Subgroups — #26234812

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂²⋊D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂²⋊D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	#20244105	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244103	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243568	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243567	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243564	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243366	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243365	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15688877	C₂	1	1	yes	maximal, characteristic, complemented
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
20	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	1	yes	characteristic
21	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	1	yes	characteristic
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₄₇	—	2	4	no	—
25	(C₂²⋊D₄₇)⋊C₈	—	2	4	no	—
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
38	#15688974	C₄	1	1	yes	characteristic
39	#15688974	C₄	1	1	yes	characteristic
40	C₂²⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
42	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
43	#15688970	C₄	1	1	yes	characteristic
44	#15688970	C₄	1	1	yes	characteristic
45	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	—	2	2	no	—
68	C₂²×C₄₇⋊C₈	—	2	2	no	—
69	C₂²×C₄₇⋊C₈	—	4	1	no	—
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	—	2	2	no	—
76	C₂×C₈×D₄₇	—	2	2	no	—
77	C₂×C₈×D₄₇	—	2	2	no	—
78	C₂×C₈×D₄₇	—	4	1	no	—
79	C₂×C₈×D₄₇	—	4	1	no	—
80	C₄×C₂²⋊D₄₇	D₄	1	4	yes	—
81	C₄×C₂²⋊D₄₇	Q₈	1	4	yes	—
82	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
83	(C₂²⋊D₄₇)⋊C₄	C₈	1	8	yes	complemented
84	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	—	4	1	no	—
92	C₂×C₄×Dic₄₇	—	4	1	no	—
93	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
104	C₄²×D₄₇	—	4	1	no	—
105	C₄²×D₄₇	—	4	1	no	—
106	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
107	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
108	Dic₄₇⋊C₈	—	2	2	no	—
109	Dic₄₇⋊C₈	—	2	2	no	—
110	Dic₄₇⋊C₈	—	4	1	no	—
111	Dic₄₇⋊C₈	—	4	1	no	—
112	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
113	(C₂×D₄₇)⋊C₈	—	2	2	no	—
114	(C₂×D₄₇)⋊C₈	—	2	2	no	—
115	C₈×Dic₄₇	—	2	2	no	—
116	C₈×Dic₄₇	—	2	2	no	—
117	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
118	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
119	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
120	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
121	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	—	2	2	no	—
123	C₂²×C₈×C₄₇	—	2	2	no	—
124	C₂²×C₈×C₄₇	—	4	1	no	—
125	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₄₇	—	2	2	no	—
134	C₄⋊C₈×C₄₇	—	4	1	no	—
135	C₂²⋊C₈×C₄₇	—	2	2	no	—
136	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
137	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	—	2	1	no	—
141	C₂²×C₄×C₄₇	—	2	1	no	—
142	C₂²×C₄×C₄₇	—	2	1	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
153	C₂×C₂²⋊D₄₇	C₂×C₈	1	4	yes	—
154	C₂×C₂²⋊D₄₇	M₁₆	1	4	yes	—
155	C₂²×Dic₄₇	—	2	2	no	—
156	C₂²×Dic₄₇	—	2	2	no	—
157	C₂²×Dic₄₇	—	4	1	no	—
158	C₂²×Dic₄₇	—	4	1	no	—
159	C₂²×Dic₄₇	—	4	1	no	—
160	C₂²×Dic₄₇	C₂×C₈	1	4	yes	complemented
161	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₄₇	—	2	1	no	—
169	C₂×C₄×D₄₇	—	2	1	no	—
170	C₂×C₄×D₄₇	—	2	1	no	—
171	C₂×C₄×D₄₇	—	2	1	no	—
172	C₂×C₄×D₄₇	—	2	2	no	—
173	C₂×C₄×D₄₇	—	2	2	no	—
174	C₂×C₄×D₄₇	—	4	1	no	—
175	C₂×C₄×D₄₇	—	4	1	no	—
176	C₂×C₄×D₄₇	—	4	1	no	—
177	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	complemented
178	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
179	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
180	C₂×C₈×C₄₇	—	2	1	no	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	1	no	—
183	C₂×C₈×C₄₇	—	2	1	no	—
184	C₂×C₈×C₄₇	—	2	1	no	—
185	C₂×C₈×C₄₇	—	2	1	no	—
186	C₂×C₈×C₄₇	—	2	1	no	—
187	C₂×C₈×C₄₇	—	2	1	no	—
188	C₂×C₈×C₄₇	—	2	1	no	—
189	C₂×C₈×C₄₇	—	2	1	no	—
190	C₂×C₈×C₄₇	—	2	1	no	—
191	C₂×C₈×C₄₇	—	4	4	no	—
192	C₂×C₈×C₄₇	#41	1	2	yes	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
195	C₄²×C₄₇	—	2	1	no	—
196	C₄²×C₄₇	—	2	1	no	—
197	C₄²×C₄₇	—	2	1	no	—
198	C₄²×C₄₇	—	2	1	no	—
199	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
200	(C₂×D₄₇)⋊C₄	—	2	2	no	—
201	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
202	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
203	Dic₄₇⋊C₄	—	2	2	no	—
204	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
205	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
206	C₄×Dic₄₇	—	2	1	no	—
207	C₄×Dic₄₇	—	2	1	no	—
208	C₄×Dic₄₇	—	2	1	no	—
209	C₄×Dic₄₇	—	2	1	no	—
210	C₄×Dic₄₇	—	2	2	no	—
211	C₄×Dic₄₇	—	2	2	no	—
212	C₄×Dic₄₇	—	4	1	no	—
213	C₄×Dic₄₇	—	4	1	no	—
214	C₄×Dic₄₇	—	4	1	no	—
215	C₄×Dic₄₇	—	4	1	no	—
216	C₄×Dic₄₇	—	4	1	no	—
217	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
218	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
219	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
220	C₂×C₄₇⋊C₈	—	2	1	no	—
221	C₂×C₄₇⋊C₈	—	2	1	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	2	1	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	1	no	—
227	C₂×C₄₇⋊C₈	—	2	1	no	—
228	C₂×C₄₇⋊C₈	—	2	1	no	—
229	C₂×C₄₇⋊C₈	—	2	1	no	—
230	C₂×C₄₇⋊C₈	—	2	1	no	—
231	C₂×C₄₇⋊C₈	—	4	4	no	—
232	C₂×C₄₇⋊C₈	#41	1	2	yes	—
233	C₈×D₄₇	—	4	4	no	—
234	C₈×D₄₇	—	4	4	no	—
235	C₂³×C₄₇	—	2	1	no	—
236	C₂³×C₄₇	—	2	1	no	—
237	C₂³×C₄₇	—	2	1	no	—
238	C₂³×C₄₇	—	2	1	no	—
239	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
240	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
241	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
242	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
243	C₂²×D₄₇	—	2	1	no	—
244	C₂²×D₄₇	—	2	1	no	—
245	C₂²×D₄₇	—	2	1	no	—
246	C₂²×D₄₇	—	2	1	no	—
247	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
248	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
249	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	2	1	no	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	1	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	2	no	—
260	C₂×C₄×C₄₇	—	2	1	no	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	1	no	—
264	C₂×C₄×C₄₇	—	2	1	no	—
265	C₂×C₄×C₄₇	—	2	1	no	—
266	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
268	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
269	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂²⋊D₄₇	C₄⋊C₈	1	16	yes	complemented
276	C₂×Dic₄₇	—	2	1	no	—
277	C₂×Dic₄₇	—	2	1	no	—
278	C₂×Dic₄₇	—	2	1	no	—
279	C₂×Dic₄₇	—	2	1	no	—
280	C₂×Dic₄₇	—	2	1	no	—
281	C₂×Dic₄₇	—	2	1	no	—
282	C₂×Dic₄₇	—	2	1	no	—
283	C₂×Dic₄₇	—	2	1	no	—
284	C₂×Dic₄₇	—	2	1	no	—
285	C₂×Dic₄₇	—	2	1	no	—
286	C₂×Dic₄₇	—	2	1	no	—
287	C₂×Dic₄₇	—	2	1	no	—
288	C₂×Dic₄₇	—	2	1	no	—
289	C₂×Dic₄₇	—	4	4	no	—
290	C₂×Dic₄₇	—	4	4	no	—
291	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
292	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
293	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
294	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
295	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
296	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
297	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
298	C₂×Dic₄₇	#131	1	2	yes	—
299	C₄×D₄₇	—	2	2	no	—
300	C₄×D₄₇	—	2	2	no	—
301	C₄×D₄₇	—	2	2	no	—
302	C₄×D₄₇	—	2	2	no	—
303	C₄×D₄₇	—	4	4	no	—
304	C₄×D₄₇	—	4	4	no	—
305	C₈×C₄₇	—	2	2	no	—
306	C₈×C₄₇	—	4	1	no	—
307	C₈×C₄₇	—	4	1	no	—
308	C₈×C₄₇	—	4	1	no	—
309	C₄₇⋊C₈	—	2	2	no	—
310	C₄₇⋊C₈	—	4	1	no	—
311	C₄₇⋊C₈	—	4	1	no	—
312	C₄₇⋊C₈	—	4	1	no	—
313	#22696	—	47	1	no	maximal, Sylow
314	C₂²×C₄₇	—	2	2	no	—
315	C₂²×C₄₇	—	2	2	no	—
316	C₂²×C₄₇	—	2	2	no	—
317	C₂²×C₄₇	—	2	2	no	—
318	C₂²×C₄₇	—	2	2	no	—
319	C₂²×C₄₇	—	2	2	no	—
320	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
321	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
322	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
323	C₂²×C₄₇	#518	1	1	yes	characteristic
324	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
325	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
326	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
327	C₂²×C₄₇	#568	1	1	yes	characteristic
328	C₂×D₄₇	—	2	2	no	—
329	C₂×D₄₇	—	2	2	no	—
330	C₂×D₄₇	—	2	2	no	—
331	C₂×D₄₇	—	2	2	no	—
332	C₂×D₄₇	—	2	2	no	—
333	C₂×D₄₇	—	2	2	no	—
334	C₂×D₄₇	C₂×C₄⋊C₈	1	4	yes	—
335	C₄×C₄₇	—	2	2	no	—
336	C₄×C₄₇	—	2	2	no	—
337	C₄×C₄₇	—	2	2	no	—
338	C₄×C₄₇	—	4	1	no	—
339	C₄×C₄₇	—	4	1	no	—
340	C₄×C₄₇	#546	1	1	yes	characteristic
341	C₄×C₄₇	#546	1	1	yes	characteristic
342	C₄×C₄₇	#554	1	1	yes	characteristic
343	C₄×C₄₇	#554	1	1	yes	characteristic
344	Dic₄₇	—	2	2	no	—
345	Dic₄₇	—	2	2	no	—
346	Dic₄₇	—	2	2	no	—
347	Dic₄₇	—	2	2	no	—
348	Dic₄₇	—	2	2	no	—
349	Dic₄₇	—	4	1	no	—
350	Dic₄₇	C₂×C₄⋊C₈	1	4	yes	—
351	C₂×C₈×D₄	—	47	1	no	—
352	C₂×C₈×D₄	—	47	1	no	—
353	C₄²×D₄	—	47	1	no	—
354	#1939	—	47	1	no	—
355	#1939	—	47	1	no	—
356	#1850	—	47	1	no	—
357	#1850	—	47	1	no	—
358	#1850	—	47	1	no	—
359	#1850	D₄₇	1	1	yes	characteristic, complemented
360	#1831	—	47	1	no	—
361	#1797	—	47	1	no	—
362	#1797	—	47	1	no	—
363	C₄×C₄⋊C₈	—	47	1	no	—
364	C₂×#336	—	47	1	no	—
365	C₂×#336	—	47	1	no	—
366	C₂×C₄₇	—	2	4	no	—
367	C₂×C₄₇	#2349	1	1	yes	characteristic
368	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
369	C₂×C₄₇	#2906	1	1	yes	characteristic
370	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
371	C₂×C₄₇	#2970	1	1	yes	characteristic
372	C₂×C₄₇	#2972	1	1	yes	characteristic
373	C₂×C₄₇	#2974	1	1	yes	characteristic
374	D₄₇	—	2	4	no	—
375	C₂³×C₈	—	47	1	no	—
376	C₂³×C₈	—	47	1	no	—
377	C₂³×C₈	—	47	1	no	—
378	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
379	C₂×C₄×D₄	—	47	1	no	—
380	C₂×C₄×D₄	—	47	1	no	—
381	C₂×C₄×D₄	—	47	1	no	—
382	C₂²×C₄²	—	47	1	no	—
383	C₂²×C₄²	—	47	1	no	—
384	C₈×D₄	—	94	4	no	—
385	C₈×D₄	—	94	4	no	—
386	C₂×C₄⋊C₈	—	47	1	no	—
387	C₂×C₄⋊C₈	—	47	1	no	—
388	C₂×C₄⋊C₈	—	47	1	no	—
389	C₂×C₄⋊C₈	—	47	1	no	—
390	C₂×C₄⋊C₈	—	47	1	no	—
391	C₂×C₄⋊C₈	—	47	1	no	—
392	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
393	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	—	47	1	no	—
395	C₂×C₂²⋊C₈	—	47	1	no	—
396	C₂×C₂²⋊C₈	—	47	1	no	—
397	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
398	C₂×C₄×C₈	—	47	1	no	—
399	C₂×C₄×C₈	—	47	1	no	—
400	C₄×C₄⋊C₄	—	47	1	no	—
401	C₄×C₄⋊C₄	—	47	1	no	—
402	C₄×C₄⋊C₄	—	47	1	no	—
403	C₄×C₂²⋊C₄	—	47	1	no	—
404	C₄×C₂²⋊C₄	—	47	1	no	—
405	C₄×C₂²⋊C₄	—	47	1	no	—
406	C₄×C₂²⋊C₄	—	47	1	no	—
407	C₄×C₂²⋊C₄	—	47	1	no	—
408	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
409	C₄³	—	47	1	no	—
410	#336	—	47	1	no	—
411	#336	—	47	1	no	—
412	#336	—	47	1	no	—
413	#336	—	47	1	no	—
414	#336	—	47	1	no	—
415	#336	—	47	1	no	—
416	#336	—	47	1	no	—
417	#336	—	47	1	no	—
418	#336	C₂×D₄₇	1	1	yes	characteristic
419	#336	C₂×D₄₇	1	1	yes	characteristic
420	C₄₇	#22696	1	1	yes	characteristic, complemented, Sylow
421	C₂²×D₄	—	47	1	no	—
422	C₂³×C₄	—	47	1	no	—
423	C₂³×C₄	—	47	1	no	—
424	C₂³×C₄	—	47	1	no	—
425	C₂³×C₄	—	47	1	no	—
426	C₂³×C₄	—	47	1	no	—
427	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
428	C₂²×C₈	—	2	2	no	—
429	C₂²×C₈	—	2	2	no	—
430	C₂²×C₈	—	4	1	no	—
431	C₂²×C₈	—	47	1	no	—
432	C₂²×C₈	—	47	1	no	—
433	C₂²×C₈	—	47	1	no	—
434	C₂²×C₈	—	47	1	no	—
435	C₂²×C₈	—	94	2	no	—
436	C₂²×C₈	—	94	2	no	—
437	C₂²×C₈	—	94	2	no	—
438	C₂²×C₈	—	94	2	no	—
439	C₂²×C₈	—	94	2	no	—
440	C₂²×C₈	—	94	2	no	—
441	C₂²×C₈	—	188	1	no	—
442	C₂²×C₈	—	188	1	no	—
443	C₂²×C₈	—	188	1	no	—
444	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
445	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
446	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
447	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
448	C₄×D₄	—	47	4	no	—
449	C₄×D₄	—	47	4	no	—
450	C₄×D₄	—	47	8	no	—
451	C₄×D₄	—	94	4	no	—
452	C₂×C₄⋊C₄	—	47	1	no	—
453	C₂×C₄⋊C₄	—	47	1	no	—
454	C₂×C₄⋊C₄	—	47	1	no	—
455	C₂×C₂²⋊C₄	—	47	1	no	—
456	C₂×C₂²⋊C₄	—	47	1	no	—
457	C₂×C₂²⋊C₄	—	47	1	no	—
458	C₂×C₂²⋊C₄	—	47	1	no	—
459	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
461	C₂×C₄²	—	47	1	no	—
462	C₂×C₄²	—	47	1	no	—
463	C₂×C₄²	—	47	1	no	—
464	C₂×C₄²	—	47	1	no	—
465	C₂×C₄²	—	47	1	no	—
466	C₂×C₄²	—	47	1	no	—
467	C₂×C₄²	—	47	1	no	—
468	C₂×C₄²	—	47	1	no	—
469	C₂×C₄²	—	47	1	no	—
470	C₂×C₄²	—	47	1	no	—
471	C₂×C₄²	—	47	1	no	—
472	C₂×C₄²	—	188	1	no	—
473	C₂×C₄²	—	188	1	no	—
474	C₂×C₄²	—	188	1	no	—
475	C₂×C₄²	—	188	1	no	—
476	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
477	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
478	C₄⋊C₈	—	2	2	no	—
479	C₄⋊C₈	—	4	1	no	—
480	C₄⋊C₈	—	94	2	no	—
481	C₄⋊C₈	—	94	2	no	—
482	C₄⋊C₈	—	94	2	no	—
483	C₄⋊C₈	—	188	1	no	—
484	C₄⋊C₈	—	188	1	no	—
485	C₄⋊C₈	—	188	1	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₂²⋊C₈	—	94	2	no	—
488	C₂²⋊C₈	—	94	2	no	—
489	C₂²⋊C₈	—	94	2	no	—
490	C₄×C₈	—	94	2	no	—
491	C₄×C₈	—	94	2	no	—
492	#95	—	47	1	no	—
493	#95	—	47	1	no	—
494	#95	—	47	1	no	—
495	#95	—	47	1	no	—
496	#95	C₄×D₄₇	1	1	yes	characteristic
497	#95	C₄×D₄₇	1	1	yes	characteristic
498	C₂⁴	—	47	1	no	—
499	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
500	C₂×D₄	—	47	4	no	—
501	C₂×D₄	—	47	4	no	—
502	C₂×D₄	—	47	4	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	47	1	no	—
508	C₂²×C₄	—	47	1	no	—
509	C₂²×C₄	—	47	1	no	—
510	C₂²×C₄	—	47	1	no	—
511	C₂²×C₄	—	47	1	no	—
512	C₂²×C₄	—	47	1	no	—
513	C₂²×C₄	—	47	4	no	—
514	C₂²×C₄	—	47	2	no	—
515	C₂²×C₄	—	47	2	no	—
516	C₂²×C₄	—	47	4	no	—
517	C₂²×C₄	—	47	1	no	—
518	C₂²×C₄	—	94	2	no	—
519	C₂²×C₄	—	94	2	no	—
520	C₂²×C₄	—	94	2	no	—
521	C₂²×C₄	—	94	1	no	—
522	C₂²×C₄	—	94	1	no	—
523	C₂²×C₄	—	94	1	no	—
524	C₂²×C₄	—	94	1	no	—
525	C₂²×C₄	—	94	2	no	—
526	C₂²×C₄	—	188	1	no	—
527	C₂²×C₄	—	188	1	no	—
528	C₂²×C₄	—	188	1	no	—
529	C₂²×C₄	—	188	1	no	—
530	C₂²×C₄	—	188	1	no	—
531	C₂²×C₄	—	188	1	no	—
532	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
533	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
537	C₂²×C₄	D₄×D₄₇	1	2	yes	—
538	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
539	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	4	4	no	—
552	C₂×C₈	—	47	2	no	—
553	C₂×C₈	—	94	1	no	—
554	C₂×C₈	—	94	1	no	—
555	C₂×C₈	—	94	1	no	—
556	C₂×C₈	—	94	1	no	—
557	C₂×C₈	—	94	1	no	—
558	C₂×C₈	—	94	1	no	—
559	C₂×C₈	—	94	1	no	—
560	C₂×C₈	—	94	1	no	—
561	C₂×C₈	—	94	1	no	—
562	C₂×C₈	—	94	1	no	—
563	C₂×C₈	—	94	1	no	—
564	C₂×C₈	—	188	4	no	—
565	C₂×C₈	—	188	4	no	—
566	C₂×C₈	—	188	4	no	—
567	C₂×C₈	#10625352	1	2	yes	—
568	C₄⋊C₄	—	47	4	no	—
569	C₄⋊C₄	—	47	4	no	—
570	C₄⋊C₄	—	94	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	47	4	no	—
573	C₂²⋊C₄	—	47	4	no	—
574	C₂²⋊C₄	—	47	4	no	—
575	C₂²⋊C₄	—	94	2	no	—
576	C₂²⋊C₄	C₈×D₄₇	1	4	yes	complemented
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	47	4	no	—
582	C₄²	—	47	2	no	—
583	C₄²	—	47	2	no	—
584	C₄²	—	94	2	no	—
585	C₄²	—	94	2	no	—
586	C₄²	—	94	1	no	—
587	C₄²	—	94	1	no	—
588	C₄²	—	94	1	no	—
589	C₄²	—	94	1	no	—
590	C₄²	—	188	1	no	—
591	C₄²	—	188	1	no	—
592	C₄²	—	188	1	no	—
593	C₄²	—	188	1	no	—
594	C₄²	—	188	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	47	2	no	—
600	C₂³	—	47	2	no	—
601	C₂³	—	47	2	no	—
602	C₂³	—	94	1	no	—
603	C₂³	—	94	1	no	—
604	C₂³	—	94	1	no	—
605	C₂³	—	94	1	no	—
606	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
607	C₂³	C₂×C₈×D₄₇	1	2	yes	—
608	C₂³	M₁₆×D₄₇	1	2	yes	—
609	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
610	D₄	—	47	16	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	47	2	no	—
628	C₂×C₄	—	47	2	no	—
629	C₂×C₄	—	47	2	no	—
630	C₂×C₄	—	47	2	no	—
631	C₂×C₄	—	47	2	no	—
632	C₂×C₄	—	47	2	no	—
633	C₂×C₄	—	47	2	no	—
634	C₂×C₄	—	47	2	no	—
635	C₂×C₄	—	94	1	no	—
636	C₂×C₄	—	94	1	no	—
637	C₂×C₄	—	94	1	no	—
638	C₂×C₄	—	94	1	no	—
639	C₂×C₄	—	94	1	no	—
640	C₂×C₄	—	94	1	no	—
641	C₂×C₄	—	94	1	no	—
642	C₂×C₄	—	94	1	no	—
643	C₂×C₄	—	94	1	no	—
644	C₂×C₄	—	94	1	no	—
645	C₂×C₄	—	94	2	no	—
646	C₂×C₄	—	94	2	no	—
647	C₂×C₄	—	94	2	no	—
648	C₂×C₄	—	94	2	no	—
649	C₂×C₄	—	94	1	no	—
650	C₂×C₄	—	94	1	no	—
651	C₂×C₄	—	94	1	no	—
652	C₂×C₄	—	188	4	no	—
653	C₂×C₄	—	188	4	no	—
654	C₂×C₄	—	188	4	no	—
655	C₂×C₄	—	188	4	no	—
656	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
657	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
658	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
659	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
660	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
661	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
662	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
663	C₂×C₄	#13094069	1	1	yes	characteristic
664	C₂×C₄	#13094070	1	1	yes	characteristic
665	C₈	—	2	2	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	94	2	no	—
670	C₈	—	188	1	no	—
671	C₈	—	188	1	no	—
672	C₈	—	188	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	47	4	no	—
680	C₂²	—	94	2	no	—
681	C₂²	—	94	2	no	—
682	C₂²	—	94	2	no	—
683	C₂²	—	94	2	no	—
684	C₂²	—	94	2	no	—
685	C₂²	—	94	2	no	—
686	C₂²	C₄⋊C₈×D₄₇	1	4	yes	—
687	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
688	C₂²	C₄×#10625352	1	1	yes	characteristic
689	C₂²	#15689595	1	1	yes	characteristic
690	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
691	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
692	C₂²	#131×D₄₇	1	1	yes	characteristic
693	C₂²	#15689888	1	1	yes	characteristic
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	47	4	no	—
700	C₄	—	94	2	no	—
701	C₄	—	94	2	no	—
702	C₄	—	94	2	no	—
703	C₄	—	94	2	no	—
704	C₄	—	94	2	no	—
705	C₄	—	188	1	no	—
706	C₄	#15689760	1	1	yes	characteristic
707	C₄	#15689765	1	1	yes	characteristic
708	C₄	#15689827	1	1	yes	characteristic
709	C₄	#15689831	1	1	yes	characteristic
710	C₂	—	2	4	no	—
711	C₂	—	94	4	no	—
712	C₂	#20246294	1	1	yes	characteristic
713	C₂	C₂×C₄⋊C₈×D₄₇	1	1	yes	characteristic
714	C₂	#20251955	1	1	yes	characteristic
715	C₂	C₈×#10625352	1	1	yes	characteristic
716	C₂	#20252398	1	1	yes	characteristic
717	C₂	#20252409	1	1	yes	characteristic
718	C₂	#20252418	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1850	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1850	D₄₇
hypocenter	C₄₇	#22696
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1850

Complements

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

N	H ≅ G/N	type
4. #20244105	C₂	semidirect
5. #20244103	C₂	semidirect
6. #20243568	C₂	semidirect
7. #20243567	C₂	semidirect
8. #20243564	C₂	semidirect
9. #20243503	C₂	semidirect
10. #20243366	C₂	semidirect
11. #20243365	C₂	semidirect
12. C₄⋊C₈×Dic₄₇	C₂	semidirect
13. C₂×#15688877	C₂	semidirect
14. #336×D₄₇	C₂	semidirect
15. C₄₇×#1850	C₂	semidirect
83. (C₂²⋊D₄₇)⋊C₄	C₈	semidirect
160. C₂²×Dic₄₇	C₂×C₈	semidirect
177. C₂×C₄×D₄₇	C₂×C₈	semidirect
194. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
202. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
205. Dic₄₇⋊C₄	C₂×C₈	semidirect
217. C₄×Dic₄₇	C₂×C₈	semidirect
275. C₂²⋊D₄₇	C₄⋊C₈	semidirect
359. #1850	D₄₇	semidirect
420. C₄₇	#22696	semidirect
576. C₂²⋊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×C₂²⋊D₄₇	2
C₂×(C₂²⋊D₄₇)⋊C₈	2
C₄×(C₂²⋊D₄₇)⋊C₄	2
#20244105	2
#20244103	2
#20243568	2
#20243567	2
#20243564	2
#20243503	2
#20243366	2
#20243365	2
C₄⋊C₈×Dic₄₇	2
C₂×#15688877	2
#336×D₄₇	2
C₄₇×#1850	2
#22696	47