Subgroups — #26234348

Order 12032.

1096 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689200	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689145	C₂	1	2	yes	maximal, complemented
4	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
5	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243572	C₂	1	2	yes	maximal, complemented
7	#20243569	C₂	1	2	yes	maximal, complemented
8	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243367	C₂	1	2	yes	maximal, complemented
10	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×#10625324	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093986	C₄	1	1	yes	characteristic
16	C₂×#13093986	C₄	1	1	yes	characteristic
17	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
18	#15689202	—	2	4	no	—
19	#15689200	—	2	4	no	—
20	#15689145	—	2	8	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
28	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
31	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
32	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
33	#15688970	C₄	1	2	yes	—
34	#15688970	C₄	1	2	yes	—
35	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
36	#15688878	C₂²	1	2	yes	—
37	#15688877	C₂²	1	1	yes	characteristic
38	#15688877	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
48	C₂×#10625324	—	2	4	no	—
49	C₂×#10625324	—	2	4	no	—
50	C₂×#10625324	—	2	4	no	—
51	C₂×#10625324	—	2	4	no	—
52	C₂×#10625324	—	4	2	no	—
53	C₂×#10625324	—	4	2	no	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₄×D₁₈₈	D₄	1	4	yes	—
58	C₄×D₁₈₈	Q₈	1	4	yes	—
59	#13093986	—	2	4	no	—
60	#13093986	—	2	4	no	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₄²×D₄₇	—	2	4	no	—
74	C₄²×D₄₇	—	2	4	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
77	Dic₄₇⋊C₈	—	2	4	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	4	2	no	—
80	Dic₄₇⋊C₈	D₄	1	4	yes	complemented
81	(C₂×D₄₇)⋊C₈	—	2	4	no	—
82	(C₂×D₄₇)⋊C₈	—	2	4	no	—
83	C₄×C₄₇⋊C₈	—	2	2	no	—
84	C₄₇⋊#95	C₂×C₄	1	2	yes	—
85	C₄₇⋊#95	C₂×C₄	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	—	2	4	no	—
94	C₄⋊C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	#95×C₄₇	C₂×C₄	1	2	yes	—
97	C₂³×D₄₇	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	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₁₈₈	—	2	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	—	2	4	no	—
116	C₂×C₄×D₄₇	—	2	4	no	—
117	C₂×C₄×D₄₇	—	2	4	no	—
118	C₂×C₄×D₄₇	—	2	4	no	—
119	C₂×C₄×D₄₇	—	2	4	no	—
120	C₂×C₄×D₄₇	—	4	2	no	—
121	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
122	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	C₂×D₄	1	2	yes	—
137	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
138	(C₂×D₄₇)⋊C₄	—	2	4	no	—
139	(C₂×D₄₇)⋊C₄	—	2	4	no	—
140	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
141	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	4	no	—
146	C₄×Dic₄₇	—	2	4	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	4	1	no	—
149	C₄×Dic₄₇	M₁₆	1	4	yes	complemented
150	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
151	C₄×Dic₄₇	#41	1	2	yes	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	1	no	—
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	#10625324	—	4	8	no	—
162	#10625324	—	4	8	no	—
163	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂²×D₄₇	—	2	2	no	—
165	C₂²×D₄₇	—	2	2	no	—
166	C₂²×D₄₇	—	2	2	no	—
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	2	2	no	—
169	C₂²×D₄₇	—	2	2	no	—
170	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
199	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
200	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
201	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
202	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
203	C₂×Dic₄₇	#131	1	2	yes	—
204	D₁₈₈	—	2	8	no	—
205	C₄×D₄₇	—	2	4	no	—
206	C₄×D₄₇	—	2	4	no	—
207	C₄×D₄₇	—	2	4	no	—
208	C₄×D₄₇	—	2	4	no	—
209	C₄×D₄₇	—	4	8	no	—
210	C₄×D₄₇	—	4	8	no	—
211	C₈×C₄₇	—	2	2	no	—
212	C₈×C₄₇	—	4	2	no	—
213	C₈×C₄₇	—	4	1	no	—
214	C₄₇⋊C₈	—	2	2	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	C₄₇⋊C₈	—	4	1	no	—
217	#22650	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₇	#520	1	1	yes	characteristic
221	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
222	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
224	C₂²×C₄₇	#568	1	1	yes	characteristic
225	C₂×D₄₇	—	2	4	no	—
226	C₂×D₄₇	—	2	4	no	—
227	C₂×D₄₇	—	2	4	no	—
228	C₂×D₄₇	—	4	2	no	—
229	C₂×D₄₇	—	4	2	no	—
230	C₂×D₄₇	—	4	2	no	—
231	C₂×D₄₇	—	4	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	#423	1	4	yes	complemented
236	C₄×C₄₇	D₄²	1	1	yes	characteristic
237	C₄×C₄₇	#547	1	1	yes	characteristic
238	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
239	C₄×C₄₇	#554	1	1	yes	characteristic
240	Dic₄₇	—	2	4	no	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	4	1	no	—
244	Dic₄₇	#436	1	4	yes	complemented
245	C₂×#436	—	47	1	no	—
246	C₂×#436	—	47	1	no	—
247	C₂×#423	—	47	2	no	—
248	C₄²×D₄	—	47	1	no	—
249	#1939	—	47	1	no	—
250	#1939	D₄₇	1	1	yes	characteristic, complemented
251	#1851	—	47	2	no	—
252	#1851	—	47	2	no	—
253	#1842	—	47	1	no	—
254	#1797	—	47	2	no	—
255	C₄×C₄⋊C₈	—	47	1	no	—
256	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
258	C₂×C₄₇	#2906	1	1	yes	characteristic
259	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
260	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
261	C₂×C₄₇	#2989	1	1	yes	characteristic
262	C₂×C₄₇	#2991	1	1	yes	characteristic
263	D₄₇	—	4	4	no	—
264	C₂²×M₁₆	—	47	2	no	—
265	C₂²×M₁₆	—	47	2	no	—
266	C₂×C₄×D₄	—	47	1	no	—
267	C₂×C₄×D₄	—	47	1	no	—
268	C₂×C₄×D₄	—	47	1	no	—
269	C₂²×C₄²	—	47	2	no	—
270	#436	—	94	4	no	—
271	#436	—	94	4	no	—
272	#423	—	94	8	no	—
273	C₂×C₄⋊C₈	—	47	1	no	—
274	C₂×C₄⋊C₈	—	47	1	no	—
275	C₂×C₄⋊C₈	—	47	2	no	—
276	C₂×C₄⋊C₈	—	47	1	no	—
277	C₂×C₄⋊C₈	—	47	2	no	—
278	C₂×C₄⋊C₈	—	47	2	no	—
279	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
281	C₂×C₂²⋊C₈	—	47	2	no	—
282	C₂×C₂²⋊C₈	—	47	2	no	—
283	C₂×C₄×C₈	—	47	1	no	—
284	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	47	1	no	—
286	C₄×C₄⋊C₄	—	47	1	no	—
287	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
288	C₄×C₂²⋊C₄	—	47	2	no	—
289	C₄×C₂²⋊C₄	—	47	2	no	—
290	C₄×C₂²⋊C₄	—	47	2	no	—
291	C₄³	—	47	1	no	—
292	#336	—	47	1	no	—
293	#336	—	47	1	no	—
294	#336	—	47	2	no	—
295	#336	C₂×D₄₇	1	2	yes	—
296	C₄₇	#22650	1	1	yes	characteristic, complemented, Sylow
297	C₂²×D₄	—	47	1	no	—
298	C₂³×C₄	—	47	2	no	—
299	C₂³×C₄	—	47	2	no	—
300	C₂³×C₄	—	47	2	no	—
301	C₂×M₁₆	—	94	4	no	—
302	C₂×M₁₆	—	94	4	no	—
303	C₂×M₁₆	—	94	4	no	—
304	C₂×M₁₆	—	94	4	no	—
305	C₂×M₁₆	—	188	2	no	—
306	C₂×M₁₆	—	188	2	no	—
307	C₂²×C₈	—	47	1	no	—
308	C₂²×C₈	—	47	2	no	—
309	C₂²×C₈	—	47	1	no	—
310	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
311	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₄×D₄	—	47	4	no	—
314	C₄×D₄	—	47	4	no	—
315	C₄×D₄	—	94	4	no	—
316	C₄×D₄	—	94	4	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	47	2	no	—
321	C₂×C₂²⋊C₄	—	47	2	no	—
322	C₂×C₂²⋊C₄	—	47	2	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	2	no	—
328	C₂×C₄²	—	47	2	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	47	1	no	—
331	C₂×C₄²	—	94	4	no	—
332	C₂×C₄²	—	94	4	no	—
333	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
334	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
335	C₄⋊C₈	—	2	4	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	47	4	no	—
338	C₄⋊C₈	—	94	4	no	—
339	C₄⋊C₈	—	94	2	no	—
340	C₄⋊C₈	—	94	4	no	—
341	C₄⋊C₈	—	94	2	no	—
342	C₄⋊C₈	—	188	2	no	—
343	C₂²⋊C₈	—	94	4	no	—
344	C₂²⋊C₈	—	94	4	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	94	2	no	—
347	#95	—	47	2	no	—
348	#95	—	47	2	no	—
349	#95	C₄×D₄₇	1	2	yes	—
350	C₂⁴	—	47	2	no	—
351	C₂×D₄	—	47	4	no	—
352	C₂×D₄	—	94	2	no	—
353	C₂×D₄	—	94	2	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	2	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	4	no	—
359	C₂²×C₄	—	47	4	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	94	4	no	—
362	C₂²×C₄	—	94	4	no	—
363	C₂²×C₄	—	94	4	no	—
364	C₂²×C₄	—	94	4	no	—
365	C₂²×C₄	—	94	2	no	—
366	C₂²×C₄	—	94	2	no	—
367	C₂²×C₄	—	94	2	no	—
368	C₂²×C₄	—	94	2	no	—
369	C₂²×C₄	—	94	4	no	—
370	C₂²×C₄	—	188	2	no	—
371	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
372	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
376	M₁₆	—	188	8	no	—
377	M₁₆	—	188	8	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	47	2	no	—
387	C₂×C₈	—	94	1	no	—
388	C₂×C₈	—	94	1	no	—
389	C₂×C₈	—	94	1	no	—
390	C₂×C₈	—	94	2	no	—
391	C₂×C₈	—	94	2	no	—
392	C₂×C₈	—	94	1	no	—
393	C₂×C₈	—	94	2	no	—
394	C₂×C₈	—	94	1	no	—
395	C₂×C₈	D₄×D₄₇	1	2	yes	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	47	4	no	—
398	C₄⋊C₄	#10625324	1	4	yes	complemented
399	C₂²⋊C₄	—	47	8	no	—
400	C₂²⋊C₄	—	94	4	no	—
401	C₂²⋊C₄	—	94	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	47	4	no	—
405	C₄²	—	47	2	no	—
406	C₄²	—	47	2	no	—
407	C₄²	—	94	2	no	—
408	C₄²	—	94	4	no	—
409	C₄²	—	94	4	no	—
410	C₄²	—	94	2	no	—
411	C₄²	—	94	1	no	—
412	C₄²	—	94	1	no	—
413	C₄²	—	188	1	no	—
414	C₄²	D₄×D₄₇	1	2	yes	—
415	C₄²	Q₈×D₄₇	1	2	yes	—
416	C₂³	—	47	4	no	—
417	C₂³	—	94	2	no	—
418	C₂³	—	94	2	no	—
419	C₂³	—	94	2	no	—
420	C₂³	—	94	2	no	—
421	C₂³	—	94	2	no	—
422	C₂³	—	94	2	no	—
423	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
424	D₄	—	94	8	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	47	2	no	—
433	C₂×C₄	—	47	2	no	—
434	C₂×C₄	—	47	2	no	—
435	C₂×C₄	—	47	4	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	47	2	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	94	1	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	4	no	—
445	C₂×C₄	—	94	4	no	—
446	C₂×C₄	—	94	4	no	—
447	C₂×C₄	—	94	4	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	188	8	no	—
452	C₂×C₄	—	188	8	no	—
453	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
454	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
455	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
456	C₂×C₄	C₂×#10625324	1	4	yes	—
457	C₂×C₄	C₂×#10625324	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
461	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
462	C₂×C₄	#13094070	1	1	yes	characteristic
463	C₂×C₄	#13094072	1	1	yes	characteristic
464	C₈	—	2	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	94	2	no	—
468	C₈	—	188	2	no	—
469	C₈	—	188	1	no	—
470	C₂²	—	94	4	no	—
471	C₂²	—	94	4	no	—
472	C₂²	—	94	4	no	—
473	C₂²	—	188	2	no	—
474	C₂²	—	188	2	no	—
475	C₂²	—	188	2	no	—
476	C₂²	—	188	2	no	—
477	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
478	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
479	C₂²	#15689605	1	1	yes	characteristic
480	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
481	C₂²	C₂²×#10625324	1	1	yes	characteristic
482	C₂²	#131×D₄₇	1	1	yes	characteristic
483	C₂²	#15689888	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	47	4	no	—
488	C₄	—	94	4	no	—
489	C₄	—	94	2	no	—
490	C₄	—	94	2	no	—
491	C₄	—	188	1	no	—
492	C₄	#15689145	1	4	yes	complemented
493	C₄	#15689757	1	1	yes	characteristic
494	C₄	#15689775	1	1	yes	characteristic
495	C₄	#15689788	1	1	yes	characteristic
496	C₄	#15689829	1	1	yes	characteristic
497	C₂	—	188	4	no	—
498	C₂	#20246289	1	1	yes	characteristic
499	C₂	C₂×#15689145	1	1	yes	characteristic
500	C₂	#20251955	1	1	yes	characteristic
501	C₂	#436×D₄₇	1	1	yes	characteristic
502	C₂	D₄×#10625324	1	1	yes	characteristic
503	C₂	#20252504	1	1	yes	characteristic
504	C₂	#20252519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1939	C₂
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#22650
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
3. C₂×#15689145	C₂	semidirect
5. #20244107	C₂	semidirect
6. #20243572	C₂	semidirect
7. #20243569	C₂	semidirect
8. #20243539	C₂	semidirect
9. #20243367	C₂	semidirect
10. C₄×Dic₄₇⋊C₈	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
80. Dic₄₇⋊C₈	D₄	semidirect
133. C₄⋊C₄×C₄₇	M₁₆	semidirect
149. C₄×Dic₄₇	M₁₆	semidirect
235. C₄×C₄₇	#423	semidirect
244. Dic₄₇	#436	semidirect
250. #1939	D₄₇	semidirect
296. C₄₇	#22650	semidirect
398. C₄⋊C₄	#10625324	semidirect
492. C₄	#15689145	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×#15689200	2
C₂×#15689145	2
C₄×#13093986	2
#20244107	2
#20243572	2
#20243569	2
#20243539	2
#20243367	2
C₄×Dic₄₇⋊C₈	2
C₄₇×#1939	2
#22650	47