Subgroups — C₂×#41×Dic₉ #11899957

Order 1152.

2592 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	#41×Dic₉	C₂	1	16	yes	maximal, direct product factor
3	C₂×Q₈×Dic₉	C₂	1	2	yes	maximal, complemented
4	C₂×D₄×Dic₉	C₂	1	6	yes	maximal, complemented
5	C₂×#63488	C₂	1	3	yes	maximal, complemented
6	C₂²×C₄×Dic₉	C₂	1	3	yes	maximal, complemented
7	C₂×Dic₃×#41	—	3	1	no	maximal
8	C₂×C₉×#41	C₄	1	16	yes	complemented
9	C₂×C₉×#41	C₂²	1	8	yes	—
10	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₉	C₂²	1	3	yes	—
12	C₂³×C₄×C₉	C₂²	1	3	yes	—
13	C₂³×Dic₉	C₂²	1	6	yes	—
14	C₂×#3676	C₂²	1	6	yes	—
15	Q₈×Dic₉	C₂²	1	16	yes	complemented
16	D₄×Dic₉	C₂²	1	48	yes	complemented
17	#63488	C₂²	1	24	yes	complemented
18	C₂×C₄⋊Dic₉	C₂²	1	6	yes	—
19	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₉	C₂²	1	3	yes	—
21	C₂×C₄×Dic₉	C₂²	1	6	yes	—
22	C₂×C₄×Dic₉	C₂²	1	24	yes	complemented
23	C₂²×C₃×#41	D₃	1	1	yes	characteristic
24	Dic₃×#41	—	3	16	no	—
25	C₂×Q₈×Dic₃	—	3	2	no	—
26	C₂×D₄×Dic₃	—	3	6	no	—
27	C₂×#926	—	3	3	no	—
28	C₂²×C₄×Dic₃	—	3	3	no	—
29	C₂⁴×C₉	C₂³	1	3	yes	—
30	C₉×#41	C₂×C₄	1	64	yes	complemented
31	C₂×Q₈×C₉	C₂×C₄	1	8	yes	complemented
32	C₂×Q₈×C₉	C₂³	1	4	yes	—
33	C₂×D₄×C₉	C₂×C₄	1	24	yes	complemented
34	C₂×D₄×C₉	C₂³	1	12	yes	—
35	C₂²×C₄×C₉	C₂×C₄	1	24	yes	complemented
36	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₉	C₂³	1	3	yes	—
38	C₂²×C₄×C₉	C₂³	1	12	yes	—
39	C₂²×Dic₉	—	2	24	no	—
40	C₂²×Dic₉	C₂³	1	24	yes	—
41	C₂²×Dic₉	C₂³	1	6	yes	—
42	C₂²×Dic₉	C₂³	1	2	yes	—
43	#3676	C₂³	1	24	yes	—
44	C₄⋊Dic₉	C₂³	1	24	yes	—
45	C₄×Dic₉	C₂³	1	12	yes	—
46	C₄×Dic₉	C₂³	1	24	yes	—
47	C₄×Dic₉	C₂³	1	4	yes	—
48	C₂×C₄×#41	—	9	1	no	Sylow
49	C₂×C₃×#41	Dic₃	1	16	yes	—
50	C₂×C₃×#41	C₂×D₃	1	8	yes	—
51	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
52	C₂²×C₃×D₄	C₂×D₃	1	3	yes	—
53	C₂³×C₃×C₄	C₂×D₃	1	3	yes	—
54	C₂³×Dic₃	—	3	6	no	—
55	C₂×#217	—	3	6	no	—
56	Q₈×Dic₃	—	3	16	no	—
57	D₄×Dic₃	—	3	48	no	—
58	#926	—	3	24	no	—
59	C₂×C₄⋊Dic₃	—	3	6	no	—
60	C₂×C₄×Dic₃	—	3	1	no	—
61	C₂×C₄×Dic₃	—	3	3	no	—
62	C₂×C₄×Dic₃	—	3	6	no	—
63	C₂×C₄×Dic₃	—	3	24	no	—
64	C₂³×C₉	—	2	12	no	—
65	C₂³×C₉	C₂²×C₄	1	12	yes	—
66	C₂³×C₉	C₂⁴	1	6	yes	—
67	C₂³×C₉	C₂⁴	1	1	yes	characteristic
68	Q₈×C₉	C₂²×C₄	1	16	yes	complemented
69	D₄×C₉	C₂²×C₄	1	48	yes	complemented
70	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₉	C₂²×C₄	1	12	yes	—
72	C₂×C₄×C₉	C₂²×C₄	1	48	yes	complemented
73	C₂×C₄×C₉	C₂⁴	1	2	yes	—
74	C₂×C₄×C₉	C₂⁴	1	6	yes	—
75	C₂×Dic₉	—	2	12	no	—
76	C₂×Dic₉	—	2	48	no	—
77	C₂×Dic₉	#41	1	8	yes	direct product factor
78	C₂×Dic₉	C₂⁴	1	12	yes	—
79	C₂×Dic₉	C₂⁴	1	4	yes	—
80	C₂²×#41	D₉	1	1	yes	characteristic
81	C₄×#41	—	9	16	no	—
82	C₂×C₄×Q₈	—	9	2	no	—
83	C₂×C₄×D₄	—	9	6	no	—
84	C₂×#117	—	9	3	no	—
85	C₂²×C₄²	—	9	3	no	—
86	C₂⁴×C₃	C₂²×D₃	1	3	yes	—
87	C₃×#41	C₂×Dic₃	1	64	yes	—
88	C₂×C₃×Q₈	C₂×Dic₃	1	8	yes	—
89	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
90	C₂×C₃×D₄	C₂×Dic₃	1	24	yes	—
91	C₂×C₃×D₄	C₂²×D₃	1	12	yes	—
92	C₂²×C₃×C₄	C₂×Dic₃	1	24	yes	—
93	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
94	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	—
95	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
96	C₂²×Dic₃	—	3	2	no	—
97	C₂²×Dic₃	—	3	6	no	—
98	C₂²×Dic₃	—	3	24	no	—
99	C₂²×Dic₃	—	6	24	no	—
100	#217	—	3	24	no	—
101	C₄⋊Dic₃	—	3	24	no	—
102	C₄×Dic₃	—	3	4	no	—
103	C₄×Dic₃	—	3	12	no	—
104	C₄×Dic₃	—	3	24	no	—
105	C₂²×C₉	—	2	24	no	—
106	C₂²×C₉	—	2	12	no	—
107	C₂²×C₉	C₂³×C₄	1	12	yes	—
108	C₂²×C₉	C₂³×C₄	1	2	yes	—
109	C₂²×C₉	C₂×#41	1	4	yes	—
110	C₂²×C₉	C₂⁵	1	1	yes	characteristic
111	C₄×C₉	C₂³×C₄	1	4	yes	—
112	C₄×C₉	C₂³×C₄	1	12	yes	—
113	Dic₉	—	2	12	no	—
114	Dic₉	C₂×#41	1	8	yes	direct product factor
115	C₂×#41	Dic₉	1	16	yes	direct product factor
116	C₂×#41	C₂×D₉	1	8	yes	—
117	C₂²×Q₈	C₂×D₉	1	1	yes	characteristic
118	C₂²×D₄	C₂×D₉	1	3	yes	—
119	C₂³×C₄	—	9	6	no	—
120	C₂³×C₄	C₂×D₉	1	3	yes	—
121	C₄×Q₈	—	9	16	no	—
122	C₄×D₄	—	9	48	no	—
123	#117	—	9	24	no	—
124	C₂×C₄⋊C₄	—	9	6	no	—
125	C₂×C₂²⋊C₄	—	9	6	no	—
126	C₂×C₄²	—	9	6	no	—
127	C₂×C₄²	—	9	24	no	—
128	C₂×C₄²	—	9	3	no	—
129	C₂×C₄²	—	9	1	no	—
130	C₂³×C₃	—	2	12	no	—
131	C₂³×C₃	C₂²×Dic₃	1	12	yes	—
132	C₂³×C₃	C₂³×D₃	1	6	yes	—
133	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
134	C₃×Q₈	C₂²×Dic₃	1	16	yes	—
135	C₃×D₄	C₂²×Dic₃	1	48	yes	—
136	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
137	C₂×C₃×C₄	C₂²×Dic₃	1	12	yes	—
138	C₂×C₃×C₄	C₂²×Dic₃	1	48	yes	—
139	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
140	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
141	C₂×Dic₃	—	3	8	no	—
142	C₂×Dic₃	—	3	4	no	—
143	C₂×Dic₃	—	3	12	no	—
144	C₂×Dic₃	—	6	48	no	—
145	C₂×Dic₃	—	6	12	no	—
146	C₂×C₉	—	2	12	no	—
147	C₂×C₉	C₄×#41	1	4	yes	complemented
148	C₂×C₉	C₂⁴×C₄	1	1	yes	characteristic
149	C₂×C₉	C₂²×#41	1	2	yes	—
150	C₂⁴	C₂²×D₉	1	3	yes	—
151	#41	C₂×Dic₉	1	64	yes	direct product factor
152	C₂×Q₈	C₂×Dic₉	1	8	yes	complemented
153	C₂×Q₈	C₂²×D₉	1	4	yes	—
154	C₂×D₄	C₂×Dic₉	1	24	yes	complemented
155	C₂×D₄	C₂²×D₉	1	12	yes	—
156	C₂²×C₄	—	9	2	no	—
157	C₂²×C₄	—	9	6	no	—
158	C₂²×C₄	—	9	24	no	—
159	C₂²×C₄	—	18	24	no	—
160	C₂²×C₄	C₂×Dic₉	1	24	yes	complemented
161	C₂²×C₄	C₂²×D₉	1	3	yes	—
162	C₂²×C₄	C₂²×D₉	1	12	yes	—
163	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
164	C₄⋊C₄	—	9	24	no	—
165	C₂²⋊C₄	—	9	24	no	—
166	C₄²	—	9	4	no	—
167	C₄²	—	9	12	no	—
168	C₄²	—	9	24	no	—
169	C₂²×C₃	—	2	12	no	—
170	C₂²×C₃	—	2	24	no	—
171	C₂²×C₃	D₃×#41	1	4	yes	—
172	C₂²×C₃	C₂³×Dic₃	1	12	yes	—
173	C₂²×C₃	C₂³×Dic₃	1	2	yes	—
174	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
175	C₃×C₄	C₂³×Dic₃	1	4	yes	—
176	C₃×C₄	C₂³×Dic₃	1	12	yes	—
177	Dic₃	—	3	8	no	—
178	Dic₃	—	6	12	no	—
179	C₉	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
180	C₂³	—	2	12	no	—
181	C₂³	C₂²×Dic₉	1	12	yes	—
182	C₂³	C₂³×D₉	1	6	yes	—
183	C₂³	C₂³×D₉	1	1	yes	characteristic
184	Q₈	C₂²×Dic₉	1	16	yes	complemented
185	D₄	C₂²×Dic₉	1	48	yes	complemented
186	C₂×C₄	—	9	4	no	—
187	C₂×C₄	—	9	8	no	—
188	C₂×C₄	—	9	12	no	—
189	C₂×C₄	—	18	48	no	—
190	C₂×C₄	—	18	12	no	—
191	C₂×C₄	C₂²×Dic₉	1	4	yes	—
192	C₂×C₄	C₂²×Dic₉	1	12	yes	—
193	C₂×C₄	C₂²×Dic₉	1	48	yes	complemented
194	C₂×C₄	C₂³×D₉	1	2	yes	—
195	C₂×C₄	C₂³×D₉	1	6	yes	—
196	C₂×C₃	—	2	12	no	—
197	C₂×C₃	Dic₃×#41	1	4	yes	—
198	C₂×C₃	C₂×D₃×#41	1	2	yes	—
199	C₂×C₃	C₂⁴×Dic₃	1	1	yes	characteristic
200	C₂²	—	2	12	no	—
201	C₂²	—	2	24	no	—
202	C₂²	#41×D₉	1	4	yes	—
203	C₂²	C₂³×Dic₉	1	12	yes	—
204	C₂²	C₂³×Dic₉	1	2	yes	—
205	C₂²	C₂⁴×D₉	1	1	yes	characteristic
206	C₄	—	9	8	no	—
207	C₄	—	18	12	no	—
208	C₄	C₂³×Dic₉	1	4	yes	—
209	C₄	C₂³×Dic₉	1	12	yes	—
210	C₃	C₂×Dic₃×#41	1	1	yes	characteristic
211	C₂	—	2	12	no	—
212	C₂	#41×Dic₉	1	4	yes	direct product factor
213	C₂	C₂×#41×D₉	1	2	yes	—
214	C₂	C₂⁴×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂×C₉	C₂⁴×C₄
Frattini	C₂²×C₃	C₂⁴×D₃
Fitting	C₂²×C₉×#41	C₂
socle	C₂³×C₃	C₂³×D₃
prime radical	C₂²×C₃×#41	D₃
cosocle	C₂²×C₉	C₂⁵
hypercenter	C₂²×#41	D₉
hypocenter	C₉	C₂×C₄×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
2. #41×Dic₉	C₂	direct (N × H)
3. C₂×Q₈×Dic₉	C₂	semidirect
4. C₂×D₄×Dic₉	C₂	semidirect
5. C₂×#63488	C₂	semidirect
6. C₂²×C₄×Dic₉	C₂	semidirect
8. C₂×C₉×#41	C₄	semidirect
15. Q₈×Dic₉	C₂²	semidirect
16. D₄×Dic₉	C₂²	semidirect
17. #63488	C₂²	semidirect
22. C₂×C₄×Dic₉	C₂²	semidirect
30. C₉×#41	C₂×C₄	semidirect
31. C₂×Q₈×C₉	C₂×C₄	semidirect
33. C₂×D₄×C₉	C₂×C₄	semidirect
35. C₂²×C₄×C₉	C₂×C₄	semidirect
68. Q₈×C₉	C₂²×C₄	semidirect
69. D₄×C₉	C₂²×C₄	semidirect
72. C₂×C₄×C₉	C₂²×C₄	semidirect
77. C₂×Dic₉	#41	direct (N × H)
114. Dic₉	C₂×#41	direct (N × H)
115. C₂×#41	Dic₉	direct (N × H)
147. C₂×C₉	C₄×#41	semidirect
151. #41	C₂×Dic₉	direct (N × H)
152. C₂×Q₈	C₂×Dic₉	semidirect
154. C₂×D₄	C₂×Dic₉	semidirect
160. C₂²×C₄	C₂×Dic₉	semidirect
179. C₉	C₂×C₄×#41	semidirect
184. Q₈	C₂²×Dic₉	semidirect
185. D₄	C₂²×Dic₉	semidirect
193. C₂×C₄	C₂²×Dic₉	semidirect
212. C₂	#41×Dic₉	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×#41	2
#41×Dic₉	2
C₂×Q₈×Dic₉	2
C₂×D₄×Dic₉	2
C₂×#63488	2
C₂²×C₄×Dic₉	2
C₂×Dic₃×#41	3

Subgroups — C2×#41×Dic9 #11899957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×Dic₉ #11899957