Subgroups — #20246656

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689062	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689059	C₂	1	1	yes	maximal, characteristic
4	#15689056	C₂	1	2	yes	maximal, complemented
5	#15689046	C₂	1	2	yes	maximal
6	#15689043	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689035	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₄₇⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
11	C₂×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₄×Dic₉₄	—	2	4	no	—
14	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
19	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
22	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
23	C₄₇⋊#95	C₂²	1	2	yes	—
24	C₄₇⋊#95	C₂²	1	2	yes	—
25	C₄₇⋊#95	C₂²	1	1	yes	characteristic
26	C₄₇⋊#95	C₂²	1	1	yes	characteristic
27	C₄₇⋊#95	C₂²	1	2	yes	—
28	C₄₇⋊#95	C₂²	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
30	#117×C₄₇	—	2	4	no	—
31	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₄₇	—	2	2	no	—
39	C₂²×C₄×C₄₇	—	2	2	no	—
40	C₂²×C₄×C₄₇	Q₈	1	4	yes	complemented
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²×Dic₄₇	C₂³	1	2	yes	—
48	C₂²×Dic₄₇	C₂³	1	2	yes	—
49	C₂²×Dic₄₇	C₂³	1	2	yes	—
50	C₂²×Dic₄₇	C₂³	1	2	yes	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₂×Dic₉₄	—	2	4	no	—
53	C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂²⋊C₄×C₄₇	—	2	2	no	—
57	C₄²×C₄₇	—	2	2	no	—
58	C₄²×C₄₇	D₄	1	4	yes	—
59	C₂²⋊Dic₄₇	—	2	4	no	—
60	C₂²⋊Dic₄₇	—	2	4	no	—
61	C₄⋊Dic₄₇	—	2	2	no	—
62	C₄⋊Dic₄₇	—	2	4	no	—
63	Dic₄₇⋊C₄	—	2	4	no	—
64	Dic₄₇⋊C₄	—	2	4	no	—
65	Dic₄₇⋊C₄	—	2	4	no	—
66	C₄×Dic₄₇	—	2	4	no	—
67	C₄×Dic₄₇	—	2	4	no	—
68	C₂³×C₄₇	—	2	1	no	—
69	C₂³×C₄₇	—	2	2	no	—
70	C₂³×C₄₇	—	2	2	no	—
71	C₂³×C₄₇	—	2	1	no	—
72	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
73	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	8	no	—
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
87	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
88	C₂×C₄×C₄₇	#41	1	2	yes	—
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	—	2	2	no	—
97	C₂×Dic₄₇	—	2	2	no	—
98	C₂×Dic₄₇	—	2	2	no	—
99	C₂×Dic₄₇	#41	1	4	yes	—
100	C₂×Dic₄₇	#41	1	4	yes	—
101	Dic₉₄	—	2	8	no	—
102	C₂²×C₄₇	—	2	2	no	—
103	C₂²×C₄₇	—	2	4	no	—
104	C₂²×C₄₇	—	4	1	no	—
105	C₂²×C₄₇	—	4	2	no	—
106	C₂²×C₄₇	—	4	1	no	—
107	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
108	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
109	C₂²×C₄₇	C₂×#41	1	2	yes	—
110	C₂²×C₄₇	C₂×#41	1	2	yes	—
111	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
112	C₄×C₄₇	—	2	2	no	—
113	C₄×C₄₇	—	2	2	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	4	1	no	—
116	C₄×C₄₇	—	4	1	no	—
117	C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
118	Dic₄₇	—	2	4	no	—
119	Dic₄₇	—	2	4	no	—
120	Dic₄₇	—	4	2	no	—
121	Dic₄₇	—	4	2	no	—
122	#2396	—	47	1	no	maximal, Sylow
123	C₂×C₄₇	—	4	2	no	—
124	C₂×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
125	C₂×C₄₇	#525	1	1	yes	characteristic
126	C₂×C₄₇	#529	1	2	yes	—
127	C₂×C₄₇	#532	1	1	yes	characteristic
128	C₂×C₄₇	#533	1	2	yes	—
129	C₂×C₄×Q₈	—	47	1	no	—
130	C₂×#117	D₄₇	1	1	yes	characteristic
131	#400	—	47	1	no	—
132	#399	—	47	1	no	—
133	#398	—	47	2	no	—
134	#396	—	47	2	no	—
135	#395	—	47	1	no	—
136	#393	—	47	1	no	—
137	C₄×C₄⋊C₄	—	47	1	no	—
138	C₄×C₄⋊C₄	—	47	2	no	—
139	C₄×C₂²⋊C₄	—	47	2	no	—
140	C₄₇	#2396	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	1	no	—
142	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
143	C₄×Q₈	—	94	4	no	—
144	#117	—	2	4	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	2	no	—
150	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
151	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
152	C₂×C₂²⋊C₄	—	47	2	no	—
153	C₂×C₂²⋊C₄	—	47	2	no	—
154	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
156	C₂×C₄²	—	47	2	no	—
157	C₂×C₄²	—	47	2	no	—
158	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
159	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
160	#95	—	47	2	no	—
161	#95	—	47	2	no	—
162	#95	—	47	2	no	—
163	#95	—	47	1	no	—
164	#95	—	47	1	no	—
165	#95	—	47	2	no	—
166	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
167	C₂×Q₈	—	94	4	no	—
168	C₂×Q₈	—	94	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	47	2	no	—
172	C₂²×C₄	—	47	2	no	—
173	C₂²×C₄	—	47	2	no	—
174	C₂²×C₄	—	47	2	no	—
175	C₂²×C₄	Dic₉₄	1	4	yes	complemented
176	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
177	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
179	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
180	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	94	4	no	—
185	C₄⋊C₄	—	94	4	no	—
186	C₄⋊C₄	—	94	4	no	—
187	C₄⋊C₄	—	94	4	no	—
188	C₄⋊C₄	—	94	2	no	—
189	C₂²⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	94	4	no	—
192	C₂²⋊C₄	—	94	4	no	—
193	C₄²	—	2	2	no	—
194	C₄²	—	94	4	no	—
195	C₄²	—	94	4	no	—
196	C₄²	C₂²⋊D₄₇	1	4	yes	—
197	C₂³	—	2	1	no	—
198	C₂³	—	2	2	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	1	no	—
201	C₂³	C₂×Dic₉₄	1	2	yes	—
202	C₂³	C₂³×D₄₇	1	1	yes	characteristic
203	Q₈	—	94	8	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	47	4	no	—
214	C₂×C₄	—	47	4	no	—
215	C₂×C₄	—	94	2	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	C₂×Dic₉₄	1	2	yes	—
226	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
227	C₂×C₄	#10625350	1	2	yes	—
228	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
229	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
230	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	4	no	—
233	C₂²	—	4	1	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
237	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
238	C₂²	#41×D₄₇	1	2	yes	—
239	C₂²	#41×D₄₇	1	2	yes	—
240	C₂²	C₂×#10625350	1	1	yes	characteristic
241	C₄	—	2	2	no	—
242	C₄	—	2	2	no	—
243	C₄	—	2	2	no	—
244	C₄	—	4	1	no	—
245	C₄	—	4	1	no	—
246	C₄	—	94	4	no	—
247	C₄	—	94	4	no	—
248	C₄	—	188	2	no	—
249	C₄	—	188	2	no	—
250	C₄	#13094003	1	4	yes	—
251	C₂	—	4	2	no	—
252	C₂	C₂×#13094003	1	1	yes	characteristic
253	C₂	#15689630	1	1	yes	characteristic
254	C₂	#15689651	1	2	yes	—
255	C₂	#15689669	1	1	yes	characteristic
256	C₂	#15689676	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂×#117×C₄₇	C₂
hypercenter	C₂×#117	D₄₇
hypocenter	C₄₇	#2396
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Dic₉₄	C₂	semidirect
2. #15689062	C₂	semidirect
4. #15689056	C₂	semidirect
6. #15689043	C₂	semidirect
8. C₄×Dic₄₇⋊C₄	C₂	semidirect
9. C₄×C₄⋊Dic₄₇	C₂	semidirect
40. C₂²×C₄×C₄₇	Q₈	semidirect
140. C₄₇	#2396	semidirect
175. C₂²×C₄	Dic₉₄	semidirect