Subgroups — C₂×#20243076 #26213606

Order 12032.

1614 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093934	C₂	1	2	yes	maximal
2	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×Dic₄₇	C₂	1	2	yes	maximal
4	C₂×#15688969	C₂	1	1	yes	maximal, characteristic
5	#20243076	C₂	1	8	yes	maximal, direct product factor
6	C₂²×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
10	C₂×#13093934	C₄	1	16	yes	complemented
11	C₂×#13093934	C₂²	1	8	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₄	1	8	yes	complemented
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
14	C₂×C₈×Dic₄₇	C₄	1	16	yes	complemented
15	C₂×C₈×Dic₄₇	C₂²	1	8	yes	—
16	#15688969	C₄	1	4	yes	—
17	#15688969	C₂²	1	4	yes	—
18	C₂×C₄₇⋊#95	C₄	1	4	yes	—
19	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₇	C₄	1	8	yes	complemented
22	C₂×#97×C₄₇	C₂²	1	4	yes	—
23	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
24	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
25	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
28	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
29	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
30	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
32	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
33	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
34	#13093934	C₂×C₄	1	32	yes	complemented
35	C₄×C₄₇⋊C₈	C₂×C₄	1	16	yes	complemented
36	C₈×Dic₄₇	C₂×C₄	1	32	yes	complemented
37	C₄₇⋊#95	C₂×C₄	1	16	yes	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
42	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
44	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
48	#97×C₄₇	C₂×C₄	1	16	yes	complemented
49	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	—	2	8	no	—
51	C₂²×C₄×C₄₇	C₄²	1	8	yes	—
52	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
53	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
56	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
59	C₂²×Dic₄₇	—	2	16	no	—
60	C₂²×Dic₄₇	C₄²	1	16	yes	—
61	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
62	C₂×C₈×C₄₇	C₄²	1	32	yes	—
63	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
64	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
65	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
66	C₄²×C₄₇	C₄²	1	8	yes	—
67	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
68	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
69	C₄×Dic₄₇	C₄²	1	16	yes	—
70	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
71	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
72	C₂×C₄₇⋊C₈	C₄²	1	16	yes	—
73	C₂×C₄₇⋊C₈	C₄²	1	16	yes	—
74	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
75	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
76	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
77	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
78	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
79	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
80	C₂³×C₄₇	#131	1	8	yes	—
81	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
82	C₂×C₄×C₄₇	—	2	8	no	—
83	C₂×C₄×C₄₇	—	2	16	no	—
84	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
85	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
86	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
87	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
88	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
89	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
90	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
92	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
93	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
94	C₂×Dic₄₇	—	2	16	no	—
95	C₂×Dic₄₇	—	2	32	no	—
96	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
97	C₈×C₄₇	C₂×C₄²	1	16	yes	—
98	C₄₇⋊C₈	C₂×C₄²	1	8	yes	—
99	C₄₇⋊C₈	C₂×C₄²	1	8	yes	—
100	C₂×#1726	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	C₄³	1	4	yes	—
102	C₂²×C₄₇	#405	1	16	yes	—
103	C₂²×C₄₇	#405	1	8	yes	—
104	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
105	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
106	C₂²×C₄₇	C₂×#131	1	4	yes	—
107	C₄×C₄₇	—	2	8	no	—
108	C₄×C₄₇	C₄³	1	4	yes	—
109	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
110	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
111	C₄×C₄₇	C₂²×C₄²	1	2	yes	—
112	Dic₄₇	—	2	16	no	—
113	C₂²×#97	—	47	2	no	—
114	C₂²×#97	D₄₇	1	1	yes	characteristic
115	C₂²×C₄×C₈	—	47	1	no	—
116	C₂²×C₄×C₈	—	47	2	no	—
117	C₂×#376	—	47	1	no	—
118	#1726	—	47	8	no	—
119	C₂×C₄₇	#1726	1	8	yes	complemented
120	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
121	C₂×C₄₇	C₂×#405	1	4	yes	—
122	C₂×C₄₇	C₂×#405	1	2	yes	—
123	C₂³×C₈	—	47	1	no	—
124	C₂³×C₈	—	47	1	no	—
125	C₂³×C₈	C₂×D₄₇	1	2	yes	—
126	C₂²×C₄²	—	47	2	no	—
127	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
128	C₂×#97	—	47	16	no	—
129	C₂×#97	—	47	8	no	—
130	C₂×#97	Dic₄₇	1	8	yes	complemented
131	C₂×#97	C₂×D₄₇	1	4	yes	—
132	C₂×C₄×C₈	—	47	16	no	—
133	C₂×C₄×C₈	—	47	8	no	—
134	C₂×C₄×C₈	—	47	8	no	—
135	C₂×C₄×C₈	—	47	4	no	—
136	#376	—	47	4	no	—
137	#376	—	47	4	no	—
138	C₂×#95	—	47	4	no	—
139	C₄₇	C₂×#1726	1	1	yes	characteristic, complemented, Sylow
140	C₂³×C₄	—	47	4	no	—
141	C₂³×C₄	C₄×D₄₇	1	2	yes	—
142	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
143	C₂²×C₈	—	47	4	no	—
144	C₂²×C₈	—	47	4	no	—
145	C₂²×C₈	—	47	8	no	—
146	C₂²×C₈	—	47	8	no	—
147	C₂²×C₈	—	47	2	no	—
148	C₂²×C₈	—	47	2	no	—
149	C₂²×C₈	C₄×D₄₇	1	8	yes	—
150	C₂²×C₈	C₄×D₄₇	1	8	yes	—
151	C₂²×C₈	C₂×Dic₄₇	1	8	yes	—
152	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
153	C₂×C₄²	—	47	4	no	—
154	C₂×C₄²	—	47	8	no	—
155	C₂×C₄²	—	47	8	no	—
156	C₂×C₄²	—	47	4	no	—
157	C₂×C₄²	C₄×D₄₇	1	2	yes	—
158	C₂×C₄²	C₄×D₄₇	1	4	yes	—
159	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
160	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
161	#97	—	47	32	no	—
162	#97	C₂×Dic₄₇	1	16	yes	complemented
163	C₄×C₈	—	47	32	no	—
164	C₄×C₈	—	47	16	no	—
165	#95	—	47	16	no	—
166	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	—	47	16	no	—
169	C₂²×C₄	—	47	8	no	—
170	C₂²×C₄	—	94	16	no	—
171	C₂²×C₄	C₄×Dic₄₇	1	8	yes	—
172	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
175	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
176	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
177	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
178	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
179	C₂×C₈	—	47	16	no	—
180	C₂×C₈	—	47	16	no	—
181	C₂×C₈	—	47	4	no	—
182	C₂×C₈	—	47	4	no	—
183	C₂×C₈	—	47	8	no	—
184	C₂×C₈	—	47	8	no	—
185	C₂×C₈	C₄×Dic₄₇	1	32	yes	—
186	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
187	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
188	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
189	C₄²	—	47	16	no	—
190	C₄²	—	47	8	no	—
191	C₄²	—	47	8	no	—
192	C₄²	C₄×Dic₄₇	1	8	yes	—
193	C₄²	C₂×C₄×D₄₇	1	4	yes	—
194	C₄²	C₂²×Dic₄₇	1	4	yes	—
195	C₂³	C₄²×D₄₇	1	4	yes	—
196	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
197	C₂³	#13094032	1	8	yes	—
198	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
199	C₂×C₄	—	2	16	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	47	16	no	—
202	C₂×C₄	—	94	32	no	—
203	C₂×C₄	—	94	16	no	—
204	C₂×C₄	C₄²×D₄₇	1	4	yes	—
205	C₂×C₄	C₄²×D₄₇	1	4	yes	—
206	C₂×C₄	C₄²×D₄₇	1	4	yes	—
207	C₂×C₄	C₂×C₄×Dic₄₇	1	8	yes	—
208	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
209	C₂×C₄	C₂×C₄×Dic₄₇	1	8	yes	—
210	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
211	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
212	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
213	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
214	C₈	—	47	8	no	—
215	C₈	—	47	8	no	—
216	C₈	C₂×C₄×Dic₄₇	1	16	yes	—
217	C₂²	C₄²×Dic₄₇	1	4	yes	—
218	C₂²	#15689080	1	16	yes	—
219	C₂²	#15689081	1	8	yes	—
220	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
221	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
222	C₂²	C₂×#13094032	1	4	yes	—
223	C₄	—	2	8	no	—
224	C₄	—	94	16	no	—
225	C₄	C₄²×Dic₄₇	1	4	yes	—
226	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
227	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
228	C₄	C₂²×C₄×Dic₄₇	1	2	yes	—
229	C₂	#20243076	1	8	yes	direct product factor
230	C₂	C₂×C₄²×Dic₄₇	1	1	yes	characteristic
231	C₂	C₂×#15689080	1	4	yes	—
232	C₂	C₂×#15689081	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#97×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#97	D₄₇
hypocenter	C₄₇	C₂×#1726
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
5. #20243076	C₂	direct (N × H)
10. C₂×#13093934	C₄	semidirect
12. C₂×C₄×C₄₇⋊C₈	C₄	semidirect
14. C₂×C₈×Dic₄₇	C₄	semidirect
21. C₂×#97×C₄₇	C₄	semidirect
34. #13093934	C₂×C₄	semidirect
35. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
36. C₈×Dic₄₇	C₂×C₄	semidirect
48. #97×C₄₇	C₂×C₄	semidirect
119. C₂×C₄₇	#1726	semidirect
130. C₂×#97	Dic₄₇	semidirect
139. C₄₇	C₂×#1726	semidirect
162. #97	C₂×Dic₄₇	semidirect
229. C₂	#20243076	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×#13093934	2
C₂²×C₄×C₄₇⋊C₈	2
C₂²×C₈×Dic₄₇	2
C₂×#15688969	2
#20243076	2
C₂²×#97×C₄₇	2
C₂×#1726	47

Subgroups — C2×#20243076 #26213606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243076 #26213606