Subgroups — C₂×#10588701 #11861287

Order 1152.

600 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	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	#10588701	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₉⋊C₈)	C₂	1	2	yes	maximal
5	C₂×#63362	C₂	1	2	yes	maximal
6	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×#5024	—	3	1	no	maximal
8	C₂²×Q₈×C₉	C₄	1	1	yes	characteristic
9	C₄×Q₈×C₉	C₄	1	4	yes	—
10	C₄×Q₈×C₉	C₂²	1	4	yes	—
11	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₉	C₂²	1	2	yes	—
15	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
17	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊(C₉⋊C₈)	C₂²	1	8	yes	—
19	C₄⋊(C₉⋊C₈)	C₂²	1	4	yes	—
20	#63362	C₂²	1	8	yes	—
21	C₄×C₉⋊C₈	C₂²	1	4	yes	—
22	C₂×C₃×C₄×Q₈	D₃	1	1	yes	characteristic
23	#5024	—	3	8	no	—
24	C₂×C₄⋊(C₃⋊C₈)	—	3	2	no	—
25	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
26	C₂×#803	—	3	2	no	—
27	C₂×C₄×C₃⋊C₈	—	3	1	no	—
28	C₂×Q₈×C₉	—	2	4	no	—
29	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
36	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
37	C₄²×C₉	C₂×C₄	1	4	yes	—
38	C₄²×C₉	C₂×C₄	1	2	yes	—
39	C₄²×C₉	C₂³	1	2	yes	—
40	C₄²×C₉	C₂³	1	4	yes	—
41	C₂×C₉⋊C₈	—	2	2	no	—
42	C₂×C₉⋊C₈	—	2	4	no	—
43	C₂×C₉⋊C₈	Q₈	1	4	yes	complemented
44	C₂×C₉⋊C₈	C₂³	1	2	yes	—
45	C₂×C₉⋊C₈	C₂³	1	4	yes	—
46	C₂×C₉⋊C₈	C₂³	1	2	yes	—
47	C₂×#446	—	9	1	no	Sylow
48	C₂²×C₃×Q₈	Dic₃	1	1	yes	characteristic
49	C₃×C₄×Q₈	Dic₃	1	4	yes	—
50	C₃×C₄×Q₈	C₂×D₃	1	4	yes	—
51	C₂×C₃×C₄⋊C₄	Dic₃	1	2	yes	—
52	C₂×C₃×C₄⋊C₄	Dic₃	1	1	yes	characteristic
53	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
54	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
55	C₂²×C₃⋊C₈	—	3	1	no	—
56	C₂²×C₃⋊C₈	—	3	1	no	—
57	C₂²×C₃⋊C₈	—	3	2	no	—
58	C₄⋊(C₃⋊C₈)	—	3	8	no	—
59	C₄⋊(C₃⋊C₈)	—	3	4	no	—
60	#803	—	3	8	no	—
61	C₄×C₃⋊C₈	—	3	4	no	—
62	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
63	Q₈×C₉	—	2	8	no	—
64	C₂×C₄×C₉	—	2	4	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	—	2	4	no	—
67	C₂×C₄×C₉	M₁₆	1	4	yes	—
68	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
70	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
73	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
74	C₂×C₄×C₉	#41	1	2	yes	—
75	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
76	C₉⋊C₈	—	2	2	no	—
77	C₉⋊C₈	—	2	4	no	—
78	C₉⋊C₈	C₂×Q₈	1	4	yes	complemented
79	C₂×C₄×Q₈	D₉	1	1	yes	characteristic
80	#446	—	9	8	no	—
81	C₂×C₄⋊C₈	—	9	1	no	—
82	C₂×C₄⋊C₈	—	9	2	no	—
83	C₂×#97	—	9	2	no	—
84	C₂×C₄×C₈	—	9	1	no	—
85	C₂×C₃×Q₈	—	2	4	no	—
86	C₂×C₃×Q₈	C₂×Dic₃	1	4	yes	—
87	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
88	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
89	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
90	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
91	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
92	C₃×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
93	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
94	C₃×C₄²	C₂×Dic₃	1	4	yes	—
95	C₃×C₄²	C₂×Dic₃	1	2	yes	—
96	C₃×C₄²	C₂²×D₃	1	2	yes	—
97	C₃×C₄²	C₂²×D₃	1	4	yes	—
98	C₂×C₃⋊C₈	—	3	4	no	—
99	C₂×C₃⋊C₈	—	3	2	no	—
100	C₂×C₃⋊C₈	—	3	2	no	—
101	C₂×C₃⋊C₈	—	3	4	no	—
102	C₂×C₃⋊C₈	—	6	2	no	—
103	C₂×C₃⋊C₈	—	6	4	no	—
104	C₂²×C₉	C₄×Q₈	1	2	yes	—
105	C₂²×C₉	C₂×M₁₆	1	2	yes	—
106	C₂²×C₉	#131	1	2	yes	—
107	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
108	C₄×C₉	—	2	4	no	—
109	C₄×C₉	—	2	2	no	—
110	C₄×C₉	—	2	4	no	—
111	C₄×C₉	C₄×Q₈	1	2	yes	—
112	C₄×C₉	C₂×M₁₆	1	4	yes	—
113	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
114	C₄×C₉	C₂×#41	1	1	yes	characteristic
115	C₂²×Q₈	Dic₉	1	1	yes	characteristic
116	C₂²×C₈	—	9	1	no	—
117	C₂²×C₈	—	9	1	no	—
118	C₂²×C₈	—	9	2	no	—
119	C₄×Q₈	Dic₉	1	4	yes	—
120	C₄×Q₈	C₂×D₉	1	4	yes	—
121	C₂×C₄⋊C₄	Dic₉	1	2	yes	—
122	C₂×C₄⋊C₄	Dic₉	1	1	yes	characteristic
123	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
124	C₂×C₄²	C₂×D₉	1	2	yes	—
125	C₄⋊C₈	—	9	4	no	—
126	C₄⋊C₈	—	9	8	no	—
127	#97	—	9	8	no	—
128	C₄×C₈	—	9	4	no	—
129	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
130	C₃×Q₈	—	2	8	no	—
131	C₂×C₃×C₄	—	2	4	no	—
132	C₂×C₃×C₄	—	2	2	no	—
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	#208	1	4	yes	—
135	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
136	C₂×C₃×C₄	#239	1	2	yes	—
137	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
138	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
139	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
140	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
141	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
142	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
143	C₃⋊C₈	—	3	4	no	—
144	C₃⋊C₈	—	6	2	no	—
145	C₃⋊C₈	—	6	4	no	—
146	C₂×C₉	#446	1	4	yes	complemented
147	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₂×C₉	C₂²×M₁₆	1	1	yes	characteristic
149	C₂×C₉	C₂×#131	1	1	yes	characteristic
150	C₂×Q₈	—	2	4	no	—
151	C₂×Q₈	C₂×Dic₉	1	4	yes	—
152	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
153	C₂²×C₄	C₂×Dic₉	1	2	yes	—
154	C₂²×C₄	C₂×Dic₉	1	2	yes	—
155	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
156	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
157	C₂×C₈	—	9	4	no	—
158	C₂×C₈	—	9	2	no	—
159	C₂×C₈	—	9	2	no	—
160	C₂×C₈	—	9	4	no	—
161	C₂×C₈	—	18	2	no	—
162	C₂×C₈	—	18	4	no	—
163	C₄⋊C₄	C₂×Dic₉	1	8	yes	—
164	C₄⋊C₄	C₂×Dic₉	1	4	yes	—
165	C₄²	C₂×Dic₉	1	4	yes	—
166	C₄²	C₂×Dic₉	1	2	yes	—
167	C₄²	C₂²×D₉	1	2	yes	—
168	C₄²	C₂²×D₉	1	4	yes	—
169	C₂²×C₃	C₂×#208	1	2	yes	—
170	C₂²×C₃	Q₈×Dic₃	1	2	yes	—
171	C₂²×C₃	#948	1	2	yes	—
172	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
173	C₃×C₄	—	2	4	no	—
174	C₃×C₄	—	2	2	no	—
175	C₃×C₄	—	2	4	no	—
176	C₃×C₄	C₂×#208	1	4	yes	—
177	C₃×C₄	Q₈×Dic₃	1	2	yes	—
178	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
179	C₃×C₄	C₂×#239	1	1	yes	characteristic
180	C₉	C₂×#446	1	1	yes	characteristic, complemented, Sylow
181	C₂³	C₂²×Dic₉	1	1	yes	characteristic
182	Q₈	—	2	8	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	#3667	1	4	yes	—
187	C₂×C₄	Q₈×D₉	1	2	yes	—
188	C₂×C₄	#3701	1	2	yes	—
189	C₂×C₄	C₂²×Dic₉	1	2	yes	—
190	C₂×C₄	C₂²×Dic₉	1	4	yes	—
191	C₂×C₄	C₂²×Dic₉	1	4	yes	—
192	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
193	C₂×C₄	C₂²×Dic₉	1	2	yes	—
194	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
195	C₈	—	9	4	no	—
196	C₈	—	18	2	no	—
197	C₈	—	18	4	no	—
198	C₂×C₃	#5024	1	4	yes	—
199	C₂×C₃	C₂²×#208	1	1	yes	characteristic
200	C₂×C₃	C₂×Q₈×Dic₃	1	1	yes	characteristic
201	C₂×C₃	C₂×#948	1	1	yes	characteristic
202	C₂²	C₂×#3667	1	2	yes	—
203	C₂²	Q₈×Dic₉	1	2	yes	—
204	C₂²	#63510	1	2	yes	—
205	C₂²	C₂³×Dic₉	1	1	yes	characteristic
206	C₄	—	2	4	no	—
207	C₄	—	2	2	no	—
208	C₄	—	2	4	no	—
209	C₄	C₂×#3667	1	4	yes	—
210	C₄	Q₈×Dic₉	1	2	yes	—
211	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
212	C₄	C₂×#3701	1	1	yes	characteristic
213	C₃	C₂×#5024	1	1	yes	characteristic
214	C₂	#10588701	1	4	yes	direct product factor
215	C₂	C₂²×#3667	1	1	yes	characteristic
216	C₂	C₂×Q₈×Dic₉	1	1	yes	characteristic
217	C₂	C₂×#63510	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₄×Q₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×C₄×Q₈	D₉
hypocenter	C₉	C₂×#446
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #10588701	C₂	direct (N × H)
43. C₂×C₉⋊C₈	Q₈	semidirect
78. C₉⋊C₈	C₂×Q₈	semidirect
146. C₂×C₉	#446	semidirect
180. C₉	C₂×#446	semidirect
214. C₂	#10588701	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₈×C₉	2
#10588701	2
C₂×C₄⋊(C₉⋊C₈)	2
C₂×#63362	2
C₂×C₄×C₉⋊C₈	2
C₂×#5024	3

Subgroups — C2×#10588701 #11861287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588701 #11861287