Subgroups — C₂²×#63380 #11857721

Order 1152.

1608 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#63380	C₂	1	12	yes	maximal, direct product factor
5	C₂²×#821	—	3	1	no	maximal
6	C₂⁴×D₉	—	2	1	no	—
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂³×Dic₉	—	2	1	no	—
9	C₂²×D₃₆	—	2	3	no	—
10	C₂²×D₃₆	—	2	4	no	—
11	C₂²×D₃₆	C₄	1	8	yes	complemented
12	C₂²×D₃₆	C₂²	1	6	yes	—
13	C₂²×C₈×C₉	—	2	4	no	—
14	C₂²×C₈×C₉	C₂²	1	6	yes	complemented
15	C₂×C₄⋊Dic₉	—	2	3	no	—
16	C₂×C₄⋊Dic₉	C₂²	1	6	yes	complemented
17	#63380	C₂²	1	16	yes	direct product factor
18	C₂³×D₁₂	—	3	1	no	—
19	C₂³×C₃×C₈	D₃	1	1	yes	characteristic
20	C₂²×C₄⋊Dic₃	—	3	1	no	—
21	C₂×#821	—	3	12	no	—
22	C₂⁴×C₉	D₄	1	1	yes	characteristic
23	C₂³×D₉	—	2	8	no	—
24	C₂³×D₉	—	2	6	no	—
25	C₂³×D₉	—	4	4	no	—
26	C₂³×D₉	—	4	4	no	—
27	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
28	C₂²×C₄×C₉	D₄	1	3	yes	—
29	C₂²×C₄×C₉	D₄	1	4	yes	—
30	C₂²×C₄×C₉	C₂³	1	3	yes	—
31	C₂²×Dic₉	—	2	6	no	—
32	C₂²×Dic₉	—	4	4	no	—
33	C₂×D₃₆	—	2	24	no	—
34	C₂×D₃₆	—	2	6	no	—
35	C₂×D₃₆	—	2	12	no	—
36	C₂×D₃₆	C₂×C₄	1	24	yes	complemented
37	C₂×D₃₆	C₂³	1	4	yes	—
38	C₂×C₈×C₉	—	2	12	no	—
39	C₂×C₈×C₉	C₂³	1	4	yes	complemented
40	C₄⋊Dic₉	—	2	6	no	—
41	C₄⋊Dic₉	C₂³	1	4	yes	complemented
42	C₂²×#102	—	9	1	no	Sylow
43	C₂⁴×D₃	—	6	1	no	—
44	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
45	C₂³×Dic₃	—	6	1	no	—
46	C₂²×D₁₂	—	3	8	no	—
47	C₂²×D₁₂	—	3	6	no	—
48	C₂²×D₁₂	—	6	3	no	—
49	C₂²×D₁₂	—	6	4	no	—
50	C₂²×C₃×C₈	—	2	4	no	—
51	C₂²×C₃×C₈	C₂×D₃	1	6	yes	—
52	C₂×C₄⋊Dic₃	—	3	6	no	—
53	C₂×C₄⋊Dic₃	—	6	3	no	—
54	#821	—	3	16	no	—
55	C₂³×C₉	C₂²⋊C₄	1	4	yes	—
56	C₂³×C₉	D₈	1	4	yes	—
57	C₂³×C₉	SD₁₆	1	4	yes	—
58	C₂³×C₉	C₂×D₄	1	3	yes	—
59	C₂²×D₉	—	2	24	no	—
60	C₂²×D₉	—	2	4	no	—
61	C₂²×D₉	—	4	32	no	—
62	C₂²×D₉	—	4	12	no	—
63	C₂²×D₉	—	4	12	no	—
64	C₂×C₄×C₉	C₂²⋊C₄	1	12	yes	—
65	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
66	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
67	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
68	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
69	C₂×Dic₉	—	2	4	no	—
70	C₂×Dic₉	—	4	12	no	—
71	D₃₆	—	2	24	no	—
72	D₃₆	—	2	4	no	—
73	D₃₆	C₂²×C₄	1	8	yes	complemented
74	C₈×C₉	—	2	4	no	—
75	C₂³×D₄	—	9	1	no	—
76	C₂³×C₈	D₉	1	1	yes	characteristic, complemented
77	C₂²×C₄⋊C₄	—	9	1	no	—
78	C₂×#102	—	9	12	no	—
79	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
80	C₂³×D₃	—	6	8	no	—
81	C₂³×D₃	—	6	6	no	—
82	C₂³×D₃	—	12	4	no	—
83	C₂³×D₃	—	12	4	no	—
84	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
85	C₂²×C₃×C₄	D₁₂	1	3	yes	—
86	C₂²×C₃×C₄	#67	1	4	yes	—
87	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
88	C₂²×Dic₃	—	6	6	no	—
89	C₂²×Dic₃	—	12	4	no	—
90	C₂×D₁₂	—	3	24	no	—
91	C₂×D₁₂	—	3	4	no	—
92	C₂×D₁₂	—	6	24	no	—
93	C₂×D₁₂	—	6	6	no	—
94	C₂×D₁₂	—	6	12	no	—
95	C₂×C₃×C₈	—	2	12	no	—
96	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
97	C₄⋊Dic₃	—	3	4	no	—
98	C₄⋊Dic₃	—	6	6	no	—
99	C₂²×C₉	#102	1	16	yes	complemented
100	C₂²×C₉	C₂×C₂²⋊C₄	1	6	yes	—
101	C₂²×C₉	C₂×D₈	1	6	yes	—
102	C₂²×C₉	C₂×SD₁₆	1	6	yes	—
103	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
104	C₂×D₉	—	2	8	no	—
105	C₂×D₉	—	4	4	no	—
106	C₂×D₉	—	4	4	no	—
107	C₂×D₉	—	4	48	no	—
108	C₄×C₉	C₂×C₂²⋊C₄	1	6	yes	—
109	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
110	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
111	Dic₉	—	4	4	no	—
112	C₂⁵	—	18	1	no	—
113	C₂²×D₄	—	9	8	no	—
114	C₂²×D₄	—	9	6	no	—
115	C₂²×D₄	—	18	3	no	—
116	C₂²×D₄	—	18	4	no	—
117	C₂³×C₄	—	18	1	no	—
118	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
119	C₂²×C₈	—	2	4	no	—
120	C₂²×C₈	C₂×D₉	1	6	yes	complemented
121	C₂×C₄⋊C₄	—	9	6	no	—
122	C₂×C₄⋊C₄	—	18	3	no	—
123	#102	—	9	16	no	—
124	C₂³×C₃	#204	1	4	yes	—
125	C₂³×C₃	D₂₄	1	4	yes	—
126	C₂³×C₃	(C₂×D₃)⋊C₄	1	4	yes	—
127	C₂³×C₃	C₂×D₁₂	1	3	yes	—
128	C₂²×D₃	—	6	24	no	—
129	C₂²×D₃	—	6	4	no	—
130	C₂²×D₃	—	12	32	no	—
131	C₂²×D₃	—	12	12	no	—
132	C₂²×D₃	—	12	12	no	—
133	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	12	yes	—
134	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
135	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
136	C₂×C₃×C₄	C₂×#67	1	6	yes	—
137	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
138	C₂×Dic₃	—	6	4	no	—
139	C₂×Dic₃	—	12	12	no	—
140	D₁₂	—	3	8	no	—
141	D₁₂	—	6	24	no	—
142	D₁₂	—	6	4	no	—
143	C₃×C₈	—	2	4	no	—
144	C₂×C₉	C₂×#102	1	12	yes	complemented
145	C₂×C₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₉	C₂²×D₈	1	1	yes	characteristic
147	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
148	D₉	—	4	8	no	—
149	C₂⁴	—	18	8	no	—
150	C₂⁴	—	18	6	no	—
151	C₂⁴	—	36	4	no	—
152	C₂⁴	—	36	4	no	—
153	C₂⁴	D₃₆	1	1	yes	characteristic
154	C₂×D₄	—	9	24	no	—
155	C₂×D₄	—	9	4	no	—
156	C₂×D₄	—	18	24	no	—
157	C₂×D₄	—	18	6	no	—
158	C₂×D₄	—	18	12	no	—
159	C₂²×C₄	—	18	6	no	—
160	C₂²×C₄	—	36	4	no	—
161	C₂²×C₄	C₄×D₉	1	4	yes	—
162	C₂²×C₄	D₃₆	1	3	yes	—
163	C₂²×C₄	#611	1	4	yes	—
164	C₂²×C₄	C₂²×D₉	1	3	yes	—
165	C₂×C₈	—	2	12	no	—
166	C₂×C₈	C₂²×D₉	1	4	yes	complemented
167	C₄⋊C₄	—	9	4	no	—
168	C₄⋊C₄	—	18	6	no	—
169	C₂²×C₃	#821	1	16	yes	—
170	C₂²×C₃	C₂×#204	1	6	yes	—
171	C₂²×C₃	C₂×D₂₄	1	6	yes	—
172	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
173	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
174	C₂×D₃	—	6	8	no	—
175	C₂×D₃	—	12	4	no	—
176	C₂×D₃	—	12	4	no	—
177	C₂×D₃	—	12	48	no	—
178	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
179	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
180	C₃×C₄	C₂²×#67	1	1	yes	characteristic
181	Dic₃	—	12	4	no	—
182	C₉	C₂²×#102	1	1	yes	characteristic, complemented, Sylow
183	C₂³	—	18	24	no	—
184	C₂³	—	18	4	no	—
185	C₂³	—	36	32	no	—
186	C₂³	—	36	12	no	—
187	C₂³	—	36	12	no	—
188	C₂³	#3664	1	4	yes	—
189	C₂³	D₇₂	1	4	yes	—
190	C₂³	(C₂×D₉)⋊C₄	1	4	yes	—
191	C₂³	C₂×D₃₆	1	3	yes	—
192	D₄	—	9	8	no	—
193	D₄	—	18	24	no	—
194	D₄	—	18	4	no	—
195	C₂×C₄	—	18	4	no	—
196	C₂×C₄	—	36	12	no	—
197	C₂×C₄	(C₂×D₉)⋊C₄	1	12	yes	—
198	C₂×C₄	C₂×C₄×D₉	1	6	yes	—
199	C₂×C₄	C₂×D₃₆	1	3	yes	—
200	C₂×C₄	C₂×#611	1	6	yes	—
201	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
202	C₈	—	2	4	no	—
203	C₂×C₃	C₂×#821	1	12	yes	—
204	C₂×C₃	C₂²×#204	1	1	yes	characteristic
205	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
206	C₂×C₃	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
207	D₃	—	12	8	no	—
208	C₂²	—	18	8	no	—
209	C₂²	—	36	48	no	—
210	C₂²	—	36	4	no	—
211	C₂²	—	36	4	no	—
212	C₂²	#63380	1	16	yes	direct product factor
213	C₂²	C₂×#3664	1	6	yes	—
214	C₂²	C₂×D₇₂	1	6	yes	—
215	C₂²	C₂×(C₂×D₉)⋊C₄	1	6	yes	—
216	C₂²	C₂²×D₃₆	1	1	yes	characteristic
217	C₄	—	36	4	no	—
218	C₄	C₂×(C₂×D₉)⋊C₄	1	6	yes	—
219	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
220	C₄	C₂²×#611	1	1	yes	characteristic
221	C₃	C₂²×#821	1	1	yes	characteristic
222	C₂	—	36	8	no	—
223	C₂	C₂×#63380	1	12	yes	direct product factor
224	C₂	C₂²×#3664	1	1	yes	characteristic
225	C₂	C₂²×D₇₂	1	1	yes	characteristic
226	C₂	C₂²×(C₂×D₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₃₆
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂³×C₈×C₉	C₂
socle	C₂⁴×C₃	D₁₂
prime radical	C₂³×D₃₆	C₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂³×C₈	D₉
hypocenter	C₉	C₂²×#102
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂³×C₈×C₉	C₂	semidirect
3. C₂²×C₄⋊Dic₉	C₂	semidirect
4. C₂×#63380	C₂	direct (N × H)
11. C₂²×D₃₆	C₄	semidirect
14. C₂²×C₈×C₉	C₂²	semidirect
16. C₂×C₄⋊Dic₉	C₂²	semidirect
17. #63380	C₂²	direct (N × H)
36. C₂×D₃₆	C₂×C₄	semidirect
39. C₂×C₈×C₉	C₂³	semidirect
41. C₄⋊Dic₉	C₂³	semidirect
73. D₃₆	C₂²×C₄	semidirect
76. C₂³×C₈	D₉	semidirect
99. C₂²×C₉	#102	semidirect
120. C₂²×C₈	C₂×D₉	semidirect
144. C₂×C₉	C₂×#102	semidirect
166. C₂×C₈	C₂²×D₉	semidirect
182. C₉	C₂²×#102	semidirect
212. C₂²	#63380	direct (N × H)
223. C₂	C₂×#63380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃₆	2
C₂³×C₈×C₉	2
C₂²×C₄⋊Dic₉	2
C₂×#63380	2
C₂²×#821	3

Subgroups — C22×#63380 #11857721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#63380 #11857721