Subgroups — D₄₇×#1776 #26214331

Order 12032.

1318 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#97×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊C₄×D₄₇	C₂	1	2	yes	maximal
5	#20243288	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243287	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243286	C₂	1	2	yes	maximal, complemented
8	#20243285	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243284	C₂	1	2	yes	maximal, complemented
10	#340×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	—	2	2	no	—
17	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093957	C₂²	1	2	yes	—
20	#107×D₄₇	C₄	1	8	yes	complemented
21	C₂×#13093956	C₂²	1	1	yes	characteristic
22	C₂×#13093955	C₂²	1	2	yes	—
23	#106×D₄₇	C₄	1	8	yes	complemented
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	#97×D₄₇	C₄	1	8	yes	complemented
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₄×Dic₄₇⋊C₄	—	2	2	no	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
32	#15688974	—	2	2	no	—
33	#95×D₄₇	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄×D₄₇	—	2	2	no	—
44	C₂²×C₄×D₄₇	D₄	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₈×D₄₇	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
53	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×Dic₄₇⋊C₄	—	2	2	no	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₄⋊C₄×D₄₇	—	2	4	no	—
59	C₄⋊C₄×D₄₇	—	2	4	no	—
60	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
61	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₄²×D₄₇	—	4	8	no	—
68	C₄²×D₄₇	C₂×C₄	1	4	yes	—
69	C₄²×D₄₇	Q₈	1	4	yes	—
70	#13093958	C₂×C₄	1	4	yes	complemented
71	#13093957	C₂×C₄	1	8	yes	complemented
72	#13093956	C₂×C₄	1	4	yes	complemented
73	#13093955	C₂×C₄	1	8	yes	complemented
74	#13093935	C₂×C₄	1	4	yes	complemented
75	#13093934	C₂×C₄	1	4	yes	complemented
76	#13093934	C₂×C₄	1	4	yes	complemented
77	C₄₇⋊#95	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	#107×C₄₇	C₂×C₄	1	4	yes	complemented
87	#106×C₄₇	C₂×C₄	1	4	yes	complemented
88	#97×C₄₇	C₂×C₄	1	4	yes	complemented
89	#95×C₄₇	—	2	2	no	—
90	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	—	2	4	no	—
100	C₂×C₄×D₄₇	—	2	4	no	—
101	C₂×C₄×D₄₇	—	2	8	no	—
102	C₂×C₄×D₄₇	—	2	8	no	—
103	C₂×C₄×D₄₇	—	4	4	no	—
104	C₂×C₄×D₄₇	—	4	4	no	—
105	C₂×C₄×D₄₇	—	4	4	no	—
106	C₂×C₄×D₄₇	—	4	4	no	—
107	C₂×C₄×D₄₇	C₄⋊C₄	1	8	yes	—
108	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
112	C₂×C₄×D₄₇	#41	1	2	yes	—
113	C₂×C₄×D₄₇	#41	1	2	yes	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₄²×C₄₇	—	4	4	no	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
131	Dic₄₇⋊C₄	—	2	8	no	—
132	Dic₄₇⋊C₄	—	2	8	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	—	4	4	no	—
135	C₄×Dic₄₇	—	4	4	no	—
136	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
137	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₈×D₄₇	—	2	8	no	—
146	C₈×D₄₇	C₄²	1	16	yes	complemented
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
149	C₂²×D₄₇	C₄×D₄	1	2	yes	—
150	C₂²×D₄₇	C₄×D₄	1	2	yes	—
151	C₂²×D₄₇	AGL(1,ℤ/8)	1	4	yes	—
152	C₂²×D₄₇	#137	1	4	yes	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	4	no	—
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
179	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
180	C₄×D₄₇	—	2	16	no	—
181	C₄×D₄₇	—	4	16	no	—
182	C₄×D₄₇	—	4	16	no	—
183	C₄×D₄₇	C₂×C₄²	1	4	yes	—
184	C₄×D₄₇	#117	1	4	yes	—
185	C₄×D₄₇	C₄×Q₈	1	4	yes	—
186	C₄×D₄₇	C₄×Q₈	1	4	yes	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	C₂×C₄²	1	4	yes	complemented
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	C₂×C₄²	1	4	yes	complemented
191	C₂×#1776	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
196	C₂²×C₄₇	C₂×#137	1	2	yes	—
197	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
198	C₂×D₄₇	#428	1	8	yes	—
199	C₂×D₄₇	#440	1	8	yes	—
200	C₂×D₄₇	#441	1	4	yes	—
201	C₂×D₄₇	#442	1	4	yes	—
202	C₄×C₄₇	—	2	4	no	—
203	C₄×C₄₇	—	4	4	no	—
204	C₄×C₄₇	—	4	4	no	—
205	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
207	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
209	Dic₄₇	—	2	4	no	—
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	—	4	4	no	—
212	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
213	C₂²×#107	—	47	1	no	—
214	C₂²×#106	—	47	1	no	—
215	C₂²×#97	—	47	1	no	—
216	C₂×C₄×C₄⋊C₄	—	47	2	no	—
217	#1776	—	47	1	no	—
218	#1776	—	47	1	no	—
219	#1776	—	47	1	no	—
220	#1776	—	47	2	no	—
221	#1776	—	47	2	no	—
222	#1776	D₄₇	1	1	yes	characteristic, direct product factor
223	C₂×#340	—	47	2	no	—
224	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#428	1	2	yes	—
226	C₂×C₄₇	C₂×#440	1	2	yes	—
227	C₂×C₄₇	C₂×#441	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
229	D₄₇	#1776	1	8	yes	direct product factor
230	C₂³×C₈	—	47	1	no	—
231	C₂³×C₈	—	47	1	no	—
232	C₂²×C₄⋊C₄	—	47	2	no	—
233	C₂²×C₄⋊C₄	—	47	2	no	—
234	C₂²×C₄²	—	47	1	no	—
235	C₂²×C₄²	—	94	2	no	—
236	C₂×#107	—	47	1	no	—
237	C₂×#107	—	47	2	no	—
238	C₂×#107	—	47	8	no	—
239	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#106	—	47	1	no	—
241	C₂×#106	—	47	2	no	—
242	C₂×#106	—	47	8	no	—
243	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
244	C₂×#97	—	47	1	no	—
245	C₂×#97	—	47	1	no	—
246	C₂×#97	—	47	1	no	—
247	C₂×#97	—	47	8	no	—
248	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	—	47	2	no	—
250	C₄×C₄⋊C₄	—	47	2	no	—
251	C₄×C₄⋊C₄	—	47	2	no	—
252	C₄×C₄⋊C₄	—	94	2	no	—
253	C₄×C₄⋊C₄	—	94	2	no	—
254	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
255	C₂×#95	—	94	2	no	—
256	#340	—	47	2	no	—
257	#340	—	47	2	no	—
258	#340	—	47	2	no	—
259	#340	C₂×D₄₇	1	2	yes	—
260	C₄₇	C₂×#1776	1	1	yes	characteristic, complemented, Sylow
261	C₂³×C₄	—	47	1	no	—
262	C₂³×C₄	—	47	2	no	—
263	C₂³×C₄	—	94	2	no	—
264	C₂³×C₄	—	94	2	no	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	47	4	no	—
267	C₂²×C₈	—	47	4	no	—
268	C₂²×C₈	—	47	4	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	4	no	—
271	C₂²×C₈	—	94	2	no	—
272	C₂²×C₈	—	94	2	no	—
273	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	—	47	2	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	47	8	no	—
278	C₂×C₄⋊C₄	—	47	8	no	—
279	C₂×C₄⋊C₄	—	94	4	no	—
280	C₂×C₄⋊C₄	—	94	4	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	4	no	—
289	C₂×C₄²	—	47	4	no	—
290	C₂×C₄²	—	94	2	no	—
291	C₂×C₄²	—	94	2	no	—
292	C₂×C₄²	—	94	2	no	—
293	C₂×C₄²	—	188	8	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	47	4	no	—
296	#107	—	47	8	no	—
297	#107	C₄×D₄₇	1	4	yes	complemented
298	#106	—	47	4	no	—
299	#106	—	47	8	no	—
300	#106	C₄×D₄₇	1	4	yes	complemented
301	#97	—	47	4	no	—
302	#97	—	47	4	no	—
303	#97	—	47	4	no	—
304	#97	C₄×D₄₇	1	4	yes	complemented
305	#95	—	2	2	no	—
306	#95	—	94	2	no	—
307	#95	—	94	2	no	—
308	#95	—	94	2	no	—
309	C₂⁴	—	47	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	47	2	no	—
315	C₂²×C₄	—	47	2	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	47	2	no	—
318	C₂²×C₄	—	47	2	no	—
319	C₂²×C₄	—	47	2	no	—
320	C₂²×C₄	—	47	8	no	—
321	C₂²×C₄	—	94	4	no	—
322	C₂²×C₄	—	94	4	no	—
323	C₂²×C₄	—	94	8	no	—
324	C₂²×C₄	—	94	8	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	188	4	no	—
328	C₂²×C₄	—	188	4	no	—
329	C₂²×C₄	—	188	4	no	—
330	C₂²×C₄	—	188	4	no	—
331	C₂²×C₄	D₄×D₄₇	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	47	16	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	94	8	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	94	1	no	—
343	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
344	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
346	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	47	4	no	—
350	C₄⋊C₄	—	47	4	no	—
351	C₄⋊C₄	—	94	8	no	—
352	C₄⋊C₄	—	94	8	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₄⋊C₄	—	94	2	no	—
355	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
356	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
357	C₄²	—	4	4	no	—
358	C₄²	—	47	8	no	—
359	C₄²	—	47	2	no	—
360	C₄²	—	47	2	no	—
361	C₄²	—	188	4	no	—
362	C₄²	—	188	4	no	—
363	C₄²	—	188	4	no	—
364	C₄²	C₂×C₄×D₄₇	1	2	yes	—
365	C₄²	Q₈×D₄₇	1	2	yes	—
366	C₂³	—	47	2	no	—
367	C₂³	—	47	2	no	—
368	C₂³	—	47	2	no	—
369	C₂³	—	47	4	no	—
370	C₂³	—	47	4	no	—
371	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	47	2	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	2	no	—
383	C₂×C₄	—	47	4	no	—
384	C₂×C₄	—	47	4	no	—
385	C₂×C₄	—	47	4	no	—
386	C₂×C₄	—	47	4	no	—
387	C₂×C₄	—	47	4	no	—
388	C₂×C₄	—	94	16	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	94	4	no	—
393	C₂×C₄	—	188	16	no	—
394	C₂×C₄	—	188	16	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
404	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
405	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	47	4	no	—
408	C₈	—	94	2	no	—
409	C₈	C₄²×D₄₇	1	4	yes	complemented
410	C₂²	—	47	8	no	—
411	C₂²	—	47	4	no	—
412	C₂²	—	47	4	no	—
413	C₂²	—	47	8	no	—
414	C₂²	—	47	4	no	—
415	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
416	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
417	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
418	C₂²	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
419	C₂²	#137×D₄₇	1	2	yes	—
420	C₄	—	2	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	4	no	—
423	C₄	—	47	4	no	—
424	C₄	—	94	4	no	—
425	C₄	—	188	4	no	—
426	C₄	—	188	4	no	—
427	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
428	C₄	#117×D₄₇	1	1	yes	characteristic
429	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
430	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
431	C₂	—	47	8	no	—
432	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
433	C₂	#428×D₄₇	1	2	yes	—
434	C₂	#440×D₄₇	1	2	yes	—
435	C₂	#441×D₄₇	1	1	yes	characteristic
436	C₂	#442×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1776	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1776	D₄₇
hypocenter	C₄₇	C₂×#1776
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1776

Complements

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

N	H ≅ G/N	type
5. #20243288	C₂	semidirect
6. #20243287	C₂	semidirect
7. #20243286	C₂	semidirect
8. #20243285	C₂	semidirect
9. #20243284	C₂	semidirect
11. C₄₇×#1776	C₂	semidirect
20. #107×D₄₇	C₄	semidirect
23. #106×D₄₇	C₄	semidirect
27. #97×D₄₇	C₄	semidirect
70. #13093958	C₂×C₄	semidirect
71. #13093957	C₂×C₄	semidirect
72. #13093956	C₂×C₄	semidirect
73. #13093955	C₂×C₄	semidirect
74. #13093935	C₂×C₄	semidirect
75. #13093934	C₂×C₄	semidirect
76. #13093934	C₂×C₄	semidirect
86. #107×C₄₇	C₂×C₄	semidirect
87. #106×C₄₇	C₂×C₄	semidirect
88. #97×C₄₇	C₂×C₄	semidirect
146. C₈×D₄₇	C₄²	semidirect
188. C₈×C₄₇	C₂×C₄²	semidirect
190. C₄₇⋊C₈	C₂×C₄²	semidirect
222. #1776	D₄₇	direct (N × H)
229. D₄₇	#1776	direct (N × H)
260. C₄₇	C₂×#1776	semidirect
297. #107	C₄×D₄₇	semidirect
300. #106	C₄×D₄₇	semidirect
304. #97	C₄×D₄₇	semidirect
409. C₈	C₄²×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#107×D₄₇	2
C₂×#106×D₄₇	2
C₂×#97×D₄₇	2
C₄×C₄⋊C₄×D₄₇	2
#20243288	2
#20243287	2
#20243286	2
#20243285	2
#20243284	2
#340×D₄₇	2
C₄₇×#1776	2
C₂×#1776	47

Subgroups — D47×#1776 #26214331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1776 #26214331