Subgroups — C₂×C₄₇×#2092 #26063422

Order 12032.

1366 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2092	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₇	—	2	4	no	—
18	C₂×#107×C₄₇	C₂²	1	4	yes	complemented
19	C₂×#106×C₄₇	—	2	4	no	—
20	C₂×#106×C₄₇	C₂²	1	4	yes	complemented
21	C₂×#102×C₄₇	—	2	4	no	—
22	C₂×#102×C₄₇	—	2	4	no	—
23	C₂×#102×C₄₇	C₂²	1	4	yes	—
24	C₂×#102×C₄₇	C₂²	1	4	yes	—
25	C₄₇×#390	—	2	2	no	—
26	C₄₇×#390	C₂²	1	4	yes	—
27	C₄₇×#382	—	2	2	no	—
28	C₄₇×#382	C₂²	1	4	yes	complemented
29	C₂×#95×C₄₇	—	2	2	no	—
30	C₄₇×#336	C₂²	1	4	yes	complemented
31	C₂⁵×C₄₇	—	2	1	no	—
32	C₂²×D₄×C₄₇	—	2	2	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	2	1	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
39	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	—	2	1	no	—
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	D₄	1	4	yes	—
50	C₂²×C₈×C₄₇	D₄	1	4	yes	—
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	D₄	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
71	#107×C₄₇	—	2	8	no	—
72	#106×C₄₇	—	2	8	no	—
73	#102×C₄₇	—	2	8	no	—
74	#102×C₄₇	—	2	8	no	—
75	#95×C₄₇	—	2	8	no	—
76	C₂⁴×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂⁴×C₄₇	—	4	2	no	—
79	C₂⁴×C₄₇	—	4	2	no	—
80	C₂⁴×C₄₇	—	4	4	no	—
81	C₂⁴×C₄₇	—	4	4	no	—
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	8	no	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	4	4	no	—
92	C₂×D₄×C₄₇	—	4	4	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	2	no	—
105	C₂²×C₄×C₄₇	—	4	4	no	—
106	C₂²×C₄×C₄₇	—	4	4	no	—
107	C₂²×C₄×C₄₇	—	4	4	no	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	#41	1	2	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₄₇	—	2	8	no	—
118	C₂×C₈×C₄₇	—	2	8	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	2	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄⋊C₄×C₄₇	—	4	2	no	—
134	C₂²⋊C₄×C₄₇	—	4	16	no	—
135	C₄²×C₄₇	—	2	4	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	4	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	—	4	16	no	—
145	C₂³×C₄₇	—	8	8	no	—
146	C₂³×C₄₇	—	8	4	no	—
147	C₂³×C₄₇	—	8	4	no	—
148	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂³×C₄₇	#123	1	2	yes	—
150	C₂³×C₄₇	#127	1	2	yes	—
151	C₂³×C₄₇	#135	1	4	yes	—
152	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	4	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	8	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	8	4	no	—
170	C₂×C₄×C₄₇	—	8	4	no	—
171	C₂×C₄×C₄₇	—	8	4	no	—
172	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
173	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
174	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₄₇	#123	1	4	yes	—
176	C₂×C₄×C₄₇	#123	1	4	yes	—
177	C₂×C₄×C₄₇	#123	1	2	yes	—
178	C₂×C₄×C₄₇	#127	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₈×C₄₇	—	2	4	no	—
186	C₈×C₄₇	—	2	4	no	—
187	C₂×#2092	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₇	—	4	8	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	8	4	no	—
191	C₂²×C₄₇	—	8	16	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	#399	1	4	yes	—
195	C₂²×C₄₇	#478	1	8	yes	—
196	C₂²×C₄₇	#482	1	8	yes	—
197	C₂²×C₄₇	#495	1	4	yes	—
198	C₂²×C₄₇	#496	1	4	yes	—
199	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×#135	1	2	yes	—
203	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
204	C₄×C₄₇	—	4	4	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	—	8	2	no	—
207	C₄×C₄₇	—	8	2	no	—
208	C₄×C₄₇	#399	1	4	yes	—
209	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
212	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
213	C₂²×#107	C₂×C₄₇	1	1	yes	characteristic, complemented
214	C₂²×#106	C₂×C₄₇	1	1	yes	characteristic, complemented
215	C₂²×#102	C₂×C₄₇	1	1	yes	characteristic
216	C₂²×#102	C₂×C₄₇	1	1	yes	characteristic
217	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
218	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
219	#2092	C₂×C₄₇	1	8	yes	direct product factor
220	C₂×#336	C₂×C₄₇	1	1	yes	characteristic, complemented
221	C₂×C₄₇	—	8	4	no	—
222	C₂×C₄₇	#2092	1	8	yes	direct product factor
223	C₂×C₄₇	C₂×#399	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#478	1	2	yes	—
225	C₂×C₄₇	C₂×#482	1	2	yes	—
226	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#496	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
230	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	—	2	2	no	—
235	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×#107	—	2	4	no	—
237	C₂×#107	C₂²×C₄₇	1	4	yes	complemented
238	C₂×#106	—	2	4	no	—
239	C₂×#106	C₂²×C₄₇	1	4	yes	complemented
240	C₂×#102	—	2	4	no	—
241	C₂×#102	—	2	4	no	—
242	C₂×#102	C₂²×C₄₇	1	4	yes	—
243	C₂×#102	C₂²×C₄₇	1	4	yes	—
244	#390	—	2	2	no	—
245	#390	C₂²×C₄₇	1	4	yes	—
246	#382	—	2	2	no	—
247	#382	C₂²×C₄₇	1	4	yes	complemented
248	C₂×#95	—	2	2	no	—
249	#336	C₂²×C₄₇	1	4	yes	complemented
250	C₄₇	C₂×#2092	1	1	yes	characteristic, direct product factor, Sylow
251	C₂⁵	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
259	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₄₇	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	D₄×C₄₇	1	4	yes	—
270	C₂²×C₈	D₄×C₄₇	1	4	yes	—
271	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
272	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	8	no	—
286	C₂×C₂²⋊C₄	—	4	8	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	D₄×C₄₇	1	2	yes	—
290	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
291	#107	—	2	8	no	—
292	#106	—	2	8	no	—
293	#102	—	2	8	no	—
294	#102	—	2	8	no	—
295	#95	—	2	8	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	—	4	2	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	C₂×Q₈×C₄₇	1	4	yes	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
333	C₂²×C₄	#41×C₄₇	1	2	yes	—
334	C₂²×C₄	#41×C₄₇	1	2	yes	—
335	C₂²×C₄	#41×C₄₇	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	8	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
344	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	16	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	8	8	no	—
366	C₂³	—	8	4	no	—
367	C₂³	—	8	4	no	—
368	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
369	C₂³	#123×C₄₇	1	2	yes	—
370	C₂³	#127×C₄₇	1	2	yes	—
371	C₂³	#135×C₄₇	1	4	yes	—
372	C₂³	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
373	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	D₄	—	2	4	no	—
375	D₄	—	2	4	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	—	8	4	no	—
392	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
393	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
394	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
395	C₂×C₄	#123×C₄₇	1	4	yes	—
396	C₂×C₄	#123×C₄₇	1	4	yes	—
397	C₂×C₄	#123×C₄₇	1	2	yes	—
398	C₂×C₄	#127×C₄₇	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	2	4	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	16	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₄₇×#399	1	4	yes	—
414	C₂²	C₄₇×#478	1	8	yes	—
415	C₂²	C₄₇×#482	1	8	yes	—
416	C₂²	C₄₇×#495	1	4	yes	—
417	C₂²	C₄₇×#496	1	4	yes	—
418	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
419	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
420	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
421	C₂²	C₂×#135×C₄₇	1	2	yes	—
422	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
423	C₄	—	4	4	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	C₄₇×#399	1	4	yes	—
428	C₄	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
429	C₄	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
430	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
431	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
432	C₂	—	8	4	no	—
433	C₂	C₄₇×#2092	1	8	yes	direct product factor
434	C₂	C₂×C₄₇×#399	1	1	yes	characteristic
435	C₂	C₂×C₄₇×#478	1	2	yes	—
436	C₂	C₂×C₄₇×#482	1	2	yes	—
437	C₂	C₂×C₄₇×#495	1	1	yes	characteristic
438	C₂	C₂×C₄₇×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#107×C₄₇	C₂	semidirect
2. C₂²×#106×C₄₇	C₂	semidirect
6. C₂×C₄₇×#382	C₂	semidirect
7. C₄₇×#2092	C₂	direct (N × H)
8. C₂×C₄₇×#336	C₂	semidirect
18. C₂×#107×C₄₇	C₂²	semidirect
20. C₂×#106×C₄₇	C₂²	semidirect
28. C₄₇×#382	C₂²	semidirect
30. C₄₇×#336	C₂²	semidirect
187. C₂×#2092	C₄₇	direct (N × H)
213. C₂²×#107	C₂×C₄₇	semidirect
214. C₂²×#106	C₂×C₄₇	semidirect
218. C₂×#382	C₂×C₄₇	semidirect
219. #2092	C₂×C₄₇	direct (N × H)
220. C₂×#336	C₂×C₄₇	semidirect
222. C₂×C₄₇	#2092	direct (N × H)
237. C₂×#107	C₂²×C₄₇	semidirect
239. C₂×#106	C₂²×C₄₇	semidirect
247. #382	C₂²×C₄₇	semidirect
249. #336	C₂²×C₄₇	semidirect
250. C₄₇	C₂×#2092	direct (N × H)
433. C₂	C₄₇×#2092	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#107×C₄₇	2
C₂²×#106×C₄₇	2
C₂²×#102×C₄₇	2
C₂×C₄₇×#390	2
C₂×C₄₇×#382	2
C₄₇×#2092	2
C₂×C₄₇×#336	2
C₂×#2092	47

Subgroups — C2×C47×#2092 #26063422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2092 #26063422