Subgroups — #548×D₄₇ #20256850

Order 6016.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689785	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689784	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689783	C₂	1	3	yes	maximal, complemented
6	#15689782	C₂	1	3	yes	maximal, complemented
7	#15689781	C₂	1	3	yes	maximal, complemented
8	#15689780	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689779	C₂	1	3	yes	maximal, complemented
10	#124×D₄₇	C₂	1	3	yes	maximal, complemented
11	C₂²⋊Q₈×D₄₇	C₂	1	3	yes	maximal, complemented
12	#121×D₄₇	C₂	1	3	yes	maximal, complemented
13	C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₄₇	C₂	1	3	yes	maximal, complemented
15	C₄₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
17	C₂×#10625350	C₂²	1	3	yes	complemented
18	C₂×#10625352	C₂²	1	3	yes	complemented
19	#41×D₄₇	—	2	8	no	—
20	C₂²×Dic₉₄	C₂²	1	3	yes	complemented
21	C₂×Q₈×D₄₇	—	2	8	no	—
22	C₂×Q₈×D₄₇	C₂²	1	3	yes	—
23	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₄₇	C₂²	1	3	yes	complemented
26	C₂×D₄×D₄₇	C₂²	1	3	yes	—
27	C₂×D₄×D₄₇	C₂²	1	3	yes	—
28	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
29	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
30	#13094013	C₂²	1	3	yes	complemented
31	#13094012	C₂²	1	3	yes	complemented
32	#13094011	C₂²	1	3	yes	complemented
33	#13094010	C₂²	1	6	yes	complemented
34	#13094010	C₂²	1	6	yes	complemented
35	#13094004	C₂²	1	3	yes	complemented
36	#13094003	C₂²	1	3	yes	complemented
37	#13094002	C₂²	1	6	yes	complemented
38	#13094001	C₂²	1	6	yes	complemented
39	#13094000	C₂²	1	3	yes	complemented
40	#13093999	C₂²	1	3	yes	complemented
41	#13093998	C₂²	1	3	yes	complemented
42	#13093997	C₂²	1	6	yes	complemented
43	#13093996	C₂²	1	6	yes	complemented
44	#13093995	C₂²	1	3	yes	complemented
45	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₉₄	C₂²	1	3	yes	complemented
47	#13093989	C₂²	1	3	yes	complemented
48	C₄×D₁₈₈	C₂²	1	3	yes	complemented
49	D₄×Dic₄₇	C₂²	1	3	yes	complemented
50	#13093986	C₂²	1	3	yes	complemented
51	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
52	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
53	(C₂²⋊D₄₇)⋊C₄	C₂²	1	3	yes	complemented
54	(C₂²⋊D₄₇)⋊C₄	C₂²	1	3	yes	complemented
55	C₄⋊C₄×D₄₇	C₂²	1	3	yes	—
56	C₄⋊C₄×D₄₇	C₂²	1	3	yes	—
57	C₂²⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
58	C₂²⋊C₄×D₄₇	C₂²	1	3	yes	—
59	C₂²⋊C₄×D₄₇	C₂²	1	6	yes	—
60	C₄²×D₄₇	C₂²	1	3	yes	—
61	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
62	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
63	#124×C₄₇	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₄₇	C₂²	1	3	yes	complemented
65	#121×C₄₇	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₄₇	C₂²	1	3	yes	complemented
68	C₂³×D₄₇	C₂³	1	3	yes	—
69	C₂³×D₄₇	C₂³	1	1	yes	characteristic
70	#41×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	C₂³	1	3	yes	—
73	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₄₇	C₂³	1	3	yes	—
75	C₂×D₄×C₄₇	C₂³	1	3	yes	—
76	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
77	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
78	C₂×C₂²⋊D₄₇	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₄₇	C₂³	1	3	yes	—
80	C₂×C₂²⋊D₄₇	C₂³	1	6	yes	—
81	C₂²×Dic₄₇	C₂³	1	3	yes	—
82	C₂²×Dic₄₇	C₂³	1	3	yes	—
83	#10625354	—	2	4	no	—
84	Q₈×D₄₇	—	2	4	no	—
85	Q₈×D₄₇	—	2	12	no	—
86	Q₈×D₄₇	—	2	12	no	—
87	Q₈×D₄₇	D₄	1	8	yes	complemented
88	#10625352	—	2	12	no	—
89	D₄×D₄₇	—	2	12	no	—
90	D₄×D₄₇	—	2	12	no	—
91	#10625350	—	2	12	no	—
92	C₂×D₁₈₈	C₂³	1	3	yes	—
93	C₂×D₁₈₈	C₂³	1	3	yes	—
94	C₂×C₄×D₄₇	—	2	12	no	—
95	C₂×C₄×D₄₇	—	2	12	no	—
96	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₂³	1	3	yes	—
98	C₂×C₄×D₄₇	C₂³	1	3	yes	—
99	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₂³	1	3	yes	—
101	C₂×C₄×D₄₇	C₂³	1	3	yes	—
102	C₂×C₄×D₄₇	C₂³	1	3	yes	—
103	C₂×C₄×D₄₇	C₂³	1	3	yes	—
104	C₂×C₄×D₄₇	C₂³	1	3	yes	—
105	C₂×Dic₉₄	—	2	12	no	—
106	C₂×Dic₉₄	C₂³	1	6	yes	—
107	C₂×Dic₉₄	C₂³	1	3	yes	—
108	C₂×Dic₉₄	C₂³	1	3	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
110	C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
111	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₄₇	C₂³	1	3	yes	—
113	C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
114	C₄²×C₄₇	C₂³	1	3	yes	—
115	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₄₇	C₂³	1	3	yes	—
117	C₂²⋊Dic₄₇	C₂³	1	6	yes	—
118	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
119	(C₂×D₄₇)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
121	(C₂×D₄₇)⋊C₄	C₂³	1	3	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	6	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	6	yes	—
124	C₄⋊Dic₄₇	C₂³	1	3	yes	—
125	C₄⋊Dic₄₇	C₂³	1	3	yes	—
126	Dic₄₇⋊C₄	C₂³	1	3	yes	—
127	Dic₄₇⋊C₄	C₂³	1	3	yes	—
128	Dic₄₇⋊C₄	C₂³	1	6	yes	—
129	C₄×Dic₄₇	C₂³	1	3	yes	—
130	C₄×Dic₄₇	C₂³	1	3	yes	—
131	C₄×Dic₄₇	C₂³	1	3	yes	—
132	C₂³×C₄₇	C₂⁴	1	3	yes	—
133	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	—	2	6	no	—
137	C₂²×D₄₇	—	2	6	no	—
138	C₂²×D₄₇	—	2	6	no	—
139	C₂²×D₄₇	#41	1	4	yes	complemented
140	C₂²×D₄₇	C₂⁴	1	3	yes	—
141	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
143	Q₈×C₄₇	—	2	6	no	—
144	Q₈×C₄₇	C₂×D₄	1	4	yes	complemented
145	D₄×C₄₇	—	2	6	no	—
146	D₄×C₄₇	—	2	6	no	—
147	C₂×C₄×C₄₇	—	2	6	no	—
148	C₂×C₄×C₄₇	—	2	6	no	—
149	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
151	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
153	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
154	C₂²⋊D₄₇	—	2	6	no	—
155	C₂²⋊D₄₇	—	2	6	no	—
156	C₂²⋊D₄₇	—	2	12	no	—
157	C₂×Dic₄₇	—	2	6	no	—
158	C₂×Dic₄₇	—	2	6	no	—
159	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₄₇	C₂⁴	1	3	yes	—
161	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₄₇	C₂⁴	1	3	yes	—
163	C₂×Dic₄₇	C₂⁴	1	3	yes	—
164	D₁₈₈	—	2	6	no	—
165	D₁₈₈	—	2	6	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	6	no	—
168	C₄×D₄₇	—	2	6	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	6	no	—
171	C₄×D₄₇	—	2	6	no	—
172	C₄×D₄₇	—	2	6	no	—
173	C₄×D₄₇	—	2	6	no	—
174	C₄×D₄₇	C₂×D₄	1	12	yes	—
175	Dic₉₄	—	2	6	no	—
176	Dic₉₄	—	2	12	no	—
177	Dic₉₄	C₂×D₄	1	12	yes	complemented
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	3	no	—
181	C₂²×C₄₇	—	2	3	no	—
182	C₂²×C₄₇	—	2	3	no	—
183	C₂²×C₄₇	C₂×#41	1	2	yes	complemented
184	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
185	C₂×D₄₇	—	2	1	no	—
186	C₂×D₄₇	—	2	1	no	—
187	C₂×D₄₇	—	2	8	no	—
188	C₂×D₄₇	—	2	3	no	—
189	C₂×D₄₇	—	2	3	no	—
190	C₂×D₄₇	—	2	3	no	—
191	C₂×D₄₇	—	4	12	no	—
192	C₂×D₄₇	C₂²×D₄	1	2	yes	—
193	C₂×D₄₇	C₂×#41	1	2	yes	—
194	C₂×D₄₇	C₂×#41	1	2	yes	complemented
195	C₂×D₄₇	2₋¹⁺⁴	1	2	yes	—
196	C₄×C₄₇	—	2	3	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	3	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	C₂²×D₄	1	6	yes	—
201	Dic₄₇	—	2	3	no	—
202	Dic₄₇	—	2	1	no	—
203	Dic₄₇	—	2	3	no	—
204	Dic₄₇	—	2	1	no	—
205	Dic₄₇	C₂²×D₄	1	6	yes	—
206	C₂×#548	—	47	1	no	maximal, Sylow
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	4	3	no	—
209	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
211	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
212	D₄₇	—	2	2	no	—
213	D₄₇	—	4	3	no	—
214	D₄₇	#548	1	4	yes	direct product factor
215	C₂²×#41	—	47	1	no	—
216	C₂³×Q₈	—	47	1	no	—
217	#548	—	47	1	no	—
218	#548	—	47	1	no	—
219	#548	—	47	3	no	—
220	#548	—	47	3	no	—
221	#548	—	47	3	no	—
222	#548	—	47	1	no	—
223	#548	—	47	3	no	—
224	#548	D₄₇	1	1	yes	characteristic, direct product factor
225	C₂×#124	—	47	3	no	—
226	C₂×C₂²⋊Q₈	—	47	3	no	—
227	C₂×#121	—	47	3	no	—
228	C₂×C₄×Q₈	—	47	1	no	—
229	C₂×C₄×D₄	—	47	3	no	—
230	C₄₇	C₂×#548	1	1	yes	characteristic, complemented, Sylow
231	C₂×#41	—	47	1	no	—
232	C₂×#41	—	47	3	no	—
233	C₂×#41	—	47	3	no	—
234	C₂×#41	—	94	8	no	—
235	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
236	C₂²×Q₈	—	47	1	no	—
237	C₂²×Q₈	—	47	3	no	—
238	C₂²×Q₈	—	47	3	no	—
239	C₂²×Q₈	—	47	1	no	—
240	C₂²×Q₈	—	47	3	no	—
241	C₂²×Q₈	—	94	8	no	—
242	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	47	3	no	—
244	C₂²×D₄	—	47	3	no	—
245	C₂³×C₄	—	47	3	no	—
246	C₂³×C₄	—	47	3	no	—
247	#124	—	47	3	no	—
248	#124	—	47	3	no	—
249	#124	—	47	6	no	—
250	#124	—	47	6	no	—
251	#124	—	47	3	no	—
252	#124	C₂×D₄₇	1	3	yes	complemented
253	C₂²⋊Q₈	—	47	3	no	—
254	C₂²⋊Q₈	—	47	3	no	—
255	C₂²⋊Q₈	—	47	6	no	—
256	C₂²⋊Q₈	—	47	3	no	—
257	C₂²⋊Q₈	—	47	6	no	—
258	C₂²⋊Q₈	C₂×D₄₇	1	3	yes	complemented
259	#121	—	47	3	no	—
260	#121	—	47	6	no	—
261	#121	—	47	3	no	—
262	#121	—	47	3	no	—
263	#121	—	47	6	no	—
264	#121	C₂×D₄₇	1	3	yes	complemented
265	C₄×Q₈	—	47	1	no	—
266	C₄×Q₈	—	47	3	no	—
267	C₄×Q₈	—	47	3	no	—
268	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
269	C₄×D₄	—	47	3	no	—
270	C₄×D₄	—	47	3	no	—
271	C₄×D₄	—	47	3	no	—
272	C₄×D₄	—	47	3	no	—
273	C₄×D₄	—	47	3	no	—
274	C₄×D₄	—	47	3	no	—
275	C₄×D₄	—	47	3	no	—
276	C₄×D₄	C₂×D₄₇	1	3	yes	complemented
277	C₂×C₄⋊C₄	—	47	3	no	—
278	C₂×C₄⋊C₄	—	47	3	no	—
279	C₂×C₂²⋊C₄	—	47	1	no	—
280	C₂×C₂²⋊C₄	—	47	3	no	—
281	C₂×C₂²⋊C₄	—	47	6	no	—
282	C₂×C₄²	—	47	3	no	—
283	C₂⁴	—	47	1	no	—
284	C₂⁴	—	47	3	no	—
285	#41	—	2	4	no	—
286	#41	—	94	12	no	—
287	#41	—	94	12	no	—
288	#41	—	94	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	47	8	no	—
291	C₂×Q₈	—	47	3	no	—
292	C₂×Q₈	—	47	6	no	—
293	C₂×Q₈	—	47	3	no	—
294	C₂×Q₈	—	94	12	no	—
295	C₂×Q₈	—	94	12	no	—
296	C₂×Q₈	—	94	12	no	—
297	C₂×Q₈	—	94	4	no	—
298	C₂×Q₈	C₂²×D₄₇	1	3	yes	—
299	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×D₄	—	47	3	no	—
301	C₂×D₄	—	47	3	no	—
302	C₂×D₄	—	47	6	no	—
303	C₂×D₄	—	47	3	no	—
304	C₂×D₄	—	47	3	no	—
305	C₂×D₄	—	94	12	no	—
306	C₂×D₄	—	94	12	no	—
307	C₂×D₄	C₂²×D₄₇	1	3	yes	—
308	C₂×D₄	C₂²×D₄₇	1	3	yes	—
309	C₂²×C₄	—	47	3	no	—
310	C₂²×C₄	—	47	3	no	—
311	C₂²×C₄	—	47	3	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	3	no	—
314	C₂²×C₄	—	47	3	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	3	no	—
317	C₂²×C₄	—	47	3	no	—
318	C₂²×C₄	—	47	3	no	—
319	C₂²×C₄	—	47	3	no	—
320	C₂²×C₄	—	94	12	no	—
321	C₂²×C₄	—	94	12	no	—
322	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
323	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
324	C₄⋊C₄	—	47	3	no	—
325	C₄⋊C₄	—	47	3	no	—
326	C₄⋊C₄	—	47	6	no	—
327	C₄⋊C₄	—	47	3	no	—
328	C₄⋊C₄	—	47	3	no	—
329	C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
330	C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
331	C₂²⋊C₄	—	47	1	no	—
332	C₂²⋊C₄	—	47	3	no	—
333	C₂²⋊C₄	—	47	6	no	—
334	C₂²⋊C₄	—	47	1	no	—
335	C₂²⋊C₄	—	47	1	no	—
336	C₂²⋊C₄	—	47	3	no	—
337	C₂²⋊C₄	—	47	3	no	—
338	C₂²⋊C₄	—	47	6	no	—
339	C₂²⋊C₄	—	47	6	no	—
340	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
341	C₂²⋊C₄	C₂²×D₄₇	1	3	yes	—
342	C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
343	C₄²	—	47	3	no	—
344	C₄²	—	47	3	no	—
345	C₄²	—	47	3	no	—
346	C₄²	C₂²×D₄₇	1	3	yes	—
347	C₂³	—	47	1	no	—
348	C₂³	—	47	4	no	—
349	C₂³	—	47	1	no	—
350	C₂³	—	47	3	no	—
351	C₂³	—	94	2	no	—
352	C₂³	—	94	2	no	—
353	C₂³	—	94	6	no	—
354	C₂³	—	94	6	no	—
355	C₂³	—	94	6	no	—
356	C₂³	C₂³×D₄₇	1	3	yes	—
357	C₂³	C₂³×D₄₇	1	1	yes	characteristic
358	Q₈	—	2	6	no	—
359	Q₈	—	47	12	no	—
360	Q₈	—	94	12	no	—
361	Q₈	—	94	6	no	—
362	Q₈	D₄×D₄₇	1	4	yes	complemented
363	D₄	—	2	6	no	—
364	D₄	—	2	6	no	—
365	D₄	—	94	6	no	—
366	D₄	—	94	12	no	—
367	D₄	—	94	6	no	—
368	D₄	—	94	6	no	—
369	D₄	—	94	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	47	3	no	—
373	C₂×C₄	—	47	12	no	—
374	C₂×C₄	—	47	1	no	—
375	C₂×C₄	—	47	3	no	—
376	C₂×C₄	—	47	3	no	—
377	C₂×C₄	—	47	1	no	—
378	C₂×C₄	—	94	6	no	—
379	C₂×C₄	—	94	6	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	6	no	—
383	C₂×C₄	—	94	6	no	—
384	C₂×C₄	—	94	6	no	—
385	C₂×C₄	—	94	6	no	—
386	C₂×C₄	—	94	6	no	—
387	C₂×C₄	—	94	6	no	—
388	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₄₇	1	3	yes	—
390	C₂×C₄	C₂³×D₄₇	1	3	yes	—
391	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₇	1	3	yes	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	47	2	no	—
399	C₂²	—	47	2	no	—
400	C₂²	—	47	2	no	—
401	C₂²	—	47	2	no	—
402	C₂²	—	94	8	no	—
403	C₂²	—	94	1	no	—
404	C₂²	—	94	1	no	—
405	C₂²	—	94	3	no	—
406	C₂²	—	94	3	no	—
407	C₂²	—	94	3	no	—
408	C₂²	—	188	12	no	—
409	C₂²	#41×D₄₇	1	2	yes	complemented
410	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	3	no	—
413	C₄	—	2	3	no	—
414	C₄	—	2	1	no	—
415	C₄	—	47	6	no	—
416	C₄	—	94	1	no	—
417	C₄	—	94	3	no	—
418	C₄	—	94	3	no	—
419	C₄	—	94	1	no	—
420	C₄	C₂×D₄×D₄₇	1	6	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	4	3	no	—
423	C₂	—	47	4	no	—
424	C₂	—	94	2	no	—
425	C₂	—	188	3	no	—
426	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic
427	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
428	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#548	C₂
hypercenter	#548	D₄₇
hypocenter	C₄₇	C₂×#548
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₄₇	C₂	semidirect
2. C₂²×Q₈×D₄₇	C₂	semidirect
3. #15689785	C₂	semidirect
4. #15689784	C₂	semidirect
5. #15689783	C₂	semidirect
6. #15689782	C₂	semidirect
7. #15689781	C₂	semidirect
8. #15689780	C₂	semidirect
9. #15689779	C₂	semidirect
10. #124×D₄₇	C₂	semidirect
11. C₂²⋊Q₈×D₄₇	C₂	semidirect
12. #121×D₄₇	C₂	semidirect
13. C₄×Q₈×D₄₇	C₂	semidirect
14. C₄×D₄×D₄₇	C₂	semidirect
15. C₄₇×#548	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
17. C₂×#10625350	C₂²	semidirect
18. C₂×#10625352	C₂²	semidirect
20. C₂²×Dic₉₄	C₂²	semidirect
24. C₂×Q₈×D₄₇	C₂²	semidirect
25. C₂×Q₈×D₄₇	C₂²	semidirect
30. #13094013	C₂²	semidirect
31. #13094012	C₂²	semidirect
32. #13094011	C₂²	semidirect
33. #13094010	C₂²	semidirect
34. #13094010	C₂²	semidirect
35. #13094004	C₂²	semidirect
36. #13094003	C₂²	semidirect
37. #13094002	C₂²	semidirect
38. #13094001	C₂²	semidirect
39. #13094000	C₂²	semidirect
40. #13093999	C₂²	semidirect
41. #13093998	C₂²	semidirect
42. #13093997	C₂²	semidirect
43. #13093996	C₂²	semidirect
44. #13093995	C₂²	semidirect
45. Q₈×Dic₄₇	C₂²	semidirect
46. C₄×Dic₉₄	C₂²	semidirect
47. #13093989	C₂²	semidirect
48. C₄×D₁₈₈	C₂²	semidirect
49. D₄×Dic₄₇	C₂²	semidirect
50. #13093986	C₂²	semidirect
51. C₄×C₂²⋊D₄₇	C₂²	semidirect
52. C₄×C₂²⋊D₄₇	C₂²	semidirect
53. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
54. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
61. C₂×#41×C₄₇	C₂²	semidirect
62. C₂²×Q₈×C₄₇	C₂²	semidirect
63. #124×C₄₇	C₂²	semidirect
64. C₂²⋊Q₈×C₄₇	C₂²	semidirect
65. #121×C₄₇	C₂²	semidirect
66. C₄×Q₈×C₄₇	C₂²	semidirect
67. C₄×D₄×C₄₇	C₂²	semidirect
87. Q₈×D₄₇	D₄	semidirect
139. C₂²×D₄₇	#41	semidirect
144. Q₈×C₄₇	C₂×D₄	semidirect
177. Dic₉₄	C₂×D₄	semidirect
183. C₂²×C₄₇	C₂×#41	semidirect
194. C₂×D₄₇	C₂×#41	semidirect
214. D₄₇	#548	direct (N × H)
224. #548	D₄₇	direct (N × H)
230. C₄₇	C₂×#548	semidirect
235. C₂×#41	C₂×D₄₇	semidirect
242. C₂²×Q₈	C₂×D₄₇	semidirect
252. #124	C₂×D₄₇	semidirect
258. C₂²⋊Q₈	C₂×D₄₇	semidirect
264. #121	C₂×D₄₇	semidirect
268. C₄×Q₈	C₂×D₄₇	semidirect
276. C₄×D₄	C₂×D₄₇	semidirect
362. Q₈	D₄×D₄₇	semidirect
409. C₂²	#41×D₄₇	semidirect

Subgroups — #548×D47 #20256850

Conjugacy classes of subgroups

Complements

Subgroups — #548×D₄₇ #20256850