Subgroups — #26234815

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243567	C₂	1	2	yes	maximal, complemented
6	#20243564	C₂	1	2	yes	maximal, complemented
7	#20243504	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243365	C₂	1	2	yes	maximal, complemented
9	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#336×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	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	C₈×D₁₈₈	—	2	4	no	—
19	#15689188	—	2	4	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
25	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
28	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
30	#15688970	C₄	1	2	yes	—
31	#15688970	C₄	1	2	yes	—
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	1	yes	characteristic
35	#15688877	C₂²	1	1	yes	characteristic
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	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	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₄₇	—	2	4	no	—
51	C₂×C₈×D₄₇	—	2	4	no	—
52	C₂×C₈×D₄₇	—	2	4	no	—
53	C₂×C₈×D₄₇	—	2	4	no	—
54	C₂×C₈×D₄₇	—	4	2	no	—
55	C₂×C₈×D₄₇	—	4	2	no	—
56	C₄×D₁₈₈	D₄	1	4	yes	—
57	C₄×D₁₈₈	Q₈	1	4	yes	—
58	#13093986	—	2	4	no	—
59	#13093986	C₈	1	8	yes	complemented
60	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄²×D₄₇	—	4	2	no	—
73	C₄²×D₄₇	—	4	2	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
76	Dic₄₇⋊C₈	—	2	2	no	—
77	Dic₄₇⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	—	2	4	no	—
79	(C₂×D₄₇)⋊C₈	—	2	4	no	—
80	C₄×C₄₇⋊C₈	—	2	2	no	—
81	C₄₇⋊#95	C₂×C₄	1	2	yes	—
82	C₄₇⋊#95	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	2	no	—
91	C₄⋊C₈×C₄₇	—	4	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	#95×C₄₇	C₂×C₄	1	2	yes	—
94	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
106	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
107	C₂×D₁₈₈	M₁₆	1	4	yes	—
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	4	no	—
113	C₂×C₄×D₄₇	—	2	4	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₂×C₄×D₄₇	—	4	2	no	—
117	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	complemented
118	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
119	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
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	1	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
135	(C₂×D₄₇)⋊C₄	—	2	4	no	—
136	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
137	(C₂×D₄₇)⋊C₄	C₂×C₈	1	8	yes	complemented
138	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	4	2	no	—
146	C₄×Dic₄₇	—	4	2	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	#41	1	2	yes	—
158	C₈×D₄₇	—	4	8	no	—
159	C₈×D₄₇	—	4	8	no	—
160	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	—	2	2	no	—
165	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
166	C₂²×D₄₇	C₂²×C₈	1	4	yes	—
167	C₂²×D₄₇	C₂×M₁₆	1	4	yes	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
178	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	1	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	C₂×C₄⋊C₄	1	4	yes	—
198	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
199	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
200	C₂×Dic₄₇	#131	1	2	yes	—
201	D₁₈₈	C₄⋊C₈	1	16	yes	complemented
202	C₄×D₄₇	—	2	4	no	—
203	C₄×D₄₇	—	2	4	no	—
204	C₄×D₄₇	—	2	4	no	—
205	C₄×D₄₇	—	2	4	no	—
206	C₄×D₄₇	—	4	8	no	—
207	C₄×D₄₇	—	4	8	no	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	4	2	no	—
210	C₈×C₄₇	—	4	1	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	—	4	2	no	—
213	C₄₇⋊C₈	—	4	1	no	—
214	#22696	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
217	C₂²×C₄₇	#518	1	1	yes	characteristic
218	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
219	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
221	C₂²×C₄₇	#568	1	1	yes	characteristic
222	C₂×D₄₇	—	2	4	no	—
223	C₂×D₄₇	—	2	4	no	—
224	C₂×D₄₇	—	2	4	no	—
225	C₂×D₄₇	—	2	4	no	—
226	C₂×D₄₇	—	2	4	no	—
227	C₂×D₄₇	—	2	4	no	—
228	C₂×D₄₇	C₂×C₄⋊C₈	1	8	yes	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	4	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
233	C₄×C₄₇	#546	1	1	yes	characteristic
234	C₄×C₄₇	#546	1	1	yes	characteristic
235	C₄×C₄₇	#554	1	1	yes	characteristic
236	C₄×C₄₇	#554	1	1	yes	characteristic
237	Dic₄₇	—	2	4	no	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	2	2	no	—
240	Dic₄₇	—	2	2	no	—
241	Dic₄₇	—	4	1	no	—
242	C₂×C₈×D₄	—	47	1	no	—
243	C₂×C₈×D₄	—	47	1	no	—
244	C₄²×D₄	—	47	1	no	—
245	#1939	—	47	1	no	—
246	#1939	D₄₇	1	1	yes	characteristic, complemented
247	#1850	—	47	2	no	—
248	#1850	—	47	2	no	—
249	#1831	—	47	1	no	—
250	#1797	—	47	2	no	—
251	C₄×C₄⋊C₈	—	47	1	no	—
252	C₂×#336	—	47	2	no	—
253	C₂×C₄₇	#2349	1	1	yes	characteristic
254	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
255	C₂×C₄₇	#2906	1	1	yes	characteristic
256	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
257	C₂×C₄₇	#2970	1	1	yes	characteristic
258	C₂×C₄₇	#2972	1	1	yes	characteristic
259	C₂×C₄₇	#2974	1	1	yes	characteristic
260	D₄₇	—	2	8	no	—
261	C₂³×C₈	—	47	2	no	—
262	C₂³×C₈	—	47	2	no	—
263	C₂×C₄×D₄	—	47	1	no	—
264	C₂×C₄×D₄	—	47	1	no	—
265	C₂×C₄×D₄	—	47	1	no	—
266	C₂²×C₄²	—	47	2	no	—
267	C₈×D₄	—	94	4	no	—
268	C₈×D₄	—	94	4	no	—
269	C₂×C₄⋊C₈	—	47	1	no	—
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	—	47	1	no	—
272	C₂×C₄⋊C₈	—	47	2	no	—
273	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
275	C₂×C₂²⋊C₈	—	47	2	no	—
276	C₂×C₂²⋊C₈	—	47	2	no	—
277	C₂×C₄×C₈	—	47	1	no	—
278	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
279	C₄×C₄⋊C₄	—	47	1	no	—
280	C₄×C₄⋊C₄	—	47	1	no	—
281	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	47	2	no	—
283	C₄×C₂²⋊C₄	—	47	2	no	—
284	C₄×C₂²⋊C₄	—	47	2	no	—
285	C₄³	—	47	1	no	—
286	#336	—	47	1	no	—
287	#336	—	47	2	no	—
288	#336	—	47	2	no	—
289	#336	—	47	1	no	—
290	#336	—	47	2	no	—
291	#336	C₂×D₄₇	1	2	yes	—
292	C₄₇	#22696	1	1	yes	characteristic, complemented, Sylow
293	C₂²×D₄	—	47	1	no	—
294	C₂³×C₄	—	47	2	no	—
295	C₂³×C₄	—	47	2	no	—
296	C₂³×C₄	—	47	2	no	—
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	47	2	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	94	4	no	—
301	C₂²×C₈	—	94	4	no	—
302	C₂²×C₈	—	94	4	no	—
303	C₂²×C₈	—	94	4	no	—
304	C₂²×C₈	—	188	2	no	—
305	C₂²×C₈	—	188	2	no	—
306	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
307	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄×D₄	—	47	8	no	—
310	C₄×D₄	—	47	4	no	—
311	C₄×D₄	—	47	4	no	—
312	C₄×D₄	—	94	4	no	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	47	2	no	—
317	C₂×C₂²⋊C₄	—	47	2	no	—
318	C₂×C₂²⋊C₄	—	47	2	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	2	no	—
326	C₂×C₄²	—	47	2	no	—
327	C₂×C₄²	—	188	2	no	—
328	C₂×C₄²	—	188	2	no	—
329	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
330	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	4	2	no	—
333	C₄⋊C₈	—	94	2	no	—
334	C₄⋊C₈	—	94	2	no	—
335	C₄⋊C₈	—	94	2	no	—
336	C₄⋊C₈	—	188	2	no	—
337	C₂²⋊C₈	—	94	4	no	—
338	C₂²⋊C₈	—	94	4	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	94	2	no	—
341	#95	—	47	2	no	—
342	#95	—	47	2	no	—
343	#95	C₄×D₄₇	1	2	yes	—
344	C₂⁴	—	47	2	no	—
345	C₂×D₄	—	47	4	no	—
346	C₂×D₄	—	47	4	no	—
347	C₂×D₄	—	47	4	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	1	no	—
352	C₂²×C₄	—	47	4	no	—
353	C₂²×C₄	—	47	4	no	—
354	C₂²×C₄	—	47	8	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	94	4	no	—
357	C₂²×C₄	—	94	4	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	188	2	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	—	188	2	no	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
368	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	47	2	no	—
379	C₂×C₈	—	94	1	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	2	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	188	8	no	—
388	C₂×C₈	—	188	8	no	—
389	C₂×C₈	#10625354	1	2	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	47	4	no	—
392	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
393	C₂²⋊C₄	—	47	8	no	—
394	C₂²⋊C₄	—	47	8	no	—
395	C₂²⋊C₄	—	94	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	47	4	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	94	2	no	—
401	C₄²	—	94	1	no	—
402	C₄²	—	94	1	no	—
403	C₄²	—	94	1	no	—
404	C₄²	—	94	1	no	—
405	C₄²	—	188	1	no	—
406	C₄²	—	188	2	no	—
407	C₄²	—	188	2	no	—
408	C₄²	D₄×D₄₇	1	2	yes	—
409	C₄²	Q₈×D₄₇	1	2	yes	—
410	C₂³	—	47	4	no	—
411	C₂³	—	47	4	no	—
412	C₂³	—	47	4	no	—
413	C₂³	—	94	2	no	—
414	C₂³	—	94	2	no	—
415	C₂³	—	94	2	no	—
416	C₂³	—	94	2	no	—
417	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
418	D₄	—	47	16	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	47	4	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	47	2	no	—
430	C₂×C₄	—	94	1	no	—
431	C₂×C₄	—	94	2	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	4	no	—
439	C₂×C₄	—	94	4	no	—
440	C₂×C₄	—	94	4	no	—
441	C₂×C₄	—	94	4	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	188	8	no	—
446	C₂×C₄	—	188	8	no	—
447	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
448	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
449	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
450	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
451	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
452	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
454	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
456	C₂×C₄	#13094069	1	1	yes	characteristic
457	C₂×C₄	#13094070	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₈	—	94	2	no	—
462	C₈	—	188	1	no	—
463	C₈	—	188	2	no	—
464	C₂²	—	47	8	no	—
465	C₂²	—	94	4	no	—
466	C₂²	—	94	4	no	—
467	C₂²	—	94	4	no	—
468	C₂²	—	94	4	no	—
469	C₂²	—	94	4	no	—
470	C₂²	—	94	4	no	—
471	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
472	C₂²	C₄×#10625354	1	1	yes	characteristic
473	C₂²	#15689595	1	1	yes	characteristic
474	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
475	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
476	C₂²	#131×D₄₇	1	1	yes	characteristic
477	C₂²	#15689888	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	4	no	—
480	C₄	—	4	2	no	—
481	C₄	—	94	2	no	—
482	C₄	—	94	4	no	—
483	C₄	—	94	2	no	—
484	C₄	—	94	2	no	—
485	C₄	—	188	1	no	—
486	C₄	C₄⋊C₈×D₄₇	1	4	yes	—
487	C₄	#15689764	1	1	yes	characteristic
488	C₄	#15689770	1	1	yes	characteristic
489	C₄	#15689829	1	1	yes	characteristic
490	C₄	#15689834	1	1	yes	characteristic
491	C₂	—	94	8	no	—
492	C₂	#20246297	1	1	yes	characteristic
493	C₂	C₂×C₄⋊C₈×D₄₇	1	1	yes	characteristic
494	C₂	#20251955	1	1	yes	characteristic
495	C₂	C₈×#10625354	1	1	yes	characteristic
496	C₂	#20252401	1	1	yes	characteristic
497	C₂	#20252409	1	1	yes	characteristic
498	C₂	#20252420	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1939	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#22696
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
4. #20244107	C₂	semidirect
5. #20243567	C₂	semidirect
6. #20243564	C₂	semidirect
7. #20243504	C₂	semidirect
8. #20243365	C₂	semidirect
9. C₄×Dic₄₇⋊C₈	C₂	semidirect
10. #336×D₄₇	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
59. #13093986	C₈	semidirect
117. C₂×C₄×D₄₇	C₂×C₈	semidirect
130. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
137. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
148. C₄×Dic₄₇	C₂×C₈	semidirect
201. D₁₈₈	C₄⋊C₈	semidirect
246. #1939	D₄₇	semidirect
292. C₄₇	#22696	semidirect
392. C₄⋊C₄	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₈₈	2
C₂×#15689188	2
C₄×#13093986	2
#20244107	2
#20243567	2
#20243564	2
#20243504	2
#20243365	2
C₄×Dic₄₇⋊C₈	2
#336×D₄₇	2
C₄₇×#1939	2
#22696	47