Subgroups — C₄₇×#17574 #26057272

Order 12032.

1338 conjugacy classes of subgroups.

The subgroup lattice has 594 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×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1519	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1517	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1502	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₄₇	—	2	1	no	—
8	C₄₇×#532	—	2	1	no	—
9	C₄₇×#532	—	2	1	no	—
10	C₄₇×#532	—	2	1	no	—
11	C₄₇×#532	—	2	1	no	—
12	C₄₇×#532	C₄	1	2	yes	complemented
13	C₄₇×#532	C₄	1	2	yes	complemented
14	C₄₇×#532	C₂²	1	2	yes	—
15	C₄₇×#532	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
17	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
18	C₂×#124×C₄₇	—	2	1	no	—
19	C₂×#121×C₄₇	—	2	1	no	—
20	C₂×#121×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₇	—	2	1	no	—
22	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
23	C₂×#117×C₄₇	—	2	1	no	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#431	—	2	1	no	—
26	C₄₇×#431	—	2	1	no	—
27	C₄₇×#431	C₂²	1	2	yes	complemented
28	C₄₇×#431	C₂²	1	2	yes	complemented
29	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₄₇	—	2	1	no	—
32	C₄₇×#384	—	2	1	no	—
33	C₄₇×#382	C₂²	1	2	yes	complemented
34	C₄₇×#380	—	2	1	no	—
35	C₄₇×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
38	C₄₇×#327	C₂²	1	16	yes	complemented
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	4	4	no	—
44	C₂×#41×C₄₇	—	4	4	no	—
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	—	2	2	no	—
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	—	2	1	no	—
56	C₄⋊Q₈×C₄₇	—	2	1	no	—
57	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
58	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
59	#127×C₄₇	—	2	1	no	—
60	#127×C₄₇	—	2	1	no	—
61	#127×C₄₇	C₂×C₄	1	2	yes	—
62	#127×C₄₇	C₂×C₄	1	2	yes	—
63	#124×C₄₇	—	2	2	no	—
64	#124×C₄₇	—	2	2	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	2	no	—
67	#121×C₄₇	—	2	2	no	—
68	#121×C₄₇	—	2	2	no	—
69	#121×C₄₇	—	2	2	no	—
70	#121×C₄₇	—	2	2	no	—
71	#121×C₄₇	—	2	2	no	—
72	#121×C₄₇	—	2	2	no	—
73	#121×C₄₇	C₂×C₄	1	4	yes	—
74	#121×C₄₇	C₂³	1	4	yes	—
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	—	2	2	no	—
79	C₄×D₄×C₄₇	—	2	2	no	—
80	C₄×D₄×C₄₇	—	2	2	no	—
81	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
82	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
83	#117×C₄₇	—	4	4	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₄²×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₇	—	2	2	no	—
106	C₄⋊C₈×C₄₇	—	2	2	no	—
107	C₂²⋊C₈×C₄₇	—	2	2	no	—
108	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
109	C₄×C₈×C₄₇	—	2	2	no	—
110	C₄×C₈×C₄₇	—	2	2	no	—
111	#95×C₄₇	—	2	2	no	—
112	#95×C₄₇	C₂³	1	4	yes	—
113	C₂⁴×C₄₇	—	2	2	no	—
114	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
115	#41×C₄₇	—	4	8	no	—
116	#41×C₄₇	—	4	8	no	—
117	#41×C₄₇	—	4	4	no	—
118	#41×C₄₇	—	4	4	no	—
119	#41×C₄₇	—	4	4	no	—
120	#41×C₄₇	—	4	4	no	—
121	C₂×Q₈×C₄₇	—	2	2	no	—
122	C₂×Q₈×C₄₇	—	2	2	no	—
123	C₂×Q₈×C₄₇	—	4	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	4	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	4	4	no	—
132	C₂×D₄×C₄₇	—	4	4	no	—
133	C₂×D₄×C₄₇	—	4	4	no	—
134	C₂×D₄×C₄₇	—	4	4	no	—
135	C₂×D₄×C₄₇	—	4	4	no	—
136	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	4	2	no	—
142	C₂²×C₄×C₄₇	—	4	2	no	—
143	C₂²×C₄×C₄₇	—	4	8	no	—
144	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	D₈	1	4	yes	—
153	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
154	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₄₇	—	2	4	no	—
165	C₂×C₈×C₄₇	—	4	4	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	—	4	4	no	—
170	C₄⋊C₄×C₄₇	—	4	4	no	—
171	C₄⋊C₄×C₄₇	—	4	4	no	—
172	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
173	C₂²⋊C₄×C₄₇	—	2	4	no	—
174	C₂²⋊C₄×C₄₇	—	2	4	no	—
175	C₂²⋊C₄×C₄₇	—	2	4	no	—
176	C₂²⋊C₄×C₄₇	—	2	4	no	—
177	C₂²⋊C₄×C₄₇	—	4	4	no	—
178	C₄²×C₄₇	—	4	4	no	—
179	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
186	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
187	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₄₇	—	2	4	no	—
196	C₂³×C₄₇	—	4	1	no	—
197	C₂³×C₄₇	—	4	1	no	—
198	C₂³×C₄₇	—	4	4	no	—
199	C₂³×C₄₇	—	4	4	no	—
200	C₂³×C₄₇	—	4	4	no	—
201	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₄₇	C₂×D₈	1	2	yes	—
204	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
205	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₇	—	4	4	no	—
207	Q₈×C₄₇	—	4	4	no	—
208	D₄×C₄₇	—	4	4	no	—
209	D₄×C₄₇	—	4	4	no	—
210	D₄×C₄₇	—	4	4	no	—
211	D₄×C₄₇	—	4	4	no	—
212	D₄×C₄₇	—	4	8	no	—
213	D₄×C₄₇	—	4	4	no	—
214	D₄×C₄₇	—	4	4	no	—
215	D₄×C₄₇	—	4	4	no	—
216	D₄×C₄₇	—	4	4	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	4	no	—
224	C₂×C₄×C₄₇	—	4	1	no	—
225	C₂×C₄×C₄₇	—	4	1	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	4	1	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	4	4	no	—
231	C₂×C₄×C₄₇	—	4	8	no	—
232	C₂×C₄×C₄₇	—	4	8	no	—
233	C₂×C₄×C₄₇	—	4	4	no	—
234	C₂×C₄×C₄₇	—	4	4	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	#102	1	4	yes	—
237	C₂×C₄×C₄₇	#102	1	4	yes	—
238	C₂×C₄×C₄₇	#102	1	4	yes	—
239	C₂×C₄×C₄₇	#102	1	4	yes	—
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
251	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
252	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
253	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
254	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₄₇	—	4	4	no	—
257	#17574	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	—	4	4	no	—
269	C₂²×C₄₇	—	8	8	no	—
270	C₂²×C₄₇	C₂×#102	1	2	yes	—
271	C₂²×C₄₇	C₂×#102	1	2	yes	—
272	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
274	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	4	no	—
282	C₄×C₄₇	—	8	4	no	—
283	C₄×C₄₇	#410	1	2	yes	—
284	C₄×C₄₇	C₂×#102	1	2	yes	—
285	C₄×C₄₇	C₂×#102	1	2	yes	—
286	C₄×C₄₇	C₂×#102	1	2	yes	—
287	C₄×C₄₇	C₂×#102	1	2	yes	—
288	C₄×C₄₇	#421	1	2	yes	—
289	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
290	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
291	#2285	C₂×C₄₇	1	1	yes	characteristic, complemented
292	#1519	C₂×C₄₇	1	4	yes	complemented
293	#1517	C₂×C₄₇	1	4	yes	complemented
294	#1502	C₂×C₄₇	1	4	yes	complemented
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	2	2	no	—
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	2	2	no	—
299	C₂×C₄₇	—	8	4	no	—
300	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
301	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
302	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
303	C₂²×#41	—	2	1	no	—
304	#532	—	2	1	no	—
305	#532	—	2	1	no	—
306	#532	—	2	1	no	—
307	#532	—	2	1	no	—
308	#532	C₄×C₄₇	1	2	yes	complemented
309	#532	C₄×C₄₇	1	2	yes	complemented
310	#532	C₂²×C₄₇	1	2	yes	—
311	#532	C₂²×C₄₇	1	2	yes	—
312	C₂×C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic, complemented
313	C₂×#127	C₄×C₄₇	1	1	yes	characteristic, complemented
314	C₂×#124	—	2	1	no	—
315	C₂×#121	—	2	1	no	—
316	C₂×#121	C₂²×C₄₇	1	2	yes	—
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	complemented
319	C₂×#117	—	2	1	no	—
320	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
321	#431	—	2	1	no	—
322	#431	—	2	1	no	—
323	#431	C₂²×C₄₇	1	2	yes	complemented
324	#431	C₂²×C₄₇	1	2	yes	complemented
325	C₂×C₄⋊C₈	—	2	1	no	—
326	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
327	C₂×C₄×C₈	—	2	1	no	—
328	#384	—	2	1	no	—
329	#382	C₂²×C₄₇	1	2	yes	complemented
330	#380	—	2	1	no	—
331	#380	C₂²×C₄₇	1	2	yes	—
332	C₄×C₄⋊C₄	—	2	1	no	—
333	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
334	#327	C₂²×C₄₇	1	16	yes	complemented
335	C₄₇	#17574	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	4	4	no	—
341	C₂×#41	—	4	4	no	—
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
347	C₂³×C₄	—	2	2	no	—
348	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
349	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
351	C₂²×C₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
355	C₄⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
356	#127	—	2	1	no	—
357	#127	—	2	1	no	—
358	#127	C₂×C₄×C₄₇	1	2	yes	—
359	#127	C₂×C₄×C₄₇	1	2	yes	—
360	#124	—	2	2	no	—
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	2	no	—
370	#121	C₂×C₄×C₄₇	1	4	yes	—
371	#121	C₂³×C₄₇	1	4	yes	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
379	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
380	#117	—	4	4	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
391	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
392	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
393	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
394	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
395	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
396	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
397	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
398	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
399	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
402	C₄⋊C₈	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
406	C₄×C₈	—	2	2	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	2	2	no	—
409	#95	C₂³×C₄₇	1	4	yes	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
412	#41	—	4	4	no	—
413	#41	—	4	4	no	—
414	#41	—	4	4	no	—
415	#41	—	4	4	no	—
416	#41	—	4	8	no	—
417	#41	—	4	8	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
449	C₂²×C₄	D₈×C₄₇	1	4	yes	—
450	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
451	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	4	4	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	4	4	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₄²	—	4	4	no	—
476	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
477	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
478	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
479	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
480	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
481	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
482	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
483	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
484	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
485	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
486	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
487	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
492	C₂³	—	2	4	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
499	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
500	C₂³	C₂×D₈×C₄₇	1	2	yes	—
501	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
502	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
503	Q₈	—	4	4	no	—
504	Q₈	—	4	4	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	8	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	#102×C₄₇	1	4	yes	—
534	C₂×C₄	#102×C₄₇	1	4	yes	—
535	C₂×C₄	#102×C₄₇	1	4	yes	—
536	C₂×C₄	#102×C₄₇	1	4	yes	—
537	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
544	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
548	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
549	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
550	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
551	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
553	C₈	—	4	4	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	8	8	no	—
566	C₂²	C₂×#102×C₄₇	1	2	yes	—
567	C₂²	C₂×#102×C₄₇	1	2	yes	—
568	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
569	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
570	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	4	4	no	—
578	C₄	—	8	4	no	—
579	C₄	C₄₇×#410	1	2	yes	—
580	C₄	C₂×#102×C₄₇	1	2	yes	—
581	C₄	C₂×#102×C₄₇	1	2	yes	—
582	C₄	C₂×#102×C₄₇	1	2	yes	—
583	C₄	C₂×#102×C₄₇	1	2	yes	—
584	C₄	C₄₇×#421	1	2	yes	—
585	C₂	—	2	1	no	—
586	C₂	—	2	2	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	8	4	no	—
590	C₂	C₂×C₄₇×#410	1	1	yes	characteristic
591	C₂	C₂²×#102×C₄₇	1	1	yes	characteristic
592	C₂	C₂×C₄₇×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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×#431	C₂	semidirect
3. C₄₇×#2285	C₂	semidirect
4. C₄₇×#1519	C₂	semidirect
5. C₄₇×#1517	C₂	semidirect
6. C₄₇×#1502	C₂	semidirect
12. C₄₇×#532	C₄	semidirect
13. C₄₇×#532	C₄	semidirect
16. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
17. C₂×#127×C₄₇	C₄	semidirect
22. C₂×C₄×D₄×C₄₇	C₄	semidirect
27. C₄₇×#431	C₂²	semidirect
28. C₄₇×#431	C₂²	semidirect
33. C₄₇×#382	C₂²	semidirect
37. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
38. C₄₇×#327	C₂²	semidirect
257. #17574	C₄₇	direct (N × H)
290. C₂×#431	C₂×C₄₇	semidirect
291. #2285	C₂×C₄₇	semidirect
292. #1519	C₂×C₄₇	semidirect
293. #1517	C₂×C₄₇	semidirect
294. #1502	C₂×C₄₇	semidirect
308. #532	C₄×C₄₇	semidirect
309. #532	C₄×C₄₇	semidirect
312. C₂×C₄⋊Q₈	C₄×C₄₇	semidirect
313. C₂×#127	C₄×C₄₇	semidirect
318. C₂×C₄×D₄	C₄×C₄₇	semidirect
323. #431	C₂²×C₄₇	semidirect
324. #431	C₂²×C₄₇	semidirect
329. #382	C₂²×C₄₇	semidirect
333. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
334. #327	C₂²×C₄₇	semidirect
335. C₄₇	#17574	direct (N × H)

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×#431	2
C₄₇×#2285	2
C₄₇×#1519	2
C₄₇×#1517	2
C₄₇×#1502	2
#17574	47

Subgroups — C47×#17574 #26057272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17574 #26057272