Subgroups — #26185702

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252344	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094057	C₂	1	1	yes	maximal, characteristic
4	#20242206	C₂	1	2	yes	maximal, complemented
5	#20242199	C₂	1	2	yes	maximal, complemented
6	#20242194	C₂	1	2	yes	maximal, complemented
7	#20242187	C₂	1	2	yes	maximal, complemented
8	#20241782	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241773	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094057	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689247	—	2	1	no	—
16	#15689247	—	2	1	no	—
17	#15689247	C₂²	1	2	yes	—
18	#15689247	C₂²	1	1	yes	characteristic
19	#15689247	C₂²	1	2	yes	—
20	#15689247	C₂²	1	1	yes	characteristic
21	#15689231	C₄	1	2	yes	—
22	#15689225	C₄	1	2	yes	—
23	C₄×Dic₁₈₈	C₂²	1	2	yes	—
24	C₄×#10625325	C₂²	1	2	yes	—
25	#15689188	C₂²	1	1	yes	characteristic
26	#15689188	C₂²	1	1	yes	characteristic
27	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
28	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689174	—	2	1	no	—
31	#15689165	C₄	1	1	yes	characteristic
32	C₂×Dic₄₇⋊C₈	—	2	1	no	—
33	#15689133	C₄	1	1	yes	characteristic
34	#15689125	C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	—	2	1	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688853	C₂²	1	2	yes	—
39	#15688853	C₂²	1	2	yes	—
40	#15688853	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	—
42	#15688844	C₂²	1	2	yes	—
43	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	—
48	C₄₇×#334	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
51	#13094057	C₈	1	8	yes	complemented
52	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
53	C₂×#10625325	C₂×C₄	1	2	yes	—
54	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
56	C₂×C₈×D₄₇	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₄×Dic₉₄	—	2	1	no	—
59	C₄×Dic₉₄	—	2	1	no	—
60	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
61	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	2	yes	—
64	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	#13093983	C₂×C₄	1	1	yes	characteristic
69	#13093981	—	2	1	no	—
70	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₄₇⋊C₄	—	2	1	no	—
72	C₂×C₄×Dic₄₇	—	2	1	no	—
73	C₄²×D₄₇	—	2	1	no	—
74	#13093958	C₂×C₄	1	2	yes	—
75	#13093956	C₂×C₄	1	2	yes	—
76	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
77	Dic₄₇⋊C₈	—	2	2	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	1	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093949	C₂×C₄	1	2	yes	—
83	#13093949	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
89	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
91	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₈×Dic₄₇	—	2	2	no	—
94	C₈×Dic₄₇	—	2	2	no	—
95	C₈×Dic₄₇	—	2	1	no	—
96	C₈×Dic₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	—	2	1	no	—
102	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²⋊C₈×C₄₇	—	2	1	no	—
106	#97×C₄₇	C₂×C₄	1	2	yes	—
107	C₄×C₈×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	C₂³	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	2	1	no	—
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	#10625350	—	2	2	no	—
116	#10625350	C₂×C₈	1	4	yes	—
117	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	C₂×Dic₉₄	—	2	2	no	—
123	C₂×Dic₉₄	C₂×C₈	1	4	yes	complemented
124	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
125	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
126	M₁₆×C₄₇	—	2	2	no	—
127	M₁₆×C₄₇	C₂×C₈	1	4	yes	complemented
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	4	2	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	#41	1	1	yes	characteristic
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₇	—	2	1	no	—
139	(C₂×D₄₇)⋊C₄	—	2	1	no	—
140	(C₂×D₄₇)⋊C₄	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	Dic₄₇⋊C₄	—	2	2	no	—
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	2	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	C₄×Dic₄₇	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	2	no	—
152	C₄×Dic₄₇	—	2	1	no	—
153	C₄×Dic₄₇	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	4	1	no	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
161	Dic₁₈₈	C₂×C₈	1	8	yes	complemented
162	#10625325	C₂×C₈	1	8	yes	complemented
163	C₈×D₄₇	—	4	2	no	—
164	C₈×D₄₇	—	4	2	no	—
165	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
174	C₂×C₄×C₄₇	#131	1	2	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	4	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	D₁₈₈	—	2	1	no	—
187	D₁₈₈	C₂²×C₈	1	2	yes	—
188	C₄×D₄₇	—	2	4	no	—
189	C₄×D₄₇	—	4	2	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	1	no	—
192	Dic₉₄	—	2	2	no	—
193	Dic₉₄	—	2	1	no	—
194	Dic₉₄	—	2	4	no	—
195	Dic₉₄	C₂²×C₈	1	4	yes	—
196	Dic₉₄	C₂²×C₈	1	2	yes	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	4	1	no	—
199	C₈×C₄₇	—	4	1	no	—
200	C₈×C₄₇	—	4	2	no	—
201	C₈×C₄₇	C₂²×C₈	1	4	yes	—
202	C₄₇⋊C₈	—	2	1	no	—
203	C₄₇⋊C₈	—	2	1	no	—
204	C₄₇⋊C₈	—	2	1	no	—
205	C₄₇⋊C₈	—	4	2	no	—
206	C₄₇⋊C₈	#137	1	2	yes	complemented
207	C₈×#137	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	C₈×D₄	1	2	yes	—
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	4	1	no	—
214	C₂×D₄₇	—	4	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	C₈×D₄	1	2	yes	—
219	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
220	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
221	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
222	C₄×C₄₇	#575	1	1	yes	characteristic
223	Dic₄₇	—	2	4	no	—
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	4	1	no	—
226	Dic₄₇	—	4	1	no	—
227	Dic₄₇	—	4	2	no	—
228	C₈×#41	—	47	1	no	—
229	C₂×C₈×Q₈	—	47	1	no	—
230	C₄×#137	—	47	1	no	—
231	#1579	—	47	2	no	—
232	SD₁₆⋊C₈	—	47	2	no	—
233	C₈×Q₁₆	—	47	2	no	—
234	C₈×SD₁₆	—	47	2	no	—
235	#1565	D₄₇	1	1	yes	characteristic, complemented
236	#1479	—	47	1	no	—
237	#1477	—	47	1	no	—
238	C₈×M₁₆	—	47	1	no	—
239	C₂×C₄₇	—	2	2	no	—
240	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
241	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
242	C₂×C₄₇	#2955	1	1	yes	characteristic
243	D₄₇	—	4	2	no	—
244	C₂×#137	—	47	1	no	—
245	C₄×#41	—	47	1	no	—
246	C₂×C₄×Q₈	—	47	1	no	—
247	C₈×Q₈	—	47	2	no	—
248	C₈×Q₈	—	47	1	no	—
249	C₈×Q₈	—	47	2	no	—
250	C₈×Q₈	—	47	1	no	—
251	C₈×Q₈	—	94	1	no	—
252	C₈×Q₈	—	94	1	no	—
253	#441	—	47	2	no	—
254	#440	—	47	2	no	—
255	C₄×Q₁₆	—	47	2	no	—
256	C₄×SD₁₆	—	47	2	no	—
257	C₈×D₄	—	47	1	no	—
258	C₈×D₄	—	47	1	no	—
259	C₈×D₄	—	94	1	no	—
260	C₈×D₄	—	94	1	no	—
261	#431	—	47	1	no	—
262	#431	—	94	1	no	—
263	#431	C₂×D₄₇	1	1	yes	characteristic
264	#428	—	47	1	no	—
265	C₂×C₄⋊C₈	—	94	1	no	—
266	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
267	#419	—	47	1	no	—
268	#417	—	47	1	no	—
269	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	—	94	1	no	—
272	C₂×C₄×C₈	—	94	1	no	—
273	#335	C₂×D₄₇	1	2	yes	—
274	#334	C₂×D₄₇	1	2	yes	—
275	Q₈⋊C₈	—	47	2	no	—
276	Q₈⋊C₈	—	47	2	no	—
277	Q₈⋊C₈	—	47	2	no	—
278	D₄⋊C₈	—	47	2	no	—
279	#322	—	47	2	no	—
280	C₈²	—	47	2	no	—
281	C₄₇	C₈×#137	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	47	1	no	—
283	C₂²×Q₈	—	47	1	no	—
284	#137	—	47	8	no	—
285	C₂×Q₁₆	—	47	2	no	—
286	C₂×SD₁₆	—	47	2	no	—
287	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
288	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	94	1	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₄×Q₈	—	47	2	no	—
295	C₄×Q₈	—	47	1	no	—
296	C₄×Q₈	—	47	2	no	—
297	C₄×Q₈	—	47	1	no	—
298	C₄×Q₈	—	94	1	no	—
299	C₄×Q₈	—	94	1	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	47	1	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	—	94	1	no	—
304	#117	—	47	1	no	—
305	#117	—	94	1	no	—
306	C₂×C₄⋊C₄	—	47	1	no	—
307	C₂×C₄⋊C₄	—	94	1	no	—
308	C₂×C₄²	—	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	—	94	2	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	1	no	—
317	C₄⋊C₈	—	94	1	no	—
318	C₄⋊C₈	—	94	1	no	—
319	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
320	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
322	#103	—	47	2	no	—
323	#103	—	47	2	no	—
324	#103	—	47	2	no	—
325	#102	—	47	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	94	1	no	—
328	C₂²⋊C₈	—	94	1	no	—
329	C₂²⋊C₈	—	94	1	no	—
330	#97	C₄×D₄₇	1	2	yes	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	47	1	no	—
333	C₄×C₈	—	47	1	no	—
334	C₄×C₈	—	47	1	no	—
335	C₄×C₈	—	47	1	no	—
336	C₄×C₈	—	47	2	no	—
337	C₄×C₈	—	94	1	no	—
338	C₄×C₈	—	94	1	no	—
339	C₄×C₈	—	94	2	no	—
340	C₄×C₈	—	94	2	no	—
341	C₄×C₈	C₂²×D₄₇	1	2	yes	—
342	#41	—	47	4	no	—
343	#41	—	94	2	no	—
344	C₂×Q₈	—	47	4	no	—
345	C₂×Q₈	—	47	2	no	—
346	C₂×Q₈	—	47	1	no	—
347	C₂×Q₈	—	94	1	no	—
348	C₂×Q₈	—	94	2	no	—
349	C₂×D₄	—	47	1	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	1	no	—
355	C₂²×C₄	—	94	1	no	—
356	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
358	C₂²×C₄	#10625354	1	1	yes	characteristic
359	Q₁₆	—	47	8	no	—
360	SD₁₆	—	47	8	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	C₈×D₄₇	1	4	yes	complemented
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	47	1	no	—
368	C₂×C₈	—	47	1	no	—
369	C₂×C₈	—	47	1	no	—
370	C₂×C₈	—	47	1	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	188	2	no	—
374	C₂×C₈	—	188	2	no	—
375	C₂×C₈	—	188	1	no	—
376	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
377	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
378	C₄⋊C₄	—	47	2	no	—
379	C₄⋊C₄	—	47	1	no	—
380	C₄⋊C₄	—	47	1	no	—
381	C₄⋊C₄	—	94	2	no	—
382	C₄⋊C₄	—	94	1	no	—
383	C₄⋊C₄	—	94	1	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₂²⋊C₄	—	94	1	no	—
387	C₂²⋊C₄	—	94	1	no	—
388	C₂²⋊C₄	—	94	1	no	—
389	C₄²	—	94	1	no	—
390	C₄²	—	94	1	no	—
391	C₄²	—	94	2	no	—
392	C₄²	—	94	1	no	—
393	C₄²	—	94	2	no	—
394	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
395	C₄²	D₄×D₄₇	1	1	yes	characteristic
396	C₄²	#10625354	1	1	yes	characteristic
397	C₄²	C₂³×D₄₇	1	1	yes	characteristic
398	C₂³	—	94	1	no	—
399	C₂³	#13093986	1	1	yes	characteristic
400	Q₈	—	47	4	no	—
401	Q₈	—	47	2	no	—
402	Q₈	—	94	2	no	—
403	Q₈	—	94	1	no	—
404	Q₈	—	94	4	no	—
405	D₄	—	47	2	no	—
406	D₄	—	94	4	no	—
407	D₄	—	94	1	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	2	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	4	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	188	2	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	—	188	1	no	—
421	C₂×C₄	—	188	1	no	—
422	C₂×C₄	#13093986	1	1	yes	characteristic
423	C₂×C₄	#13093986	1	1	yes	characteristic
424	C₂×C₄	#13093986	1	1	yes	characteristic
425	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
426	C₂×C₄	#13094032	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	47	2	no	—
435	C₈	—	94	1	no	—
436	C₈	—	94	1	no	—
437	C₈	—	94	1	no	—
438	C₈	—	188	2	no	—
439	C₈	C₂×C₈×D₄₇	1	4	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	188	1	no	—
444	C₂²	—	188	1	no	—
445	C₂²	#15689188	1	2	yes	—
446	C₂²	C₂×#13093986	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	94	2	no	—
451	C₄	—	94	4	no	—
452	C₄	—	188	1	no	—
453	C₄	—	188	1	no	—
454	C₄	—	188	2	no	—
455	C₄	#15689188	1	2	yes	—
456	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
457	C₄	C₂×#13094032	1	1	yes	characteristic
458	C₄	#137×D₄₇	1	1	yes	characteristic
459	C₄	#15689919	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	188	2	no	—
462	C₂	C₂×#15689188	1	1	yes	characteristic
463	C₂	#20252206	1	1	yes	characteristic
464	C₂	#20252290	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1565	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1565	D₄₇
hypocenter	C₄₇	C₈×#137
LCS	G ▷ 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
2. C₂×#15689247	C₂	semidirect
4. #20242206	C₂	semidirect
5. #20242199	C₂	semidirect
6. #20242194	C₂	semidirect
7. #20242187	C₂	semidirect
8. #20241782	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#1565	C₂	semidirect
51. #13094057	C₈	semidirect
123. C₂×Dic₉₄	C₂×C₈	semidirect
127. M₁₆×C₄₇	C₂×C₈	semidirect
161. Dic₁₈₈	C₂×C₈	semidirect
162. #10625325	C₂×C₈	semidirect
206. C₄₇⋊C₈	#137	semidirect
235. #1565	D₄₇	semidirect
281. C₄₇	C₈×#137	semidirect
362. M₁₆	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252344	2
C₂×#15689247	2
C₄×#13094057	2
#20242206	2
#20242199	2
#20242194	2
#20242187	2
#20241782	2
#20241773	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#1565	2
C₈×#137	47