Subgroups — C₂×#20252537 #27081368

Order 12032.

1926 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252537	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689201	C₂	1	2	yes	maximal, complemented
6	C₂×#15689195	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689184	C₂	1	2	yes	maximal, complemented
9	C₂×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15689150	C₂	1	2	yes	maximal, complemented
11	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂²×#10625329	C₂²	1	2	yes	—
15	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
16	#15689254	C₂²	1	8	yes	complemented
17	Q₈×C₄₇⋊C₈	C₂²	1	8	yes	complemented
18	#15689201	C₂²	1	8	yes	complemented
19	#15689201	C₂²	1	16	yes	complemented
20	#15689195	C₂²	1	16	yes	complemented
21	D₄×C₄₇⋊C₈	C₂²	1	8	yes	complemented
22	#15689184	C₂²	1	16	yes	complemented
23	#15689176	C₂²	1	8	yes	complemented
24	#15689150	C₂²	1	16	yes	complemented
25	#15689147	C₂²	1	8	yes	complemented
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
37	C₂×#13093935	C₂²	1	2	yes	—
38	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
41	C₄₇×#529	C₄	1	8	yes	—
42	C₄₇×#529	C₂²	1	8	yes	—
43	C₂×#126×C₄₇	C₄	1	2	yes	—
44	C₂×#125×C₄₇	C₄	1	1	yes	characteristic
45	C₂×#124×C₄₇	C₄	1	1	yes	characteristic
46	C₂×#123×C₄₇	C₄	1	2	yes	—
47	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
48	C₂×#121×C₄₇	C₄	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
52	C₂×#117×C₄₇	C₂²	1	2	yes	—
53	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×#10625329	—	4	4	no	—
55	C₂×#10625329	—	4	4	no	—
56	C₂×#10625329	C₂³	1	8	yes	—
57	C₂×#10625329	C₂³	1	8	yes	—
58	C₂²×C₄₇⋊C₈	—	4	4	no	—
59	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
64	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
65	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
70	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
71	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
72	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
73	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
74	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
75	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
76	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
77	#13093935	C₂³	1	8	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
80	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
81	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
88	#126×C₄₇	C₂×C₄	1	16	yes	—
89	#125×C₄₇	C₂×C₄	1	8	yes	—
90	#124×C₄₇	C₂×C₄	1	8	yes	—
91	#123×C₄₇	C₂×C₄	1	16	yes	—
92	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
93	#121×C₄₇	C₂×C₄	1	8	yes	—
94	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
95	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
96	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
97	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
98	C₄×D₄×C₄₇	C₂³	1	4	yes	—
99	C₄×D₄×C₄₇	C₂³	1	8	yes	—
100	#117×C₄₇	C₂×C₄	1	8	yes	—
101	#117×C₄₇	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
108	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
113	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
119	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
120	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×Q₈×C₄₇	—	2	4	no	—
123	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	4	2	no	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
150	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
152	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
153	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
154	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
155	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
156	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
157	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
158	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
159	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
160	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
163	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
164	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
165	C₄²×C₄₇	C₂⁴	1	2	yes	—
166	C₄²×C₄₇	C₂⁴	1	2	yes	—
167	C₄²×C₄₇	C₂⁴	1	4	yes	—
168	#10625329	—	4	8	no	—
169	#10625329	—	4	8	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂×C₄₇⋊C₈	—	2	4	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	4	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	—	2	2	no	—
176	C₂×C₄₇⋊C₈	—	4	8	no	—
177	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
178	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
179	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
180	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
181	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
182	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	—	2	4	no	—
189	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
190	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	Q₈×C₄₇	—	2	8	no	—
193	D₄×C₄₇	—	2	8	no	—
194	D₄×C₄₇	—	4	8	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	4	no	—
202	C₂×C₄×C₄₇	—	2	8	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	8	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	#131	1	4	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
217	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
222	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
223	C₄₇⋊C₈	—	2	2	no	—
224	C₄₇⋊C₈	—	2	4	no	—
225	C₄₇⋊C₈	—	2	4	no	—
226	C₄₇⋊C₈	—	2	2	no	—
227	C₄₇⋊C₈	—	2	2	no	—
228	C₄₇⋊C₈	—	2	2	no	—
229	C₂×#2993	—	47	1	no	maximal, Sylow
230	C₂²×C₄₇	—	2	4	no	—
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	4	4	no	—
237	C₂²×C₄₇	—	4	8	no	—
238	C₂²×C₄₇	#520	1	2	yes	—
239	C₂²×C₄₇	C₂×#131	1	2	yes	—
240	C₂²×C₄₇	#568	1	2	yes	—
241	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₄₇	—	2	4	no	—
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	2	4	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	2	4	no	—
249	C₄×C₄₇	#520	1	2	yes	—
250	C₄×C₄₇	C₂×#131	1	4	yes	—
251	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
252	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	C₂×#529	D₄₇	1	1	yes	characteristic
254	#2993	—	47	16	no	—
255	C₂×#446	—	47	1	no	—
256	C₂×C₈×Q₈	—	47	1	no	—
257	C₂×#436	—	47	1	no	—
258	C₂×#436	—	47	2	no	—
259	C₂×#435	—	47	2	no	—
260	C₂×C₈×D₄	—	47	1	no	—
261	C₂×#433	—	47	2	no	—
262	C₂×#431	—	47	1	no	—
263	C₂×#424	—	47	2	no	—
264	C₂×#423	—	47	1	no	—
265	C₂×C₄₇	—	4	2	no	—
266	C₂×C₄₇	—	4	4	no	—
267	C₂×C₄₇	#2993	1	4	yes	complemented
268	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
269	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
270	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
271	C₂²×M₁₆	—	47	2	no	—
272	C₂²×M₁₆	—	47	2	no	—
273	C₂³×C₈	—	47	2	no	—
274	#529	Dic₄₇	1	8	yes	—
275	#529	C₂×D₄₇	1	8	yes	—
276	C₂×#126	Dic₄₇	1	2	yes	—
277	C₂×#125	Dic₄₇	1	1	yes	characteristic
278	C₂×#124	Dic₄₇	1	1	yes	characteristic
279	C₂×#123	Dic₄₇	1	2	yes	—
280	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
281	C₂×#121	Dic₄₇	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
285	C₂×#117	C₂×D₄₇	1	2	yes	—
286	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
287	#446	—	47	8	no	—
288	C₈×Q₈	—	47	8	no	—
289	#436	—	47	8	no	—
290	#436	—	47	16	no	—
291	#435	—	47	16	no	—
292	C₈×D₄	—	47	8	no	—
293	#433	—	47	16	no	—
294	#431	—	47	8	no	—
295	#424	—	47	16	no	—
296	#423	—	47	8	no	—
297	C₂×C₄⋊C₈	—	47	2	no	—
298	C₂×C₄⋊C₈	—	47	1	no	—
299	C₂×C₄⋊C₈	—	47	1	no	—
300	C₂×C₄⋊C₈	—	47	1	no	—
301	C₂×C₄⋊C₈	—	47	2	no	—
302	C₂×C₄⋊C₈	—	47	2	no	—
303	C₂×C₄⋊C₈	—	47	1	no	—
304	C₂×C₂²⋊C₈	—	47	1	no	—
305	C₂×C₂²⋊C₈	—	47	1	no	—
306	C₂×C₂²⋊C₈	—	47	2	no	—
307	C₂×C₂²⋊C₈	—	47	2	no	—
308	C₂×#97	—	47	2	no	—
309	C₂×C₄×C₈	—	47	1	no	—
310	C₂×C₄×C₈	—	47	1	no	—
311	C₂×C₄×C₈	—	47	2	no	—
312	C₄₇	C₂×#2993	1	1	yes	characteristic, complemented, Sylow
313	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
314	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
315	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
316	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
317	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
318	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
319	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×M₁₆	—	47	8	no	—
321	C₂×M₁₆	—	47	8	no	—
322	C₂×M₁₆	—	188	4	no	—
323	C₂×M₁₆	—	188	4	no	—
324	C₂²×C₈	—	47	1	no	—
325	C₂²×C₈	—	47	2	no	—
326	C₂²×C₈	—	47	2	no	—
327	C₂²×C₈	—	47	1	no	—
328	C₂²×C₈	—	47	1	no	—
329	C₂²×C₈	—	47	1	no	—
330	C₂²×C₈	—	47	8	no	—
331	C₂²×C₈	—	188	4	no	—
332	#126	C₂×Dic₄₇	1	16	yes	—
333	#125	C₂×Dic₄₇	1	8	yes	—
334	#124	C₂×Dic₄₇	1	8	yes	—
335	#123	C₂×Dic₄₇	1	16	yes	—
336	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
337	#121	C₂×Dic₄₇	1	8	yes	—
338	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
339	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
340	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
341	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
342	C₄×D₄	C₂²×D₄₇	1	4	yes	—
343	C₄×D₄	C₂²×D₄₇	1	8	yes	—
344	#117	C₂×Dic₄₇	1	8	yes	—
345	#117	C₂²×D₄₇	1	8	yes	—
346	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
348	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
350	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
357	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
358	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
359	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
360	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
361	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
363	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₄⋊C₈	—	47	8	no	—
365	C₄⋊C₈	—	47	4	no	—
366	C₄⋊C₈	—	47	4	no	—
367	C₄⋊C₈	—	47	4	no	—
368	C₄⋊C₈	—	47	8	no	—
369	C₄⋊C₈	—	47	8	no	—
370	C₄⋊C₈	—	47	4	no	—
371	C₂²⋊C₈	—	47	4	no	—
372	C₂²⋊C₈	—	47	4	no	—
373	C₂²⋊C₈	—	47	8	no	—
374	C₂²⋊C₈	—	47	8	no	—
375	#97	—	47	8	no	—
376	C₄×C₈	—	47	4	no	—
377	C₄×C₈	—	47	4	no	—
378	C₄×C₈	—	47	8	no	—
379	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
380	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
386	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
395	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
399	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
400	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
401	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
402	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
403	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
404	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
406	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
407	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
408	M₁₆	—	188	8	no	—
409	M₁₆	—	188	8	no	—
410	C₂×C₈	—	47	2	no	—
411	C₂×C₈	—	47	2	no	—
412	C₂×C₈	—	47	2	no	—
413	C₂×C₈	—	47	2	no	—
414	C₂×C₈	—	47	4	no	—
415	C₂×C₈	—	47	4	no	—
416	C₂×C₈	—	94	2	no	—
417	C₂×C₈	—	94	4	no	—
418	C₂×C₈	—	94	4	no	—
419	C₂×C₈	—	94	2	no	—
420	C₂×C₈	—	94	2	no	—
421	C₂×C₈	—	94	2	no	—
422	C₂×C₈	—	188	8	no	—
423	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
424	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
425	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
426	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
427	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
428	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
429	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
430	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
431	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
432	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
433	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
434	C₄²	C₂²×Dic₄₇	1	2	yes	—
435	C₄²	C₂²×Dic₄₇	1	2	yes	—
436	C₄²	C₂²×Dic₄₇	1	4	yes	—
437	C₄²	C₂²×Dic₄₇	1	4	yes	—
438	C₄²	C₂²×Dic₄₇	1	4	yes	—
439	C₄²	C₂³×D₄₇	1	2	yes	—
440	C₄²	C₂³×D₄₇	1	4	yes	—
441	C₄²	C₂³×D₄₇	1	2	yes	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	4	no	—
448	C₂³	C₂³×Dic₄₇	1	4	yes	—
449	C₂³	C₂³×Dic₄₇	1	2	yes	—
450	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	D₄	—	2	8	no	—
453	D₄	—	4	8	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	#13094031	1	4	yes	—
470	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
471	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
472	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
473	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
474	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
475	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
476	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
477	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
478	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
479	C₂×C₄	#13094070	1	2	yes	—
480	C₂×C₄	#13094071	1	2	yes	—
481	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
482	C₈	—	94	2	no	—
483	C₈	—	94	4	no	—
484	C₈	—	94	2	no	—
485	C₈	—	94	4	no	—
486	C₈	—	94	2	no	—
487	C₈	—	94	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	8	no	—
496	C₂²	#15689606	1	2	yes	—
497	C₂²	C₂×#13094031	1	2	yes	—
498	C₂²	#15689890	1	2	yes	—
499	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	#15689606	1	2	yes	—
508	C₄	C₂×#13094031	1	4	yes	—
509	C₄	C₂×#13094070	1	1	yes	characteristic
510	C₄	C₂×#13094071	1	1	yes	characteristic
511	C₂	—	4	2	no	—
512	C₂	—	4	4	no	—
513	C₂	#20252537	1	4	yes	direct product factor
514	C₂	C₂×#15689606	1	1	yes	characteristic
515	C₂	C₂²×#13094031	1	1	yes	characteristic
516	C₂	C₂×#15689890	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#529	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂×#121×C₄₇	C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	C₂×#2993
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #20252537	C₂	direct (N × H)
2. C₂×#15689254	C₂	semidirect
3. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. C₂×#15689201	C₂	semidirect
5. C₂×#15689201	C₂	semidirect
6. C₂×#15689195	C₂	semidirect
7. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
8. C₂×#15689184	C₂	semidirect
9. C₂×#15689176	C₂	semidirect
10. C₂×#15689150	C₂	semidirect
11. C₂×#15689147	C₂	semidirect
16. #15689254	C₂²	semidirect
17. Q₈×C₄₇⋊C₈	C₂²	semidirect
18. #15689201	C₂²	semidirect
19. #15689201	C₂²	semidirect
20. #15689195	C₂²	semidirect
21. D₄×C₄₇⋊C₈	C₂²	semidirect
22. #15689184	C₂²	semidirect
23. #15689176	C₂²	semidirect
24. #15689150	C₂²	semidirect
25. #15689147	C₂²	semidirect
267. C₂×C₄₇	#2993	semidirect
312. C₄₇	C₂×#2993	semidirect
513. C₂	#20252537	direct (N × H)

Maximal subgroups

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

subgroup	index
#20252537	2
C₂×#15689254	2
C₂×Q₈×C₄₇⋊C₈	2
C₂×#15689201	2
C₂×#15689195	2
C₂×D₄×C₄₇⋊C₈	2
C₂×#15689184	2
C₂×#15689176	2
C₂×#15689150	2
C₂×#15689147	2
C₂×C₄₇×#529	2
C₂×#2993	47

Subgroups — C2×#20252537 #27081368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252537 #27081368