Subgroups — C₂×#20245015 #26368979

Order 12032.

1154 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094030	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093964	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245015	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688906	C₂	1	4	yes	maximal, complemented
5	C₂²×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10625350	C₄	1	1	yes	characteristic
7	C₂×#13094030	—	2	1	no	—
8	C₂×#13094030	—	2	2	no	—
9	C₂×#13094030	—	2	1	no	—
10	C₂×#13094030	—	2	2	no	—
11	C₂×#13094030	C₄	1	2	yes	—
12	C₂×#13094030	C₄	1	4	yes	—
13	C₂×#13094030	C₂²	1	2	yes	—
14	C₂×#13094030	C₂²	1	4	yes	—
15	C₂²×#10625329	C₄	1	1	yes	characteristic
16	C₂²×#10625324	—	2	1	no	—
17	C₂²×C₈×D₄₇	—	2	1	no	—
18	C₂×#13093964	—	2	1	no	—
19	C₂×#13093964	—	2	2	no	—
20	C₂×#13093964	C₂²	1	2	yes	complemented
21	C₂×#13093964	C₂²	1	4	yes	complemented
22	C₂²×C₄₇⋊C₁₆	—	2	1	no	—
23	#15688906	C₂²	1	16	yes	complemented
24	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×M₃₂×C₄₇	—	2	1	no	—
26	C₂×M₃₂×C₄₇	—	2	1	no	—
27	C₂×M₃₂×C₄₇	—	2	2	no	—
28	C₂×M₃₂×C₄₇	C₂²	1	4	yes	complemented
29	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	complemented
30	C₂×#10625350	—	2	1	no	—
31	C₂×#10625350	—	2	2	no	—
32	C₂×#10625350	—	2	1	no	—
33	C₂×#10625350	—	2	2	no	—
34	C₂×#10625350	C₈	1	2	yes	—
35	C₂×#10625350	C₈	1	4	yes	—
36	C₂×#10625350	C₂×C₄	1	2	yes	—
37	C₂×#10625350	C₂×C₄	1	4	yes	—
38	C₂²×Dic₉₄	C₈	1	1	yes	characteristic
39	C₂²×D₁₈₈	C₈	1	1	yes	characteristic
40	C₂²×C₂²⋊D₄₇	—	2	1	no	—
41	C₂²×C₄×D₄₇	—	2	1	no	—
42	#13094030	—	2	4	no	—
43	#13094030	—	2	4	no	—
44	#13094030	—	2	4	no	—
45	#13094030	—	2	2	no	—
46	#13094030	—	2	4	no	—
47	#13094030	—	2	4	no	—
48	#13094030	—	2	2	no	—
49	#13094030	C₂×C₄	1	4	yes	—
50	#13094030	C₂×C₄	1	8	yes	—
51	#13094030	C₂³	1	4	yes	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	2	no	—
54	C₂×#10625329	C₂×C₄	1	2	yes	—
55	C₂×#10625329	C₂×C₄	1	4	yes	—
56	C₂×#10625324	—	2	2	no	—
57	C₂×#10625324	—	2	4	no	—
58	C₂×#10625324	—	2	2	no	—
59	C₂×#10625324	—	2	4	no	—
60	C₂²×C₄₇⋊C₈	—	2	1	no	—
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₂×C₈×D₄₇	—	2	4	no	—
63	C₂×C₈×D₄₇	—	2	4	no	—
64	C₂×C₈×D₄₇	—	2	2	no	—
65	#13093964	—	2	4	no	—
66	#13093964	—	2	2	no	—
67	#13093964	C₂³	1	4	yes	complemented
68	C₂×C₄₇⋊C₁₆	—	2	4	no	—
69	C₂×C₄₇⋊C₁₆	—	2	2	no	—
70	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	D₄	1	2	yes	—
76	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	D₄	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
81	M₃₂×C₄₇	—	2	4	no	—
82	M₃₂×C₄₇	—	2	4	no	—
83	C₂×C₁₆×C₄₇	—	2	2	no	—
84	C₂×C₁₆×C₄₇	—	2	2	no	—
85	C₂×C₁₆×C₄₇	C₂³	1	4	yes	complemented
86	C₂⁴×C₄₇	M₁₆	1	1	yes	characteristic
87	C₂³×D₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₄₇	M₁₆	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₄₇	—	2	2	no	—
99	C₂×C₂²⋊D₄₇	—	2	4	no	—
100	C₂×C₂²⋊D₄₇	—	2	2	no	—
101	C₂×C₂²⋊D₄₇	—	2	4	no	—
102	C₂²×Dic₄₇	—	2	1	no	—
103	#10625350	—	2	4	no	—
104	#10625350	—	2	4	no	—
105	#10625350	—	2	4	no	—
106	#10625350	—	2	4	no	—
107	#10625350	—	2	2	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	2	4	no	—
110	#10625350	C₂×C₈	1	4	yes	—
111	#10625350	C₂×C₈	1	8	yes	—
112	#10625350	C₂²×C₄	1	4	yes	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	1	no	—
115	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
116	C₂×D₁₈₈	C₂×C₈	1	2	yes	—
117	C₂×C₄×D₄₇	—	2	4	no	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×C₄×D₄₇	—	2	4	no	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×Dic₉₄	—	2	2	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×Dic₉₄	C₂×C₈	1	4	yes	—
124	C₂×Dic₉₄	C₂×C₈	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
143	#10625329	—	2	4	no	—
144	#10625329	—	2	2	no	—
145	#10625329	C₂²×C₄	1	4	yes	—
146	C₂×C₄₇⋊C₈	—	2	4	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	#10625324	—	2	8	no	—
149	#10625324	—	2	4	no	—
150	#10625324	—	2	4	no	—
151	C₈×D₄₇	—	2	8	no	—
152	C₈×D₄₇	—	2	4	no	—
153	C₈×D₄₇	—	2	4	no	—
154	C₁₆×C₄₇	—	2	4	no	—
155	C₄₇⋊C₁₆	—	2	4	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
158	C₂³×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
159	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
160	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
161	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
162	C₂²×D₄₇	—	2	4	no	—
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₂²⋊D₄₇	—	2	4	no	—
184	C₂²⋊D₄₇	—	2	8	no	—
185	C₂²⋊D₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	2	4	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	D₁₈₈	—	2	2	no	—
189	D₁₈₈	—	2	4	no	—
190	D₁₈₈	C₂²×C₈	1	4	yes	—
191	C₄×D₄₇	—	2	4	no	—
192	C₄×D₄₇	—	2	8	no	—
193	C₄×D₄₇	—	2	4	no	—
194	Dic₉₄	—	2	2	no	—
195	Dic₉₄	—	2	4	no	—
196	Dic₉₄	C₂²×C₈	1	4	yes	—
197	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
198	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
200	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
203	C₄₇⋊C₈	—	2	4	no	—
204	C₂×#2117	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
211	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
212	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
214	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×D₄₇	—	2	4	no	—
216	C₂×D₄₇	—	4	8	no	—
217	C₂×D₄₇	—	4	4	no	—
218	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
219	C₄×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
220	C₄×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
221	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
222	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
224	Dic₄₇	—	2	4	no	—
225	C₂²×#131	—	47	1	no	—
226	C₂²×M₃₂	—	47	1	no	—
227	C₂²×M₃₂	D₄₇	1	1	yes	characteristic, complemented
228	#2117	—	47	8	no	—
229	C₂×#350	—	47	4	no	—
230	C₂×C₄₇	—	2	2	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	#2117	1	2	yes	complemented
235	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
236	D₄₇	—	4	4	no	—
237	C₂²×#41	—	47	1	no	—
238	C₂×#131	—	47	2	no	—
239	C₂×#131	—	47	4	no	—
240	C₂×#131	—	47	2	no	—
241	C₂×#131	—	47	4	no	—
242	C₂×#131	—	94	2	no	—
243	C₂×#131	—	94	1	no	—
244	C₂×#131	—	94	1	no	—
245	C₂×#131	—	94	2	no	—
246	C₂²×M₁₆	—	47	1	no	—
247	C₂²×M₁₆	—	94	1	no	—
248	C₂³×C₈	—	94	1	no	—
249	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
250	C₂×M₃₂	—	2	1	no	—
251	C₂×M₃₂	—	2	1	no	—
252	C₂×M₃₂	—	2	2	no	—
253	C₂×M₃₂	—	47	2	no	—
254	C₂×M₃₂	—	47	4	no	—
255	C₂×M₃₂	—	94	2	no	—
256	C₂×M₃₂	—	94	1	no	—
257	C₂×M₃₂	C₂×D₄₇	1	4	yes	complemented
258	C₂²×C₁₆	—	94	1	no	—
259	C₂²×C₁₆	C₂×D₄₇	1	2	yes	complemented
260	#350	—	47	16	no	—
261	C₄₇	C₂×#2117	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	47	2	no	—
263	C₂×#41	—	47	4	no	—
264	C₂×#41	—	47	2	no	—
265	C₂×#41	—	47	4	no	—
266	C₂×#41	—	94	1	no	—
267	C₂×#41	—	94	2	no	—
268	C₂×#41	—	94	2	no	—
269	C₂×#41	—	94	1	no	—
270	C₂²×Q₈	—	47	1	no	—
271	C₂²×D₄	—	47	1	no	—
272	C₂²×D₄	—	94	1	no	—
273	C₂³×C₄	—	94	1	no	—
274	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
275	#131	—	47	4	no	—
276	#131	—	47	8	no	—
277	#131	—	47	4	no	—
278	#131	—	94	4	no	—
279	#131	—	94	4	no	—
280	#131	—	94	4	no	—
281	#131	—	94	4	no	—
282	#131	—	94	2	no	—
283	#131	—	94	2	no	—
284	#131	—	94	4	no	—
285	C₂×M₁₆	—	47	2	no	—
286	C₂×M₁₆	—	47	4	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	—	94	1	no	—
289	C₂×M₁₆	—	94	4	no	—
290	C₂×M₁₆	—	94	2	no	—
291	C₂×M₁₆	—	94	2	no	—
292	C₂×M₁₆	—	94	4	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₂²×C₈	—	94	4	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₂²×C₈	—	94	4	no	—
297	C₂²×C₈	—	94	2	no	—
298	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₈	C₄×D₄₇	1	2	yes	—
300	C₂²×C₈	D₁₈₈	1	2	yes	—
301	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
302	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
303	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
306	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
307	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	M₃₂	—	2	4	no	—
309	M₃₂	—	2	4	no	—
310	M₃₂	—	47	4	no	—
311	M₃₂	—	94	4	no	—
312	M₃₂	—	94	2	no	—
313	C₂×C₁₆	—	2	2	no	—
314	C₂×C₁₆	—	2	2	no	—
315	C₂×C₁₆	—	94	4	no	—
316	C₂×C₁₆	—	94	2	no	—
317	C₂×C₁₆	C₂²×D₄₇	1	4	yes	complemented
318	C₂⁴	—	94	1	no	—
319	C₂⁴	#10625324	1	1	yes	characteristic
320	#41	—	47	4	no	—
321	#41	—	47	8	no	—
322	#41	—	47	4	no	—
323	#41	—	94	4	no	—
324	#41	—	94	4	no	—
325	#41	—	94	4	no	—
326	#41	—	94	4	no	—
327	#41	—	94	2	no	—
328	#41	—	94	2	no	—
329	#41	—	94	4	no	—
330	C₂×Q₈	—	47	4	no	—
331	C₂×Q₈	—	47	2	no	—
332	C₂×Q₈	—	94	2	no	—
333	C₂×Q₈	—	94	1	no	—
334	C₂×D₄	—	47	4	no	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	94	4	no	—
338	C₂×D₄	—	94	2	no	—
339	C₂×D₄	—	94	4	no	—
340	C₂×D₄	—	94	2	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	4	no	—
344	C₂²×C₄	—	94	2	no	—
345	C₂²×C₄	—	94	4	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₈×D₄₇	1	2	yes	—
350	C₂²×C₄	#10625324	1	1	yes	characteristic
351	C₂²×C₄	#10625324	1	2	yes	—
352	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
354	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
356	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
357	M₁₆	—	47	4	no	—
358	M₁₆	—	94	4	no	—
359	M₁₆	—	94	2	no	—
360	M₁₆	—	94	8	no	—
361	M₁₆	—	94	4	no	—
362	M₁₆	—	94	4	no	—
363	C₂×C₈	—	94	4	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	—	94	8	no	—
366	C₂×C₈	—	94	4	no	—
367	C₂×C₈	—	94	4	no	—
368	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
369	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
370	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
371	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
372	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
373	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
374	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
378	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
379	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
380	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
381	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
384	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
385	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
386	C₁₆	—	2	4	no	—
387	C₁₆	—	94	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	94	4	no	—
390	C₂³	—	94	2	no	—
391	C₂³	—	188	4	no	—
392	C₂³	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
393	C₂³	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
394	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
395	C₂³	C₂×#10625324	1	1	yes	characteristic
396	C₂³	C₂×#10625324	1	2	yes	—
397	Q₈	—	47	4	no	—
398	Q₈	—	94	2	no	—
399	Q₈	—	94	4	no	—
400	D₄	—	47	4	no	—
401	D₄	—	94	8	no	—
402	D₄	—	94	4	no	—
403	D₄	—	94	4	no	—
404	D₄	—	94	2	no	—
405	D₄	—	94	4	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	4	no	—
409	C₂×C₄	—	94	8	no	—
410	C₂×C₄	—	94	4	no	—
411	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
412	C₂×C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
413	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
414	C₂×C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
415	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
416	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
417	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
418	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
419	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
420	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
421	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
423	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
425	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625324	1	2	yes	—
427	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₈	—	94	4	no	—
430	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
431	C₈	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
432	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
433	C₈	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
434	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
435	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	94	4	no	—
442	C₂²	—	188	8	no	—
443	C₂²	—	188	4	no	—
444	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
445	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
446	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
447	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
448	C₂²	C₂²×#10625324	1	1	yes	characteristic
449	C₄	—	94	4	no	—
450	C₄	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
451	C₄	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
452	C₄	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
453	C₄	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
454	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
455	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
456	C₂	—	2	2	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	188	4	no	—
461	C₂	#20245015	1	2	yes	direct product factor
462	C₂	C₂²×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂²×M₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	C₂²×#10625350	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂²×M₃₂	D₄₇
hypocenter	C₄₇	C₂×#2117
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093964	C₂	semidirect
3. #20245015	C₂	direct (N × H)
4. C₂×#15688906	C₂	semidirect
5. C₂²×M₃₂×C₄₇	C₂	semidirect
20. C₂×#13093964	C₂²	semidirect
21. C₂×#13093964	C₂²	semidirect
23. #15688906	C₂²	semidirect
28. C₂×M₃₂×C₄₇	C₂²	semidirect
29. C₂²×C₁₆×C₄₇	C₂²	semidirect
67. #13093964	C₂³	semidirect
85. C₂×C₁₆×C₄₇	C₂³	semidirect
227. C₂²×M₃₂	D₄₇	semidirect
234. C₂×C₄₇	#2117	semidirect
257. C₂×M₃₂	C₂×D₄₇	semidirect
259. C₂²×C₁₆	C₂×D₄₇	semidirect
261. C₄₇	C₂×#2117	semidirect
317. C₂×C₁₆	C₂²×D₄₇	semidirect
461. C₂	#20245015	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×#13094030	2
C₂²×#13093964	2
#20245015	2
C₂×#15688906	2
C₂²×M₃₂×C₄₇	2
C₂×#2117	47

Subgroups — C2×#20245015 #26368979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245015 #26368979