Subgroups — C₂×#10589135 #11797056

Order 1152.

417 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#812	C₂	1	2	yes	maximal
3	#10589135	C₂	1	4	yes	maximal, direct product factor
4	C₂×#4511	—	3	2	no	maximal
5	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
7	C₂²×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
8	C₈×C₃⋊Dic₃	C₄	1	2	yes	—
9	C₈×C₃⋊Dic₃	C₂²	1	2	yes	—
10	C₃×#812	—	2	2	no	—
11	C₃×#812	C₂²	1	4	yes	—
12	C₂×C₃×C₃⋊C₁₆	—	2	2	no	—
13	C₂×C₃×M₃₂	—	3	2	no	—
14	C₂×C₈×Dic₃	—	3	2	no	—
15	C₂×C₈×Dic₃	—	6	1	no	—
16	C₂×#812	D₃	1	2	yes	—
17	#4511	—	3	8	no	—
18	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃⋊Dic₃	—	2	1	no	—
20	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
22	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
23	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
24	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
25	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
26	C₄×C₃⋊Dic₃	—	2	1	no	—
27	C₄×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
28	C₂×C₃⋊(C₃⋊C₈)	C₈	1	2	yes	—
29	C₂×C₃⋊(C₃⋊C₈)	C₈	1	2	yes	—
30	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
31	C₃×C₃⋊C₁₆	—	2	4	no	—
32	C₂×#364	—	9	1	no	Sylow
33	C₂²×C₃×C₈	—	2	1	no	—
34	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
35	C₂×C₄×Dic₃	—	3	2	no	—
36	C₂×C₄×Dic₃	—	6	1	no	—
37	C₂²×C₃⋊C₈	—	3	2	no	—
38	C₂²×C₃⋊C₈	—	6	1	no	—
39	C₃×M₃₂	—	3	4	no	—
40	C₃×M₃₂	—	6	2	no	—
41	C₂×C₃×C₁₆	—	6	2	no	—
42	C₈×Dic₃	—	3	4	no	—
43	C₈×Dic₃	—	3	4	no	—
44	C₈×Dic₃	—	6	2	no	—
45	C₈×Dic₃	—	6	2	no	—
46	#812	—	2	2	no	—
47	#812	C₂×D₃	1	4	yes	—
48	C₂×C₃⋊C₁₆	—	2	2	no	—
49	C₂³×C₃²	M₁₆	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
53	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
54	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
55	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₃⋊Dic₃	—	2	4	no	—
57	C₂×C₃⋊Dic₃	—	2	2	no	—
58	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
61	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
62	C₃⋊(C₃⋊C₈)	C₂×C₈	1	4	yes	—
63	C₂×M₃₂	—	3	2	no	—
64	C₂×C₄×C₈	—	9	1	no	—
65	#364	—	9	4	no	—
66	C₂²×C₃×C₄	—	2	1	no	—
67	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
68	C₂²×Dic₃	—	6	2	no	—
69	C₂²×Dic₃	—	6	2	no	—
70	C₂×C₃×C₈	—	2	1	no	—
71	C₂×C₃×C₈	—	2	1	no	—
72	C₂×C₃×C₈	—	2	1	no	—
73	C₂×C₃×C₈	—	2	1	no	—
74	C₂×C₃×C₈	—	2	1	no	—
75	C₂×C₃×C₈	—	2	1	no	—
76	C₂×C₃×C₈	Dic₆	1	2	yes	—
77	C₂×C₃×C₈	Dic₆	1	2	yes	—
78	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
79	C₂×C₃×C₈	#67	1	2	yes	—
80	C₂×C₃×C₈	#67	1	2	yes	—
81	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
82	C₄×Dic₃	—	3	4	no	—
83	C₄×Dic₃	—	6	2	no	—
84	C₄×Dic₃	—	6	2	no	—
85	C₄×Dic₃	—	6	2	no	—
86	C₂×C₃⋊C₈	—	3	4	no	—
87	C₂×C₃⋊C₈	—	3	4	no	—
88	C₂×C₃⋊C₈	—	3	4	no	—
89	C₂×C₃⋊C₈	—	6	2	no	—
90	C₂×C₃⋊C₈	—	6	2	no	—
91	C₂×C₃⋊C₈	—	6	2	no	—
92	C₃×C₁₆	—	6	4	no	—
93	C₃⋊C₁₆	—	2	4	no	—
94	C₂²×C₃²	—	2	2	no	—
95	C₂²×C₃²	C₄⋊C₈	1	1	yes	characteristic
96	C₂²×C₃²	C₄⋊C₈	1	1	yes	characteristic
97	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
98	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
99	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
100	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
102	C₃⋊Dic₃	—	2	4	no	—
103	C₂²×C₈	—	9	1	no	—
104	C₂²×C₈	D₃²	1	1	yes	characteristic
105	C₂×C₄²	—	9	1	no	—
106	M₃₂	—	3	4	no	—
107	M₃₂	—	6	2	no	—
108	C₂×C₁₆	—	6	2	no	—
109	C₄×C₈	—	9	2	no	—
110	C₄×C₈	—	9	2	no	—
111	C₂³×C₃	—	2	1	no	—
112	C₂³×C₃	ΓL(1,𝔽₂₅)	1	2	yes	—
113	C₂×C₃×C₄	—	2	1	no	—
114	C₂×C₃×C₄	—	2	1	no	—
115	C₂×C₃×C₄	—	2	1	no	—
116	C₂×C₃×C₄	—	2	1	no	—
117	C₂×C₃×C₄	—	2	1	no	—
118	C₂×C₃×C₄	—	2	1	no	—
119	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
120	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
121	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
122	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
123	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
124	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
125	C₂×Dic₃	—	6	4	no	—
126	C₂×Dic₃	—	6	8	no	—
127	C₂×Dic₃	—	6	8	no	—
128	C₂×Dic₃	—	6	4	no	—
129	C₃×C₈	—	2	1	no	—
130	C₃×C₈	—	2	1	no	—
131	C₃×C₈	—	2	1	no	—
132	C₃×C₈	—	2	1	no	—
133	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
134	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
135	C₃×C₈	C₂×Dic₆	1	2	yes	—
136	C₃×C₈	C₂×#67	1	2	yes	—
137	C₃⋊C₈	—	3	8	no	—
138	C₃⋊C₈	—	6	4	no	—
139	C₂×C₃²	—	2	1	no	—
140	C₂×C₃²	—	2	1	no	—
141	C₂×C₃²	#364	1	2	yes	complemented
142	C₂×C₃²	C₂×C₄⋊C₈	1	1	yes	characteristic
143	C₂²×C₄	—	18	1	no	—
144	C₂²×C₄	#624	1	1	yes	characteristic
145	C₂×C₈	—	9	2	no	—
146	C₂×C₈	—	9	2	no	—
147	C₂×C₈	—	9	2	no	—
148	C₂×C₈	#624	1	1	yes	characteristic
149	C₂×C₈	#625	1	1	yes	characteristic
150	C₂×C₈	#625	1	1	yes	characteristic
151	C₂×C₈	#627	1	1	yes	characteristic
152	C₂×C₈	#627	1	1	yes	characteristic
153	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
154	C₄²	—	9	2	no	—
155	C₄²	—	18	1	no	—
156	C₁₆	—	6	4	no	—
157	C₂²×C₃	—	2	4	no	—
158	C₂²×C₃	—	2	4	no	—
159	C₂²×C₃	—	2	1	no	—
160	C₂²×C₃	—	2	1	no	—
161	C₂²×C₃	—	2	1	no	—
162	C₂²×C₃	Dic₃⋊C₈	1	2	yes	—
163	C₂²×C₃	Dic₃⋊C₈	1	2	yes	—
164	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
165	C₃×C₄	—	2	1	no	—
166	C₃×C₄	—	2	1	no	—
167	C₃×C₄	—	2	1	no	—
168	C₃×C₄	—	2	1	no	—
169	C₃×C₄	Dic₃⋊C₈	1	2	yes	—
170	C₃×C₄	Dic₃⋊C₈	1	2	yes	—
171	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
172	C₃×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
173	Dic₃	—	6	8	no	—
174	Dic₃	—	6	8	no	—
175	C₃²	C₂×#364	1	1	yes	characteristic, complemented, Sylow
176	C₂³	#3712	1	1	yes	characteristic
177	C₂×C₄	—	18	4	no	—
178	C₂×C₄	—	18	2	no	—
179	C₂×C₄	#3710	1	1	yes	characteristic
180	C₂×C₄	#3710	1	1	yes	characteristic
181	C₂×C₄	#3712	1	1	yes	characteristic
182	C₂×C₄	#3724	1	1	yes	characteristic
183	C₂×C₄	#3724	1	1	yes	characteristic
184	C₂×C₄	C₂×#624	1	1	yes	characteristic
185	C₈	—	9	4	no	—
186	C₈	#3724	1	1	yes	characteristic
187	C₈	#3724	1	1	yes	characteristic
188	C₈	C₂×#625	1	1	yes	characteristic
189	C₈	C₂×#627	1	1	yes	characteristic
190	C₂×C₃	—	2	2	no	—
191	C₂×C₃	—	2	2	no	—
192	C₂×C₃	—	2	2	no	—
193	C₂×C₃	—	2	2	no	—
194	C₂×C₃	—	2	1	no	—
195	C₂×C₃	—	2	2	no	—
196	C₂×C₃	#4511	1	4	yes	complemented
197	C₂×C₃	C₂×Dic₃⋊C₈	1	2	yes	—
198	C₂²	—	2	2	no	—
199	C₂²	#63572	1	1	yes	characteristic
200	C₂²	#63572	1	1	yes	characteristic
201	C₂²	C₂×#3712	1	1	yes	characteristic
202	C₄	—	18	4	no	—
203	C₄	#63572	1	1	yes	characteristic
204	C₄	#63572	1	1	yes	characteristic
205	C₄	C₂×#3710	1	1	yes	characteristic
206	C₄	C₂×#3724	1	1	yes	characteristic
207	C₃	—	2	1	no	—
208	C₃	C₂×#4511	1	2	yes	complemented
209	C₂	—	2	1	no	—
210	C₂	—	2	1	no	—
211	C₂	#10589135	1	2	yes	direct product factor
212	C₂	C₂×#63572	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#625
commutator	C₃²×C₄	C₂²×C₈
Frattini	C₂×C₈	C₂×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₄⋊C₈
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#364
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #10589135	C₂	direct (N × H)
141. C₂×C₃²	#364	semidirect
175. C₃²	C₂×#364	semidirect
196. C₂×C₃	#4511	semidirect
208. C₃	C₂×#4511	semidirect
211. C₂	#10589135	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×C₈×C₃⋊Dic₃	2
C₂×C₃×#812	2
#10589135	2
C₂×#4511	3

Subgroups — C2×#10589135 #11797056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589135 #11797056