Subgroups — #26187164

Order 12032.

748 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253388	C₂	1	1	yes	maximal, characteristic
2	#20252134	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242271	C₂	1	2	yes	maximal, complemented
4	#20242217	C₂	1	2	yes	maximal, complemented
5	#20242215	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242164	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241838	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689436	C₄	1	2	yes	—
15	#15689403	C₄	1	1	yes	characteristic
16	#15689403	C₄	1	1	yes	characteristic
17	#15689318	C₄	1	1	yes	characteristic
18	#15689318	C₄	1	1	yes	characteristic
19	#15689257	C₄	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	C₄×#10625334	C₂²	1	2	yes	—
22	#15689202	C₂²	1	2	yes	complemented
23	#15689196	—	2	2	no	—
24	C₈×D₁₈₈	C₂²	1	2	yes	complemented
25	#15689176	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	#15689091	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688875	C₂²	1	2	yes	complemented
30	#15688875	C₂²	1	2	yes	complemented
31	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	#15688850	C₂²	1	2	yes	complemented
36	#15688850	C₂²	1	2	yes	complemented
37	#15688844	C₂²	1	2	yes	complemented
38	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
39	C₂²×M₁₆×C₄₇	—	2	1	no	—
40	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#436	C₂²	1	2	yes	—
42	C₄₇×#435	—	2	2	no	—
43	C₈×D₄×C₄₇	C₂²	1	2	yes	—
44	C₄₇×#423	C₂²	1	1	yes	characteristic
45	C₄₇×#407	—	2	1	no	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625334	C₂×C₄	1	2	yes	—
49	C₂×#10625334	C₂×C₄	1	2	yes	—
50	#13094032	—	4	4	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	#13094024	C₂×C₄	1	1	yes	characteristic
56	#13094021	C₂×C₄	1	1	yes	characteristic
57	#13094012	—	2	1	no	—
58	#13093998	—	2	1	no	—
59	#13093998	C₂×C₄	1	2	yes	—
60	C₄×D₁₈₈	—	2	1	no	—
61	C₄×D₁₈₈	C₂³	1	2	yes	—
62	#13093957	C₂×C₄	1	2	yes	—
63	#13093957	C₂×C₄	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	#13093945	C₂×C₄	1	2	yes	—
70	#13093945	C₂×C₄	1	2	yes	—
71	#13093944	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	C₄×C₄₇⋊C₈	—	2	1	no	—
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	2	no	—
84	C₂×M₁₆×C₄₇	—	4	4	no	—
85	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	—	2	2	no	—
88	C₄×D₄×C₄₇	—	2	1	no	—
89	C₄×D₄×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
99	C₂²⋊C₈×C₄₇	—	2	2	no	—
100	C₂²⋊C₈×C₄₇	—	2	2	no	—
101	#97×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	C₂⁴×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	4	1	no	—
107	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₇	—	2	2	no	—
120	#10625350	—	4	2	no	—
121	#10625350	—	4	2	no	—
122	C₂×D₁₈₈	—	2	1	no	—
123	C₂×D₁₈₈	—	2	1	no	—
124	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
125	C₂×C₄×D₄₇	—	2	2	no	—
126	C₂×Dic₉₄	—	2	1	no	—
127	M₁₆×C₄₇	—	2	2	no	—
128	M₁₆×C₄₇	—	4	2	no	—
129	M₁₆×C₄₇	—	4	4	no	—
130	M₁₆×C₄₇	D₈	1	4	yes	complemented
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	4	4	no	—
133	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₄₇	—	2	1	no	—
139	C₂²⋊C₄×C₄₇	—	2	1	no	—
140	C₂²⋊C₄×C₄₇	—	2	1	no	—
141	C₂²⋊C₄×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₇	#41	1	1	yes	characteristic
145	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
146	#10625334	—	2	4	no	—
147	#10625334	—	4	2	no	—
148	(C₂×D₄₇)⋊C₄	—	2	2	no	—
149	(C₂×D₄₇)⋊C₄	—	2	2	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	4	2	no	—
157	C₂×C₄₇⋊C₈	—	4	2	no	—
158	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
160	#10625324	—	4	4	no	—
161	C₈×D₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	8	1	no	—
167	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₄₇	—	2	2	no	—
169	D₄×C₄₇	—	2	1	no	—
170	D₄×C₄₇	—	2	1	no	—
171	D₄×C₄₇	—	2	1	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	#131	1	2	yes	complemented
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
190	C₂×C₄×C₄₇	#135	1	2	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂²⋊D₄₇	—	4	4	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	D₁₈₈	—	2	2	no	—
197	D₁₈₈	—	2	2	no	—
198	D₁₈₈	—	4	2	no	—
199	D₁₈₈	—	8	1	no	—
200	C₄×D₄₇	—	4	2	no	—
201	C₄×D₄₇	—	4	2	no	—
202	Dic₉₄	—	4	2	no	—
203	C₈×C₄₇	—	2	2	no	—
204	C₈×C₄₇	—	4	2	no	—
205	C₈×C₄₇	C₂×D₈	1	4	yes	—
206	C₄₇⋊C₈	—	2	2	no	—
207	C₄₇⋊C₈	—	2	2	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	—	4	1	no	—
210	C₄₇⋊C₈	—	4	1	no	—
211	C₄₇⋊C₈	—	4	1	no	—
212	#17994	—	47	1	no	maximal, Sylow
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	2	no	—
216	C₂²×C₄₇	—	4	1	no	—
217	C₂²×C₄₇	—	4	1	no	—
218	C₂²×C₄₇	—	4	1	no	—
219	C₂²×C₄₇	—	4	1	no	—
220	C₂²×C₄₇	—	4	1	no	—
221	C₂²×C₄₇	—	8	4	no	—
222	C₂²×C₄₇	C₄×D₈	1	2	yes	—
223	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂×D₄₇	—	4	2	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₂×D₄₇	—	4	2	no	—
227	C₄×C₄₇	—	2	1	no	—
228	C₄×C₄₇	—	2	1	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	4	1	no	—
231	C₄×C₄₇	—	4	1	no	—
232	C₄×C₄₇	C₄×D₈	1	2	yes	—
233	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
234	C₄×C₄₇	#568	1	1	yes	characteristic
235	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
236	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
237	Dic₄₇	—	4	2	no	—
238	#3100	—	47	1	no	—
239	#2935	—	47	1	no	—
240	D₄×M₁₆	D₄₇	1	1	yes	characteristic, complemented
241	#1589	—	47	2	no	—
242	#1581	—	47	2	no	—
243	#1581	—	47	2	no	—
244	C₈×D₈	—	47	2	no	—
245	#1571	—	47	1	no	—
246	#1492	—	47	1	no	—
247	C₂×D₄⋊C₈	—	47	1	no	—
248	C₈×M₁₆	—	47	1	no	—
249	C₂×C₄₇	—	2	2	no	—
250	C₂×C₄₇	—	4	2	no	—
251	C₂×C₄₇	—	8	1	no	—
252	C₂×C₄₇	#2933	1	1	yes	characteristic
253	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
254	C₂×C₄₇	#2956	1	1	yes	characteristic
255	D₄₇	—	8	2	no	—
256	C₂×#131	—	94	1	no	—
257	C₂²×M₁₆	—	2	1	no	—
258	#532	—	47	1	no	—
259	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
260	#480	—	47	2	no	—
261	#474	—	47	1	no	—
262	#474	—	47	1	no	—
263	#459	—	47	1	no	—
264	#459	—	47	1	no	—
265	#447	—	47	2	no	—
266	C₄×D₈	—	47	2	no	—
267	C₄×D₈	—	47	2	no	—
268	#436	—	47	2	no	—
269	#436	C₂×D₄₇	1	2	yes	—
270	#435	—	2	2	no	—
271	#435	—	94	2	no	—
272	C₈×D₄	—	47	2	no	—
273	C₈×D₄	C₂×D₄₇	1	2	yes	—
274	#431	—	47	1	no	—
275	#423	C₂×D₄₇	1	1	yes	characteristic
276	C₂×C₄⋊C₈	—	47	1	no	—
277	#408	—	94	1	no	—
278	#407	—	2	1	no	—
279	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
280	C₂×C₄×C₈	—	47	1	no	—
281	#335	—	47	2	no	—
282	#335	—	47	2	no	—
283	D₄⋊C₈	—	47	1	no	—
284	D₄⋊C₈	—	47	1	no	—
285	D₄⋊C₈	—	47	1	no	—
286	D₄⋊C₈	—	47	1	no	—
287	D₄⋊C₈	—	47	2	no	—
288	D₄⋊C₈	—	47	2	no	—
289	#322	—	47	2	no	—
290	C₈²	—	47	2	no	—
291	C₄₇	#17994	1	1	yes	characteristic, complemented, Sylow
292	C₂×#41	—	94	1	no	—
293	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂×D₈	—	47	2	no	—
296	C₂×D₈	—	47	2	no	—
297	#131	—	188	4	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	4	4	no	—
301	C₂×M₁₆	—	94	2	no	—
302	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
303	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	94	1	no	—
306	C₂²×C₈	—	94	1	no	—
307	C₂²×C₈	—	94	2	no	—
308	C₄⋊Q₈	—	47	1	no	—
309	#127	—	47	1	no	—
310	#124	—	94	1	no	—
311	#121	—	47	2	no	—
312	#121	—	94	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	47	2	no	—
316	C₄×D₄	—	94	1	no	—
317	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
318	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
319	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
324	#107	—	47	2	no	—
325	#107	—	47	2	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	47	1	no	—
328	C₄⋊C₈	—	47	1	no	—
329	C₄⋊C₈	—	47	1	no	—
330	C₄⋊C₈	—	47	1	no	—
331	C₄⋊C₈	—	94	1	no	—
332	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
333	#102	—	47	2	no	—
334	#102	—	47	2	no	—
335	#102	—	47	2	no	—
336	#102	—	47	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	47	2	no	—
340	C₂²⋊C₈	—	94	2	no	—
341	C₂²⋊C₈	—	94	2	no	—
342	#97	C₂²⋊D₄₇	1	2	yes	—
343	C₄×C₈	—	47	2	no	—
344	C₄×C₈	—	47	1	no	—
345	C₄×C₈	—	47	1	no	—
346	C₄×C₈	—	94	1	no	—
347	C₄×C₈	C₂²×D₄₇	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	#41	—	188	2	no	—
350	#41	—	188	2	no	—
351	C₂×Q₈	—	94	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	47	2	no	—
356	C₂×D₄	—	94	2	no	—
357	C₂×D₄	—	94	1	no	—
358	C₂×D₄	—	94	1	no	—
359	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
360	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	94	2	no	—
369	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	#10625350	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
372	D₈	—	94	4	no	—
373	D₈	—	188	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	—	188	4	no	—
378	M₁₆	#10625334	1	4	yes	complemented
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	—	47	2	no	—
382	C₂×C₈	—	47	2	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	188	2	no	—
388	C₂×C₈	—	188	2	no	—
389	C₂×C₈	—	188	4	no	—
390	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
391	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	47	2	no	—
394	C₄⋊C₄	—	94	1	no	—
395	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
396	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	94	2	no	—
402	C₂²⋊C₄	—	94	2	no	—
403	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
404	C₄²	#10625350	1	1	yes	characteristic
405	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₄²	C₂³×D₄₇	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	94	2	no	—
413	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
414	Q₈	—	188	2	no	—
415	D₄	—	2	1	no	—
416	D₄	—	2	1	no	—
417	D₄	—	2	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	94	2	no	—
420	D₄	—	94	2	no	—
421	D₄	—	376	1	no	—
422	D₄	—	188	4	no	—
423	D₄	—	188	2	no	—
424	D₄	#13094032	1	2	yes	complemented
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
441	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625334	1	2	yes	—
444	C₂×C₄	#13094044	1	2	yes	—
445	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
447	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	4	2	no	—
450	C₈	—	94	2	no	—
451	C₈	—	94	2	no	—
452	C₈	—	94	2	no	—
453	C₈	—	188	1	no	—
454	C₈	—	188	1	no	—
455	C₈	—	188	1	no	—
456	C₈	C₂×#10625334	1	4	yes	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	8	4	no	—
466	C₂²	—	188	2	no	—
467	C₂²	—	188	2	no	—
468	C₂²	—	188	2	no	—
469	C₂²	C₄×#10625334	1	2	yes	—
470	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	188	2	no	—
477	C₄	C₄×#10625334	1	2	yes	—
478	C₄	C₂×#13094032	1	1	yes	characteristic
479	C₄	#15689889	1	1	yes	characteristic
480	C₄	C₂²×#10625334	1	1	yes	characteristic
481	C₄	C₂×#13094044	1	1	yes	characteristic
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	8	1	no	—
485	C₂	—	376	2	no	—
486	C₂	#20252113	1	1	yes	characteristic
487	C₂	C₂×C₄×#10625334	1	1	yes	characteristic
488	C₂	#20252295	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	D₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253388	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	D₄×M₁₆	D₄₇
hypocenter	C₄₇	#17994
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #20252134	C₂	semidirect
3. #20242271	C₂	semidirect
4. #20242217	C₂	semidirect
5. #20242215	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242164	C₂	semidirect
8. #20241838	C₂	semidirect
9. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. D₄×M₁₆×C₄₇	C₂	semidirect
22. #15689202	C₂²	semidirect
24. C₈×D₁₈₈	C₂²	semidirect
29. #15688875	C₂²	semidirect
30. #15688875	C₂²	semidirect
35. #15688850	C₂²	semidirect
36. #15688850	C₂²	semidirect
37. #15688844	C₂²	semidirect
38. C₈×C₄₇⋊C₈	C₂²	semidirect
130. M₁₆×C₄₇	D₈	semidirect
173. D₄×C₄₇	#131	semidirect
240. D₄×M₁₆	D₄₇	semidirect
291. C₄₇	#17994	semidirect
378. M₁₆	#10625334	semidirect
424. D₄	#13094032	semidirect

Maximal subgroups

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

subgroup	index
#20253388	2
#20252134	2
#20242271	2
#20242217	2
#20242215	2
C₈×#10625334	2
#20242164	2
#20241838	2
C₂×D₄⋊(C₄₇⋊C₈)	2
M₁₆×C₄₇⋊C₈	2
D₄×M₁₆×C₄₇	2
#17994	47