Subgroups — #26121749

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689140	C₂	1	2	yes	maximal
2	C₂×#15688895	C₂	1	2	yes	maximal, complemented
3	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243105	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	C₂×#13093983	C₂²	1	2	yes	—
8	#15689140	—	2	4	no	—
9	#15689140	C₄	1	8	yes	complemented
10	C₂×#13093951	—	2	4	no	—
11	#15688895	—	2	4	no	—
12	#15688888	—	2	1	no	—
13	#15688888	—	2	1	no	—
14	#15688886	—	2	2	no	—
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#131×C₄₇	—	2	4	no	—
17	C₂×#131×C₄₇	—	2	4	no	—
18	C₂×#131×C₄₇	—	2	2	no	—
19	C₂×#131×C₄₇	C₄	1	4	yes	complemented
20	C₂²×M₁₆×C₄₇	—	2	1	no	—
21	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₇	—	2	1	no	—
23	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	C₂×C₄	1	4	yes	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	#13093983	—	2	2	no	—
32	#13093983	—	2	2	no	—
33	#13093983	—	2	2	no	—
34	#13093983	C₂×C₄	1	4	yes	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	#13093951	—	2	16	no	—
39	C₂×#41×C₄₇	—	2	1	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
44	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
45	C₂×#41×C₄₇	D₄	1	2	yes	—
46	C₂×#41×C₄₇	D₄	1	4	yes	—
47	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
48	C₂²×D₄×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	—	2	1	no	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	#131×C₄₇	—	2	16	no	—
53	#131×C₄₇	—	2	8	no	—
54	#131×C₄₇	—	2	8	no	—
55	C₂×M₁₆×C₄₇	—	2	8	no	—
56	C₂×M₁₆×C₄₇	—	2	1	no	—
57	C₂×M₁₆×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	—	2	4	no	—
59	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
61	C₂²×C₈×C₄₇	—	2	8	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	2	2	no	—
65	C₂²×C₈×C₄₇	—	2	4	no	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₄₇	D₄	1	2	yes	—
70	C₂⁴×C₄₇	—	2	1	no	—
71	C₂⁴×C₄₇	#41	1	1	yes	characteristic
72	#41×C₄₇	—	2	2	no	—
73	#41×C₄₇	—	2	2	no	—
74	#41×C₄₇	—	2	4	no	—
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	C₄²	1	4	yes	—
80	#41×C₄₇	C₂²⋊C₄	1	8	yes	—
81	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
82	C₂×Q₈×C₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
85	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
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	1	no	—
92	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	4	2	no	—
110	M₁₆×C₄₇	—	2	16	no	—
111	M₁₆×C₄₇	—	2	2	no	—
112	M₁₆×C₄₇	—	2	4	no	—
113	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₂×C₈×C₄₇	—	2	16	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	4	no	—
122	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₂²⋊Dic₄₇	—	2	4	no	—
125	C₂²⋊Dic₄₇	—	4	2	no	—
126	C₄⋊Dic₄₇	—	2	4	no	—
127	C₄⋊Dic₄₇	—	4	2	no	—
128	C₄×Dic₄₇	—	2	4	no	—
129	C₄×Dic₄₇	—	4	2	no	—
130	#10625329	—	2	4	no	—
131	#10625329	—	2	4	no	—
132	#10625329	—	4	2	no	—
133	#10625329	—	4	2	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	4	2	no	—
136	C₂×C₄₇⋊C₈	—	4	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	#117	1	1	yes	characteristic
142	C₂³×C₄₇	C₄×D₄	1	2	yes	—
143	C₂³×C₄₇	#121	1	1	yes	characteristic
144	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂³×C₄₇	#123	1	2	yes	—
146	Q₈×C₄₇	—	2	2	no	—
147	Q₈×C₄₇	—	2	4	no	—
148	Q₈×C₄₇	#95	1	4	yes	—
149	D₄×C₄₇	—	2	4	no	—
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	8	no	—
152	D₄×C₄₇	—	2	2	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	#95	1	4	yes	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	#120	1	2	yes	—
172	C₂×C₄×C₄₇	#120	1	2	yes	—
173	C₂×C₄×C₄₇	#121	1	2	yes	—
174	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#123	1	2	yes	—
178	C₂×Dic₄₇	—	4	4	no	—
179	C₂×Dic₄₇	—	8	4	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	4	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₄₇⋊C₈	—	4	4	no	—
184	#10773	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	8	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄₇	#380	1	1	yes	characteristic
195	C₂²×C₄₇	#381	1	1	yes	characteristic
196	C₂²×C₄₇	#385	1	2	yes	—
197	C₂²×C₄₇	#386	1	2	yes	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
200	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
201	C₄×C₄₇	#379	1	1	yes	characteristic
202	C₄×C₄₇	#380	1	1	yes	characteristic
203	C₄×C₄₇	#385	1	2	yes	—
204	C₄×C₄₇	#386	1	2	yes	—
205	Dic₄₇	—	8	4	no	—
206	C₂²×#131	D₄₇	1	1	yes	characteristic
207	C₂×#421	—	47	2	no	—
208	C₂×#344	—	47	2	no	—
209	C₂×#341	—	47	1	no	—
210	#1735	—	47	1	no	—
211	C₂×C₄₇	—	2	2	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	4	4	no	—
216	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
217	C₂×C₄₇	#1814	1	2	yes	—
218	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
219	C₂×#131	—	2	4	no	—
220	C₂×#131	—	2	4	no	—
221	C₂×#131	—	2	2	no	—
222	C₂×#131	Dic₄₇	1	4	yes	complemented
223	C₂²×M₁₆	—	2	1	no	—
224	C₂²×M₁₆	—	47	2	no	—
225	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
226	C₂³×C₈	—	2	1	no	—
227	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#117	—	47	2	no	—
229	#421	—	47	8	no	—
230	#421	—	94	4	no	—
231	C₂×#104	—	94	4	no	—
232	#344	—	94	4	no	—
233	#341	—	94	1	no	—
234	#341	—	94	1	no	—
235	#340	—	94	2	no	—
236	C₄₇	#10773	1	1	yes	characteristic, complemented, Sylow
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	1	no	—
239	C₂×#41	—	2	1	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	C₄×D₄₇	1	4	yes	—
242	C₂×#41	D₁₈₈	1	2	yes	—
243	C₂×#41	C₂×Dic₄₇	1	2	yes	—
244	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
245	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	#131	—	2	16	no	—
251	#131	—	2	8	no	—
252	#131	—	2	8	no	—
253	C₂×M₁₆	—	2	8	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	47	4	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
264	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
265	C₂²×C₈	—	2	8	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	—	94	2	no	—
271	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
272	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
275	#117	—	47	4	no	—
276	#117	—	94	2	no	—
277	#117	—	94	2	no	—
278	#117	—	94	2	no	—
279	C₂×C₄⋊C₄	—	94	2	no	—
280	C₂×C₂²⋊C₄	—	94	2	no	—
281	C₂×C₄²	—	94	2	no	—
282	#104	—	94	16	no	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	#10625350	1	1	yes	characteristic
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	C₄×Dic₄₇	1	4	yes	—
293	#41	(C₂×D₄₇)⋊C₄	1	8	yes	—
294	#41	C₂²⋊Dic₄₇	1	4	yes	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	Dic₄₇⋊C₄	1	4	yes	—
298	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
306	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	188	2	no	—
313	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
315	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
316	C₂²×C₄	#10625350	1	2	yes	—
317	C₂²×C₄	#10625350	1	1	yes	characteristic
318	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	M₁₆	—	2	16	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	94	4	no	—
327	M₁₆	—	94	4	no	—
328	M₁₆	—	188	2	no	—
329	M₁₆	—	188	2	no	—
330	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
331	C₂×C₈	—	2	16	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	94	4	no	—
340	C₂×C₈	—	188	2	no	—
341	C₂×C₈	—	188	2	no	—
342	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
343	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
344	C₄⋊C₄	—	94	4	no	—
345	C₄⋊C₄	—	188	2	no	—
346	C₂²⋊C₄	—	94	4	no	—
347	C₂²⋊C₄	—	188	2	no	—
348	C₄²	—	94	4	no	—
349	C₄²	—	188	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	4	no	—
354	C₂³	#13093983	1	1	yes	characteristic
355	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
356	C₂³	#13093998	1	1	yes	characteristic
357	C₂³	#13094003	1	1	yes	characteristic
358	C₂³	#13094007	1	2	yes	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	4	no	—
361	Q₈	C₄₇⋊#95	1	4	yes	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	8	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	4	no	—
367	D₄	C₄₇⋊#95	1	4	yes	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	376	4	no	—
374	C₂×C₄	—	188	4	no	—
375	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
381	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
382	C₂×C₄	#13093983	1	1	yes	characteristic
383	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
384	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
385	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
386	C₂×C₄	#13093993	1	2	yes	—
387	C₂×C₄	#13093993	1	2	yes	—
388	C₂×C₄	#13093998	1	2	yes	—
389	C₂×C₄	#13093998	1	1	yes	characteristic
390	C₂×C₄	#13094003	1	2	yes	—
391	C₂×C₄	#13094003	1	1	yes	characteristic
392	C₂×C₄	#13094007	1	2	yes	—
393	C₈	—	2	2	no	—
394	C₈	—	2	4	no	—
395	C₈	—	2	2	no	—
396	C₈	—	188	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	4	no	—
405	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
406	C₂²	#15688983	1	1	yes	characteristic
407	C₂²	#15688986	1	1	yes	characteristic
408	C₂²	#15688996	1	2	yes	—
409	C₂²	#15689002	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	376	4	no	—
412	C₄	C₂×C₄₇⋊#95	1	1	yes	characteristic
413	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
414	C₄	#15688979	1	1	yes	characteristic
415	C₄	#15688983	1	1	yes	characteristic
416	C₄	#15688996	1	2	yes	—
417	C₄	#15689002	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	4	4	no	—
423	C₂	#20241611	1	1	yes	characteristic
424	C₂	#20243442	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093998
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	#10773
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#15688895	C₂	semidirect
3. C₂×#15688888	C₂	semidirect
4. #20243105	C₂	semidirect
9. #15689140	C₄	semidirect
19. C₂×#131×C₄₇	C₄	semidirect
222. C₂×#131	Dic₄₇	semidirect
236. C₄₇	#10773	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689140	2
C₂×#15688895	2
C₂×#15688888	2
#20243105	2
C₂²×#131×C₄₇	2
#10773	47