Subgroups — #26109036

Order 12032.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243368	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688860	C₂	1	2	yes	maximal
3	#20241618	C₂	1	1	yes	maximal, characteristic
4	#20241266	C₂	1	2	yes	maximal
5	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄₇⋊#95	—	2	1	no	—
10	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
11	#15688878	—	2	1	no	—
12	#15688860	—	2	4	no	—
13	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#391	C₄	1	1	yes	characteristic, complemented
17	C₄₇×#389	C₄	1	1	yes	characteristic, complemented
18	C₄₇×#387	—	2	1	no	—
19	C₄₇×#385	—	2	1	no	—
20	C₄₇×#380	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
22	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	4	no	—
27	C₂×C₄⋊Dic₄₇	—	4	2	no	—
28	C₂×C₄⋊Dic₄₇	—	4	2	no	—
29	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄₇⋊#95	—	2	2	no	—
33	C₄₇⋊#95	—	2	2	no	—
34	C₄₇⋊#95	—	4	2	no	—
35	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²⋊Q₈×C₄₇	—	2	1	no	—
40	C₂²⋊Q₈×C₄₇	—	2	1	no	—
41	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
42	C₂²⋊Q₈×C₄₇	Q₈	1	2	yes	—
43	C₄×Q₈×C₄₇	—	4	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄²×C₄₇	—	2	1	no	—
53	C₂×C₄²×C₄₇	—	2	1	no	—
54	C₂×C₄²×C₄₇	—	4	2	no	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
59	#95×C₄₇	—	2	1	no	—
60	#95×C₄₇	—	2	1	no	—
61	#95×C₄₇	—	2	1	no	—
62	#95×C₄₇	—	2	1	no	—
63	#95×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₇	—	2	1	no	—
66	C₂×Q₈×C₄₇	—	4	1	no	—
67	C₂×Q₈×C₄₇	—	4	1	no	—
68	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	complemented
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	4	1	no	—
78	C₂²×C₄×C₄₇	—	4	1	no	—
79	C₂²×C₄×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	—	4	1	no	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
93	C₂²×Dic₄₇	—	2	4	no	—
94	C₂²×Dic₄₇	—	4	2	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	—	4	2	no	—
98	C₂²×Dic₄₇	—	4	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	2	1	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	4	1	no	—
104	C₄⋊C₄×C₄₇	—	4	1	no	—
105	C₄⋊C₄×C₄₇	—	4	2	no	—
106	C₄⋊C₄×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	complemented
108	C₂²⋊C₄×C₄₇	—	2	2	no	—
109	C₂²⋊C₄×C₄₇	—	2	2	no	—
110	C₂²⋊C₄×C₄₇	—	4	1	no	—
111	C₂²⋊C₄×C₄₇	—	4	1	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	4	1	no	—
115	C₄²×C₄₇	—	4	1	no	—
116	C₄²×C₄₇	—	4	2	no	—
117	C₄²×C₄₇	—	4	2	no	—
118	C₄⋊Dic₄₇	—	4	8	no	—
119	C₂×C₄₇⋊C₈	—	4	2	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	4	2	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	—	2	1	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₄₇	#121	1	1	yes	characteristic
128	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
131	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
132	C₂³×C₄₇	#137	1	1	yes	characteristic
133	Q₈×C₄₇	—	4	2	no	—
134	Q₈×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	1	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	#99	1	2	yes	—
168	C₂×C₄×C₄₇	#103	1	2	yes	—
169	C₂×C₄×C₄₇	#103	1	2	yes	—
170	C₂×C₄×C₄₇	#104	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	4	4	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	8	2	no	—
179	C₂×Dic₄₇	—	8	2	no	—
180	C₂×Dic₄₇	—	8	2	no	—
181	C₂×Dic₄₇	—	8	2	no	—
182	C₄₇⋊C₈	—	8	2	no	—
183	#8578	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	#380	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
198	C₂²×C₄₇	#410	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
200	C₂²×C₄₇	#417	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
202	C₂²×C₄₇	#421	1	1	yes	characteristic
203	C₂²×C₄₇	#460	1	1	yes	characteristic
204	C₂²×C₄₇	#462	1	1	yes	characteristic
205	C₂²×C₄₇	#475	1	1	yes	characteristic
206	C₂²×C₄₇	#477	1	1	yes	characteristic
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	4	2	no	—
217	C₄×C₄₇	—	8	1	no	—
218	C₄×C₄₇	—	8	1	no	—
219	Dic₄₇	—	8	4	no	—
220	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
221	#1797	—	47	1	no	—
222	C₂×#328	—	47	2	no	—
223	C₄⋊#95	—	47	1	no	—
224	#1294	—	47	2	no	—
225	C₂×C₄₇	—	2	1	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	—	2	1	no	—
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	#1503	1	1	yes	characteristic
230	C₂×C₄₇	#1504	1	1	yes	characteristic
231	C₂×C₄₇	#1512	1	1	yes	characteristic
232	C₂×C₄₇	#1520	1	1	yes	characteristic
233	C₂×C₄₇	#1799	1	1	yes	characteristic
234	C₂×C₄₇	#1803	1	1	yes	characteristic
235	C₂×C₄₇	#1806	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
238	C₂²×C₄⋊C₄	—	94	1	no	—
239	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄⋊C₈	—	94	1	no	—
241	C₂×C₂²⋊C₈	—	47	2	no	—
242	#391	Dic₄₇	1	1	yes	characteristic, complemented
243	#389	Dic₄₇	1	1	yes	characteristic, complemented
244	#387	—	2	1	no	—
245	#385	—	2	1	no	—
246	#380	C₂×D₄₇	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	2	1	no	—
248	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic, complemented
249	C₄×C₂²⋊C₄	—	2	1	no	—
250	C₂×#95	—	47	2	no	—
251	C₂×#95	—	94	1	no	—
252	#336	—	94	1	no	—
253	#328	—	94	4	no	—
254	C₄₇	#8578	1	1	yes	characteristic, complemented, Sylow
255	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
256	C₂³×C₄	—	94	2	no	—
257	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
259	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
260	C₂²×C₈	—	94	2	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	Dic₉₄	1	2	yes	—
264	C₂²⋊Q₈	D₁₈₈	1	2	yes	—
265	C₄×Q₈	—	4	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	94	4	no	—
270	C₂×C₄⋊C₄	—	188	2	no	—
271	C₂×C₄⋊C₄	—	188	2	no	—
272	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
281	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
282	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
284	C₄⋊C₈	—	188	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₂²⋊C₈	—	94	2	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	#95	—	188	2	no	—
295	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	complemented
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	94	4	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	—	188	2	no	—
315	C₂²×C₄	—	188	2	no	—
316	C₂²×C₄	—	188	2	no	—
317	C₂²×C₄	—	188	2	no	—
318	C₂²×C₄	—	188	2	no	—
319	C₂²×C₄	#10625336	1	2	yes	—
320	C₂²×C₄	#10625337	1	2	yes	—
321	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
327	C₂²×C₄	#10625350	1	1	yes	characteristic
328	C₂²×C₄	#10625350	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
331	C₂×C₈	—	188	2	no	—
332	C₂×C₈	—	188	2	no	—
333	C₂×C₈	—	188	2	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	188	8	no	—
342	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	complemented
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
358	C₂³	#13093998	1	1	yes	characteristic
359	C₂³	#13094003	1	1	yes	characteristic
360	C₂³	C₂×#10625336	1	1	yes	characteristic
361	C₂³	C₂×#10625337	1	1	yes	characteristic
362	C₂³	#13094049	1	1	yes	characteristic
363	C₂³	#13094054	1	1	yes	characteristic
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	376	2	no	—
399	C₂×C₄	—	376	2	no	—
400	C₂×C₄	—	376	2	no	—
401	C₂×C₄	—	376	2	no	—
402	C₂×C₄	—	188	4	no	—
403	C₂×C₄	—	188	4	no	—
404	C₂×C₄	—	188	4	no	—
405	C₂×C₄	#13093939	1	2	yes	—
406	C₂×C₄	#13093948	1	2	yes	—
407	C₂×C₄	#13093948	1	2	yes	—
408	C₂×C₄	#13093951	1	2	yes	—
409	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
410	C₂×C₄	#13093983	1	1	yes	characteristic
411	C₂×C₄	#13093998	1	1	yes	characteristic
412	C₂×C₄	#13094003	1	1	yes	characteristic
413	C₈	—	376	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	#15688983	1	1	yes	characteristic
427	C₂²	C₂×#13093939	1	1	yes	characteristic
428	C₂²	#15689097	1	1	yes	characteristic
429	C₂²	C₂×#13093948	1	1	yes	characteristic
430	C₂²	#15689124	1	1	yes	characteristic
431	C₂²	C₂×#13093951	1	1	yes	characteristic
432	C₂²	#15689140	1	1	yes	characteristic
433	C₂²	#15689323	1	1	yes	characteristic
434	C₂²	#15689333	1	1	yes	characteristic
435	C₂²	#15689408	1	1	yes	characteristic
436	C₂²	#15689418	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	—	376	4	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	#20241887	1	1	yes	characteristic
455	C₂	#20241892	1	1	yes	characteristic
456	C₂	#20241926	1	1	yes	characteristic
457	C₂	#20241960	1	1	yes	characteristic
458	C₂	#20243376	1	1	yes	characteristic
459	C₂	#20243393	1	1	yes	characteristic
460	C₂	#20243408	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#8578
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
14. C₂×C₄×Q₈×C₄₇	C₄	semidirect
16. C₄₇×#391	C₄	semidirect
17. C₄₇×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
68. C₂×Q₈×C₄₇	C₄⋊C₄	semidirect
107. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
237. C₂×C₄×Q₈	Dic₄₇	semidirect
242. #391	Dic₄₇	semidirect
243. #389	Dic₄₇	semidirect
248. C₄×C₄⋊C₄	Dic₄₇	semidirect
254. C₄₇	#8578	semidirect
299. C₂×Q₈	C₄⋊Dic₄₇	semidirect
342. C₄⋊C₄	C₄⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20243368	2
C₂×#15688860	2
#20241618	2
#20241266	2
C₄×C₂²⋊Q₈×C₄₇	2
#8578	47