Subgroups — #20246442

Order 6016.

552 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094022	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093989	C₂	1	1	yes	maximal, characteristic
3	#15689030	C₂	1	1	yes	maximal, characteristic
4	#15689029	C₂	1	1	yes	maximal, characteristic
5	#15689018	C₂	1	2	yes	maximal
6	#15689007	C₂	1	2	yes	maximal
7	#15689004	C₂	1	2	yes	maximal
8	C₄⋊C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	C₄×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
10	C₄×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
13	#13094022	C₄	1	8	yes	complemented
14	#13093989	—	2	4	no	—
15	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
22	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
23	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄₇⋊#95	C₂²	1	1	yes	characteristic
26	C₄₇⋊#95	C₂²	1	2	yes	—
27	C₄₇⋊#95	C₂²	1	1	yes	characteristic
28	C₄₇⋊#95	C₂²	1	2	yes	—
29	C₄₇⋊#95	C₂²	1	2	yes	—
30	C₄₇⋊#95	C₂²	1	2	yes	—
31	C₄₇⋊#95	C₂²	1	2	yes	—
32	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₄₇	—	2	4	no	—
34	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
37	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×Q₈×C₄₇	—	2	2	no	—
39	C₂×Q₈×C₄₇	—	2	2	no	—
40	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×Dic₄₇	C₂³	1	2	yes	—
47	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
48	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
49	C₂²×Dic₄₇	C₂³	1	2	yes	—
50	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
52	C₂×Dic₉₄	—	2	2	no	—
53	C₂×Dic₉₄	—	2	2	no	—
54	C₂×Dic₉₄	C₂×C₄	1	4	yes	—
55	C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₄⋊C₄×C₄₇	D₄	1	4	yes	—
57	C₄²×C₄₇	—	2	4	no	—
58	C₄²×C₄₇	—	2	2	no	—
59	C₄⋊Dic₄₇	—	2	2	no	—
60	Dic₄₇⋊C₄	—	2	4	no	—
61	Dic₄₇⋊C₄	—	2	2	no	—
62	Dic₄₇⋊C₄	C₂×C₄	1	8	yes	—
63	Dic₄₇⋊C₄	C₂×C₄	1	8	yes	—
64	Dic₄₇⋊C₄	Q₈	1	4	yes	complemented
65	C₄×Dic₄₇	—	2	4	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	4	no	—
68	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
69	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
70	Q₈×C₄₇	—	2	8	no	—
71	C₂×C₄×C₄₇	—	2	1	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	2	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	1	no	—
80	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
81	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
83	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂×C₄×C₄₇	#41	1	2	yes	—
86	C₂×Dic₄₇	—	2	1	no	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	2	1	no	—
90	C₂×Dic₄₇	—	2	1	no	—
91	C₂×Dic₄₇	—	2	1	no	—
92	C₂×Dic₄₇	—	2	1	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	1	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	—	2	1	no	—
97	C₂×Dic₄₇	—	2	2	no	—
98	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
99	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
100	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
101	C₂×Dic₄₇	C₂×Q₈	1	2	yes	—
102	C₂×Dic₄₇	C₂×Q₈	1	2	yes	—
103	C₂×Dic₄₇	#41	1	2	yes	—
104	Dic₉₄	—	2	8	no	—
105	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
106	C₂²×C₄₇	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
110	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
111	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
112	C₄×C₄₇	—	2	4	no	—
113	C₄×C₄₇	—	2	4	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	4	1	no	—
116	C₄×C₄₇	C₄×D₄	1	4	yes	—
117	Dic₄₇	—	2	4	no	—
118	Dic₄₇	—	2	2	no	—
119	Dic₄₇	—	2	2	no	—
120	Dic₄₇	—	4	1	no	—
121	Dic₄₇	—	4	2	no	—
122	Dic₄₇	C₄×Q₈	1	4	yes	complemented
123	#2365	—	47	1	no	maximal, Sylow
124	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
125	C₂×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
126	C₂×C₄₇	#519	1	1	yes	characteristic
127	C₂×C₄₇	#547	1	1	yes	characteristic
128	C₂×C₄₇	D₄×Q₈	1	1	yes	characteristic
129	C₂×C₄₇	#556	1	1	yes	characteristic
130	C₂×C₄₇	#557	1	1	yes	characteristic
131	C₂×C₄⋊Q₈	—	47	1	no	—
132	C₂×C₄×Q₈	—	47	1	no	—
133	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic
134	#391	—	47	1	no	—
135	#391	—	47	1	no	—
136	#389	—	47	2	no	—
137	#387	—	47	2	no	—
138	#387	—	47	2	no	—
139	C₄×C₄⋊C₄	—	47	1	no	—
140	C₄×C₄⋊C₄	—	47	1	no	—
141	C₄×C₄⋊C₄	—	47	2	no	—
142	C₄₇	#2365	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	47	1	no	—
144	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
145	C₄⋊Q₈	—	47	8	no	—
146	C₄×Q₈	—	2	4	no	—
147	C₄×Q₈	—	94	4	no	—
148	C₂×C₄⋊C₄	—	47	2	no	—
149	C₂×C₄⋊C₄	—	47	2	no	—
150	C₂×C₄⋊C₄	—	47	1	no	—
151	C₂×C₄⋊C₄	—	47	2	no	—
152	C₂×C₄⋊C₄	—	47	1	no	—
153	C₂×C₄⋊C₄	—	47	1	no	—
154	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
155	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
156	C₂×C₄²	—	47	1	no	—
157	C₂×C₄²	—	47	2	no	—
158	C₂×C₄²	—	47	1	no	—
159	C₂×C₄²	—	47	2	no	—
160	C₂×C₄²	C₂×D₄₇	1	2	yes	—
161	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
162	#95	—	47	1	no	—
163	#95	—	47	2	no	—
164	#95	—	47	1	no	—
165	#95	—	47	2	no	—
166	#95	—	47	2	no	—
167	#95	—	47	2	no	—
168	#95	—	47	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	47	4	no	—
172	C₂×Q₈	—	94	2	no	—
173	C₂×Q₈	—	94	2	no	—
174	C₂×Q₈	C₄×D₄₇	1	4	yes	—
175	C₂²×C₄	—	47	1	no	—
176	C₂²×C₄	—	47	1	no	—
177	C₂²×C₄	—	47	1	no	—
178	C₂²×C₄	—	47	2	no	—
179	C₂²×C₄	—	47	2	no	—
180	C₂²×C₄	—	47	1	no	—
181	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
182	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
183	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
184	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
185	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	47	8	no	—
188	C₄⋊C₄	—	47	8	no	—
189	C₄⋊C₄	—	47	4	no	—
190	C₄⋊C₄	—	94	2	no	—
191	C₄⋊C₄	—	94	2	no	—
192	C₄⋊C₄	—	94	4	no	—
193	C₄⋊C₄	C₂²⋊D₄₇	1	4	yes	—
194	C₄²	—	2	4	no	—
195	C₄²	—	2	2	no	—
196	C₄²	—	47	4	no	—
197	C₄²	—	94	4	no	—
198	C₄²	—	94	4	no	—
199	C₄²	—	94	2	no	—
200	C₂³	C₂³×D₄₇	1	1	yes	characteristic
201	Q₈	—	2	8	no	—
202	Q₈	—	94	8	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	47	2	no	—
213	C₂×C₄	—	47	2	no	—
214	C₂×C₄	—	47	2	no	—
215	C₂×C₄	—	47	2	no	—
216	C₂×C₄	—	47	4	no	—
217	C₂×C₄	—	47	2	no	—
218	C₂×C₄	—	94	1	no	—
219	C₂×C₄	—	94	2	no	—
220	C₂×C₄	—	94	2	no	—
221	C₂×C₄	—	94	1	no	—
222	C₂×C₄	—	94	1	no	—
223	C₂×C₄	—	94	1	no	—
224	C₂×C₄	—	94	1	no	—
225	C₂×C₄	—	94	2	no	—
226	C₂×C₄	—	94	1	no	—
227	C₂×C₄	—	94	2	no	—
228	C₂×C₄	—	94	1	no	—
229	C₂×C₄	—	94	2	no	—
230	C₂×C₄	C₂×C₄×D₄₇	1	4	yes	—
231	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
232	C₂×C₄	#10625350	1	2	yes	—
233	C₂×C₄	Q₈×D₄₇	1	2	yes	—
234	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
235	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
236	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
237	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
238	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
239	C₂²	#41×D₄₇	1	1	yes	characteristic
240	C₂²	C₂×#10625350	1	1	yes	characteristic
241	C₂²	#13094071	1	1	yes	characteristic
242	C₂²	#13094072	1	1	yes	characteristic
243	C₄	—	2	4	no	—
244	C₄	—	2	2	no	—
245	C₄	—	2	4	no	—
246	C₄	—	4	1	no	—
247	C₄	—	47	4	no	—
248	C₄	—	94	2	no	—
249	C₄	—	94	4	no	—
250	C₄	—	94	2	no	—
251	C₄	—	188	1	no	—
252	C₄	—	188	2	no	—
253	C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
254	C₂	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
255	C₂	C₄×Q₈×D₄₇	1	1	yes	characteristic
256	C₂	#15689599	1	1	yes	characteristic
257	C₂	#15689772	1	1	yes	characteristic
258	C₂	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
259	C₂	#15689845	1	1	yes	characteristic
260	C₂	#15689851	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×C₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	#2365
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
13. #13094022	C₄	semidirect
64. Dic₄₇⋊C₄	Q₈	semidirect
122. Dic₄₇	C₄×Q₈	semidirect
142. C₄₇	#2365	semidirect