Subgroups — #552×D₄₇ #20256891

Order 6016.

1124 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689815	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689814	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689813	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689812	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689811	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689810	C₂	1	2	yes	maximal, complemented
7	#15689809	C₂	1	2	yes	maximal, complemented
8	#15689808	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689807	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689806	C₂	1	2	yes	maximal, complemented
11	#15689805	C₂	1	2	yes	maximal, complemented
12	#126×D₄₇	C₂	1	2	yes	maximal, complemented
13	#125×D₄₇	C₂	1	2	yes	maximal, complemented
14	#125×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₄₇	C₂	1	2	yes	maximal
16	C₂²⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
20	#117×D₄₇	C₂	1	2	yes	maximal, complemented
21	#117×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₄₇	C₂²	1	2	yes	—
27	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
29	#13094019	C₂²	1	2	yes	complemented
30	#13094019	C₂²	1	2	yes	complemented
31	#13094019	C₂²	1	2	yes	complemented
32	#13094018	C₂²	1	2	yes	complemented
33	#13094017	C₂²	1	2	yes	complemented
34	#13094017	C₂²	1	2	yes	complemented
35	#13094017	C₂²	1	2	yes	complemented
36	#13094016	C₂²	1	2	yes	complemented
37	#13094016	C₂²	1	1	yes	characteristic, complemented
38	#13094015	C₂²	1	1	yes	characteristic, complemented
39	#13094015	C₂²	1	2	yes	complemented
40	#13094015	C₂²	1	2	yes	complemented
41	#13094015	C₂²	1	1	yes	characteristic, complemented
42	#13094014	C₂²	1	2	yes	complemented
43	#13094014	C₂²	1	2	yes	complemented
44	#13094014	C₂²	1	2	yes	complemented
45	#13094014	C₂²	1	2	yes	complemented
46	#13094014	C₂²	1	2	yes	complemented
47	#13094014	C₂²	1	2	yes	complemented
48	#13094009	C₂²	1	2	yes	—
49	#13094009	C₂²	1	2	yes	—
50	#13094008	C₂²	1	2	yes	—
51	#13094007	C₂²	1	2	yes	—
52	#13094006	C₂²	1	2	yes	—
53	#13094006	C₂²	1	2	yes	—
54	#13094005	C₂²	1	2	yes	—
55	#13094004	C₂²	1	1	yes	characteristic, complemented
56	#13094004	C₂²	1	1	yes	characteristic, complemented
57	#13094003	C₂²	1	1	yes	characteristic, complemented
58	#13094003	C₂²	1	1	yes	characteristic, complemented
59	#13094002	C₂²	1	2	yes	complemented
60	#13094002	C₂²	1	2	yes	complemented
61	#13094001	C₂²	1	2	yes	complemented
62	#13094001	C₂²	1	2	yes	complemented
63	#13094000	C₂²	1	1	yes	characteristic, complemented
64	#13094000	C₂²	1	1	yes	characteristic, complemented
65	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₉₄	C₂²	1	2	yes	complemented
67	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
68	#13093989	C₂²	1	2	yes	complemented
69	#13093989	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
71	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
72	#13093986	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
75	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
76	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
77	#13093983	C₂²	1	1	yes	characteristic, complemented
78	#13093983	C₂²	1	2	yes	complemented
79	#13093982	C₂²	1	2	yes	complemented
80	#13093982	C₂²	1	1	yes	characteristic, complemented
81	#13093982	C₂²	1	2	yes	complemented
82	#13093982	C₂²	1	1	yes	characteristic, complemented
83	#13093981	C₂²	1	2	yes	complemented
84	#13093981	C₂²	1	2	yes	complemented
85	#13093981	C₂²	1	2	yes	complemented
86	#13093980	C₂²	1	2	yes	complemented
87	#13093980	C₂²	1	2	yes	complemented
88	#13093980	C₂²	1	2	yes	complemented
89	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
90	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
92	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
93	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
94	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
95	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
97	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
99	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
100	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
101	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
105	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
109	C₄²×D₄₇	C₂²	1	2	yes	—
110	C₄²×D₄₇	C₂²	1	2	yes	—
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic
112	#126×C₄₇	C₂²	1	2	yes	complemented
113	#125×C₄₇	C₂²	1	2	yes	complemented
114	#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₄₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
120	#117×C₄₇	C₂²	1	2	yes	complemented
121	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₄₇	C₂³	1	1	yes	characteristic
124	C₂³×D₄₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂³	1	2	yes	—
134	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
135	Q₈×D₄₇	—	2	4	no	—
136	D₄×D₄₇	—	2	4	no	—
137	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₄₇	—	2	8	no	—
139	C₂×C₄×D₄₇	—	2	4	no	—
140	C₂×C₄×D₄₇	—	2	4	no	—
141	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₄₇	C₂³	1	2	yes	—
144	C₂×C₄×D₄₇	C₂³	1	2	yes	—
145	C₂×C₄×D₄₇	C₂³	1	2	yes	—
146	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₄₇	C₂³	1	2	yes	—
149	C₂×C₄×D₄₇	C₂³	1	2	yes	—
150	C₂×C₄×D₄₇	C₂³	1	2	yes	—
151	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
156	C₂×Dic₉₄	C₂³	1	2	yes	—
157	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
173	C₄²×C₄₇	C₂³	1	2	yes	—
174	C₄²×C₄₇	C₂³	1	2	yes	—
175	C₄²×C₄₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
181	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
191	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₄₇	C₂³	1	2	yes	—
194	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₄₇	C₂³	1	2	yes	—
196	C₄⋊Dic₄₇	C₂³	1	2	yes	—
197	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₄₇	C₂³	1	2	yes	—
199	C₄⋊Dic₄₇	C₂³	1	2	yes	—
200	C₄⋊Dic₄₇	C₂³	1	2	yes	—
201	Dic₄₇⋊C₄	C₂³	1	2	yes	—
202	Dic₄₇⋊C₄	C₂³	1	2	yes	—
203	Dic₄₇⋊C₄	C₂³	1	2	yes	—
204	Dic₄₇⋊C₄	C₂³	1	2	yes	—
205	Dic₄₇⋊C₄	C₂³	1	2	yes	—
206	Dic₄₇⋊C₄	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	2	yes	—
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₄₇⋊C₄	C₂³	1	2	yes	—
213	Dic₄₇⋊C₄	C₂³	1	2	yes	—
214	Dic₄₇⋊C₄	C₂³	1	2	yes	—
215	Dic₄₇⋊C₄	C₂³	1	2	yes	—
216	Dic₄₇⋊C₄	C₂³	1	2	yes	—
217	Dic₄₇⋊C₄	C₂³	1	2	yes	—
218	C₄×Dic₄₇	C₂³	1	2	yes	—
219	C₄×Dic₄₇	C₂³	1	2	yes	—
220	C₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×Dic₄₇	C₂³	1	2	yes	—
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
225	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
227	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
228	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₂²×D₄₇	—	2	2	no	—
230	C₂²×D₄₇	—	2	2	no	—
231	C₂²×D₄₇	—	2	2	no	—
232	C₂²×D₄₇	—	2	2	no	—
233	C₂²×D₄₇	—	2	2	no	—
234	C₂²×D₄₇	#41	1	4	yes	—
235	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
236	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
238	Q₈×C₄₇	—	2	2	no	—
239	D₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
248	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
249	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₄₇	—	2	2	no	—
253	C₂²⋊D₄₇	—	2	2	no	—
254	C₂×Dic₄₇	—	2	4	no	—
255	C₂×Dic₄₇	—	2	2	no	—
256	C₂×Dic₄₇	—	2	2	no	—
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₄₇	C₂⁴	1	2	yes	—
262	C₂×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂×Dic₄₇	C₂⁴	1	2	yes	—
264	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
266	D₁₈₈	—	2	2	no	—
267	C₄×D₄₇	—	2	4	no	—
268	C₄×D₄₇	—	2	4	no	—
269	C₄×D₄₇	—	2	4	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	2	2	no	—
272	C₄×D₄₇	—	2	2	no	—
273	C₄×D₄₇	—	2	2	no	—
274	C₄×D₄₇	—	2	4	no	—
275	C₄×D₄₇	—	2	2	no	—
276	C₄×D₄₇	—	2	4	no	—
277	C₄×D₄₇	—	2	2	no	—
278	C₄×D₄₇	—	2	2	no	—
279	C₄×D₄₇	—	2	2	no	—
280	C₄×D₄₇	—	2	2	no	—
281	C₄×D₄₇	#41	1	4	yes	—
282	Dic₉₄	—	2	2	no	—
283	Dic₉₄	—	2	4	no	—
284	C₂²×C₄₇	—	2	1	no	—
285	C₂²×C₄₇	—	2	1	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	C₂×#41	1	2	yes	—
290	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
291	C₂×D₄₇	—	2	1	no	—
292	C₂×D₄₇	—	2	1	no	—
293	C₂×D₄₇	—	2	8	no	—
294	C₂×D₄₇	—	2	1	no	—
295	C₂×D₄₇	—	2	1	no	—
296	C₂×D₄₇	—	2	1	no	—
297	C₂×D₄₇	—	4	4	no	—
298	C₂×D₄₇	C₂×#41	1	2	yes	—
299	C₂×D₄₇	C₂×#41	1	2	yes	—
300	C₂×D₄₇	C₂×#41	1	2	yes	—
301	C₂×D₄₇	2₋¹⁺⁴	1	2	yes	—
302	C₄×C₄₇	—	2	2	no	—
303	C₄×C₄₇	—	2	2	no	—
304	C₄×C₄₇	—	2	2	no	—
305	C₄×C₄₇	—	2	1	no	—
306	C₄×C₄₇	—	2	1	no	—
307	C₄×C₄₇	—	2	1	no	—
308	C₄×C₄₇	—	2	1	no	—
309	C₄×C₄₇	—	2	2	no	—
310	C₄×C₄₇	C₂×#41	1	2	yes	—
311	Dic₄₇	—	2	2	no	—
312	Dic₄₇	—	2	2	no	—
313	Dic₄₇	—	2	2	no	—
314	Dic₄₇	—	2	1	no	—
315	Dic₄₇	—	2	1	no	—
316	Dic₄₇	—	2	1	no	—
317	Dic₄₇	—	2	1	no	—
318	Dic₄₇	—	2	2	no	—
319	Dic₄₇	C₂×#41	1	2	yes	—
320	C₂×#552	—	47	1	no	maximal, Sylow
321	C₂×C₄₇	—	2	2	no	—
322	C₂×C₄₇	—	4	1	no	—
323	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
324	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
325	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₄₇	—	2	2	no	—
327	D₄₇	—	4	1	no	—
328	D₄₇	#552	1	4	yes	direct product factor
329	#552	—	47	2	no	—
330	#552	—	47	2	no	—
331	#552	—	47	1	no	—
332	#552	—	47	2	no	—
333	#552	—	47	1	no	—
334	#552	—	47	1	no	—
335	#552	—	47	1	no	—
336	#552	—	47	1	no	—
337	#552	—	47	2	no	—
338	#552	—	47	1	no	—
339	#552	—	47	1	no	—
340	#552	D₄₇	1	1	yes	characteristic, direct product factor
341	C₂×#126	—	47	2	no	—
342	C₂×#125	—	47	2	no	—
343	C₂×#125	—	47	1	no	—
344	C₂×#123	—	47	2	no	—
345	C₂×C₂²⋊Q₈	—	47	1	no	—
346	C₂×C₂²⋊Q₈	—	47	1	no	—
347	C₂×C₄×Q₈	—	47	1	no	—
348	C₂×C₄×D₄	—	47	1	no	—
349	C₂×#117	—	47	1	no	—
350	C₂×#117	—	47	2	no	—
351	C₂²×C₄⋊C₄	—	47	1	no	—
352	C₄₇	C₂×#552	1	1	yes	characteristic, complemented, Sylow
353	C₂²×Q₈	—	47	1	no	—
354	C₂²×D₄	—	47	1	no	—
355	C₂³×C₄	—	47	2	no	—
356	C₂³×C₄	—	47	1	no	—
357	C₂³×C₄	—	47	1	no	—
358	#126	—	47	2	no	—
359	#126	—	47	2	no	—
360	#126	—	47	2	no	—
361	#126	—	47	2	no	—
362	#126	—	47	2	no	—
363	#126	—	47	2	no	—
364	#126	—	47	2	no	—
365	#126	C₂×D₄₇	1	2	yes	complemented
366	#125	—	47	2	no	—
367	#125	—	47	2	no	—
368	#125	—	47	2	no	—
369	#125	—	47	2	no	—
370	#125	—	47	2	no	—
371	#125	—	47	2	no	—
372	#125	—	47	2	no	—
373	#125	—	47	2	no	—
374	#125	—	47	1	no	—
375	#125	—	47	1	no	—
376	#125	—	47	2	no	—
377	#125	—	47	1	no	—
378	#125	C₂×D₄₇	1	2	yes	complemented
379	#125	C₂×D₄₇	1	1	yes	characteristic, complemented
380	#123	—	47	2	no	—
381	#123	—	47	2	no	—
382	#123	—	47	2	no	—
383	#123	—	47	2	no	—
384	#123	—	47	2	no	—
385	#123	—	47	2	no	—
386	#123	—	47	2	no	—
387	#123	C₂×D₄₇	1	2	yes	—
388	C₂²⋊Q₈	—	47	1	no	—
389	C₂²⋊Q₈	—	47	1	no	—
390	C₂²⋊Q₈	—	47	1	no	—
391	C₂²⋊Q₈	—	47	1	no	—
392	C₂²⋊Q₈	—	47	2	no	—
393	C₂²⋊Q₈	—	47	2	no	—
394	C₂²⋊Q₈	—	47	1	no	—
395	C₂²⋊Q₈	—	47	1	no	—
396	C₂²⋊Q₈	—	47	2	no	—
397	C₂²⋊Q₈	—	47	2	no	—
398	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
399	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
400	C₄×Q₈	—	47	1	no	—
401	C₄×Q₈	—	47	2	no	—
402	C₄×Q₈	—	47	1	no	—
403	C₄×Q₈	—	47	1	no	—
404	C₄×Q₈	—	47	2	no	—
405	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
406	C₄×D₄	—	47	1	no	—
407	C₄×D₄	—	47	1	no	—
408	C₄×D₄	—	47	1	no	—
409	C₄×D₄	—	47	1	no	—
410	C₄×D₄	—	47	1	no	—
411	C₄×D₄	—	47	1	no	—
412	C₄×D₄	—	47	1	no	—
413	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
414	#117	—	47	1	no	—
415	#117	—	47	2	no	—
416	#117	—	47	1	no	—
417	#117	—	47	1	no	—
418	#117	—	47	2	no	—
419	#117	—	47	2	no	—
420	#117	—	47	2	no	—
421	#117	—	47	2	no	—
422	#117	—	47	2	no	—
423	#117	—	47	2	no	—
424	#117	—	47	2	no	—
425	#117	—	47	2	no	—
426	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
427	#117	C₂×D₄₇	1	2	yes	complemented
428	C₂×C₄⋊C₄	—	47	2	no	—
429	C₂×C₄⋊C₄	—	47	1	no	—
430	C₂×C₄⋊C₄	—	47	1	no	—
431	C₂×C₄⋊C₄	—	47	1	no	—
432	C₂×C₄⋊C₄	—	47	2	no	—
433	C₂×C₄⋊C₄	—	47	2	no	—
434	C₂×C₄⋊C₄	—	47	1	no	—
435	C₂×C₄⋊C₄	—	47	1	no	—
436	C₂×C₄⋊C₄	—	47	1	no	—
437	C₂×C₄⋊C₄	—	47	2	no	—
438	C₂×C₄⋊C₄	—	47	2	no	—
439	C₂×C₄⋊C₄	—	47	1	no	—
440	C₂×C₄⋊C₄	—	47	2	no	—
441	C₂×C₄⋊C₄	—	47	2	no	—
442	C₂×C₄⋊C₄	—	47	2	no	—
443	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
444	C₂×C₂²⋊C₄	—	47	1	no	—
445	C₂×C₂²⋊C₄	—	47	2	no	—
446	C₂×C₂²⋊C₄	—	47	2	no	—
447	C₂×C₂²⋊C₄	—	47	1	no	—
448	C₂×C₂²⋊C₄	—	47	2	no	—
449	C₂×C₄²	—	47	2	no	—
450	C₂×C₄²	—	47	2	no	—
451	C₂×C₄²	—	47	1	no	—
452	C₂⁴	—	47	1	no	—
453	C₂⁴	—	47	1	no	—
454	C₂×Q₈	—	47	2	no	—
455	C₂×Q₈	—	47	1	no	—
456	C₂×Q₈	—	94	4	no	—
457	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×D₄	—	47	1	no	—
459	C₂×D₄	—	47	1	no	—
460	C₂×D₄	—	47	1	no	—
461	C₂×D₄	—	94	4	no	—
462	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	—	47	1	no	—
464	C₂²×C₄	—	47	2	no	—
465	C₂²×C₄	—	47	1	no	—
466	C₂²×C₄	—	47	1	no	—
467	C₂²×C₄	—	47	1	no	—
468	C₂²×C₄	—	47	1	no	—
469	C₂²×C₄	—	47	2	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	2	no	—
472	C₂²×C₄	—	47	1	no	—
473	C₂²×C₄	—	47	1	no	—
474	C₂²×C₄	—	47	2	no	—
475	C₂²×C₄	—	47	2	no	—
476	C₂²×C₄	—	47	2	no	—
477	C₂²×C₄	—	47	1	no	—
478	C₂²×C₄	—	47	1	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	1	no	—
481	C₂²×C₄	—	94	4	no	—
482	C₂²×C₄	—	94	4	no	—
483	C₂²×C₄	—	94	8	no	—
484	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
485	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	2	no	—
489	C₄⋊C₄	—	47	2	no	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	—	47	2	no	—
492	C₄⋊C₄	—	47	2	no	—
493	C₄⋊C₄	—	47	2	no	—
494	C₄⋊C₄	—	47	2	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	1	no	—
497	C₄⋊C₄	—	47	1	no	—
498	C₄⋊C₄	—	47	2	no	—
499	C₄⋊C₄	—	47	2	no	—
500	C₄⋊C₄	—	47	2	no	—
501	C₄⋊C₄	—	47	2	no	—
502	C₄⋊C₄	—	47	2	no	—
503	C₄⋊C₄	—	47	2	no	—
504	C₄⋊C₄	—	47	1	no	—
505	C₄⋊C₄	—	47	1	no	—
506	C₄⋊C₄	—	47	2	no	—
507	C₄⋊C₄	—	47	2	no	—
508	C₄⋊C₄	—	47	1	no	—
509	C₄⋊C₄	—	47	2	no	—
510	C₄⋊C₄	—	47	1	no	—
511	C₄⋊C₄	—	47	2	no	—
512	C₄⋊C₄	—	47	2	no	—
513	C₄⋊C₄	—	47	2	no	—
514	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
517	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
518	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
522	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
523	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
524	C₂²⋊C₄	—	47	1	no	—
525	C₂²⋊C₄	—	47	2	no	—
526	C₂²⋊C₄	—	47	2	no	—
527	C₂²⋊C₄	—	47	1	no	—
528	C₂²⋊C₄	—	47	2	no	—
529	C₂²⋊C₄	—	47	1	no	—
530	C₂²⋊C₄	—	47	1	no	—
531	C₂²⋊C₄	—	47	2	no	—
532	C₂²⋊C₄	—	47	2	no	—
533	C₂²⋊C₄	—	47	2	no	—
534	C₂²⋊C₄	—	47	2	no	—
535	C₂²⋊C₄	—	47	1	no	—
536	C₂²⋊C₄	—	47	1	no	—
537	C₂²⋊C₄	—	47	2	no	—
538	C₂²⋊C₄	—	47	2	no	—
539	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
544	C₄²	—	47	2	no	—
545	C₄²	—	47	2	no	—
546	C₄²	—	47	2	no	—
547	C₄²	—	47	2	no	—
548	C₄²	—	47	2	no	—
549	C₄²	—	47	2	no	—
550	C₄²	—	47	1	no	—
551	C₄²	—	47	1	no	—
552	C₄²	—	47	1	no	—
553	C₄²	C₂²×D₄₇	1	2	yes	—
554	C₄²	C₂²×D₄₇	1	2	yes	—
555	C₄²	C₂²×D₄₇	1	1	yes	characteristic
556	C₂³	—	47	1	no	—
557	C₂³	—	47	4	no	—
558	C₂³	—	47	1	no	—
559	C₂³	—	47	1	no	—
560	C₂³	—	94	2	no	—
561	C₂³	—	94	2	no	—
562	C₂³	—	94	2	no	—
563	C₂³	—	94	2	no	—
564	C₂³	—	94	2	no	—
565	C₂³	C₂³×D₄₇	1	1	yes	characteristic
566	C₂³	C₂³×D₄₇	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	94	4	no	—
569	Q₈	—	94	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	94	2	no	—
572	D₄	—	94	2	no	—
573	D₄	—	94	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	47	1	no	—
578	C₂×C₄	—	47	4	no	—
579	C₂×C₄	—	47	1	no	—
580	C₂×C₄	—	47	1	no	—
581	C₂×C₄	—	47	2	no	—
582	C₂×C₄	—	47	2	no	—
583	C₂×C₄	—	47	2	no	—
584	C₂×C₄	—	47	1	no	—
585	C₂×C₄	—	47	1	no	—
586	C₂×C₄	—	47	2	no	—
587	C₂×C₄	—	94	2	no	—
588	C₂×C₄	—	94	2	no	—
589	C₂×C₄	—	94	2	no	—
590	C₂×C₄	—	94	4	no	—
591	C₂×C₄	—	94	2	no	—
592	C₂×C₄	—	94	2	no	—
593	C₂×C₄	—	94	4	no	—
594	C₂×C₄	—	94	4	no	—
595	C₂×C₄	—	94	4	no	—
596	C₂×C₄	—	94	4	no	—
597	C₂×C₄	—	94	2	no	—
598	C₂×C₄	—	94	4	no	—
599	C₂×C₄	—	94	2	no	—
600	C₂×C₄	—	94	2	no	—
601	C₂×C₄	—	94	4	no	—
602	C₂×C₄	—	94	2	no	—
603	C₂×C₄	—	94	2	no	—
604	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₄₇	1	2	yes	—
607	C₂×C₄	C₂³×D₄₇	1	2	yes	—
608	C₂×C₄	C₂³×D₄₇	1	2	yes	—
609	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₄₇	1	2	yes	—
612	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	47	2	no	—
619	C₂²	—	47	2	no	—
620	C₂²	—	47	2	no	—
621	C₂²	—	47	2	no	—
622	C₂²	—	94	8	no	—
623	C₂²	—	94	1	no	—
624	C₂²	—	94	1	no	—
625	C₂²	—	94	1	no	—
626	C₂²	—	94	1	no	—
627	C₂²	—	94	1	no	—
628	C₂²	—	188	4	no	—
629	C₂²	#41×D₄₇	1	2	yes	—
630	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	47	2	no	—
640	C₄	—	94	2	no	—
641	C₄	—	94	2	no	—
642	C₄	—	94	1	no	—
643	C₄	—	94	1	no	—
644	C₄	—	94	1	no	—
645	C₄	—	94	2	no	—
646	C₄	—	94	1	no	—
647	C₄	—	94	2	no	—
648	C₄	#41×D₄₇	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	47	4	no	—
652	C₂	—	94	2	no	—
653	C₂	—	188	1	no	—
654	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
655	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
656	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#552	C₂
hypercenter	#552	D₄₇
hypocenter	C₄₇	C₂×#552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #15689815	C₂	semidirect
2. #15689814	C₂	semidirect
3. #15689813	C₂	semidirect
4. #15689812	C₂	semidirect
5. #15689811	C₂	semidirect
6. #15689810	C₂	semidirect
7. #15689809	C₂	semidirect
8. #15689808	C₂	semidirect
9. #15689807	C₂	semidirect
10. #15689806	C₂	semidirect
11. #15689805	C₂	semidirect
12. #126×D₄₇	C₂	semidirect
13. #125×D₄₇	C₂	semidirect
14. #125×D₄₇	C₂	semidirect
16. C₂²⋊Q₈×D₄₇	C₂	semidirect
17. C₂²⋊Q₈×D₄₇	C₂	semidirect
18. C₄×Q₈×D₄₇	C₂	semidirect
20. #117×D₄₇	C₂	semidirect
21. #117×D₄₇	C₂	semidirect
22. C₂×C₄⋊C₄×D₄₇	C₂	semidirect
23. C₄₇×#552	C₂	semidirect
29. #13094019	C₂²	semidirect
30. #13094019	C₂²	semidirect
31. #13094019	C₂²	semidirect
32. #13094018	C₂²	semidirect
33. #13094017	C₂²	semidirect
34. #13094017	C₂²	semidirect
35. #13094017	C₂²	semidirect
36. #13094016	C₂²	semidirect
37. #13094016	C₂²	semidirect
38. #13094015	C₂²	semidirect
39. #13094015	C₂²	semidirect
40. #13094015	C₂²	semidirect
41. #13094015	C₂²	semidirect
42. #13094014	C₂²	semidirect
43. #13094014	C₂²	semidirect
44. #13094014	C₂²	semidirect
45. #13094014	C₂²	semidirect
46. #13094014	C₂²	semidirect
47. #13094014	C₂²	semidirect
55. #13094004	C₂²	semidirect
56. #13094004	C₂²	semidirect
57. #13094003	C₂²	semidirect
58. #13094003	C₂²	semidirect
59. #13094002	C₂²	semidirect
60. #13094002	C₂²	semidirect
61. #13094001	C₂²	semidirect
62. #13094001	C₂²	semidirect
63. #13094000	C₂²	semidirect
64. #13094000	C₂²	semidirect
65. Q₈×Dic₄₇	C₂²	semidirect
66. C₄×Dic₉₄	C₂²	semidirect
67. C₄×Dic₉₄	C₂²	semidirect
68. #13093989	C₂²	semidirect
69. #13093989	C₂²	semidirect
77. #13093983	C₂²	semidirect
78. #13093983	C₂²	semidirect
79. #13093982	C₂²	semidirect
80. #13093982	C₂²	semidirect
81. #13093982	C₂²	semidirect
82. #13093982	C₂²	semidirect
83. #13093981	C₂²	semidirect
84. #13093981	C₂²	semidirect
85. #13093981	C₂²	semidirect
86. #13093980	C₂²	semidirect
87. #13093980	C₂²	semidirect
88. #13093980	C₂²	semidirect
89. C₂×C₄⋊Dic₄₇	C₂²	semidirect
90. C₂×Dic₄₇⋊C₄	C₂²	semidirect
101. C₄⋊C₄×D₄₇	C₂²	semidirect
102. C₄⋊C₄×D₄₇	C₂²	semidirect
103. C₄⋊C₄×D₄₇	C₂²	semidirect
112. #126×C₄₇	C₂²	semidirect
113. #125×C₄₇	C₂²	semidirect
114. #125×C₄₇	C₂²	semidirect
116. C₂²⋊Q₈×C₄₇	C₂²	semidirect
117. C₂²⋊Q₈×C₄₇	C₂²	semidirect
118. C₄×Q₈×C₄₇	C₂²	semidirect
120. #117×C₄₇	C₂²	semidirect
121. #117×C₄₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
328. D₄₇	#552	direct (N × H)
340. #552	D₄₇	direct (N × H)
352. C₄₇	C₂×#552	semidirect
365. #126	C₂×D₄₇	semidirect
378. #125	C₂×D₄₇	semidirect
379. #125	C₂×D₄₇	semidirect
398. C₂²⋊Q₈	C₂×D₄₇	semidirect
399. C₂²⋊Q₈	C₂×D₄₇	semidirect
405. C₄×Q₈	C₂×D₄₇	semidirect
426. #117	C₂×D₄₇	semidirect
427. #117	C₂×D₄₇	semidirect
443. C₂×C₄⋊C₄	C₂×D₄₇	semidirect

Subgroups — #552×D47 #20256891

Conjugacy classes of subgroups

Complements

Subgroups — #552×D₄₇ #20256891