Subgroups — #26122003

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	2	yes	maximal
4	#20241617	C₂	1	2	yes	maximal
5	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₄₇	—	2	2	no	—
10	C₂×C₈×Dic₄₇	—	2	2	no	—
11	C₂×C₈×Dic₄₇	C₄	1	4	yes	complemented
12	C₂×C₄₇⋊#95	—	2	2	no	—
13	C₂×C₄₇⋊#95	—	2	2	no	—
14	#15688886	—	2	2	no	—
15	#15688885	C₄	1	8	yes	complemented
16	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#340	—	2	2	no	—
19	C₂³×Dic₄₇	—	2	2	no	—
20	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
21	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
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	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
33	C₂×C₄×Dic₄₇	—	2	1	no	—
34	C₂×C₄×Dic₄₇	—	2	1	no	—
35	C₂×C₄×Dic₄₇	—	2	1	no	—
36	C₂×C₄×Dic₄₇	—	2	1	no	—
37	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
39	C₈×Dic₄₇	—	2	8	no	—
40	C₄₇⋊#95	—	4	4	no	—
41	C₄₇⋊#95	—	4	4	no	—
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₈×C₄₇	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
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	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	—	2	4	no	—
57	C₂²×C₄×C₄₇	—	4	2	no	—
58	C₂²×C₄×C₄₇	—	4	2	no	—
59	C₂²×C₄×C₄₇	—	4	2	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	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	#41	1	2	yes	—
71	C₂²×C₄×C₄₇	#41	1	2	yes	—
72	C₂²×C₄×C₄₇	#41	1	2	yes	—
73	C₂²×Dic₄₇	—	2	1	no	—
74	C₂²×Dic₄₇	—	2	1	no	—
75	C₂²×Dic₄₇	—	2	1	no	—
76	C₂²×Dic₄₇	—	2	1	no	—
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	1	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	C₄⋊C₄	1	2	yes	—
88	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
89	C₂²×Dic₄₇	D₈	1	2	yes	—
90	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
91	C₂²×Dic₄₇	Q₁₆	1	2	yes	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	2	4	no	—
95	C₂×C₈×C₄₇	—	2	4	no	—
96	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	4	2	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	2	4	no	—
103	C₄⋊Dic₄₇	—	4	2	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄×Dic₄₇	—	2	2	no	—
106	C₄×Dic₄₇	—	2	2	no	—
107	C₄×Dic₄₇	—	2	2	no	—
108	C₄×Dic₄₇	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	2	4	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
114	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	C₄×D₄	1	2	yes	—
116	C₂³×C₄₇	#121	1	1	yes	characteristic
117	C₂³×C₄₇	#121	1	1	yes	characteristic
118	C₂³×C₄₇	#124	1	2	yes	—
119	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
120	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
121	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
122	C₂³×C₄₇	#135	1	1	yes	characteristic
123	C₂³×C₄₇	#135	1	2	yes	—
124	C₂³×C₄₇	#135	1	1	yes	characteristic
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	—	8	2	no	—
129	C₂×C₄×C₄₇	—	8	2	no	—
130	C₂×C₄×C₄₇	—	8	2	no	—
131	C₂×C₄×C₄₇	—	8	2	no	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#117	1	2	yes	—
136	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
137	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#117	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#123	1	2	yes	—
146	C₂×C₄×C₄₇	#123	1	2	yes	—
147	C₂×C₄×C₄₇	#125	1	2	yes	—
148	C₂×C₄×C₄₇	#126	1	2	yes	—
149	C₂×C₄×C₄₇	#126	1	2	yes	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	4	no	—
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	8	2	no	—
164	C₂×Dic₄₇	—	8	2	no	—
165	C₂×Dic₄₇	—	8	2	no	—
166	C₂×Dic₄₇	—	8	2	no	—
167	C₂×Dic₄₇	#106	1	4	yes	—
168	C₂×Dic₄₇	#107	1	4	yes	—
169	C₈×C₄₇	—	2	4	no	—
170	C₄₇⋊C₈	—	2	4	no	—
171	#10820	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₇	#380	1	1	yes	characteristic
174	C₂²×C₄₇	#382	1	1	yes	characteristic
175	C₂²×C₄₇	#388	1	2	yes	—
176	C₂²×C₄₇	#388	1	2	yes	—
177	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
179	C₂²×C₄₇	#427	1	1	yes	characteristic
180	C₂²×C₄₇	#427	1	1	yes	characteristic
181	C₂²×C₄₇	C₄×D₈	1	2	yes	—
182	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
183	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
184	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
185	C₂²×C₄₇	#465	1	2	yes	—
186	C₂²×C₄₇	#465	1	2	yes	—
187	C₂²×C₄₇	#466	1	1	yes	characteristic
188	C₂²×C₄₇	#466	1	1	yes	characteristic
189	C₂²×C₄₇	#467	1	1	yes	characteristic
190	C₂²×C₄₇	#467	1	1	yes	characteristic
191	C₂²×C₄₇	#486	1	2	yes	—
192	C₂²×C₄₇	#487	1	2	yes	—
193	C₂²×C₄₇	#488	1	2	yes	—
194	C₂²×C₄₇	#488	1	2	yes	—
195	C₄×C₄₇	—	8	4	no	—
196	C₄×C₄₇	#376	1	1	yes	characteristic
197	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
198	C₄×C₄₇	#381	1	1	yes	characteristic
199	C₄×C₄₇	#383	1	1	yes	characteristic
200	C₄×C₄₇	#387	1	2	yes	—
201	C₄×C₄₇	#387	1	2	yes	—
202	Dic₄₇	—	2	4	no	—
203	Dic₄₇	—	2	4	no	—
204	Dic₄₇	—	8	4	no	—
205	C₂²×C₄×C₈	—	47	1	no	—
206	C₂×#340	—	47	1	no	—
207	C₂×#340	—	47	2	no	—
208	C₂×#340	D₄₇	1	1	yes	characteristic
209	C₄⋊#95	—	47	2	no	—
210	C₂×C₄₇	#1434	1	1	yes	characteristic
211	C₂×C₄₇	C₄×#106	1	1	yes	characteristic
212	C₂×C₄₇	C₄×#107	1	1	yes	characteristic
213	C₂×C₄₇	#1807	1	1	yes	characteristic
214	C₂×C₄₇	#1808	1	1	yes	characteristic
215	C₂×C₄₇	#1834	1	1	yes	characteristic
216	C₂×C₄₇	#1835	1	1	yes	characteristic
217	C₂×C₄₇	#1933	1	2	yes	—
218	C₂×C₄₇	#1933	1	2	yes	—
219	C₂×C₄₇	#1934	1	2	yes	—
220	C₂×C₄₇	#1934	1	2	yes	—
221	C₂³×C₈	—	47	1	no	—
222	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	—	47	2	no	—
224	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
225	C₂²×C₄²	—	47	1	no	—
226	C₂×C₄×C₈	—	47	4	no	—
227	C₂×C₄×C₈	—	94	2	no	—
228	C₂×C₄×C₈	—	94	2	no	—
229	C₂×#95	—	94	2	no	—
230	C₂×#95	—	94	2	no	—
231	#340	—	2	2	no	—
232	#340	—	47	8	no	—
233	#340	—	94	2	no	—
234	C₄₇	#10820	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	—	47	1	no	—
237	C₂³×C₄	—	47	1	no	—
238	C₂³×C₄	—	94	2	no	—
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	47	4	no	—
243	C₂²×C₈	—	47	2	no	—
244	C₂²×C₈	—	94	1	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₂²×C₈	—	94	1	no	—
247	C₂²×C₈	C₄×D₄₇	1	2	yes	—
248	C₂²×C₈	D₁₈₈	1	2	yes	—
249	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	47	4	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	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
262	C₂×C₄²	—	47	2	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	—	94	1	no	—
265	C₂×C₄²	—	94	1	no	—
266	C₂×C₄²	—	94	1	no	—
267	C₂×C₄²	—	94	1	no	—
268	C₄×C₈	—	94	8	no	—
269	#95	—	188	4	no	—
270	#95	—	188	4	no	—
271	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
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	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	4	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	1	no	—
286	C₂²×C₄	—	94	1	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	4	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	—	188	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
300	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
301	C₂²×C₄	#10625350	1	2	yes	—
302	C₂²×C₄	#10625352	1	1	yes	characteristic
303	C₂²×C₄	#10625352	1	2	yes	—
304	C₂²×C₄	#10625352	1	2	yes	—
305	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	#10625354	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	47	4	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	94	4	no	—
323	C₄⋊C₄	—	94	4	no	—
324	C₄⋊C₄	—	188	2	no	—
325	C₄⋊C₄	—	188	2	no	—
326	C₄²	—	94	2	no	—
327	C₄²	—	94	2	no	—
328	C₄²	—	94	2	no	—
329	C₄²	—	94	2	no	—
330	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
331	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
332	C₂³	#13093995	1	1	yes	characteristic
333	C₂³	#13093999	1	1	yes	characteristic
334	C₂³	#13094010	1	2	yes	—
335	C₂³	D₈×D₄₇	1	1	yes	characteristic
336	C₂³	SD₁₆×D₄₇	1	2	yes	—
337	C₂³	Q₁₆×D₄₇	1	1	yes	characteristic
338	C₂³	#13094043	1	1	yes	characteristic
339	C₂³	#13094045	1	2	yes	—
340	C₂³	#13094047	1	1	yes	characteristic
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	47	4	no	—
349	C₂×C₄	—	47	4	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	4	no	—
353	C₂×C₄	—	94	4	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	376	2	no	—
361	C₂×C₄	—	376	2	no	—
362	C₂×C₄	—	376	2	no	—
363	C₂×C₄	—	376	2	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	4	no	—
366	C₂×C₄	—	188	4	no	—
367	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	#13093980	1	1	yes	characteristic
370	C₂×C₄	#13093980	1	2	yes	—
371	C₂×C₄	#13093980	1	1	yes	characteristic
372	C₂×C₄	#13093981	1	1	yes	characteristic
373	C₂×C₄	#13093982	1	1	yes	characteristic
374	C₂×C₄	#13093982	1	2	yes	—
375	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
376	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
377	C₂×C₄	#13093989	1	2	yes	—
378	C₂×C₄	#13094000	1	1	yes	characteristic
379	C₂×C₄	#13094004	1	1	yes	characteristic
380	C₂×C₄	#13094005	1	2	yes	—
381	C₂×C₄	#13094008	1	2	yes	—
382	C₂×C₄	#13094014	1	2	yes	—
383	C₂×C₄	#13094017	1	2	yes	—
384	C₂×C₄	#13094019	1	2	yes	—
385	C₈	—	2	4	no	—
386	C₈	—	94	4	no	—
387	C₂²	#15688974	1	1	yes	characteristic
388	C₂²	#15688980	1	1	yes	characteristic
389	C₂²	#15688987	1	1	yes	characteristic
390	C₂²	#15689011	1	2	yes	—
391	C₂²	#15689015	1	2	yes	—
392	C₂²	#106×D₄₇	1	1	yes	characteristic
393	C₂²	#107×D₄₇	1	1	yes	characteristic
394	C₂²	#15689158	1	1	yes	characteristic
395	C₂²	#15689160	1	1	yes	characteristic
396	C₂²	#15689203	1	2	yes	—
397	C₂²	#15689208	1	2	yes	—
398	C₂²	#15689214	1	2	yes	—
399	C₂²	#15689215	1	2	yes	—
400	C₂²	#15689349	1	2	yes	—
401	C₂²	#15689353	1	2	yes	—
402	C₂²	#15689356	1	1	yes	characteristic
403	C₂²	#15689360	1	1	yes	characteristic
404	C₂²	#15689361	1	1	yes	characteristic
405	C₂²	#15689365	1	1	yes	characteristic
406	C₂²	#15689468	1	2	yes	—
407	C₂²	#15689472	1	2	yes	—
408	C₂²	#15689476	1	2	yes	—
409	C₂²	#15689479	1	2	yes	—
410	C₄	—	8	4	no	—
411	C₄	—	94	4	no	—
412	C₄	—	94	4	no	—
413	C₄	—	376	4	no	—
414	C₄	#15688968	1	1	yes	characteristic
415	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
416	C₄	#15688984	1	1	yes	characteristic
417	C₄	#15688990	1	1	yes	characteristic
418	C₄	#15689004	1	2	yes	—
419	C₄	#15689008	1	2	yes	—
420	C₂	#20241612	1	1	yes	characteristic
421	C₂	#20243276	1	1	yes	characteristic
422	C₂	#20243280	1	1	yes	characteristic
423	C₂	#20243410	1	1	yes	characteristic
424	C₂	#20243414	1	1	yes	characteristic
425	C₂	#20243514	1	1	yes	characteristic
426	C₂	#20243517	1	1	yes	characteristic
427	C₂	#20244061	1	2	yes	—
428	C₂	#20244065	1	2	yes	—
429	C₂	#20244068	1	2	yes	—
430	C₂	#20244072	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
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	#10820
LCS	G ▷ C₂×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
11. C₂×C₈×Dic₄₇	C₄	semidirect
15. #15688885	C₄	semidirect
234. C₄₇	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₄₇	2
C₂×#15688886	2
C₂×#15688885	2
#20241617	2
C₂×C₄₇×#340	2
#10820	47