Subgroups — #20246121

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094003	C₂	1	1	yes	maximal, characteristic
2	#15689027	C₂	1	2	yes	maximal, complemented
3	#15689020	C₂	1	2	yes	maximal, complemented
4	#15689010	C₂	1	2	yes	maximal, complemented
5	#15689006	C₂	1	2	yes	maximal, complemented
6	#15688996	C₂	1	2	yes	maximal
7	#15688983	C₂	1	1	yes	maximal, characteristic
8	C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
9	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
11	#13094003	C₄	1	8	yes	complemented
12	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
20	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
22	C₄₇⋊#95	C₂²	1	2	yes	—
23	C₄₇⋊#95	C₂²	1	2	yes	—
24	C₄₇⋊#95	C₂²	1	2	yes	—
25	C₄₇⋊#95	C₂²	1	2	yes	—
26	C₄₇⋊#95	C₂²	1	2	yes	—
27	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
30	#95×C₄₇	C₂²	1	2	yes	—
31	#95×C₄₇	C₂²	1	2	yes	—
32	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₄₇	—	2	2	no	—
34	C₂²×C₄×C₄₇	—	4	1	no	—
35	C₂²×C₄×C₄₇	—	4	1	no	—
36	C₂²×C₄×C₄₇	—	4	1	no	—
37	C₂²×C₄×C₄₇	—	4	1	no	—
38	C₂²×C₄×C₄₇	—	4	1	no	—
39	C₂²×C₄×C₄₇	—	4	1	no	—
40	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
41	C₂²×C₄×C₄₇	Q₈	1	4	yes	complemented
42	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
46	C₂²×Dic₄₇	C₂³	1	2	yes	—
47	C₂²×Dic₄₇	C₂³	1	2	yes	—
48	C₂²×Dic₄₇	C₂³	1	2	yes	—
49	C₂²×Dic₄₇	C₂³	1	2	yes	—
50	C₂×Dic₉₄	—	4	1	no	—
51	C₂×Dic₉₄	—	4	1	no	—
52	C₂×Dic₉₄	C₂×C₄	1	4	yes	complemented
53	C₂²⋊Dic₄₇	—	2	4	no	—
54	C₂²⋊Dic₄₇	C₂×C₄	1	8	yes	—
55	C₄⋊Dic₄₇	—	4	1	no	—
56	C₄⋊Dic₄₇	—	4	1	no	—
57	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	complemented
58	Dic₄₇⋊C₄	—	4	2	no	—
59	Dic₄₇⋊C₄	—	4	2	no	—
60	Dic₄₇⋊C₄	C₂×C₄	1	8	yes	complemented
61	C₄×Dic₄₇	—	4	2	no	—
62	C₄×Dic₄₇	—	4	2	no	—
63	C₂³×C₄₇	—	2	1	no	—
64	C₂³×C₄₇	—	2	1	no	—
65	C₂³×C₄₇	—	2	1	no	—
66	C₂³×C₄₇	—	2	1	no	—
67	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
68	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
69	C₂³×C₄₇	#41	1	2	yes	—
70	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	1	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	4	4	no	—
81	C₂×C₄×C₄₇	—	4	4	no	—
82	C₂×C₄×C₄₇	—	4	4	no	—
83	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	2	2	no	—
90	C₂×Dic₄₇	—	2	2	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	2	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
97	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
98	Dic₉₄	—	4	4	no	—
99	C₂²×C₄₇	—	2	2	no	—
100	C₂²×C₄₇	—	2	2	no	—
101	C₂²×C₄₇	—	2	2	no	—
102	C₂²×C₄₇	—	2	2	no	—
103	C₂²×C₄₇	—	2	2	no	—
104	C₂²×C₄₇	—	2	2	no	—
105	C₂²×C₄₇	C₄×Q₈	1	4	yes	—
106	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
107	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
108	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
109	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
110	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
111	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
112	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
113	C₄×C₄₇	—	2	2	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	2	4	no	—
116	C₄×C₄₇	—	4	2	no	—
117	Dic₄₇	—	2	4	no	—
118	Dic₄₇	—	2	4	no	—
119	Dic₄₇	—	4	2	no	—
120	Dic₄₇	—	4	2	no	—
121	#2329	—	47	1	no	maximal, Sylow
122	C₂×C₄₇	—	2	4	no	—
123	C₂×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
124	C₂×C₄₇	#518	1	1	yes	characteristic
125	C₂×C₄₇	#520	1	1	yes	characteristic
126	C₂×C₄₇	#538	1	1	yes	characteristic
127	C₂×C₄₇	#539	1	1	yes	characteristic
128	C₂×C₄₇	#543	1	1	yes	characteristic
129	C₂×C₄₇	#544	1	1	yes	characteristic
130	C₂×C₂²⋊Q₈	—	47	1	no	—
131	#391	—	47	2	no	—
132	#389	—	47	2	no	—
133	#387	—	47	2	no	—
134	#387	—	47	2	no	—
135	#385	—	47	2	no	—
136	#380	—	47	1	no	—
137	C₄×C₂²⋊C₄	—	47	2	no	—
138	C₂×#95	D₄₇	1	1	yes	characteristic
139	C₄₇	#2329	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	47	1	no	—
141	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
142	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
143	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
144	C₂²⋊Q₈	—	47	8	no	—
145	C₂×C₄⋊C₄	—	47	2	no	—
146	C₂×C₄⋊C₄	—	47	1	no	—
147	C₂×C₄⋊C₄	—	47	2	no	—
148	C₂×C₄⋊C₄	—	47	2	no	—
149	C₂×C₄⋊C₄	—	47	1	no	—
150	C₂×C₄⋊C₄	—	47	1	no	—
151	C₂×C₂²⋊C₄	—	47	2	no	—
152	C₂×C₂²⋊C₄	—	47	2	no	—
153	C₂×C₄²	—	47	2	no	—
154	C₂×C₄²	—	47	2	no	—
155	#95	—	47	2	no	—
156	#95	—	47	2	no	—
157	#95	—	47	2	no	—
158	#95	—	47	2	no	—
159	#95	—	47	2	no	—
160	#95	C₂×D₄₇	1	2	yes	—
161	#95	C₂×D₄₇	1	2	yes	—
162	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
163	C₂×Q₈	—	47	4	no	—
164	C₂×Q₈	—	188	1	no	—
165	C₂×Q₈	—	188	1	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	4	1	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	4	1	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	—	4	1	no	—
172	C₂²×C₄	—	4	1	no	—
173	C₂²×C₄	—	47	2	no	—
174	C₂²×C₄	—	47	2	no	—
175	C₂²×C₄	—	47	2	no	—
176	C₂²×C₄	—	47	2	no	—
177	C₂²×C₄	Dic₉₄	1	4	yes	complemented
178	C₂²×C₄	C₄×D₄₇	1	4	yes	—
179	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
180	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
181	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
182	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
183	C₄⋊C₄	—	47	8	no	—
184	C₄⋊C₄	—	47	4	no	—
185	C₄⋊C₄	—	188	2	no	—
186	C₄⋊C₄	—	188	2	no	—
187	C₄⋊C₄	—	188	1	no	—
188	C₄⋊C₄	—	188	1	no	—
189	C₂²⋊C₄	—	47	8	no	—
190	C₂²⋊C₄	—	94	4	no	—
191	C₄²	—	188	2	no	—
192	C₄²	—	188	2	no	—
193	C₂³	—	2	1	no	—
194	C₂³	—	2	1	no	—
195	C₂³	—	2	1	no	—
196	C₂³	—	2	1	no	—
197	C₂³	C₂×Dic₉₄	1	2	yes	—
198	C₂³	C₂×C₄×D₄₇	1	2	yes	—
199	C₂³	#10625350	1	2	yes	—
200	C₂³	C₂³×D₄₇	1	1	yes	characteristic
201	Q₈	—	188	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	—	47	4	no	—
215	C₂×C₄	—	47	4	no	—
216	C₂×C₄	—	94	2	no	—
217	C₂×C₄	—	94	2	no	—
218	C₂×C₄	—	94	2	no	—
219	C₂×C₄	—	94	2	no	—
220	C₂×C₄	—	94	2	no	—
221	C₂×C₄	—	94	2	no	—
222	C₂×C₄	—	94	2	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	94	2	no	—
225	C₂×C₄	—	94	2	no	—
226	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
227	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
228	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
229	C₂²	—	2	2	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	C₄×Dic₉₄	1	4	yes	—
236	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
237	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
238	C₂²	C₂×#10625350	1	1	yes	characteristic
239	C₂²	#13094069	1	1	yes	characteristic
240	C₂²	#13094069	1	1	yes	characteristic
241	C₂²	#13094069	1	1	yes	characteristic
242	C₂²	#13094072	1	1	yes	characteristic
243	C₄	—	2	4	no	—
244	C₄	—	2	2	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	—	94	4	no	—
248	C₄	—	94	4	no	—
249	C₄	—	188	2	no	—
250	C₄	—	188	2	no	—
251	C₂	—	2	4	no	—
252	C₂	C₂×C₄×Dic₉₄	1	1	yes	characteristic
253	C₂	#15689596	1	1	yes	characteristic
254	C₂	#15689604	1	1	yes	characteristic
255	C₂	#15689711	1	1	yes	characteristic
256	C₂	#15689720	1	1	yes	characteristic
257	C₂	#15689749	1	1	yes	characteristic
258	C₂	#15689754	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×#95×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#2329
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
2. #15689027	C₂	semidirect
3. #15689020	C₂	semidirect
4. #15689010	C₂	semidirect
5. #15689006	C₂	semidirect
11. #13094003	C₄	semidirect
41. C₂²×C₄×C₄₇	Q₈	semidirect
52. C₂×Dic₉₄	C₂×C₄	semidirect
57. C₄⋊Dic₄₇	C₂×C₄	semidirect
60. Dic₄₇⋊C₄	C₂×C₄	semidirect
139. C₄₇	#2329	semidirect
177. C₂²×C₄	Dic₉₄	semidirect