Subgroups — C₄₇×#25719 #26065417

Order 12032.

1598 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#452	C₂	1	4	yes	maximal, complemented
5	C₄₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2015	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₇	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₄₇	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₄₇	C₂²	1	4	yes	—
13	C₄₇×#532	—	2	4	no	—
14	C₄₇×#532	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
20	C₂×#121×C₄₇	—	2	2	no	—
21	C₂×C₄×D₄×C₄₇	—	2	2	no	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#494	—	2	4	no	—
24	C₄₇×#492	—	2	4	no	—
25	C₄₇×#452	—	2	16	no	—
26	C₂×#103×C₄₇	C₂²	1	4	yes	—
27	C₂×#102×C₄₇	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#391	C₂²	1	2	yes	—
32	C₄₇×#389	—	2	2	no	—
33	C₄₇×#384	C₂²	1	1	yes	characteristic
34	C₄₇×#380	—	2	2	no	—
35	C₄₇×#336	C₂²	1	2	yes	—
36	C₂×#41×C₄₇	—	2	4	no	—
37	C₂×#41×C₄₇	—	2	4	no	—
38	C₂×#41×C₄₇	—	2	8	no	—
39	C₂×#41×C₄₇	—	4	4	no	—
40	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
41	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	—	2	2	no	—
44	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	D₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₄₇	—	2	8	no	—
49	C₂×Q₁₆×C₄₇	—	2	8	no	—
50	C₂×Q₁₆×C₄₇	—	4	4	no	—
51	C₂×SD₁₆×C₄₇	—	2	8	no	—
52	C₂×SD₁₆×C₄₇	—	2	8	no	—
53	C₂×SD₁₆×C₄₇	—	4	4	no	—
54	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₄₇	—	2	2	no	—
57	C₄⋊Q₈×C₄₇	—	2	2	no	—
58	C₄⋊Q₈×C₄₇	—	2	2	no	—
59	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
60	#127×C₄₇	—	2	2	no	—
61	#127×C₄₇	D₄	1	4	yes	—
62	#124×C₄₇	—	2	4	no	—
63	#124×C₄₇	—	2	4	no	—
64	C₂²⋊Q₈×C₄₇	—	2	8	no	—
65	#121×C₄₇	—	2	16	no	—
66	C₄×D₄×C₄₇	—	2	16	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	D₄	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#103×C₄₇	—	2	8	no	—
80	#102×C₄₇	—	2	8	no	—
81	C₂²⋊C₈×C₄₇	D₄	1	8	yes	complemented
82	C₄×C₈×C₄₇	—	2	2	no	—
83	C₄×C₈×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	#41×C₄₇	—	4	16	no	—
88	#41×C₄₇	—	4	16	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	4	no	—
91	C₂×Q₈×C₄₇	—	2	4	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	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	8	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	—	4	4	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	8	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	4	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
118	C₂²×C₄×C₄₇	—	4	4	no	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₄₇	—	4	16	no	—
125	SD₁₆×C₄₇	—	4	16	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₄₇	—	2	8	no	—
133	C₄⋊C₄×C₄₇	—	2	4	no	—
134	C₄⋊C₄×C₄₇	—	4	4	no	—
135	C₄⋊C₄×C₄₇	—	4	4	no	—
136	C₄⋊C₄×C₄₇	—	4	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	16	no	—
138	C₂²⋊C₄×C₄₇	—	4	4	no	—
139	C₄²×C₄₇	—	2	4	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	C₂×D₄	1	2	yes	—
143	C₄²×C₄₇	C₂×D₄	1	2	yes	—
144	C₂³×C₄₇	—	2	1	no	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	4	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	4	4	no	—
152	C₂³×C₄₇	—	4	4	no	—
153	C₂³×C₄₇	#127	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₇	—	2	8	no	—
156	Q₈×C₄₇	—	4	4	no	—
157	Q₈×C₄₇	—	4	4	no	—
158	Q₈×C₄₇	—	4	4	no	—
159	D₄×C₄₇	—	2	8	no	—
160	D₄×C₄₇	—	4	16	no	—
161	D₄×C₄₇	—	4	4	no	—
162	D₄×C₄₇	—	4	16	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	16	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	8	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	#120	1	4	yes	—
181	C₂×C₄×C₄₇	#127	1	2	yes	—
182	C₂×C₄×C₄₇	#135	1	4	yes	—
183	C₂×C₄×C₄₇	#137	1	4	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
188	C₈×C₄₇	—	2	4	no	—
189	C₈×C₄₇	—	2	4	no	—
190	#25719	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	4	no	—
197	C₂²×C₄₇	—	4	8	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	—	8	4	no	—
201	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
203	C₂²×C₄₇	#535	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#135	1	2	yes	—
205	C₂²×C₄₇	C₂×#137	1	2	yes	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	—	8	2	no	—
211	C₄×C₄₇	#452	1	8	yes	complemented
212	C₄×C₄₇	D₄²	1	2	yes	—
213	C₄×C₄₇	D₄²	1	2	yes	—
214	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
215	C₂×#494	C₂×C₄₇	1	1	yes	characteristic, complemented
216	C₂×#492	C₂×C₄₇	1	1	yes	characteristic, complemented
217	C₂×#452	C₂×C₄₇	1	4	yes	complemented
218	#2857	C₂×C₄₇	1	1	yes	characteristic, complemented
219	#2015	C₂×C₄₇	1	4	yes	complemented
220	#1957	C₂×C₄₇	1	1	yes	characteristic, complemented
221	#1956	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₄×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
223	C₂×C₄₇	—	4	2	no	—
224	C₂×C₄₇	—	8	4	no	—
225	C₂×C₄₇	#2433	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#452	1	2	yes	—
227	C₂×C₄₇	#3147	1	1	yes	characteristic
228	C₂×C₄₇	#3152	1	1	yes	characteristic
229	C₂×C₄₇	#3210	1	2	yes	—
230	C₂²×#41	C₂²×C₄₇	1	2	yes	—
231	C₂²×Q₁₆	C₂²×C₄₇	1	4	yes	—
232	C₂²×SD₁₆	C₂²×C₄₇	1	4	yes	—
233	#532	—	2	4	no	—
234	#532	—	2	4	no	—
235	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
237	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
238	C₂×#124	C₂²×C₄₇	1	2	yes	—
239	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
240	C₂×#121	—	2	2	no	—
241	C₂×C₄×D₄	—	2	2	no	—
242	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
243	#494	—	2	4	no	—
244	#492	—	2	4	no	—
245	#452	—	2	16	no	—
246	C₂×#103	C₂²×C₄₇	1	4	yes	—
247	C₂×#102	C₂²×C₄₇	1	4	yes	—
248	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
251	#391	C₂²×C₄₇	1	2	yes	—
252	#389	—	2	2	no	—
253	#384	C₂²×C₄₇	1	1	yes	characteristic
254	#380	—	2	2	no	—
255	#336	C₂²×C₄₇	1	2	yes	—
256	C₄₇	#25719	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	—	4	4	no	—
261	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
262	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	D₄×C₄₇	1	2	yes	—
268	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
269	C₂×Q₁₆	—	2	8	no	—
270	C₂×Q₁₆	—	2	8	no	—
271	C₂×Q₁₆	—	4	4	no	—
272	C₂×SD₁₆	—	2	8	no	—
273	C₂×SD₁₆	—	2	8	no	—
274	C₂×SD₁₆	—	4	4	no	—
275	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
281	#127	—	2	2	no	—
282	#127	D₄×C₄₇	1	4	yes	—
283	#124	—	2	4	no	—
284	#124	—	2	4	no	—
285	C₂²⋊Q₈	—	2	8	no	—
286	#121	—	2	16	no	—
287	C₄×D₄	—	2	16	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	D₄×C₄₇	1	2	yes	—
298	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
300	#103	—	2	8	no	—
301	#102	—	2	8	no	—
302	C₂²⋊C₈	D₄×C₄₇	1	8	yes	complemented
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	4	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
308	#41	—	4	16	no	—
309	#41	—	4	16	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
345	Q₁₆	—	4	16	no	—
346	SD₁₆	—	4	16	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
352	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	2	16	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	C₂×D₄×C₄₇	1	2	yes	—
364	C₄²	C₂×D₄×C₄₇	1	2	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	#127×C₄₇	1	2	yes	—
375	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
376	Q₈	—	2	8	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	4	no	—
379	Q₈	—	4	4	no	—
380	D₄	—	2	8	no	—
381	D₄	—	4	16	no	—
382	D₄	—	4	16	no	—
383	D₄	—	4	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	16	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	#120×C₄₇	1	4	yes	—
402	C₂×C₄	#127×C₄₇	1	2	yes	—
403	C₂×C₄	#135×C₄₇	1	4	yes	—
404	C₂×C₄	#137×C₄₇	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
408	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
409	C₈	—	2	4	no	—
410	C₈	—	2	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	4	no	—
421	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
422	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
423	C₂²	C₄₇×#535	1	1	yes	characteristic
424	C₂²	C₂×#135×C₄₇	1	2	yes	—
425	C₂²	C₂×#137×C₄₇	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₄₇×#452	1	8	yes	complemented
432	C₄	D₄²×C₄₇	1	2	yes	—
433	C₄	D₄²×C₄₇	1	2	yes	—
434	C₂	—	4	2	no	—
435	C₂	—	8	4	no	—
436	C₂	C₄₇×#2433	1	1	yes	characteristic
437	C₂	C₂×C₄₇×#452	1	2	yes	—
438	C₂	C₄₇×#3147	1	1	yes	characteristic
439	C₂	C₄₇×#3152	1	1	yes	characteristic
440	C₂	C₄₇×#3210	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#494	C₂	semidirect
3. C₂×C₄₇×#492	C₂	semidirect
4. C₂×C₄₇×#452	C₂	semidirect
5. C₄₇×#2857	C₂	semidirect
6. C₄₇×#2015	C₂	semidirect
7. C₄₇×#1957	C₂	semidirect
8. C₄₇×#1956	C₂	semidirect
9. C₄×C₂²⋊C₈×C₄₇	C₂	semidirect
81. C₂²⋊C₈×C₄₇	D₄	semidirect
190. #25719	C₄₇	direct (N × H)
211. C₄×C₄₇	#452	semidirect
215. C₂×#494	C₂×C₄₇	semidirect
216. C₂×#492	C₂×C₄₇	semidirect
217. C₂×#452	C₂×C₄₇	semidirect
218. #2857	C₂×C₄₇	semidirect
219. #2015	C₂×C₄₇	semidirect
220. #1957	C₂×C₄₇	semidirect
221. #1956	C₂×C₄₇	semidirect
222. C₄×C₂²⋊C₈	C₂×C₄₇	semidirect
256. C₄₇	#25719	direct (N × H)
302. C₂²⋊C₈	D₄×C₄₇	semidirect
431. C₄	C₄₇×#452	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×#494	2
C₂×C₄₇×#492	2
C₂×C₄₇×#452	2
C₄₇×#2857	2
C₄₇×#2015	2
C₄₇×#1957	2
C₄₇×#1956	2
C₄×C₂²⋊C₈×C₄₇	2
#25719	47

Subgroups — C47×#25719 #26065417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25719 #26065417