Subgroups — #26124163

Order 12032.

934 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688878	C₂	1	2	yes	maximal
3	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688878	C₂	1	2	yes	maximal
5	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	#15688878	—	2	4	no	—
11	#15688878	—	2	2	no	—
12	#15688878	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
20	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
21	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
35	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	C₈	1	4	yes	complemented
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	1	no	—
52	C₂×C₄²×C₄₇	—	2	1	no	—
53	C₂×C₄²×C₄₇	—	2	1	no	—
54	C₂×C₄²×C₄₇	—	2	1	no	—
55	C₂×C₄²×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	—	2	1	no	—
58	C₂×C₄²×C₄₇	—	2	1	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	D₄	1	2	yes	—
61	C₂×C₄²×C₄₇	D₄	1	2	yes	—
62	C₂×C₄²×C₄₇	D₄	1	2	yes	—
63	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
64	#95×C₄₇	—	2	2	no	—
65	#95×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	1	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	1	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	1	no	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	1	no	—
81	C₂²×C₄×C₄₇	—	2	1	no	—
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
97	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
98	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₄⋊C₄×C₄₇	—	2	8	no	—
110	C₄⋊C₄×C₄₇	—	2	8	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	4	1	no	—
119	C₄²×C₄₇	—	4	2	no	—
120	C₄²×C₄₇	—	4	1	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	2	4	no	—
124	C₂×C₄₇⋊C₈	—	2	4	no	—
125	C₂×C₄₇⋊C₈	—	2	4	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂×C₄₇⋊C₈	—	4	2	no	—
129	C₂×C₄₇⋊C₈	—	4	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂×C₄₇⋊C₈	—	4	2	no	—
132	C₂×C₄₇⋊C₈	—	4	2	no	—
133	C₂×C₄₇⋊C₈	—	4	2	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₄₇	#117	1	1	yes	characteristic
138	C₂³×C₄₇	C₄×D₄	1	2	yes	—
139	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
140	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
144	C₂³×C₄₇	#131	1	2	yes	—
145	C₂³×C₄₇	#131	1	2	yes	—
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	4	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	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	C₂²⋊C₈	1	4	yes	—
177	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	complemented
178	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
179	C₂×C₄×C₄₇	#121	1	2	yes	—
180	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#121	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
188	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#123	1	2	yes	—
190	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#125	1	2	yes	—
192	C₂×C₄×C₄₇	#125	1	2	yes	—
193	C₂×C₄×C₄₇	#126	1	2	yes	—
194	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
196	C₄₇⋊C₈	—	4	4	no	—
197	C₄₇⋊C₈	—	4	4	no	—
198	#11202	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	#380	1	1	yes	characteristic
200	C₂²×C₄₇	#386	1	1	yes	characteristic
201	C₂²×C₄₇	#387	1	2	yes	—
202	C₂²×C₄₇	#389	1	2	yes	—
203	C₂²×C₄₇	#391	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
205	C₂²×C₄₇	#407	1	1	yes	characteristic
206	C₂²×C₄₇	#408	1	1	yes	characteristic
207	C₂²×C₄₇	#408	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
209	C₂²×C₄₇	#423	1	1	yes	characteristic
210	C₂²×C₄₇	#424	1	2	yes	—
211	C₂²×C₄₇	#431	1	1	yes	characteristic
212	C₂²×C₄₇	#432	1	1	yes	characteristic
213	C₂²×C₄₇	#433	1	2	yes	—
214	C₂²×C₄₇	C₈×D₄	1	2	yes	—
215	C₂²×C₄₇	#435	1	2	yes	—
216	C₂²×C₄₇	#435	1	2	yes	—
217	C₂²×C₄₇	#436	1	2	yes	—
218	C₂²×C₄₇	C₈×Q₈	1	2	yes	—
219	C₂²×C₄₇	#446	1	2	yes	—
220	C₂²×C₄₇	#446	1	2	yes	—
221	C₂²×C₄₇	#446	1	2	yes	—
222	C₄×C₄₇	—	2	4	no	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	#394	1	1	yes	characteristic
229	C₄×C₄₇	#395	1	1	yes	characteristic
230	C₄×C₄₇	#396	1	2	yes	—
231	C₄×C₄₇	#398	1	1	yes	characteristic
232	C₄×C₄₇	#398	1	2	yes	—
233	C₄×C₄₇	#400	1	1	yes	characteristic
234	C₂²×C₄⋊C₈	—	47	1	no	—
235	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
236	C₂×#336	—	47	2	no	—
237	C₂×#336	—	47	2	no	—
238	C₂×#336	—	47	1	no	—
239	C₂×C₄₇	#1441	1	1	yes	characteristic
240	C₂×C₄₇	#1797	1	1	yes	characteristic
241	C₂×C₄₇	#1798	1	1	yes	characteristic
242	C₂×C₄₇	#1869	1	1	yes	characteristic
243	C₂×C₄₇	#1870	1	1	yes	characteristic
244	C₂×C₄₇	#1916	1	2	yes	—
245	C₂×C₄₇	#1917	1	2	yes	—
246	C₂×C₄₇	#1939	1	2	yes	—
247	C₂×C₄₇	#1940	1	2	yes	—
248	C₂×C₄₇	#1984	1	1	yes	characteristic
249	C₂×C₄₇	#1985	1	1	yes	characteristic
250	C₂³×C₈	—	47	2	no	—
251	C₂³×C₈	—	47	2	no	—
252	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
254	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
255	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
256	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	94	4	no	—
258	C₂×C₄⋊C₈	—	94	2	no	—
259	C₄×C₄⋊C₄	—	2	2	no	—
260	C₄×C₄⋊C₄	—	2	2	no	—
261	C₂×#95	Dic₄₇	1	1	yes	characteristic
262	C₂×#95	Dic₄₇	1	1	yes	characteristic
263	#336	—	94	4	no	—
264	#336	—	94	4	no	—
265	#336	—	94	2	no	—
266	C₄₇	#11202	1	1	yes	characteristic, complemented, Sylow
267	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
270	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
272	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
274	C₂²×C₈	—	47	4	no	—
275	C₂²×C₈	—	47	4	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	2	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₂²×C₈	—	94	2	no	—
281	C₂²×C₈	—	94	2	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	—	94	2	no	—
285	C₂²×C₈	—	94	2	no	—
286	C₂²×C₈	—	94	2	no	—
287	C₂²×C₈	—	94	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	C₄₇⋊C₈	1	4	yes	complemented
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	Dic₉₄	1	2	yes	—
305	C₂×C₄²	D₁₈₈	1	2	yes	—
306	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
307	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
308	C₄⋊C₈	—	94	8	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
335	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
336	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
337	C₂²×C₄	#10625329	1	2	yes	—
338	C₂²×C₄	#10625329	1	2	yes	—
339	C₂²×C₄	#10625329	1	2	yes	—
340	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
341	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
342	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
344	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
346	C₂²×C₄	#10625350	1	1	yes	characteristic
347	C₂²×C₄	#10625350	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₄₇	1	2	yes	—
349	C₂²×C₄	#10625352	1	2	yes	—
350	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
351	C₂²×C₄	#10625354	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₈	—	94	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	—	94	4	no	—
357	C₂×C₈	—	94	4	no	—
358	C₂×C₈	—	94	4	no	—
359	C₂×C₈	—	94	4	no	—
360	C₂×C₈	—	188	2	no	—
361	C₂×C₈	—	188	2	no	—
362	C₂×C₈	—	188	2	no	—
363	C₂×C₈	—	188	2	no	—
364	C₂×C₈	—	188	2	no	—
365	C₂×C₈	—	188	2	no	—
366	C₂×C₈	—	188	2	no	—
367	C₂×C₈	—	188	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	2	no	—
379	C₄²	—	4	1	no	—
380	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
381	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
382	C₂³	#13093983	1	1	yes	characteristic
383	C₂³	D₄×Dic₄₇	1	2	yes	—
384	C₂³	Q₈×Dic₄₇	1	2	yes	—
385	C₂³	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
386	C₂³	C₂×#10625329	1	1	yes	characteristic
387	C₂³	C₂×#10625329	1	1	yes	characteristic
388	C₂³	C₂×#10625329	1	1	yes	characteristic
389	C₂³	#13094031	1	2	yes	—
390	C₂³	#13094031	1	2	yes	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	4	yes	—
422	C₂×C₄	C₄⋊(C₄₇⋊C₈)	1	4	yes	complemented
423	C₂×C₄	#13093992	1	1	yes	characteristic
424	C₂×C₄	#13093996	1	2	yes	—
425	C₂×C₄	#13093998	1	1	yes	characteristic
426	C₂×C₄	#13093998	1	1	yes	characteristic
427	C₂×C₄	#13093999	1	2	yes	—
428	C₂×C₄	#13094000	1	2	yes	—
429	C₂×C₄	#13094002	1	2	yes	—
430	C₂×C₄	#13094003	1	1	yes	characteristic
431	C₂×C₄	#13094003	1	1	yes	characteristic
432	C₂×C₄	#13094004	1	2	yes	—
433	C₂×C₄	#13094005	1	1	yes	characteristic
434	C₂×C₄	#13094009	1	2	yes	—
435	C₂×C₄	#13094013	1	1	yes	characteristic
436	C₂×C₄	#13094014	1	2	yes	—
437	C₂×C₄	#13094015	1	2	yes	—
438	C₂×C₄	#13094019	1	2	yes	—
439	C₂×C₄	#13094022	1	1	yes	characteristic
440	C₂×C₄	#13094023	1	2	yes	—
441	C₈	—	188	4	no	—
442	C₈	—	188	4	no	—
443	C₂²	#15688983	1	1	yes	characteristic
444	C₂²	#15689003	1	1	yes	characteristic
445	C₂²	#15689009	1	2	yes	—
446	C₂²	#15689022	1	2	yes	—
447	C₂²	#15689030	1	1	yes	characteristic
448	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
449	C₂²	#15689087	1	1	yes	characteristic
450	C₂²	#15689090	1	1	yes	characteristic
451	C₂²	#15689090	1	1	yes	characteristic
452	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
453	C₂²	#15689147	1	1	yes	characteristic
454	C₂²	#15689150	1	2	yes	—
455	C₂²	#15689176	1	1	yes	characteristic
456	C₂²	#15689180	1	1	yes	characteristic
457	C₂²	#15689184	1	2	yes	—
458	C₂²	D₄×C₄₇⋊C₈	1	2	yes	—
459	C₂²	#15689195	1	2	yes	—
460	C₂²	#15689195	1	2	yes	—
461	C₂²	#15689201	1	2	yes	—
462	C₂²	Q₈×C₄₇⋊C₈	1	2	yes	—
463	C₂²	#15689254	1	2	yes	—
464	C₂²	#15689254	1	2	yes	—
465	C₂²	#15689254	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	#15689040	1	1	yes	characteristic
473	C₄	#15689043	1	1	yes	characteristic
474	C₄	#15689045	1	2	yes	—
475	C₄	#15689053	1	1	yes	characteristic
476	C₄	#15689056	1	2	yes	—
477	C₄	#15689062	1	1	yes	characteristic
478	C₂	#20241641	1	1	yes	characteristic
479	C₂	#20243368	1	1	yes	characteristic
480	C₂	#20243372	1	1	yes	characteristic
481	C₂	#20243681	1	1	yes	characteristic
482	C₂	#20243686	1	1	yes	characteristic
483	C₂	#20243947	1	2	yes	—
484	C₂	#20243954	1	2	yes	—
485	C₂	#20244107	1	2	yes	—
486	C₂	#20244112	1	2	yes	—
487	C₂	#20244325	1	1	yes	characteristic
488	C₂	#20244329	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#11202
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
49. C₂×C₄⋊C₄×C₄₇	C₈	semidirect
177. C₂×C₄×C₄₇	C₄⋊C₈	semidirect
266. C₄₇	#11202	semidirect
293. C₂×C₄⋊C₄	C₄₇⋊C₈	semidirect
422. C₂×C₄	C₄⋊(C₄₇⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688878	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#11202	47