Subgroups — C₂×#10588384 #11860107

Order 1152.

720 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₈	C₂	1	2	yes	maximal
3	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×#63377	C₂	1	1	yes	maximal, characteristic
5	C₂×#63376	C₂	1	2	yes	maximal
6	#10588384	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4716	—	3	1	no	maximal
8	C₂²×Dic₁₈	C₂²	1	2	yes	—
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
13	C₂×Dic₉⋊C₄	—	2	2	no	—
14	C₂×C₄×Dic₉	—	2	2	no	—
15	C₂×Dic₃₆	C₄	1	8	yes	complemented
16	C₂×Dic₃₆	C₂²	1	4	yes	—
17	C₄×Dic₁₈	—	2	4	no	—
18	C₄×Dic₁₈	C₂²	1	8	yes	—
19	C₉×#97	C₂²	1	4	yes	—
20	#63377	C₂²	1	4	yes	—
21	#63376	C₂²	1	8	yes	—
22	C₂²×Dic₁₂	—	3	1	no	—
23	C₂×C₄×Dic₆	—	3	2	no	—
24	C₂×C₃×#97	D₃	1	1	yes	characteristic
25	C₂×#817	—	3	1	no	—
26	C₂×#816	—	3	2	no	—
27	#4716	—	3	8	no	—
28	C₂²×C₄×C₉	D₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₉	—	2	2	no	—
31	C₂²×Dic₉	—	2	2	no	—
32	C₂×Dic₁₈	—	2	2	no	—
33	C₂×Dic₁₈	—	2	4	no	—
34	C₂×Dic₁₈	C₂×C₄	1	8	yes	—
35	C₂×Dic₁₈	C₂³	1	4	yes	—
36	C₂×C₈×C₉	—	2	2	no	—
37	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
38	C₂×C₈×C₉	C₂³	1	2	yes	—
39	C₂×C₈×C₉	C₂³	1	2	yes	—
40	C₄²×C₉	D₄	1	2	yes	—
41	C₄²×C₉	C₂³	1	2	yes	—
42	C₄⋊Dic₉	—	2	2	no	—
43	C₄⋊Dic₉	C₂³	1	4	yes	—
44	Dic₉⋊C₄	—	2	8	no	—
45	C₄×Dic₉	—	2	8	no	—
46	Dic₃₆	C₂×C₄	1	16	yes	complemented
47	C₂×#441	—	9	1	no	Sylow
48	C₂²×Dic₆	—	3	2	no	—
49	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
50	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
51	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	C₂×C₄⋊Dic₃	—	3	2	no	—
53	C₂×Dic₃⋊C₄	—	6	2	no	—
54	C₂×C₄×Dic₃	—	6	2	no	—
55	C₂×Dic₁₂	—	3	8	no	—
56	C₂×Dic₁₂	—	3	4	no	—
57	C₄×Dic₆	—	3	8	no	—
58	C₄×Dic₆	—	6	4	no	—
59	C₃×#97	C₂×D₃	1	4	yes	—
60	#817	—	3	4	no	—
61	#816	—	3	8	no	—
62	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₉	#41	1	2	yes	—
68	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
69	C₂×Dic₉	—	2	8	no	—
70	C₂×Dic₉	—	2	4	no	—
71	C₂×Dic₉	—	2	4	no	—
72	C₂×Dic₉	—	4	4	no	—
73	Dic₁₈	—	2	8	no	—
74	Dic₁₈	—	2	4	no	—
75	Dic₁₈	C₂²×C₄	1	8	yes	—
76	C₈×C₉	—	2	2	no	—
77	C₈×C₉	C₂²×C₄	1	4	yes	—
78	C₂²×Q₁₆	—	9	1	no	—
79	C₂×C₄×Q₈	—	9	2	no	—
80	#441	—	9	8	no	—
81	C₂×#106	—	9	1	no	—
82	C₂×#103	—	9	2	no	—
83	C₂×#97	D₉	1	1	yes	characteristic
84	C₂²×C₃×C₄	D₁₂	1	2	yes	—
85	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
86	C₂²×Dic₃	—	6	2	no	—
87	C₂²×Dic₃	—	6	2	no	—
88	C₂×Dic₆	—	3	8	no	—
89	C₂×Dic₆	—	3	4	no	—
90	C₂×Dic₆	—	6	2	no	—
91	C₂×Dic₆	—	6	4	no	—
92	C₂×C₃×C₈	—	2	2	no	—
93	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
94	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
95	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
96	C₃×C₄²	D₁₂	1	2	yes	—
97	C₃×C₄²	C₂²×D₃	1	2	yes	—
98	C₄⋊Dic₃	—	3	4	no	—
99	C₄⋊Dic₃	—	6	2	no	—
100	Dic₃⋊C₄	—	6	8	no	—
101	C₄×Dic₃	—	6	8	no	—
102	Dic₁₂	—	3	16	no	—
103	C₂²×C₉	C₄×D₄	1	2	yes	—
104	C₂²×C₉	#137	1	4	yes	—
105	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₉	—	2	4	no	—
107	C₄×C₉	C₄×D₄	1	2	yes	—
108	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
109	C₄×C₉	C₂×#41	1	1	yes	characteristic
110	Dic₉	—	2	8	no	—
111	Dic₉	—	4	4	no	—
112	C₂²×Q₈	—	9	2	no	—
113	C₂×Q₁₆	—	9	8	no	—
114	C₂×Q₁₆	—	9	4	no	—
115	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
116	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
117	C₄×Q₈	—	9	8	no	—
118	C₄×Q₈	—	18	4	no	—
119	C₂×C₄⋊C₄	—	9	2	no	—
120	C₂×C₄⋊C₄	—	18	2	no	—
121	C₂×C₄²	—	18	2	no	—
122	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
123	#106	—	9	4	no	—
124	#103	—	9	8	no	—
125	#97	C₂×D₉	1	4	yes	—
126	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
129	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
130	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
131	C₂×C₃×C₄	#235	1	2	yes	—
132	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
133	C₂×Dic₃	—	6	8	no	—
134	C₂×Dic₃	—	6	4	no	—
135	C₂×Dic₃	—	6	4	no	—
136	C₂×Dic₃	—	12	4	no	—
137	Dic₆	—	3	8	no	—
138	Dic₆	—	6	8	no	—
139	Dic₆	—	6	4	no	—
140	C₃×C₈	—	2	2	no	—
141	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
142	C₂×C₉	#441	1	4	yes	complemented
143	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂×C₉	C₂×#137	1	2	yes	—
145	C₂×Q₈	—	9	8	no	—
146	C₂×Q₈	—	9	4	no	—
147	C₂×Q₈	—	18	2	no	—
148	C₂×Q₈	—	18	4	no	—
149	C₂²×C₄	—	18	2	no	—
150	C₂²×C₄	—	18	2	no	—
151	C₂²×C₄	D₃₆	1	2	yes	—
152	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
153	Q₁₆	—	9	16	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	C₄×D₉	1	4	yes	—
156	C₂×C₈	C₂²×D₉	1	2	yes	—
157	C₂×C₈	C₂²×D₉	1	2	yes	—
158	C₄⋊C₄	—	9	4	no	—
159	C₄⋊C₄	—	18	2	no	—
160	C₄⋊C₄	—	18	8	no	—
161	C₄²	—	18	8	no	—
162	C₄²	D₃₆	1	2	yes	—
163	C₄²	C₂²×D₉	1	2	yes	—
164	C₂²×C₃	C₄×D₁₂	1	2	yes	—
165	C₂²×C₃	#909	1	4	yes	—
166	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
167	C₃×C₄	—	2	4	no	—
168	C₃×C₄	C₄×D₁₂	1	2	yes	—
169	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
170	C₃×C₄	C₂×#235	1	1	yes	characteristic
171	Dic₃	—	6	8	no	—
172	Dic₃	—	12	4	no	—
173	C₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×D₃₆	1	1	yes	characteristic
175	Q₈	—	9	8	no	—
176	Q₈	—	18	8	no	—
177	Q₈	—	18	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	18	8	no	—
180	C₂×C₄	—	18	4	no	—
181	C₂×C₄	—	18	4	no	—
182	C₂×C₄	—	36	4	no	—
183	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
184	C₂×C₄	C₂×D₃₆	1	4	yes	—
185	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
186	C₂×C₄	#3697	1	2	yes	—
187	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
188	C₈	—	2	2	no	—
189	C₈	C₂×C₄×D₉	1	4	yes	—
190	C₂×C₃	#4716	1	4	yes	—
191	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
192	C₂×C₃	C₂×#909	1	2	yes	—
193	C₂²	C₄×D₃₆	1	2	yes	—
194	C₂²	#63471	1	4	yes	—
195	C₂²	C₂²×D₃₆	1	1	yes	characteristic
196	C₄	—	2	4	no	—
197	C₄	—	18	8	no	—
198	C₄	—	36	4	no	—
199	C₄	C₄×D₃₆	1	2	yes	—
200	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
201	C₄	C₂×#3697	1	1	yes	characteristic
202	C₃	C₂×#4716	1	1	yes	characteristic
203	C₂	#10588384	1	4	yes	direct product factor
204	C₂	C₂×C₄×D₃₆	1	1	yes	characteristic
205	C₂	C₂×#63471	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#97	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×#97	D₉
hypocenter	C₉	C₂×#441
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #10588384	C₂	direct (N × H)
15. C₂×Dic₃₆	C₄	semidirect
46. Dic₃₆	C₂×C₄	semidirect
142. C₂×C₉	#441	semidirect
173. C₉	C₂×#441	semidirect
203. C₂	#10588384	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×Dic₃₆	2
C₂×C₄×Dic₁₈	2
C₂×C₉×#97	2
C₂×#63377	2
C₂×#63376	2
#10588384	2
C₂×#4716	3

Subgroups — C2×#10588384 #11860107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588384 #11860107