Subgroups — C₄₇×#34259 #26073957

Order 12032.

5106 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	C₂²×2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊C₄×C₄₇	C₂	1	4	yes	maximal, complemented
5	C₄₇×#2339	C₂	1	12	yes	maximal, complemented
6	C₄₇×#2311	C₂	1	3	yes	maximal, complemented
7	C₄₇×#2310	C₂	1	3	yes	maximal, complemented
8	C₄₇×#2297	C₂	1	3	yes	maximal, complemented
9	C₂×C₄₇×#391	C₂	1	3	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₄₇	—	2	8	no	—
11	C₂×2₋¹⁺⁴×C₄₇	—	2	8	no	—
12	C₂×2₋¹⁺⁴×C₄₇	C₄	1	16	yes	complemented
13	C₂²×#41×C₄₇	C₂²	1	3	yes	—
14	C₂²×#41×C₄₇	C₂²	1	6	yes	—
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₄₇	C₂²	1	3	yes	—
17	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#520	—	2	8	no	—
19	C₄×#41×C₄₇	—	2	8	no	—
20	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₇	C₂²	1	6	yes	—
23	C₂×C₄×D₄×C₄₇	C₂²	1	6	yes	—
24	C₂×#117×C₄₇	C₂²	1	3	yes	—
25	C₂×#117×C₄₇	C₂²	1	3	yes	—
26	C₂²×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
27	C₂²×C₄²×C₄₇	C₂²	1	3	yes	—
28	C₄₇×#391	C₂²	1	3	yes	—
29	C₄₇×#391	C₂²	1	6	yes	—
30	C₄₇×#391	C₂²	1	12	yes	—
31	C₄₇×#391	C₂²	1	3	yes	—
32	C₄₇×#391	C₂²	1	12	yes	—
33	C₄₇×#390	C₂²	1	1	yes	characteristic
34	C₄₇×#390	C₂²	1	3	yes	—
35	C₄₇×#386	C₂²	1	12	yes	—
36	C₄₇×#386	C₂²	1	12	yes	—
37	C₄₇×#381	C₂²	1	12	yes	—
38	C₄₇×#380	C₂²	1	12	yes	—
39	C₄×C₂²⋊C₄×C₄₇	C₂²	1	12	yes	—
40	C₂×#95×C₄₇	C₂²	1	12	yes	—
41	2₋¹⁺⁴×C₄₇	—	2	128	no	—
42	C₂×#41×C₄₇	—	2	24	no	—
43	C₂×#41×C₄₇	—	2	24	no	—
44	C₂×#41×C₄₇	—	2	12	no	—
45	C₂×#41×C₄₇	—	2	12	no	—
46	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
47	C₂×#41×C₄₇	C₂×C₄	1	48	yes	complemented
48	C₂×#41×C₄₇	C₂×C₄	1	24	yes	complemented
49	C₂×#41×C₄₇	D₄	1	8	yes	—
50	C₂×#41×C₄₇	D₄	1	8	yes	—
51	C₂²×Q₈×C₄₇	—	2	8	no	—
52	C₂²×Q₈×C₄₇	—	2	8	no	—
53	C₂²×Q₈×C₄₇	—	2	12	no	—
54	C₂²×Q₈×C₄₇	—	2	12	no	—
55	C₂²×Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
56	C₂²×Q₈×C₄₇	C₂×C₄	1	24	yes	complemented
57	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
58	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
59	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
61	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
68	C₄×Q₈×C₄₇	—	2	8	no	—
69	C₄×Q₈×C₄₇	—	2	8	no	—
70	C₄×D₄×C₄₇	—	2	24	no	—
71	C₄×D₄×C₄₇	—	2	24	no	—
72	#117×C₄₇	—	2	12	no	—
73	#117×C₄₇	—	2	12	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	12	no	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
83	C₂×C₄²×C₄₇	—	2	12	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
88	#95×C₄₇	C₂³	1	12	yes	—
89	#95×C₄₇	C₂³	1	24	yes	—
90	#95×C₄₇	C₂³	1	12	yes	—
91	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
92	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
93	#41×C₄₇	—	2	192	no	—
94	#41×C₄₇	—	2	96	no	—
95	#41×C₄₇	C₂²⋊C₄	1	64	yes	complemented
96	C₂×Q₈×C₄₇	—	2	64	no	—
97	C₂×Q₈×C₄₇	—	2	96	no	—
98	C₂×Q₈×C₄₇	—	2	6	no	—
99	C₂×Q₈×C₄₇	—	2	12	no	—
100	C₂×Q₈×C₄₇	—	2	12	no	—
101	C₂×Q₈×C₄₇	—	2	6	no	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	24	yes	—
103	C₂×Q₈×C₄₇	C₂²×C₄	1	12	yes	—
104	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
106	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₄₇	—	2	12	no	—
108	C₂×D₄×C₄₇	—	2	12	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂×D₄×C₄₇	C₂²×C₄	1	12	yes	—
114	C₂×D₄×C₄₇	C₂×D₄	1	12	yes	—
115	C₂×D₄×C₄₇	C₂×D₄	1	12	yes	—
116	C₂²×C₄×C₄₇	—	2	12	no	—
117	C₂²×C₄×C₄₇	—	2	12	no	—
118	C₂²×C₄×C₄₇	—	2	12	no	—
119	C₂²×C₄×C₄₇	—	2	12	no	—
120	C₂²×C₄×C₄₇	—	2	12	no	—
121	C₂²×C₄×C₄₇	—	2	12	no	—
122	C₂²×C₄×C₄₇	—	2	12	no	—
123	C₂²×C₄×C₄₇	—	4	6	no	—
124	C₂²×C₄×C₄₇	—	4	12	no	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
137	C₄⋊C₄×C₄₇	—	2	6	no	—
138	C₄⋊C₄×C₄₇	—	2	12	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	12	no	—
141	C₂²⋊C₄×C₄₇	—	2	12	no	—
142	C₂²⋊C₄×C₄₇	—	2	12	no	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₂²⋊C₄×C₄₇	—	4	12	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	6	no	—
147	C₄²×C₄₇	—	2	12	no	—
148	C₄²×C₄₇	—	2	12	no	—
149	C₂³×C₄₇	—	2	6	no	—
150	C₂³×C₄₇	—	2	6	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	—	2	4	no	—
155	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
156	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
157	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
159	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	48	no	—
161	Q₈×C₄₇	—	2	24	no	—
162	Q₈×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
163	D₄×C₄₇	—	2	48	no	—
164	D₄×C₄₇	—	2	8	no	—
165	D₄×C₄₇	C₂×C₂²⋊C₄	1	48	yes	—
166	C₂×C₄×C₄₇	—	2	48	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	6	no	—
169	C₂×C₄×C₄₇	—	2	6	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	48	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	6	no	—
174	C₂×C₄×C₄₇	—	2	6	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	6	no	—
177	C₂×C₄×C₄₇	—	2	6	no	—
178	C₂×C₄×C₄₇	—	2	12	no	—
179	C₂×C₄×C₄₇	—	4	24	no	—
180	C₂×C₄×C₄₇	—	8	12	no	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	48	yes	—
182	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
183	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	2₋¹⁺⁴	1	4	yes	complemented
190	#34259	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₇	—	2	12	no	—
192	C₂²×C₄₇	—	2	12	no	—
193	C₂²×C₄₇	—	2	6	no	—
194	C₂²×C₄₇	—	2	6	no	—
195	C₂²×C₄₇	—	2	4	no	—
196	C₂²×C₄₇	—	2	8	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	12	yes	—
201	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
202	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
205	C₂²×C₄₇	#585	1	2	yes	—
206	C₄×C₄₇	—	2	12	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	4	6	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	6	no	—
211	C₄×C₄₇	C₂²×C₂²⋊C₄	1	12	yes	—
212	C₄×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
213	C₂²×2₋¹⁺⁴	C₂×C₄₇	1	1	yes	characteristic
214	C₂×#520	C₂×C₄₇	1	1	yes	characteristic, complemented
215	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
216	Q₈×C₂²⋊C₄	C₂×C₄₇	1	4	yes	complemented
217	#2339	C₂×C₄₇	1	12	yes	complemented
218	#2311	C₂×C₄₇	1	3	yes	complemented
219	#2310	C₂×C₄₇	1	3	yes	complemented
220	#2297	C₂×C₄₇	1	3	yes	complemented
221	C₂×#391	C₂×C₄₇	1	3	yes	complemented
222	C₂×C₄₇	—	2	12	no	—
223	C₂×C₄₇	—	4	4	no	—
224	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄₇	C₄×2₋¹⁺⁴	1	2	yes	—
226	C₂×C₄₇	#3489	1	2	yes	—
227	C₂×C₄₇	#3499	1	1	yes	characteristic
228	C₂×C₄₇	#3500	1	1	yes	characteristic
229	C₂×2₋¹⁺⁴	—	2	8	no	—
230	C₂×2₋¹⁺⁴	—	2	8	no	—
231	C₂×2₋¹⁺⁴	C₄×C₄₇	1	16	yes	complemented
232	C₂²×#41	C₂²×C₄₇	1	3	yes	—
233	C₂²×#41	C₂²×C₄₇	1	6	yes	—
234	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
235	C₂³×Q₈	C₂²×C₄₇	1	3	yes	—
236	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
237	#520	—	2	8	no	—
238	C₄×#41	—	2	8	no	—
239	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
240	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₄₇	1	6	yes	—
242	C₂×C₄×D₄	C₂²×C₄₇	1	6	yes	—
243	C₂×#117	C₂²×C₄₇	1	3	yes	—
244	C₂×#117	C₂²×C₄₇	1	3	yes	—
245	C₂²×C₄⋊C₄	C₂²×C₄₇	1	3	yes	—
246	C₂²×C₄²	C₂²×C₄₇	1	3	yes	—
247	#391	C₂²×C₄₇	1	3	yes	—
248	#391	C₂²×C₄₇	1	6	yes	—
249	#391	C₂²×C₄₇	1	12	yes	—
250	#391	C₂²×C₄₇	1	12	yes	—
251	#391	C₂²×C₄₇	1	3	yes	—
252	#390	C₂²×C₄₇	1	3	yes	—
253	#390	C₂²×C₄₇	1	1	yes	characteristic
254	#386	C₂²×C₄₇	1	12	yes	—
255	#386	C₂²×C₄₇	1	12	yes	—
256	#381	C₂²×C₄₇	1	12	yes	—
257	#380	C₂²×C₄₇	1	12	yes	—
258	C₄×C₂²⋊C₄	C₂²×C₄₇	1	12	yes	—
259	C₂×#95	C₂²×C₄₇	1	12	yes	—
260	C₄₇	#34259	1	1	yes	characteristic, direct product factor, Sylow
261	2₋¹⁺⁴	—	2	128	no	—
262	C₂×#41	—	2	24	no	—
263	C₂×#41	—	2	24	no	—
264	C₂×#41	—	2	12	no	—
265	C₂×#41	—	2	12	no	—
266	C₂×#41	C₂×C₄×C₄₇	1	8	yes	—
267	C₂×#41	C₂×C₄×C₄₇	1	48	yes	complemented
268	C₂×#41	C₂×C₄×C₄₇	1	24	yes	complemented
269	C₂×#41	D₄×C₄₇	1	8	yes	—
270	C₂×#41	D₄×C₄₇	1	8	yes	—
271	C₂²×Q₈	—	2	8	no	—
272	C₂²×Q₈	—	2	8	no	—
273	C₂²×Q₈	—	2	12	no	—
274	C₂²×Q₈	—	2	12	no	—
275	C₂²×Q₈	C₂×C₄×C₄₇	1	16	yes	complemented
276	C₂²×Q₈	C₂×C₄×C₄₇	1	24	yes	complemented
277	C₂²×Q₈	C₂³×C₄₇	1	3	yes	—
278	C₂²×Q₈	C₂³×C₄₇	1	6	yes	—
279	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
280	C₂²×D₄	C₂³×C₄₇	1	6	yes	—
281	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₄₇	1	3	yes	—
283	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
284	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
285	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
286	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
287	C₂³×C₄	C₂³×C₄₇	1	3	yes	—
288	C₄×Q₈	—	2	8	no	—
289	C₄×Q₈	—	2	8	no	—
290	C₄×D₄	—	2	24	no	—
291	C₄×D₄	—	2	24	no	—
292	#117	—	2	12	no	—
293	#117	—	2	12	no	—
294	C₂×C₄⋊C₄	—	2	12	no	—
295	C₂×C₄⋊C₄	C₂³×C₄₇	1	3	yes	—
296	C₂×C₄⋊C₄	C₂³×C₄₇	1	6	yes	—
297	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₄₇	1	6	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₄₇	1	6	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₄₇	1	12	yes	—
303	C₂×C₄²	—	2	12	no	—
304	C₂×C₄²	C₂³×C₄₇	1	3	yes	—
305	C₂×C₄²	C₂³×C₄₇	1	6	yes	—
306	C₂×C₄²	C₂³×C₄₇	1	6	yes	—
307	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
308	#95	C₂³×C₄₇	1	12	yes	—
309	#95	C₂³×C₄₇	1	24	yes	—
310	#95	C₂³×C₄₇	1	12	yes	—
311	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
312	C₂⁴	C₂⁴×C₄₇	1	3	yes	—
313	#41	—	2	192	no	—
314	#41	—	2	96	no	—
315	#41	C₂²⋊C₄×C₄₇	1	64	yes	complemented
316	C₂×Q₈	—	2	64	no	—
317	C₂×Q₈	—	2	96	no	—
318	C₂×Q₈	—	2	6	no	—
319	C₂×Q₈	—	2	12	no	—
320	C₂×Q₈	—	2	12	no	—
321	C₂×Q₈	—	2	6	no	—
322	C₂×Q₈	C₂²×C₄×C₄₇	1	24	yes	—
323	C₂×Q₈	C₂²×C₄×C₄₇	1	12	yes	—
324	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
325	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
326	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
327	C₂×D₄	—	2	12	no	—
328	C₂×D₄	—	2	12	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	C₂²×C₄×C₄₇	1	24	yes	—
332	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
333	C₂×D₄	C₂²×C₄×C₄₇	1	12	yes	—
334	C₂×D₄	C₂×D₄×C₄₇	1	12	yes	—
335	C₂×D₄	C₂×D₄×C₄₇	1	12	yes	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	2	12	no	—
338	C₂²×C₄	—	2	12	no	—
339	C₂²×C₄	—	2	12	no	—
340	C₂²×C₄	—	2	12	no	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	2	12	no	—
343	C₂²×C₄	—	4	6	no	—
344	C₂²×C₄	—	4	12	no	—
345	C₂²×C₄	C₂²×C₄×C₄₇	1	24	yes	—
346	C₂²×C₄	C₂²×C₄×C₄₇	1	24	yes	—
347	C₂²×C₄	C₂²×C₄×C₄₇	1	12	yes	—
348	C₂²×C₄	C₂×D₄×C₄₇	1	12	yes	—
349	C₂²×C₄	C₂×D₄×C₄₇	1	12	yes	—
350	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₄₇	1	6	yes	—
352	C₂²×C₄	C₂⁴×C₄₇	1	6	yes	—
353	C₂²×C₄	C₂⁴×C₄₇	1	6	yes	—
354	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₄₇	1	3	yes	—
357	C₄⋊C₄	—	2	6	no	—
358	C₄⋊C₄	—	2	12	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	12	no	—
361	C₂²⋊C₄	—	2	12	no	—
362	C₂²⋊C₄	—	2	12	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	4	12	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	6	no	—
367	C₄²	—	2	12	no	—
368	C₄²	—	2	12	no	—
369	C₂³	—	2	6	no	—
370	C₂³	—	2	6	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	4	no	—
375	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
376	C₂³	C₂³×C₄×C₄₇	1	6	yes	—
377	C₂³	C₂²×D₄×C₄₇	1	6	yes	—
378	C₂³	C₂²×D₄×C₄₇	1	6	yes	—
379	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
380	Q₈	—	2	48	no	—
381	Q₈	—	2	24	no	—
382	Q₈	C₂×C₂²⋊C₄×C₄₇	1	16	yes	—
383	D₄	—	2	48	no	—
384	D₄	—	2	8	no	—
385	D₄	C₂×C₂²⋊C₄×C₄₇	1	48	yes	—
386	C₂×C₄	—	2	48	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	6	no	—
389	C₂×C₄	—	2	6	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	48	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	6	no	—
394	C₂×C₄	—	2	6	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	6	no	—
397	C₂×C₄	—	2	6	no	—
398	C₂×C₄	—	2	12	no	—
399	C₂×C₄	—	4	24	no	—
400	C₂×C₄	—	8	12	no	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	48	yes	—
402	C₂×C₄	C₂³×C₄×C₄₇	1	12	yes	—
403	C₂×C₄	C₂³×C₄×C₄₇	1	6	yes	—
404	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₄₇	1	6	yes	—
407	C₂×C₄	C₂²×D₄×C₄₇	1	6	yes	—
408	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
409	C₂×C₄	2₋¹⁺⁴×C₄₇	1	4	yes	complemented
410	C₂²	—	2	12	no	—
411	C₂²	—	2	12	no	—
412	C₂²	—	2	6	no	—
413	C₂²	—	2	6	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	8	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	12	yes	—
420	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
421	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
422	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
423	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
424	C₂²	C₄₇×#585	1	2	yes	—
425	C₄	—	2	12	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	6	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	6	no	—
430	C₄	C₂²×C₂²⋊C₄×C₄₇	1	12	yes	—
431	C₄	C₂²×C₂²⋊C₄×C₄₇	1	4	yes	—
432	C₂	—	2	12	no	—
433	C₂	—	4	4	no	—
434	C₂	C₂³×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
435	C₂	C₄×2₋¹⁺⁴×C₄₇	1	2	yes	—
436	C₂	C₄₇×#3489	1	2	yes	—
437	C₂	C₄₇×#3499	1	1	yes	characteristic
438	C₂	C₄₇×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂²×2₋¹⁺⁴×C₄₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#520	C₂	semidirect
3. C₂×C₄×#41×C₄₇	C₂	semidirect
4. Q₈×C₂²⋊C₄×C₄₇	C₂	semidirect
5. C₄₇×#2339	C₂	semidirect
6. C₄₇×#2311	C₂	semidirect
7. C₄₇×#2310	C₂	semidirect
8. C₄₇×#2297	C₂	semidirect
9. C₂×C₄₇×#391	C₂	semidirect
12. C₂×2₋¹⁺⁴×C₄₇	C₄	semidirect
47. C₂×#41×C₄₇	C₂×C₄	semidirect
48. C₂×#41×C₄₇	C₂×C₄	semidirect
55. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
56. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
95. #41×C₄₇	C₂²⋊C₄	semidirect
189. C₂×C₄×C₄₇	2₋¹⁺⁴	semidirect
190. #34259	C₄₇	direct (N × H)
214. C₂×#520	C₂×C₄₇	semidirect
215. C₂×C₄×#41	C₂×C₄₇	semidirect
216. Q₈×C₂²⋊C₄	C₂×C₄₇	semidirect
217. #2339	C₂×C₄₇	semidirect
218. #2311	C₂×C₄₇	semidirect
219. #2310	C₂×C₄₇	semidirect
220. #2297	C₂×C₄₇	semidirect
221. C₂×#391	C₂×C₄₇	semidirect
231. C₂×2₋¹⁺⁴	C₄×C₄₇	semidirect
260. C₄₇	#34259	direct (N × H)
267. C₂×#41	C₂×C₄×C₄₇	semidirect
268. C₂×#41	C₂×C₄×C₄₇	semidirect
275. C₂²×Q₈	C₂×C₄×C₄₇	semidirect
276. C₂²×Q₈	C₂×C₄×C₄₇	semidirect
315. #41	C₂²⋊C₄×C₄₇	semidirect
409. C₂×C₄	2₋¹⁺⁴×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₄₇	2
C₂×C₄₇×#520	2
C₂×C₄×#41×C₄₇	2
Q₈×C₂²⋊C₄×C₄₇	2
C₄₇×#2339	2
C₄₇×#2311	2
C₄₇×#2310	2
C₄₇×#2297	2
C₂×C₄₇×#391	2
#34259	47

Subgroups — C47×#34259 #26073957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#34259 #26073957