Subgroups — C₄₇×#25568 #26065266

Order 12032.

1190 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#555	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2000	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1873	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
11	C₄₇×#555	—	2	4	no	—
12	C₄₇×#555	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	—
17	C₂×#121×C₄₇	—	2	1	no	—
18	C₂×#121×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₇	—	2	1	no	—
22	C₂×#117×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#487	—	2	4	no	—
24	C₄₇×#461	—	2	4	no	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₇	C₂²	1	2	yes	—
27	C₂×#103×C₄₇	C₂²	1	4	yes	—
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#399	—	2	2	no	—
32	C₄₇×#390	—	2	1	no	—
33	C₄₇×#384	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#340	C₂²	1	2	yes	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₇	—	2	1	no	—
38	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂×SD₁₆×C₄₇	—	2	4	no	—
45	C₂×SD₁₆×C₄₇	—	4	4	no	—
46	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₄₇	—	2	2	no	—
49	C₄⋊Q₈×C₄₇	—	2	2	no	—
50	C₄⋊Q₈×C₄₇	—	2	2	no	—
51	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
52	#124×C₄₇	—	2	16	no	—
53	C₂²⋊Q₈×C₄₇	—	2	8	no	—
54	C₂²⋊Q₈×C₄₇	—	4	4	no	—
55	#121×C₄₇	—	2	8	no	—
56	#121×C₄₇	—	2	4	no	—
57	#121×C₄₇	—	2	4	no	—
58	C₄×D₄×C₄₇	—	2	2	no	—
59	C₄×D₄×C₄₇	—	2	2	no	—
60	C₄×D₄×C₄₇	—	2	2	no	—
61	C₄×D₄×C₄₇	D₄	1	4	yes	—
62	#117×C₄₇	—	2	8	no	—
63	#117×C₄₇	—	2	4	no	—
64	#117×C₄₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	—	2	2	no	—
82	#103×C₄₇	—	2	4	no	—
83	#103×C₄₇	—	2	8	no	—
84	#102×C₄₇	—	2	4	no	—
85	C₂²⋊C₈×C₄₇	—	4	4	no	—
86	C₄×C₈×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	—	2	1	no	—
89	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₄₇	—	2	4	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	4	no	—
94	C₂×Q₈×C₄₇	—	2	4	no	—
95	C₂×Q₈×C₄₇	—	8	2	no	—
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	8	4	no	—
104	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	SD₁₆×C₄₇	—	4	8	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	8	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄⋊C₄×C₄₇	—	4	2	no	—
134	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₄₇	#41	1	4	yes	—
137	C₂²⋊C₄×C₄₇	—	2	8	no	—
138	C₂²⋊C₄×C₄₇	—	2	8	no	—
139	C₂²⋊C₄×C₄₇	—	2	4	no	—
140	C₂²⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	4	8	no	—
142	C₄²×C₄₇	—	2	8	no	—
143	C₄²×C₄₇	—	4	2	no	—
144	C₄²×C₄₇	C₂×D₄	1	2	yes	—
145	C₄²×C₄₇	C₂×D₄	1	2	yes	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	4	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₄₇	—	4	2	no	—
158	Q₈×C₄₇	—	4	2	no	—
159	Q₈×C₄₇	—	4	4	no	—
160	Q₈×C₄₇	—	8	4	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	8	8	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	4	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	—	4	8	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	#120	1	2	yes	—
184	C₂×C₄×C₄₇	#120	1	2	yes	—
185	C₂×C₄×C₄₇	#135	1	2	yes	—
186	C₂×C₄×C₄₇	#137	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
190	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	—	4	2	no	—
193	#25568	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	8	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
205	C₂²×C₄₇	#546	1	2	yes	—
206	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₇	#577	1	2	yes	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	#452	1	4	yes	—
216	C₄×C₄₇	#532	1	1	yes	characteristic
217	C₄×C₄₇	#535	1	1	yes	characteristic
218	C₄×C₄₇	#550	1	2	yes	—
219	C₂×#555	C₂×C₄₇	1	1	yes	characteristic
220	C₂×#487	C₂×C₄₇	1	1	yes	characteristic, complemented
221	C₂×#461	C₂×C₄₇	1	1	yes	characteristic, complemented
222	#2542	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#2000	C₂×C₄₇	1	4	yes	complemented
224	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1954	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#1873	C₂×C₄₇	1	4	yes	complemented
227	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	8	2	no	—
229	C₂×C₄₇	—	8	2	no	—
230	C₂×C₄₇	#2431	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
232	C₂×C₄₇	#3009	1	1	yes	characteristic
233	C₂×C₄₇	#3303	1	2	yes	—
234	C₂×C₄₇	#3329	1	2	yes	—
235	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
236	#555	—	2	4	no	—
237	#555	—	2	4	no	—
238	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
240	C₂×#124	—	2	2	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	4	yes	—
242	C₂×#121	—	2	1	no	—
243	C₂×#121	C₂²×C₄₇	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₂×#117	—	2	1	no	—
247	C₂×#117	C₂²×C₄₇	1	2	yes	—
248	#487	—	2	4	no	—
249	#461	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#103	C₂²×C₄₇	1	4	yes	—
252	C₂×#103	C₂²×C₄₇	1	2	yes	—
253	C₂×#102	C₂²×C₄₇	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
255	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
256	#399	—	2	2	no	—
257	#390	—	2	1	no	—
258	#384	—	2	1	no	—
259	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
260	#340	C₂²×C₄₇	1	2	yes	—
261	#340	C₂²×C₄₇	1	4	yes	—
262	C₄₇	#25568	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	4	4	no	—
272	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
273	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
278	#124	—	2	16	no	—
279	C₂²⋊Q₈	—	2	8	no	—
280	C₂²⋊Q₈	—	4	4	no	—
281	#121	—	2	8	no	—
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	D₄×C₄₇	1	4	yes	—
288	#117	—	2	8	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	2	4	no	—
309	#103	—	2	8	no	—
310	#102	—	2	4	no	—
311	C₂²⋊C₈	—	4	4	no	—
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	1	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	8	4	no	—
330	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
346	SD₁₆	—	4	8	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	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	8	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
361	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
362	C₄⋊C₄	#41×C₄₇	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	8	no	—
368	C₄²	—	2	8	no	—
369	C₄²	—	4	2	no	—
370	C₄²	C₂×D₄×C₄₇	1	2	yes	—
371	C₄²	C₂×D₄×C₄₇	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	8	4	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	#120×C₄₇	1	2	yes	—
410	C₂×C₄	#120×C₄₇	1	2	yes	—
411	C₂×C₄	#135×C₄₇	1	2	yes	—
412	C₂×C₄	#137×C₄₇	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
416	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
430	C₂²	C₄₇×#546	1	2	yes	—
431	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
432	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
433	C₂²	C₄₇×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	8	2	no	—
440	C₄	C₄₇×#452	1	4	yes	—
441	C₄	C₄₇×#532	1	1	yes	characteristic
442	C₄	C₄₇×#535	1	1	yes	characteristic
443	C₄	C₄₇×#550	1	2	yes	—
444	C₂	—	8	2	no	—
445	C₂	—	8	2	no	—
446	C₂	C₄₇×#2431	1	1	yes	characteristic
447	C₂	C₂×C₄₇×#452	1	1	yes	characteristic
448	C₂	C₄₇×#3009	1	1	yes	characteristic
449	C₂	C₄₇×#3303	1	2	yes	—
450	C₂	C₄₇×#3329	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#555	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#487	C₂	semidirect
3. C₂×C₄₇×#461	C₂	semidirect
4. C₄₇×#2542	C₂	semidirect
5. C₄₇×#2000	C₂	semidirect
6. C₄₇×#1987	C₂	semidirect
7. C₄₇×#1954	C₂	semidirect
8. C₄₇×#1873	C₂	semidirect
9. C₄×#102×C₄₇	C₂	semidirect
193. #25568	C₄₇	direct (N × H)
220. C₂×#487	C₂×C₄₇	semidirect
221. C₂×#461	C₂×C₄₇	semidirect
222. #2542	C₂×C₄₇	semidirect
223. #2000	C₂×C₄₇	semidirect
224. #1987	C₂×C₄₇	semidirect
225. #1954	C₂×C₄₇	semidirect
226. #1873	C₂×C₄₇	semidirect
227. C₄×#102	C₂×C₄₇	semidirect
262. C₄₇	#25568	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×#555	2
C₂×C₄₇×#487	2
C₂×C₄₇×#461	2
C₄₇×#2542	2
C₄₇×#2000	2
C₄₇×#1987	2
C₄₇×#1954	2
C₄₇×#1873	2
C₄×#102×C₄₇	2
#25568	47

Subgroups — C47×#25568 #26065266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25568 #26065266