Subgroups — C₄₇×#18302 #26058000

Order 12032.

1032 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3208	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2619	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1599	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1596	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1518	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#544	—	2	2	no	—
9	C₄₇×#544	—	2	2	no	—
10	C₄₇×#544	—	2	1	no	—
11	C₄₇×#544	C₂²	1	2	yes	—
12	C₄₇×#543	—	2	1	no	—
13	C₄₇×#543	C₂²	1	2	yes	—
14	C₄₇×#533	—	2	4	no	—
15	C₄₇×#533	—	2	1	no	—
16	C₄₇×#533	C₂²	1	2	yes	—
17	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₇	—	2	1	no	—
19	C₂×#117×C₄₇	—	2	1	no	—
20	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#492	—	2	2	no	—
22	C₄₇×#486	—	2	2	no	—
23	C₄₇×#460	—	2	4	no	—
24	C₄₇×#450	C₂²	1	8	yes	—
25	C₄₇×#431	C₂²	1	2	yes	—
26	C₄₇×#394	—	2	1	no	—
27	C₄₇×#394	C₂²	1	2	yes	—
28	C₄₇×#392	—	2	1	no	—
29	C₄₇×#392	C₂²	1	2	yes	—
30	C₄₇×#390	—	2	1	no	—
31	C₄₇×#382	C₂²	1	1	yes	characteristic
32	C₄₇×#328	C₂²	1	8	yes	—
33	C₄₇×#324	C₂²	1	2	yes	—
34	C₄₇×#323	C₂²	1	2	yes	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	1	no	—
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂×SD₁₆×C₄₇	—	2	8	no	—
41	C₄⋊Q₈×C₄₇	—	2	4	no	—
42	C₄⋊Q₈×C₄₇	—	2	1	no	—
43	C₄⋊Q₈×C₄₇	—	2	1	no	—
44	C₄⋊Q₈×C₄₇	—	2	4	no	—
45	C₄⋊Q₈×C₄₇	D₄	1	2	yes	complemented
46	C₄⋊Q₈×C₄₇	D₄	1	2	yes	complemented
47	#127×C₄₇	—	2	2	no	—
48	#127×C₄₇	—	2	2	no	—
49	#125×C₄₇	—	2	4	no	—
50	#125×C₄₇	—	2	2	no	—
51	#125×C₄₇	—	2	4	no	—
52	#125×C₄₇	—	2	2	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	4	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	2	2	no	—
57	C₂²⋊Q₈×C₄₇	—	2	2	no	—
58	C₂²⋊Q₈×C₄₇	—	2	2	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
61	#121×C₄₇	—	4	4	no	—
62	C₄×Q₈×C₄₇	—	2	2	no	—
63	C₄×Q₈×C₄₇	—	2	2	no	—
64	C₄×Q₈×C₄₇	—	2	2	no	—
65	C₄×Q₈×C₄₇	D₄	1	4	yes	complemented
66	#117×C₄₇	—	2	2	no	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	2	no	—
69	#117×C₄₇	—	2	2	no	—
70	#117×C₄₇	—	2	2	no	—
71	#117×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	#102×C₄₇	—	2	8	no	—
88	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
89	C₄×C₈×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	1	no	—
91	#95×C₄₇	C₂³	1	2	yes	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	4	4	no	—
100	C₂×D₄×C₄₇	—	4	2	no	—
101	C₂×D₄×C₄₇	—	4	1	no	—
102	C₂×D₄×C₄₇	—	4	1	no	—
103	C₂×D₄×C₄₇	—	4	2	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	8	2	no	—
106	C₂×D₄×C₄₇	—	8	2	no	—
107	C₂×D₄×C₄₇	—	8	2	no	—
108	C₂×D₄×C₄₇	—	8	2	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	complemented
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₄₇	—	8	8	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	4	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	4	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	4	2	no	—
138	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
139	C₂²⋊C₄×C₄₇	—	2	4	no	—
140	C₂²⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	2	2	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₂²⋊C₄×C₄₇	—	4	4	no	—
144	C₂²⋊C₄×C₄₇	—	8	2	no	—
145	C₂²⋊C₄×C₄₇	—	8	2	no	—
146	C₄²×C₄₇	—	2	4	no	—
147	C₄²×C₄₇	—	2	4	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	C₂×D₄	1	2	yes	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
164	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₇	—	4	4	no	—
166	Q₈×C₄₇	—	8	2	no	—
167	Q₈×C₄₇	—	8	2	no	—
168	Q₈×C₄₇	—	8	2	no	—
169	D₄×C₄₇	—	4	8	no	—
170	D₄×C₄₇	—	8	4	no	—
171	D₄×C₄₇	—	8	8	no	—
172	D₄×C₄₇	—	8	2	no	—
173	D₄×C₄₇	—	8	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	8	2	no	—
190	C₂×C₄×C₄₇	—	8	2	no	—
191	C₂×C₄×C₄₇	#120	1	2	yes	—
192	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
193	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
196	C₂×C₄×C₄₇	#137	1	2	yes	—
197	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
198	C₈×C₄₇	—	4	4	no	—
199	#18302	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	1	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	—	8	1	no	—
207	C₂²×C₄₇	—	8	2	no	—
208	C₂²×C₄₇	—	8	2	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	—	8	2	no	—
213	C₂²×C₄₇	—	8	2	no	—
214	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
215	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	4	1	no	—
221	C₄×C₄₇	—	4	4	no	—
222	C₄×C₄₇	—	4	1	no	—
223	C₄×C₄₇	—	4	4	no	—
224	C₄×C₄₇	—	8	2	no	—
225	C₄×C₄₇	#448	1	2	yes	—
226	C₄×C₄₇	#448	1	2	yes	—
227	#3458	C₂×C₄₇	1	1	yes	characteristic, complemented
228	#3208	C₂×C₄₇	1	2	yes	complemented
229	#2619	C₂×C₄₇	1	1	yes	characteristic
230	#1599	C₂×C₄₇	1	4	yes	complemented
231	#1596	C₂×C₄₇	1	4	yes	complemented
232	#1518	C₂×C₄₇	1	2	yes	complemented
233	#1458	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	—	2	1	no	—
236	C₂×C₄₇	—	4	2	no	—
237	C₂×C₄₇	—	16	2	no	—
238	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
239	C₂×C₄₇	#3021	1	1	yes	characteristic
240	C₂×C₄₇	#3027	1	1	yes	characteristic
241	#544	—	2	2	no	—
242	#544	—	2	2	no	—
243	#544	—	2	1	no	—
244	#544	C₂²×C₄₇	1	2	yes	—
245	#543	—	2	1	no	—
246	#543	C₂²×C₄₇	1	2	yes	—
247	#533	—	2	4	no	—
248	#533	—	2	1	no	—
249	#533	C₂²×C₄₇	1	2	yes	—
250	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#121	—	2	1	no	—
252	C₂×#117	—	2	1	no	—
253	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
254	#492	—	2	2	no	—
255	#486	—	2	2	no	—
256	#460	—	2	4	no	—
257	#450	C₂²×C₄₇	1	8	yes	—
258	#431	C₂²×C₄₇	1	2	yes	—
259	#394	—	2	1	no	—
260	#394	C₂²×C₄₇	1	2	yes	—
261	#392	—	2	1	no	—
262	#392	C₂²×C₄₇	1	2	yes	—
263	#390	—	2	1	no	—
264	#382	C₂²×C₄₇	1	1	yes	characteristic
265	#328	C₂²×C₄₇	1	8	yes	—
266	#324	C₂²×C₄₇	1	2	yes	—
267	#323	C₂²×C₄₇	1	2	yes	—
268	C₄₇	#18302	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
273	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
274	C₂×SD₁₆	—	2	8	no	—
275	C₄⋊Q₈	—	2	4	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄⋊Q₈	D₄×C₄₇	1	2	yes	complemented
280	C₄⋊Q₈	D₄×C₄₇	1	2	yes	complemented
281	#127	—	2	2	no	—
282	#127	—	2	2	no	—
283	#125	—	2	4	no	—
284	#125	—	2	2	no	—
285	#125	—	2	4	no	—
286	#125	—	2	2	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
295	#121	—	4	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	D₄×C₄₇	1	4	yes	complemented
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
320	C₄⋊C₈	—	2	2	no	—
321	#102	—	2	8	no	—
322	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	C₂³×C₄₇	1	2	yes	—
326	C₂⁴	—	2	2	no	—
327	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	complemented
350	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
356	SD₁₆	—	8	8	no	—
357	C₂×C₈	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	8	2	no	—
379	C₂²⋊C₄	—	8	2	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	C₂×D₄×C₄₇	1	2	yes	—
385	C₄²	C₂×D₄×C₄₇	1	2	yes	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
398	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
399	Q₈	—	4	4	no	—
400	Q₈	—	8	2	no	—
401	Q₈	—	8	2	no	—
402	Q₈	—	8	2	no	—
403	D₄	—	4	8	no	—
404	D₄	—	8	4	no	—
405	D₄	—	8	8	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	#120×C₄₇	1	2	yes	—
426	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
427	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
429	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
430	C₂×C₄	#137×C₄₇	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
432	C₈	—	4	4	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
448	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
449	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	C₄₇×#448	1	2	yes	—
459	C₄	C₄₇×#448	1	2	yes	—
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	16	2	no	—
464	C₂	C₂×C₄₇×#448	1	1	yes	characteristic
465	C₂	C₄₇×#3021	1	1	yes	characteristic
466	C₂	C₄₇×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3458	C₂	semidirect
2. C₄₇×#3208	C₂	semidirect
4. C₄₇×#1599	C₂	semidirect
5. C₄₇×#1596	C₂	semidirect
6. C₄₇×#1518	C₂	semidirect
7. C₄₇×#1458	C₂	semidirect
45. C₄⋊Q₈×C₄₇	D₄	semidirect
46. C₄⋊Q₈×C₄₇	D₄	semidirect
65. C₄×Q₈×C₄₇	D₄	semidirect
115. C₂²×C₄×C₄₇	SD₁₆	semidirect
199. #18302	C₄₇	direct (N × H)
227. #3458	C₂×C₄₇	semidirect
228. #3208	C₂×C₄₇	semidirect
230. #1599	C₂×C₄₇	semidirect
231. #1596	C₂×C₄₇	semidirect
232. #1518	C₂×C₄₇	semidirect
233. #1458	C₂×C₄₇	semidirect
268. C₄₇	#18302	direct (N × H)
279. C₄⋊Q₈	D₄×C₄₇	semidirect
280. C₄⋊Q₈	D₄×C₄₇	semidirect
299. C₄×Q₈	D₄×C₄₇	semidirect
349. C₂²×C₄	SD₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3458	2
C₄₇×#3208	2
C₄₇×#2619	2
C₄₇×#1599	2
C₄₇×#1596	2
C₄₇×#1518	2
C₄₇×#1458	2
#18302	47

Subgroups — C47×#18302 #26058000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18302 #26058000