Subgroups — #26200171

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689499	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252868	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242746	C₂	1	4	yes	maximal, complemented
5	#20242741	C₂	1	4	yes	maximal, complemented
6	#20242146	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242057	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094049	—	2	1	no	—
11	C₂²×#10625334	—	2	2	no	—
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	#15689499	—	2	1	no	—
14	#15689499	—	2	1	no	—
15	#15689499	C₂²	1	4	yes	—
16	#15689323	—	2	1	no	—
17	#15689323	C₂²	1	2	yes	complemented
18	#15689318	—	2	1	no	—
19	#15689318	C₂²	1	2	yes	complemented
20	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
21	D₄×C₄₇⋊C₈	—	2	2	no	—
22	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
23	#15689176	—	2	1	no	—
24	#15689176	C₂²	1	1	yes	characteristic
25	#15689147	C₂²	1	1	yes	characteristic
26	#15689127	—	2	1	no	—
27	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688875	C₂²	1	4	yes	complemented
30	#15688867	C₂²	1	4	yes	complemented
31	#15688866	C₂²	1	4	yes	complemented
32	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
33	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#460	—	2	1	no	—
36	C₄₇×#460	C₂²	1	2	yes	complemented
37	C₄₇×#459	—	2	1	no	—
38	C₄₇×#459	C₂²	1	2	yes	complemented
39	C₄₇×#423	C₂²	1	1	yes	characteristic
40	C₄₇×#418	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	—	2	1	no	—
43	C₂²×D₁₈₈	—	2	1	no	—
44	#13094049	—	4	4	no	—
45	C₂×#10625336	—	2	2	no	—
46	C₂×#10625334	—	2	2	no	—
47	C₂×#10625334	—	2	4	no	—
48	C₂×#10625334	—	2	4	no	—
49	C₂×#10625334	—	4	8	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
53	#13094021	—	2	1	no	—
54	#13094021	—	2	1	no	—
55	#13094021	—	2	1	no	—
56	#13094021	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	#13093944	—	2	2	no	—
62	#13093944	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄×C₄₇⋊C₈	—	2	1	no	—
66	C₄×C₄₇⋊C₈	—	2	2	no	—
67	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
68	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₄₇	—	2	1	no	—
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	C₂²×D₄×C₄₇	—	2	1	no	—
74	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
75	C₂×SD₁₆×C₄₇	—	2	2	no	—
76	C₂×D₈×C₄₇	—	2	2	no	—
77	C₂×M₁₆×C₄₇	—	2	1	no	—
78	#127×C₄₇	—	2	1	no	—
79	#127×C₄₇	—	2	1	no	—
80	#127×C₄₇	—	2	1	no	—
81	#127×C₄₇	C₂³	1	2	yes	—
82	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
87	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
94	#102×C₄₇	—	2	2	no	—
95	#102×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	4	1	no	—
97	C₂³×D₄₇	—	4	1	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	D₈	1	4	yes	complemented
100	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	—	4	1	no	—
107	C₂×D₄×C₄₇	—	4	1	no	—
108	C₂×D₄×C₄₇	—	4	1	no	—
109	C₂×D₄×C₄₇	—	4	2	no	—
110	C₂×D₄×C₄₇	—	4	2	no	—
111	C₂×D₄×C₄₇	—	8	2	no	—
112	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	—	2	2	no	—
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	4	4	no	—
123	C₂×D₁₈₈	—	4	2	no	—
124	C₂×D₁₈₈	—	4	2	no	—
125	C₂×D₁₈₈	—	4	1	no	—
126	C₂×D₁₈₈	—	4	1	no	—
127	C₂×D₁₈₈	—	4	1	no	—
128	C₂×D₁₈₈	—	8	2	no	—
129	SD₁₆×C₄₇	—	4	4	no	—
130	D₈×C₄₇	—	4	4	no	—
131	M₁₆×C₄₇	—	4	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₄₇	—	2	1	no	—
138	C₂²⋊C₄×C₄₇	—	2	1	no	—
139	C₂²⋊C₄×C₄₇	—	2	1	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₇	#41	1	1	yes	characteristic
146	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
147	#10625336	—	4	4	no	—
148	#10625334	—	4	8	no	—
149	#10625334	—	4	4	no	—
150	#10625334	—	4	8	no	—
151	#10625329	—	4	2	no	—
152	C₂×C₄₇⋊C₈	—	2	4	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	4	4	no	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	8	2	no	—
161	C₂³×C₄₇	—	8	2	no	—
162	C₂³×C₄₇	—	8	2	no	—
163	C₂³×C₄₇	#121	1	1	yes	characteristic
164	C₂²×D₄₇	—	4	2	no	—
165	C₂²×D₄₇	—	8	2	no	—
166	C₂²×D₄₇	—	8	2	no	—
167	C₂²×D₄₇	—	8	2	no	—
168	Q₈×C₄₇	—	2	1	no	—
169	Q₈×C₄₇	C₂×D₈	1	2	yes	complemented
170	D₄×C₄₇	—	2	4	no	—
171	D₄×C₄₇	—	2	1	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	4	no	—
175	D₄×C₄₇	—	8	2	no	—
176	D₄×C₄₇	—	8	2	no	—
177	D₄×C₄₇	—	8	2	no	—
178	D₄×C₄₇	—	8	2	no	—
179	D₄×C₄₇	C₂×D₈	1	2	yes	complemented
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
190	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₄₇	#135	1	2	yes	—
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	D₁₈₈	—	4	2	no	—
197	D₁₈₈	—	4	2	no	—
198	D₁₈₈	—	4	4	no	—
199	D₁₈₈	—	8	2	no	—
200	D₁₈₈	—	8	2	no	—
201	D₁₈₈	—	8	2	no	—
202	D₁₈₈	—	8	2	no	—
203	C₈×C₄₇	—	4	2	no	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	4	2	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	C₄₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	complemented
208	#19267	—	47	1	no	maximal, Sylow
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	2	1	no	—
211	C₂²×C₄₇	—	2	2	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	1	no	—
214	C₂²×C₄₇	—	8	2	no	—
215	C₂²×C₄₇	—	8	2	no	—
216	C₂²×C₄₇	—	8	2	no	—
217	C₂²×C₄₇	—	16	4	no	—
218	C₂²×C₄₇	#466	1	2	yes	—
219	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
220	C₂×D₄₇	—	8	2	no	—
221	C₂×D₄₇	—	8	2	no	—
222	C₂×D₄₇	—	8	2	no	—
223	C₂×D₄₇	—	16	4	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	2	1	no	—
227	C₄×C₄₇	—	4	1	no	—
228	C₄×C₄₇	—	4	1	no	—
229	C₄×C₄₇	#466	1	2	yes	—
230	C₄×C₄₇	#472	1	2	yes	—
231	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
232	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
233	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
234	C₂×#493	—	47	1	no	—
235	#3038	—	47	1	no	—
236	#3038	D₄₇	1	1	yes	characteristic, complemented
237	C₈×#41	—	47	1	no	—
238	#1668	—	47	4	no	—
239	#1667	—	47	4	no	—
240	#1567	—	47	1	no	—
241	#1545	—	47	1	no	—
242	#1545	—	47	1	no	—
243	C₂×C₄₇	—	2	2	no	—
244	C₂×C₄₇	—	4	2	no	—
245	C₂×C₄₇	—	16	2	no	—
246	C₂×C₄₇	#3038	1	1	yes	characteristic
247	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
249	D₄₇	—	16	2	no	—
250	C₂×AGL(1,ℤ/8)	—	2	1	no	—
251	C₂×AGL(1,ℤ/8)	—	94	1	no	—
252	C₂²×D₈	—	94	2	no	—
253	C₂×#127	—	47	1	no	—
254	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
255	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
256	#493	—	47	4	no	—
257	#493	—	94	1	no	—
258	#493	—	94	1	no	—
259	#460	—	2	1	no	—
260	#460	—	47	2	no	—
261	#460	—	94	1	no	—
262	#460	C₂×D₄₇	1	2	yes	complemented
263	#459	—	2	1	no	—
264	#459	—	47	2	no	—
265	#459	—	94	1	no	—
266	#459	C₂×D₄₇	1	2	yes	complemented
267	C₈×Q₈	—	47	2	no	—
268	C₈×D₄	—	47	2	no	—
269	C₈×D₄	—	94	2	no	—
270	#431	—	47	1	no	—
271	#431	—	94	1	no	—
272	#423	—	47	1	no	—
273	#423	C₂×D₄₇	1	1	yes	characteristic
274	#418	—	2	1	no	—
275	#418	—	94	1	no	—
276	C₂×C₄×C₈	—	47	1	no	—
277	C₂×C₄×C₈	—	94	1	no	—
278	#335	—	47	4	no	—
279	#331	—	47	4	no	—
280	#331	—	47	4	no	—
281	C₄₇	#19267	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	94	1	no	—
287	C₂²×D₄	—	94	1	no	—
288	C₂²×D₄	—	94	1	no	—
289	AGL(1,ℤ/8)	—	4	4	no	—
290	AGL(1,ℤ/8)	—	188	4	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	94	2	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	94	4	no	—
295	C₂×D₈	—	94	4	no	—
296	C₂×D₈	—	94	2	no	—
297	C₂×D₈	—	188	8	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	94	1	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	—	94	2	no	—
302	#127	—	2	1	no	—
303	#127	—	2	1	no	—
304	#127	—	2	1	no	—
305	#127	—	47	2	no	—
306	#127	—	94	1	no	—
307	#127	—	94	1	no	—
308	#127	—	94	1	no	—
309	#127	C₂²×D₄₇	1	2	yes	—
310	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
311	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
316	#117	—	2	1	no	—
317	#117	C₂²⋊D₄₇	1	1	yes	characteristic
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	47	2	no	—
322	C₄⋊C₈	—	47	2	no	—
323	C₄⋊C₈	—	94	2	no	—
324	C₄⋊C₈	—	94	1	no	—
325	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
326	#102	—	2	2	no	—
327	#102	—	2	2	no	—
328	#102	—	94	2	no	—
329	#102	—	94	2	no	—
330	C₂²⋊C₈	—	94	2	no	—
331	C₂²⋊C₈	—	94	1	no	—
332	C₄×C₈	—	47	1	no	—
333	C₄×C₈	—	47	1	no	—
334	C₄×C₈	—	47	2	no	—
335	C₄×C₈	—	94	2	no	—
336	C₄×C₈	—	94	1	no	—
337	C₂⁴	—	4	1	no	—
338	C₂⁴	—	188	1	no	—
339	#41	—	2	2	no	—
340	#41	#10625334	1	4	yes	complemented
341	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	—	94	2	no	—
354	C₂×D₄	—	94	2	no	—
355	C₂×D₄	—	94	2	no	—
356	C₂×D₄	—	376	2	no	—
357	C₂×D₄	—	188	4	no	—
358	C₂×D₄	—	188	1	no	—
359	C₂×D₄	—	188	1	no	—
360	C₂×D₄	—	188	1	no	—
361	C₂×D₄	—	188	2	no	—
362	C₂×D₄	—	188	2	no	—
363	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	#10625352	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	SD₁₆	—	4	4	no	—
371	SD₁₆	—	188	4	no	—
372	D₈	—	4	4	no	—
373	D₈	—	188	8	no	—
374	D₈	—	188	8	no	—
375	D₈	—	188	4	no	—
376	M₁₆	—	4	2	no	—
377	M₁₆	—	188	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	47	2	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	94	4	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	188	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	D₄×D₄₇	1	1	yes	characteristic
396	C₄²	#10625352	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₄²	C₂³×D₄₇	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	—	8	2	no	—
403	C₂³	—	8	2	no	—
404	C₂³	—	376	2	no	—
405	C₂³	—	376	2	no	—
406	C₂³	—	376	2	no	—
407	C₂³	—	188	2	no	—
408	C₂³	#13093996	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	C₂×#10625334	1	2	yes	complemented
411	D₄	—	2	4	no	—
412	D₄	—	2	1	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	8	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	D₄	—	376	2	no	—
421	D₄	—	376	2	no	—
422	D₄	—	376	2	no	—
423	D₄	—	376	2	no	—
424	D₄	—	188	2	no	—
425	D₄	—	188	2	no	—
426	D₄	—	188	4	no	—
427	D₄	C₂×#10625334	1	2	yes	complemented
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	#13093996	1	1	yes	characteristic
437	C₂×C₄	#13093996	1	1	yes	characteristic
438	C₂×C₄	#13093996	1	1	yes	characteristic
439	C₂×C₄	C₂×#10625334	1	2	yes	—
440	C₂×C₄	#13094044	1	2	yes	—
441	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
444	C₈	—	4	2	no	—
445	C₈	—	47	4	no	—
446	C₈	—	94	2	no	—
447	C₈	—	188	2	no	—
448	C₈	—	188	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	16	4	no	—
458	C₂²	—	376	2	no	—
459	C₂²	—	376	2	no	—
460	C₂²	—	376	2	no	—
461	C₂²	—	752	4	no	—
462	C₂²	#15689357	1	2	yes	—
463	C₂²	C₂×#13093996	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	#15689357	1	2	yes	—
470	C₄	#15689391	1	2	yes	—
471	C₄	C₂²×#10625334	1	1	yes	characteristic
472	C₄	C₂×#13094044	1	1	yes	characteristic
473	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
474	C₂	—	2	2	no	—
475	C₂	—	4	2	no	—
476	C₂	—	16	2	no	—
477	C₂	—	752	2	no	—
478	C₂	#20252866	1	1	yes	characteristic
479	C₂	C₂×#15689357	1	1	yes	characteristic
480	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3038	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3038	D₄₇
hypocenter	C₄₇	#19267
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3038

Complements

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

N	H ≅ G/N	type
1. C₂×#15689499	C₂	semidirect
2. #20252868	C₂	semidirect
3. #41×C₄₇⋊C₈	C₂	semidirect
4. #20242746	C₂	semidirect
5. #20242741	C₂	semidirect
6. #20242146	C₂	semidirect
7. #20242057	C₂	semidirect
8. #20242056	C₂	semidirect
9. C₄₇×#3038	C₂	semidirect
17. #15689323	C₂²	semidirect
19. #15689318	C₂²	semidirect
20. Q₈×C₄₇⋊C₈	C₂²	semidirect
22. D₄×C₄₇⋊C₈	C₂²	semidirect
29. #15688875	C₂²	semidirect
30. #15688867	C₂²	semidirect
31. #15688866	C₂²	semidirect
36. C₄₇×#460	C₂²	semidirect
38. C₄₇×#459	C₂²	semidirect
99. #41×C₄₇	D₈	semidirect
169. Q₈×C₄₇	C₂×D₈	semidirect
179. D₄×C₄₇	C₂×D₈	semidirect
207. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
236. #3038	D₄₇	semidirect
262. #460	C₂×D₄₇	semidirect
266. #459	C₂×D₄₇	semidirect
281. C₄₇	#19267	semidirect
340. #41	#10625334	semidirect
410. Q₈	C₂×#10625334	semidirect
427. D₄	C₂×#10625334	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689499	2
#20252868	2
#41×C₄₇⋊C₈	2
#20242746	2
#20242741	2
#20242146	2
#20242057	2
#20242056	2
C₄₇×#3038	2
#19267	47