Subgroups — C₂×#20251815 #27079687

Order 12032.

3278 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094032	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13094030	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689591	C₂	1	1	yes	maximal, characteristic
4	#20251815	C₂	1	16	yes	maximal, direct product factor
5	C₂×#15689080	C₂	1	2	yes	maximal, complemented
6	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689077	C₂	1	2	yes	maximal, complemented
8	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×#10625324	C₂	1	2	yes	maximal, complemented
10	C₂²×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#97×D₄₇	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625350	C₂²	1	1	yes	characteristic
14	C₂×#13094032	C₄	1	16	yes	complemented
15	C₂×#13094032	C₂²	1	8	yes	—
16	C₂×#13094030	C₄	1	16	yes	complemented
17	C₂×#13094030	C₂²	1	8	yes	—
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×#10625324	C₂²	1	2	yes	—
20	C₂²×#10625324	C₂²	1	2	yes	—
21	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
23	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
24	#15689591	C₄	1	8	yes	—
25	#15689591	C₂²	1	8	yes	—
26	C₂×#13093989	C₄	1	2	yes	—
27	C₂×#13093986	C₄	1	2	yes	—
28	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	4	yes	—
29	C₂×#13093981	C₂²	1	2	yes	—
30	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
32	#15689080	C₂²	1	16	yes	complemented
33	#15689079	C₂²	1	8	yes	complemented
34	#15689077	C₂²	1	16	yes	complemented
35	M₁₆×Dic₄₇	C₂²	1	8	yes	complemented
36	C₄×#10625324	C₂²	1	16	yes	complemented
37	C₂×#13093935	C₂²	1	2	yes	—
38	C₂×#13093934	C₂²	1	1	yes	characteristic
39	C₂×#13093934	C₂²	1	2	yes	—
40	C₂×#13093934	C₂²	1	1	yes	characteristic
41	C₂×#13093934	C₂²	1	1	yes	characteristic
42	C₂×#13093934	C₂²	1	1	yes	characteristic
43	C₂×#13093934	C₂²	1	8	yes	complemented
44	#97×D₄₇	C₂²	1	16	yes	complemented
45	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
46	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
47	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
48	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
50	C₄₇×#405	C₂²	1	8	yes	complemented
51	C₂×#97×C₄₇	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
53	C₂×#10625350	C₂×C₄	1	8	yes	—
54	C₂×#10625350	C₂×C₄	1	8	yes	—
55	C₂×#10625350	C₂×C₄	1	4	yes	—
56	C₂×#10625350	C₂³	1	4	yes	—
57	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
60	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
62	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
63	#13094032	C₂×C₄	1	64	yes	complemented
64	#13094030	C₂×C₄	1	64	yes	complemented
65	C₂×#10625329	C₂×C₄	1	8	yes	complemented
66	C₂×#10625329	C₂³	1	4	yes	—
67	C₂×#10625324	C₂×C₄	1	16	yes	complemented
68	C₂×#10625324	C₂×C₄	1	16	yes	complemented
69	C₂×#10625324	C₂³	1	8	yes	—
70	C₂×#10625324	C₂³	1	8	yes	—
71	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
72	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
73	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
76	C₂×C₈×D₄₇	C₂×C₄	1	16	yes	complemented
77	C₂×C₈×D₄₇	C₂×C₄	1	16	yes	complemented
78	C₂×C₈×D₄₇	C₂³	1	8	yes	—
79	C₂×C₈×D₄₇	C₂³	1	8	yes	—
80	#13093989	C₂×C₄	1	16	yes	—
81	#13093986	C₂×C₄	1	16	yes	—
82	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	32	yes	—
83	#13093981	C₂×C₄	1	8	yes	—
84	#13093981	C₂³	1	8	yes	—
85	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
86	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
87	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
88	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
93	C₄²×D₄₇	C₂×C₄	1	8	yes	—
94	C₄²×D₄₇	C₂³	1	8	yes	—
95	#13093935	C₂³	1	8	yes	—
96	#13093934	C₂³	1	4	yes	—
97	#13093934	C₂³	1	8	yes	—
98	#13093934	C₂³	1	4	yes	—
99	#13093934	C₂³	1	4	yes	—
100	#13093934	C₂³	1	4	yes	—
101	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
102	C₈×Dic₄₇	C₂³	1	8	yes	—
103	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
105	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
107	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
111	#117×C₄₇	C₂×C₄	1	4	yes	—
112	#117×C₄₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
114	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
116	#97×C₄₇	C₂³	1	8	yes	—
117	C₄×C₈×C₄₇	C₂³	1	8	yes	—
118	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₇	C₄²	1	16	yes	—
128	C₂×C₂²⋊D₄₇	C₂²×C₄	1	8	yes	—
129	C₂²×Dic₄₇	—	4	4	no	—
130	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
132	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
133	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
134	#10625350	C₄²	1	32	yes	—
135	#10625350	C₂²×C₄	1	16	yes	—
136	#10625350	C₂²×C₄	1	16	yes	—
137	C₂×D₁₈₈	C₄²	1	8	yes	—
138	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
139	C₂×C₄×D₄₇	—	4	8	no	—
140	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
141	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
142	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
143	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
144	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
145	C₂×Dic₉₄	C₄²	1	8	yes	—
146	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
147	M₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
148	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
150	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
152	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
153	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
154	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
156	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
157	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
158	C₄²×C₄₇	C₂⁴	1	4	yes	—
159	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
160	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
161	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
162	C₄×Dic₄₇	C₂²×C₄	1	16	yes	—
163	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
164	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
165	C₄×Dic₄₇	C₂⁴	1	2	yes	—
166	C₄×Dic₄₇	C₂⁴	1	2	yes	—
167	#10625329	C₂²×C₄	1	16	yes	complemented
168	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
169	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
170	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
171	C₂×C₄₇⋊C₈	C₂²×C₄	1	16	yes	complemented
172	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
173	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
174	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
175	#10625324	C₂²×C₄	1	32	yes	complemented
176	#10625324	C₂²×C₄	1	32	yes	complemented
177	C₈×D₄₇	C₂²×C₄	1	32	yes	complemented
178	C₈×D₄₇	C₂²×C₄	1	32	yes	complemented
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
181	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
182	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₂²×D₄₇	—	2	8	no	—
184	C₂²×D₄₇	C₂×C₄²	1	8	yes	—
185	C₂²×D₄₇	C₂³×C₄	1	4	yes	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
188	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
197	C₂²⋊D₄₇	C₂×C₄²	1	32	yes	—
198	C₂×Dic₄₇	—	2	4	no	—
199	C₂×Dic₄₇	—	2	4	no	—
200	C₂×Dic₄₇	—	4	8	no	—
201	C₂×Dic₄₇	C₂×C₄²	1	8	yes	—
202	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
203	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
204	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
205	D₁₈₈	C₂×C₄²	1	16	yes	—
206	C₄×D₄₇	—	4	16	no	—
207	C₄×D₄₇	C₂×C₄²	1	16	yes	—
208	C₄×D₄₇	C₂³×C₄	1	8	yes	—
209	C₄×D₄₇	C₂³×C₄	1	8	yes	—
210	Dic₉₄	C₂×C₄²	1	16	yes	—
211	C₈×C₄₇	C₂³×C₄	1	4	yes	—
212	C₈×C₄₇	C₂³×C₄	1	8	yes	—
213	C₈×C₄₇	C₂³×C₄	1	4	yes	—
214	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
215	C₄₇⋊C₈	C₂³×C₄	1	8	yes	—
216	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
217	C₂×#2875	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	8	no	—
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
221	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
222	C₂²×C₄₇	#568	1	4	yes	—
223	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
224	C₂×D₄₇	—	2	16	no	—
225	C₂×D₄₇	—	2	8	no	—
226	C₂×D₄₇	C₂²×C₄²	1	8	yes	—
227	C₄×C₄₇	—	2	8	no	—
228	C₄×C₄₇	C₂²×C₄²	1	4	yes	—
229	C₄×C₄₇	C₂²×C₄²	1	2	yes	—
230	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
232	Dic₄₇	—	2	4	no	—
233	Dic₄₇	—	2	4	no	—
234	Dic₄₇	C₂²×C₄²	1	8	yes	—
235	C₂²×#131	—	47	1	no	—
236	C₂²×#131	—	47	1	no	—
237	C₂×C₄×#41	—	47	1	no	—
238	#2875	—	47	16	no	—
239	C₂×#405	—	47	2	no	—
240	C₂×#405	—	47	2	no	—
241	C₂×#405	—	47	1	no	—
242	C₂×#405	D₄₇	1	1	yes	characteristic, complemented
243	C₂×C₄×M₁₆	—	47	2	no	—
244	C₂×C₄×M₁₆	—	47	1	no	—
245	C₂²×#97	—	47	2	no	—
246	C₂²×#97	—	47	1	no	—
247	C₂×C₄₇	—	2	4	no	—
248	C₂×C₄₇	#2875	1	4	yes	complemented
249	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#568	1	2	yes	—
251	D₄₇	—	2	8	no	—
252	C₂²×#41	—	47	1	no	—
253	C₂×#131	—	47	16	no	—
254	C₂×#131	—	47	8	no	—
255	C₂×#131	—	47	16	no	—
256	C₂×#131	—	47	8	no	—
257	C₂²×M₁₆	—	47	1	no	—
258	C₂²×M₁₆	—	47	2	no	—
259	C₂²×M₁₆	—	47	2	no	—
260	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
261	C₂³×C₈	—	47	1	no	—
262	C₂³×C₈	—	47	2	no	—
263	C₂³×C₈	—	47	2	no	—
264	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
265	C₄×#41	—	47	8	no	—
266	C₄×#41	—	47	8	no	—
267	C₂×C₄×Q₈	—	47	2	no	—
268	C₂×C₄×D₄	—	47	2	no	—
269	C₂×C₄×D₄	—	47	4	no	—
270	C₂×#117	—	47	2	no	—
271	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
272	C₂²×C₄²	—	47	1	no	—
273	C₂²×C₄²	—	47	2	no	—
274	#405	—	47	8	no	—
275	#405	—	47	16	no	—
276	#405	—	47	16	no	—
277	#405	C₂×D₄₇	1	8	yes	complemented
278	C₄×M₁₆	—	47	8	no	—
279	C₄×M₁₆	—	47	16	no	—
280	C₂×#97	—	47	1	no	—
281	C₂×#97	—	47	2	no	—
282	C₂×#97	—	47	1	no	—
283	C₂×#97	—	47	1	no	—
284	C₂×#97	—	47	1	no	—
285	C₂×#97	—	47	8	no	—
286	C₂×#97	—	47	2	no	—
287	C₂×#97	—	47	16	no	—
288	C₂×#97	C₂×D₄₇	1	2	yes	—
289	C₂×C₄×C₈	—	47	2	no	—
290	C₂×C₄×C₈	—	47	2	no	—
291	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
292	C₄₇	C₂×#2875	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	—	47	4	no	—
294	C₂×#41	—	47	8	no	—
295	C₂×#41	—	47	8	no	—
296	C₂×#41	—	47	4	no	—
297	C₂²×Q₈	—	47	1	no	—
298	C₂²×D₄	—	47	2	no	—
299	C₂²×D₄	—	47	1	no	—
300	C₂³×C₄	—	47	2	no	—
301	C₂³×C₄	—	47	2	no	—
302	C₂³×C₄	—	47	4	no	—
303	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
304	#131	—	47	64	no	—
305	#131	—	47	64	no	—
306	C₂×M₁₆	—	47	8	no	—
307	C₂×M₁₆	—	47	4	no	—
308	C₂×M₁₆	—	47	16	no	—
309	C₂×M₁₆	—	47	16	no	—
310	C₂×M₁₆	—	47	8	no	—
311	C₂×M₁₆	—	47	8	no	—
312	C₂×M₁₆	C₄×D₄₇	1	8	yes	complemented
313	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
314	C₂²×C₈	—	47	8	no	—
315	C₂²×C₈	—	47	4	no	—
316	C₂²×C₈	—	47	1	no	—
317	C₂²×C₈	—	47	1	no	—
318	C₂²×C₈	—	47	2	no	—
319	C₂²×C₈	—	47	16	no	—
320	C₂²×C₈	—	47	16	no	—
321	C₂²×C₈	—	47	8	no	—
322	C₂²×C₈	—	47	8	no	—
323	C₂²×C₈	C₄×D₄₇	1	8	yes	complemented
324	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
326	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
328	C₄×Q₈	—	47	16	no	—
329	C₄×D₄	—	47	16	no	—
330	C₄×D₄	—	47	32	no	—
331	#117	—	47	8	no	—
332	#117	—	47	8	no	—
333	#117	C₄×D₄₇	1	4	yes	—
334	#117	C₂²×D₄₇	1	4	yes	—
335	C₂×C₄⋊C₄	—	47	4	no	—
336	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
337	C₂×C₂²⋊C₄	—	47	4	no	—
338	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
339	C₂×C₄²	—	47	4	no	—
340	C₂×C₄²	—	47	2	no	—
341	C₂×C₄²	—	47	4	no	—
342	C₂×C₄²	—	47	4	no	—
343	C₂×C₄²	—	47	1	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	8	no	—
346	C₂×C₄²	—	47	8	no	—
347	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
348	#97	—	47	4	no	—
349	#97	—	47	8	no	—
350	#97	—	47	4	no	—
351	#97	—	47	4	no	—
352	#97	—	47	4	no	—
353	#97	—	47	8	no	—
354	#97	C₂²×D₄₇	1	8	yes	—
355	C₄×C₈	—	47	8	no	—
356	C₄×C₈	—	47	8	no	—
357	C₄×C₈	C₂²×D₄₇	1	8	yes	—
358	C₂⁴	—	47	2	no	—
359	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
360	#41	—	47	32	no	—
361	#41	—	47	16	no	—
362	#41	—	47	16	no	—
363	C₂×Q₈	—	47	8	no	—
364	C₂×Q₈	—	47	4	no	—
365	C₂×D₄	—	47	16	no	—
366	C₂×D₄	—	47	8	no	—
367	C₂×D₄	—	47	8	no	—
368	C₂×D₄	—	47	4	no	—
369	C₂²×C₄	—	47	2	no	—
370	C₂²×C₄	—	47	4	no	—
371	C₂²×C₄	—	47	8	no	—
372	C₂²×C₄	—	47	8	no	—
373	C₂²×C₄	—	47	4	no	—
374	C₂²×C₄	—	47	2	no	—
375	C₂²×C₄	—	47	2	no	—
376	C₂²×C₄	—	47	8	no	—
377	C₂²×C₄	—	47	16	no	—
378	C₂²×C₄	—	188	8	no	—
379	C₂²×C₄	—	188	4	no	—
380	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
381	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
383	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
385	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
386	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
387	M₁₆	—	47	16	no	—
388	M₁₆	—	47	32	no	—
389	M₁₆	—	47	32	no	—
390	M₁₆	C₂×C₄×D₄₇	1	16	yes	complemented
391	C₂×C₈	—	47	4	no	—
392	C₂×C₈	—	47	8	no	—
393	C₂×C₈	—	47	4	no	—
394	C₂×C₈	—	47	16	no	—
395	C₂×C₈	—	47	4	no	—
396	C₂×C₈	—	47	2	no	—
397	C₂×C₈	—	47	2	no	—
398	C₂×C₈	—	47	32	no	—
399	C₂×C₈	—	47	32	no	—
400	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
401	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
402	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
403	C₂×C₈	C₂×C₄×D₄₇	1	16	yes	complemented
404	C₂×C₈	C₂³×D₄₇	1	4	yes	—
405	C₂×C₈	C₂³×D₄₇	1	2	yes	—
406	C₂×C₈	C₂³×D₄₇	1	2	yes	—
407	C₄⋊C₄	—	47	16	no	—
408	C₄⋊C₄	C₂×C₄×D₄₇	1	8	yes	—
409	C₂²⋊C₄	—	47	16	no	—
410	C₂²⋊C₄	C₂×C₄×D₄₇	1	8	yes	—
411	C₄²	—	47	2	no	—
412	C₄²	—	47	2	no	—
413	C₄²	—	47	16	no	—
414	C₄²	—	47	8	no	—
415	C₄²	—	47	2	no	—
416	C₄²	—	47	2	no	—
417	C₄²	C₂×C₄×D₄₇	1	4	yes	—
418	C₄²	C₂³×D₄₇	1	4	yes	—
419	C₂³	—	2	4	no	—
420	C₂³	—	47	8	no	—
421	C₂³	—	47	4	no	—
422	C₂³	—	94	8	no	—
423	C₂³	C₄²×D₄₇	1	4	yes	—
424	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
425	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
426	Q₈	—	47	16	no	—
427	D₄	—	47	32	no	—
428	D₄	—	47	16	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	47	8	no	—
431	C₂×C₄	—	47	4	no	—
432	C₂×C₄	—	47	16	no	—
433	C₂×C₄	—	47	8	no	—
434	C₂×C₄	—	47	8	no	—
435	C₂×C₄	—	47	4	no	—
436	C₂×C₄	—	47	4	no	—
437	C₂×C₄	—	94	4	no	—
438	C₂×C₄	—	94	4	no	—
439	C₂×C₄	—	188	16	no	—
440	C₂×C₄	—	188	8	no	—
441	C₂×C₄	C₄²×D₄₇	1	4	yes	—
442	C₂×C₄	C₄²×D₄₇	1	8	yes	—
443	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
444	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
446	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
447	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
448	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
449	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
450	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
451	C₈	—	47	4	no	—
452	C₈	—	47	8	no	—
453	C₈	—	47	4	no	—
454	C₈	C₂²×C₄×D₄₇	1	4	yes	—
455	C₈	C₂²×C₄×D₄₇	1	8	yes	—
456	C₈	C₂²×C₄×D₄₇	1	4	yes	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	47	8	no	—
460	C₂²	—	94	8	no	—
461	C₂²	—	94	16	no	—
462	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
463	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
464	C₂²	#15689888	1	4	yes	—
465	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
466	C₄	—	2	8	no	—
467	C₄	—	47	8	no	—
468	C₄	—	94	4	no	—
469	C₄	—	94	4	no	—
470	C₄	C₂×C₄²×D₄₇	1	2	yes	—
471	C₄	C₂×C₄²×D₄₇	1	4	yes	—
472	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
473	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
474	C₂	—	2	4	no	—
475	C₂	—	94	8	no	—
476	C₂	#20251815	1	4	yes	direct product factor
477	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
478	C₂	C₂×#15689888	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	C₂×#2875
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. #20251815	C₂	direct (N × H)
5. C₂×#15689080	C₂	semidirect
6. C₂×#15689079	C₂	semidirect
7. C₂×#15689077	C₂	semidirect
8. C₂×M₁₆×Dic₄₇	C₂	semidirect
9. C₂×C₄×#10625324	C₂	semidirect
10. C₂²×#13093934	C₂	semidirect
11. C₂×#97×D₄₇	C₂	semidirect
12. C₂×C₄₇×#405	C₂	semidirect
14. C₂×#13094032	C₄	semidirect
16. C₂×#13094030	C₄	semidirect
32. #15689080	C₂²	semidirect
33. #15689079	C₂²	semidirect
34. #15689077	C₂²	semidirect
35. M₁₆×Dic₄₇	C₂²	semidirect
36. C₄×#10625324	C₂²	semidirect
43. C₂×#13093934	C₂²	semidirect
44. #97×D₄₇	C₂²	semidirect
50. C₄₇×#405	C₂²	semidirect
63. #13094032	C₂×C₄	semidirect
64. #13094030	C₂×C₄	semidirect
65. C₂×#10625329	C₂×C₄	semidirect
67. C₂×#10625324	C₂×C₄	semidirect
68. C₂×#10625324	C₂×C₄	semidirect
71. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
76. C₂×C₈×D₄₇	C₂×C₄	semidirect
77. C₂×C₈×D₄₇	C₂×C₄	semidirect
104. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
106. C₂²×C₈×C₄₇	C₂×C₄	semidirect
147. M₁₆×C₄₇	C₂²×C₄	semidirect
151. C₂×C₈×C₄₇	C₂²×C₄	semidirect
167. #10625329	C₂²×C₄	semidirect
171. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
175. #10625324	C₂²×C₄	semidirect
176. #10625324	C₂²×C₄	semidirect
177. C₈×D₄₇	C₂²×C₄	semidirect
178. C₈×D₄₇	C₂²×C₄	semidirect
242. C₂×#405	D₄₇	semidirect
248. C₂×C₄₇	#2875	semidirect
277. #405	C₂×D₄₇	semidirect
292. C₄₇	C₂×#2875	semidirect
312. C₂×M₁₆	C₄×D₄₇	semidirect
323. C₂²×C₈	C₄×D₄₇	semidirect
390. M₁₆	C₂×C₄×D₄₇	semidirect
403. C₂×C₈	C₂×C₄×D₄₇	semidirect
476. C₂	#20251815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094032	2
C₂²×#13094030	2
C₂×#15689591	2
#20251815	2
C₂×#15689080	2
C₂×#15689079	2
C₂×#15689077	2
C₂×M₁₆×Dic₄₇	2
C₂×C₄×#10625324	2
C₂²×#13093934	2
C₂×#97×D₄₇	2
C₂×C₄₇×#405	2
C₂×#2875	47

Subgroups — C2×#20251815 #27079687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20251815 #27079687