Subgroups — #26218364

Order 12032.

1018 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20243954	C₂	1	4	yes	maximal, complemented
4	#20243947	C₂	1	4	yes	maximal, complemented
5	#20243082	C₂	1	1	yes	maximal, characteristic
6	#20243082	C₂	1	1	yes	maximal, characteristic
7	#20243082	C₂	1	1	yes	maximal, characteristic
8	#20243082	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	#15689147	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
16	C₄×#10625329	—	2	4	no	—
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	#15688878	C₂²	1	2	yes	—
20	#15688878	C₂²	1	4	yes	—
21	#15688878	C₂²	1	4	yes	—
22	#15688878	C₂²	1	4	yes	—
23	#15688878	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
32	C₂×#95×C₄₇	C₄	1	2	yes	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	D₄	1	4	yes	—
44	C₂×#10625329	Q₈	1	4	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
50	#13093935	—	2	4	no	—
51	C₄×C₄₇⋊C₈	—	2	4	no	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	2	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
76	#95×C₄₇	C₂×C₄	1	2	yes	—
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	#95×C₄₇	C₂×C₄	1	2	yes	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
109	C₄²×C₄₇	—	2	4	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	4	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	1	no	—
121	#10625329	—	2	8	no	—
122	#10625329	—	2	8	no	—
123	#10625329	—	4	4	no	—
124	#10625329	—	4	4	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
136	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	#117	1	2	yes	—
140	C₂³×C₄₇	C₄×D₄	1	2	yes	—
141	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
142	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	—	2	8	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	8	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	#117	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
165	C₂×C₄×C₄₇	#123	1	4	yes	—
166	C₂×C₄×C₄₇	#125	1	4	yes	—
167	C₂×C₄×C₄₇	#126	1	4	yes	—
168	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
170	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₄₇⋊C₈	—	2	4	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	#21023	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	#387	1	4	yes	—
187	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
191	C₂²×C₄₇	#568	1	2	yes	—
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	—	2	4	no	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	4	2	no	—
197	C₄×C₄₇	—	4	2	no	—
198	C₄×C₄₇	#387	1	4	yes	—
199	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
203	C₂×#423	—	47	1	no	—
204	C₂×C₄×M₁₆	—	47	1	no	—
205	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
206	#1917	—	47	4	no	—
207	#1916	—	47	4	no	—
208	#1728	—	47	1	no	—
209	#1728	—	47	1	no	—
210	#1728	—	47	1	no	—
211	#1728	—	47	1	no	—
212	C₂×C₄₇	—	2	4	no	—
213	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
214	C₂×C₄₇	#2920	1	1	yes	characteristic
215	C₂×C₄₇	#2921	1	1	yes	characteristic
216	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
217	C₂×C₄₇	Q₈×M₁₆	1	2	yes	—
218	C₂²×M₁₆	—	47	1	no	—
219	C₂²×M₁₆	—	47	1	no	—
220	C₂²×M₁₆	—	47	1	no	—
221	C₂²×M₁₆	—	47	1	no	—
222	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
223	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
226	#423	—	94	4	no	—
227	C₂×C₄⋊C₈	—	47	4	no	—
228	C₄×M₁₆	—	94	4	no	—
229	C₂×#97	—	47	2	no	—
230	C₂×C₄×C₈	—	47	2	no	—
231	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
232	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
233	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
234	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
235	C₂×#95	Dic₄₇	1	2	yes	—
236	#336	—	47	2	no	—
237	#336	—	47	4	no	—
238	#336	—	47	4	no	—
239	#336	—	47	4	no	—
240	#336	—	47	2	no	—
241	C₄₇	#21023	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
244	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
245	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂×M₁₆	—	47	4	no	—
248	C₂×M₁₆	—	47	4	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂²×C₈	—	47	2	no	—
260	C₂²×C₈	—	47	2	no	—
261	C₂²×C₈	—	47	2	no	—
262	C₂²×C₈	—	47	2	no	—
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
265	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
275	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
277	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
278	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
282	C₄⋊C₈	—	94	8	no	—
283	#97	—	94	4	no	—
284	C₄×C₈	—	94	4	no	—
285	#95	C₂×Dic₄₇	1	2	yes	—
286	#95	C₂×Dic₄₇	1	2	yes	—
287	#95	C₂×Dic₄₇	1	2	yes	—
288	#95	C₂×Dic₄₇	1	2	yes	—
289	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	#10625350	1	2	yes	—
301	C₂²×C₄	#10625350	1	2	yes	—
302	C₂²×C₄	D₄×D₄₇	1	2	yes	—
303	C₂²×C₄	#10625352	1	2	yes	—
304	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
305	C₂²×C₄	#10625354	1	2	yes	—
306	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
307	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
309	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
310	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
312	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
314	M₁₆	—	94	8	no	—
315	M₁₆	—	94	8	no	—
316	M₁₆	—	188	4	no	—
317	M₁₆	—	188	4	no	—
318	C₂×C₈	—	47	4	no	—
319	C₂×C₈	—	47	4	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	#10625329	1	8	yes	complemented
334	C₄²	—	2	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	#13093983	1	2	yes	—
349	C₂³	D₄×Dic₄₇	1	2	yes	—
350	C₂³	Q₈×Dic₄₇	1	2	yes	—
351	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	#13093983	1	2	yes	—
371	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
372	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
373	C₂×C₄	#13094002	1	4	yes	—
374	C₂×C₄	#13094009	1	4	yes	—
375	C₂×C₄	#13094014	1	4	yes	—
376	C₂×C₄	#13094019	1	4	yes	—
377	C₂×C₄	C₂×#10625329	1	4	yes	—
378	C₂×C₄	C₂×#10625329	1	4	yes	—
379	C₂×C₄	C₂×#10625329	1	4	yes	—
380	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
385	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
386	C₈	—	94	4	no	—
387	C₈	—	94	4	no	—
388	C₈	—	188	2	no	—
389	C₈	—	188	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	#15689009	1	4	yes	—
395	C₂²	C₂×#13093983	1	1	yes	characteristic
396	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
397	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
398	C₂²	C₂²×#10625329	1	2	yes	—
399	C₂²	#15689890	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	#15689009	1	4	yes	—
407	C₄	C₂×#13094002	1	1	yes	characteristic
408	C₄	C₂×#13094009	1	1	yes	characteristic
409	C₄	C₂×#13094014	1	1	yes	characteristic
410	C₄	C₂×#13094019	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	C₂×#15689009	1	1	yes	characteristic
413	C₂	#20252021	1	1	yes	characteristic
414	C₂	#20252026	1	1	yes	characteristic
415	C₂	D₄×#10625329	1	2	yes	—
416	C₂	Q₈×#10625329	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#21023
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #20243954	C₂	semidirect
4. #20243947	C₂	semidirect
108. C₄⋊C₄×C₄₇	M₁₆	semidirect
241. C₄₇	#21023	semidirect
333. C₄⋊C₄	#10625329	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×C₄×#10625329	2
#20243954	2
#20243947	2
#20243082	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#21023	47