Subgroups — C₂×Q₈×D₃₆ #11902653

Order 1152.

2352 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	C₂²×Q₈×D₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₃₆	C₂	1	16	yes	maximal, direct product factor
4	C₂×#63459	C₂	1	6	yes	maximal, complemented
5	C₂×C₄×D₃₆	C₂	1	3	yes	maximal
6	C₂×#63431	C₂	1	3	yes	maximal, complemented
7	C₂×Q₈×D₁₂	—	3	1	no	maximal
8	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
9	C₂×Q₈×D₉	—	2	16	no	—
10	C₂×Q₈×D₉	C₂²	1	16	yes	complemented
11	C₂²×D₃₆	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₉	C₂²	1	6	yes	—
13	C₂²×Dic₁₈	C₂²	1	6	yes	—
14	C₄×Q₈×C₉	C₂²	1	8	yes	complemented
15	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	—
16	C₂×C₄²×C₉	C₂²	1	3	yes	—
17	C₂×(C₂×D₉)⋊C₄	C₂²	1	6	yes	—
18	C₂×C₄⋊Dic₉	C₂²	1	3	yes	—
19	C₂×C₄⋊Dic₉	C₂²	1	6	yes	—
20	#63459	C₂²	1	48	yes	complemented
21	C₄×D₃₆	C₂²	1	24	yes	—
22	#63431	C₂²	1	24	yes	complemented
23	C₂²×D₃×Q₈	—	3	2	no	—
24	C₂×C₃×C₄×Q₈	D₃	1	1	yes	characteristic
25	Q₈×D₁₂	—	3	16	no	—
26	C₂×#897	—	3	6	no	—
27	C₂×C₄×D₁₂	—	3	3	no	—
28	C₂×#869	—	3	3	no	—
29	C₂³×D₉	C₂³	1	2	yes	—
30	C₂×Q₈×C₉	D₄	1	8	yes	complemented
31	C₂×Q₈×C₉	C₂³	1	4	yes	—
32	C₂²×C₄×C₉	C₂³	1	3	yes	—
33	C₂²×C₄×C₉	C₂³	1	3	yes	—
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₉	C₂³	1	6	yes	—
36	Q₈×D₉	—	2	64	no	—
37	C₂×D₃₆	Q₈	1	8	yes	direct product factor
38	C₂×D₃₆	C₂³	1	4	yes	—
39	C₂×C₄×D₉	—	2	24	no	—
40	C₂×C₄×D₉	C₂³	1	24	yes	—
41	C₂×Dic₁₈	—	2	24	no	—
42	C₂×Dic₁₈	C₂³	1	24	yes	—
43	C₉×C₄⋊C₄	C₂³	1	12	yes	—
44	C₄²×C₉	C₂³	1	12	yes	—
45	(C₂×D₉)⋊C₄	C₂³	1	24	yes	—
46	C₄⋊Dic₉	C₂³	1	12	yes	—
47	C₄⋊Dic₉	C₂³	1	24	yes	—
48	C₂×D₄×Q₈	—	9	1	no	Sylow
49	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
50	C₂×D₃×Q₈	—	3	16	no	—
51	C₂×D₃×Q₈	—	6	16	no	—
52	C₂²×D₁₂	—	3	1	no	—
53	C₂²×C₄×D₃	—	3	6	no	—
54	C₂²×Dic₆	—	3	6	no	—
55	C₃×C₄×Q₈	C₂×D₃	1	8	yes	—
56	C₂×C₃×C₄⋊C₄	C₂×D₃	1	3	yes	—
57	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
58	C₂×(C₂×D₃)⋊C₄	—	3	6	no	—
59	C₂×C₄⋊Dic₃	—	3	3	no	—
60	C₂×C₄⋊Dic₃	—	3	6	no	—
61	#897	—	3	48	no	—
62	C₄×D₁₂	—	3	24	no	—
63	#869	—	3	24	no	—
64	C₂³×C₉	C₂⁴	1	1	yes	characteristic
65	C₂²×D₉	—	2	4	no	—
66	C₂²×D₉	—	2	4	no	—
67	C₂²×D₉	C₂×Q₈	1	8	yes	complemented
68	C₂²×D₉	C₂⁴	1	4	yes	—
69	Q₈×C₉	C₂×D₄	1	16	yes	complemented
70	C₂×C₄×C₉	—	2	6	no	—
71	C₂×C₄×C₉	C₂×D₄	1	12	yes	—
72	C₂×C₄×C₉	C₂×Q₈	1	4	yes	complemented
73	C₂×C₄×C₉	C₂⁴	1	6	yes	—
74	C₂×C₄×C₉	C₂⁴	1	6	yes	—
75	C₂×C₄×C₉	C₂⁴	1	2	yes	—
76	C₂×Dic₉	—	2	12	no	—
77	C₂×Dic₉	C₂⁴	1	12	yes	—
78	D₃₆	C₂×Q₈	1	16	yes	direct product factor
79	C₄×D₉	—	2	48	no	—
80	Dic₁₈	—	2	48	no	—
81	C₂³×Q₈	—	9	2	no	—
82	D₄×Q₈	—	9	16	no	—
83	C₂×C₄⋊Q₈	—	9	3	no	—
84	C₂×C₂²⋊Q₈	—	9	6	no	—
85	C₂×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
86	C₂×C₄×D₄	—	9	3	no	—
87	C₂³×D₃	—	3	2	no	—
88	C₂×C₃×Q₈	D₁₂	1	8	yes	—
89	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
90	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
91	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
92	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
93	C₂²×Dic₃	—	3	6	no	—
94	D₃×Q₈	—	6	64	no	—
95	C₂×D₁₂	—	3	8	no	—
96	C₂×D₁₂	—	3	4	no	—
97	C₂×C₄×D₃	—	3	24	no	—
98	C₂×C₄×D₃	—	6	24	no	—
99	C₂×Dic₆	—	3	24	no	—
100	C₂×Dic₆	—	6	24	no	—
101	C₃×C₄⋊C₄	C₂²×D₃	1	12	yes	—
102	C₃×C₄²	C₂²×D₃	1	12	yes	—
103	(C₂×D₃)⋊C₄	—	3	24	no	—
104	C₄⋊Dic₃	—	3	12	no	—
105	C₄⋊Dic₃	—	3	24	no	—
106	C₂²×C₉	C₂²×D₄	1	2	yes	—
107	C₂²×C₉	C₂²×Q₈	1	2	yes	—
108	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
109	C₂²×C₉	C₂⁵	1	1	yes	characteristic
110	C₂×D₉	—	2	16	no	—
111	C₂×D₉	—	2	4	no	—
112	C₂×D₉	—	2	4	no	—
113	C₂×D₉	C₂²×Q₈	1	8	yes	complemented
114	C₄×C₉	—	2	6	no	—
115	C₄×C₉	C₂²×D₄	1	12	yes	—
116	C₄×C₉	C₂²×Q₈	1	4	yes	complemented
117	Dic₉	—	2	12	no	—
118	C₂²×Q₈	—	9	16	no	—
119	C₂²×Q₈	—	9	6	no	—
120	C₂²×Q₈	—	18	16	no	—
121	C₂²×Q₈	C₂×D₉	1	1	yes	characteristic
122	C₂²×D₄	—	9	1	no	—
123	C₂³×C₄	—	9	6	no	—
124	C₄⋊Q₈	—	9	24	no	—
125	C₂²⋊Q₈	—	9	48	no	—
126	C₄×Q₈	C₂×D₉	1	8	yes	complemented
127	C₄×D₄	—	9	24	no	—
128	C₂×C₄⋊C₄	—	9	3	no	—
129	C₂×C₄⋊C₄	—	9	6	no	—
130	C₂×C₄⋊C₄	C₂×D₉	1	3	yes	—
131	C₂×C₂²⋊C₄	—	9	6	no	—
132	C₂×C₄²	C₂×D₉	1	3	yes	—
133	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
134	C₂²×D₃	—	3	8	no	—
135	C₂²×D₃	—	3	4	no	—
136	C₂²×D₃	—	6	4	no	—
137	C₂²×D₃	—	6	4	no	—
138	C₃×Q₈	C₂×D₁₂	1	16	yes	—
139	C₂×C₃×C₄	—	2	6	no	—
140	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	—
141	C₂×C₃×C₄	D₃×Q₈	1	4	yes	—
142	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
143	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
144	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
145	C₂×Dic₃	—	3	12	no	—
146	C₂×Dic₃	—	6	12	no	—
147	D₁₂	—	3	16	no	—
148	C₄×D₃	—	6	48	no	—
149	Dic₆	—	6	48	no	—
150	C₂×C₉	D₄×Q₈	1	4	yes	complemented
151	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
152	C₂×C₉	C₂³×Q₈	1	1	yes	characteristic
153	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
154	D₉	—	2	8	no	—
155	C₂⁴	—	9	2	no	—
156	C₂×Q₈	—	9	24	no	—
157	C₂×Q₈	—	18	64	no	—
158	C₂×Q₈	—	18	24	no	—
159	C₂×Q₈	D₃₆	1	8	yes	direct product factor
160	C₂×Q₈	C₂²×D₉	1	4	yes	—
161	C₂×D₄	—	9	8	no	—
162	C₂×D₄	—	9	4	no	—
163	C₂²×C₄	—	9	6	no	—
164	C₂²×C₄	—	9	24	no	—
165	C₂²×C₄	—	18	24	no	—
166	C₂²×C₄	C₂²×D₉	1	3	yes	—
167	C₂²×C₄	C₂²×D₉	1	3	yes	—
168	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
169	C₄⋊C₄	—	9	12	no	—
170	C₄⋊C₄	—	9	24	no	—
171	C₄⋊C₄	C₂²×D₉	1	12	yes	—
172	C₂²⋊C₄	—	9	24	no	—
173	C₄²	C₂²×D₉	1	12	yes	—
174	C₂²×C₃	C₂²×D₁₂	1	2	yes	—
175	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
176	C₂²×C₃	#1010	1	2	yes	—
177	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
178	C₂×D₃	—	3	8	no	—
179	C₂×D₃	—	6	4	no	—
180	C₂×D₃	—	6	4	no	—
181	C₂×D₃	—	6	16	no	—
182	C₃×C₄	—	2	6	no	—
183	C₃×C₄	C₂²×D₁₂	1	12	yes	—
184	C₃×C₄	C₂×D₃×Q₈	1	4	yes	—
185	Dic₃	—	6	12	no	—
186	C₉	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
187	C₂³	—	9	4	no	—
188	C₂³	—	9	8	no	—
189	C₂³	—	18	4	no	—
190	C₂³	—	18	4	no	—
191	C₂³	C₂³×D₉	1	1	yes	characteristic
192	Q₈	—	18	48	no	—
193	Q₈	C₂×D₃₆	1	16	yes	direct product factor
194	D₄	—	9	16	no	—
195	C₂×C₄	—	2	6	no	—
196	C₂×C₄	—	9	12	no	—
197	C₂×C₄	—	18	12	no	—
198	C₂×C₄	—	18	48	no	—
199	C₂×C₄	C₂×D₃₆	1	12	yes	—
200	C₂×C₄	Q₈×D₉	1	4	yes	complemented
201	C₂×C₄	C₂³×D₉	1	6	yes	—
202	C₂×C₄	C₂³×D₉	1	6	yes	—
203	C₂×C₄	C₂³×D₉	1	2	yes	—
204	C₂×C₃	Q₈×D₁₂	1	4	yes	—
205	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
206	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
207	C₂×C₃	C₂×#1010	1	1	yes	characteristic
208	D₃	—	6	8	no	—
209	C₂²	—	9	8	no	—
210	C₂²	—	18	4	no	—
211	C₂²	—	18	4	no	—
212	C₂²	—	18	16	no	—
213	C₂²	C₂²×D₃₆	1	2	yes	—
214	C₂²	C₂×Q₈×D₉	1	2	yes	—
215	C₂²	#63716	1	2	yes	—
216	C₂²	C₂⁴×D₉	1	1	yes	characteristic
217	C₄	—	2	6	no	—
218	C₄	—	18	12	no	—
219	C₄	C₂²×D₃₆	1	12	yes	—
220	C₄	C₂×Q₈×D₉	1	4	yes	complemented
221	C₃	C₂×Q₈×D₁₂	1	1	yes	characteristic
222	C₂	—	18	8	no	—
223	C₂	Q₈×D₃₆	1	4	yes	direct product factor
224	C₂	C₂³×D₃₆	1	1	yes	characteristic
225	C₂	C₂²×Q₈×D₉	1	1	yes	characteristic
226	C₂	C₂×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁵
Frattini	C₂²×C₃	C₂⁴×D₃
Fitting	C₂×C₄×Q₈×C₉	C₂
socle	C₂³×C₃	C₂³×D₃
prime radical	C₂²×D₃₆	C₂²
hypercenter	C₂×C₄×Q₈	D₉
hypocenter	C₉	C₂×D₄×Q₈
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×D₉	C₂	semidirect
2. C₂×C₄×Q₈×C₉	C₂	semidirect
3. Q₈×D₃₆	C₂	direct (N × H)
4. C₂×#63459	C₂	semidirect
6. C₂×#63431	C₂	semidirect
10. C₂×Q₈×D₉	C₂²	semidirect
14. C₄×Q₈×C₉	C₂²	semidirect
20. #63459	C₂²	semidirect
22. #63431	C₂²	semidirect
30. C₂×Q₈×C₉	D₄	semidirect
37. C₂×D₃₆	Q₈	direct (N × H)
67. C₂²×D₉	C₂×Q₈	semidirect
69. Q₈×C₉	C₂×D₄	semidirect
72. C₂×C₄×C₉	C₂×Q₈	semidirect
78. D₃₆	C₂×Q₈	direct (N × H)
85. C₂×C₄×Q₈	D₉	semidirect
113. C₂×D₉	C₂²×Q₈	semidirect
116. C₄×C₉	C₂²×Q₈	semidirect
126. C₄×Q₈	C₂×D₉	semidirect
150. C₂×C₉	D₄×Q₈	semidirect
159. C₂×Q₈	D₃₆	direct (N × H)
186. C₉	C₂×D₄×Q₈	semidirect
193. Q₈	C₂×D₃₆	direct (N × H)
200. C₂×C₄	Q₈×D₉	semidirect
220. C₄	C₂×Q₈×D₉	semidirect
223. C₂	Q₈×D₃₆	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×Q₈×D₉	2
C₂×C₄×Q₈×C₉	2
Q₈×D₃₆	2
C₂×#63459	2
C₂×C₄×D₃₆	2
C₂×#63431	2
C₂×Q₈×D₁₂	3

Subgroups — C2×Q8×D36 #11902653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×D₃₆ #11902653