Subgroups — C₄₇×#14340 #26054038

Order 12032.

1926 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#380	C₂	1	2	yes	maximal
5	C₄₇×#1441	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1439	C₂	1	4	yes	maximal
7	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×#117×C₄₇	—	2	4	no	—
10	C₂×#117×C₄₇	—	2	4	no	—
11	C₂×#117×C₄₇	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#384	—	2	4	no	—
21	C₄₇×#382	—	2	4	no	—
22	C₄₇×#380	—	2	8	no	—
23	C₂×#95×C₄₇	C₂²	1	4	yes	—
24	C₂×#95×C₄₇	C₂²	1	4	yes	—
25	C₂×#95×C₄₇	C₂²	1	8	yes	—
26	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	—	2	2	no	—
28	C₂³×C₄×C₄₇	—	2	2	no	—
29	C₂³×C₄×C₄₇	—	2	2	no	—
30	C₂³×C₄×C₄₇	—	2	2	no	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₄₇	D₄	1	4	yes	—
33	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	#117×C₄₇	—	2	32	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₇	—	4	8	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
56	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₄₇	D₄	1	4	yes	—
62	C₂×C₄²×C₄₇	D₄	1	4	yes	—
63	#95×C₄₇	—	2	8	no	—
64	#95×C₄₇	—	2	8	no	—
65	#95×C₄₇	—	4	8	no	—
66	C₂⁴×C₄₇	—	2	1	no	—
67	C₂⁴×C₄₇	—	2	1	no	—
68	C₂⁴×C₄₇	—	2	1	no	—
69	C₂⁴×C₄₇	—	2	1	no	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
75	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	1	no	—
78	C₂²×C₄×C₄₇	—	2	1	no	—
79	C₂²×C₄×C₄₇	—	2	1	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	8	no	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	—	2	8	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	—	2	8	no	—
102	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	complemented
103	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×C₄×C₄₇	#41	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	16	no	—
118	C₄⋊C₄×C₄₇	—	4	16	no	—
119	C₄⋊C₄×C₄₇	—	4	8	no	—
120	C₄⋊C₄×C₄₇	—	4	8	no	—
121	C₂²⋊C₄×C₄₇	—	2	16	no	—
122	C₂²⋊C₄×C₄₇	—	4	16	no	—
123	C₄²×C₄₇	—	2	8	no	—
124	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	complemented
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	2	8	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
142	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
150	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	32	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	8	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	—	4	4	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	8	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	8	no	—
175	C₂×C₄×C₄₇	—	4	8	no	—
176	C₂×C₄×C₄₇	—	4	8	no	—
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
181	C₂×C₄×C₄₇	#117	1	4	yes	—
182	C₂×C₄×C₄₇	#121	1	4	yes	—
183	C₂×C₄×C₄₇	#121	1	4	yes	—
184	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
185	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
186	#14340	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
199	C₂²×C₄₇	#520	1	4	yes	—
200	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×C₄₇	#535	1	2	yes	—
205	C₂²×C₄₇	#535	1	2	yes	—
206	C₂²×C₄₇	#536	1	2	yes	—
207	C₂²×C₄₇	#536	1	2	yes	—
208	C₂²×C₄₇	#537	1	4	yes	—
209	C₂²×C₄₇	#540	1	2	yes	—
210	C₂²×C₄₇	#541	1	2	yes	—
211	C₂²×C₄₇	#542	1	4	yes	—
212	C₂²×C₄₇	#544	1	4	yes	—
213	C₄×C₄₇	—	2	8	no	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	4	4	no	—
216	C₄×C₄₇	—	8	4	no	—
217	C₄×C₄₇	—	8	4	no	—
218	C₄×C₄₇	#380	1	8	yes	—
219	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
220	C₂×#384	C₂×C₄₇	1	1	yes	characteristic, complemented
221	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₂×#380	C₂×C₄₇	1	2	yes	—
223	#1441	C₂×C₄₇	1	4	yes	complemented
224	#1439	C₂×C₄₇	1	4	yes	—
225	C₄⋊#95	C₂×C₄₇	1	2	yes	complemented
226	C₂×C₄₇	—	4	4	no	—
227	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
228	C₂×C₄₇	#2311	1	2	yes	—
229	C₂×C₄₇	#2314	1	2	yes	—
230	C₂×C₄₇	#2317	1	2	yes	—
231	C₂×C₄₇	#2619	1	1	yes	characteristic
232	C₂×C₄₇	#2620	1	2	yes	—
233	C₂×C₄₇	#2621	1	1	yes	characteristic
234	C₂×C₄₇	#2628	1	2	yes	—
235	C₂×C₄₇	#2629	1	2	yes	—
236	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
237	C₂×#117	—	2	4	no	—
238	C₂×#117	—	2	4	no	—
239	C₂×#117	C₄×C₄₇	1	8	yes	complemented
240	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
242	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
246	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
248	#384	—	2	4	no	—
249	#382	—	2	4	no	—
250	#380	—	2	8	no	—
251	C₂×#95	C₂²×C₄₇	1	4	yes	—
252	C₂×#95	C₂²×C₄₇	1	4	yes	—
253	C₂×#95	C₂²×C₄₇	1	8	yes	—
254	C₄₇	#14340	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	2	2	no	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
261	C₂³×C₄	D₄×C₄₇	1	4	yes	—
262	C₂³×C₄	Q₈×C₄₇	1	4	yes	—
263	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
264	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
265	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
266	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
267	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
269	#117	—	2	32	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	4	8	no	—
280	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	4	8	no	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
289	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
290	C₂×C₄²	D₄×C₄₇	1	4	yes	—
291	C₂×C₄²	D₄×C₄₇	1	4	yes	—
292	#95	—	2	8	no	—
293	#95	—	2	8	no	—
294	#95	—	4	8	no	—
295	C₂⁴	—	2	1	no	—
296	C₂⁴	—	2	1	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
302	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
303	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
304	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	C₄⋊C₄×C₄₇	1	16	yes	complemented
332	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
337	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
342	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
343	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
344	C₂²×C₄	#41×C₄₇	1	2	yes	—
345	C₂²×C₄	#41×C₄₇	1	2	yes	—
346	C₄⋊C₄	—	2	16	no	—
347	C₄⋊C₄	—	4	16	no	—
348	C₄⋊C₄	—	4	8	no	—
349	C₄⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	—	4	16	no	—
352	C₄²	—	2	8	no	—
353	C₄²	C₂²⋊C₄×C₄₇	1	16	yes	complemented
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	4	no	—
370	C₂³	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
371	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
372	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
373	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
375	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
376	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
377	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
378	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
379	C₂³	2₋¹⁺⁴×C₄₇	1	4	yes	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	32	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
408	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
409	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
410	C₂×C₄	#117×C₄₇	1	4	yes	—
411	C₂×C₄	#121×C₄₇	1	4	yes	—
412	C₂×C₄	#121×C₄₇	1	4	yes	—
413	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
414	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
425	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
426	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
427	C₂²	C₄₇×#520	1	4	yes	—
428	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
429	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
430	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
431	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
432	C₂²	C₄₇×#535	1	2	yes	—
433	C₂²	C₄₇×#535	1	2	yes	—
434	C₂²	C₄₇×#536	1	2	yes	—
435	C₂²	C₄₇×#536	1	2	yes	—
436	C₂²	C₄₇×#537	1	4	yes	—
437	C₂²	C₄₇×#540	1	2	yes	—
438	C₂²	C₄₇×#541	1	2	yes	—
439	C₂²	C₄₇×#542	1	4	yes	—
440	C₂²	C₄₇×#544	1	4	yes	—
441	C₄	—	2	4	no	—
442	C₄	—	2	8	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	4	no	—
445	C₄	—	8	4	no	—
446	C₄	C₄₇×#380	1	8	yes	—
447	C₂	—	4	4	no	—
448	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
449	C₂	C₄₇×#2311	1	2	yes	—
450	C₂	C₄₇×#2314	1	2	yes	—
451	C₂	C₄₇×#2317	1	2	yes	—
452	C₂	C₄₇×#2619	1	1	yes	characteristic
453	C₂	C₄₇×#2620	1	2	yes	—
454	C₂	C₄₇×#2621	1	1	yes	characteristic
455	C₂	C₄₇×#2628	1	2	yes	—
456	C₂	C₄₇×#2629	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#384	C₂	semidirect
3. C₂×C₄₇×#382	C₂	semidirect
5. C₄₇×#1441	C₂	semidirect
7. C₄₇×C₄⋊#95	C₂	semidirect
11. C₂×#117×C₄₇	C₄	semidirect
102. C₂²×C₄×C₄₇	C₄⋊C₄	semidirect
124. C₄²×C₄₇	C₂²⋊C₄	semidirect
186. #14340	C₄₇	direct (N × H)
220. C₂×#384	C₂×C₄₇	semidirect
221. C₂×#382	C₂×C₄₇	semidirect
223. #1441	C₂×C₄₇	semidirect
225. C₄⋊#95	C₂×C₄₇	semidirect
239. C₂×#117	C₄×C₄₇	semidirect
254. C₄₇	#14340	direct (N × H)
331. C₂²×C₄	C₄⋊C₄×C₄₇	semidirect
353. C₄²	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₇	2
C₂×C₄₇×#384	2
C₂×C₄₇×#382	2
C₂×C₄₇×#380	2
C₄₇×#1441	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
#14340	47

Subgroups — C47×#14340 #26054038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#14340 #26054038