Subgroups — #20257949

Order 6016.

1032 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	#15689874	C₂	1	2	yes	maximal, complemented
2	#15689870	C₂	1	2	yes	maximal, complemented
3	#15689847	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689842	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689801	C₂	1	2	yes	maximal, complemented
6	#15689800	C₂	1	2	yes	maximal, complemented
7	#15689788	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689784	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689780	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689766	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689761	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689748	C₂	1	2	yes	maximal, complemented
14	#15689744	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689743	C₂	1	2	yes	maximal, complemented
16	#15689742	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689741	C₂	1	2	yes	maximal, complemented
18	#15689709	C₂	1	2	yes	maximal, complemented
19	#15689698	C₂	1	1	yes	maximal, characteristic, complemented
20	#15689678	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689651	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625354	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
28	#13094024	C₂²	1	1	yes	characteristic, complemented
29	#13094023	C₂²	1	2	yes	complemented
30	#13094022	C₂²	1	2	yes	complemented
31	#13094022	C₂²	1	1	yes	characteristic, complemented
32	#13094019	C₂²	1	2	yes	complemented
33	#13094019	C₂²	1	1	yes	characteristic, complemented
34	#13094019	C₂²	1	2	yes	complemented
35	#13094019	C₂²	1	2	yes	complemented
36	#13094017	C₂²	1	1	yes	characteristic, complemented
37	#13094017	C₂²	1	2	yes	complemented
38	#13094017	C₂²	1	2	yes	complemented
39	#13094017	C₂²	1	2	yes	complemented
40	#13094015	C₂²	1	2	yes	complemented
41	#13094014	C₂²	1	1	yes	characteristic, complemented
42	#13094013	C₂²	1	1	yes	characteristic
43	#13094013	C₂²	1	1	yes	characteristic
44	#13094013	C₂²	1	2	yes	complemented
45	#13094012	C₂²	1	1	yes	characteristic
46	#13094011	C₂²	1	1	yes	characteristic
47	#13094011	C₂²	1	2	yes	complemented
48	#13094010	C₂²	1	2	yes	—
49	#13094010	C₂²	1	2	yes	—
50	#13094010	C₂²	1	2	yes	complemented
51	#13094010	C₂²	1	2	yes	complemented
52	#13094010	C₂²	1	1	yes	characteristic, complemented
53	#13094009	C₂²	1	1	yes	characteristic
54	#13094009	C₂²	1	2	yes	complemented
55	#13094009	C₂²	1	2	yes	complemented
56	#13094008	C₂²	1	2	yes	complemented
57	#13094007	C₂²	1	2	yes	—
58	#13094006	C₂²	1	2	yes	—
59	#13094006	C₂²	1	1	yes	characteristic
60	#13094006	C₂²	1	2	yes	complemented
61	#13094004	C₂²	1	2	yes	—
62	#13094004	C₂²	1	2	yes	complemented
63	#13094003	C₂²	1	2	yes	complemented
64	#13094003	C₂²	1	1	yes	characteristic, complemented
65	#13094003	C₂²	1	2	yes	complemented
66	#13094002	C₂²	1	1	yes	characteristic
67	#13094002	C₂²	1	2	yes	—
68	#13094002	C₂²	1	2	yes	complemented
69	#13094002	C₂²	1	2	yes	complemented
70	#13094002	C₂²	1	2	yes	complemented
71	#13094002	C₂²	1	2	yes	complemented
72	#13094001	C₂²	1	2	yes	complemented
73	#13094001	C₂²	1	2	yes	complemented
74	#13094000	C₂²	1	2	yes	—
75	#13094000	C₂²	1	1	yes	characteristic
76	#13094000	C₂²	1	1	yes	characteristic
77	#13094000	C₂²	1	1	yes	characteristic, complemented
78	#13094000	C₂²	1	2	yes	complemented
79	#13093998	C₂²	1	1	yes	characteristic
80	#13093998	C₂²	1	2	yes	complemented
81	#13093997	C₂²	1	2	yes	—
82	#13093997	C₂²	1	1	yes	characteristic
83	#13093996	C₂²	1	2	yes	—
84	#13093995	C₂²	1	1	yes	characteristic
85	#13093995	C₂²	1	2	yes	complemented
86	#13093994	C₂²	1	2	yes	—
87	#13093992	C₂²	1	2	yes	—
88	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
89	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
90	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
93	#13093989	C₂²	1	2	yes	complemented
94	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
95	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
96	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
97	#13093986	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
103	#13093982	C₂²	1	2	yes	—
104	#13093982	C₂²	1	2	yes	complemented
105	#13093981	C₂²	1	1	yes	characteristic, complemented
106	#13093980	C₂²	1	2	yes	complemented
107	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic
112	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
114	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
116	#124×C₄₇	C₂²	1	1	yes	characteristic
117	#124×C₄₇	C₂²	1	1	yes	characteristic
118	#123×C₄₇	C₂²	1	2	yes	complemented
119	#123×C₄₇	C₂²	1	2	yes	complemented
120	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
121	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
122	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₄₇	C₂³	1	2	yes	—
124	#41×C₄₇	—	4	2	no	—
125	C₂×Q₈×C₄₇	—	4	2	no	—
126	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
130	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₄₇	C₂³	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
140	C₂²×Dic₄₇	C₂³	1	2	yes	—
141	#10625354	—	4	2	no	—
142	Q₈×D₄₇	—	4	2	no	—
143	Q₈×D₄₇	—	4	2	no	—
144	D₄×D₄₇	—	4	2	no	—
145	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
146	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
147	C₂×D₁₈₈	C₂³	1	2	yes	—
148	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₄₇	C₂³	1	2	yes	—
153	C₂×C₄×D₄₇	C₂³	1	2	yes	—
154	C₂×C₄×D₄₇	C₂³	1	2	yes	—
155	C₂×C₄×D₄₇	C₂³	1	2	yes	—
156	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
157	C₂×Dic₉₄	C₂³	1	2	yes	—
158	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
159	C₂×Dic₉₄	C₂³	1	2	yes	—
160	C₂×Dic₉₄	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
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	2	yes	—
172	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
173	C₄²×C₄₇	C₂³	1	1	yes	characteristic
174	C₄²×C₄₇	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
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	1	yes	characteristic
181	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
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	2	yes	—
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	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₄₇	C₂³	1	2	yes	—
200	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₄₇	C₂³	1	2	yes	—
205	C₄⋊Dic₄₇	C₂³	1	2	yes	—
206	C₄⋊Dic₄₇	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₄₇⋊C₄	C₂³	1	2	yes	—
212	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₄₇⋊C₄	C₂³	1	2	yes	—
214	Dic₄₇⋊C₄	C₂³	1	2	yes	—
215	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₄₇⋊C₄	C₂³	1	2	yes	—
217	Dic₄₇⋊C₄	C₂³	1	2	yes	—
218	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₄₇⋊C₄	C₂³	1	2	yes	—
220	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₇	C₂³	1	2	yes	—
227	C₄×Dic₄₇	C₂³	1	2	yes	—
228	C₂³×C₄₇	C₂⁴	1	2	yes	—
229	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₄₇	—	2	4	no	—
231	C₂²×D₄₇	—	4	2	no	—
232	C₂²×D₄₇	—	4	2	no	—
233	C₂²×D₄₇	C₂⁴	1	2	yes	—
234	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₄₇	—	2	2	no	—
237	Q₈×C₄₇	—	2	2	no	—
238	Q₈×C₄₇	—	2	2	no	—
239	Q₈×C₄₇	—	4	2	no	—
240	D₄×C₄₇	—	2	2	no	—
241	D₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₄₇	—	2	2	no	—
255	C₂²⋊D₄₇	—	4	2	no	—
256	C₂²⋊D₄₇	—	4	2	no	—
257	C₂²⋊D₄₇	—	4	1	no	—
258	C₂²⋊D₄₇	—	4	2	no	—
259	C₂×Dic₄₇	—	4	2	no	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₄₇	C₂⁴	1	2	yes	—
264	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₄₇	C₂⁴	1	2	yes	—
266	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₄₇	C₂⁴	1	2	yes	—
268	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
269	D₁₈₈	—	2	2	no	—
270	D₁₈₈	—	2	2	no	—
271	D₁₈₈	—	4	2	no	—
272	C₄×D₄₇	—	2	2	no	—
273	C₄×D₄₇	—	2	2	no	—
274	C₄×D₄₇	—	2	2	no	—
275	C₄×D₄₇	—	4	1	no	—
276	C₄×D₄₇	—	4	2	no	—
277	C₄×D₄₇	—	4	2	no	—
278	C₄×D₄₇	—	4	2	no	—
279	C₄×D₄₇	—	4	2	no	—
280	Dic₉₄	—	2	2	no	—
281	Dic₉₄	—	4	1	no	—
282	Dic₉₄	—	4	2	no	—
283	Dic₉₄	—	4	2	no	—
284	Dic₉₄	—	4	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	2	no	—
289	C₂²×C₄₇	—	2	2	no	—
290	C₂²×C₄₇	—	2	1	no	—
291	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
292	C₂×D₄₇	—	2	1	no	—
293	C₂×D₄₇	—	2	1	no	—
294	C₂×D₄₇	—	2	1	no	—
295	C₂×D₄₇	—	2	2	no	—
296	C₂×D₄₇	—	2	1	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	2	2	no	—
299	C₂×D₄₇	—	2	1	no	—
300	C₂×D₄₇	—	8	4	no	—
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	1	no	—
310	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
311	Dic₄₇	—	2	2	no	—
312	Dic₄₇	—	2	1	no	—
313	Dic₄₇	—	2	1	no	—
314	Dic₄₇	—	2	1	no	—
315	Dic₄₇	—	2	1	no	—
316	Dic₄₇	—	2	1	no	—
317	Dic₄₇	—	2	2	no	—
318	Dic₄₇	—	2	1	no	—
319	Dic₄₇	—	2	2	no	—
320	#3561	—	47	1	no	maximal, Sylow
321	C₂×C₄₇	—	4	2	no	—
322	C₂×C₄₇	—	4	1	no	—
323	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₂×C₄₇	#585	1	1	yes	characteristic
326	D₄₇	—	2	2	no	—
327	D₄₇	—	4	1	no	—
328	D₄₇	—	4	2	no	—
329	#563	—	47	2	no	—
330	#562	—	47	2	no	—
331	#556	—	47	1	no	—
332	#556	—	47	1	no	—
333	#551	—	47	2	no	—
334	#551	—	47	2	no	—
335	D₄×Q₈	—	47	1	no	—
336	D₄×Q₈	—	47	1	no	—
337	#548	—	47	1	no	—
338	#548	—	47	1	no	—
339	#546	—	47	1	no	—
340	#546	—	47	1	no	—
341	#543	—	47	2	no	—
342	#542	—	47	1	no	—
343	#542	—	47	2	no	—
344	#542	—	47	2	no	—
345	#542	—	47	1	no	—
346	#538	—	47	2	no	—
347	#536	—	47	1	no	—
348	#536	D₄₇	1	1	yes	characteristic, complemented
349	#533	—	47	1	no	—
350	#529	—	47	1	no	—
351	C₂×#124	—	47	1	no	—
352	C₄₇	#3561	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	47	1	no	—
354	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
355	C₂²×Q₈	—	47	1	no	—
356	C₂²×Q₈	—	47	1	no	—
357	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
358	C₂²×D₄	—	47	1	no	—
359	C₄⋊Q₈	—	47	1	no	—
360	C₄⋊Q₈	—	47	2	no	—
361	C₄⋊Q₈	—	47	2	no	—
362	C₄⋊Q₈	—	47	1	no	—
363	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
364	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
365	#126	—	47	1	no	—
366	#126	—	47	2	no	—
367	#126	—	47	2	no	—
368	#126	—	47	2	no	—
369	#126	—	47	1	no	—
370	#126	—	47	2	no	—
371	#126	—	47	2	no	—
372	#126	—	47	2	no	—
373	#125	—	47	1	no	—
374	#125	—	47	2	no	—
375	#124	—	47	1	no	—
376	#124	—	47	1	no	—
377	#124	—	47	2	no	—
378	#124	—	47	1	no	—
379	#124	—	47	2	no	—
380	#124	—	47	2	no	—
381	#124	—	47	2	no	—
382	#124	—	47	1	no	—
383	#124	—	47	2	no	—
384	#124	—	47	2	no	—
385	#124	—	47	1	no	—
386	#124	C₂×D₄₇	1	1	yes	characteristic
387	#124	C₂×D₄₇	1	1	yes	characteristic
388	#123	—	47	2	no	—
389	#123	—	47	1	no	—
390	#123	—	47	2	no	—
391	#123	—	47	2	no	—
392	#123	—	47	1	no	—
393	#123	—	47	2	no	—
394	#123	—	47	2	no	—
395	#123	—	47	2	no	—
396	#123	C₂×D₄₇	1	2	yes	complemented
397	#123	C₂×D₄₇	1	2	yes	complemented
398	C₂²⋊Q₈	—	47	1	no	—
399	C₂²⋊Q₈	—	47	1	no	—
400	C₂²⋊Q₈	—	47	1	no	—
401	C₂²⋊Q₈	—	47	2	no	—
402	C₂²⋊Q₈	—	47	2	no	—
403	C₂²⋊Q₈	—	47	1	no	—
404	C₂²⋊Q₈	—	47	2	no	—
405	C₂²⋊Q₈	—	47	2	no	—
406	C₂²⋊Q₈	—	47	1	no	—
407	C₂²⋊Q₈	—	47	2	no	—
408	C₂²⋊Q₈	—	47	2	no	—
409	C₂²⋊Q₈	—	47	2	no	—
410	C₂²⋊Q₈	—	47	2	no	—
411	C₂²⋊Q₈	—	47	2	no	—
412	C₂²⋊Q₈	—	47	2	no	—
413	C₂²⋊Q₈	—	47	2	no	—
414	C₂²⋊Q₈	—	47	2	no	—
415	C₂²⋊Q₈	—	47	2	no	—
416	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
417	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
418	#121	—	47	2	no	—
419	#121	—	47	1	no	—
420	#121	—	47	2	no	—
421	#121	—	47	2	no	—
422	#121	—	47	1	no	—
423	#121	—	47	1	no	—
424	#121	—	47	2	no	—
425	#120	—	47	2	no	—
426	#120	—	47	2	no	—
427	C₄×Q₈	—	47	1	no	—
428	C₄×Q₈	—	47	1	no	—
429	C₄×Q₈	—	47	1	no	—
430	C₄×Q₈	—	47	2	no	—
431	C₄×Q₈	—	47	1	no	—
432	C₄×Q₈	—	47	1	no	—
433	C₄×D₄	—	47	1	no	—
434	C₄×D₄	—	47	1	no	—
435	C₄×D₄	—	47	1	no	—
436	C₄×D₄	—	47	2	no	—
437	C₄×D₄	—	47	2	no	—
438	C₄×D₄	—	47	2	no	—
439	C₄×D₄	—	47	2	no	—
440	C₄×D₄	—	47	1	no	—
441	C₄×D₄	—	47	1	no	—
442	#117	—	47	2	no	—
443	#117	—	47	2	no	—
444	#117	—	47	2	no	—
445	#117	—	47	1	no	—
446	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
447	C₂×C₂²⋊C₄	—	47	2	no	—
448	C₂×C₂²⋊C₄	—	47	2	no	—
449	C₂×C₂²⋊C₄	—	47	2	no	—
450	C₂×C₂²⋊C₄	—	47	2	no	—
451	C₂×C₄²	—	47	1	no	—
452	C₂⁴	—	47	2	no	—
453	#41	—	4	2	no	—
454	#41	—	188	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	47	1	no	—
457	C₂×Q₈	—	47	1	no	—
458	C₂×Q₈	—	47	2	no	—
459	C₂×Q₈	—	47	2	no	—
460	C₂×Q₈	—	47	2	no	—
461	C₂×Q₈	—	188	2	no	—
462	C₂×Q₈	—	188	2	no	—
463	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
467	C₂×D₄	—	47	1	no	—
468	C₂×D₄	—	47	2	no	—
469	C₂×D₄	—	47	2	no	—
470	C₂×D₄	—	47	1	no	—
471	C₂×D₄	—	47	2	no	—
472	C₂×D₄	—	47	1	no	—
473	C₂×D₄	—	47	1	no	—
474	C₂×D₄	—	47	2	no	—
475	C₂×D₄	—	188	2	no	—
476	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₄₇	1	2	yes	—
478	C₂²×C₄	—	47	2	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	1	no	—
481	C₂²×C₄	—	47	1	no	—
482	C₂²×C₄	—	47	1	no	—
483	C₂²×C₄	—	47	2	no	—
484	C₂²×C₄	—	47	2	no	—
485	C₂²×C₄	—	47	2	no	—
486	C₂²×C₄	—	47	2	no	—
487	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
489	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
490	C₄⋊C₄	—	47	1	no	—
491	C₄⋊C₄	—	47	1	no	—
492	C₄⋊C₄	—	47	2	no	—
493	C₄⋊C₄	—	47	1	no	—
494	C₄⋊C₄	—	47	1	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	2	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	—	47	1	no	—
499	C₄⋊C₄	—	47	2	no	—
500	C₄⋊C₄	—	47	2	no	—
501	C₄⋊C₄	—	47	1	no	—
502	C₄⋊C₄	—	47	2	no	—
503	C₄⋊C₄	—	47	1	no	—
504	C₄⋊C₄	—	47	2	no	—
505	C₄⋊C₄	—	47	1	no	—
506	C₄⋊C₄	—	47	1	no	—
507	C₄⋊C₄	—	47	1	no	—
508	C₄⋊C₄	—	47	2	no	—
509	C₄⋊C₄	—	47	2	no	—
510	C₄⋊C₄	—	47	2	no	—
511	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
513	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
517	C₂²⋊C₄	—	47	2	no	—
518	C₂²⋊C₄	—	47	2	no	—
519	C₂²⋊C₄	—	47	2	no	—
520	C₂²⋊C₄	—	47	1	no	—
521	C₂²⋊C₄	—	47	2	no	—
522	C₂²⋊C₄	—	47	1	no	—
523	C₂²⋊C₄	—	47	2	no	—
524	C₂²⋊C₄	—	47	1	no	—
525	C₂²⋊C₄	—	47	1	no	—
526	C₂²⋊C₄	—	47	2	no	—
527	C₂²⋊C₄	—	47	2	no	—
528	C₂²⋊C₄	—	47	2	no	—
529	C₂²⋊C₄	—	47	2	no	—
530	C₂²⋊C₄	—	47	2	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	1	no	—
538	C₂²⋊C₄	—	47	2	no	—
539	C₂²⋊C₄	—	47	1	no	—
540	C₂²⋊C₄	—	47	2	no	—
541	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
547	C₄²	—	47	1	no	—
548	C₄²	—	47	1	no	—
549	C₄²	—	47	1	no	—
550	C₄²	—	47	2	no	—
551	C₄²	—	47	2	no	—
552	C₄²	—	47	1	no	—
553	C₄²	—	47	2	no	—
554	C₄²	—	47	2	no	—
555	C₄²	C₂²×D₄₇	1	1	yes	characteristic
556	C₄²	C₂²×D₄₇	1	1	yes	characteristic
557	C₂³	—	47	1	no	—
558	C₂³	—	47	2	no	—
559	C₂³	—	47	1	no	—
560	C₂³	—	94	4	no	—
561	C₂³	—	188	2	no	—
562	C₂³	—	188	2	no	—
563	C₂³	C₂³×D₄₇	1	2	yes	—
564	C₂³	C₂³×D₄₇	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	94	2	no	—
570	Q₈	—	188	1	no	—
571	Q₈	—	188	2	no	—
572	Q₈	—	188	2	no	—
573	Q₈	—	188	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	94	2	no	—
577	D₄	—	94	2	no	—
578	D₄	—	94	2	no	—
579	D₄	—	188	2	no	—
580	D₄	—	188	2	no	—
581	D₄	—	188	2	no	—
582	D₄	—	188	1	no	—
583	D₄	—	188	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	47	1	no	—
588	C₂×C₄	—	47	1	no	—
589	C₂×C₄	—	47	2	no	—
590	C₂×C₄	—	47	1	no	—
591	C₂×C₄	—	47	2	no	—
592	C₂×C₄	—	47	1	no	—
593	C₂×C₄	—	47	1	no	—
594	C₂×C₄	—	47	2	no	—
595	C₂×C₄	—	47	1	no	—
596	C₂×C₄	—	94	2	no	—
597	C₂×C₄	—	94	2	no	—
598	C₂×C₄	—	94	2	no	—
599	C₂×C₄	—	188	2	no	—
600	C₂×C₄	—	188	1	no	—
601	C₂×C₄	—	188	2	no	—
602	C₂×C₄	—	188	2	no	—
603	C₂×C₄	—	188	2	no	—
604	C₂×C₄	—	188	2	no	—
605	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₄₇	1	2	yes	—
609	C₂×C₄	C₂³×D₄₇	1	2	yes	—
610	C₂×C₄	C₂³×D₄₇	1	2	yes	—
611	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	47	2	no	—
621	C₂²	—	94	1	no	—
622	C₂²	—	94	1	no	—
623	C₂²	—	94	1	no	—
624	C₂²	—	94	2	no	—
625	C₂²	—	94	1	no	—
626	C₂²	—	94	2	no	—
627	C₂²	—	94	2	no	—
628	C₂²	—	94	1	no	—
629	C₂²	—	376	4	no	—
630	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	94	1	no	—
640	C₄	—	94	1	no	—
641	C₄	—	94	2	no	—
642	C₄	—	94	1	no	—
643	C₄	—	94	1	no	—
644	C₄	—	94	1	no	—
645	C₄	—	94	1	no	—
646	C₄	—	94	2	no	—
647	C₄	—	94	2	no	—
648	C₄	#13094069	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	94	2	no	—
652	C₂	—	188	2	no	—
653	C₂	—	188	1	no	—
654	C₂	C₂×#13094069	1	1	yes	characteristic
655	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
656	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#536	C₂
hypercenter	#536	D₄₇
hypocenter	C₄₇	#3561
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #15689874	C₂	semidirect
2. #15689870	C₂	semidirect
3. #15689847	C₂	semidirect
4. #15689842	C₂	semidirect
5. #15689801	C₂	semidirect
6. #15689800	C₂	semidirect
7. #15689788	C₂	semidirect
8. Q₈×C₂²⋊D₄₇	C₂	semidirect
9. #15689784	C₂	semidirect
10. #15689780	C₂	semidirect
11. #15689766	C₂	semidirect
12. #15689761	C₂	semidirect
13. #15689748	C₂	semidirect
14. #15689744	C₂	semidirect
15. #15689743	C₂	semidirect
16. #15689742	C₂	semidirect
17. #15689741	C₂	semidirect
18. #15689709	C₂	semidirect
19. #15689698	C₂	semidirect
20. #15689678	C₂	semidirect
21. #15689651	C₂	semidirect
22. #124×D₄₇	C₂	semidirect
23. C₄₇×#536	C₂	semidirect
26. C₂×Q₈×D₄₇	C₂²	semidirect
28. #13094024	C₂²	semidirect
29. #13094023	C₂²	semidirect
30. #13094022	C₂²	semidirect
31. #13094022	C₂²	semidirect
32. #13094019	C₂²	semidirect
33. #13094019	C₂²	semidirect
34. #13094019	C₂²	semidirect
35. #13094019	C₂²	semidirect
36. #13094017	C₂²	semidirect
37. #13094017	C₂²	semidirect
38. #13094017	C₂²	semidirect
39. #13094017	C₂²	semidirect
40. #13094015	C₂²	semidirect
41. #13094014	C₂²	semidirect
44. #13094013	C₂²	semidirect
47. #13094011	C₂²	semidirect
50. #13094010	C₂²	semidirect
51. #13094010	C₂²	semidirect
52. #13094010	C₂²	semidirect
54. #13094009	C₂²	semidirect
55. #13094009	C₂²	semidirect
56. #13094008	C₂²	semidirect
60. #13094006	C₂²	semidirect
62. #13094004	C₂²	semidirect
63. #13094003	C₂²	semidirect
64. #13094003	C₂²	semidirect
65. #13094003	C₂²	semidirect
68. #13094002	C₂²	semidirect
69. #13094002	C₂²	semidirect
70. #13094002	C₂²	semidirect
71. #13094002	C₂²	semidirect
72. #13094001	C₂²	semidirect
73. #13094001	C₂²	semidirect
77. #13094000	C₂²	semidirect
78. #13094000	C₂²	semidirect
80. #13093998	C₂²	semidirect
85. #13093995	C₂²	semidirect
88. Q₈×Dic₄₇	C₂²	semidirect
89. Q₈×Dic₄₇	C₂²	semidirect
90. Q₈×Dic₄₇	C₂²	semidirect
91. C₄×Dic₉₄	C₂²	semidirect
92. C₄×Dic₉₄	C₂²	semidirect
93. #13093989	C₂²	semidirect
100. C₄×C₂²⋊D₄₇	C₂²	semidirect
101. C₄×C₂²⋊D₄₇	C₂²	semidirect
102. C₄×C₂²⋊D₄₇	C₂²	semidirect
104. #13093982	C₂²	semidirect
105. #13093981	C₂²	semidirect
106. #13093980	C₂²	semidirect
113. C₂²×Q₈×C₄₇	C₂²	semidirect
114. C₄⋊Q₈×C₄₇	C₂²	semidirect
115. C₄⋊Q₈×C₄₇	C₂²	semidirect
118. #123×C₄₇	C₂²	semidirect
119. #123×C₄₇	C₂²	semidirect
120. C₂²⋊Q₈×C₄₇	C₂²	semidirect
121. C₂²⋊Q₈×C₄₇	C₂²	semidirect
122. #117×C₄₇	C₂²	semidirect
348. #536	D₄₇	semidirect
352. C₄₇	#3561	semidirect
357. C₂²×Q₈	C₂×D₄₇	semidirect
363. C₄⋊Q₈	C₂×D₄₇	semidirect
364. C₄⋊Q₈	C₂×D₄₇	semidirect
396. #123	C₂×D₄₇	semidirect
397. #123	C₂×D₄₇	semidirect
416. C₂²⋊Q₈	C₂×D₄₇	semidirect
417. C₂²⋊Q₈	C₂×D₄₇	semidirect
446. #117	C₂×D₄₇	semidirect