Subgroups — C₂×#15689733 #20256754

Order 6016.

1004 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	#15689733	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13094022	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13094017	C₂	1	2	yes	maximal
4	C₂×#13094017	C₂	1	2	yes	maximal
5	C₂×#13094015	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094015	C₂	1	2	yes	maximal, complemented
7	C₂×#13094014	C₂	1	2	yes	maximal, complemented
8	C₂×#13094003	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13093989	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13093983	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
14	#13094022	C₂²	1	8	yes	complemented
15	#13094017	C₂²	1	16	yes	—
16	#13094017	C₂²	1	16	yes	—
17	#13094015	C₂²	1	8	yes	complemented
18	#13094015	C₂²	1	16	yes	complemented
19	#13094014	C₂²	1	16	yes	complemented
20	#13094003	C₂²	1	8	yes	—
21	Q₈×Dic₄₇	C₂²	1	8	yes	complemented
22	#13093989	C₂²	1	8	yes	complemented
23	#13093983	C₂²	1	8	yes	—
24	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
30	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
31	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
32	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
33	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
34	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
37	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
40	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²⋊Q₈×C₄₇	C₂²	1	8	yes	—
44	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
46	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
47	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×Q₈×C₄₇	—	2	4	no	—
49	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
50	C₂²×C₄×C₄₇	—	2	4	no	—
51	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
55	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂²×Dic₄₇	C₂³	1	2	yes	—
60	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂²×Dic₄₇	C₂³	1	2	yes	—
62	C₂×Dic₉₄	—	2	4	no	—
63	C₂×Dic₉₄	C₂³	1	4	yes	—
64	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
65	C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
66	C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
67	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
68	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
69	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
70	C₄⋊Dic₄₇	C₂³	1	4	yes	—
71	C₄⋊Dic₄₇	C₂³	1	4	yes	—
72	C₄⋊Dic₄₇	C₂³	1	4	yes	—
73	C₄⋊Dic₄₇	C₂³	1	8	yes	—
74	C₄⋊Dic₄₇	C₂³	1	8	yes	—
75	Dic₄₇⋊C₄	C₂³	1	8	yes	—
76	Dic₄₇⋊C₄	C₂³	1	8	yes	—
77	Dic₄₇⋊C₄	C₂³	1	8	yes	—
78	Dic₄₇⋊C₄	C₂³	1	8	yes	—
79	Dic₄₇⋊C₄	C₂³	1	8	yes	—
80	C₄×Dic₄₇	C₂³	1	4	yes	—
81	C₄×Dic₄₇	C₂³	1	4	yes	—
82	C₄×Dic₄₇	C₂³	1	8	yes	—
83	C₄×Dic₄₇	C₂³	1	8	yes	—
84	C₂³×C₄₇	—	2	2	no	—
85	C₂³×C₄₇	—	2	2	no	—
86	C₂³×C₄₇	—	2	2	no	—
87	C₂³×C₄₇	C₂⁴	1	2	yes	—
88	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
89	Q₈×C₄₇	—	2	8	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	4	no	—
92	C₂×C₄×C₄₇	—	2	4	no	—
93	C₂×C₄×C₄₇	—	2	8	no	—
94	C₂×C₄×C₄₇	#41	1	4	yes	—
95	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
96	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
97	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
98	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
99	C₂×Dic₄₇	—	2	4	no	—
100	C₂×Dic₄₇	—	2	2	no	—
101	C₂×Dic₄₇	—	2	2	no	—
102	C₂×Dic₄₇	—	2	2	no	—
103	C₂×Dic₄₇	—	2	2	no	—
104	C₂×Dic₄₇	—	2	4	no	—
105	C₂×Dic₄₇	C₂⁴	1	2	yes	—
106	C₂×Dic₄₇	C₂⁴	1	2	yes	—
107	C₂×Dic₄₇	C₂⁴	1	2	yes	—
108	C₂×Dic₄₇	C₂⁴	1	4	yes	—
109	C₂×Dic₄₇	C₂⁴	1	2	yes	—
110	C₂×Dic₄₇	C₂⁴	1	4	yes	—
111	Dic₉₄	—	2	8	no	—
112	C₂²×C₄₇	—	2	2	no	—
113	C₂²×C₄₇	—	2	2	no	—
114	C₂²×C₄₇	—	2	2	no	—
115	C₂²×C₄₇	—	4	4	no	—
116	C₂²×C₄₇	C₂×#41	1	2	yes	—
117	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
118	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
119	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
120	C₄×C₄₇	—	2	2	no	—
121	C₄×C₄₇	—	2	4	no	—
122	C₄×C₄₇	—	2	4	no	—
123	C₄×C₄₇	C₂×#41	1	4	yes	—
124	Dic₄₇	—	2	4	no	—
125	Dic₄₇	—	2	2	no	—
126	Dic₄₇	—	2	2	no	—
127	Dic₄₇	—	2	2	no	—
128	Dic₄₇	—	2	2	no	—
129	Dic₄₇	—	2	4	no	—
130	C₂×#541	—	47	1	no	maximal, Sylow
131	C₂×C₄₇	—	4	2	no	—
132	C₂×C₄₇	#541	1	4	yes	complemented
133	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
134	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
135	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
136	#541	—	47	16	no	—
137	C₂×C₄⋊Q₈	—	47	1	no	—
138	C₂×#126	—	47	2	no	—
139	C₂×#126	—	47	2	no	—
140	C₂×#125	—	47	2	no	—
141	C₂×#125	—	47	1	no	—
142	C₂×#125	—	47	2	no	—
143	C₂×C₂²⋊Q₈	—	47	1	no	—
144	C₂×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
145	C₂×C₄×Q₈	—	47	1	no	—
146	C₂×C₄×Q₈	—	47	1	no	—
147	C₂×#117	—	47	1	no	—
148	C₄₇	C₂×#541	1	1	yes	characteristic, complemented, Sylow
149	C₂²×Q₈	—	47	1	no	—
150	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
151	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
152	C₄⋊Q₈	—	47	8	no	—
153	#126	—	47	16	no	—
154	#126	—	47	16	no	—
155	#125	—	47	16	no	—
156	#125	—	47	8	no	—
157	#125	—	47	16	no	—
158	C₂²⋊Q₈	—	47	8	no	—
159	C₂²⋊Q₈	C₂×D₄₇	1	8	yes	—
160	C₄×Q₈	—	47	8	no	—
161	C₄×Q₈	—	47	8	no	—
162	#117	—	47	8	no	—
163	C₂×C₄⋊C₄	—	47	1	no	—
164	C₂×C₄⋊C₄	—	47	1	no	—
165	C₂×C₄⋊C₄	—	47	1	no	—
166	C₂×C₄⋊C₄	—	47	2	no	—
167	C₂×C₄⋊C₄	—	47	2	no	—
168	C₂×C₄⋊C₄	—	47	2	no	—
169	C₂×C₄⋊C₄	—	47	2	no	—
170	C₂×C₄⋊C₄	—	47	2	no	—
171	C₂×C₄⋊C₄	—	47	2	no	—
172	C₂×C₄⋊C₄	—	47	2	no	—
173	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
175	C₂×C₂²⋊C₄	—	47	1	no	—
176	C₂×C₂²⋊C₄	—	47	1	no	—
177	C₂×C₂²⋊C₄	—	47	2	no	—
178	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
179	C₂×C₄²	—	47	1	no	—
180	C₂×C₄²	—	47	1	no	—
181	C₂×C₄²	—	47	2	no	—
182	C₂×C₄²	—	47	2	no	—
183	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	47	4	no	—
186	C₂×Q₈	—	94	4	no	—
187	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	47	1	no	—
190	C₂²×C₄	—	47	1	no	—
191	C₂²×C₄	—	47	1	no	—
192	C₂²×C₄	—	47	1	no	—
193	C₂²×C₄	—	47	2	no	—
194	C₂²×C₄	—	47	2	no	—
195	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
196	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
197	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
198	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
199	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
200	C₄⋊C₄	—	47	8	no	—
201	C₄⋊C₄	—	47	8	no	—
202	C₄⋊C₄	—	47	8	no	—
203	C₄⋊C₄	—	47	8	no	—
204	C₄⋊C₄	—	47	8	no	—
205	C₄⋊C₄	—	47	4	no	—
206	C₄⋊C₄	—	47	4	no	—
207	C₄⋊C₄	—	47	4	no	—
208	C₄⋊C₄	—	47	8	no	—
209	C₄⋊C₄	—	47	8	no	—
210	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
211	C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
212	C₂²⋊C₄	—	47	4	no	—
213	C₂²⋊C₄	—	47	4	no	—
214	C₂²⋊C₄	—	47	8	no	—
215	C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
216	C₄²	—	47	4	no	—
217	C₄²	—	47	4	no	—
218	C₄²	—	47	8	no	—
219	C₄²	—	47	8	no	—
220	C₂³	—	2	2	no	—
221	C₂³	—	2	2	no	—
222	C₂³	—	2	2	no	—
223	C₂³	C₂³×D₄₇	1	2	yes	—
224	C₂³	C₂³×D₄₇	1	1	yes	characteristic
225	Q₈	—	2	8	no	—
226	Q₈	—	94	8	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	4	no	—
230	C₂×C₄	—	2	8	no	—
231	C₂×C₄	—	47	2	no	—
232	C₂×C₄	—	47	2	no	—
233	C₂×C₄	—	47	2	no	—
234	C₂×C₄	—	47	2	no	—
235	C₂×C₄	—	47	4	no	—
236	C₂×C₄	—	47	4	no	—
237	C₂×C₄	—	94	4	no	—
238	C₂×C₄	—	94	2	no	—
239	C₂×C₄	—	94	2	no	—
240	C₂×C₄	—	94	2	no	—
241	C₂×C₄	—	94	2	no	—
242	C₂×C₄	—	94	4	no	—
243	C₂×C₄	#10625352	1	4	yes	—
244	C₂×C₄	C₂³×D₄₇	1	4	yes	—
245	C₂×C₄	C₂³×D₄₇	1	4	yes	—
246	C₂×C₄	C₂³×D₄₇	1	2	yes	—
247	C₂×C₄	C₂³×D₄₇	1	2	yes	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	4	4	no	—
252	C₂²	C₂×#10625352	1	2	yes	—
253	C₂²	#13094071	1	2	yes	—
254	C₂²	#13094072	1	2	yes	—
255	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
256	C₄	—	2	2	no	—
257	C₄	—	2	4	no	—
258	C₄	—	2	4	no	—
259	C₄	—	94	4	no	—
260	C₄	—	94	2	no	—
261	C₄	—	94	2	no	—
262	C₄	—	94	2	no	—
263	C₄	—	94	2	no	—
264	C₄	—	94	4	no	—
265	C₄	C₂×#10625352	1	4	yes	—
266	C₂	—	4	2	no	—
267	C₂	#15689733	1	4	yes	direct product factor
268	C₂	C₂²×#10625352	1	1	yes	characteristic
269	C₂	C₂×#13094071	1	1	yes	characteristic
270	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#541
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #15689733	C₂	direct (N × H)
2. C₂×#13094022	C₂	semidirect
5. C₂×#13094015	C₂	semidirect
6. C₂×#13094015	C₂	semidirect
7. C₂×#13094014	C₂	semidirect
9. C₂×Q₈×Dic₄₇	C₂	semidirect
10. C₂×#13093989	C₂	semidirect
14. #13094022	C₂²	semidirect
17. #13094015	C₂²	semidirect
18. #13094015	C₂²	semidirect
19. #13094014	C₂²	semidirect
21. Q₈×Dic₄₇	C₂²	semidirect
22. #13093989	C₂²	semidirect
132. C₂×C₄₇	#541	semidirect
148. C₄₇	C₂×#541	semidirect
267. C₂	#15689733	direct (N × H)

Subgroups — C2×#15689733 #20256754

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689733 #20256754