Subgroups — #26185926

Order 12032.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252497	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094052	C₂	1	1	yes	maximal, characteristic
4	#20242265	C₂	1	2	yes	maximal, complemented
5	#20242251	C₂	1	2	yes	maximal, complemented
6	#20242230	C₂	1	2	yes	maximal, complemented
7	#20242216	C₂	1	2	yes	maximal, complemented
8	#20241768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688850	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094052	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	#15689247	C₂²	1	2	yes	complemented
16	#15689236	C₄	1	2	yes	—
17	#15689225	C₄	1	2	yes	—
18	C₄×#10625325	C₂²	1	2	yes	—
19	C₄×D₃₇₆	C₂²	1	2	yes	—
20	#15689202	—	2	1	no	—
21	#15689202	—	2	1	no	—
22	#15689200	C₂²	1	2	yes	—
23	#15689200	C₂²	1	2	yes	—
24	#15689188	C₂²	1	2	yes	complemented
25	C₈×C₂²⋊D₄₇	—	2	2	no	—
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689175	—	2	1	no	—
28	#15689165	C₄	1	1	yes	characteristic
29	C₄⋊C₈×D₄₇	—	2	1	no	—
30	#15689129	C₄	1	1	yes	characteristic
31	#15689125	C₄	1	1	yes	characteristic
32	#15689085	—	2	2	no	—
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688853	C₂²	1	1	yes	characteristic, complemented
35	#15688853	C₂²	1	1	yes	characteristic, complemented
36	#15688850	C₂²	1	2	yes	—
37	#15688850	C₂²	1	2	yes	—
38	#15688850	C₂²	1	1	yes	characteristic, complemented
39	#15688850	C₂²	1	1	yes	characteristic, complemented
40	#15688845	C₂²	1	2	yes	complemented
41	#15688845	C₂²	1	2	yes	complemented
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	complemented
46	C₄₇×#334	C₂²	1	2	yes	complemented
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₄₇	—	2	1	no	—
50	#13094052	—	2	4	no	—
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
53	C₂×#10625324	—	2	2	no	—
54	C₂×#10625324	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂×C₈×D₄₇	—	2	2	no	—
57	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
59	C₄×D₁₈₈	—	2	1	no	—
60	C₄×D₁₈₈	—	2	1	no	—
61	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
62	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₈₈	C₂³	1	2	yes	—
64	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₄₇	—	2	1	no	—
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	#13093983	C₂×C₄	1	1	yes	characteristic
68	#13093981	—	2	1	no	—
69	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
71	C₄²×D₄₇	—	2	1	no	—
72	#13093958	C₂×C₄	1	2	yes	—
73	#13093956	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
75	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
76	Dic₄₇⋊C₈	—	2	2	no	—
77	#13093949	C₂×C₄	1	2	yes	—
78	#13093946	C₂×C₄	1	2	yes	—
79	#13093946	C₂×C₄	1	2	yes	—
80	#13093946	C₂×C₄	1	2	yes	—
81	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	(C₂×D₄₇)⋊C₈	—	2	2	no	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
88	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	—	2	1	no	—
95	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₄₇	—	2	1	no	—
99	#97×C₄₇	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₄₇	—	2	1	no	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂³×D₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	#10625350	—	2	2	no	—
109	#10625350	M₁₆	1	4	yes	complemented
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
114	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	—	8	1	no	—
121	C₂×C₄×D₄₇	—	8	1	no	—
122	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
123	M₁₆×C₄₇	—	2	2	no	—
124	M₁₆×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	8	1	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	#41	1	1	yes	characteristic
134	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	2	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	2	no	—
139	(C₂×D₄₇)⋊C₄	—	2	1	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
144	Dic₄₇⋊C₄	—	2	1	no	—
145	Dic₄₇⋊C₄	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	C₄×Dic₄₇	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	4	2	no	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	D₃₇₆	—	2	4	no	—
155	#10625325	—	2	4	no	—
156	#10625324	—	8	2	no	—
157	#10625324	—	8	2	no	—
158	C₈×D₄₇	—	8	2	no	—
159	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	4	2	no	—
163	C₂²×D₄₇	—	8	1	no	—
164	C₂²×D₄₇	—	8	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₄₇	#131	1	2	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	8	1	no	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	—	2	1	no	—
184	D₁₈₈	—	2	2	no	—
185	D₁₈₈	—	4	2	no	—
186	D₁₈₈	C₂×M₁₆	1	2	yes	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	2	no	—
190	C₄×D₄₇	—	4	2	no	—
191	C₄×D₄₇	—	4	1	no	—
192	C₄×D₄₇	—	8	1	no	—
193	C₄×D₄₇	—	8	2	no	—
194	Dic₉₄	—	2	1	no	—
195	Dic₉₄	C₂×M₁₆	1	2	yes	—
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₈×C₄₇	—	4	1	no	—
200	C₈×C₄₇	—	4	1	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	2	2	no	—
203	C₄₇⋊C₈	—	2	2	no	—
204	C₄₇⋊C₈	—	4	1	no	—
205	#17875	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	#435	1	2	yes	—
209	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	4	1	no	—
212	C₂×D₄₇	—	4	1	no	—
213	C₂×D₄₇	—	4	2	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	2	no	—
216	C₂×D₄₇	—	8	4	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	#435	1	2	yes	—
221	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
222	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
223	C₄×C₄₇	#576	1	1	yes	characteristic
224	C₄×C₄₇	#577	1	1	yes	characteristic
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	4	2	no	—
227	Dic₄₇	—	4	1	no	—
228	Dic₄₇	—	4	1	no	—
229	#2988	—	47	1	no	—
230	#2975	—	47	1	no	—
231	C₄×AGL(1,ℤ/8)	—	47	1	no	—
232	#1588	—	47	2	no	—
233	#1586	—	47	2	no	—
234	#1583	—	47	2	no	—
235	#1581	—	47	2	no	—
236	#1565	D₄₇	1	1	yes	characteristic, complemented
237	#1476	—	47	1	no	—
238	C₂×D₄⋊C₈	—	47	1	no	—
239	#1451	—	47	1	no	—
240	C₂×C₄₇	—	2	2	no	—
241	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
242	C₂×C₄₇	#2946	1	1	yes	characteristic
243	C₂×C₄₇	#2956	1	1	yes	characteristic
244	D₄₇	—	4	2	no	—
245	D₄₇	—	8	2	no	—
246	C₂×AGL(1,ℤ/8)	—	47	1	no	—
247	C₄×#41	—	47	1	no	—
248	C₂×C₄×D₄	—	47	1	no	—
249	C₈×Q₈	—	47	2	no	—
250	#442	—	47	2	no	—
251	#440	—	47	2	no	—
252	C₄×SD₁₆	—	47	2	no	—
253	C₄×D₈	—	47	2	no	—
254	#436	—	47	2	no	—
255	#436	—	47	2	no	—
256	#436	—	94	1	no	—
257	#436	—	94	1	no	—
258	C₈×D₄	—	47	2	no	—
259	C₈×D₄	—	94	2	no	—
260	#431	—	47	1	no	—
261	#431	—	94	1	no	—
262	#431	C₂×D₄₇	1	1	yes	characteristic
263	#428	—	47	1	no	—
264	C₂×C₄⋊C₈	—	94	1	no	—
265	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
266	#418	—	47	1	no	—
267	#417	—	47	1	no	—
268	#407	—	94	2	no	—
269	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
270	C₂×C₄×C₈	—	47	1	no	—
271	#335	C₂×D₄₇	1	2	yes	complemented
272	#334	C₂×D₄₇	1	2	yes	complemented
273	Q₈⋊C₈	—	47	1	no	—
274	Q₈⋊C₈	—	47	1	no	—
275	D₄⋊C₈	—	47	1	no	—
276	D₄⋊C₈	—	47	2	no	—
277	D₄⋊C₈	—	47	1	no	—
278	D₄⋊C₈	—	47	2	no	—
279	#322	—	47	2	no	—
280	#322	—	47	2	no	—
281	C₄₇	#17875	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	47	1	no	—
283	C₂²×D₄	—	47	1	no	—
284	C₂³×C₄	—	94	1	no	—
285	AGL(1,ℤ/8)	—	94	4	no	—
286	C₂×SD₁₆	—	47	2	no	—
287	C₂×D₈	—	47	2	no	—
288	C₂×M₁₆	—	94	2	no	—
289	C₂×M₁₆	—	94	2	no	—
290	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
291	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₄×Q₈	—	47	1	no	—
296	C₄×Q₈	—	47	1	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	—	47	1	no	—
299	C₄×D₄	—	47	2	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	94	1	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	—	94	1	no	—
304	C₄×D₄	—	94	1	no	—
305	#117	—	47	1	no	—
306	#117	—	94	1	no	—
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₂²⋊C₄	—	94	1	no	—
309	C₂×C₄²	—	94	1	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#107	—	47	2	no	—
312	#106	—	47	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	47	1	no	—
315	C₄⋊C₈	—	47	1	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
318	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
320	#103	—	47	2	no	—
321	#102	—	47	2	no	—
322	#102	—	47	2	no	—
323	#102	—	47	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	47	2	no	—
326	C₂²⋊C₈	—	94	2	no	—
327	C₂²⋊C₈	—	94	2	no	—
328	C₂²⋊C₈	—	94	2	no	—
329	#97	C₄×D₄₇	1	2	yes	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	47	2	no	—
332	C₄×C₈	—	47	1	no	—
333	C₄×C₈	—	47	1	no	—
334	C₄×C₈	—	94	2	no	—
335	C₄×C₈	—	94	1	no	—
336	C₄×C₈	C₂²×D₄₇	1	2	yes	—
337	C₂⁴	—	94	1	no	—
338	#41	—	47	4	no	—
339	#41	—	94	2	no	—
340	C₂×Q₈	—	47	1	no	—
341	C₂×D₄	—	47	1	no	—
342	C₂×D₄	—	47	2	no	—
343	C₂×D₄	—	94	1	no	—
344	C₂×D₄	—	94	1	no	—
345	C₂×D₄	—	94	2	no	—
346	C₂×D₄	—	94	2	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	94	1	no	—
349	C₂²×C₄	—	94	1	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	2	no	—
353	C₂²×C₄	—	376	1	no	—
354	C₂²×C₄	—	376	1	no	—
355	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₄	#10625354	1	1	yes	characteristic
358	SD₁₆	—	94	4	no	—
359	D₈	—	94	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	376	2	no	—
363	M₁₆	—	376	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	8	1	no	—
368	C₂×C₈	—	47	2	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	376	2	no	—
373	C₂×C₈	—	188	2	no	—
374	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
376	C₄⋊C₄	—	47	1	no	—
377	C₄⋊C₄	—	47	1	no	—
378	C₄⋊C₄	—	47	2	no	—
379	C₄⋊C₄	—	94	1	no	—
380	C₄⋊C₄	—	94	1	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₂²⋊C₄	—	94	1	no	—
383	C₂²⋊C₄	—	94	2	no	—
384	C₂²⋊C₄	—	94	1	no	—
385	C₂²⋊C₄	—	94	2	no	—
386	C₂²⋊C₄	—	94	1	no	—
387	C₄²	—	94	1	no	—
388	C₄²	—	94	1	no	—
389	C₄²	—	94	1	no	—
390	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₄²	D₄×D₄₇	1	1	yes	characteristic
392	C₄²	#10625354	1	1	yes	characteristic
393	C₄²	C₂³×D₄₇	1	1	yes	characteristic
394	C₂³	—	94	1	no	—
395	C₂³	—	94	2	no	—
396	C₂³	—	376	1	no	—
397	C₂³	—	376	1	no	—
398	C₂³	—	188	2	no	—
399	C₂³	#13093986	1	1	yes	characteristic
400	Q₈	—	47	2	no	—
401	Q₈	—	94	1	no	—
402	D₄	—	47	2	no	—
403	D₄	—	94	4	no	—
404	D₄	—	94	2	no	—
405	D₄	—	94	1	no	—
406	D₄	—	94	2	no	—
407	D₄	—	188	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	4	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	376	1	no	—
417	C₂×C₄	—	376	2	no	—
418	C₂×C₄	—	376	1	no	—
419	C₂×C₄	—	188	1	no	—
420	C₂×C₄	—	188	2	no	—
421	C₂×C₄	—	188	2	no	—
422	C₂×C₄	—	188	1	no	—
423	C₂×C₄	#13093986	1	1	yes	characteristic
424	C₂×C₄	#13093986	1	1	yes	characteristic
425	C₂×C₄	#13093986	1	1	yes	characteristic
426	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
427	C₂×C₄	#13094030	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₈	—	94	2	no	—
437	C₈	—	94	2	no	—
438	C₈	—	94	2	no	—
439	C₈	—	188	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	376	4	no	—
444	C₂²	—	188	2	no	—
445	C₂²	—	188	2	no	—
446	C₂²	—	188	2	no	—
447	C₂²	—	188	1	no	—
448	C₂²	—	188	1	no	—
449	C₂²	#15689193	1	2	yes	—
450	C₂²	C₂×#13093986	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	94	2	no	—
455	C₄	—	188	2	no	—
456	C₄	—	188	1	no	—
457	C₄	—	188	1	no	—
458	C₄	#15689193	1	2	yes	—
459	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
460	C₄	C₂×#13094030	1	1	yes	characteristic
461	C₄	#15689927	1	1	yes	characteristic
462	C₄	#15689932	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	376	2	no	—
465	C₂	—	188	2	no	—
466	C₂	C₂×#15689193	1	1	yes	characteristic
467	C₂	#20252218	1	1	yes	characteristic
468	C₂	#20252297	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1565	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094052	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1565	D₄₇
hypocenter	C₄₇	#17875
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
1. #20252497	C₂	semidirect
2. #20252428	C₂	semidirect
4. #20242265	C₂	semidirect
5. #20242251	C₂	semidirect
6. #20242230	C₂	semidirect
7. #20242216	C₂	semidirect
8. #20241768	C₂	semidirect
9. C₂×#15688850	C₂	semidirect
10. #20241675	C₂	semidirect
11. C₄₇×#1565	C₂	semidirect
15. #15689247	C₂²	semidirect
24. #15689188	C₂²	semidirect
34. #15688853	C₂²	semidirect
35. #15688853	C₂²	semidirect
38. #15688850	C₂²	semidirect
39. #15688850	C₂²	semidirect
40. #15688845	C₂²	semidirect
41. #15688845	C₂²	semidirect
45. C₄₇×#335	C₂²	semidirect
46. C₄₇×#334	C₂²	semidirect
109. #10625350	M₁₆	semidirect
236. #1565	D₄₇	semidirect
271. #335	C₂×D₄₇	semidirect
272. #334	C₂×D₄₇	semidirect
281. C₄₇	#17875	semidirect

Maximal subgroups

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

subgroup	index
#20252497	2
#20252428	2
C₄×#13094052	2
#20242265	2
#20242251	2
#20242230	2
#20242216	2
#20241768	2
C₂×#15688850	2
#20241675	2
C₄₇×#1565	2
#17875	47