Subgroups — D₄₇×#1772 #26214282

Order 12032.

1102 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#427×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#405×D₄₇	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
5	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243269	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243268	C₂	1	2	yes	maximal, complemented
8	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243266	C₂	1	2	yes	maximal, complemented
10	#339×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	#117×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	C₂×#13093960	C₂²	1	1	yes	characteristic
18	C₂×#13093959	C₂²	1	2	yes	—
19	#108×D₄₇	C₄	1	8	yes	complemented
20	#15689161	C₂²	1	1	yes	characteristic
21	#15689160	C₄	1	2	yes	complemented
22	#15689159	C₂²	1	2	yes	—
23	#15689158	C₄	1	2	yes	complemented
24	#107×D₄₇	C₄	1	2	yes	complemented
25	#106×D₄₇	C₄	1	2	yes	complemented
26	#15689081	C₂²	1	2	yes	—
27	#15689080	—	2	2	no	—
28	#15689079	C₂²	1	2	yes	—
29	#15689078	C₂²	1	2	yes	—
30	#15689077	—	2	2	no	—
31	#97×D₄₇	—	2	2	no	—
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₄₇	—	2	2	no	—
36	C₄×C₈×D₄₇	C₄	1	8	yes	complemented
37	#15688884	C₂²	1	2	yes	—
38	#15688883	C₂²	1	2	yes	—
39	#15688882	C₂²	1	2	yes	—
40	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#427	C₂²	1	1	yes	characteristic
42	C₄₇×#405	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#339	C₂²	1	2	yes	—
45	C₂²×C₄×D₄₇	—	2	1	no	—
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂×#10625324	—	2	2	no	—
49	M₁₆×D₄₇	—	2	4	no	—
50	M₁₆×D₄₇	C₂×C₄	1	8	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
62	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
63	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
64	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
65	C₂×C₈×D₄₇	Q₈	1	4	yes	—
66	#13093983	C₂³	1	2	yes	—
67	#13093982	C₂×C₄	1	4	yes	—
68	#13093981	—	2	2	no	—
69	#13093980	—	2	2	no	—
70	C₄⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
71	C₂²⋊C₄×D₄₇	—	2	2	no	—
72	C₂×C₄×Dic₄₇	—	2	1	no	—
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₄²×D₄₇	—	2	2	no	—
75	C₄²×D₄₇	—	2	2	no	—
76	C₄²×D₄₇	C₂×C₄	1	4	yes	—
77	#13093960	C₂×C₄	1	4	yes	complemented
78	#13093959	C₂×C₄	1	8	yes	complemented
79	#13093958	C₂×C₄	1	2	yes	complemented
80	#13093957	C₂×C₄	1	4	yes	complemented
81	#13093956	C₂×C₄	1	2	yes	complemented
82	#13093955	C₂×C₄	1	4	yes	complemented
83	#13093935	—	2	2	no	—
84	#13093934	—	2	2	no	—
85	#13093934	—	2	2	no	—
86	C₄×C₄₇⋊C₈	—	2	2	no	—
87	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
88	C₈×Dic₄₇	—	2	2	no	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
91	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
92	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	#117×C₄₇	C₂³	1	2	yes	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	#108×C₄₇	C₂×C₄	1	4	yes	complemented
98	#107×C₄₇	C₂×C₄	1	2	yes	complemented
99	#106×C₄₇	C₂×C₄	1	2	yes	complemented
100	#97×C₄₇	—	2	2	no	—
101	C₄×C₈×C₄₇	—	2	2	no	—
102	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
103	C₂³×D₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	#41	1	1	yes	characteristic
108	C₂×C₄×D₄₇	—	2	8	no	—
109	C₂×C₄×D₄₇	—	2	4	no	—
110	C₂×C₄×D₄₇	—	2	4	no	—
111	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
118	C₂×C₄×D₄₇	#41	1	2	yes	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²⋊C₄×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²⋊Dic₄₇	—	2	2	no	—
136	(C₂×D₄₇)⋊C₄	—	2	4	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
138	Dic₄₇⋊C₄	—	2	4	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	4	no	—
142	C₄×Dic₄₇	—	2	4	no	—
143	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
144	#10625329	—	2	2	no	—
145	#10625329	C₂²×C₄	1	4	yes	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
155	#10625324	—	2	8	no	—
156	C₈×D₄₇	—	2	8	no	—
157	C₈×D₄₇	C₄²	1	4	yes	—
158	C₈×D₄₇	C₄²	1	4	yes	—
159	C₈×D₄₇	C₄²	1	4	yes	—
160	C₈×D₄₇	C₄²	1	4	yes	—
161	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
162	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
163	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
164	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
165	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	4	no	—
167	C₂²×D₄₇	#117	1	2	yes	—
168	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×Dic₄₇	—	2	4	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	4	no	—
183	C₂×Dic₄₇	#117	1	2	yes	—
184	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
187	C₄×D₄₇	—	2	16	no	—
188	C₄×D₄₇	—	4	8	no	—
189	C₄×D₄₇	C₂×C₄²	1	2	yes	—
190	C₄×D₄₇	C₂×C₄²	1	2	yes	—
191	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
192	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
193	C₄×D₄₇	C₄×D₄	1	2	yes	—
194	C₄×D₄₇	C₄×D₄	1	2	yes	—
195	C₄×D₄₇	C₄×Q₈	1	2	yes	—
196	C₄×D₄₇	C₄×Q₈	1	2	yes	—
197	C₈×C₄₇	—	2	4	no	—
198	C₈×C₄₇	C₂×C₄²	1	2	yes	—
199	C₈×C₄₇	C₂×C₄²	1	2	yes	—
200	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
201	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
202	C₄₇⋊C₈	—	2	4	no	—
203	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
204	C₄₇⋊C₈	C₂×C₄²	1	2	yes	—
205	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
206	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×#1772	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	4	no	—
214	C₂×D₄₇	—	2	4	no	—
215	C₂×D₄₇	C₄×C₄⋊C₄	1	2	yes	—
216	C₂×D₄₇	C₄×C₄⋊C₄	1	2	yes	—
217	C₂×D₄₇	#443	1	4	yes	—
218	C₄×C₄₇	—	2	4	no	—
219	C₄×C₄₇	—	4	4	no	—
220	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
221	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
223	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
224	Dic₄₇	—	2	4	no	—
225	Dic₄₇	—	4	4	no	—
226	Dic₄₇	C₄×C₄⋊C₄	1	2	yes	—
227	Dic₄₇	C₄×C₄⋊C₄	1	2	yes	—
228	C₂²×#108	—	47	1	no	—
229	C₂×#427	—	47	1	no	—
230	C₂×#405	—	47	2	no	—
231	C₂²×C₄×C₈	—	47	1	no	—
232	#1772	—	47	1	no	—
233	#1772	—	47	1	no	—
234	#1772	—	47	2	no	—
235	#1772	—	47	1	no	—
236	#1772	—	47	2	no	—
237	#1772	D₄₇	1	1	yes	characteristic, direct product factor
238	C₂×#339	—	47	2	no	—
239	C₂×C₄₇	—	2	1	no	—
240	C₂×C₄₇	—	2	1	no	—
241	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#443	1	2	yes	—
243	D₄₇	—	2	2	no	—
244	D₄₇	#1772	1	4	yes	direct product factor
245	C₂²×M₁₆	—	47	2	no	—
246	C₂³×C₈	—	47	1	no	—
247	C₂³×C₈	—	47	1	no	—
248	C₂×#117	—	47	2	no	—
249	C₂²×C₄²	—	47	1	no	—
250	C₂×#108	—	47	2	no	—
251	C₂×#108	—	47	1	no	—
252	C₂×#108	—	47	8	no	—
253	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
254	#427	—	47	1	no	—
255	#427	—	47	2	no	—
256	#427	—	47	2	no	—
257	#427	—	47	2	no	—
258	#427	C₂×D₄₇	1	1	yes	characteristic
259	C₂×#107	—	47	2	no	—
260	C₂×#106	—	47	2	no	—
261	#405	—	47	2	no	—
262	#405	—	47	2	no	—
263	#405	—	47	2	no	—
264	#405	—	94	2	no	—
265	#405	—	94	2	no	—
266	#405	C₂×D₄₇	1	2	yes	—
267	C₂×#97	—	94	2	no	—
268	C₂×C₄×C₈	—	47	1	no	—
269	C₂×C₄×C₈	—	47	1	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	—	47	8	no	—
272	C₂×C₄×C₈	—	94	2	no	—
273	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
274	#339	—	47	2	no	—
275	#339	—	47	2	no	—
276	#339	—	47	2	no	—
277	#339	C₂×D₄₇	1	2	yes	—
278	C₄₇	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
279	C₂³×C₄	—	47	1	no	—
280	C₂³×C₄	—	94	1	no	—
281	C₂×M₁₆	—	47	2	no	—
282	C₂×M₁₆	—	47	8	no	—
283	C₂×M₁₆	—	94	2	no	—
284	C₂×M₁₆	—	94	4	no	—
285	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	47	4	no	—
289	C₂²×C₈	—	47	4	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	4	no	—
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	4	no	—
300	C₂²×C₈	—	94	2	no	—
301	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
302	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	#117	—	47	2	no	—
304	#117	—	47	4	no	—
305	#117	—	94	2	no	—
306	#117	—	94	2	no	—
307	#117	C₂²×D₄₇	1	2	yes	—
308	C₂×C₄⋊C₄	—	47	4	no	—
309	C₂×C₂²⋊C₄	—	94	2	no	—
310	C₂×C₄²	—	47	1	no	—
311	C₂×C₄²	—	47	4	no	—
312	C₂×C₄²	—	94	2	no	—
313	C₂×C₄²	—	94	2	no	—
314	C₂×C₄²	—	94	1	no	—
315	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
316	#108	—	47	8	no	—
317	#108	—	47	4	no	—
318	#108	C₄×D₄₇	1	4	yes	complemented
319	#107	—	47	2	no	—
320	#107	—	47	4	no	—
321	#107	C₄×D₄₇	1	2	yes	complemented
322	#106	—	47	2	no	—
323	#106	—	47	4	no	—
324	#106	C₄×D₄₇	1	2	yes	complemented
325	#97	—	2	2	no	—
326	#97	—	94	2	no	—
327	#97	—	94	2	no	—
328	#97	—	94	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	47	4	no	—
331	C₄×C₈	—	47	4	no	—
332	C₄×C₈	—	47	4	no	—
333	C₄×C₈	—	94	2	no	—
334	C₄×C₈	—	94	2	no	—
335	C₄×C₈	—	94	2	no	—
336	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
337	C₂⁴	—	47	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	1	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	94	4	no	—
349	C₂²×C₄	—	94	8	no	—
350	C₂²×C₄	—	94	4	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
353	M₁₆	—	2	2	no	—
354	M₁₆	—	47	4	no	—
355	M₁₆	—	94	8	no	—
356	M₁₆	—	94	2	no	—
357	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	1	no	—
362	C₂×C₈	—	47	1	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	47	1	no	—
365	C₂×C₈	—	47	1	no	—
366	C₂×C₈	—	47	2	no	—
367	C₂×C₈	—	47	4	no	—
368	C₂×C₈	—	47	4	no	—
369	C₂×C₈	—	47	4	no	—
370	C₂×C₈	—	47	4	no	—
371	C₂×C₈	—	47	4	no	—
372	C₂×C₈	—	47	4	no	—
373	C₂×C₈	—	47	4	no	—
374	C₂×C₈	—	47	4	no	—
375	C₂×C₈	—	94	8	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
378	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
381	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
382	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
383	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
384	C₂×C₈	Q₈×D₄₇	1	2	yes	—
385	C₄⋊C₄	—	47	4	no	—
386	C₄⋊C₄	—	94	4	no	—
387	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	94	4	no	—
390	C₂²⋊C₄	—	94	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	47	2	no	—
394	C₄²	—	94	4	no	—
395	C₄²	—	94	4	no	—
396	C₄²	—	94	2	no	—
397	C₄²	—	94	1	no	—
398	C₄²	C₂×C₄×D₄₇	1	2	yes	—
399	C₂³	—	47	1	no	—
400	C₂³	—	47	2	no	—
401	C₂³	—	47	1	no	—
402	C₂³	—	47	2	no	—
403	C₂³	—	94	4	no	—
404	C₂³	#41×D₄₇	1	1	yes	characteristic
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	47	2	no	—
409	C₂×C₄	—	47	1	no	—
410	C₂×C₄	—	47	1	no	—
411	C₂×C₄	—	47	2	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	2	no	—
415	C₂×C₄	—	47	2	no	—
416	C₂×C₄	—	47	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	94	16	no	—
421	C₂×C₄	—	94	4	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	4	no	—
424	C₂×C₄	—	188	8	no	—
425	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
430	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	47	2	no	—
433	C₈	—	47	2	no	—
434	C₈	—	47	2	no	—
435	C₈	—	47	2	no	—
436	C₈	—	94	4	no	—
437	C₈	C₄²×D₄₇	1	2	yes	—
438	C₈	C₄²×D₄₇	1	2	yes	—
439	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
440	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
441	C₂²	—	2	2	no	—
442	C₂²	—	47	4	no	—
443	C₂²	—	47	2	no	—
444	C₂²	—	47	2	no	—
445	C₂²	—	94	4	no	—
446	C₂²	—	94	4	no	—
447	C₂²	—	94	2	no	—
448	C₂²	#117×D₄₇	1	1	yes	characteristic
449	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
450	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	4	4	no	—
453	C₄	—	47	2	no	—
454	C₄	—	47	2	no	—
455	C₄	—	94	4	no	—
456	C₄	—	188	4	no	—
457	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
458	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
459	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
460	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	47	4	no	—
464	C₂	—	94	2	no	—
465	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
466	C₂	#443×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1772	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1772	D₄₇
hypocenter	C₄₇	C₂×#1772
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #20243270	C₂	semidirect
6. #20243269	C₂	semidirect
7. #20243268	C₂	semidirect
8. #20243267	C₂	semidirect
9. #20243266	C₂	semidirect
11. C₄₇×#1772	C₂	semidirect
19. #108×D₄₇	C₄	semidirect
21. #15689160	C₄	semidirect
23. #15689158	C₄	semidirect
24. #107×D₄₇	C₄	semidirect
25. #106×D₄₇	C₄	semidirect
36. C₄×C₈×D₄₇	C₄	semidirect
77. #13093960	C₂×C₄	semidirect
78. #13093959	C₂×C₄	semidirect
79. #13093958	C₂×C₄	semidirect
80. #13093957	C₂×C₄	semidirect
81. #13093956	C₂×C₄	semidirect
82. #13093955	C₂×C₄	semidirect
87. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
90. C₈×Dic₄₇	C₂×C₄	semidirect
91. C₈×Dic₄₇	C₂×C₄	semidirect
97. #108×C₄₇	C₂×C₄	semidirect
98. #107×C₄₇	C₂×C₄	semidirect
99. #106×C₄₇	C₂×C₄	semidirect
102. C₄×C₈×C₄₇	C₂×C₄	semidirect
237. #1772	D₄₇	direct (N × H)
244. D₄₇	#1772	direct (N × H)
278. C₄₇	C₂×#1772	semidirect
318. #108	C₄×D₄₇	semidirect
321. #107	C₄×D₄₇	semidirect
324. #106	C₄×D₄₇	semidirect
336. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₄₇	2
#427×D₄₇	2
#405×D₄₇	2
C₂×C₄×C₈×D₄₇	2
#20243270	2
#20243269	2
#20243268	2
#20243267	2
#20243266	2
#339×D₄₇	2
C₄₇×#1772	2
C₂×#1772	47

Subgroups — D47×#1772 #26214282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1772 #26214282