Subgroups — #26215263

Order 12032.

970 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689199	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689192	C₂	1	1	yes	maximal, characteristic
3	#20245831	C₂	1	1	yes	maximal, characteristic
4	#20243261	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243254	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243244	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243170	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243169	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243169	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243163	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243153	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243150	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₂×#13093981	C₂²	1	1	yes	characteristic
20	#15689199	C₄	1	8	yes	complemented
21	#15689192	C₄	1	8	yes	complemented
22	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#13093935	C₂²	1	1	yes	characteristic
29	C₂×#13093935	C₂²	1	1	yes	characteristic
30	C₂×#13093934	C₂²	1	1	yes	characteristic
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	#15689014	C₄	1	2	yes	—
37	#15689007	C₄	1	2	yes	—
38	#15689002	C₄	1	2	yes	—
39	#15688996	C₄	1	2	yes	—
40	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
43	#15688969	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
51	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
53	C₄₇×#336	C₂²	1	1	yes	characteristic
54	C₄₇×#336	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
59	C₂×#10625324	—	4	1	no	—
60	C₂×#10625324	—	4	1	no	—
61	C₂×#10625324	C₂×C₄	1	4	yes	complemented
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₄₇	—	4	1	no	—
67	C₂×C₈×D₄₇	—	4	1	no	—
68	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	complemented
69	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
70	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
71	#13093981	—	4	1	no	—
72	#13093981	—	4	1	no	—
73	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
84	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
85	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
86	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
87	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
88	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
89	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
90	#13093935	—	4	1	no	—
91	#13093935	—	4	1	no	—
92	#13093934	—	4	1	no	—
93	#13093934	—	4	1	no	—
94	#13093934	C₂×C₄	1	4	yes	complemented
95	C₈×Dic₄₇	—	4	1	no	—
96	C₈×Dic₄₇	—	4	1	no	—
97	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
98	C₄₇⋊#95	C₂×C₄	1	2	yes	—
99	C₄₇⋊#95	C₂×C₄	1	2	yes	—
100	C₄₇⋊#95	C₂×C₄	1	2	yes	—
101	C₄₇⋊#95	C₂×C₄	1	2	yes	—
102	C₄₇⋊#95	C₂×C₄	1	2	yes	—
103	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
104	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₄₇	—	4	1	no	—
106	C₂×M₁₆×C₄₇	—	4	1	no	—
107	C₂×M₁₆×C₄₇	—	4	1	no	—
108	C₂×M₁₆×C₄₇	—	4	1	no	—
109	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
110	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
111	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	—	4	1	no	—
116	C₂×C₄²×C₄₇	—	4	1	no	—
117	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	—	4	2	no	—
128	C₂²×C₄×C₄₇	—	4	2	no	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₇	—	4	2	no	—
136	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
137	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
139	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	2	1	no	—
144	C₂×C₄×D₄₇	—	2	1	no	—
145	C₂×C₄×D₄₇	—	2	1	no	—
146	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
147	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
148	M₁₆×C₄₇	—	4	4	no	—
149	M₁₆×C₄₇	—	4	4	no	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₄²×C₄₇	—	2	1	no	—
164	C₄²×C₄₇	—	2	1	no	—
165	C₄²×C₄₇	—	2	1	no	—
166	C₄²×C₄₇	—	4	2	no	—
167	C₂²⋊Dic₄₇	—	4	2	no	—
168	C₂²⋊Dic₄₇	C₄²	1	4	yes	—
169	(C₂×D₄₇)⋊C₄	—	4	2	no	—
170	(C₂×D₄₇)⋊C₄	—	4	2	no	—
171	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
172	Dic₄₇⋊C₄	—	4	2	no	—
173	Dic₄₇⋊C₄	—	4	2	no	—
174	Dic₄₇⋊C₄	C₄²	1	4	yes	—
175	C₄×Dic₄₇	—	2	1	no	—
176	C₄×Dic₄₇	—	2	1	no	—
177	C₄×Dic₄₇	—	2	1	no	—
178	C₄×Dic₄₇	—	2	1	no	—
179	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
180	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	1	no	—
184	C₂×C₄₇⋊C₈	—	2	1	no	—
185	C₂×C₄₇⋊C₈	—	2	1	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
190	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
193	#10625324	—	4	4	no	—
194	C₈×D₄₇	—	4	4	no	—
195	C₂³×C₄₇	—	2	1	no	—
196	C₂³×C₄₇	—	2	1	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
200	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
201	C₂²×D₄₇	—	2	1	no	—
202	C₂²×D₄₇	—	2	1	no	—
203	C₂²×D₄₇	—	2	2	no	—
204	C₂²×D₄₇	—	2	2	no	—
205	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	4	8	no	—
219	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
220	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂²⋊D₄₇	—	4	4	no	—
227	C₂×Dic₄₇	—	2	1	no	—
228	C₂×Dic₄₇	—	2	1	no	—
229	C₂×Dic₄₇	—	2	2	no	—
230	C₂×Dic₄₇	—	2	2	no	—
231	C₂×Dic₄₇	—	2	2	no	—
232	C₂×Dic₄₇	—	2	2	no	—
233	C₂×Dic₄₇	—	2	2	no	—
234	C₂×Dic₄₇	—	2	2	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	2	no	—
237	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
238	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
239	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
240	C₄×D₄₇	—	2	2	no	—
241	C₄×D₄₇	—	2	2	no	—
242	C₄×D₄₇	—	2	2	no	—
243	C₄×D₄₇	—	2	2	no	—
244	C₈×C₄₇	—	2	2	no	—
245	C₈×C₄₇	—	2	2	no	—
246	C₈×C₄₇	—	2	2	no	—
247	C₈×C₄₇	—	2	2	no	—
248	C₄₇⋊C₈	—	2	2	no	—
249	C₄₇⋊C₈	—	2	2	no	—
250	C₄₇⋊C₈	—	2	2	no	—
251	C₄₇⋊C₈	—	2	2	no	—
252	#20564	—	47	1	no	maximal, Sylow
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	2	no	—
255	C₂²×C₄₇	—	2	2	no	—
256	C₂²×C₄₇	—	4	2	no	—
257	C₂²×C₄₇	—	4	2	no	—
258	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
259	C₂²×C₄₇	#518	1	1	yes	characteristic
260	C₂²×C₄₇	#520	1	1	yes	characteristic
261	C₂²×C₄₇	#568	1	2	yes	—
262	C₂²×C₄₇	#568	1	2	yes	—
263	C₂×D₄₇	—	2	2	no	—
264	C₂×D₄₇	—	2	2	no	—
265	C₂×D₄₇	—	2	2	no	—
266	C₂×D₄₇	—	4	2	no	—
267	C₂×D₄₇	—	4	2	no	—
268	C₄×C₄₇	—	2	2	no	—
269	C₄×C₄₇	—	4	2	no	—
270	C₄×C₄₇	—	4	2	no	—
271	C₄×C₄₇	#518	1	1	yes	characteristic
272	C₄×C₄₇	#518	1	1	yes	characteristic
273	C₄×C₄₇	#520	1	1	yes	characteristic
274	C₄×C₄₇	#520	1	1	yes	characteristic
275	Dic₄₇	—	2	2	no	—
276	Dic₄₇	—	2	2	no	—
277	Dic₄₇	—	2	2	no	—
278	Dic₄₇	—	4	2	no	—
279	Dic₄₇	—	4	2	no	—
280	C₂×#436	—	47	1	no	—
281	C₂×#435	—	47	1	no	—
282	#2290	—	47	1	no	—
283	#1771	—	47	1	no	—
284	#1770	—	47	1	no	—
285	#1768	—	47	1	no	—
286	#1753	—	47	1	no	—
287	#1753	—	47	1	no	—
288	#1753	—	47	1	no	—
289	#1752	—	47	1	no	—
290	#1750	—	47	1	no	—
291	#1749	—	47	1	no	—
292	#1746	—	47	1	no	—
293	#1729	—	47	1	no	—
294	#1728	D₄₇	1	1	yes	characteristic, complemented
295	C₂×C₄₇	—	4	2	no	—
296	C₂×C₄₇	#2275	1	1	yes	characteristic
297	C₂×C₄₇	#2873	1	1	yes	characteristic
298	C₂×C₄₇	#2875	1	1	yes	characteristic
299	C₂×C₄₇	#2978	1	2	yes	—
300	C₂×C₄₇	#2995	1	2	yes	—
301	D₄₇	—	4	2	no	—
302	C₂²×M₁₆	—	47	1	no	—
303	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
304	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
305	C₂³×C₈	—	47	1	no	—
306	C₂×C₄×D₄	—	47	1	no	—
307	C₂×#117	—	47	1	no	—
308	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
309	#436	—	47	8	no	—
310	#435	—	47	8	no	—
311	C₂×C₄⋊C₈	—	47	1	no	—
312	C₂×C₄⋊C₈	—	47	1	no	—
313	C₂×C₂²⋊C₈	—	47	1	no	—
314	C₂×C₂²⋊C₈	—	47	1	no	—
315	C₂×C₂²⋊C₈	—	47	1	no	—
316	C₂×C₂²⋊C₈	—	47	1	no	—
317	C₂×#97	—	47	1	no	—
318	C₂×#97	—	47	1	no	—
319	C₂×#97	—	47	1	no	—
320	C₂×#97	—	47	1	no	—
321	C₂×#97	—	47	1	no	—
322	C₂×C₄×C₈	—	47	1	no	—
323	C₂×C₄×C₈	—	47	1	no	—
324	C₂×C₄×C₈	—	47	1	no	—
325	#388	—	47	2	no	—
326	#387	—	47	2	no	—
327	#386	—	47	2	no	—
328	#385	—	47	2	no	—
329	C₄×C₄⋊C₄	—	47	1	no	—
330	C₄×C₂²⋊C₄	—	47	1	no	—
331	C₄×C₂²⋊C₄	—	47	1	no	—
332	#376	—	47	1	no	—
333	#336	—	47	1	no	—
334	#336	—	47	1	no	—
335	#336	—	47	1	no	—
336	#336	—	47	1	no	—
337	#336	—	47	1	no	—
338	#336	—	47	1	no	—
339	#336	C₂×D₄₇	1	1	yes	characteristic
340	#336	C₂×D₄₇	1	1	yes	characteristic
341	#336	C₂×D₄₇	1	1	yes	characteristic
342	#336	C₂×D₄₇	1	1	yes	characteristic
343	C₄₇	#20564	1	1	yes	characteristic, complemented, Sylow
344	C₂²×D₄	—	47	1	no	—
345	C₂³×C₄	—	47	1	no	—
346	C₂³×C₄	C₄×D₄₇	1	2	yes	—
347	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
348	C₂×M₁₆	—	4	1	no	—
349	C₂×M₁₆	—	4	1	no	—
350	C₂×M₁₆	—	4	1	no	—
351	C₂×M₁₆	—	4	1	no	—
352	C₂×M₁₆	—	47	4	no	—
353	C₂×M₁₆	—	188	1	no	—
354	C₂×M₁₆	—	188	1	no	—
355	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
356	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	47	1	no	—
359	C₂²×C₈	—	47	1	no	—
360	C₂²×C₈	—	47	1	no	—
361	C₂²×C₈	—	47	4	no	—
362	C₂²×C₈	—	188	1	no	—
363	C₂²×C₈	—	188	1	no	—
364	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
366	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
367	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
368	C₄×D₄	—	47	4	no	—
369	C₄×D₄	—	47	4	no	—
370	#117	—	188	1	no	—
371	#117	—	188	1	no	—
372	C₂×C₄⋊C₄	—	47	1	no	—
373	C₂×C₄⋊C₄	—	47	2	no	—
374	C₂×C₄⋊C₄	—	47	2	no	—
375	C₂×C₂²⋊C₄	—	47	1	no	—
376	C₂×C₂²⋊C₄	—	47	1	no	—
377	C₂×C₂²⋊C₄	—	47	2	no	—
378	C₂×C₂²⋊C₄	—	47	2	no	—
379	C₂×C₂²⋊C₄	—	47	2	no	—
380	C₂×C₄²	—	4	1	no	—
381	C₂×C₄²	—	4	1	no	—
382	C₂×C₄²	—	47	1	no	—
383	C₂×C₄²	—	47	1	no	—
384	C₂×C₄²	—	47	1	no	—
385	C₂×C₄²	C₄×D₄₇	1	2	yes	—
386	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
387	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
388	C₄⋊C₈	—	47	4	no	—
389	C₄⋊C₈	—	47	4	no	—
390	C₂²⋊C₈	—	47	4	no	—
391	C₂²⋊C₈	—	47	4	no	—
392	C₂²⋊C₈	—	47	4	no	—
393	C₂²⋊C₈	—	47	4	no	—
394	#97	—	47	4	no	—
395	#97	—	188	1	no	—
396	#97	—	188	1	no	—
397	#97	—	188	1	no	—
398	#97	—	188	1	no	—
399	C₄×C₈	—	47	4	no	—
400	C₄×C₈	—	188	1	no	—
401	C₄×C₈	—	188	1	no	—
402	#95	—	47	2	no	—
403	#95	—	47	2	no	—
404	#95	—	47	2	no	—
405	#95	—	47	2	no	—
406	#95	—	47	2	no	—
407	C₂⁴	—	47	1	no	—
408	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
409	C₂×D₄	—	47	4	no	—
410	C₂×D₄	—	188	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	47	1	no	—
419	C₂²×C₄	—	47	1	no	—
420	C₂²×C₄	—	47	1	no	—
421	C₂²×C₄	—	47	2	no	—
422	C₂²×C₄	—	47	2	no	—
423	C₂²×C₄	—	47	2	no	—
424	C₂²×C₄	—	47	2	no	—
425	C₂²×C₄	—	94	1	no	—
426	C₂²×C₄	—	94	1	no	—
427	C₂²×C₄	—	94	1	no	—
428	C₂²×C₄	—	94	1	no	—
429	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
430	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
431	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
433	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
434	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
435	M₁₆	—	4	4	no	—
436	M₁₆	—	4	4	no	—
437	M₁₆	—	188	4	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	47	2	no	—
447	C₂×C₈	—	47	2	no	—
448	C₂×C₈	—	47	2	no	—
449	C₂×C₈	—	47	2	no	—
450	C₂×C₈	—	94	1	no	—
451	C₂×C₈	—	94	1	no	—
452	C₂×C₈	—	94	1	no	—
453	C₂×C₈	—	94	1	no	—
454	C₂×C₈	—	94	1	no	—
455	C₂×C₈	—	94	1	no	—
456	C₂×C₈	—	94	1	no	—
457	C₂×C₈	—	94	1	no	—
458	C₂×C₈	—	188	4	no	—
459	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
460	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
461	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
462	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
463	C₄⋊C₄	—	47	4	no	—
464	C₄⋊C₄	—	188	2	no	—
465	C₄⋊C₄	—	188	2	no	—
466	C₂²⋊C₄	—	47	4	no	—
467	C₂²⋊C₄	—	47	4	no	—
468	C₂²⋊C₄	—	188	2	no	—
469	C₂²⋊C₄	—	188	2	no	—
470	C₂²⋊C₄	—	188	2	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	4	2	no	—
476	C₄²	—	47	2	no	—
477	C₄²	—	47	2	no	—
478	C₄²	—	94	1	no	—
479	C₄²	—	94	1	no	—
480	C₄²	—	94	1	no	—
481	C₄²	—	94	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	47	2	no	—
487	C₂³	—	94	1	no	—
488	C₂³	—	94	1	no	—
489	C₂³	—	94	2	no	—
490	C₂³	—	94	2	no	—
491	C₂³	C₄²×D₄₇	1	2	yes	—
492	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
493	D₄	—	188	4	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	47	2	no	—
508	C₂×C₄	—	47	2	no	—
509	C₂×C₄	—	47	2	no	—
510	C₂×C₄	—	94	1	no	—
511	C₂×C₄	—	94	1	no	—
512	C₂×C₄	—	94	2	no	—
513	C₂×C₄	—	94	2	no	—
514	C₂×C₄	—	94	2	no	—
515	C₂×C₄	—	94	2	no	—
516	C₂×C₄	—	94	2	no	—
517	C₂×C₄	—	94	2	no	—
518	C₂×C₄	—	94	2	no	—
519	C₂×C₄	—	94	2	no	—
520	C₂×C₄	—	94	2	no	—
521	C₂×C₄	—	94	2	no	—
522	C₂×C₄	—	94	2	no	—
523	C₂×C₄	—	94	2	no	—
524	C₂×C₄	C₄²×D₄₇	1	2	yes	—
525	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
527	C₂×C₄	#13094069	1	1	yes	characteristic
528	C₂×C₄	#13094069	1	1	yes	characteristic
529	C₂×C₄	#13094069	1	1	yes	characteristic
530	C₂×C₄	#13094072	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	94	2	no	—
536	C₈	—	94	2	no	—
537	C₈	—	94	2	no	—
538	C₈	—	94	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	94	2	no	—
545	C₂²	—	94	2	no	—
546	C₂²	—	94	2	no	—
547	C₂²	—	188	2	no	—
548	C₂²	—	188	2	no	—
549	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
550	C₂²	#15689596	1	1	yes	characteristic
551	C₂²	#15689604	1	1	yes	characteristic
552	C₂²	#15689889	1	2	yes	—
553	C₂²	#15689889	1	2	yes	—
554	C₄	—	2	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	94	2	no	—
558	C₄	—	94	2	no	—
559	C₄	—	94	2	no	—
560	C₄	—	188	2	no	—
561	C₄	—	188	2	no	—
562	C₄	#15689596	1	1	yes	characteristic
563	C₄	#15689596	1	1	yes	characteristic
564	C₄	#15689604	1	1	yes	characteristic
565	C₄	#15689604	1	1	yes	characteristic
566	C₂	—	4	2	no	—
567	C₂	—	188	2	no	—
568	C₂	#20245746	1	1	yes	characteristic
569	C₂	#20251805	1	1	yes	characteristic
570	C₂	#20251817	1	1	yes	characteristic
571	C₂	#20252448	1	2	yes	—
572	C₂	#20252555	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1728	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1728	D₄₇
hypocenter	C₄₇	#20564
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1728

Complements

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

N	H ≅ G/N	type
4. #20243261	C₂	semidirect
5. #20243254	C₂	semidirect
6. #20243244	C₂	semidirect
7. #20243170	C₂	semidirect
8. #20243169	C₂	semidirect
9. #20243169	C₂	semidirect
10. #20243163	C₂	semidirect
11. #20243153	C₂	semidirect
12. #20243150	C₂	semidirect
13. #20243138	C₂	semidirect
14. #20243083	C₂	semidirect
15. C₄₇×#1728	C₂	semidirect
20. #15689199	C₄	semidirect
21. #15689192	C₄	semidirect
61. C₂×#10625324	C₂×C₄	semidirect
68. C₂×C₈×D₄₇	C₂×C₄	semidirect
84. Dic₄₇⋊C₈	C₂×C₄	semidirect
85. Dic₄₇⋊C₈	C₂×C₄	semidirect
88. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
89. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
94. #13093934	C₂×C₄	semidirect
97. C₈×Dic₄₇	C₂×C₄	semidirect
294. #1728	D₄₇	semidirect
343. C₄₇	#20564	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689199	2
C₂×#15689192	2
#20245831	2
#20243261	2
#20243254	2
#20243244	2
#20243170	2
#20243169	2
#20243163	2
#20243153	2
#20243150	2
#20243138	2
#20243083	2
C₄₇×#1728	2
#20564	47