Subgroups — #26186263

Order 12032.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253470	C₂	1	1	yes	maximal, characteristic
2	#20252363	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242268	C₂	1	2	yes	maximal, complemented
5	#20242261	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₁₈₈	C₂	1	2	yes	maximal, complemented
7	C₈×#10625325	C₂	1	2	yes	maximal, complemented
8	#20242173	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241836	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241802	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689657	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	#15689454	C₄	1	1	yes	characteristic
15	#15689437	C₄	1	1	yes	characteristic
16	#15689431	C₄	1	2	yes	—
17	#15689346	C₄	1	2	yes	—
18	#15689281	C₄	1	1	yes	characteristic
19	#15689264	C₄	1	1	yes	characteristic
20	#15689253	C₂²	1	1	yes	characteristic
21	C₈×Dic₉₄	—	2	1	no	—
22	C₈×Dic₉₄	—	2	1	no	—
23	C₈×Dic₉₄	C₂²	1	2	yes	—
24	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
25	C₈×Dic₉₄	C₂²	1	2	yes	—
26	C₄×Dic₁₈₈	C₂²	1	2	yes	—
27	C₄×#10625325	C₂²	1	2	yes	—
28	#15689202	C₂²	1	1	yes	characteristic
29	#15689194	—	2	1	no	—
30	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₄₇	—	2	1	no	—
32	#15689182	—	2	1	no	—
33	#15689180	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₇⋊C₈	—	2	1	no	—
36	#15689077	—	2	1	no	—
37	C₂×C₈×Dic₄₇	—	2	1	no	—
38	#15688876	C₂²	1	2	yes	—
39	#15688874	C₂²	1	2	yes	—
40	#15688855	C₂²	1	2	yes	—
41	#15688855	C₂²	1	2	yes	—
42	#15688855	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	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×#10625324	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	#13094018	—	2	1	no	—
56	#13094016	C₂×C₄	1	1	yes	characteristic
57	#13094012	C₂×C₄	1	1	yes	characteristic
58	#13094007	—	2	1	no	—
59	#13094003	C₂×C₄	1	1	yes	characteristic
60	#13093998	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₉₄	—	2	1	no	—
62	C₄×Dic₉₄	—	2	1	no	—
63	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
64	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
65	C₄×Dic₉₄	C₂³	1	2	yes	—
66	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	#13093981	—	2	1	no	—
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	#13093958	C₂×C₄	1	2	yes	—
73	#13093956	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	Dic₄₇⋊C₈	—	2	1	no	—
82	#13093949	C₂×C₄	1	2	yes	—
83	#13093949	C₂×C₄	1	2	yes	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₄₇⋊C₈)	—	2	1	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	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	—	2	2	no	—
93	C₈×Dic₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	1	no	—
95	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
101	#97×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₇	C₂³	1	2	yes	—
105	C₄×C₈×C₄₇	C₂³	1	2	yes	—
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₇	—	2	1	no	—
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	2	4	no	—
118	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
120	M₁₆×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₇	#41	1	1	yes	characteristic
133	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₄₇	—	2	1	no	—
135	(C₂×D₄₇)⋊C₄	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	1	no	—
140	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
141	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	Dic₄₇⋊C₄	—	2	2	no	—
144	Dic₄₇⋊C₄	—	2	1	no	—
145	Dic₄₇⋊C₄	—	2	1	no	—
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	2	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	—	2	2	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	4	2	no	—
156	Dic₁₈₈	—	2	4	no	—
157	#10625325	—	2	4	no	—
158	#10625324	—	4	2	no	—
159	C₈×D₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	D₁₈₈	—	2	2	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	4	1	no	—
183	Dic₉₄	—	2	4	no	—
184	Dic₉₄	—	2	2	no	—
185	Dic₉₄	—	2	2	no	—
186	Dic₉₄	#131	1	4	yes	—
187	C₈×C₄₇	—	2	4	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	1	no	—
191	C₈×C₄₇	—	2	1	no	—
192	C₈×C₄₇	—	2	1	no	—
193	C₈×C₄₇	#137	1	2	yes	—
194	C₄₇⋊C₈	—	4	1	no	—
195	C₄₇⋊C₈	—	4	1	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	#17911	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	#443	1	2	yes	—
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×D₄₇	—	4	1	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	4	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	C₂×#131	1	2	yes	—
210	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
211	C₄×C₄₇	#575	1	1	yes	characteristic
212	Dic₄₇	—	2	4	no	—
213	Dic₄₇	—	4	1	no	—
214	Dic₄₇	—	4	1	no	—
215	Dic₄₇	—	4	2	no	—
216	Dic₄₇	—	4	1	no	—
217	#3108	—	47	1	no	—
218	#2966	—	47	1	no	—
219	C₂×C₈×Q₈	—	47	1	no	—
220	#1588	—	47	2	no	—
221	#1587	—	47	2	no	—
222	C₈×Q₁₆	—	47	2	no	—
223	C₈×SD₁₆	—	47	2	no	—
224	#1573	—	47	1	no	—
225	#1491	—	47	1	no	—
226	#1483	—	47	1	no	—
227	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	#2929	1	1	yes	characteristic
230	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
232	D₄₇	—	8	1	no	—
233	#529	—	47	1	no	—
234	C₂×C₄×Q₈	—	47	1	no	—
235	#483	—	47	1	no	—
236	#480	—	47	1	no	—
237	#479	—	47	2	no	—
238	#464	—	47	2	no	—
239	#451	—	47	1	no	—
240	#448	—	47	1	no	—
241	#446	—	47	1	no	—
242	C₈×Q₈	—	47	2	no	—
243	C₈×Q₈	—	47	1	no	—
244	C₈×Q₈	—	47	2	no	—
245	C₈×Q₈	—	94	1	no	—
246	C₈×Q₈	—	94	1	no	—
247	C₄×Q₁₆	—	47	2	no	—
248	C₄×SD₁₆	—	47	2	no	—
249	#436	—	47	1	no	—
250	#435	—	94	1	no	—
251	C₈×D₄	—	47	1	no	—
252	C₈×D₄	—	94	1	no	—
253	#433	—	94	1	no	—
254	#432	—	47	1	no	—
255	#431	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	47	1	no	—
257	C₂×C₄⋊C₈	—	94	1	no	—
258	#405	—	94	1	no	—
259	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
260	C₂×C₄×C₈	—	94	1	no	—
261	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
262	#335	—	47	2	no	—
263	#334	—	47	2	no	—
264	Q₈⋊C₈	—	47	2	no	—
265	Q₈⋊C₈	—	47	2	no	—
266	Q₈⋊C₈	—	47	2	no	—
267	D₄⋊C₈	—	47	2	no	—
268	#322	C₂×D₄₇	1	2	yes	—
269	C₈²	C₂×D₄₇	1	2	yes	—
270	C₄₇	#17911	1	1	yes	characteristic, complemented, Sylow
271	C₂²×Q₈	—	47	1	no	—
272	C₂×Q₁₆	—	47	2	no	—
273	C₂×SD₁₆	—	47	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	94	1	no	—
276	C₂²×C₈	—	94	1	no	—
277	C₂²×C₈	—	94	1	no	—
278	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
279	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
280	#126	—	94	1	no	—
281	#125	—	47	1	no	—
282	#124	—	47	1	no	—
283	#123	—	94	1	no	—
284	C₂²⋊Q₈	—	47	1	no	—
285	#121	—	47	1	no	—
286	C₄×Q₈	—	47	2	no	—
287	C₄×Q₈	—	47	2	no	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	—	94	1	no	—
290	C₄×Q₈	—	94	1	no	—
291	C₄×D₄	—	47	1	no	—
292	C₄×D₄	—	94	1	no	—
293	#117	—	94	1	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄²	—	94	1	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	47	2	no	—
299	#106	—	47	2	no	—
300	C₄⋊C₈	—	47	2	no	—
301	C₄⋊C₈	—	47	1	no	—
302	C₄⋊C₈	—	47	1	no	—
303	C₄⋊C₈	—	94	2	no	—
304	C₄⋊C₈	—	94	2	no	—
305	C₄⋊C₈	—	94	1	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	—	94	1	no	—
308	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
309	#103	—	47	2	no	—
310	#103	—	47	2	no	—
311	#103	—	47	2	no	—
312	#102	—	47	2	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	C₂²⋊C₈	—	94	1	no	—
315	C₂²⋊C₈	—	94	1	no	—
316	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
317	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
318	#97	—	2	1	no	—
319	#97	—	94	1	no	—
320	#97	—	94	1	no	—
321	C₄×C₈	—	94	2	no	—
322	C₄×C₈	—	94	2	no	—
323	C₄×C₈	—	94	1	no	—
324	C₄×C₈	D₁₈₈	1	1	yes	characteristic
325	C₄×C₈	D₁₈₈	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₇	1	2	yes	—
327	C₄×C₈	C₂²×D₄₇	1	2	yes	—
328	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
330	C₂×Q₈	—	47	2	no	—
331	C₂×Q₈	—	47	1	no	—
332	C₂×Q₈	—	94	4	no	—
333	C₂×Q₈	—	94	1	no	—
334	C₂×D₄	—	47	1	no	—
335	C₂×D₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
341	C₂²×C₄	#10625350	1	1	yes	characteristic
342	Q₁₆	—	94	4	no	—
343	SD₁₆	—	94	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	188	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	1	no	—
351	C₂×C₈	—	94	1	no	—
352	C₂×C₈	—	188	2	no	—
353	C₂×C₈	—	188	2	no	—
354	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
356	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
357	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
358	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
360	C₄⋊C₄	—	47	2	no	—
361	C₄⋊C₄	—	47	1	no	—
362	C₄⋊C₄	—	47	1	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	94	1	no	—
370	C₂²⋊C₄	—	94	1	no	—
371	C₂²⋊C₄	—	94	1	no	—
372	C₂²⋊C₄	—	94	1	no	—
373	C₂²⋊C₄	—	94	1	no	—
374	C₂²⋊C₄	—	94	1	no	—
375	C₄²	—	94	2	no	—
376	C₄²	—	94	2	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	1	no	—
383	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
384	Q₈	—	47	4	no	—
385	Q₈	—	94	4	no	—
386	Q₈	—	94	2	no	—
387	Q₈	—	94	2	no	—
388	D₄	—	94	2	no	—
389	D₄	—	188	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	94	4	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	1	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
404	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
405	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	2	1	no	—
415	C₈	—	188	1	no	—
416	C₈	—	188	2	no	—
417	C₈	—	188	1	no	—
418	C₈	#13094057	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	188	1	no	—
422	C₂²	—	188	1	no	—
423	C₂²	—	188	1	no	—
424	C₂²	#15689241	1	2	yes	—
425	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	94	4	no	—
431	C₄	—	188	1	no	—
432	C₄	—	188	2	no	—
433	C₄	—	188	1	no	—
434	C₄	—	188	1	no	—
435	C₄	#131×D₄₇	1	2	yes	—
436	C₄	C₂×#13094057	1	1	yes	characteristic
437	C₄	#15689923	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	376	1	no	—
440	C₂	#20252084	1	1	yes	characteristic
441	C₂	C₄×#13094057	1	1	yes	characteristic
442	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	#13093998	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	#17911
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
3. C₂×C₈×Dic₉₄	C₂	semidirect
4. #20242268	C₂	semidirect
5. #20242261	C₂	semidirect
6. C₈×Dic₁₈₈	C₂	semidirect
7. C₈×#10625325	C₂	semidirect
8. #20242173	C₂	semidirect
9. #20241836	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
227. C₈×M₁₆	D₄₇	semidirect
270. C₄₇	#17911	semidirect

Maximal subgroups

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

subgroup	index
#20253470	2
#20252363	2
C₂×C₈×Dic₉₄	2
#20242268	2
#20242261	2
C₈×Dic₁₈₈	2
C₈×#10625325	2
#20242173	2
#20241836	2
#20241802	2
C₈×M₁₆×C₄₇	2
#17911	47