Subgroups — #26121754

Order 12032.

1230 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689124	C₂	1	2	yes	maximal
2	C₂×#15688891	C₂	1	2	yes	maximal, complemented
3	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688886	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	#15689124	—	2	4	no	—
9	#15689124	C₄	1	8	yes	complemented
10	C₂×#13093948	—	2	2	no	—
11	C₂×#13093945	—	2	2	no	—
12	#15688891	—	2	4	no	—
13	#15688888	—	2	2	no	—
14	#15688886	—	2	1	no	—
15	#15688886	—	2	1	no	—
16	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#131×C₄₇	—	2	4	no	—
18	C₂×#131×C₄₇	—	2	4	no	—
19	C₂×#131×C₄₇	—	2	2	no	—
20	C₂×#131×C₄₇	C₄	1	4	yes	complemented
21	C₂²×M₁₆×C₄₇	—	2	1	no	—
22	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₄₇	—	2	1	no	—
24	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂³×Dic₄₇	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	C₂×C₄	1	4	yes	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
39	#13093948	—	2	8	no	—
40	#13093945	—	2	8	no	—
41	C₂×#41×C₄₇	—	2	1	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	1	no	—
45	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
46	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×#41×C₄₇	D₄	1	4	yes	—
48	C₂×#41×C₄₇	Q₈	1	2	yes	—
49	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	#131×C₄₇	—	2	16	no	—
55	#131×C₄₇	—	2	8	no	—
56	#131×C₄₇	—	2	8	no	—
57	C₂×M₁₆×C₄₇	—	2	8	no	—
58	C₂×M₁₆×C₄₇	—	2	1	no	—
59	C₂×M₁₆×C₄₇	—	2	2	no	—
60	C₂×M₁₆×C₄₇	—	2	4	no	—
61	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
63	C₂²×C₈×C₄₇	—	2	8	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	—	2	2	no	—
66	C₂²×C₈×C₄₇	—	2	2	no	—
67	C₂²×C₈×C₄₇	—	2	4	no	—
68	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	D₄	1	2	yes	—
72	C₂⁴×C₄₇	—	2	1	no	—
73	C₂⁴×C₄₇	#41	1	1	yes	characteristic
74	#41×C₄₇	—	2	2	no	—
75	#41×C₄₇	—	2	2	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	C₄²	1	4	yes	—
82	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
83	#41×C₄₇	C₄⋊C₄	1	8	yes	—
84	C₂×Q₈×C₄₇	—	2	1	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
87	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
95	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	4	no	—
112	C₂²×Dic₄₇	—	4	2	no	—
113	C₂²×Dic₄₇	—	4	2	no	—
114	C₂²×Dic₄₇	—	8	2	no	—
115	C₂²×Dic₄₇	—	8	2	no	—
116	M₁₆×C₄₇	—	2	16	no	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	4	no	—
119	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
120	C₂×C₈×C₄₇	—	2	16	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	4	no	—
128	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄⋊Dic₄₇	—	4	2	no	—
133	C₄⋊Dic₄₇	—	4	2	no	—
134	#10625329	—	2	4	no	—
135	#10625329	—	2	4	no	—
136	#10625329	—	4	2	no	—
137	#10625329	—	4	2	no	—
138	C₂×C₄₇⋊C₈	—	2	4	no	—
139	C₂×C₄₇⋊C₈	—	4	2	no	—
140	C₂×C₄₇⋊C₈	—	4	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	1	no	—
143	C₂³×C₄₇	—	2	1	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	#117	1	1	yes	characteristic
150	C₂³×C₄₇	C₄×D₄	1	2	yes	—
151	C₂³×C₄₇	#121	1	1	yes	characteristic
152	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₄₇	#123	1	2	yes	—
154	Q₈×C₄₇	—	2	2	no	—
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	#95	1	4	yes	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	2	4	no	—
159	D₄×C₄₇	—	2	8	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	4	no	—
162	D₄×C₄₇	#95	1	4	yes	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₄₇	#120	1	2	yes	—
180	C₂×C₄×C₄₇	#120	1	2	yes	—
181	C₂×C₄×C₄₇	#121	1	2	yes	—
182	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₄₇	#123	1	2	yes	—
186	C₂×Dic₄₇	—	4	4	no	—
187	C₂×Dic₄₇	—	8	4	no	—
188	C₂×Dic₄₇	—	8	2	no	—
189	C₂×Dic₄₇	—	8	2	no	—
190	C₂×Dic₄₇	—	8	4	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	4	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₄₇⋊C₈	—	4	4	no	—
195	#10774	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	4	no	—
208	C₂²×C₄₇	—	4	4	no	—
209	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₄₇	#380	1	1	yes	characteristic
211	C₂²×C₄₇	#381	1	1	yes	characteristic
212	C₂²×C₄₇	#385	1	2	yes	—
213	C₂²×C₄₇	#386	1	2	yes	—
214	C₂²×C₄₇	#471	1	2	yes	—
215	C₂²×C₄₇	#472	1	1	yes	characteristic
216	C₂²×C₄₇	#473	1	1	yes	characteristic
217	C₄×C₄₇	—	2	4	no	—
218	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
219	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
220	C₄×C₄₇	#379	1	1	yes	characteristic
221	C₄×C₄₇	#380	1	1	yes	characteristic
222	C₄×C₄₇	#385	1	2	yes	—
223	C₄×C₄₇	#386	1	2	yes	—
224	Dic₄₇	—	8	4	no	—
225	C₂²×#131	D₄₇	1	1	yes	characteristic
226	C₂×#417	—	47	2	no	—
227	C₂×#343	—	47	2	no	—
228	C₂×#341	—	47	1	no	—
229	C₂×#340	—	47	1	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	4	4	no	—
234	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
235	C₂×C₄₇	#1815	1	1	yes	characteristic
236	C₂×C₄₇	#1816	1	1	yes	characteristic
237	C₂×C₄₇	#1907	1	2	yes	—
238	C₂×C₄₇	#1908	1	2	yes	—
239	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#131	—	2	4	no	—
241	C₂×#131	—	2	4	no	—
242	C₂×#131	—	2	2	no	—
243	C₂×#131	Dic₄₇	1	4	yes	complemented
244	C₂²×M₁₆	—	2	1	no	—
245	C₂²×M₁₆	—	47	2	no	—
246	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
247	C₂³×C₈	—	2	1	no	—
248	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	—	47	2	no	—
250	#417	—	47	8	no	—
251	#417	—	94	4	no	—
252	C₂×#103	—	94	2	no	—
253	C₂×#102	—	94	2	no	—
254	#343	—	94	4	no	—
255	#341	—	94	2	no	—
256	#340	—	94	1	no	—
257	#340	—	94	1	no	—
258	C₄₇	#10774	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	1	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	Dic₉₄	1	2	yes	—
264	C₂×#41	C₄×D₄₇	1	4	yes	—
265	C₂×#41	C₂×Dic₄₇	1	2	yes	—
266	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
267	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	94	2	no	—
272	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
273	#131	—	2	16	no	—
274	#131	—	2	8	no	—
275	#131	—	2	8	no	—
276	C₂×M₁₆	—	2	8	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	47	4	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	—	94	2	no	—
283	C₂×M₁₆	—	94	2	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
287	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
288	C₂²×C₈	—	2	8	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
295	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
298	C₂×C₄⋊C₄	—	47	4	no	—
299	C₂×C₄⋊C₄	—	94	2	no	—
300	C₂×C₄⋊C₄	—	94	2	no	—
301	C₂×C₄⋊C₄	—	94	2	no	—
302	C₂×C₄⋊C₄	—	94	2	no	—
303	C₂×C₄⋊C₄	—	94	2	no	—
304	#103	—	94	8	no	—
305	#102	—	94	8	no	—
306	C₂⁴	—	2	1	no	—
307	C₂⁴	#10625350	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	2	4	no	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	C₄×Dic₄₇	1	4	yes	—
316	#41	Dic₄₇⋊C₄	1	8	yes	—
317	#41	C₂²⋊Dic₄₇	1	4	yes	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
321	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
329	C₂×D₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	94	4	no	—
336	C₂²×C₄	—	376	2	no	—
337	C₂²×C₄	—	376	2	no	—
338	C₂²×C₄	—	188	2	no	—
339	C₂²×C₄	—	188	2	no	—
340	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
342	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
343	C₂²×C₄	#10625350	1	2	yes	—
344	C₂²×C₄	#10625350	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
350	M₁₆	—	2	16	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	94	4	no	—
354	M₁₆	—	94	4	no	—
355	M₁₆	—	188	2	no	—
356	M₁₆	—	188	2	no	—
357	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
358	C₂×C₈	—	2	16	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	94	4	no	—
367	C₂×C₈	—	188	2	no	—
368	C₂×C₈	—	188	2	no	—
369	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
370	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
371	C₄⋊C₄	—	94	4	no	—
372	C₄⋊C₄	—	94	4	no	—
373	C₄⋊C₄	—	188	2	no	—
374	C₄⋊C₄	—	188	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	#13093983	1	1	yes	characteristic
384	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
385	C₂³	#13093998	1	1	yes	characteristic
386	C₂³	#13094003	1	1	yes	characteristic
387	C₂³	#13094007	1	2	yes	—
388	Q₈	—	2	2	no	—
389	Q₈	—	2	4	no	—
390	Q₈	C₄₇⋊#95	1	4	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	4	no	—
396	D₄	C₄₇⋊#95	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	376	4	no	—
403	C₂×C₄	—	376	2	no	—
404	C₂×C₄	—	376	2	no	—
405	C₂×C₄	—	376	4	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
409	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
413	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
414	C₂×C₄	#13093983	1	1	yes	characteristic
415	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
416	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
417	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
418	C₂×C₄	#13093993	1	2	yes	—
419	C₂×C₄	#13093993	1	2	yes	—
420	C₂×C₄	#13093998	1	2	yes	—
421	C₂×C₄	#13093998	1	1	yes	characteristic
422	C₂×C₄	#13094003	1	2	yes	—
423	C₂×C₄	#13094003	1	1	yes	characteristic
424	C₂×C₄	#13094007	1	2	yes	—
425	C₈	—	2	2	no	—
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	188	4	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
443	C₂²	#15688983	1	1	yes	characteristic
444	C₂²	#15688986	1	1	yes	characteristic
445	C₂²	#15688996	1	2	yes	—
446	C₂²	#15689002	1	2	yes	—
447	C₂²	#15689386	1	2	yes	—
448	C₂²	#15689393	1	1	yes	characteristic
449	C₂²	#15689398	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	376	4	no	—
452	C₄	C₂×C₄₇⋊#95	1	1	yes	characteristic
453	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
454	C₄	#15688979	1	1	yes	characteristic
455	C₄	#15688983	1	1	yes	characteristic
456	C₄	#15688996	1	2	yes	—
457	C₄	#15689002	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	4	4	no	—
462	C₂	#20241611	1	1	yes	characteristic
463	C₂	#20243447	1	1	yes	characteristic
464	C₂	#20243452	1	1	yes	characteristic
465	C₂	#20243896	1	2	yes	—
466	C₂	#20243903	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093998
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	#10774
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#15688891	C₂	semidirect
3. C₂×#15688888	C₂	semidirect
4. C₂×#15688886	C₂	semidirect
9. #15689124	C₄	semidirect
20. C₂×#131×C₄₇	C₄	semidirect
243. C₂×#131	Dic₄₇	semidirect
258. C₄₇	#10774	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689124	2
C₂×#15688891	2
C₂×#15688888	2
C₂×#15688886	2
C₂²×#131×C₄₇	2
#10774	47