Subgroups — #20253239

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689430	C₂	1	2	yes	maximal, complemented
3	#15689423	C₂	1	2	yes	maximal, complemented
4	#15689418	C₂	1	2	yes	maximal, complemented
5	#15689403	C₂	1	2	yes	maximal, complemented
6	#15689163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13093957	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689150	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689124	C₂	1	1	yes	maximal, characteristic
10	#15689119	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#520	C₂	1	1	yes	maximal, characteristic
12	C₂×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#13094024	C₂²	1	2	yes	—
15	#13094023	—	2	1	no	—
16	#13094016	C₂²	1	2	yes	—
17	#13094015	—	2	1	no	—
18	#13094001	—	2	2	no	—
19	#13093983	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
21	#13093957	C₂²	1	2	yes	—
22	#13093957	C₂²	1	2	yes	—
23	#13093957	C₂²	1	2	yes	—
24	#13093955	C₂²	1	2	yes	—
25	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
26	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	#13093948	C₂²	1	1	yes	characteristic
28	#13093948	C₂²	1	1	yes	characteristic
29	#13093948	C₂²	1	2	yes	—
30	#13093945	C₂²	1	1	yes	characteristic
31	#13093945	C₂²	1	1	yes	characteristic
32	#13093945	C₂²	1	2	yes	—
33	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
35	C₄×D₄×C₄₇	—	2	2	no	—
36	C₄×D₄×C₄₇	C₂²	1	2	yes	—
37	#117×C₄₇	—	2	1	no	—
38	#117×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	#41×C₄₇	—	2	2	no	—
42	#41×C₄₇	Q₈	1	4	yes	complemented
43	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₄₇	—	2	1	no	—
45	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	—	2	1	no	—
48	C₂²×C₄×C₄₇	—	2	2	no	—
49	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×Dic₄₇	—	2	1	no	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
57	C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	C₂³	1	2	yes	—
61	C₂²⋊Dic₄₇	—	2	1	no	—
62	C₄⋊Dic₄₇	—	2	1	no	—
63	C₄⋊Dic₄₇	—	2	2	no	—
64	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊Dic₄₇	C₂³	1	2	yes	—
66	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
67	Dic₄₇⋊C₄	—	2	2	no	—
68	Dic₄₇⋊C₄	—	2	2	no	—
69	C₄×Dic₄₇	—	2	1	no	—
70	#10625329	—	2	2	no	—
71	C₂×C₄₇⋊C₈	—	2	2	no	—
72	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
73	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂³×C₄₇	—	2	1	no	—
76	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
77	Q₈×C₄₇	—	2	1	no	—
78	Q₈×C₄₇	C₂×Q₈	1	2	yes	—
79	D₄×C₄₇	—	2	4	no	—
80	D₄×C₄₇	—	2	1	no	—
81	D₄×C₄₇	C₂×Q₈	1	2	yes	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	2	4	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	—	8	2	no	—
86	C₂×C₄×C₄₇	—	8	1	no	—
87	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂×C₄×C₄₇	#41	1	2	yes	—
92	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂×Dic₄₇	—	2	1	no	—
94	C₂×Dic₄₇	—	2	1	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	—	8	1	no	—
97	Dic₉₄	—	8	2	no	—
98	C₄₇⋊C₈	—	2	1	no	—
99	C₄₇⋊C₈	—	2	1	no	—
100	C₄₇⋊C₈	—	2	2	no	—
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	—	2	2	no	—
104	C₂²×C₄₇	—	4	1	no	—
105	C₂²×C₄₇	—	4	1	no	—
106	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
107	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₄₇	—	2	2	no	—
109	C₄×C₄₇	—	2	2	no	—
110	C₄×C₄₇	—	2	2	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
113	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
114	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
115	Dic₄₇	—	4	1	no	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	4	1	no	—
118	#3083	—	47	1	no	maximal, Sylow
119	C₂×C₄₇	—	2	2	no	—
120	C₂×C₄₇	—	4	2	no	—
121	C₂×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
122	C₂×C₄₇	#576	1	1	yes	characteristic
123	C₂×C₄₇	#578	1	1	yes	characteristic
124	#544	—	47	1	no	—
125	#520	D₄₇	1	1	yes	characteristic
126	#479	—	47	2	no	—
127	#478	—	47	2	no	—
128	#477	—	47	2	no	—
129	#474	—	47	2	no	—
130	#428	—	47	1	no	—
131	C₂×#107	—	47	1	no	—
132	#424	—	47	1	no	—
133	#417	—	47	1	no	—
134	#416	—	47	1	no	—
135	C₄₇	#3083	1	1	yes	characteristic, complemented, Sylow
136	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
137	C₂×M₁₆	—	47	1	no	—
138	C₂²×C₈	—	47	1	no	—
139	C₄⋊Q₈	—	47	2	no	—
140	C₄⋊Q₈	—	94	1	no	—
141	#125	—	47	2	no	—
142	#125	—	94	1	no	—
143	C₂²⋊Q₈	—	94	2	no	—
144	C₄×Q₈	C₂×D₄₇	1	2	yes	—
145	C₄×D₄	—	2	2	no	—
146	C₄×D₄	C₂×D₄₇	1	2	yes	—
147	#117	—	2	1	no	—
148	#117	—	47	1	no	—
149	#117	C₂×D₄₇	1	1	yes	characteristic
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	47	1	no	—
152	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
153	#107	—	47	2	no	—
154	#107	—	47	2	no	—
155	#107	—	47	2	no	—
156	#106	—	47	2	no	—
157	C₄⋊C₈	—	47	2	no	—
158	C₄⋊C₈	—	47	2	no	—
159	#103	—	47	1	no	—
160	#103	—	47	1	no	—
161	#103	—	47	2	no	—
162	#102	—	47	1	no	—
163	#102	—	47	1	no	—
164	#102	—	47	2	no	—
165	#41	—	2	2	no	—
166	#41	Dic₉₄	1	4	yes	complemented
167	C₂×Q₈	—	94	2	no	—
168	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	94	1	no	—
175	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
176	M₁₆	—	94	2	no	—
177	C₂×C₈	—	47	2	no	—
178	C₂×C₈	—	47	1	no	—
179	C₂×C₈	—	47	1	no	—
180	C₂×C₈	—	94	2	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	47	1	no	—
184	C₄⋊C₄	—	47	2	no	—
185	C₄⋊C₄	—	47	1	no	—
186	C₄⋊C₄	—	94	2	no	—
187	C₄⋊C₄	—	94	2	no	—
188	C₄⋊C₄	—	94	1	no	—
189	C₄⋊C₄	—	94	2	no	—
190	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
191	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
192	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
193	C₂²⋊C₄	—	2	2	no	—
194	C₂²⋊C₄	—	94	1	no	—
195	C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
196	C₄²	—	2	2	no	—
197	C₄²	—	94	1	no	—
198	C₄²	C₂²×D₄₇	1	2	yes	—
199	C₂³	—	2	1	no	—
200	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	Q₈	—	2	1	no	—
202	Q₈	—	376	2	no	—
203	Q₈	C₂×Dic₉₄	1	2	yes	—
204	D₄	—	2	4	no	—
205	D₄	—	2	1	no	—
206	D₄	C₂×Dic₉₄	1	2	yes	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	4	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	8	2	no	—
211	C₂×C₄	—	8	1	no	—
212	C₂×C₄	—	94	1	no	—
213	C₂×C₄	—	94	1	no	—
214	C₂×C₄	—	94	2	no	—
215	C₂×C₄	—	376	1	no	—
216	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
217	C₂×C₄	#10625350	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
220	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
221	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
222	C₈	—	94	1	no	—
223	C₈	—	94	1	no	—
224	C₈	—	94	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	#13094003	1	2	yes	—
231	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	—	188	2	no	—
237	C₄	—	188	1	no	—
238	C₄	—	188	1	no	—
239	C₄	#13094003	1	2	yes	—
240	C₄	C₂²×Dic₉₄	1	1	yes	characteristic
241	C₄	C₂×#10625350	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	4	2	no	—
244	C₂	C₂×#13094003	1	1	yes	characteristic
245	C₂	#15689926	1	1	yes	characteristic
246	C₂	#15689938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#520	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#520	D₄₇
hypocenter	C₄₇	#3083
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #520

Complements

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

N	H ≅ G/N	type
1. #15689751	C₂	semidirect
2. #15689430	C₂	semidirect
3. #15689423	C₂	semidirect
4. #15689418	C₂	semidirect
5. #15689403	C₂	semidirect
6. #15689163	C₂	semidirect
7. C₂×#13093957	C₂	semidirect
8. #15689150	C₂	semidirect
42. #41×C₄₇	Q₈	semidirect
135. C₄₇	#3083	semidirect
166. #41	Dic₉₄	semidirect