Subgroups — #26124913

Order 12032.

958 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	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689022	C₂	1	2	yes	maximal
3	C₂×#15688885	C₂	1	2	yes	maximal
4	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×#13093958	—	2	4	no	—
11	C₂×#13093958	—	2	2	no	—
12	#15689022	—	2	4	no	—
13	#15689022	—	2	4	no	—
14	C₂×C₄₇⋊#95	—	2	2	no	—
15	#15688885	—	2	4	no	—
16	#15688877	—	2	2	no	—
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#340	C₄	1	4	yes	complemented
20	C₂³×Dic₄₇	—	2	2	no	—
21	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
22	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	1	no	—
27	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	8	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	4	4	no	—
35	C₂×C₄⋊Dic₄₇	—	4	4	no	—
36	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	1	no	—
40	C₂×C₄×Dic₄₇	—	2	1	no	—
41	#13093958	—	2	8	no	—
42	C₄₇⋊#95	—	2	8	no	—
43	C₂³×C₄×C₄₇	—	2	2	no	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₄₇	D₄	1	2	yes	—
49	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
56	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	—	2	4	no	—
58	C₂²×C₄×C₄₇	—	2	4	no	—
59	C₂²×C₄×C₄₇	—	2	4	no	—
60	C₂²×C₄×C₄₇	—	4	2	no	—
61	C₂²×C₄×C₄₇	—	4	2	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	2	yes	—
72	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	2	1	no	—
77	C₂²×Dic₄₇	—	2	1	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂²×Dic₄₇	—	2	2	no	—
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂²×Dic₄₇	—	2	4	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂²×Dic₄₇	—	4	2	no	—
88	C₂²×Dic₄₇	—	4	2	no	—
89	C₂²×Dic₄₇	D₈	1	2	yes	—
90	C₂²×Dic₄₇	Q₁₆	1	2	yes	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	complemented
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	4	16	no	—
103	C₄⋊Dic₄₇	—	4	2	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄×Dic₄₇	—	4	1	no	—
106	C₄×Dic₄₇	—	4	2	no	—
107	C₄×Dic₄₇	—	4	1	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	4	1	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	1	no	—
113	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
114	C₂³×C₄₇	#120	1	2	yes	—
115	C₂³×C₄₇	#121	1	1	yes	characteristic
116	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
117	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
119	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
120	C₂³×C₄₇	#135	1	1	yes	characteristic
121	C₂³×C₄₇	#135	1	1	yes	characteristic
122	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₄₇	#137	1	2	yes	—
124	C₂×C₄×C₄₇	—	2	8	no	—
125	C₂×C₄×C₄₇	—	4	4	no	—
126	C₂×C₄×C₄₇	—	4	4	no	—
127	C₂×C₄×C₄₇	—	4	4	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	—	4	4	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#121	1	2	yes	—
137	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
138	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#123	1	2	yes	—
143	C₂×C₄×C₄₇	#125	1	2	yes	—
144	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	2	4	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	4	1	no	—
154	C₂×Dic₄₇	—	4	1	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	1	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	8	2	no	—
163	C₂×Dic₄₇	—	8	2	no	—
164	C₂×Dic₄₇	—	8	2	no	—
165	C₂×Dic₄₇	—	8	2	no	—
166	C₈×C₄₇	—	2	4	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	#11328	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	#385	1	2	yes	—
170	C₂²×C₄₇	#389	1	1	yes	characteristic
171	C₂²×C₄₇	#392	1	1	yes	characteristic
172	C₂²×C₄₇	#395	1	2	yes	—
173	C₂²×C₄₇	#398	1	1	yes	characteristic
174	C₂²×C₄₇	C₄×D₈	1	1	yes	characteristic
175	C₂²×C₄₇	C₄×Q₁₆	1	1	yes	characteristic
176	C₂²×C₄₇	#440	1	2	yes	—
177	C₂²×C₄₇	#447	1	2	yes	—
178	C₂²×C₄₇	#449	1	2	yes	—
179	C₂²×C₄₇	#451	1	2	yes	—
180	C₂²×C₄₇	#452	1	2	yes	—
181	C₂²×C₄₇	#466	1	1	yes	characteristic
182	C₂²×C₄₇	#467	1	1	yes	characteristic
183	C₂²×C₄₇	#469	1	1	yes	characteristic
184	C₂²×C₄₇	#470	1	1	yes	characteristic
185	C₂²×C₄₇	#474	1	2	yes	—
186	C₂²×C₄₇	#477	1	2	yes	—
187	C₂²×C₄₇	#478	1	2	yes	—
188	C₂²×C₄₇	#479	1	2	yes	—
189	C₂²×C₄₇	#499	1	1	yes	characteristic
190	C₂²×C₄₇	#500	1	1	yes	characteristic
191	C₂²×C₄₇	#501	1	2	yes	—
192	C₄×C₄₇	—	4	8	no	—
193	C₄×C₄₇	#384	1	1	yes	characteristic
194	C₄×C₄₇	#385	1	1	yes	characteristic
195	C₄×C₄₇	#389	1	2	yes	—
196	C₄×C₄₇	#395	1	1	yes	characteristic
197	C₄×C₄₇	#398	1	2	yes	—
198	C₄×C₄₇	#399	1	1	yes	characteristic
199	Dic₄₇	—	4	2	no	—
200	Dic₄₇	—	4	2	no	—
201	Dic₄₇	—	8	4	no	—
202	C₂²×#107	—	47	1	no	—
203	C₂×#389	—	47	2	no	—
204	C₂×#340	—	47	2	no	—
205	C₂×#340	D₄₇	1	1	yes	characteristic
206	C₂×#336	—	47	1	no	—
207	C₂×C₄₇	#1444	1	1	yes	characteristic
208	C₂×C₄₇	#1862	1	2	yes	—
209	C₂×C₄₇	#1863	1	2	yes	—
210	C₂×C₄₇	#1942	1	1	yes	characteristic
211	C₂×C₄₇	#1944	1	1	yes	characteristic
212	C₂×C₄₇	#1999	1	1	yes	characteristic
213	C₂×C₄₇	#2001	1	1	yes	characteristic
214	C₂×C₄₇	#2057	1	2	yes	—
215	C₂×C₄₇	#2059	1	2	yes	—
216	C₂×C₄₇	#2086	1	1	yes	characteristic
217	C₂×C₄₇	#2087	1	1	yes	characteristic
218	C₂³×C₈	—	47	1	no	—
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	47	2	no	—
221	C₂²×C₄⋊C₄	—	94	2	no	—
222	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
223	C₂²×C₄²	—	47	1	no	—
224	C₂×#107	—	94	4	no	—
225	C₂×#107	—	94	2	no	—
226	#389	—	94	4	no	—
227	#389	—	94	4	no	—
228	C₂×#95	—	94	2	no	—
229	#340	—	94	4	no	—
230	#340	Dic₄₇	1	4	yes	complemented
231	#336	—	94	2	no	—
232	C₄₇	#11328	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	47	1	no	—
235	C₂³×C₄	—	47	1	no	—
236	C₂³×C₄	—	94	2	no	—
237	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	47	2	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₂²×C₈	—	94	2	no	—
243	C₂²×C₈	—	94	2	no	—
244	C₂²×C₈	—	94	1	no	—
245	C₂²×C₈	Dic₉₄	1	2	yes	—
246	C₂²×C₈	D₁₈₈	1	2	yes	—
247	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	47	4	no	—
252	C₂×C₄⋊C₄	—	94	2	no	—
253	C₂×C₄⋊C₄	—	94	2	no	—
254	C₂×C₄⋊C₄	—	94	2	no	—
255	C₂×C₄⋊C₄	—	94	2	no	—
256	C₂×C₄⋊C₄	—	94	8	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	188	4	no	—
259	C₂×C₄⋊C₄	—	188	4	no	—
260	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
261	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
262	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
263	C₂×C₄²	—	94	1	no	—
264	C₂×C₄²	—	94	2	no	—
265	C₂×C₄²	—	94	2	no	—
266	C₂×C₄²	—	94	1	no	—
267	#107	—	94	8	no	—
268	#95	—	94	8	no	—
269	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	94	2	no	—
280	C₂²×C₄	—	94	2	no	—
281	C₂²×C₄	—	94	1	no	—
282	C₂²×C₄	—	94	1	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	4	no	—
288	C₂²×C₄	—	188	2	no	—
289	C₂²×C₄	—	188	2	no	—
290	C₂²×C₄	—	188	2	no	—
291	C₂²×C₄	—	188	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
296	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
298	C₂²×C₄	D₄×D₄₇	1	2	yes	—
299	C₂²×C₄	#10625352	1	2	yes	—
300	C₂²×C₄	#10625352	1	1	yes	characteristic
301	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	#10625354	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	94	4	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	188	1	no	—
311	C₂×C₈	—	188	2	no	—
312	C₂×C₈	—	188	1	no	—
313	C₂×C₈	C₄⋊Dic₄₇	1	4	yes	complemented
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	94	4	no	—
319	C₄⋊C₄	—	188	16	no	—
320	C₄⋊C₄	—	188	2	no	—
321	C₄⋊C₄	—	188	2	no	—
322	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	complemented
323	C₄²	—	188	1	no	—
324	C₄²	—	188	2	no	—
325	C₄²	—	188	1	no	—
326	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
327	C₂³	#13093994	1	2	yes	—
328	C₂³	#13093999	1	1	yes	characteristic
329	C₂³	#13094001	1	2	yes	—
330	C₂³	#13094023	1	1	yes	characteristic
331	C₂³	D₈×D₄₇	1	1	yes	characteristic
332	C₂³	Q₁₆×D₄₇	1	1	yes	characteristic
333	C₂³	#13094043	1	1	yes	characteristic
334	C₂³	#13094047	1	1	yes	characteristic
335	C₂³	#13094051	1	2	yes	—
336	C₂³	#13094053	1	2	yes	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	94	4	no	—
345	C₂×C₄	—	94	4	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	376	2	no	—
349	C₂×C₄	—	376	2	no	—
350	C₂×C₄	—	376	2	no	—
351	C₂×C₄	—	376	2	no	—
352	C₂×C₄	—	188	4	no	—
353	C₂×C₄	—	188	4	no	—
354	C₂×C₄	—	188	4	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	1	no	—
358	C₂×C₄	—	188	1	no	—
359	C₂×C₄	—	188	1	no	—
360	C₂×C₄	—	188	1	no	—
361	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
363	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
364	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
365	C₂×C₄	#13093994	1	1	yes	characteristic
366	C₂×C₄	#13093999	1	2	yes	—
367	C₂×C₄	#13094001	1	2	yes	—
368	C₂×C₄	#13094001	1	2	yes	—
369	C₂×C₄	#13094004	1	2	yes	—
370	C₂×C₄	#13094004	1	1	yes	characteristic
371	C₂×C₄	#13094008	1	1	yes	characteristic
372	C₂×C₄	#13094008	1	2	yes	—
373	C₂×C₄	#13094015	1	2	yes	—
374	C₂×C₄	#13094015	1	1	yes	characteristic
375	C₂×C₄	#13094021	1	1	yes	characteristic
376	C₂×C₄	#13094023	1	2	yes	—
377	C₂×C₄	#13094024	1	1	yes	characteristic
378	C₂×C₄	#13094024	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	188	2	no	—
381	C₂²	#15688998	1	2	yes	—
382	C₂²	#15689022	1	1	yes	characteristic
383	C₂²	#15689033	1	1	yes	characteristic
384	C₂²	#15689044	1	2	yes	—
385	C₂²	#15689055	1	1	yes	characteristic
386	C₂²	D₈×Dic₄₇	1	1	yes	characteristic
387	C₂²	Q₁₆×Dic₄₇	1	1	yes	characteristic
388	C₂²	#15689224	1	2	yes	—
389	C₂²	#15689258	1	2	yes	—
390	C₂²	#15689271	1	2	yes	—
391	C₂²	#15689280	1	2	yes	—
392	C₂²	#15689286	1	2	yes	—
393	C₂²	#15689360	1	1	yes	characteristic
394	C₂²	#15689365	1	1	yes	characteristic
395	C₂²	#15689377	1	1	yes	characteristic
396	C₂²	#15689382	1	1	yes	characteristic
397	C₂²	#15689401	1	2	yes	—
398	C₂²	#15689416	1	2	yes	—
399	C₂²	#15689421	1	2	yes	—
400	C₂²	#15689432	1	2	yes	—
401	C₂²	#15689524	1	1	yes	characteristic
402	C₂²	#15689527	1	1	yes	characteristic
403	C₂²	#15689530	1	2	yes	—
404	C₄	—	4	8	no	—
405	C₄	—	376	4	no	—
406	C₄	—	188	2	no	—
407	C₄	—	188	2	no	—
408	C₄	#15688993	1	1	yes	characteristic
409	C₄	#15688998	1	1	yes	characteristic
410	C₄	#15689022	1	2	yes	—
411	C₄	#15689044	1	1	yes	characteristic
412	C₄	#15689055	1	2	yes	—
413	C₄	#15689060	1	1	yes	characteristic
414	C₂	#20241653	1	1	yes	characteristic
415	C₂	#20243637	1	2	yes	—
416	C₂	#20243644	1	2	yes	—
417	C₂	#20244122	1	1	yes	characteristic
418	C₂	#20244132	1	1	yes	characteristic
419	C₂	#20244387	1	1	yes	characteristic
420	C₂	#20244399	1	1	yes	characteristic
421	C₂	#20244715	1	2	yes	—
422	C₂	#20244729	1	2	yes	—
423	C₂	#20244878	1	1	yes	characteristic
424	C₂	#20244883	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	#11328
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
19. C₄₇×#340	C₄	semidirect
95. C₂×C₈×C₄₇	C₄⋊C₄	semidirect
99. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
230. #340	Dic₄₇	semidirect
232. C₄₇	#11328	semidirect
313. C₂×C₈	C₄⋊Dic₄₇	semidirect
322. 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
C₂²×#13093958	2
C₂×#15689022	2
C₂×#15688885	2
C₂×#15688877	2
C₂×C₄₇×#340	2
#11328	47