Subgroups — C₂×C₄₇×#1967 #26060915

Order 12032.

1646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#101×C₄₇	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₄₇	C₂	1	2	yes	maximal
5	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1967	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₂×#124×C₄₇	—	2	1	no	—
12	C₂×#124×C₄₇	—	2	1	no	—
13	C₂×#124×C₄₇	—	2	2	no	—
14	C₂×#124×C₄₇	—	2	2	no	—
15	C₂×#124×C₄₇	—	2	2	no	—
16	C₂×#124×C₄₇	C₄	1	4	yes	—
17	C₂×#124×C₄₇	C₂²	1	4	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₄	1	4	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#423	—	2	2	no	—
21	C₄₇×#423	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
23	C₂×#101×C₄₇	—	2	8	no	—
24	C₂×#101×C₄₇	C₂²	1	8	yes	complemented
25	C₂×#100×C₄₇	—	2	8	no	—
26	C₂×#100×C₄₇	C₂²	1	8	yes	—
27	C₄×M₁₆×C₄₇	—	2	2	no	—
28	C₄×M₁₆×C₄₇	C₂²	1	4	yes	complemented
29	C₂×#97×C₄₇	—	2	1	no	—
30	C₂×C₄×C₈×C₄₇	—	2	1	no	—
31	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
32	C₂²×Q₈×C₄₇	—	2	1	no	—
33	C₂²×Q₈×C₄₇	—	2	1	no	—
34	C₂²×Q₈×C₄₇	—	2	1	no	—
35	C₂²×Q₈×C₄₇	—	2	1	no	—
36	C₂²×Q₈×C₄₇	—	2	4	no	—
37	C₂²×Q₈×C₄₇	—	2	4	no	—
38	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
39	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₄₇	—	2	1	no	—
41	C₂²×D₄×C₄₇	—	2	1	no	—
42	C₂²×D₄×C₄₇	—	2	1	no	—
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	—	2	4	no	—
45	C₂²×D₄×C₄₇	—	2	4	no	—
46	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	4	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	4	no	—
55	C₂×M₁₆×C₄₇	—	2	4	no	—
56	C₂×M₁₆×C₄₇	D₄	1	8	yes	—
57	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
58	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	#124×C₄₇	—	2	4	no	—
62	#124×C₄₇	—	2	4	no	—
63	#124×C₄₇	—	2	8	no	—
64	#124×C₄₇	—	2	8	no	—
65	#124×C₄₇	—	2	4	no	—
66	#124×C₄₇	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	D₄	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₄⋊C₈×C₄₇	—	2	8	no	—
79	#101×C₄₇	—	2	16	no	—
80	#100×C₄₇	—	2	16	no	—
81	#97×C₄₇	—	2	4	no	—
82	C₄×C₈×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	8	no	—
86	C₂⁴×C₄₇	—	4	8	no	—
87	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	8	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	4	no	—
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	—	4	4	no	—
97	C₂×Q₈×C₄₇	—	4	4	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×Q₈×C₄₇	—	4	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	8	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	2	4	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	4	no	—
111	C₂×D₄×C₄₇	—	4	2	no	—
112	C₂×D₄×C₄₇	—	4	2	no	—
113	C₂×D₄×C₄₇	—	4	2	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	8	no	—
118	C₂²×C₄×C₄₇	—	4	4	no	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₄₇	—	2	8	no	—
133	M₁₆×C₄₇	—	2	4	no	—
134	M₁₆×C₄₇	—	2	4	no	—
135	M₁₆×C₄₇	—	2	4	no	—
136	M₁₆×C₄₇	—	4	4	no	—
137	M₁₆×C₄₇	C₂×D₄	1	8	yes	—
138	C₂×C₈×C₄₇	—	2	8	no	—
139	C₂×C₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	—	2	4	no	—
141	C₂×C₈×C₄₇	—	4	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	16	no	—
143	C₂²⋊C₄×C₄₇	—	2	16	no	—
144	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
145	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
146	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
147	C₄²×C₄₇	C₂×D₄	1	4	yes	—
148	C₄²×C₄₇	C₂×D₄	1	2	yes	—
149	C₄²×C₄₇	C₂×D₄	1	2	yes	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	8	no	—
153	C₂³×C₄₇	—	4	8	no	—
154	C₂³×C₄₇	—	4	8	no	—
155	C₂³×C₄₇	—	4	4	no	—
156	C₂³×C₄₇	—	4	4	no	—
157	C₂³×C₄₇	—	4	8	no	—
158	C₂³×C₄₇	—	8	16	no	—
159	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₄₇	C₄×D₄	1	4	yes	—
162	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	Q₈×C₄₇	—	4	4	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	Q₈×C₄₇	—	4	4	no	—
167	Q₈×C₄₇	—	4	4	no	—
168	D₄×C₄₇	—	4	4	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	4	2	no	—
171	D₄×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	8	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₄₇	#121	1	4	yes	—
187	C₂×C₄×C₄₇	#121	1	4	yes	—
188	C₂×C₄×C₄₇	#124	1	2	yes	—
189	C₂×C₄×C₄₇	#124	1	2	yes	—
190	C₂×C₄×C₄₇	#127	1	2	yes	—
191	C₂×C₄×C₄₇	#127	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
196	C₈×C₄₇	—	2	8	no	—
197	C₈×C₄₇	—	4	4	no	—
198	C₂×#1967	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	8	no	—
202	C₂²×C₄₇	—	4	8	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	8	8	no	—
205	C₂²×C₄₇	—	8	8	no	—
206	C₂²×C₄₇	—	8	8	no	—
207	C₂²×C₄₇	#390	1	2	yes	—
208	C₂²×C₄₇	#390	1	2	yes	—
209	C₂²×C₄₇	#413	1	4	yes	—
210	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
212	C₄×C₄₇	—	2	4	no	—
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	#390	1	2	yes	—
216	C₄×C₄₇	#390	1	2	yes	—
217	C₄×C₄₇	C₂×#121	1	2	yes	—
218	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
220	C₂²×#124	C₂×C₄₇	1	1	yes	characteristic
221	C₂×#423	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₂²×#101	C₂×C₄₇	1	2	yes	complemented
223	C₂²×#100	C₂×C₄₇	1	2	yes	—
224	C₂×C₄×M₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1967	C₂×C₄₇	1	8	yes	direct product factor
226	C₂×C₄₇	—	2	2	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	8	4	no	—
229	C₂×C₄₇	#1967	1	4	yes	direct product factor
230	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#413	1	2	yes	—
232	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
233	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
236	C₂×#124	—	2	1	no	—
237	C₂×#124	—	2	1	no	—
238	C₂×#124	—	2	2	no	—
239	C₂×#124	—	2	2	no	—
240	C₂×#124	—	2	2	no	—
241	C₂×#124	C₄×C₄₇	1	4	yes	—
242	C₂×#124	C₂²×C₄₇	1	4	yes	—
243	C₂²×C₂²⋊C₄	C₄×C₄₇	1	4	yes	—
244	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
245	#423	—	2	2	no	—
246	#423	C₂²×C₄₇	1	4	yes	complemented
247	C₂×C₄⋊C₈	—	2	2	no	—
248	C₂×#101	—	2	8	no	—
249	C₂×#101	C₂²×C₄₇	1	8	yes	complemented
250	C₂×#100	—	2	8	no	—
251	C₂×#100	C₂²×C₄₇	1	8	yes	—
252	C₄×M₁₆	—	2	2	no	—
253	C₄×M₁₆	C₂²×C₄₇	1	4	yes	complemented
254	C₂×#97	—	2	1	no	—
255	C₂×C₄×C₈	—	2	1	no	—
256	C₄₇	C₂×#1967	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	—	2	4	no	—
263	C₂²×Q₈	—	2	4	no	—
264	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
265	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
273	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
274	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
275	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
276	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	D₄×C₄₇	1	8	yes	—
283	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
284	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	2	no	—
287	#124	—	2	4	no	—
288	#124	—	2	4	no	—
289	#124	—	2	8	no	—
290	#124	—	2	4	no	—
291	#124	—	2	4	no	—
292	#124	—	2	8	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₂²⋊C₄	—	2	8	no	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	—
297	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
298	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₄₇	1	2	yes	—
301	C₂×C₄²	D₄×C₄₇	1	2	yes	—
302	C₂×C₄²	D₄×C₄₇	1	2	yes	—
303	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
304	C₄⋊C₈	—	2	8	no	—
305	#101	—	2	16	no	—
306	#100	—	2	16	no	—
307	#97	—	2	4	no	—
308	C₄×C₈	—	2	4	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	2	8	no	—
312	C₂⁴	—	4	8	no	—
313	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
314	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
346	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
349	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
350	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
356	C₂²×C₄	#41×C₄₇	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
358	M₁₆	—	2	8	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	4	no	—
362	M₁₆	—	4	4	no	—
363	M₁₆	C₂×D₄×C₄₇	1	8	yes	—
364	C₂×C₈	—	2	8	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂²⋊C₄	—	2	16	no	—
369	C₂²⋊C₄	—	2	16	no	—
370	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
371	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
372	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
373	C₄²	C₂×D₄×C₄₇	1	2	yes	—
374	C₄²	C₂×D₄×C₄₇	1	2	yes	—
375	C₄²	C₂×D₄×C₄₇	1	4	yes	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	8	16	no	—
385	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
386	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
387	C₂³	C₄×D₄×C₄₇	1	4	yes	—
388	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
389	Q₈	—	4	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	4	no	—
393	Q₈	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
412	C₂×C₄	#121×C₄₇	1	4	yes	—
413	C₂×C₄	#121×C₄₇	1	4	yes	—
414	C₂×C₄	#124×C₄₇	1	2	yes	—
415	C₂×C₄	#124×C₄₇	1	2	yes	—
416	C₂×C₄	#127×C₄₇	1	2	yes	—
417	C₂×C₄	#127×C₄₇	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
422	C₈	—	2	8	no	—
423	C₈	—	4	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	8	8	no	—
430	C₂²	—	8	8	no	—
431	C₂²	—	8	8	no	—
432	C₂²	C₄₇×#390	1	2	yes	—
433	C₂²	C₄₇×#390	1	2	yes	—
434	C₂²	C₄₇×#413	1	4	yes	—
435	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
436	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
437	C₄	—	2	4	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	4	no	—
440	C₄	C₄₇×#390	1	2	yes	—
441	C₄	C₄₇×#390	1	2	yes	—
442	C₄	C₂×#121×C₄₇	1	2	yes	—
443	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
444	C₄	C₂×#127×C₄₇	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	2	2	no	—
447	C₂	—	8	4	no	—
448	C₂	C₄₇×#1967	1	4	yes	direct product factor
449	C₂	C₂×C₄₇×#390	1	1	yes	characteristic
450	C₂	C₂×C₄₇×#413	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#423	C₂	semidirect
3. C₂²×#101×C₄₇	C₂	semidirect
5. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
6. C₄₇×#1967	C₂	direct (N × H)
21. C₄₇×#423	C₂²	semidirect
24. C₂×#101×C₄₇	C₂²	semidirect
28. C₄×M₁₆×C₄₇	C₂²	semidirect
198. C₂×#1967	C₄₇	direct (N × H)
221. C₂×#423	C₂×C₄₇	semidirect
222. C₂²×#101	C₂×C₄₇	semidirect
224. C₂×C₄×M₁₆	C₂×C₄₇	semidirect
225. #1967	C₂×C₄₇	direct (N × H)
229. C₂×C₄₇	#1967	direct (N × H)
246. #423	C₂²×C₄₇	semidirect
249. C₂×#101	C₂²×C₄₇	semidirect
253. C₄×M₁₆	C₂²×C₄₇	semidirect
256. C₄₇	C₂×#1967	direct (N × H)
448. C₂	C₄₇×#1967	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×#124×C₄₇	2
C₂×C₄₇×#423	2
C₂²×#101×C₄₇	2
C₂²×#100×C₄₇	2
C₂×C₄×M₁₆×C₄₇	2
C₄₇×#1967	2
C₂×#1967	47

Subgroups — C2×C47×#1967 #26060915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1967 #26060915