Subgroups — #26214262

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689150	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
5	#20243263	C₂	1	2	yes	maximal, complemented
6	#20243263	C₂	1	2	yes	maximal, complemented
7	#20243257	C₂	1	2	yes	maximal, complemented
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
9	#20243085	C₂	1	1	yes	maximal, characteristic
10	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2296	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	#15689150	C₄	1	8	yes	complemented
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	#15689079	—	2	4	no	—
20	#15689079	C₄	1	8	yes	complemented
21	C₄×#10625329	—	2	4	no	—
22	C₂×#13093935	C₂²	1	2	yes	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	#15688878	C₂²	1	1	yes	characteristic
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	1	yes	characteristic
32	#15688878	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#389	C₄	1	2	yes	—
38	C₄₇×#389	C₄	1	2	yes	—
39	C₄₇×#385	C₄	1	4	yes	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	C₂×C₄	1	4	yes	—
45	C₂×#10625329	C₂×C₄	1	4	yes	—
46	C₂×#10625329	D₄	1	4	yes	—
47	C₂×#10625329	Q₈	1	4	yes	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
53	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
61	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
62	#13093935	—	2	4	no	—
63	#13093935	—	2	4	no	—
64	#13093935	C₂×C₄	1	8	yes	complemented
65	C₄×C₄₇⋊C₈	—	2	4	no	—
66	C₄×C₄₇⋊C₈	—	2	4	no	—
67	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
68	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	#117×C₄₇	—	2	2	no	—
71	#117×C₄₇	—	2	2	no	—
72	#117×C₄₇	C₂×C₄	1	4	yes	—
73	#117×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	—	2	2	no	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	#95×C₄₇	C₂×C₄	1	4	yes	—
89	#95×C₄₇	C₂×C₄	1	4	yes	—
90	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	#41	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	8	no	—
109	C₄⋊C₄×C₄₇	—	4	4	no	—
110	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
111	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
112	C₂²⋊C₄×C₄₇	—	2	4	no	—
113	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	2	1	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄²×C₄₇	—	2	1	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
123	#10625329	—	2	8	no	—
124	#10625329	C₄⋊C₄	1	16	yes	complemented
125	C₂×C₄₇⋊C₈	—	2	8	no	—
126	C₂×C₄₇⋊C₈	—	2	8	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
144	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
148	C₂³×C₄₇	C₄×D₄	1	2	yes	—
149	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
150	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
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	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	4	8	no	—
162	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₇	#117	1	4	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
170	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	#131	1	4	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	—	2	2	no	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	2	4	no	—
183	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	—
184	#20439	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
190	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#131	1	2	yes	—
194	C₂²×C₄₇	#568	1	2	yes	—
195	C₄×C₄₇	—	2	4	no	—
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	4	4	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
201	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
203	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂×#424	—	47	1	no	—
206	C₂×#405	—	47	1	no	—
207	C₂×#405	—	47	1	no	—
208	C₂×C₄×M₁₆	—	47	1	no	—
209	#2296	D₄₇	1	1	yes	characteristic
210	#1771	—	47	2	no	—
211	#1771	—	47	2	no	—
212	#1770	—	47	2	no	—
213	C₈×C₄⋊C₄	—	47	2	no	—
214	#1729	—	47	1	no	—
215	C₂×#336	—	47	1	no	—
216	C₂×C₄₇	—	2	4	no	—
217	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
219	C₂×C₄₇	#2875	1	1	yes	characteristic
220	C₂×C₄₇	#2933	1	2	yes	—
221	C₂×C₄₇	#2962	1	2	yes	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂²×M₁₆	—	47	1	no	—
224	C₂³×C₈	—	47	1	no	—
225	C₂³×C₈	—	47	1	no	—
226	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
228	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
229	#424	—	47	8	no	—
230	C₂×C₄⋊C₈	—	47	2	no	—
231	C₂×C₄⋊C₈	—	47	2	no	—
232	#405	—	47	8	no	—
233	#405	—	94	4	no	—
234	C₄×M₁₆	—	94	4	no	—
235	C₂×#97	—	47	2	no	—
236	C₂×#97	—	47	2	no	—
237	C₂×#97	—	47	2	no	—
238	C₂×C₄×C₈	—	47	2	no	—
239	C₂×C₄×C₈	—	47	2	no	—
240	C₂×C₄×C₈	—	47	2	no	—
241	#389	Dic₄₇	1	2	yes	—
242	#389	Dic₄₇	1	2	yes	—
243	#385	Dic₄₇	1	4	yes	—
244	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
245	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
246	#336	—	47	1	no	—
247	#336	—	47	1	no	—
248	#336	—	47	1	no	—
249	#336	—	47	1	no	—
250	#336	—	47	2	no	—
251	#336	—	47	2	no	—
252	C₄₇	#20439	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
254	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×M₁₆	—	47	4	no	—
256	C₂×M₁₆	—	47	4	no	—
257	C₂×M₁₆	—	47	4	no	—
258	C₂×M₁₆	—	47	4	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂²×C₈	—	47	2	no	—
262	C₂²×C₈	—	47	4	no	—
263	C₂²×C₈	—	47	4	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	2	no	—
269	C₂²×C₈	—	94	2	no	—
270	C₂²×C₈	—	94	2	no	—
271	C₂²×C₈	—	94	2	no	—
272	C₂²×C₈	—	94	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	C₄×D₄₇	1	4	yes	—
276	#117	C₄×D₄₇	1	4	yes	—
277	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
280	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
287	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
291	C₄⋊C₈	—	47	8	no	—
292	C₄⋊C₈	—	47	8	no	—
293	#97	—	47	8	no	—
294	#97	—	94	4	no	—
295	#97	—	94	4	no	—
296	C₄×C₈	—	47	8	no	—
297	C₄×C₈	—	94	4	no	—
298	C₄×C₈	—	94	4	no	—
299	#95	C₂×Dic₄₇	1	4	yes	—
300	#95	C₂×Dic₄₇	1	4	yes	—
301	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
307	C₂²×C₄	D₄×D₄₇	1	2	yes	—
308	C₂²×C₄	#10625352	1	2	yes	—
309	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
310	C₂²×C₄	#10625354	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
312	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
313	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
318	M₁₆	—	47	16	no	—
319	M₁₆	—	94	8	no	—
320	C₂×C₈	—	47	4	no	—
321	C₂×C₈	—	47	4	no	—
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	47	2	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	47	4	no	—
328	C₂×C₈	—	94	8	no	—
329	C₂×C₈	—	94	8	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
344	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂×C₄×D₄₇	1	4	yes	—
355	C₄²	C₂×C₄×D₄₇	1	4	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
359	C₂³	D₄×Dic₄₇	1	2	yes	—
360	C₂³	Q₈×Dic₄₇	1	2	yes	—
361	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
374	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
375	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
376	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
377	C₂×C₄	#13093982	1	4	yes	—
378	C₂×C₄	#13093986	1	4	yes	—
379	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
380	C₂×C₄	#13093989	1	4	yes	—
381	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
382	C₂×C₄	#13094031	1	4	yes	—
383	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
389	C₈	—	47	8	no	—
390	C₈	—	94	2	no	—
391	C₈	—	94	2	no	—
392	C₈	—	94	2	no	—
393	C₈	—	94	2	no	—
394	C₈	—	94	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₄⋊C₄×Dic₄₇	1	4	yes	—
400	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
401	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
402	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
403	C₂²	C₂×#13094031	1	2	yes	—
404	C₂²	#15689890	1	2	yes	—
405	C₄	—	2	4	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	C₄⋊C₄×Dic₄₇	1	4	yes	—
411	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
412	C₄	C₂×#13093982	1	1	yes	characteristic
413	C₄	C₂×#13093986	1	1	yes	characteristic
414	C₄	C₂×#13093989	1	1	yes	characteristic
415	C₂	—	2	4	no	—
416	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
417	C₂	C₄×#13094031	1	1	yes	characteristic
418	C₂	#20251816	1	1	yes	characteristic
419	C₂	#20252115	1	2	yes	—
420	C₂	#20252337	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#2296	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2296	D₄₇
hypocenter	C₄₇	#20439
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
5. #20243263	C₂	semidirect
6. #20243263	C₂	semidirect
7. #20243257	C₂	semidirect
8. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
16. #15689150	C₄	semidirect
20. #15689079	C₄	semidirect
60. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
61. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
64. #13093935	C₂×C₄	semidirect
67. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
124. #10625329	C₄⋊C₄	semidirect
252. C₄₇	#20439	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689150	2
C₂×#15689079	2
C₂×C₄×#10625329	2
#20243263	2
#20243257	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243085	2
C₂×#15688878	2
C₄₇×#2296	2
#20439	47