Subgroups — C₂×#10588230 #11796027

Order 1152.

354 conjugacy classes of subgroups.

The subgroup lattice has 219 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×#63371	C₂	1	2	yes	maximal, complemented
3	#10588230	C₂	1	4	yes	maximal, direct product factor
4	C₂×#4553	—	3	1	no	maximal
5	C₂³×C₄×C₉	C₄	1	1	yes	characteristic
6	C₂×C₉×M₁₆	—	2	2	no	—
7	C₂×C₉×M₁₆	—	2	2	no	—
8	C₂×C₉×M₁₆	C₄	1	2	yes	—
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₈×C₉	C₄	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	#63371	—	2	2	no	—
13	#63371	C₂²	1	4	yes	complemented
14	C₂×C₉⋊C₁₆	—	2	2	no	—
15	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic
16	C₂×#812	—	3	2	no	—
17	#4553	—	3	4	no	—
18	C₂⁴×C₉	C₈	1	1	yes	characteristic
19	C₂²×C₄×C₉	—	2	1	no	—
20	C₂²×C₄×C₉	—	2	1	no	—
21	C₂²×C₄×C₉	—	2	1	no	—
22	C₂²×C₄×C₉	—	2	1	no	—
23	C₂²×C₄×C₉	C₈	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₈	1	2	yes	—
25	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
27	C₉×M₁₆	—	2	4	no	—
28	C₉×M₁₆	—	2	4	no	—
29	C₂×C₈×C₉	—	2	1	no	—
30	C₂×C₈×C₉	—	2	1	no	—
31	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×C₉	D₄	1	2	yes	—
34	C₂×C₈×C₉	D₄	1	2	yes	—
35	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
36	C₉⋊C₁₆	—	2	4	no	—
37	C₂×#349	—	9	1	no	Sylow
38	C₂³×C₃×C₄	Dic₃	1	1	yes	characteristic
39	C₂×C₃×M₁₆	—	2	2	no	—
40	C₂×C₃×M₁₆	—	2	2	no	—
41	C₂×C₃×M₁₆	Dic₃	1	2	yes	—
42	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
43	C₂²×C₃×C₈	Dic₃	1	1	yes	characteristic
44	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
45	#812	—	3	4	no	—
46	#812	—	6	2	no	—
47	C₂×C₃⋊C₁₆	—	6	2	no	—
48	C₂³×C₉	—	2	1	no	—
49	C₂³×C₉	—	2	1	no	—
50	C₂³×C₉	—	4	2	no	—
51	C₂³×C₉	C₂×C₈	1	1	yes	characteristic
52	C₂³×C₉	C₂×C₈	1	2	yes	—
53	C₂×C₄×C₉	—	2	1	no	—
54	C₂×C₄×C₉	—	2	1	no	—
55	C₂×C₄×C₉	—	2	2	no	—
56	C₂×C₄×C₉	—	2	2	no	—
57	C₂×C₄×C₉	—	2	2	no	—
58	C₂×C₄×C₉	—	2	2	no	—
59	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
62	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
63	C₂×C₄×C₉	M₁₆	1	1	yes	characteristic
64	C₂×C₄×C₉	M₁₆	1	1	yes	characteristic
65	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
66	C₈×C₉	—	2	2	no	—
67	C₈×C₉	C₂²⋊C₄	1	2	yes	—
68	C₈×C₉	C₂×D₄	1	2	yes	—
69	C₂²×M₁₆	D₉	1	1	yes	characteristic
70	C₂×M₃₂	—	9	2	no	—
71	#349	—	9	4	no	—
72	C₂⁴×C₃	C₃⋊C₈	1	1	yes	characteristic
73	C₂²×C₃×C₄	—	2	1	no	—
74	C₂²×C₃×C₄	—	2	1	no	—
75	C₂²×C₃×C₄	—	2	1	no	—
76	C₂²×C₃×C₄	—	2	1	no	—
77	C₂²×C₃×C₄	C₃⋊C₈	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₃⋊C₈	1	2	yes	—
79	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
80	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
81	C₃×M₁₆	—	2	4	no	—
82	C₃×M₁₆	—	2	4	no	—
83	C₂×C₃×C₈	—	2	1	no	—
84	C₂×C₃×C₈	—	2	1	no	—
85	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
86	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
87	C₂×C₃×C₈	#67	1	2	yes	—
88	C₂×C₃×C₈	#67	1	2	yes	—
89	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
90	C₃⋊C₁₆	—	6	4	no	—
91	C₂²×C₉	—	2	2	no	—
92	C₂²×C₉	—	2	2	no	—
93	C₂²×C₉	—	4	2	no	—
94	C₂²×C₉	—	4	2	no	—
95	C₂²×C₉	—	4	2	no	—
96	C₂²×C₉	C₂²⋊C₈	1	1	yes	characteristic
97	C₂²×C₉	C₂²⋊C₈	1	1	yes	characteristic
98	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
99	C₄×C₉	—	2	2	no	—
100	C₄×C₉	C₂²⋊C₈	1	1	yes	characteristic
101	C₄×C₉	C₂²⋊C₈	1	1	yes	characteristic
102	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₄×C₉	C₂×M₁₆	1	1	yes	characteristic
104	C₂³×C₄	Dic₉	1	1	yes	characteristic
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	—	2	2	no	—
107	C₂×M₁₆	Dic₉	1	2	yes	—
108	C₂×M₁₆	C₂×D₉	1	2	yes	—
109	C₂²×C₈	Dic₉	1	1	yes	characteristic
110	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
111	M₃₂	—	9	4	no	—
112	M₃₂	—	18	2	no	—
113	C₂×C₁₆	—	18	2	no	—
114	C₂³×C₃	—	2	1	no	—
115	C₂³×C₃	—	2	1	no	—
116	C₂³×C₃	—	4	2	no	—
117	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
118	C₂³×C₃	C₂×C₃⋊C₈	1	2	yes	—
119	C₂×C₃×C₄	—	2	1	no	—
120	C₂×C₃×C₄	—	2	1	no	—
121	C₂×C₃×C₄	—	2	2	no	—
122	C₂×C₃×C₄	—	2	2	no	—
123	C₂×C₃×C₄	—	2	2	no	—
124	C₂×C₃×C₄	—	2	2	no	—
125	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
126	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
127	C₂×C₃×C₄	#208	1	1	yes	characteristic
128	C₂×C₃×C₄	#208	1	1	yes	characteristic
129	C₂×C₃×C₄	#217	1	1	yes	characteristic
130	C₂×C₃×C₄	#217	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
132	C₃×C₈	—	2	2	no	—
133	C₃×C₈	#217	1	2	yes	—
134	C₃×C₈	C₂×#67	1	2	yes	—
135	C₂×C₉	—	2	1	no	—
136	C₂×C₉	—	2	1	no	—
137	C₂×C₉	—	4	2	no	—
138	C₂×C₉	#349	1	2	yes	complemented
139	C₂×C₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
140	C₂⁴	C₉⋊C₈	1	1	yes	characteristic
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	C₉⋊C₈	1	1	yes	characteristic
146	C₂²×C₄	C₉⋊C₈	1	2	yes	—
147	C₂²×C₄	C₂×Dic₉	1	2	yes	—
148	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
149	M₁₆	—	2	4	no	—
150	M₁₆	—	2	4	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	C₂×Dic₉	1	2	yes	—
154	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
155	C₂×C₈	#611	1	2	yes	—
156	C₂×C₈	#611	1	2	yes	—
157	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
158	C₁₆	—	18	4	no	—
159	C₂²×C₃	—	2	2	no	—
160	C₂²×C₃	—	2	2	no	—
161	C₂²×C₃	—	4	2	no	—
162	C₂²×C₃	—	4	2	no	—
163	C₂²×C₃	—	4	2	no	—
164	C₂²×C₃	#830	1	1	yes	characteristic
165	C₂²×C₃	#830	1	1	yes	characteristic
166	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
167	C₃×C₄	—	2	2	no	—
168	C₃×C₄	#830	1	1	yes	characteristic
169	C₃×C₄	#830	1	1	yes	characteristic
170	C₃×C₄	C₂×#208	1	1	yes	characteristic
171	C₃×C₄	C₂×#217	1	1	yes	characteristic
172	C₉	C₂×#349	1	1	yes	characteristic, complemented, Sylow
173	C₂³	—	2	1	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	4	2	no	—
176	C₂³	C₂×C₉⋊C₈	1	1	yes	characteristic
177	C₂³	C₂×C₉⋊C₈	1	2	yes	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	C₂×C₉⋊C₈	1	2	yes	—
185	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
186	C₂×C₄	#3667	1	1	yes	characteristic
187	C₂×C₄	#3667	1	1	yes	characteristic
188	C₂×C₄	#3676	1	1	yes	characteristic
189	C₂×C₄	#3676	1	1	yes	characteristic
190	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
191	C₈	—	2	2	no	—
192	C₈	#3676	1	2	yes	—
193	C₈	C₂×#611	1	2	yes	—
194	C₂×C₃	—	2	1	no	—
195	C₂×C₃	—	2	1	no	—
196	C₂×C₃	—	4	2	no	—
197	C₂×C₃	#4553	1	2	yes	—
198	C₂×C₃	C₂×#830	1	1	yes	characteristic
199	C₂²	—	2	2	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	4	2	no	—
203	C₂²	—	4	2	no	—
204	C₂²	#63389	1	1	yes	characteristic
205	C₂²	#63389	1	1	yes	characteristic
206	C₂²	C₂²×C₉⋊C₈	1	1	yes	characteristic
207	C₄	—	2	2	no	—
208	C₄	#63389	1	1	yes	characteristic
209	C₄	#63389	1	1	yes	characteristic
210	C₄	C₂×#3667	1	1	yes	characteristic
211	C₄	C₂×#3676	1	1	yes	characteristic
212	C₃	C₂×#4553	1	1	yes	characteristic
213	C₂	—	2	1	no	—
214	C₂	—	2	1	no	—
215	C₂	—	4	2	no	—
216	C₂	#10588230	1	2	yes	direct product factor
217	C₂	C₂×#63389	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3676
commutator	C₂²×C₉	C₂²×C₈
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₂²×C₉×M₁₆	C₂
socle	C₂²×C₃	#830
prime radical	C₂⁴×C₃	C₃⋊C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₂²×M₁₆	D₉
hypocenter	C₉	C₂×#349
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#63371	C₂	semidirect
3. #10588230	C₂	direct (N × H)
13. #63371	C₂²	semidirect
138. C₂×C₉	#349	semidirect
172. C₉	C₂×#349	semidirect
216. C₂	#10588230	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×#63371	2
#10588230	2
C₂×#4553	3

Subgroups — C2×#10588230 #11796027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588230 #11796027