Subgroups — #26186274

Order 12032.

700 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253449	C₂	1	1	yes	maximal, characteristic
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252101	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242268	C₂	1	2	yes	maximal, complemented
5	#20242254	C₂	1	2	yes	maximal, complemented
6	C₈×#10625325	C₂	1	2	yes	maximal, complemented
7	C₈×D₃₇₆	C₂	1	2	yes	maximal, complemented
8	#20242177	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241828	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241806	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	#15689448	C₄	1	2	yes	—
16	#15689419	C₄	1	1	yes	characteristic
17	#15689414	C₄	1	1	yes	characteristic
18	#15689324	C₄	1	1	yes	characteristic
19	#15689319	C₄	1	1	yes	characteristic
20	#15689270	C₄	1	2	yes	—
21	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
22	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
23	C₄×#10625325	C₂²	1	2	yes	—
24	C₄×D₃₇₆	C₂²	1	2	yes	—
25	#15689202	—	2	1	no	—
26	#15689202	C₂²	1	2	yes	—
27	C₈×D₁₈₈	—	2	1	no	—
28	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
29	C₈×D₁₈₈	C₂²	1	2	yes	—
30	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₄₇	—	2	1	no	—
32	C₈×C₂²⋊D₄₇	—	2	1	no	—
33	#15689176	C₂²	1	1	yes	characteristic
34	#15689174	—	2	1	no	—
35	#15689147	C₂²	1	1	yes	characteristic
36	#15689089	—	2	1	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688876	C₂²	1	2	yes	—
39	#15688874	C₂²	1	2	yes	—
40	#15688855	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	#15688852	C₂²	1	2	yes	—
43	#15688852	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#322	C₂²	1	2	yes	—
48	C₈²×C₄₇	C₂²	1	2	yes	—
49	C₂×#10625350	—	2	1	no	—
50	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
53	#13094030	—	4	4	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625324	—	2	2	no	—
56	C₂×C₈×D₄₇	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₂×C₈×D₄₇	—	2	2	no	—
59	#13094024	C₂×C₄	1	1	yes	characteristic
60	#13094021	C₂×C₄	1	1	yes	characteristic
61	#13094012	—	2	1	no	—
62	#13093998	—	2	1	no	—
63	#13093998	C₂×C₄	1	2	yes	—
64	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
66	C₄×D₁₈₈	—	2	1	no	—
67	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
68	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
69	C₄×D₁₈₈	C₂³	1	2	yes	—
70	C₄×C₂²⋊D₄₇	—	2	1	no	—
71	C₄×C₂²⋊D₄₇	—	2	1	no	—
72	#13093983	C₂×C₄	1	1	yes	characteristic
73	#13093981	—	2	1	no	—
74	C₄²×D₄₇	—	2	1	no	—
75	#13093958	C₂×C₄	1	2	yes	—
76	#13093956	C₂×C₄	1	2	yes	—
77	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
81	Dic₄₇⋊C₈	—	2	1	no	—
82	Dic₄₇⋊C₈	—	2	1	no	—
83	#13093949	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	#13093946	C₂×C₄	1	2	yes	—
87	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
88	(C₂×D₄₇)⋊C₈	—	2	2	no	—
89	(C₂×D₄₇)⋊C₈	—	2	2	no	—
90	(C₂×D₄₇)⋊C₈	—	2	1	no	—
91	(C₂×D₄₇)⋊C₈	—	2	1	no	—
92	C₄×C₄₇⋊C₈	—	2	1	no	—
93	C₈×Dic₄₇	—	2	1	no	—
94	C₈×Dic₄₇	—	2	1	no	—
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
102	#97×C₄₇	—	2	1	no	—
103	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₄₇	C₂³	1	2	yes	—
106	C₄×C₈×C₄₇	C₂³	1	2	yes	—
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₄₇	—	2	2	no	—
114	#10625350	—	2	2	no	—
115	#10625350	—	2	2	no	—
116	#10625350	—	4	2	no	—
117	#10625350	—	4	2	no	—
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×D₁₈₈	—	2	1	no	—
120	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
121	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₄₇	—	2	1	no	—
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×C₄×D₄₇	—	2	1	no	—
125	C₂×C₄×D₄₇	—	2	2	no	—
126	C₂×Dic₉₄	—	2	1	no	—
127	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
128	M₁₆×C₄₇	—	2	4	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	4	1	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	#41	1	1	yes	characteristic
141	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₄₇	—	2	1	no	—
143	(C₂×D₄₇)⋊C₄	—	2	1	no	—
144	(C₂×D₄₇)⋊C₄	—	2	2	no	—
145	(C₂×D₄₇)⋊C₄	—	2	1	no	—
146	(C₂×D₄₇)⋊C₄	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
151	Dic₄₇⋊C₄	—	2	1	no	—
152	Dic₄₇⋊C₄	—	2	1	no	—
153	C₄×Dic₄₇	—	2	1	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	#10625329	—	4	2	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	D₃₇₆	—	2	4	no	—
161	#10625325	—	2	4	no	—
162	#10625324	—	4	4	no	—
163	C₈×D₄₇	—	4	2	no	—
164	C₈×D₄₇	—	4	2	no	—
165	C₈×D₄₇	—	4	4	no	—
166	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂²×D₄₇	—	2	1	no	—
168	C₂²×D₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	2	4	no	—
181	C₂²⋊D₄₇	—	4	4	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	D₁₈₈	—	2	1	no	—
187	D₁₈₈	—	2	2	no	—
188	D₁₈₈	—	2	2	no	—
189	D₁₈₈	—	4	2	no	—
190	D₁₈₈	—	4	2	no	—
191	D₁₈₈	#131	1	2	yes	complemented
192	C₄×D₄₇	—	2	4	no	—
193	C₄×D₄₇	—	4	2	no	—
194	C₄×D₄₇	—	4	1	no	—
195	C₄×D₄₇	—	4	1	no	—
196	C₄×D₄₇	—	4	2	no	—
197	C₄×D₄₇	—	4	2	no	—
198	Dic₉₄	—	2	1	no	—
199	Dic₉₄	—	4	2	no	—
200	Dic₉₄	#131	1	2	yes	complemented
201	C₈×C₄₇	—	2	4	no	—
202	C₈×C₄₇	—	2	2	no	—
203	C₈×C₄₇	—	2	2	no	—
204	C₈×C₄₇	—	2	1	no	—
205	C₈×C₄₇	—	2	1	no	—
206	C₈×C₄₇	—	2	1	no	—
207	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
208	C₄₇⋊C₈	—	4	2	no	—
209	C₄₇⋊C₈	—	4	1	no	—
210	C₄₇⋊C₈	—	4	1	no	—
211	#17912	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂×D₄₇	—	2	2	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₂×D₄₇	—	4	2	no	—
220	C₂×D₄₇	—	4	2	no	—
221	C₂×D₄₇	—	4	2	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	#443	1	2	yes	—
226	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
227	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
228	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₄₇	#575	1	1	yes	characteristic
230	Dic₄₇	—	2	2	no	—
231	Dic₄₇	—	4	2	no	—
232	Dic₄₇	—	4	1	no	—
233	Dic₄₇	—	4	1	no	—
234	#3106	—	47	1	no	—
235	C₈×#41	—	47	1	no	—
236	#2931	—	47	1	no	—
237	#1588	—	47	2	no	—
238	#1586	—	47	2	no	—
239	C₈×SD₁₆	—	47	2	no	—
240	C₈×D₈	—	47	2	no	—
241	#1574	—	47	1	no	—
242	#1489	—	47	1	no	—
243	#1484	—	47	1	no	—
244	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
245	C₂×C₄₇	—	4	1	no	—
246	C₂×C₄₇	#2929	1	1	yes	characteristic
247	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
249	D₄₇	—	4	2	no	—
250	D₄₇	—	8	2	no	—
251	C₂×#131	—	94	1	no	—
252	#532	—	47	1	no	—
253	C₄×#41	—	47	1	no	—
254	#482	—	47	2	no	—
255	#477	—	47	1	no	—
256	#476	—	47	1	no	—
257	#460	—	47	1	no	—
258	#459	—	47	1	no	—
259	#449	—	47	2	no	—
260	C₈×Q₈	—	47	1	no	—
261	C₈×Q₈	—	47	1	no	—
262	C₄×SD₁₆	—	47	2	no	—
263	C₄×D₈	—	47	2	no	—
264	#436	—	47	2	no	—
265	#436	—	94	1	no	—
266	C₈×D₄	—	47	1	no	—
267	C₈×D₄	—	47	2	no	—
268	C₈×D₄	—	47	1	no	—
269	C₈×D₄	—	94	1	no	—
270	C₈×D₄	—	94	1	no	—
271	C₈×D₄	—	94	1	no	—
272	#431	—	47	1	no	—
273	#431	—	94	1	no	—
274	#431	C₂×D₄₇	1	1	yes	characteristic
275	#423	—	47	1	no	—
276	#408	—	94	1	no	—
277	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
278	C₂×C₄×C₈	—	94	1	no	—
279	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
280	#335	—	47	2	no	—
281	#334	—	47	2	no	—
282	Q₈⋊C₈	—	47	2	no	—
283	D₄⋊C₈	—	47	2	no	—
284	D₄⋊C₈	—	47	2	no	—
285	D₄⋊C₈	—	47	2	no	—
286	#322	C₂×D₄₇	1	2	yes	—
287	C₈²	C₂×D₄₇	1	2	yes	—
288	C₄₇	#17912	1	1	yes	characteristic, complemented, Sylow
289	C₂×#41	—	47	1	no	—
290	C₂×#41	—	94	1	no	—
291	C₂×SD₁₆	—	47	2	no	—
292	C₂×D₈	—	47	2	no	—
293	#131	—	188	4	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	94	1	no	—
296	C₂×M₁₆	—	94	2	no	—
297	C₂²×C₈	—	94	1	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	—	94	1	no	—
300	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
301	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
302	C₄⋊Q₈	—	47	1	no	—
303	#127	—	47	1	no	—
304	#124	—	94	1	no	—
305	#121	—	47	2	no	—
306	#121	—	94	1	no	—
307	C₄×Q₈	—	47	1	no	—
308	C₄×Q₈	—	47	1	no	—
309	C₄×D₄	—	47	1	no	—
310	C₄×D₄	—	47	1	no	—
311	C₄×D₄	—	47	2	no	—
312	C₄×D₄	—	94	1	no	—
313	C₄×D₄	—	94	1	no	—
314	C₄×D₄	—	94	1	no	—
315	#117	—	47	1	no	—
316	#117	—	94	1	no	—
317	C₂×C₄²	—	94	1	no	—
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	#107	—	47	2	no	—
320	#106	—	47	2	no	—
321	C₄⋊C₈	—	47	1	no	—
322	C₄⋊C₈	—	47	1	no	—
323	C₄⋊C₈	—	47	2	no	—
324	C₄⋊C₈	—	94	1	no	—
325	C₄⋊C₈	—	94	1	no	—
326	C₄⋊C₈	—	94	1	no	—
327	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
328	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
329	#103	—	47	2	no	—
330	#102	—	47	2	no	—
331	#102	—	47	2	no	—
332	#102	—	47	2	no	—
333	C₂²⋊C₈	—	94	1	no	—
334	C₂²⋊C₈	—	94	2	no	—
335	C₂²⋊C₈	—	94	2	no	—
336	C₂²⋊C₈	—	94	1	no	—
337	C₂²⋊C₈	—	94	1	no	—
338	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
339	#97	—	2	1	no	—
340	C₄×C₈	—	94	1	no	—
341	C₄×C₈	—	94	1	no	—
342	C₄×C₈	—	94	1	no	—
343	C₄×C₈	D₁₈₈	1	1	yes	characteristic
344	C₄×C₈	D₁₈₈	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₄₇	1	2	yes	—
346	C₄×C₈	C₂²×D₄₇	1	2	yes	—
347	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
349	#41	—	94	2	no	—
350	#41	—	94	2	no	—
351	#41	—	188	2	no	—
352	#41	—	188	2	no	—
353	C₂×Q₈	—	47	1	no	—
354	C₂×Q₈	—	94	1	no	—
355	C₂×D₄	—	47	1	no	—
356	C₂×D₄	—	47	2	no	—
357	C₂×D₄	—	94	1	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂×D₄	—	94	1	no	—
360	C₂×D₄	—	94	1	no	—
361	C₂²×C₄	—	94	1	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	1	no	—
364	C₂²×C₄	—	94	2	no	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
367	C₂²×C₄	#10625350	1	1	yes	characteristic
368	SD₁₆	—	94	4	no	—
369	D₈	—	94	4	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	188	4	no	—
372	M₁₆	—	188	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	188	2	no	—
380	C₂×C₈	—	188	2	no	—
381	C₂×C₈	—	188	4	no	—
382	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
384	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
385	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
386	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
387	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
388	C₄⋊C₄	—	47	1	no	—
389	C₄⋊C₄	—	47	1	no	—
390	C₄⋊C₄	—	47	2	no	—
391	C₄⋊C₄	—	94	1	no	—
392	C₄⋊C₄	—	94	1	no	—
393	C₄⋊C₄	—	94	1	no	—
394	C₂²⋊C₄	—	94	1	no	—
395	C₂²⋊C₄	—	94	1	no	—
396	C₂²⋊C₄	—	94	2	no	—
397	C₂²⋊C₄	—	94	1	no	—
398	C₂²⋊C₄	—	94	2	no	—
399	C₄²	—	94	1	no	—
400	C₄²	—	94	1	no	—
401	C₄²	—	94	1	no	—
402	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
404	C₄²	#10625350	1	1	yes	characteristic
405	C₄²	C₂³×D₄₇	1	1	yes	characteristic
406	C₂³	—	94	1	no	—
407	C₂³	—	94	2	no	—
408	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
409	Q₈	—	47	2	no	—
410	Q₈	—	94	1	no	—
411	Q₈	—	188	2	no	—
412	D₄	—	47	2	no	—
413	D₄	—	94	4	no	—
414	D₄	—	94	1	no	—
415	D₄	—	94	2	no	—
416	D₄	—	94	2	no	—
417	D₄	—	188	2	no	—
418	D₄	—	188	4	no	—
419	D₄	—	188	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	94	4	no	—
426	C₂×C₄	—	94	1	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	188	2	no	—
431	C₂×C₄	—	188	2	no	—
432	C₂×C₄	—	188	1	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	2	no	—
435	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
436	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
437	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
440	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	188	1	no	—
448	C₈	—	188	2	no	—
449	C₈	—	188	1	no	—
450	C₈	#13094052	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	94	2	no	—
455	C₂²	—	188	2	no	—
456	C₂²	—	188	2	no	—
457	C₂²	—	188	2	no	—
458	C₂²	—	188	1	no	—
459	C₂²	—	188	1	no	—
460	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	94	2	no	—
465	C₄	—	188	2	no	—
466	C₄	—	188	1	no	—
467	C₄	—	188	1	no	—
468	C₄	#15689241	1	2	yes	—
469	C₄	#131×D₄₇	1	1	yes	characteristic
470	C₄	#131×D₄₇	1	1	yes	characteristic
471	C₄	C₂×#13094052	1	1	yes	characteristic
472	C₄	#15689923	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	376	2	no	—
475	C₂	—	188	2	no	—
476	C₂	#20252084	1	1	yes	characteristic
477	C₂	C₄×#13094052	1	1	yes	characteristic
478	C₂	C₂×#15689241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253449	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	#17912
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₈×#10625350	C₂	semidirect
3. #20252101	C₂	semidirect
4. #20242268	C₂	semidirect
5. #20242254	C₂	semidirect
6. C₈×#10625325	C₂	semidirect
7. C₈×D₃₇₆	C₂	semidirect
8. #20242177	C₂	semidirect
9. #20241828	C₂	semidirect
10. #20241806	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
191. D₁₈₈	#131	semidirect
200. Dic₉₄	#131	semidirect
244. C₈×M₁₆	D₄₇	semidirect
288. C₄₇	#17912	semidirect

Maximal subgroups

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

subgroup	index
#20253449	2
C₈×#10625350	2
#20252101	2
#20242268	2
#20242254	2
C₈×#10625325	2
C₈×D₃₇₆	2
#20242177	2
#20241828	2
#20241806	2
C₈×M₁₆×C₄₇	2
#17912	47