Subgroups — D₄₇×#3483 #27123378

Order 12032.

8418 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257015	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257014	C₂	1	6	yes	maximal, complemented
3	#20257013	C₂	1	9	yes	maximal, complemented
4	#20257012	C₂	1	9	yes	maximal, complemented
5	#20257011	C₂	1	6	yes	maximal, complemented
6	Q₈²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#555×D₄₇	C₂	1	9	yes	maximal, complemented
8	#550×D₄₇	C₂	1	6	yes	maximal, complemented
9	#532×D₄₇	C₂	1	9	yes	maximal, complemented
10	C₄×#41×D₄₇	C₂	1	6	yes	maximal, complemented
11	C₄₇×#3483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₄₇	C₂²	1	6	yes	—
13	C₂×#41×D₄₇	C₂²	1	6	yes	—
14	Q₈×Dic₉₄	C₂²	1	6	yes	complemented
15	#15689853	C₂²	1	9	yes	complemented
16	#15689839	C₂²	1	9	yes	complemented
17	#15689838	C₂²	1	18	yes	complemented
18	#15689837	C₂²	1	36	yes	complemented
19	#15689836	C₂²	1	36	yes	complemented
20	#15689835	C₂²	1	36	yes	complemented
21	#15689795	C₂²	1	6	yes	complemented
22	#15689794	C₂²	1	18	yes	complemented
23	#15689793	C₂²	1	18	yes	complemented
24	#15689792	C₂²	1	12	yes	complemented
25	#15689791	C₂²	1	36	yes	complemented
26	#15689674	C₂²	1	9	yes	complemented
27	#15689673	C₂²	1	9	yes	complemented
28	#15689672	C₂²	1	18	yes	complemented
29	#15689671	C₂²	1	9	yes	complemented
30	#15689670	C₂²	1	36	yes	complemented
31	#15689669	C₂²	1	18	yes	complemented
32	#15689668	C₂²	1	36	yes	complemented
33	C₄⋊Q₈×D₄₇	C₂²	1	9	yes	—
34	#127×D₄₇	C₂²	1	9	yes	—
35	#124×D₄₇	C₂²	1	18	yes	—
36	#121×D₄₇	C₂²	1	36	yes	—
37	#41×Dic₄₇	C₂²	1	6	yes	complemented
38	C₄×#10625354	C₂²	1	6	yes	complemented
39	C₄×#10625354	C₂²	1	6	yes	complemented
40	C₄×#10625350	C₂²	1	18	yes	complemented
41	#15689591	C₂²	1	18	yes	complemented
42	C₄×#10625352	C₂²	1	18	yes	complemented
43	C₄×#10625352	C₂²	1	18	yes	complemented
44	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
45	C₄×Q₈×D₄₇	C₂²	1	6	yes	—
46	C₄×D₄×D₄₇	C₂²	1	18	yes	—
47	C₄×D₄×D₄₇	C₂²	1	18	yes	—
48	#117×D₄₇	C₂²	1	18	yes	—
49	C₂×C₄²×D₄₇	C₂²	1	9	yes	—
50	Q₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
51	C₄₇×#555	C₂²	1	9	yes	complemented
52	C₄₇×#550	C₂²	1	6	yes	complemented
53	C₄₇×#532	C₂²	1	9	yes	complemented
54	C₄×#41×C₄₇	C₂²	1	6	yes	complemented
55	C₂×#10625354	C₂³	1	6	yes	—
56	C₂×#10625354	C₂³	1	6	yes	—
57	C₂×#10625350	C₂³	1	18	yes	—
58	C₂×#10625350	C₂³	1	18	yes	—
59	C₂×#10625352	C₂³	1	18	yes	—
60	C₂×#10625352	C₂³	1	18	yes	—
61	#41×D₄₇	—	2	48	no	—
62	#41×D₄₇	—	4	24	no	—
63	C₂×Q₈×D₄₇	C₂³	1	6	yes	—
64	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
65	C₂×D₄×D₄₇	C₂³	1	18	yes	—
66	C₂×D₄×D₄₇	C₂³	1	18	yes	—
67	C₂²×C₄×D₄₇	C₂³	1	18	yes	—
68	C₂²×C₄×D₄₇	C₂³	1	9	yes	—
69	#13094024	C₂³	1	9	yes	—
70	#13094023	C₂³	1	36	yes	—
71	#13094022	C₂³	1	18	yes	—
72	#13094021	C₂³	1	9	yes	—
73	#13094020	C₂³	1	18	yes	—
74	#13094020	C₂³	1	36	yes	—
75	#13094013	C₂³	1	18	yes	—
76	#13094012	C₂³	1	18	yes	—
77	#13094011	C₂³	1	18	yes	—
78	#13094010	C₂³	1	72	yes	—
79	#13093999	C₂³	1	36	yes	—
80	#13093998	C₂³	1	36	yes	—
81	#13093997	C₂³	1	72	yes	—
82	#13093996	C₂³	1	72	yes	—
83	#13093995	C₂³	1	36	yes	—
84	Q₈×Dic₄₇	C₂³	1	6	yes	—
85	Q₈×Dic₄₇	C₂³	1	2	yes	—
86	C₄×Dic₉₄	C₂³	1	18	yes	—
87	C₄×Dic₉₄	C₂³	1	6	yes	—
88	#13093989	C₂³	1	18	yes	—
89	#13093989	C₂³	1	6	yes	—
90	C₄×D₁₈₈	C₂³	1	18	yes	—
91	C₄×D₁₈₈	C₂³	1	18	yes	—
92	D₄×Dic₄₇	C₂³	1	18	yes	—
93	D₄×Dic₄₇	C₂³	1	18	yes	—
94	#13093986	C₂³	1	18	yes	—
95	#13093986	C₂³	1	18	yes	—
96	C₄×C₂²⋊D₄₇	C₂³	1	36	yes	—
97	C₄×C₂²⋊D₄₇	C₂³	1	36	yes	—
98	(C₂²⋊D₄₇)⋊C₄	C₂³	1	36	yes	—
99	(C₂²⋊D₄₇)⋊C₄	C₂³	1	36	yes	—
100	#13093983	C₂³	1	18	yes	—
101	#13093982	C₂³	1	18	yes	—
102	#13093982	C₂³	1	18	yes	—
103	#13093981	C₂³	1	36	yes	—
104	#13093980	C₂³	1	36	yes	—
105	C₄⋊C₄×D₄₇	C₂³	1	6	yes	—
106	C₄⋊C₄×D₄₇	C₂³	1	18	yes	—
107	C₂²⋊C₄×D₄₇	C₂³	1	36	yes	—
108	C₂×C₄×Dic₄₇	C₂³	1	9	yes	—
109	C₂×C₄×Dic₄₇	C₂³	1	18	yes	—
110	C₄²×D₄₇	C₂³	1	6	yes	—
111	C₄²×D₄₇	C₂³	1	9	yes	—
112	C₄²×D₄₇	C₂³	1	9	yes	—
113	C₄²×D₄₇	C₂³	1	9	yes	—
114	C₄²×D₄₇	C₂³	1	18	yes	—
115	C₄²×D₄₇	C₂³	1	9	yes	—
116	C₂×#41×C₄₇	C₂³	1	6	yes	—
117	C₂×#41×C₄₇	C₂³	1	6	yes	—
118	C₄⋊Q₈×C₄₇	C₂³	1	9	yes	—
119	#127×C₄₇	C₂³	1	9	yes	—
120	#124×C₄₇	C₂³	1	18	yes	—
121	#121×C₄₇	C₂³	1	36	yes	—
122	C₄×Q₈×C₄₇	C₂³	1	6	yes	—
123	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
124	C₄×D₄×C₄₇	C₂³	1	18	yes	—
125	C₄×D₄×C₄₇	C₂³	1	18	yes	—
126	#117×C₄₇	C₂³	1	18	yes	—
127	C₂×C₄²×C₄₇	C₂³	1	9	yes	—
128	C₂³×D₄₇	C₂⁴	1	9	yes	—
129	#41×C₄₇	—	2	24	no	—
130	#41×C₄₇	—	4	12	no	—
131	C₂×Q₈×C₄₇	C₂⁴	1	6	yes	—
132	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
133	C₂×D₄×C₄₇	C₂⁴	1	18	yes	—
134	C₂×D₄×C₄₇	C₂⁴	1	18	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	18	yes	—
136	C₂²×C₄×C₄₇	C₂⁴	1	9	yes	—
137	C₂×C₂²⋊D₄₇	C₂⁴	1	36	yes	—
138	C₂×C₂²⋊D₄₇	C₂⁴	1	36	yes	—
139	C₂²×Dic₄₇	C₂⁴	1	18	yes	—
140	C₂²×Dic₄₇	C₂⁴	1	9	yes	—
141	#10625354	—	2	24	no	—
142	#10625354	—	4	12	no	—
143	Q₈×D₄₇	—	4	12	no	—
144	Q₈×D₄₇	#41	1	16	yes	complemented
145	#10625352	—	2	72	no	—
146	#10625352	—	4	36	no	—
147	D₄×D₄₇	—	2	72	no	—
148	D₄×D₄₇	—	4	36	no	—
149	#10625350	—	2	72	no	—
150	#10625350	—	4	36	no	—
151	C₂×D₁₈₈	C₂⁴	1	18	yes	—
152	C₂×D₁₈₈	C₂⁴	1	18	yes	—
153	C₂×C₄×D₄₇	—	2	72	no	—
154	C₂×C₄×D₄₇	—	2	36	no	—
155	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
156	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
157	C₂×C₄×D₄₇	C₂⁴	1	18	yes	—
158	C₂×C₄×D₄₇	C₂⁴	1	18	yes	—
159	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
160	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
161	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
162	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₉₄	C₂⁴	1	18	yes	—
164	C₂×Dic₉₄	C₂⁴	1	6	yes	—
165	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
166	C₄⋊C₄×C₄₇	C₂⁴	1	18	yes	—
167	C₂²⋊C₄×C₄₇	C₂⁴	1	36	yes	—
168	C₄²×C₄₇	C₂⁴	1	6	yes	—
169	C₄²×C₄₇	C₂⁴	1	9	yes	—
170	C₄²×C₄₇	C₂⁴	1	9	yes	—
171	C₂²⋊Dic₄₇	C₂⁴	1	36	yes	—
172	(C₂×D₄₇)⋊C₄	C₂⁴	1	36	yes	—
173	(C₂×D₄₇)⋊C₄	C₂⁴	1	36	yes	—
174	C₄⋊Dic₄₇	C₂⁴	1	6	yes	—
175	C₄⋊Dic₄₇	C₂⁴	1	18	yes	—
176	Dic₄₇⋊C₄	C₂⁴	1	12	yes	—
177	Dic₄₇⋊C₄	C₂⁴	1	36	yes	—
178	C₄×Dic₄₇	C₂⁴	1	6	yes	—
179	C₄×Dic₄₇	C₂⁴	1	6	yes	—
180	C₄×Dic₄₇	C₂⁴	1	6	yes	—
181	C₄×Dic₄₇	C₂⁴	1	9	yes	—
182	C₄×Dic₄₇	C₂⁴	1	18	yes	—
183	C₄×Dic₄₇	C₂⁴	1	9	yes	—
184	C₄×Dic₄₇	C₂⁴	1	18	yes	—
185	C₂³×C₄₇	C₂⁵	1	9	yes	—
186	C₂²×D₄₇	—	2	36	no	—
187	C₂²×D₄₇	—	2	18	no	—
188	C₂²×D₄₇	C₂⁵	1	9	yes	—
189	C₂²×D₄₇	C₂⁵	1	1	yes	characteristic
190	Q₈×C₄₇	—	4	6	no	—
191	Q₈×C₄₇	C₂×#41	1	8	yes	complemented
192	D₄×C₄₇	—	2	36	no	—
193	D₄×C₄₇	—	4	18	no	—
194	C₂×C₄×C₄₇	—	2	36	no	—
195	C₂×C₄×C₄₇	—	2	18	no	—
196	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
197	C₂×C₄×C₄₇	C₂⁵	1	9	yes	—
198	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
199	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
200	C₂²⋊D₄₇	—	2	72	no	—
201	C₂²⋊D₄₇	—	4	36	no	—
202	C₂×Dic₄₇	—	2	36	no	—
203	C₂×Dic₄₇	—	2	18	no	—
204	C₂×Dic₄₇	C₂⁵	1	6	yes	—
205	C₂×Dic₄₇	C₂⁵	1	9	yes	—
206	C₂×Dic₄₇	C₂⁵	1	6	yes	—
207	C₂×Dic₄₇	C₂⁵	1	1	yes	characteristic
208	D₁₈₈	—	2	36	no	—
209	D₁₈₈	—	4	18	no	—
210	C₄×D₄₇	—	2	12	no	—
211	C₄×D₄₇	—	2	18	no	—
212	C₄×D₄₇	—	2	36	no	—
213	C₄×D₄₇	—	2	18	no	—
214	C₄×D₄₇	—	2	36	no	—
215	C₄×D₄₇	—	2	18	no	—
216	C₄×D₄₇	C₂×#41	1	24	yes	—
217	C₄×D₄₇	H(5,𝔽₂)	1	4	yes	—
218	Dic₉₄	—	4	18	no	—
219	Dic₉₄	C₂×#41	1	24	yes	complemented
220	C₂×#3483	—	47	1	no	maximal, Sylow
221	C₂²×C₄₇	—	2	18	no	—
222	C₂²×C₄₇	—	2	9	no	—
223	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
224	C₂×D₄₇	—	2	18	no	—
225	C₂×D₄₇	—	2	9	no	—
226	C₂×D₄₇	—	4	36	no	—
227	C₂×D₄₇	C₂²×#41	1	4	yes	—
228	C₂×D₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
229	C₄×C₄₇	—	2	6	no	—
230	C₄×C₄₇	—	2	9	no	—
231	C₄×C₄₇	C₂²×#41	1	12	yes	—
232	C₄×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
233	Dic₄₇	—	2	6	no	—
234	Dic₄₇	—	2	9	no	—
235	Dic₄₇	C₂²×#41	1	12	yes	—
236	Dic₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
237	#3483	—	47	1	no	—
238	#3483	—	47	9	no	—
239	#3483	—	47	6	no	—
240	#3483	—	47	9	no	—
241	#3483	—	47	6	no	—
242	#3483	D₄₇	1	1	yes	characteristic, direct product factor
243	C₂×Q₈²	—	47	1	no	—
244	C₂×#555	—	47	9	no	—
245	C₂×#550	—	47	6	no	—
246	C₂×#532	—	47	9	no	—
247	C₂×C₄×#41	—	47	6	no	—
248	C₂×C₄₇	—	4	9	no	—
249	C₂×C₄₇	C₂³×#41	1	2	yes	—
250	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
251	D₄₇	—	4	9	no	—
252	D₄₇	#3483	1	4	yes	direct product factor
253	C₂²×#41	—	47	6	no	—
254	C₂²×#41	—	47	6	no	—
255	Q₈²	—	47	9	no	—
256	Q₈²	—	47	6	no	—
257	Q₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
258	#555	—	47	9	no	—
259	#555	—	47	36	no	—
260	#555	—	47	36	no	—
261	#555	—	47	18	no	—
262	#555	—	47	36	no	—
263	#555	C₂×D₄₇	1	9	yes	complemented
264	#550	—	47	12	no	—
265	#550	—	47	18	no	—
266	#550	—	47	36	no	—
267	#550	—	47	6	no	—
268	#550	—	47	18	no	—
269	#550	C₂×D₄₇	1	6	yes	complemented
270	#532	—	47	18	no	—
271	#532	—	47	9	no	—
272	#532	—	47	9	no	—
273	#532	—	47	18	no	—
274	#532	—	47	36	no	—
275	#532	—	47	36	no	—
276	#532	—	47	9	no	—
277	#532	C₂×D₄₇	1	9	yes	complemented
278	C₂×C₄⋊Q₈	—	47	9	no	—
279	C₂×#127	—	47	9	no	—
280	C₂×#124	—	47	18	no	—
281	C₂×#121	—	47	36	no	—
282	C₄×#41	—	47	6	no	—
283	C₄×#41	—	47	6	no	—
284	C₄×#41	—	47	6	no	—
285	C₄×#41	—	47	18	no	—
286	C₄×#41	—	47	18	no	—
287	C₄×#41	—	47	18	no	—
288	C₄×#41	—	47	18	no	—
289	C₄×#41	C₂×D₄₇	1	6	yes	complemented
290	C₂×C₄×Q₈	—	47	2	no	—
291	C₂×C₄×Q₈	—	47	6	no	—
292	C₂×C₄×D₄	—	47	18	no	—
293	C₂×C₄×D₄	—	47	18	no	—
294	C₂×#117	—	47	18	no	—
295	C₂²×C₄²	—	47	9	no	—
296	C₄₇	C₂×#3483	1	1	yes	characteristic, complemented, Sylow
297	C₂×#41	—	47	6	no	—
298	C₂×#41	—	47	6	no	—
299	C₂×#41	—	47	18	no	—
300	C₂×#41	—	47	18	no	—
301	C₂×#41	—	47	18	no	—
302	C₂×#41	—	47	18	no	—
303	C₂×#41	—	94	48	no	—
304	C₂×#41	—	188	24	no	—
305	C₂×#41	C₂²×D₄₇	1	6	yes	—
306	C₂×#41	C₂²×D₄₇	1	6	yes	—
307	C₂²×Q₈	—	47	2	no	—
308	C₂²×Q₈	—	47	6	no	—
309	C₂²×D₄	—	47	18	no	—
310	C₂²×D₄	—	47	18	no	—
311	C₂³×C₄	—	47	18	no	—
312	C₂³×C₄	—	47	9	no	—
313	C₄⋊Q₈	—	47	18	no	—
314	C₄⋊Q₈	—	47	36	no	—
315	C₄⋊Q₈	—	47	9	no	—
316	C₄⋊Q₈	C₂²×D₄₇	1	9	yes	—
317	#127	—	47	18	no	—
318	#127	—	47	36	no	—
319	#127	—	47	9	no	—
320	#127	C₂²×D₄₇	1	9	yes	—
321	#124	—	47	18	no	—
322	#124	—	47	18	no	—
323	#124	—	47	72	no	—
324	#124	—	47	18	no	—
325	#124	C₂²×D₄₇	1	18	yes	—
326	#121	—	47	36	no	—
327	#121	—	47	72	no	—
328	#121	—	47	36	no	—
329	#121	—	47	36	no	—
330	#121	—	47	72	no	—
331	#121	C₂²×D₄₇	1	36	yes	—
332	C₄×Q₈	—	47	2	no	—
333	C₄×Q₈	—	47	6	no	—
334	C₄×Q₈	—	47	6	no	—
335	C₄×Q₈	—	47	18	no	—
336	C₄×Q₈	—	47	6	no	—
337	C₄×Q₈	—	47	18	no	—
338	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
339	C₄×Q₈	C₂²×D₄₇	1	6	yes	—
340	C₄×D₄	—	47	18	no	—
341	C₄×D₄	—	47	18	no	—
342	C₄×D₄	—	47	36	no	—
343	C₄×D₄	—	47	36	no	—
344	C₄×D₄	—	47	18	no	—
345	C₄×D₄	—	47	18	no	—
346	C₄×D₄	—	47	36	no	—
347	C₄×D₄	—	47	36	no	—
348	C₄×D₄	—	47	18	no	—
349	C₄×D₄	—	47	18	no	—
350	C₄×D₄	C₂²×D₄₇	1	18	yes	—
351	C₄×D₄	C₂²×D₄₇	1	18	yes	—
352	#117	—	47	18	no	—
353	#117	—	47	18	no	—
354	#117	—	47	18	no	—
355	#117	—	47	36	no	—
356	#117	—	47	36	no	—
357	#117	C₂²×D₄₇	1	18	yes	—
358	C₂×C₄⋊C₄	—	47	6	no	—
359	C₂×C₄⋊C₄	—	47	18	no	—
360	C₂×C₂²⋊C₄	—	47	36	no	—
361	C₂×C₄²	—	47	18	no	—
362	C₂×C₄²	—	47	9	no	—
363	C₂×C₄²	—	47	9	no	—
364	C₂×C₄²	—	47	6	no	—
365	C₂×C₄²	—	47	9	no	—
366	C₂×C₄²	—	47	9	no	—
367	C₂×C₄²	—	47	9	no	—
368	C₂×C₄²	—	47	18	no	—
369	C₂×C₄²	C₂²×D₄₇	1	9	yes	—
370	C₂⁴	—	47	9	no	—
371	#41	—	2	24	no	—
372	#41	—	4	12	no	—
373	#41	—	94	72	no	—
374	#41	—	94	72	no	—
375	#41	—	94	24	no	—
376	#41	—	188	36	no	—
377	#41	—	188	36	no	—
378	#41	—	188	12	no	—
379	C₂×Q₈	—	47	16	no	—
380	C₂×Q₈	—	47	6	no	—
381	C₂×Q₈	—	47	18	no	—
382	C₂×Q₈	—	188	12	no	—
383	C₂×Q₈	C₂³×D₄₇	1	6	yes	—
384	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
385	C₂×D₄	—	47	36	no	—
386	C₂×D₄	—	47	36	no	—
387	C₂×D₄	—	47	18	no	—
388	C₂×D₄	—	47	18	no	—
389	C₂×D₄	—	94	72	no	—
390	C₂×D₄	—	188	36	no	—
391	C₂×D₄	C₂³×D₄₇	1	18	yes	—
392	C₂×D₄	C₂³×D₄₇	1	18	yes	—
393	C₂²×C₄	—	47	6	no	—
394	C₂²×C₄	—	47	1	no	—
395	C₂²×C₄	—	47	18	no	—
396	C₂²×C₄	—	47	9	no	—
397	C₂²×C₄	—	47	6	no	—
398	C₂²×C₄	—	47	9	no	—
399	C₂²×C₄	—	47	18	no	—
400	C₂²×C₄	—	47	18	no	—
401	C₂²×C₄	—	47	9	no	—
402	C₂²×C₄	—	47	9	no	—
403	C₂²×C₄	—	94	72	no	—
404	C₂²×C₄	—	94	36	no	—
405	C₂²×C₄	C₂³×D₄₇	1	18	yes	—
406	C₂²×C₄	C₂³×D₄₇	1	9	yes	—
407	C₄⋊C₄	—	47	12	no	—
408	C₄⋊C₄	—	47	36	no	—
409	C₄⋊C₄	—	47	6	no	—
410	C₄⋊C₄	—	47	18	no	—
411	C₄⋊C₄	C₂³×D₄₇	1	6	yes	—
412	C₄⋊C₄	C₂³×D₄₇	1	18	yes	—
413	C₂²⋊C₄	—	47	36	no	—
414	C₂²⋊C₄	—	47	36	no	—
415	C₂²⋊C₄	—	47	36	no	—
416	C₂²⋊C₄	C₂³×D₄₇	1	36	yes	—
417	C₄²	—	47	6	no	—
418	C₄²	—	47	6	no	—
419	C₄²	—	47	9	no	—
420	C₄²	—	47	18	no	—
421	C₄²	—	47	9	no	—
422	C₄²	—	47	18	no	—
423	C₄²	—	47	6	no	—
424	C₄²	C₂³×D₄₇	1	9	yes	—
425	C₄²	C₂³×D₄₇	1	9	yes	—
426	C₄²	C₂³×D₄₇	1	6	yes	—
427	C₂³	—	47	1	no	—
428	C₂³	—	47	9	no	—
429	C₂³	—	94	36	no	—
430	C₂³	—	94	18	no	—
431	C₂³	C₂⁴×D₄₇	1	9	yes	—
432	Q₈	—	4	6	no	—
433	Q₈	—	47	24	no	—
434	Q₈	—	188	18	no	—
435	Q₈	#41×D₄₇	1	8	yes	complemented
436	D₄	—	2	36	no	—
437	D₄	—	4	18	no	—
438	D₄	—	94	72	no	—
439	D₄	—	94	36	no	—
440	D₄	—	188	18	no	—
441	D₄	—	188	36	no	—
442	C₂×C₄	—	2	36	no	—
443	C₂×C₄	—	2	18	no	—
444	C₂×C₄	—	47	1	no	—
445	C₂×C₄	—	47	6	no	—
446	C₂×C₄	—	47	24	no	—
447	C₂×C₄	—	47	4	no	—
448	C₂×C₄	—	47	6	no	—
449	C₂×C₄	—	47	9	no	—
450	C₂×C₄	—	94	36	no	—
451	C₂×C₄	—	94	18	no	—
452	C₂×C₄	—	94	12	no	—
453	C₂×C₄	—	94	18	no	—
454	C₂×C₄	—	94	36	no	—
455	C₂×C₄	—	94	18	no	—
456	C₂×C₄	—	94	36	no	—
457	C₂×C₄	—	94	18	no	—
458	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
459	C₂×C₄	C₂⁴×D₄₇	1	9	yes	—
460	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
461	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
462	C₂²	—	2	18	no	—
463	C₂²	—	2	9	no	—
464	C₂²	—	47	4	no	—
465	C₂²	—	47	2	no	—
466	C₂²	—	94	18	no	—
467	C₂²	—	94	9	no	—
468	C₂²	—	188	36	no	—
469	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
470	C₄	—	2	6	no	—
471	C₄	—	2	9	no	—
472	C₄	—	47	12	no	—
473	C₄	—	47	2	no	—
474	C₄	—	94	6	no	—
475	C₄	—	94	9	no	—
476	C₄	C₂×#41×D₄₇	1	12	yes	—
477	C₄	H(5,𝔽₂)×D₄₇	1	2	yes	—
478	C₂	—	4	9	no	—
479	C₂	—	47	4	no	—
480	C₂	—	188	9	no	—
481	C₂	C₂²×#41×D₄₇	1	2	yes	—
482	C₂	C₂×H(5,𝔽₂)×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₄₇×#3483	C₂
hypercenter	#3483	D₄₇
hypocenter	C₄₇	C₂×#3483
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3483

Complements

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

N	H ≅ G/N	type
1. #20257015	C₂	semidirect
2. #20257014	C₂	semidirect
3. #20257013	C₂	semidirect
4. #20257012	C₂	semidirect
5. #20257011	C₂	semidirect
6. Q₈²×D₄₇	C₂	semidirect
7. #555×D₄₇	C₂	semidirect
8. #550×D₄₇	C₂	semidirect
9. #532×D₄₇	C₂	semidirect
10. C₄×#41×D₄₇	C₂	semidirect
11. C₄₇×#3483	C₂	semidirect
14. Q₈×Dic₉₄	C₂²	semidirect
15. #15689853	C₂²	semidirect
16. #15689839	C₂²	semidirect
17. #15689838	C₂²	semidirect
18. #15689837	C₂²	semidirect
19. #15689836	C₂²	semidirect
20. #15689835	C₂²	semidirect
21. #15689795	C₂²	semidirect
22. #15689794	C₂²	semidirect
23. #15689793	C₂²	semidirect
24. #15689792	C₂²	semidirect
25. #15689791	C₂²	semidirect
26. #15689674	C₂²	semidirect
27. #15689673	C₂²	semidirect
28. #15689672	C₂²	semidirect
29. #15689671	C₂²	semidirect
30. #15689670	C₂²	semidirect
31. #15689669	C₂²	semidirect
32. #15689668	C₂²	semidirect
37. #41×Dic₄₇	C₂²	semidirect
38. C₄×#10625354	C₂²	semidirect
39. C₄×#10625354	C₂²	semidirect
40. C₄×#10625350	C₂²	semidirect
41. #15689591	C₂²	semidirect
42. C₄×#10625352	C₂²	semidirect
43. C₄×#10625352	C₂²	semidirect
50. Q₈²×C₄₇	C₂²	semidirect
51. C₄₇×#555	C₂²	semidirect
52. C₄₇×#550	C₂²	semidirect
53. C₄₇×#532	C₂²	semidirect
54. C₄×#41×C₄₇	C₂²	semidirect
144. Q₈×D₄₇	#41	semidirect
191. Q₈×C₄₇	C₂×#41	semidirect
219. Dic₉₄	C₂×#41	semidirect
242. #3483	D₄₇	direct (N × H)
252. D₄₇	#3483	direct (N × H)
257. Q₈²	C₂×D₄₇	semidirect
263. #555	C₂×D₄₇	semidirect
269. #550	C₂×D₄₇	semidirect
277. #532	C₂×D₄₇	semidirect
289. C₄×#41	C₂×D₄₇	semidirect
296. C₄₇	C₂×#3483	semidirect
435. Q₈	#41×D₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20257015	2
#20257014	2
#20257013	2
#20257012	2
#20257011	2
Q₈²×D₄₇	2
#555×D₄₇	2
#550×D₄₇	2
#532×D₄₇	2
C₄×#41×D₄₇	2
C₄₇×#3483	2
C₂×#3483	47

Subgroups — D47×#3483 #27123378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3483 #27123378