Subgroups — C₄₇×#21218 #26060916

Order 12032.

1570 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#413	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1967	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1966	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1965	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₄₇×#532	—	2	1	no	—
12	C₄₇×#532	—	2	1	no	—
13	C₄₇×#532	—	2	1	no	—
14	C₄₇×#532	—	2	1	no	—
15	C₄₇×#532	—	2	2	no	—
16	C₄₇×#532	—	2	2	no	—
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₇	C₂²	1	2	yes	—
20	C₂×#121×C₄₇	C₄	1	4	yes	—
21	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#423	—	2	2	no	—
24	C₄₇×#423	C₂²	1	2	yes	—
25	C₄₇×#423	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
27	C₄₇×#413	—	2	16	no	—
28	C₂×#101×C₄₇	C₂²	1	8	yes	—
29	C₂×#100×C₄₇	C₂²	1	8	yes	—
30	C₄×M₁₆×C₄₇	—	2	1	no	—
31	C₄×M₁₆×C₄₇	—	2	1	no	—
32	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
33	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
34	C₂×#97×C₄₇	—	2	1	no	—
35	C₂×C₄×C₈×C₄₇	—	2	1	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	2	8	no	—
41	C₂×#41×C₄₇	—	2	8	no	—
42	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	—	2	4	no	—
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	8	no	—
53	C₂×M₁₆×C₄₇	D₄	1	8	yes	complemented
54	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
55	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	—	2	2	no	—
58	C₄⋊Q₈×C₄₇	—	2	2	no	—
59	C₄⋊Q₈×C₄₇	—	2	1	no	—
60	C₄⋊Q₈×C₄₇	—	2	1	no	—
61	#127×C₄₇	—	2	2	no	—
62	#127×C₄₇	—	2	1	no	—
63	#127×C₄₇	—	2	1	no	—
64	#124×C₄₇	—	2	4	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	2	no	—
67	#121×C₄₇	—	2	4	no	—
68	#121×C₄₇	—	2	4	no	—
69	#121×C₄₇	—	2	4	no	—
70	#121×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	4	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
77	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	D₄	1	2	yes	—
83	C₂×C₄²×C₄₇	D₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	4	no	—
87	C₄⋊C₈×C₄₇	—	2	4	no	—
88	#101×C₄₇	—	2	16	no	—
89	#100×C₄₇	—	2	16	no	—
90	#97×C₄₇	—	2	2	no	—
91	#97×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	C₄×C₈×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	#41×C₄₇	—	4	8	no	—
97	#41×C₄₇	—	4	8	no	—
98	#41×C₄₇	—	4	4	no	—
99	#41×C₄₇	—	4	4	no	—
100	#41×C₄₇	—	4	4	no	—
101	#41×C₄₇	—	4	4	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	4	no	—
105	C₂×Q₈×C₄₇	—	2	4	no	—
106	C₂×D₄×C₄₇	—	2	4	no	—
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	2	16	no	—
109	C₂×D₄×C₄₇	—	2	4	no	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	4	no	—
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	4	8	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	2	4	no	—
118	C₂²×C₄×C₄₇	—	2	16	no	—
119	C₂²×C₄×C₄₇	—	4	4	no	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₄₇	#41	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₄₇	—	2	8	no	—
136	M₁₆×C₄₇	—	2	4	no	—
137	M₁₆×C₄₇	—	2	8	no	—
138	M₁₆×C₄₇	—	4	4	no	—
139	M₁₆×C₄₇	C₂×D₄	1	8	yes	—
140	C₂×C₈×C₄₇	—	2	8	no	—
141	C₂×C₈×C₄₇	—	2	4	no	—
142	C₂×C₈×C₄₇	—	2	4	no	—
143	C₂×C₈×C₄₇	—	4	4	no	—
144	C₄⋊C₄×C₄₇	—	2	4	no	—
145	C₄⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	8	no	—
147	C₂²⋊C₄×C₄₇	—	2	8	no	—
148	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
149	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₄₇	C₂×D₄	1	2	yes	—
153	C₄²×C₄₇	C₂×D₄	1	2	yes	—
154	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₄₇	—	2	4	no	—
159	C₂³×C₄₇	—	2	8	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	8	no	—
162	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂³×C₄₇	C₄×D₄	1	4	yes	—
165	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	Q₈×C₄₇	—	4	4	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	8	no	—
170	D₄×C₄₇	—	4	8	no	—
171	D₄×C₄₇	—	4	8	no	—
172	D₄×C₄₇	—	4	4	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	4	8	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	8	no	—
185	C₂×C₄×C₄₇	—	4	8	no	—
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
193	C₂×C₄×C₄₇	#121	1	4	yes	—
194	C₂×C₄×C₄₇	#121	1	4	yes	—
195	C₂×C₄×C₄₇	#124	1	2	yes	—
196	C₂×C₄×C₄₇	#124	1	2	yes	—
197	C₂×C₄×C₄₇	#127	1	2	yes	—
198	C₂×C₄×C₄₇	#127	1	2	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
203	C₈×C₄₇	—	2	8	no	—
204	C₈×C₄₇	—	4	4	no	—
205	#21218	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	4	4	no	—
210	C₂²×C₄₇	—	4	8	no	—
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	8	8	no	—
213	C₂²×C₄₇	#390	1	2	yes	—
214	C₂²×C₄₇	#390	1	2	yes	—
215	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	4	4	no	—
221	C₄×C₄₇	#390	1	2	yes	—
222	C₄×C₄₇	#390	1	2	yes	—
223	C₄×C₄₇	#413	1	4	yes	complemented
224	C₄×C₄₇	C₂×#121	1	2	yes	—
225	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
226	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
227	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
228	C₂×#423	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₂×#413	C₂×C₄₇	1	4	yes	complemented
230	C₂×C₄×M₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
231	#1967	C₂×C₄₇	1	4	yes	complemented
232	#1966	C₂×C₄₇	1	2	yes	complemented
233	#1965	C₂×C₄₇	1	2	yes	complemented
234	C₂×C₄₇	—	2	2	no	—
235	C₂×C₄₇	—	2	2	no	—
236	C₂×C₄₇	—	2	2	no	—
237	C₂×C₄₇	—	8	4	no	—
238	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
239	C₂×C₄₇	C₂×#413	1	2	yes	—
240	C₂²×#41	C₂²×C₄₇	1	2	yes	—
241	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
242	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
243	#532	—	2	1	no	—
244	#532	—	2	1	no	—
245	#532	—	2	1	no	—
246	#532	—	2	1	no	—
247	#532	—	2	2	no	—
248	#532	—	2	2	no	—
249	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#124	C₂²×C₄₇	1	2	yes	—
252	C₂×#121	C₄×C₄₇	1	4	yes	—
253	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	—
254	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
255	#423	—	2	2	no	—
256	#423	C₂²×C₄₇	1	2	yes	—
257	#423	C₂²×C₄₇	1	2	yes	—
258	C₂×C₄⋊C₈	—	2	2	no	—
259	#413	—	2	16	no	—
260	C₂×#101	C₂²×C₄₇	1	8	yes	—
261	C₂×#100	C₂²×C₄₇	1	8	yes	—
262	C₄×M₁₆	—	2	1	no	—
263	C₄×M₁₆	—	2	1	no	—
264	C₄×M₁₆	C₂²×C₄₇	1	2	yes	—
265	C₄×M₁₆	C₂²×C₄₇	1	2	yes	—
266	C₂×#97	—	2	1	no	—
267	C₂×C₄×C₈	—	2	1	no	—
268	C₄₇	#21218	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	2	8	no	—
275	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
276	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
277	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
278	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
279	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
280	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
281	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	8	no	—
286	C₂×M₁₆	D₄×C₄₇	1	8	yes	complemented
287	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
288	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	—	2	2	no	—
297	#124	—	2	2	no	—
298	#124	—	2	2	no	—
299	#124	—	2	4	no	—
300	#121	—	2	4	no	—
301	#121	—	2	4	no	—
302	#121	—	2	4	no	—
303	#121	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
310	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
311	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₄₇	1	2	yes	—
316	C₂×C₄²	D₄×C₄₇	1	2	yes	—
317	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
319	C₄⋊C₈	—	2	4	no	—
320	C₄⋊C₈	—	2	4	no	—
321	#101	—	2	16	no	—
322	#100	—	2	16	no	—
323	#97	—	2	2	no	—
324	#97	—	2	2	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	2	2	no	—
327	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
328	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
329	#41	—	4	8	no	—
330	#41	—	4	8	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	#41	—	4	4	no	—
334	#41	—	4	4	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	16	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	16	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
354	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
355	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
356	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
358	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
359	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
366	C₂²×C₄	#41×C₄₇	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
368	M₁₆	—	2	8	no	—
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	8	no	—
371	M₁₆	—	4	4	no	—
372	M₁₆	C₂×D₄×C₄₇	1	8	yes	—
373	C₂×C₈	—	2	8	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	4	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
382	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
383	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
384	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
385	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
386	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₄₇	1	2	yes	—
390	C₄²	C₂×D₄×C₄₇	1	2	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	8	no	—
395	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
396	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
397	C₂³	C₄×D₄×C₄₇	1	4	yes	—
398	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
399	Q₈	—	4	4	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
425	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
426	C₂×C₄	#121×C₄₇	1	4	yes	—
427	C₂×C₄	#121×C₄₇	1	4	yes	—
428	C₂×C₄	#124×C₄₇	1	2	yes	—
429	C₂×C₄	#124×C₄₇	1	2	yes	—
430	C₂×C₄	#127×C₄₇	1	2	yes	—
431	C₂×C₄	#127×C₄₇	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
436	C₈	—	2	8	no	—
437	C₈	—	4	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	8	no	—
444	C₂²	—	8	8	no	—
445	C₂²	C₄₇×#390	1	2	yes	—
446	C₂²	C₄₇×#390	1	2	yes	—
447	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
448	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	4	no	—
453	C₄	C₄₇×#390	1	2	yes	—
454	C₄	C₄₇×#390	1	2	yes	—
455	C₄	C₄₇×#413	1	4	yes	complemented
456	C₄	C₂×#121×C₄₇	1	2	yes	—
457	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
458	C₄	C₂×#127×C₄₇	1	1	yes	characteristic
459	C₂	—	2	2	no	—
460	C₂	—	2	2	no	—
461	C₂	—	2	2	no	—
462	C₂	—	8	4	no	—
463	C₂	C₂×C₄₇×#390	1	1	yes	characteristic
464	C₂	C₂×C₄₇×#413	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₂×C₄₇×#413	C₂	semidirect
4. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
5. C₄₇×#1967	C₂	semidirect
6. C₄₇×#1966	C₂	semidirect
7. C₄₇×#1965	C₂	semidirect
53. C₂×M₁₆×C₄₇	D₄	semidirect
205. #21218	C₄₇	direct (N × H)
223. C₄×C₄₇	#413	semidirect
228. C₂×#423	C₂×C₄₇	semidirect
229. C₂×#413	C₂×C₄₇	semidirect
230. C₂×C₄×M₁₆	C₂×C₄₇	semidirect
231. #1967	C₂×C₄₇	semidirect
232. #1966	C₂×C₄₇	semidirect
233. #1965	C₂×C₄₇	semidirect
268. C₄₇	#21218	direct (N × H)
286. C₂×M₁₆	D₄×C₄₇	semidirect
455. C₄	C₄₇×#413	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#532	2
C₂×C₄₇×#423	2
C₂×C₄₇×#413	2
C₂×C₄×M₁₆×C₄₇	2
C₄₇×#1967	2
C₄₇×#1966	2
C₄₇×#1965	2
#21218	47

Subgroups — C47×#21218 #26060916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21218 #26060916