Subgroups — #26235061

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689201	C₂	1	1	yes	maximal, characteristic
3	#20244163	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244161	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243593	C₂	1	2	yes	maximal, complemented
6	#20243592	C₂	1	2	yes	maximal, complemented
7	#20243525	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243428	C₂	1	2	yes	maximal, complemented
9	C₄×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243114	C₂	1	2	yes	maximal, complemented
11	D₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	2	yes	—
14	#15689201	—	2	1	no	—
15	#15689201	C₄	1	2	yes	—
16	#15689201	C₄	1	2	yes	—
17	#15689201	C₄	1	4	yes	—
18	#15689195	—	2	2	no	—
19	D₄×C₄₇⋊C₈	—	2	1	no	—
20	C₂×#13093959	C₂²	1	1	yes	characteristic
21	C₂×#13093959	C₂²	1	1	yes	characteristic
22	C₂×#13093959	C₂²	1	2	yes	—
23	C₂×#13093959	C₂²	1	2	yes	—
24	#15689147	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	#15689087	C₂²	1	2	yes	—
27	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
28	C₄×#10625329	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688887	C₂²	1	2	yes	—
31	#15688887	C₂²	1	2	yes	—
32	#15688887	C₂²	1	1	yes	characteristic
33	#15688887	C₂²	1	1	yes	characteristic
34	#15688887	C₂²	1	2	yes	—
35	#15688887	C₂²	1	2	yes	—
36	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#436	—	2	1	no	—
39	C₄₇×#435	—	2	2	no	—
40	C₈×D₄×C₄₇	—	2	1	no	—
41	C₄₇×#423	C₂²	1	1	yes	characteristic
42	C₄₇×#407	C₂²	1	2	yes	—
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	—	4	2	no	—
47	C₂×#10625329	—	4	2	no	—
48	C₂×#10625329	—	4	2	no	—
49	C₂×#10625329	C₂×C₄	1	4	yes	—
50	C₂×#10625329	C₂×C₄	1	4	yes	—
51	C₂×#10625329	C₂³	1	1	yes	characteristic
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
58	#13093959	—	2	2	no	—
59	#13093959	—	2	2	no	—
60	#13093959	—	4	2	no	—
61	#13093959	—	4	2	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
69	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
70	#13093935	—	2	1	no	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×M₁₆×C₄₇	—	2	2	no	—
77	C₂×M₁₆×C₄₇	—	2	4	no	—
78	C₂×M₁₆×C₄₇	—	4	2	no	—
79	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
80	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	—	2	2	no	—
83	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
87	C₄×D₄×C₄₇	D₄	1	2	yes	—
88	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₇	Q₈	1	2	yes	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	C₄⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	—	2	2	no	—
95	C₂²⋊C₈×C₄₇	—	2	2	no	—
96	#97×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂×D₄×C₄₇	—	4	2	no	—
100	C₂×D₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₄₇	—	2	1	no	—
116	M₁₆×C₄₇	—	2	2	no	—
117	M₁₆×C₄₇	—	2	1	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	1	no	—
120	M₁₆×C₄₇	—	4	4	no	—
121	M₁₆×C₄₇	#41	1	2	yes	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	4	4	no	—
126	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
127	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
130	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
132	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
133	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	#10625329	—	2	1	no	—
138	#10625329	—	2	1	no	—
139	#10625329	—	2	2	no	—
140	#10625329	—	2	1	no	—
141	#10625329	—	2	2	no	—
142	#10625329	—	4	4	no	—
143	#10625329	—	4	4	no	—
144	#10625329	—	4	4	no	—
145	#10625329	#41	1	2	yes	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	4	4	no	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
164	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	4	2	no	—
195	C₈×C₄₇	—	4	1	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	2	4	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	#22719	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	—	8	2	no	—
213	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₄₇	#554	1	1	yes	characteristic
215	C₂²×C₄₇	#554	1	1	yes	characteristic
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	#430	1	2	yes	—
222	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
223	C₄×C₄₇	#518	1	1	yes	characteristic
224	C₄×C₄₇	#546	1	1	yes	characteristic
225	C₄×C₄₇	#546	1	1	yes	characteristic
226	D₄×M₁₆	—	47	1	no	—
227	D₄×M₁₆	D₄₇	1	1	yes	characteristic
228	C₂×#436	—	47	1	no	—
229	#1950	—	47	1	no	—
230	#1950	—	47	1	no	—
231	#1855	—	47	2	no	—
232	#1855	—	47	2	no	—
233	#1837	—	47	1	no	—
234	#1811	—	47	2	no	—
235	C₄×#108	—	47	1	no	—
236	#1738	—	47	2	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	—	4	2	no	—
240	C₂×C₄₇	—	4	2	no	—
241	C₂×C₄₇	#2349	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
243	C₂×C₄₇	#2916	1	1	yes	characteristic
244	C₂²×M₁₆	—	47	2	no	—
245	C₂²×M₁₆	—	47	2	no	—
246	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
247	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
248	#436	—	2	1	no	—
249	#436	—	47	2	no	—
250	#436	—	47	2	no	—
251	#436	—	47	4	no	—
252	#436	—	94	1	no	—
253	#435	—	2	2	no	—
254	#435	—	94	2	no	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	—	94	1	no	—
257	C₂×#108	—	47	1	no	—
258	C₂×#108	—	47	1	no	—
259	C₂×#108	—	47	2	no	—
260	C₂×#108	—	47	2	no	—
261	#423	—	47	1	no	—
262	#423	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	—	47	1	no	—
264	#407	—	47	2	no	—
265	#407	C₂×D₄₇	1	2	yes	—
266	C₂×C₂²⋊C₈	—	47	2	no	—
267	C₄×M₁₆	—	47	1	no	—
268	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄×C₈	—	47	1	no	—
270	#341	—	47	1	no	—
271	#341	—	47	2	no	—
272	#341	—	47	2	no	—
273	#341	—	47	2	no	—
274	#341	—	47	2	no	—
275	#341	—	47	1	no	—
276	C₄₇	#22719	1	1	yes	characteristic, complemented, Sylow
277	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	4	2	no	—
282	C₂×M₁₆	—	47	4	no	—
283	C₂×M₁₆	—	47	4	no	—
284	C₂×M₁₆	—	47	1	no	—
285	C₂×M₁₆	—	47	2	no	—
286	C₂×M₁₆	—	47	1	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	—	94	4	no	—
289	C₂×M₁₆	—	188	2	no	—
290	C₂×M₁₆	—	188	2	no	—
291	C₂×M₁₆	—	188	2	no	—
292	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
293	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	2	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	94	2	no	—
300	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
301	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
302	C₄×D₄	C₄×D₄₇	1	2	yes	—
303	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	Dic₉₄	1	2	yes	—
308	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
309	#108	—	94	2	no	—
310	#108	—	94	2	no	—
311	#108	—	188	2	no	—
312	#108	—	188	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	47	2	no	—
316	C₄⋊C₈	—	47	2	no	—
317	C₄⋊C₈	—	94	1	no	—
318	C₄⋊C₈	—	94	1	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	47	4	no	—
322	C₂²⋊C₈	—	47	4	no	—
323	C₂²⋊C₈	—	94	2	no	—
324	C₂²⋊C₈	—	94	2	no	—
325	#97	—	2	1	no	—
326	#97	—	94	1	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	47	2	no	—
329	C₄×C₈	—	47	2	no	—
330	C₄×C₈	—	94	1	no	—
331	C₂⁴	C₂×Dic₉₄	1	2	yes	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	Dic₄₇⋊C₄	1	1	yes	characteristic
334	C₂×D₄	Dic₄₇⋊C₄	1	1	yes	characteristic
335	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
342	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
344	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
345	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	1	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	4	4	no	—
354	M₁₆	—	47	2	no	—
355	M₁₆	—	94	1	no	—
356	M₁₆	—	94	2	no	—
357	M₁₆	—	94	1	no	—
358	M₁₆	—	94	1	no	—
359	M₁₆	—	94	2	no	—
360	M₁₆	—	188	4	no	—
361	M₁₆	—	188	4	no	—
362	M₁₆	—	188	4	no	—
363	M₁₆	#10625352	1	2	yes	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	—	47	2	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	47	4	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	188	4	no	—
381	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
382	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
383	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
384	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
385	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
386	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
387	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
388	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
397	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
398	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
415	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
416	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
417	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
418	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
419	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
424	C₂×C₄	#13094069	1	1	yes	characteristic
425	C₂×C₄	#13094070	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	2	no	—
429	C₈	—	94	2	no	—
430	C₈	—	94	2	no	—
431	C₈	—	94	4	no	—
432	C₈	—	94	2	no	—
433	C₈	—	188	2	no	—
434	C₈	—	188	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
446	C₂²	#15689830	1	1	yes	characteristic
447	C₂²	#15689832	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	#15689171	1	2	yes	—
454	C₄	C₄×#10625352	1	1	yes	characteristic
455	C₄	#15689595	1	1	yes	characteristic
456	C₄	#15689761	1	1	yes	characteristic
457	C₄	#15689767	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	4	2	no	—
462	C₂	#20246293	1	1	yes	characteristic
463	C₂	C₂×#15689171	1	1	yes	characteristic
464	C₂	#20251997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	D₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	D₄×M₁₆	D₄₇
hypocenter	C₄₇	#22719
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20244163	C₂	semidirect
4. #20244161	C₂	semidirect
5. #20243593	C₂	semidirect
6. #20243592	C₂	semidirect
7. #20243525	C₂	semidirect
8. #20243428	C₂	semidirect
9. C₄×#13093959	C₂	semidirect
10. #20243114	C₂	semidirect
276. C₄₇	#22719	semidirect

Maximal subgroups

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

subgroup	index
D₄×#10625329	2
C₂×#15689201	2
#20244163	2
#20244161	2
#20243593	2
#20243592	2
#20243525	2
#20243428	2
C₄×#13093959	2
#20243114	2
D₄×M₁₆×C₄₇	2
#22719	47