃×C₄	Dic₃⋊C₄	1	8	yes	—
126	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
127	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
128	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
129	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
130	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
131	C₂×C₃×C₄	C₂×#67	1	2	yes	—
132	C₂×C₃×C₄	C₂×#67	1	4	yes	—
133	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
134	C₂×Dic₃	—	3	8	no	—
135	C₂×Dic₃	—	6	8	no	—
136	C₃×C₈	—	2	4	no	—
137	C₃⋊C₈	—	6	4	no	—
138	C₂×C₉	—	2	4	no	—
139	C₂×C₉	#424	1	4	yes	complemented
140	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₉	C₂×#131	1	2	yes	—
142	C₂⁴	C₄×D₉	1	1	yes	characteristic
143	C₂²×C₄	—	9	4	no	—
144	C₂²×C₄	Dic₁₈	1	4	yes	—
145	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
146	C₂²×C₄	C₄×D₉	1	2	yes	—
147	C₂²×C₄	#611	1	4	yes	—
148	C₂²×C₄	C₂²×D₉	1	2	yes	—
149	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
150	M₁₆	—	2	8	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	9	4	no	—
153	C₂×C₈	—	18	4	no	—
154	C₂×C₈	—	18	8	no	—
155	C₂×C₈	C₂²×D₉	1	4	yes	—
156	C₄⋊C₄	—	9	8	no	—
157	C₂²⋊C₄	—	9	8	no	—
158	C₄²	—	9	4	no	—
159	C₄²	—	9	4	no	—
160	C₂²×C₃	—	2	4	no	—
161	C₂²×C₃	—	2	8	no	—
162	C₂²×C₃	#907	1	4	yes	—
163	C₂²×C₃	C₂×Dic₃⋊C₄	1	4	yes	—
164	C₂²×C₃	C₂×Dic₃⋊C₄	1	2	yes	—
165	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
166	C₃×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
167	C₃×C₄	C₂×Dic₃⋊C₄	1	4	yes	—
168	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
169	C₃×C₄	C₂²×#67	1	1	yes	characteristic
170	Dic₃	—	6	8	no	—
171	C₉	C₂×#424	1	1	yes	characteristic, complemented, Sylow
172	C₂³	—	2	4	no	—
173	C₂³	Dic₉⋊C₄	1	4	yes	—
174	C₂³	C₂×C₄×D₉	1	2	yes	—
175	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
176	C₂×C₄	—	9	8	no	—
177	C₂×C₄	—	18	8	no	—
178	C₂×C₄	Dic₉⋊C₄	1	8	yes	—
179	C₂×C₄	Dic₉⋊C₄	1	4	yes	—
180	C₂×C₄	C₂×Dic₁₈	1	4	yes	—
181	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
182	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
184	C₂×C₄	C₂×#611	1	2	yes	—
185	C₂×C₄	C₂×#611	1	4	yes	—
186	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
187	C₈	—	2	4	no	—
188	C₈	—	18	4	no	—
189	C₂×C₃	—	2	4	no	—
190	C₂×C₃	#5119	1	4	yes	—
191	C₂×C₃	C₂×#907	1	2	yes	—
192	C₂×C₃	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
193	C₂²	—	2	8	no	—
194	C₂²	—	2	4	no	—
195	C₂²	#63469	1	4	yes	—
196	C₂²	C₂×Dic₉⋊C₄	1	4	yes	—
197	C₂²	C₂×Dic₉⋊C₄	1	2	yes	—
198	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
199	C₄	—	18	8	no	—
200	C₄	C₂×Dic₉⋊C₄	1	4	yes	—
201	C₄	C₂×Dic₉⋊C₄	1	2	yes	—
202	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
203	C₄	C₂²×#611	1	1	yes	characteristic
204	C₃	C₂×#5119	1	1	yes	characteristic
205	C₂	—	2	4	no	—
206	C₂	#10588803	1	4	yes	direct product factor
207	C₂	C₂×#63469	1	2	yes	—
208	C₂	C₂²×Dic₉⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₉×M₁₆	C₂
socle	C₂³×C₃	C₂×C₄×D₃
prime radical	C₂⁴×C₃	C₄×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×M₁₆	D₉
hypocenter	C₉	C₂×#424
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10588803	C₂	direct (N × H)
5. C₂×Dic₉⋊C₈	C₂	semidirect
19. Dic₉⋊C₈	C₂²	semidirect
139. C₂×C₉	#424	semidirect
171. C₉	C₂×#424	semidirect
206. C₂	#10588803	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×M₁₆	2
C₂×#63488	2
C₂³×C₉⋊C₈	2
#10588803	2
C₂×Dic₉⋊C₈	2
C₂×#5119	3

Subgroups — C2×#10588803 #11858273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588803 #11858273