Subgroups — #26124914

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×#15689021	C₂	1	2	yes	maximal
3	C₂×#15688886	C₂	1	2	yes	maximal
4	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×Dic₄₇⋊C₄	—	2	2	no	—
9	C₂×#13093958	—	2	4	no	—
10	C₂×#13093958	—	2	2	no	—
11	#15689021	—	2	4	no	—
12	#15689021	—	2	4	no	—
13	C₂×C₄₇⋊#95	—	2	2	no	—
14	#15688886	—	2	4	no	—
15	#15688886	C₄	1	4	yes	complemented
16	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	—	2	2	no	—
20	C₂³×Dic₄₇	—	2	2	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄⋊Dic₄₇	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
32	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
33	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
34	C₂×Dic₄₇⋊C₄	—	2	8	no	—
35	C₂×Dic₄₇⋊C₄	—	4	4	no	—
36	C₂×Dic₄₇⋊C₄	—	4	4	no	—
37	#13093958	—	2	8	no	—
38	C₄₇⋊#95	—	2	8	no	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	—	2	2	no	—
43	C₂²×C₈×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	1	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	—	2	1	no	—
48	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₄₇	D₄	1	2	yes	—
50	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
51	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	1	no	—
55	C₂×C₄²×C₄₇	—	2	1	no	—
56	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	2	1	no	—
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	D₈	1	2	yes	—
66	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	#41	1	2	yes	—
75	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	4	no	—
78	C₂²×Dic₄₇	—	2	4	no	—
79	C₂²×Dic₄₇	—	2	4	no	—
80	C₂²×Dic₄₇	—	2	4	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	2	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	—	4	2	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
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	—	2	4	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₂×C₈×C₄₇	—	4	1	no	—
100	C₂×C₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
101	C₄²×C₄₇	—	4	1	no	—
102	C₄²×C₄₇	—	4	2	no	—
103	C₄²×C₄₇	—	4	1	no	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄⋊Dic₄₇	—	2	4	no	—
106	C₄⋊Dic₄₇	—	2	4	no	—
107	C₄⋊Dic₄₇	—	2	4	no	—
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	—	4	2	no	—
110	C₄⋊Dic₄₇	—	4	2	no	—
111	C₄⋊Dic₄₇	C₄⋊C₄	1	8	yes	complemented
112	Dic₄₇⋊C₄	—	4	16	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	4	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	4	1	no	—
129	C₂×C₄×C₄₇	—	4	1	no	—
130	C₂×C₄×C₄₇	—	4	2	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	1	no	—
133	C₂×C₄×C₄₇	—	4	1	no	—
134	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#121	1	2	yes	—
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#123	1	2	yes	—
146	C₂×C₄×C₄₇	#125	1	2	yes	—
147	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	4	4	no	—
154	C₂×Dic₄₇	—	4	4	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₂×Dic₄₇	—	4	4	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	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	C₈×C₄₇	—	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	2	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	#384	1	1	yes	characteristic
195	C₄×C₄₇	#385	1	1	yes	characteristic
196	C₄×C₄₇	#389	1	2	yes	—
197	C₄×C₄₇	#395	1	1	yes	characteristic
198	C₄×C₄₇	#398	1	2	yes	—
199	C₄×C₄₇	#399	1	1	yes	characteristic
200	Dic₄₇	—	4	8	no	—
201	Dic₄₇	—	8	4	no	—
202	C₂²×#107	—	47	1	no	—
203	C₂×#389	—	47	2	no	—
204	C₂×#340	—	47	1	no	—
205	C₂×#340	—	47	2	no	—
206	C₂×#336	D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	47	2	no	—
221	C₂²×C₄⋊C₄	—	47	2	no	—
222	C₂²×C₄⋊C₄	—	94	2	no	—
223	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
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	—	47	4	no	—
230	#340	—	94	4	no	—
231	#336	—	2	2	no	—
232	C₄₇	#11328	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₄	—	94	2	no	—
234	C₂³×C₄	—	94	2	no	—
235	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
236	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
237	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	Dic₉₄	1	2	yes	—
245	C₂²×C₈	Dic₉₄	1	2	yes	—
246	C₂²×C₈	C₄×D₄₇	1	2	yes	—
247	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
248	C₂×C₄⋊C₄	—	47	4	no	—
249	C₂×C₄⋊C₄	—	47	4	no	—
250	C₂×C₄⋊C₄	—	47	4	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	2	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	8	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	188	4	no	—
262	C₂×C₄⋊C₄	—	188	4	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	#107	—	94	8	no	—
268	#95	—	94	8	no	—
269	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	94	4	no	—
279	C₂²×C₄	—	94	4	no	—
280	C₂²×C₄	—	94	4	no	—
281	C₂²×C₄	—	94	4	no	—
282	C₂²×C₄	—	188	2	no	—
283	C₂²×C₄	—	188	2	no	—
284	C₂²×C₄	—	188	2	no	—
285	C₂²×C₄	—	188	2	no	—
286	C₂²×C₄	—	188	2	no	—
287	C₂²×C₄	—	188	2	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	D₃₇₆	1	2	yes	—
293	C₂²×C₄	Dic₁₈₈	1	2	yes	—
294	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	#10625350	1	1	yes	characteristic
298	C₂²×C₄	#10625350	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₄₇	1	2	yes	—
300	C₂²×C₄	D₄×D₄₇	1	2	yes	—
301	C₂²×C₄	#10625352	1	2	yes	—
302	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
303	C₂²×C₄	C₂×C₂²⋊D₄₇	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	—	2	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	Dic₄₇⋊C₄	1	4	yes	complemented
314	C₄⋊C₄	—	47	8	no	—
315	C₄⋊C₄	—	94	4	no	—
316	C₄⋊C₄	—	94	4	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	94	4	no	—
319	C₄⋊C₄	—	94	4	no	—
320	C₄⋊C₄	—	188	16	no	—
321	C₄⋊C₄	—	188	2	no	—
322	C₄⋊C₄	—	188	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	1	no	—
326	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
327	C₂³	#13093994	1	2	yes	—
328	C₂³	#13093998	1	1	yes	characteristic
329	C₂³	#13094004	1	2	yes	—
330	C₂³	#13094024	1	1	yes	characteristic
331	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
332	C₂³	C₂×Dic₁₈₈	1	1	yes	characteristic
333	C₂³	#13094046	1	1	yes	characteristic
334	C₂³	#13094046	1	1	yes	characteristic
335	C₂³	#13094052	1	2	yes	—
336	C₂³	#13094057	1	2	yes	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	94	8	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	4	no	—
356	C₂×C₄	—	188	4	no	—
357	C₂×C₄	—	188	4	no	—
358	C₂×C₄	—	188	4	no	—
359	C₂×C₄	—	188	4	no	—
360	C₂×C₄	—	188	4	no	—
361	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
362	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
363	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
364	C₂×C₄	C₄×Dic₉₄	1	1	yes	characteristic
365	C₂×C₄	#13093992	1	1	yes	characteristic
366	C₂×C₄	#13093997	1	2	yes	—
367	C₂×C₄	#13094001	1	2	yes	—
368	C₂×C₄	#13094001	1	2	yes	—
369	C₂×C₄	#13094002	1	2	yes	—
370	C₂×C₄	#13094003	1	1	yes	characteristic
371	C₂×C₄	#13094005	1	1	yes	characteristic
372	C₂×C₄	#13094006	1	2	yes	—
373	C₂×C₄	#13094014	1	2	yes	—
374	C₂×C₄	#13094016	1	1	yes	characteristic
375	C₂×C₄	#13094020	1	1	yes	characteristic
376	C₂×C₄	#13094022	1	1	yes	characteristic
377	C₂×C₄	#13094023	1	2	yes	—
378	C₂×C₄	#13094023	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₂²	#15688997	1	2	yes	—
382	C₂²	#15689021	1	1	yes	characteristic
383	C₂²	#15689032	1	1	yes	characteristic
384	C₂²	#15689044	1	2	yes	—
385	C₂²	#15689053	1	1	yes	characteristic
386	C₂²	C₄×D₃₇₆	1	1	yes	characteristic
387	C₂²	C₄×Dic₁₈₈	1	1	yes	characteristic
388	C₂²	#15689225	1	2	yes	—
389	C₂²	#15689259	1	2	yes	—
390	C₂²	#15689270	1	2	yes	—
391	C₂²	#15689281	1	2	yes	—
392	C₂²	#15689287	1	2	yes	—
393	C₂²	#15689359	1	1	yes	characteristic
394	C₂²	#15689364	1	1	yes	characteristic
395	C₂²	#15689376	1	1	yes	characteristic
396	C₂²	#15689381	1	1	yes	characteristic
397	C₂²	#15689404	1	2	yes	—
398	C₂²	#15689419	1	2	yes	—
399	C₂²	#15689424	1	2	yes	—
400	C₂²	#15689431	1	2	yes	—
401	C₂²	#15689525	1	1	yes	characteristic
402	C₂²	#15689528	1	1	yes	characteristic
403	C₂²	#15689532	1	2	yes	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	376	4	no	—
407	C₄	—	188	8	no	—
408	C₄	#15688992	1	1	yes	characteristic
409	C₄	#15688995	1	1	yes	characteristic
410	C₄	#15689020	1	2	yes	—
411	C₄	#15689043	1	1	yes	characteristic
412	C₄	#15689057	1	2	yes	—
413	C₄	#15689059	1	1	yes	characteristic
414	C₂	#20241652	1	1	yes	characteristic
415	C₂	#20243638	1	2	yes	—
416	C₂	#20243645	1	2	yes	—
417	C₂	#20244121	1	1	yes	characteristic
418	C₂	#20244131	1	1	yes	characteristic
419	C₂	#20244386	1	1	yes	characteristic
420	C₂	#20244398	1	1	yes	characteristic
421	C₂	#20244717	1	2	yes	—
422	C₂	#20244727	1	2	yes	—
423	C₂	#20244876	1	1	yes	characteristic
424	C₂	#20244881	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11328
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
15. #15688886	C₄	semidirect
100. C₂×C₈×C₄₇	C₄⋊C₄	semidirect
111. C₄⋊Dic₄₇	C₄⋊C₄	semidirect
232. C₄₇	#11328	semidirect
313. C₂×C₈	Dic₄₇⋊C₄	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×#15689021	2
C₂×#15688886	2
C₂×C₄₇×#336	2
#11328	47