Subgroups — #20257848

Order 6016.

1022 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689870	C₂	1	2	yes	maximal, complemented
2	#15689869	C₂	1	2	yes	maximal, complemented
3	#15689857	C₂	1	2	yes	maximal, complemented
4	#15689855	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689848	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689827	C₂	1	2	yes	maximal, complemented
7	#15689792	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	#15689781	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689776	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689772	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689744	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689743	C₂	1	2	yes	maximal, complemented
15	#15689742	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689725	C₂	1	2	yes	maximal, complemented
17	#15689722	C₂	1	2	yes	maximal, complemented
18	#15689716	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	#15689672	C₂	1	1	yes	maximal, characteristic, complemented
22	#15689651	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×#10625354	C₂²	1	1	yes	characteristic
26	C₂×#10625352	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
28	#13094024	C₂²	1	1	yes	characteristic
29	#13094022	C₂²	1	2	yes	—
30	#13094022	C₂²	1	1	yes	characteristic
31	#13094022	C₂²	1	1	yes	characteristic
32	#13094020	C₂²	1	1	yes	characteristic
33	#13094020	C₂²	1	2	yes	—
34	#13094019	C₂²	1	2	yes	—
35	#13094019	C₂²	1	1	yes	characteristic
36	#13094017	C₂²	1	2	yes	—
37	#13094017	C₂²	1	1	yes	characteristic
38	#13094015	C₂²	1	2	yes	—
39	#13094015	C₂²	1	2	yes	—
40	#13094014	C₂²	1	1	yes	characteristic
41	#13094014	C₂²	1	2	yes	—
42	#13094014	C₂²	1	2	yes	—
43	#13094013	C₂²	1	2	yes	—
44	#13094013	C₂²	1	1	yes	characteristic
45	#13094012	C₂²	1	1	yes	characteristic
46	#13094010	C₂²	1	2	yes	—
47	#13094010	C₂²	1	2	yes	—
48	#13094010	C₂²	1	2	yes	—
49	#13094010	C₂²	1	2	yes	—
50	#13094010	C₂²	1	1	yes	characteristic
51	#13094009	C₂²	1	2	yes	—
52	#13094009	C₂²	1	2	yes	—
53	#13094009	C₂²	1	2	yes	—
54	#13094009	C₂²	1	1	yes	characteristic
55	#13094009	C₂²	1	2	yes	—
56	#13094008	C₂²	1	2	yes	—
57	#13094008	C₂²	1	2	yes	—
58	#13094007	C₂²	1	2	yes	—
59	#13094006	C₂²	1	2	yes	—
60	#13094006	C₂²	1	2	yes	—
61	#13094006	C₂²	1	1	yes	characteristic
62	#13094005	C₂²	1	2	yes	—
63	#13094004	C₂²	1	2	yes	—
64	#13094003	C₂²	1	1	yes	characteristic
65	#13094003	C₂²	1	2	yes	—
66	#13094002	C₂²	1	1	yes	characteristic
67	#13094002	C₂²	1	2	yes	—
68	#13094002	C₂²	1	2	yes	—
69	#13094002	C₂²	1	2	yes	—
70	#13094001	C₂²	1	2	yes	—
71	#13094001	C₂²	1	2	yes	—
72	#13094000	C₂²	1	1	yes	characteristic
73	#13094000	C₂²	1	1	yes	characteristic
74	#13094000	C₂²	1	1	yes	characteristic
75	#13094000	C₂²	1	2	yes	—
76	#13094000	C₂²	1	2	yes	—
77	#13093999	C₂²	1	2	yes	—
78	#13093998	C₂²	1	1	yes	characteristic
79	#13093998	C₂²	1	2	yes	—
80	#13093998	C₂²	1	2	yes	—
81	#13093997	C₂²	1	2	yes	—
82	#13093997	C₂²	1	2	yes	—
83	#13093997	C₂²	1	2	yes	—
84	#13093997	C₂²	1	1	yes	characteristic
85	#13093996	C₂²	1	2	yes	—
86	#13093995	C₂²	1	1	yes	characteristic
87	#13093995	C₂²	1	2	yes	—
88	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
89	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
90	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
91	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
92	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
93	#13093989	C₂²	1	2	yes	—
94	#13093989	C₂²	1	2	yes	—
95	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
96	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
97	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
103	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
105	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
107	#13093982	C₂²	1	2	yes	—
108	#13093981	C₂²	1	1	yes	characteristic
109	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
110	C₄⋊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
114	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
115	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
116	#124×C₄₇	C₂²	1	1	yes	characteristic
117	#124×C₄₇	C₂²	1	1	yes	characteristic
118	#123×C₄₇	C₂²	1	2	yes	—
119	#123×C₄₇	C₂²	1	2	yes	—
120	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
121	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
122	#117×C₄₇	C₂²	1	1	yes	characteristic
123	#41×C₄₇	—	4	2	no	—
124	C₂×Q₈×C₄₇	—	4	2	no	—
125	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
129	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₄₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₄₇	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	2	yes	—
139	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
141	C₂²×Dic₄₇	C₂³	1	2	yes	—
142	C₂²×Dic₄₇	C₂³	1	2	yes	—
143	#10625354	—	4	2	no	—
144	#10625354	—	4	2	no	—
145	Q₈×D₄₇	—	4	2	no	—
146	#10625352	—	4	2	no	—
147	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
148	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
149	C₂×D₁₈₈	C₂³	1	2	yes	—
150	C₂×D₁₈₈	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	2	yes	—
156	C₂×C₄×D₄₇	C₂³	1	2	yes	—
157	C₂×C₄×D₄₇	C₂³	1	2	yes	—
158	C₂×C₄×D₄₇	C₂³	1	2	yes	—
159	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
160	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₉₄	C₂³	1	2	yes	—
162	C₂×Dic₉₄	C₂³	1	2	yes	—
163	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
175	C₄²×C₄₇	C₂³	1	1	yes	characteristic
176	C₄²×C₄₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
182	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₄₇	C₂³	1	2	yes	—
199	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₄₇	C₂³	1	2	yes	—
203	C₄⋊Dic₄₇	C₂³	1	2	yes	—
204	C₄⋊Dic₄₇	C₂³	1	2	yes	—
205	Dic₄₇⋊C₄	C₂³	1	2	yes	—
206	Dic₄₇⋊C₄	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
217	Dic₄₇⋊C₄	C₂³	1	2	yes	—
218	Dic₄₇⋊C₄	C₂³	1	2	yes	—
219	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₄×Dic₄₇	C₂³	1	2	yes	—
226	C₄×Dic₄₇	C₂³	1	2	yes	—
227	C₄×Dic₄₇	C₂³	1	2	yes	—
228	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₄₇	C₂⁴	1	2	yes	—
230	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₄₇	C₂⁴	1	2	yes	—
233	Q₈×C₄₇	—	2	2	no	—
234	Q₈×C₄₇	—	2	2	no	—
235	Q₈×C₄₇	—	2	2	no	—
236	Q₈×C₄₇	—	4	2	no	—
237	D₄×C₄₇	—	2	2	no	—
238	D₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	4	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₄₇	—	2	4	no	—
252	C₂²⋊D₄₇	—	2	2	no	—
253	C₂²⋊D₄₇	—	4	2	no	—
254	C₂²⋊D₄₇	—	4	2	no	—
255	C₂²⋊D₄₇	—	4	2	no	—
256	C₂²⋊D₄₇	—	4	2	no	—
257	C₂²⋊D₄₇	—	4	1	no	—
258	C₂×Dic₄₇	—	4	2	no	—
259	C₂×Dic₄₇	—	4	2	no	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₄₇	C₂⁴	1	2	yes	—
262	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₄₇	C₂⁴	1	2	yes	—
265	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₄₇	C₂⁴	1	2	yes	—
267	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
269	D₁₈₈	—	2	2	no	—
270	D₁₈₈	—	4	1	no	—
271	D₁₈₈	—	4	2	no	—
272	D₁₈₈	—	4	2	no	—
273	C₄×D₄₇	—	2	2	no	—
274	C₄×D₄₇	—	2	2	no	—
275	C₄×D₄₇	—	2	2	no	—
276	C₄×D₄₇	—	4	2	no	—
277	C₄×D₄₇	—	4	1	no	—
278	C₄×D₄₇	—	4	2	no	—
279	C₄×D₄₇	—	4	2	no	—
280	C₄×D₄₇	—	4	2	no	—
281	Dic₉₄	—	2	2	no	—
282	Dic₉₄	—	2	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	2	no	—
295	C₂×D₄₇	—	2	1	no	—
296	C₂×D₄₇	—	2	1	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	2	1	no	—
299	C₂×D₄₇	—	2	2	no	—
300	C₂×D₄₇	—	2	1	no	—
301	C₄×C₄₇	—	2	2	no	—
302	C₄×C₄₇	—	2	2	no	—
303	C₄×C₄₇	—	2	2	no	—
304	C₄×C₄₇	—	2	1	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	H(5,𝔽₂)	1	2	yes	—
310	Dic₄₇	—	2	2	no	—
311	Dic₄₇	—	2	1	no	—
312	Dic₄₇	—	2	1	no	—
313	Dic₄₇	—	2	1	no	—
314	Dic₄₇	—	2	2	no	—
315	Dic₄₇	—	2	2	no	—
316	Dic₄₇	—	2	1	no	—
317	Dic₄₇	—	2	1	no	—
318	Dic₄₇	2₋¹⁺⁴	1	2	yes	—
319	#3554	—	47	1	no	maximal, Sylow
320	C₂×C₄₇	—	4	2	no	—
321	C₂×C₄₇	—	4	1	no	—
322	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₂×C₄₇	#585	1	1	yes	characteristic
325	D₄₇	—	4	1	no	—
326	D₄₇	—	4	1	no	—
327	D₄₇	—	4	2	no	—
328	#562	—	47	2	no	—
329	#562	—	47	2	no	—
330	#559	—	47	1	no	—
331	#559	—	47	2	no	—
332	#557	—	47	1	no	—
333	#554	—	47	2	no	—
334	#550	—	47	1	no	—
335	D₄×Q₈	—	47	1	no	—
336	#548	—	47	1	no	—
337	#548	—	47	1	no	—
338	#547	—	47	1	no	—
339	#547	—	47	1	no	—
340	#542	—	47	1	no	—
341	#542	—	47	2	no	—
342	#542	—	47	1	no	—
343	#540	—	47	2	no	—
344	#539	—	47	2	no	—
345	#539	—	47	2	no	—
346	#536	—	47	1	no	—
347	#536	D₄₇	1	1	yes	characteristic, complemented
348	#533	—	47	1	no	—
349	#532	—	47	1	no	—
350	#529	—	47	1	no	—
351	C₄₇	#3554	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	47	1	no	—
353	C₂×#41	—	47	1	no	—
354	C₂×#41	—	47	1	no	—
355	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
356	C₂²×Q₈	—	47	1	no	—
357	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
358	C₄⋊Q₈	—	47	1	no	—
359	C₄⋊Q₈	—	47	1	no	—
360	C₄⋊Q₈	—	47	2	no	—
361	C₄⋊Q₈	—	47	1	no	—
362	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
363	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
364	#127	—	47	1	no	—
365	#127	—	47	2	no	—
366	#126	—	47	1	no	—
367	#126	—	47	2	no	—
368	#126	—	47	1	no	—
369	#126	—	47	2	no	—
370	#125	—	47	1	no	—
371	#125	—	47	2	no	—
372	#125	—	47	2	no	—
373	#125	—	47	2	no	—
374	#125	—	47	2	no	—
375	#124	—	47	1	no	—
376	#124	—	47	2	no	—
377	#124	—	47	1	no	—
378	#124	—	47	2	no	—
379	#124	—	47	2	no	—
380	#124	—	47	2	no	—
381	#124	—	47	2	no	—
382	#124	—	47	1	no	—
383	#124	C₂×D₄₇	1	1	yes	characteristic
384	#124	C₂×D₄₇	1	1	yes	characteristic
385	#123	—	47	2	no	—
386	#123	—	47	2	no	—
387	#123	—	47	1	no	—
388	#123	—	47	2	no	—
389	#123	—	47	2	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	—	47	2	no	—
397	#123	C₂×D₄₇	1	2	yes	—
398	#123	C₂×D₄₇	1	2	yes	—
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	1	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	C₂×D₄₇	1	2	yes	—
414	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
415	#121	—	47	2	no	—
416	#121	—	47	2	no	—
417	#121	—	47	1	no	—
418	#121	—	47	2	no	—
419	#121	—	47	2	no	—
420	#121	—	47	1	no	—
421	#121	—	47	2	no	—
422	#121	—	47	1	no	—
423	#121	—	47	2	no	—
424	#121	—	47	2	no	—
425	#121	—	47	2	no	—
426	C₄×Q₈	—	47	1	no	—
427	C₄×Q₈	—	47	1	no	—
428	C₄×Q₈	—	47	1	no	—
429	C₄×Q₈	—	47	2	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	2	no	—
441	C₄×D₄	—	47	2	no	—
442	C₄×D₄	—	47	2	no	—
443	C₄×D₄	—	47	1	no	—
444	C₄×D₄	—	47	1	no	—
445	#117	—	47	2	no	—
446	#117	—	47	1	no	—
447	#117	C₂×D₄₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	—	47	2	no	—
449	C₂×C₄⋊C₄	—	47	2	no	—
450	C₂×C₄²	—	47	1	no	—
451	#41	—	4	2	no	—
452	#41	—	188	2	no	—
453	#41	—	188	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	—	188	2	no	—
461	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
465	C₂×D₄	—	47	1	no	—
466	C₂×D₄	—	47	2	no	—
467	C₂×D₄	—	47	1	no	—
468	C₂×D₄	—	47	2	no	—
469	C₂×D₄	—	47	2	no	—
470	C₂×D₄	—	47	2	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	—	47	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	2	no	—
480	C₂²×C₄	—	47	1	no	—
481	C₂²×C₄	—	47	1	no	—
482	C₂²×C₄	—	47	1	no	—
483	C₂²×C₄	—	47	1	no	—
484	C₂²×C₄	—	47	2	no	—
485	C₂²×C₄	—	47	2	no	—
486	C₂²×C₄	—	47	2	no	—
487	C₂²×C₄	—	47	2	no	—
488	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
490	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
491	C₄⋊C₄	—	47	1	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	1	no	—
499	C₄⋊C₄	—	47	1	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	2	no	—
505	C₄⋊C₄	—	47	1	no	—
506	C₄⋊C₄	—	47	1	no	—
507	C₄⋊C₄	—	47	2	no	—
508	C₄⋊C₄	—	47	1	no	—
509	C₄⋊C₄	—	47	1	no	—
510	C₄⋊C₄	—	47	2	no	—
511	C₄⋊C₄	—	47	2	no	—
512	C₄⋊C₄	—	47	2	no	—
513	C₄⋊C₄	—	47	1	no	—
514	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
519	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
520	C₂²⋊C₄	—	47	1	no	—
521	C₂²⋊C₄	—	47	1	no	—
522	C₂²⋊C₄	—	47	2	no	—
523	C₂²⋊C₄	—	47	2	no	—
524	C₂²⋊C₄	—	47	2	no	—
525	C₂²⋊C₄	—	47	2	no	—
526	C₂²⋊C₄	—	47	2	no	—
527	C₂²⋊C₄	—	47	1	no	—
528	C₂²⋊C₄	—	47	1	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	2	no	—
536	C₂²⋊C₄	—	47	1	no	—
537	C₂²⋊C₄	—	47	1	no	—
538	C₂²⋊C₄	—	47	2	no	—
539	C₂²⋊C₄	—	47	2	no	—
540	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
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	2	yes	—
546	C₄²	—	47	1	no	—
547	C₄²	—	47	1	no	—
548	C₄²	—	47	1	no	—
549	C₄²	—	47	2	no	—
550	C₄²	—	47	1	no	—
551	C₄²	—	47	2	no	—
552	C₄²	—	47	2	no	—
553	C₄²	—	47	2	no	—
554	C₄²	C₂²×D₄₇	1	1	yes	characteristic
555	C₄²	C₂²×D₄₇	1	1	yes	characteristic
556	C₂³	—	47	1	no	—
557	C₂³	—	47	1	no	—
558	C₂³	—	47	2	no	—
559	C₂³	C₂³×D₄₇	1	1	yes	characteristic
560	C₂³	C₂³×D₄₇	1	2	yes	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	94	2	no	—
566	Q₈	—	94	2	no	—
567	Q₈	—	188	2	no	—
568	Q₈	—	188	2	no	—
569	D₄	—	2	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	94	2	no	—
572	D₄	—	94	4	no	—
573	D₄	—	94	2	no	—
574	D₄	—	188	1	no	—
575	D₄	—	188	2	no	—
576	D₄	—	188	2	no	—
577	D₄	—	188	1	no	—
578	D₄	—	188	2	no	—
579	D₄	—	188	2	no	—
580	D₄	—	188	2	no	—
581	D₄	—	188	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	47	1	no	—
586	C₂×C₄	—	47	1	no	—
587	C₂×C₄	—	47	2	no	—
588	C₂×C₄	—	47	1	no	—
589	C₂×C₄	—	47	1	no	—
590	C₂×C₄	—	47	2	no	—
591	C₂×C₄	—	47	1	no	—
592	C₂×C₄	—	47	2	no	—
593	C₂×C₄	—	47	1	no	—
594	C₂×C₄	—	94	2	no	—
595	C₂×C₄	—	94	2	no	—
596	C₂×C₄	—	94	2	no	—
597	C₂×C₄	—	188	2	no	—
598	C₂×C₄	—	188	1	no	—
599	C₂×C₄	—	188	2	no	—
600	C₂×C₄	—	188	2	no	—
601	C₂×C₄	—	188	2	no	—
602	C₂×C₄	—	188	2	no	—
603	C₂×C₄	—	188	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	1	yes	characteristic
607	C₂×C₄	C₂³×D₄₇	1	2	yes	—
608	C₂×C₄	C₂³×D₄₇	1	2	yes	—
609	C₂×C₄	C₂³×D₄₇	1	2	yes	—
610	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	94	1	no	—
620	C₂²	—	94	1	no	—
621	C₂²	—	94	2	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	1	no	—
628	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	2	no	—
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	1	no	—
637	C₄	—	47	2	no	—
638	C₄	—	94	1	no	—
639	C₄	—	94	1	no	—
640	C₄	—	94	2	no	—
641	C₄	—	94	1	no	—
642	C₄	—	94	1	no	—
643	C₄	—	94	2	no	—
644	C₄	—	94	1	no	—
645	C₄	—	94	2	no	—
646	C₄	#13094069	1	2	yes	—
647	C₂	—	4	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	188	1	no	—
650	C₂	—	188	1	no	—
651	C₂	—	188	2	no	—
652	C₂	C₂×#13094069	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
654	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	#3554
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. #15689870	C₂	semidirect
2. #15689869	C₂	semidirect
3. #15689857	C₂	semidirect
4. #15689855	C₂	semidirect
5. #15689848	C₂	semidirect
6. #15689827	C₂	semidirect
7. #15689792	C₂	semidirect
8. Q₈×C₂²⋊D₄₇	C₂	semidirect
9. #15689784	C₂	semidirect
10. #15689781	C₂	semidirect
11. #15689776	C₂	semidirect
12. #15689772	C₂	semidirect
13. #15689744	C₂	semidirect
14. #15689743	C₂	semidirect
15. #15689742	C₂	semidirect
16. #15689725	C₂	semidirect
17. #15689722	C₂	semidirect
18. #15689716	C₂	semidirect
19. #15689698	C₂	semidirect
20. #15689678	C₂	semidirect
21. #15689672	C₂	semidirect
22. #15689651	C₂	semidirect
23. C₄₇×#536	C₂	semidirect
347. #536	D₄₇	semidirect
351. C₄₇	#3554	semidirect