Subgroups — #26186247

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253437	C₂	1	1	yes	maximal, characteristic
2	#20252357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689188	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242251	C₂	1	2	yes	maximal, complemented
5	#20242244	C₂	1	2	yes	maximal, complemented
6	#20242187	C₂	1	2	yes	maximal, complemented
7	#20242182	C₂	1	2	yes	maximal, complemented
8	#20241830	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241799	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1573	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	—	2	1	no	—
13	#15689657	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	#15689459	C₄	1	1	yes	characteristic
16	#15689442	C₄	1	1	yes	characteristic
17	#15689424	C₄	1	2	yes	—
18	#15689339	C₄	1	2	yes	—
19	#15689276	C₄	1	1	yes	characteristic
20	#15689259	C₄	1	1	yes	characteristic
21	#15689250	C₂²	1	1	yes	characteristic, complemented
22	#15689247	C₂²	1	1	yes	characteristic, complemented
23	C₄×#10625325	C₂²	1	2	yes	—
24	C₄×D₃₇₆	C₂²	1	2	yes	—
25	#15689200	C₂²	1	1	yes	characteristic, complemented
26	#15689191	—	2	1	no	—
27	#15689188	—	2	1	no	—
28	#15689188	—	2	1	no	—
29	#15689188	C₂²	1	2	yes	—
30	#15689188	C₂²	1	2	yes	—
31	#15689188	C₂²	1	1	yes	characteristic, complemented
32	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
33	#15689185	—	2	1	no	—
34	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
35	#15689080	—	2	1	no	—
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688853	C₂²	1	2	yes	complemented
39	#15688850	C₂²	1	2	yes	—
40	#15688850	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	complemented
42	#15688845	C₂²	1	2	yes	complemented
43	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
44	C₄₇×#432	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	complemented
48	C₄₇×#334	C₂²	1	2	yes	complemented
49	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₇	—	2	1	no	—
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625324	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₂×C₈×D₄₇	—	2	2	no	—
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₂×C₈×D₄₇	—	4	4	no	—
61	#13094018	—	2	1	no	—
62	#13094016	C₂×C₄	1	1	yes	characteristic
63	#13094012	C₂×C₄	1	1	yes	characteristic
64	#13094007	—	2	1	no	—
65	#13094003	C₂×C₄	1	1	yes	characteristic
66	#13093998	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
68	C₄×D₁₈₈	—	2	1	no	—
69	C₄×D₁₈₈	—	2	1	no	—
70	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
71	C₄×D₁₈₈	C₂³	1	2	yes	—
72	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
73	C₄×C₂²⋊D₄₇	—	2	1	no	—
74	#13093981	—	2	1	no	—
75	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
77	#13093958	C₂×C₄	1	2	yes	—
78	#13093956	C₂×C₄	1	2	yes	—
79	Dic₄₇⋊C₈	—	2	1	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093946	C₂×C₄	1	2	yes	—
83	#13093946	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	(C₂×D₄₇)⋊C₈	—	2	2	no	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	(C₂×D₄₇)⋊C₈	—	2	1	no	—
89	#13093935	—	2	1	no	—
90	#13093934	—	2	1	no	—
91	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
94	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₈×Dic₄₇	—	2	1	no	—
97	C₂²×C₈×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
101	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₄₇	—	2	1	no	—
105	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	#97×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	C₂³	1	2	yes	—
109	C₂³×D₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	C₂×D₁₈₈	—	2	1	no	—
116	C₂×D₁₈₈	—	2	4	no	—
117	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	—	2	1	no	—
121	C₂×C₄×D₄₇	—	2	2	no	—
122	C₂×C₄×D₄₇	—	4	2	no	—
123	C₂×C₄×D₄₇	—	4	2	no	—
124	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
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	—	4	2	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	1	no	—
139	(C₂×D₄₇)⋊C₄	—	2	1	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	Dic₄₇⋊C₄	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	#10625329	—	2	4	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	4	1	no	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
159	D₃₇₆	—	2	4	no	—
160	#10625325	—	2	4	no	—
161	#10625324	—	4	2	no	—
162	C₈×D₄₇	—	4	4	no	—
163	C₈×D₄₇	—	4	2	no	—
164	C₈×D₄₇	—	4	4	no	—
165	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	4	no	—
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	2	1	no	—
169	C₂²×D₄₇	—	4	2	no	—
170	C₂²×D₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	D₁₈₈	—	2	4	no	—
188	D₁₈₈	—	2	2	no	—
189	D₁₈₈	—	2	2	no	—
190	D₁₈₈	#131	1	4	yes	—
191	C₄×D₄₇	—	4	4	no	—
192	C₄×D₄₇	—	4	2	no	—
193	C₄×D₄₇	—	4	1	no	—
194	C₄×D₄₇	—	4	1	no	—
195	C₄×D₄₇	—	4	2	no	—
196	Dic₉₄	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	—	4	1	no	—
201	C₈×C₄₇	—	4	1	no	—
202	C₄₇⋊C₈	—	2	4	no	—
203	C₄₇⋊C₈	—	2	1	no	—
204	C₄₇⋊C₈	—	2	1	no	—
205	C₄₇⋊C₈	—	2	1	no	—
206	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
207	#17910	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	#443	1	2	yes	—
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₄₇	—	2	4	no	—
213	C₂×D₄₇	—	4	8	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	2	no	—
216	C₂×D₄₇	—	4	1	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	C₂×#131	1	2	yes	—
224	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₄₇	#575	1	1	yes	characteristic
226	Dic₄₇	—	4	1	no	—
227	Dic₄₇	—	4	2	no	—
228	Dic₄₇	—	4	1	no	—
229	Dic₄₇	—	4	1	no	—
230	#3105	—	47	1	no	—
231	#2966	—	47	1	no	—
232	C₂×C₈×D₄	—	47	1	no	—
233	#1586	—	47	2	no	—
234	#1585	—	47	2	no	—
235	C₈×SD₁₆	—	47	2	no	—
236	C₈×D₈	—	47	2	no	—
237	#1573	D₄₇	1	1	yes	characteristic, complemented
238	#1490	—	47	1	no	—
239	#1483	—	47	1	no	—
240	C₈×M₁₆	—	47	1	no	—
241	C₂×C₄₇	—	2	2	no	—
242	C₂×C₄₇	#2929	1	1	yes	characteristic
243	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
245	D₄₇	—	4	4	no	—
246	D₄₇	—	8	1	no	—
247	C₂³×C₈	—	94	1	no	—
248	#529	—	47	1	no	—
249	C₂×C₄×D₄	—	47	1	no	—
250	#484	—	47	1	no	—
251	#481	—	47	1	no	—
252	#478	—	47	2	no	—
253	#463	—	47	2	no	—
254	#450	—	47	1	no	—
255	#447	—	47	1	no	—
256	#446	—	47	1	no	—
257	C₈×Q₈	—	47	1	no	—
258	C₄×SD₁₆	—	47	2	no	—
259	C₄×D₈	—	47	2	no	—
260	#436	—	47	1	no	—
261	#435	—	94	1	no	—
262	C₈×D₄	—	47	1	no	—
263	C₈×D₄	—	47	2	no	—
264	C₈×D₄	—	47	2	no	—
265	C₈×D₄	—	94	1	no	—
266	C₈×D₄	—	94	1	no	—
267	C₈×D₄	—	94	1	no	—
268	#433	—	94	1	no	—
269	#432	C₂×D₄₇	1	1	yes	characteristic
270	#431	C₂×D₄₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	—	94	1	no	—
273	#405	—	94	1	no	—
274	C₄×M₁₆	—	47	1	no	—
275	C₂×C₄×C₈	—	47	1	no	—
276	#335	C₂×D₄₇	1	2	yes	complemented
277	#334	C₂×D₄₇	1	2	yes	complemented
278	Q₈⋊C₈	—	47	2	no	—
279	D₄⋊C₈	—	47	2	no	—
280	D₄⋊C₈	—	47	2	no	—
281	D₄⋊C₈	—	47	2	no	—
282	#322	—	47	2	no	—
283	C₈²	—	47	2	no	—
284	C₄₇	#17910	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	—	47	1	no	—
286	C₂³×C₄	—	94	1	no	—
287	C₂×SD₁₆	—	47	2	no	—
288	C₂×D₈	—	47	2	no	—
289	C₂×M₁₆	—	94	1	no	—
290	C₂×M₁₆	—	94	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	94	2	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₂²×C₈	—	94	1	no	—
297	C₂²×C₈	—	188	4	no	—
298	#126	—	94	1	no	—
299	#125	—	47	1	no	—
300	#124	—	47	1	no	—
301	#123	—	94	1	no	—
302	C₂²⋊Q₈	—	47	1	no	—
303	#121	—	47	1	no	—
304	C₄×Q₈	—	47	1	no	—
305	C₄×D₄	—	47	2	no	—
306	C₄×D₄	—	47	2	no	—
307	C₄×D₄	—	47	1	no	—
308	C₄×D₄	—	94	1	no	—
309	C₄×D₄	—	94	1	no	—
310	C₄×D₄	—	94	1	no	—
311	#117	—	94	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₂²⋊C₄	—	94	1	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	47	2	no	—
316	#106	—	47	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	94	1	no	—
319	C₄⋊C₈	—	94	1	no	—
320	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
321	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
323	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
324	#103	—	47	2	no	—
325	#102	—	47	2	no	—
326	#102	—	47	2	no	—
327	#102	—	47	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	2	no	—
331	C₂²⋊C₈	—	94	1	no	—
332	C₂²⋊C₈	—	94	1	no	—
333	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
334	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
335	#97	—	2	1	no	—
336	#97	—	94	1	no	—
337	#97	—	94	1	no	—
338	C₄×C₈	—	47	1	no	—
339	C₄×C₈	—	47	1	no	—
340	C₄×C₈	—	47	1	no	—
341	C₄×C₈	—	47	1	no	—
342	C₄×C₈	—	47	2	no	—
343	C₄×C₈	—	94	1	no	—
344	C₄×C₈	C₂²×D₄₇	1	2	yes	—
345	C₂⁴	—	94	1	no	—
346	C₂×Q₈	—	47	1	no	—
347	C₂×D₄	—	47	2	no	—
348	C₂×D₄	—	47	1	no	—
349	C₂×D₄	—	94	4	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂×D₄	—	94	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	2	no	—
354	C₂²×C₄	—	94	1	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	188	2	no	—
357	C₂²×C₄	—	188	2	no	—
358	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
360	C₂²×C₄	#10625354	1	1	yes	characteristic
361	SD₁₆	—	94	4	no	—
362	D₈	—	94	4	no	—
363	M₁₆	—	94	4	no	—
364	M₁₆	—	188	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	47	1	no	—
370	C₂×C₈	—	47	1	no	—
371	C₂×C₈	—	47	1	no	—
372	C₂×C₈	—	47	1	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	—	188	2	no	—
376	C₂×C₈	—	188	4	no	—
377	C₂×C₈	—	188	4	no	—
378	C₂×C₈	—	188	1	no	—
379	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
380	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
381	C₄⋊C₄	—	47	1	no	—
382	C₄⋊C₄	—	47	1	no	—
383	C₄⋊C₄	—	47	2	no	—
384	C₄⋊C₄	—	94	1	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₄⋊C₄	—	94	1	no	—
387	C₄⋊C₄	—	94	1	no	—
388	C₄⋊C₄	—	94	1	no	—
389	C₂²⋊C₄	—	94	1	no	—
390	C₂²⋊C₄	—	94	2	no	—
391	C₂²⋊C₄	—	94	1	no	—
392	C₂²⋊C₄	—	94	1	no	—
393	C₂²⋊C₄	—	94	1	no	—
394	C₂²⋊C₄	—	94	2	no	—
395	C₂²⋊C₄	—	94	1	no	—
396	C₄²	—	94	1	no	—
397	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₄²	D₄×D₄₇	1	1	yes	characteristic
399	C₄²	#10625354	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	94	4	no	—
402	C₂³	—	94	2	no	—
403	C₂³	—	94	1	no	—
404	C₂³	—	188	2	no	—
405	C₂³	—	188	2	no	—
406	C₂³	#13093986	1	1	yes	characteristic
407	Q₈	—	94	2	no	—
408	D₄	—	47	4	no	—
409	D₄	—	94	4	no	—
410	D₄	—	94	2	no	—
411	D₄	—	94	2	no	—
412	D₄	—	188	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	188	4	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	—	188	1	no	—
425	C₂×C₄	—	188	1	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	#13093986	1	1	yes	characteristic
428	C₂×C₄	#13093986	1	1	yes	characteristic
429	C₂×C₄	#13093986	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	47	2	no	—
439	C₈	—	94	4	no	—
440	C₈	—	94	1	no	—
441	C₈	—	94	1	no	—
442	C₈	—	94	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	94	4	no	—
446	C₂²	—	188	8	no	—
447	C₂²	—	188	1	no	—
448	C₂²	—	188	1	no	—
449	C₂²	—	188	1	no	—
450	C₂²	—	188	2	no	—
451	C₂²	—	188	2	no	—
452	C₂²	#15689239	1	2	yes	—
453	C₂²	C₂×#13093986	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	188	2	no	—
459	C₄	—	188	1	no	—
460	C₄	—	188	1	no	—
461	C₄	—	188	1	no	—
462	C₄	#131×D₄₇	1	2	yes	—
463	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
464	C₄	#15689922	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	376	1	no	—
467	C₂	—	188	4	no	—
468	C₂	#20252081	1	1	yes	characteristic
469	C₂	#20252195	1	1	yes	characteristic
470	C₂	C₂×#15689239	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×#1573	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689259	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1573	D₄₇
hypocenter	C₄₇	#17910
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
2. #20252357	C₂	semidirect
3. C₂×#15689188	C₂	semidirect
4. #20242251	C₂	semidirect
5. #20242244	C₂	semidirect
6. #20242187	C₂	semidirect
7. #20242182	C₂	semidirect
8. #20241830	C₂	semidirect
9. #20241799	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#1573	C₂	semidirect
21. #15689250	C₂²	semidirect
22. #15689247	C₂²	semidirect
25. #15689200	C₂²	semidirect
31. #15689188	C₂²	semidirect
38. #15688853	C₂²	semidirect
41. #15688850	C₂²	semidirect
42. #15688845	C₂²	semidirect
43. C₈×C₄₇⋊C₈	C₂²	semidirect
47. C₄₇×#335	C₂²	semidirect
48. C₄₇×#334	C₂²	semidirect
237. #1573	D₄₇	semidirect
276. #335	C₂×D₄₇	semidirect
277. #334	C₂×D₄₇	semidirect
284. C₄₇	#17910	semidirect

Maximal subgroups

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

subgroup	index
#20253437	2
#20252357	2
C₂×#15689188	2
#20242251	2
#20242244	2
#20242187	2
#20242182	2
#20241830	2
#20241799	2
#20241669	2
C₄₇×#1573	2
#17910	47