Subgroups — C₂×#20243532 #26216524

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688969	C₂	1	1	yes	maximal, characteristic
2	#20243532	C₂	1	8	yes	maximal, direct product factor
3	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688877	C₂	1	2	yes	maximal
5	C₂×#15688877	C₂	1	2	yes	maximal
6	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	#15688969	C₄	1	4	yes	—
11	#15688969	C₂²	1	4	yes	—
12	C₂×C₄₇⋊#95	C₄	1	2	yes	—
13	C₂×C₄₇⋊#95	C₄	1	2	yes	—
14	#15688878	C₂²	1	4	yes	—
15	#15688877	C₂²	1	8	yes	—
16	#15688877	C₂²	1	8	yes	—
17	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	C₂²	1	4	yes	—
20	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄₇⋊C₈	—	2	4	no	—
24	C₂²×C₄₇⋊C₈	—	2	4	no	—
25	C₂²×C₄₇⋊C₈	—	2	4	no	—
26	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
27	C₂×C₄×Dic₄₇	—	2	4	no	—
28	C₂×C₄×Dic₄₇	—	2	2	no	—
29	C₂×C₄×Dic₄₇	—	2	2	no	—
30	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
31	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
32	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
33	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
34	C₄₇⋊#95	C₂×C₄	1	8	yes	—
35	C₄₇⋊#95	C₂×C₄	1	8	yes	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	—	2	4	no	—
39	C₂²×C₈×C₄₇	—	2	4	no	—
40	C₂²×C₈×C₄₇	—	2	4	no	—
41	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
42	C₂×C₄²×C₄₇	—	2	4	no	—
43	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
45	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	—	2	4	no	—
47	C₂²×C₄×C₄₇	—	2	4	no	—
48	C₂²×C₄×C₄₇	—	2	4	no	—
49	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
50	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	#41	1	4	yes	—
52	C₂²×C₄×C₄₇	#41	1	4	yes	—
53	C₂²×C₄×C₄₇	#41	1	2	yes	—
54	C₂²×C₄×C₄₇	#41	1	2	yes	—
55	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
56	C₂²×Dic₄₇	—	2	2	no	—
57	C₂²×Dic₄₇	—	2	2	no	—
58	C₂²×Dic₄₇	—	2	4	no	—
59	C₂²×Dic₄₇	—	2	4	no	—
60	C₂²×Dic₄₇	—	2	4	no	—
61	C₂²×Dic₄₇	—	2	4	no	—
62	C₂²×Dic₄₇	—	2	4	no	—
63	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
64	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
65	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₄₇	—	2	4	no	—
67	C₂×C₈×C₄₇	—	2	4	no	—
68	C₂×C₈×C₄₇	—	2	4	no	—
69	C₂×C₈×C₄₇	—	4	8	no	—
70	C₄²×C₄₇	—	2	4	no	—
71	C₄²×C₄₇	—	2	4	no	—
72	C₄×Dic₄₇	—	2	4	no	—
73	C₄×Dic₄₇	—	2	4	no	—
74	C₄×Dic₄₇	—	2	2	no	—
75	C₄×Dic₄₇	—	2	4	no	—
76	C₄×Dic₄₇	—	2	2	no	—
77	C₂×C₄₇⋊C₈	—	2	4	no	—
78	C₂×C₄₇⋊C₈	—	2	4	no	—
79	C₂×C₄₇⋊C₈	—	2	4	no	—
80	C₂×C₄₇⋊C₈	—	4	8	no	—
81	C₂³×C₄₇	#117	1	2	yes	—
82	C₂³×C₄₇	#117	1	2	yes	—
83	C₂³×C₄₇	#117	1	2	yes	—
84	C₂³×C₄₇	#131	1	4	yes	—
85	C₂³×C₄₇	#131	1	4	yes	—
86	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	—	2	4	no	—
88	C₂×C₄×C₄₇	—	2	4	no	—
89	C₂×C₄×C₄₇	—	2	4	no	—
90	C₂×C₄×C₄₇	—	4	8	no	—
91	C₂×C₄×C₄₇	#117	1	2	yes	—
92	C₂×C₄×C₄₇	#117	1	2	yes	—
93	C₂×C₄×C₄₇	#117	1	2	yes	—
94	C₂×C₄×C₄₇	#126	1	8	yes	—
95	C₂×C₄×C₄₇	#126	1	8	yes	—
96	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
97	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
99	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
100	C₂×Dic₄₇	—	2	2	no	—
101	C₂×Dic₄₇	—	2	2	no	—
102	C₂×Dic₄₇	—	2	4	no	—
103	C₂×Dic₄₇	—	2	4	no	—
104	C₂×Dic₄₇	—	2	4	no	—
105	C₂×Dic₄₇	—	2	4	no	—
106	C₂×Dic₄₇	—	2	4	no	—
107	C₂×Dic₄₇	—	4	4	no	—
108	C₂×Dic₄₇	—	4	8	no	—
109	C₂×Dic₄₇	—	4	4	no	—
110	C₈×C₄₇	—	4	4	no	—
111	C₄₇⋊C₈	—	4	4	no	—
112	C₂×#1840	—	47	1	no	maximal, Sylow
113	C₂²×C₄₇	#383	1	4	yes	—
114	C₂²×C₄₇	#433	1	8	yes	—
115	C₂²×C₄₇	#433	1	4	yes	—
116	C₂²×C₄₇	#433	1	8	yes	—
117	C₂²×C₄₇	#433	1	4	yes	—
118	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
119	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
120	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
121	C₂²×C₄₇	C₂×#131	1	2	yes	—
122	C₂²×C₄₇	C₂×#131	1	2	yes	—
123	C₄×C₄₇	—	4	4	no	—
124	C₄×C₄₇	#383	1	4	yes	—
125	C₄×C₄₇	C₂×#126	1	2	yes	—
126	C₄×C₄₇	C₂×#126	1	2	yes	—
127	Dic₄₇	—	4	2	no	—
128	Dic₄₇	—	4	4	no	—
129	Dic₄₇	—	4	2	no	—
130	C₂×#376	—	47	1	no	—
131	#1840	—	47	8	no	—
132	C₂×#336	—	47	1	no	—
133	C₂×#336	—	47	2	no	—
134	C₂×#336	—	47	2	no	—
135	C₂×#336	D₄₇	1	1	yes	characteristic
136	C₂×C₄₇	#1840	1	8	yes	complemented
137	C₂×C₄₇	C₂×#383	1	1	yes	characteristic
138	C₂×C₄₇	C₂×#433	1	2	yes	—
139	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
140	C₂×C₄₇	C₂×#433	1	2	yes	—
141	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
142	C₂³×C₈	—	47	2	no	—
143	C₂³×C₈	C₂×D₄₇	1	2	yes	—
144	C₂²×C₄²	—	47	1	no	—
145	C₂²×C₄²	—	47	1	no	—
146	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
147	#376	—	47	4	no	—
148	#376	—	47	4	no	—
149	C₂×#95	—	47	2	no	—
150	C₂×#95	—	47	2	no	—
151	#336	—	47	8	no	—
152	#336	—	47	8	no	—
153	#336	—	47	4	no	—
154	#336	C₂×D₄₇	1	4	yes	—
155	C₄₇	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
156	C₂³×C₄	—	47	1	no	—
157	C₂³×C₄	—	47	1	no	—
158	C₂³×C₄	—	47	2	no	—
159	C₂³×C₄	C₄×D₄₇	1	2	yes	—
160	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
161	C₂²×C₈	—	2	4	no	—
162	C₂²×C₈	—	2	4	no	—
163	C₂²×C₈	—	2	4	no	—
164	C₂²×C₈	—	47	4	no	—
165	C₂²×C₈	—	94	4	no	—
166	C₂²×C₈	—	94	4	no	—
167	C₂²×C₈	—	94	4	no	—
168	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
169	C₂×C₄²	—	2	4	no	—
170	C₂×C₄²	—	47	2	no	—
171	C₂×C₄²	—	47	2	no	—
172	C₂×C₄²	—	47	2	no	—
173	C₂×C₄²	—	47	2	no	—
174	C₂×C₄²	—	94	4	no	—
175	C₂×C₄²	—	94	2	no	—
176	C₂×C₄²	—	94	2	no	—
177	C₂×C₄²	C₄×D₄₇	1	2	yes	—
178	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
179	#95	—	47	8	no	—
180	#95	—	47	8	no	—
181	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
182	C₂²×C₄	—	2	4	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	—	2	4	no	—
185	C₂²×C₄	—	47	2	no	—
186	C₂²×C₄	—	47	2	no	—
187	C₂²×C₄	—	47	4	no	—
188	C₂²×C₄	—	94	2	no	—
189	C₂²×C₄	—	94	2	no	—
190	C₂²×C₄	—	94	4	no	—
191	C₂²×C₄	—	94	4	no	—
192	C₂²×C₄	—	94	4	no	—
193	C₂²×C₄	—	94	4	no	—
194	C₂²×C₄	—	94	4	no	—
195	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
196	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
197	C₂²×C₄	#10625350	1	4	yes	—
198	C₂²×C₄	#10625352	1	4	yes	—
199	C₂²×C₄	#10625352	1	2	yes	—
200	C₂²×C₄	#10625354	1	2	yes	—
201	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
202	C₂×C₈	—	2	4	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	4	8	no	—
206	C₂×C₈	—	94	4	no	—
207	C₂×C₈	—	94	4	no	—
208	C₂×C₈	—	94	4	no	—
209	C₂×C₈	—	188	8	no	—
210	C₄²	—	2	4	no	—
211	C₄²	—	2	4	no	—
212	C₄²	—	94	4	no	—
213	C₄²	—	94	4	no	—
214	C₄²	—	94	2	no	—
215	C₄²	—	94	4	no	—
216	C₄²	—	94	2	no	—
217	C₂³	#13093980	1	2	yes	—
218	C₂³	#13093981	1	2	yes	—
219	C₂³	#13093982	1	2	yes	—
220	C₂³	#13094030	1	4	yes	—
221	C₂³	#13094032	1	4	yes	—
222	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	4	8	no	—
227	C₂×C₄	—	94	2	no	—
228	C₂×C₄	—	94	2	no	—
229	C₂×C₄	—	94	4	no	—
230	C₂×C₄	—	94	4	no	—
231	C₂×C₄	—	94	4	no	—
232	C₂×C₄	—	94	4	no	—
233	C₂×C₄	—	94	4	no	—
234	C₂×C₄	—	188	4	no	—
235	C₂×C₄	—	188	8	no	—
236	C₂×C₄	—	188	4	no	—
237	C₂×C₄	#13093980	1	2	yes	—
238	C₂×C₄	#13093981	1	2	yes	—
239	C₂×C₄	#13093982	1	2	yes	—
240	C₂×C₄	#13094017	1	8	yes	—
241	C₂×C₄	#13094019	1	8	yes	—
242	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
243	C₂×C₄	C₂×#10625352	1	2	yes	—
244	C₂×C₄	C₂×#10625350	1	2	yes	—
245	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
246	C₈	—	4	4	no	—
247	C₈	—	188	4	no	—
248	C₂²	#15688990	1	4	yes	—
249	C₂²	#15689181	1	8	yes	—
250	C₂²	#15689182	1	4	yes	—
251	C₂²	#15689183	1	8	yes	—
252	C₂²	#15689185	1	4	yes	—
253	C₂²	C₂×#13093980	1	1	yes	characteristic
254	C₂²	C₂×#13093981	1	1	yes	characteristic
255	C₂²	C₂×#13093982	1	1	yes	characteristic
256	C₂²	C₂×#13094030	1	2	yes	—
257	C₂²	C₂×#13094032	1	2	yes	—
258	C₄	—	4	4	no	—
259	C₄	—	188	2	no	—
260	C₄	—	188	4	no	—
261	C₄	—	188	2	no	—
262	C₄	#15688990	1	4	yes	—
263	C₄	C₂×#13094017	1	2	yes	—
264	C₄	C₂×#13094019	1	2	yes	—
265	C₂	#20243532	1	8	yes	direct product factor
266	C₂	C₂×#15688990	1	1	yes	characteristic
267	C₂	C₂×#15689181	1	2	yes	—
268	C₂	C₂×#15689182	1	1	yes	characteristic
269	C₂	C₂×#15689183	1	2	yes	—
270	C₂	C₂×#15689185	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	C₂×#1840
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
2. #20243532	C₂	direct (N × H)
136. C₂×C₄₇	#1840	semidirect
155. C₄₇	C₂×#1840	semidirect
265. C₂	#20243532	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×#15688969	2
#20243532	2
C₂×#15688878	2
C₂×#15688877	2
C₂×C₄₇×#336	2
C₂×#1840	47

Subgroups — C2×#20243532 #26216524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243532 #26216524