Subgroups — #26187204

Order 12032.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253420	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252134	C₂	1	1	yes	maximal, characteristic
4	#20242280	C₂	1	2	yes	maximal, complemented
5	#20242233	C₂	1	2	yes	maximal, complemented
6	#20242226	C₂	1	2	yes	maximal, complemented
7	C₈×#10625325	C₂	1	2	yes	maximal, complemented
8	#20242159	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241840	C₂	1	1	yes	maximal, characteristic
10	C₂×#15688855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689442	C₄	1	2	yes	—
16	#15689409	C₄	1	1	yes	characteristic
17	#15689409	C₄	1	1	yes	characteristic
18	#15689324	C₄	1	1	yes	characteristic
19	#15689324	C₄	1	1	yes	characteristic
20	#15689264	C₄	1	2	yes	—
21	#15689253	C₂²	1	2	yes	—
22	#15689251	—	2	2	no	—
23	C₈×Dic₉₄	C₂²	1	2	yes	—
24	C₄×#10625325	C₂²	1	2	yes	—
25	C₄×#10625325	C₂²	1	2	yes	—
26	#15689202	C₂²	1	2	yes	—
27	#15689196	—	2	2	no	—
28	C₈×D₁₈₈	C₂²	1	2	yes	—
29	#15689147	C₂²	1	1	yes	characteristic
30	#15689146	—	2	1	no	—
31	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	#15689091	—	2	1	no	—
33	M₁₆×Dic₄₇	—	2	1	no	—
34	#15688874	C₂²	1	2	yes	—
35	#15688874	C₂²	1	2	yes	—
36	#15688855	C₂²	1	1	yes	characteristic
37	#15688855	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	1	yes	characteristic
39	#15688855	C₂²	1	1	yes	characteristic
40	#15688852	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₈²×C₄₇	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	C₂×#10625325	C₂×C₄	1	2	yes	—
51	#13094032	—	4	4	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625324	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₇	—	2	2	no	—
56	#13094024	C₂×C₄	1	1	yes	characteristic
57	#13094021	C₂×C₄	1	1	yes	characteristic
58	#13094012	—	2	1	no	—
59	#13093998	—	2	1	no	—
60	#13093998	C₂×C₄	1	2	yes	—
61	C₄×Dic₉₄	—	2	1	no	—
62	C₄×Dic₉₄	—	2	1	no	—
63	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
66	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
67	C₄×D₁₈₈	—	2	1	no	—
68	C₄×D₁₈₈	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₄₇⋊C₄	—	2	1	no	—
71	C₂×C₄×Dic₄₇	—	2	1	no	—
72	#13093956	C₂×C₄	1	2	yes	—
73	#13093956	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
78	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093949	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	#13093934	—	2	2	no	—
88	C₈×Dic₄₇	—	2	2	no	—
89	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
96	#97×C₄₇	D₄	1	2	yes	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	#10625350	—	4	2	no	—
109	#10625350	—	4	2	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×Dic₉₄	—	2	2	no	—
115	C₂×Dic₉₄	—	2	1	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	4	1	no	—
118	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	SD₁₆	1	4	yes	complemented
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	4	2	no	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	#41	1	1	yes	characteristic
132	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
140	Dic₄₇⋊C₄	—	2	1	no	—
141	Dic₄₇⋊C₄	—	2	1	no	—
142	Dic₄₇⋊C₄	—	2	1	no	—
143	Dic₄₇⋊C₄	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	1	no	—
148	#10625329	—	4	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	4	2	no	—
153	#10625325	—	2	4	no	—
154	#10625325	—	4	2	no	—
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	4	4	no	—
157	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₄₇	#135	1	2	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	8	1	no	—
178	D₁₈₈	—	2	2	no	—
179	D₁₈₈	—	2	2	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	8	1	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	4	2	no	—
184	Dic₉₄	—	2	1	no	—
185	Dic₉₄	—	2	1	no	—
186	Dic₉₄	—	2	1	no	—
187	Dic₉₄	—	4	2	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	#131	1	2	yes	complemented
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	4	1	no	—
195	C₈×C₄₇	C₂×SD₁₆	1	4	yes	—
196	C₄₇⋊C₈	—	4	1	no	—
197	C₄₇⋊C₈	—	4	1	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	#17997	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	—	4	2	no	—
206	C₂×D₄₇	—	4	2	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
211	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
212	C₄×C₄₇	#568	1	1	yes	characteristic
213	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
215	Dic₄₇	—	2	2	no	—
216	Dic₄₇	—	4	1	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	4	1	no	—
220	#3103	—	47	1	no	—
221	Q₈×M₁₆	—	47	1	no	—
222	#2935	—	47	1	no	—
223	#1590	—	47	2	no	—
224	#1583	—	47	2	no	—
225	#1582	—	47	2	no	—
226	C₈×SD₁₆	—	47	2	no	—
227	#1570	—	47	1	no	—
228	#1492	—	47	1	no	—
229	C₂×Q₈⋊C₈	—	47	1	no	—
230	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	#2933	1	1	yes	characteristic
233	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
234	C₂×C₄₇	#2956	1	1	yes	characteristic
235	D₄₇	—	8	2	no	—
236	C₂×#131	—	94	1	no	—
237	#532	—	47	1	no	—
238	C₂×C₄×Q₈	—	47	1	no	—
239	#481	—	47	2	no	—
240	#475	—	47	1	no	—
241	#475	—	47	1	no	—
242	#460	—	47	1	no	—
243	#460	—	47	1	no	—
244	#448	—	47	2	no	—
245	#446	—	47	2	no	—
246	#446	—	94	2	no	—
247	C₈×Q₈	—	47	2	no	—
248	C₄×SD₁₆	—	47	2	no	—
249	C₄×SD₁₆	—	47	2	no	—
250	#436	—	47	2	no	—
251	#435	—	94	2	no	—
252	C₈×D₄	—	47	2	no	—
253	#431	C₂×D₄₇	1	1	yes	characteristic
254	#423	—	47	1	no	—
255	#423	—	94	1	no	—
256	C₂×C₄⋊C₈	—	47	1	no	—
257	#408	—	94	1	no	—
258	C₄×M₁₆	—	94	1	no	—
259	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
261	#334	—	47	2	no	—
262	#334	—	47	2	no	—
263	Q₈⋊C₈	—	47	1	no	—
264	Q₈⋊C₈	—	47	1	no	—
265	Q₈⋊C₈	—	47	1	no	—
266	Q₈⋊C₈	—	47	1	no	—
267	D₄⋊C₈	—	47	2	no	—
268	D₄⋊C₈	—	47	2	no	—
269	#322	C₂×D₄₇	1	2	yes	—
270	C₈²	C₂×D₄₇	1	2	yes	—
271	C₄₇	#17997	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	94	1	no	—
273	C₂²×Q₈	—	47	1	no	—
274	C₂×SD₁₆	—	47	2	no	—
275	C₂×SD₁₆	—	47	2	no	—
276	#131	—	188	4	no	—
277	C₂×M₁₆	—	94	1	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
280	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₄⋊Q₈	—	47	1	no	—
285	#127	—	47	1	no	—
286	#124	—	94	1	no	—
287	#121	—	47	2	no	—
288	#121	—	94	1	no	—
289	C₄×Q₈	—	47	1	no	—
290	C₄×Q₈	—	47	1	no	—
291	C₄×Q₈	—	47	1	no	—
292	C₄×Q₈	—	47	1	no	—
293	C₄×Q₈	—	94	1	no	—
294	C₄×Q₈	—	94	1	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	94	1	no	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	94	1	no	—
299	C₂×C₄²	—	94	1	no	—
300	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
301	#106	—	47	2	no	—
302	#106	—	47	2	no	—
303	C₄⋊C₈	—	47	2	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	94	2	no	—
307	C₄⋊C₈	—	94	2	no	—
308	C₄⋊C₈	—	94	1	no	—
309	C₄⋊C₈	—	94	1	no	—
310	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
311	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
312	#103	—	47	2	no	—
313	#103	—	47	2	no	—
314	#102	—	47	2	no	—
315	#102	—	47	2	no	—
316	C₂²⋊C₈	—	94	2	no	—
317	C₂²⋊C₈	—	94	2	no	—
318	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
319	#97	—	94	2	no	—
320	#97	D₁₈₈	1	2	yes	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	94	2	no	—
323	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₄₇	1	2	yes	—
326	C₄×C₈	C₂²×D₄₇	1	2	yes	—
327	#41	—	188	2	no	—
328	#41	—	188	2	no	—
329	C₂×Q₈	—	47	1	no	—
330	C₂×Q₈	—	47	1	no	—
331	C₂×Q₈	—	94	2	no	—
332	C₂×Q₈	—	94	1	no	—
333	C₂×Q₈	—	94	1	no	—
334	C₂×Q₈	—	188	1	no	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	94	1	no	—
338	C₂×D₄	—	94	1	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
344	C₂²×C₄	#10625350	1	1	yes	characteristic
345	SD₁₆	—	94	4	no	—
346	SD₁₆	—	188	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	188	2	no	—
349	M₁₆	—	188	4	no	—
350	M₁₆	#10625325	1	4	yes	complemented
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂×C₈	—	188	4	no	—
359	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
361	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
362	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
363	C₄⋊C₄	—	47	1	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	47	2	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	—	94	1	no	—
370	C₄⋊C₄	—	94	1	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₂²⋊C₄	—	94	2	no	—
373	C₂²⋊C₄	—	94	2	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₄²	—	94	1	no	—
377	C₄²	—	94	1	no	—
378	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
380	C₄²	#10625350	1	1	yes	characteristic
381	C₄²	C₂³×D₄₇	1	1	yes	characteristic
382	C₂³	—	94	2	no	—
383	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
384	Q₈	—	47	2	no	—
385	Q₈	—	94	1	no	—
386	Q₈	—	94	1	no	—
387	Q₈	—	94	1	no	—
388	Q₈	—	188	2	no	—
389	Q₈	—	188	2	no	—
390	D₄	—	94	2	no	—
391	D₄	—	94	2	no	—
392	D₄	—	376	1	no	—
393	D₄	—	188	4	no	—
394	D₄	—	188	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	376	1	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
408	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
409	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
410	C₂×C₄	C₂×#10625325	1	2	yes	—
411	C₂×C₄	#13094046	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	188	1	no	—
421	C₈	—	188	1	no	—
422	C₈	—	188	2	no	—
423	C₈	C₂×#10625325	1	4	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	188	2	no	—
427	C₂²	—	188	2	no	—
428	C₂²	—	188	2	no	—
429	C₂²	C₄×#10625325	1	2	yes	—
430	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	94	2	no	—
435	C₄	—	188	1	no	—
436	C₄	—	188	1	no	—
437	C₄	—	188	1	no	—
438	C₄	—	188	2	no	—
439	C₄	C₄×#10625325	1	2	yes	—
440	C₄	#131×D₄₇	1	1	yes	characteristic
441	C₄	#15689888	1	1	yes	characteristic
442	C₄	C₂²×#10625325	1	1	yes	characteristic
443	C₄	C₂×#13094046	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	376	2	no	—
446	C₂	#20252116	1	1	yes	characteristic
447	C₂	C₂×C₄×#10625325	1	1	yes	characteristic
448	C₂	#20252299	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689673	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	#17997
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×Dic₉₄	C₂	semidirect
4. #20242280	C₂	semidirect
5. #20242233	C₂	semidirect
6. #20242226	C₂	semidirect
7. C₈×#10625325	C₂	semidirect
8. #20242159	C₂	semidirect
10. C₂×#15688855	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
121. M₁₆×C₄₇	SD₁₆	semidirect
189. Dic₉₄	#131	semidirect
230. C₈×M₁₆	D₄₇	semidirect
271. C₄₇	#17997	semidirect
350. M₁₆	#10625325	semidirect

Maximal subgroups

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

subgroup	index
#20253420	2
M₁₆×Dic₉₄	2
#20252134	2
#20242280	2
#20242233	2
#20242226	2
C₈×#10625325	2
#20242159	2
#20241840	2
C₂×#15688855	2
C₈×M₁₆×C₄₇	2
#17997	47