Subgroups — C₂×C₄₇×#3260 #26100609

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#540	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#3260	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#460	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#541	—	2	4	no	—
16	C₄₇×#541	C₂²	1	8	yes	complemented
17	C₄₇×#540	—	2	4	no	—
18	C₄₇×#540	C₂²	1	8	yes	—
19	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#126×C₄₇	—	2	2	no	—
22	C₂×#125×C₄₇	—	2	2	no	—
23	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#123×C₄₇	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
27	C₂×#121×C₄₇	—	2	2	no	—
28	C₂×#121×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#479	C₂²	1	16	yes	complemented
33	C₄₇×#478	C₂²	1	16	yes	complemented
34	C₄₇×#468	C₂²	1	16	yes	complemented
35	C₄₇×#465	C₂²	1	16	yes	complemented
36	C₄₇×#461	C₂²	1	16	yes	complemented
37	C₄₇×#460	C₂²	1	16	yes	complemented
38	C₂×#107×C₄₇	C₂²	1	2	yes	—
39	C₂×#106×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#424	C₂²	1	8	yes	complemented
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
43	C₂×#103×C₄₇	C₂²	1	2	yes	—
44	C₂×#103×C₄₇	C₂²	1	2	yes	—
45	C₂×#102×C₄₇	C₂²	1	2	yes	—
46	C₂×#102×C₄₇	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₇	—	2	2	no	—
49	C₂²×D₄×C₄₇	—	2	2	no	—
50	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₇	—	2	2	no	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₄₇	—	4	4	no	—
54	C₂×SD₁₆×C₄₇	—	4	4	no	—
55	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
56	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
57	C₂×M₁₆×C₄₇	—	4	2	no	—
58	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
59	C₂²×C₈×C₄₇	—	4	2	no	—
60	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
63	C₄⋊Q₈×C₄₇	—	2	2	no	—
64	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
65	#127×C₄₇	—	2	2	no	—
66	#127×C₄₇	C₂³	1	4	yes	—
67	#126×C₄₇	—	2	16	no	—
68	#125×C₄₇	—	2	16	no	—
69	#125×C₄₇	—	2	2	no	—
70	#125×C₄₇	—	2	2	no	—
71	#125×C₄₇	C₂³	1	4	yes	—
72	#125×C₄₇	C₂³	1	4	yes	—
73	#123×C₄₇	—	2	16	no	—
74	C₂²⋊Q₈×C₄₇	—	2	4	no	—
75	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
76	#121×C₄₇	—	2	4	no	—
77	#121×C₄₇	—	2	16	no	—
78	#121×C₄₇	C₂³	1	8	yes	—
79	C₄×Q₈×C₄₇	—	2	4	no	—
80	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
81	C₄×D₄×C₄₇	—	2	4	no	—
82	C₄×D₄×C₄₇	C₂³	1	8	yes	—
83	#117×C₄₇	D₄	1	4	yes	—
84	#117×C₄₇	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
97	C₂×C₄²×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#107×C₄₇	C₂³	1	8	yes	—
101	#106×C₄₇	C₂³	1	8	yes	—
102	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
103	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
104	#103×C₄₇	C₂³	1	8	yes	—
105	#103×C₄₇	C₂³	1	8	yes	—
106	#102×C₄₇	C₂³	1	8	yes	—
107	#102×C₄₇	C₂³	1	8	yes	—
108	C₂⁴×C₄₇	—	2	2	no	—
109	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	—	2	4	no	—
112	C₂×Q₈×C₄₇	—	2	4	no	—
113	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
114	C₂×D₄×C₄₇	—	2	8	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	8	no	—
117	C₂×D₄×C₄₇	—	2	4	no	—
118	C₂×D₄×C₄₇	—	2	4	no	—
119	C₂×D₄×C₄₇	—	8	4	no	—
120	C₂×D₄×C₄₇	—	8	4	no	—
121	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	8	no	—
128	C₂²×C₄×C₄₇	—	8	4	no	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	SD₁₆×C₄₇	—	4	8	no	—
136	SD₁₆×C₄₇	—	4	8	no	—
137	M₁₆×C₄₇	—	4	4	no	—
138	C₂×C₈×C₄₇	—	2	4	no	—
139	C₂×C₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	—	4	4	no	—
141	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
142	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
143	C₄⋊C₄×C₄₇	—	2	8	no	—
144	C₄⋊C₄×C₄₇	—	2	8	no	—
145	C₄⋊C₄×C₄₇	—	2	8	no	—
146	C₄⋊C₄×C₄₇	—	2	8	no	—
147	C₄⋊C₄×C₄₇	—	2	8	no	—
148	C₄⋊C₄×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	—	2	2	no	—
150	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₄₇	—	2	8	no	—
154	C₂²⋊C₄×C₄₇	—	2	8	no	—
155	C₂²⋊C₄×C₄₇	—	2	8	no	—
156	C₂²⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
157	C₄²×C₄₇	—	2	8	no	—
158	C₄²×C₄₇	C₂×D₄	1	2	yes	—
159	C₄²×C₄₇	C₂×D₄	1	2	yes	—
160	C₄²×C₄₇	C₂⁴	1	2	yes	—
161	C₄²×C₄₇	C₂⁴	1	2	yes	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	4	no	—
164	C₂³×C₄₇	—	2	4	no	—
165	C₂³×C₄₇	—	4	4	no	—
166	C₂³×C₄₇	—	4	4	no	—
167	C₂³×C₄₇	—	4	4	no	—
168	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
169	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₄₇	—	2	4	no	—
171	Q₈×C₄₇	—	2	4	no	—
172	Q₈×C₄₇	—	4	4	no	—
173	D₄×C₄₇	—	2	4	no	—
174	D₄×C₄₇	—	2	4	no	—
175	D₄×C₄₇	—	4	4	no	—
176	D₄×C₄₇	—	8	8	no	—
177	D₄×C₄₇	—	8	8	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	4	4	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	4	no	—
190	C₂×C₄×C₄₇	—	8	8	no	—
191	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
197	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
198	C₈×C₄₇	—	2	4	no	—
199	C₈×C₄₇	—	2	4	no	—
200	C₂×#3260	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	4	4	no	—
205	C₂²×C₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	4	4	no	—
207	C₂²×C₄₇	—	8	8	no	—
208	C₂²×C₄₇	#537	1	2	yes	—
209	C₂²×C₄₇	#577	1	4	yes	—
210	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	4	no	—
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	—	4	4	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	#537	1	2	yes	—
218	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×#541	C₂×C₄₇	1	1	yes	characteristic, complemented
221	C₂×#540	C₂×C₄₇	1	1	yes	characteristic
222	#3260	C₂×C₄₇	1	16	yes	direct product factor
223	C₂×#479	C₂×C₄₇	1	2	yes	complemented
224	C₂×#478	C₂×C₄₇	1	2	yes	complemented
225	C₂×#468	C₂×C₄₇	1	2	yes	complemented
226	C₂×#465	C₂×C₄₇	1	2	yes	complemented
227	C₂×#460	C₂×C₄₇	1	2	yes	complemented
228	C₂×#461	C₂×C₄₇	1	2	yes	complemented
229	C₂×#424	C₂×C₄₇	1	1	yes	characteristic, complemented
230	C₂×C₄₇	—	4	2	no	—
231	C₂×C₄₇	—	8	4	no	—
232	C₂×C₄₇	#3260	1	4	yes	direct product factor
233	C₂×C₄₇	C₂×#537	1	1	yes	characteristic
234	C₂×C₄₇	C₂×#577	1	2	yes	—
235	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
236	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
237	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
239	#541	—	2	4	no	—
240	#541	C₂²×C₄₇	1	8	yes	complemented
241	#540	—	2	4	no	—
242	#540	C₂²×C₄₇	1	8	yes	—
243	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
244	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×#126	—	2	2	no	—
246	C₂×#125	—	2	2	no	—
247	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
248	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×#123	—	2	2	no	—
250	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
251	C₂×#121	—	2	2	no	—
252	C₂×#121	C₂²×C₄₇	1	2	yes	—
253	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
255	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
256	#479	C₂²×C₄₇	1	16	yes	complemented
257	#478	C₂²×C₄₇	1	16	yes	complemented
258	#468	C₂²×C₄₇	1	16	yes	complemented
259	#465	C₂²×C₄₇	1	16	yes	complemented
260	#461	C₂²×C₄₇	1	16	yes	complemented
261	#460	C₂²×C₄₇	1	16	yes	complemented
262	C₂×#107	C₂²×C₄₇	1	2	yes	—
263	C₂×#106	C₂²×C₄₇	1	2	yes	—
264	#424	C₂²×C₄₇	1	8	yes	complemented
265	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
267	C₂×#103	C₂²×C₄₇	1	2	yes	—
268	C₂×#103	C₂²×C₄₇	1	2	yes	—
269	C₂×#102	C₂²×C₄₇	1	2	yes	—
270	C₂×#102	C₂²×C₄₇	1	2	yes	—
271	C₄₇	C₂×#3260	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
278	C₂×SD₁₆	—	4	4	no	—
279	C₂×SD₁₆	—	4	4	no	—
280	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
281	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
282	C₂×M₁₆	—	4	2	no	—
283	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
284	C₂²×C₈	—	4	2	no	—
285	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
286	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
287	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₄₇	1	4	yes	—
290	#127	—	2	2	no	—
291	#127	C₂³×C₄₇	1	4	yes	—
292	#126	—	2	16	no	—
293	#125	—	2	16	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	C₂³×C₄₇	1	4	yes	—
297	#125	C₂³×C₄₇	1	4	yes	—
298	#123	—	2	16	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
301	#121	—	2	4	no	—
302	#121	—	2	16	no	—
303	#121	C₂³×C₄₇	1	8	yes	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	C₂³×C₄₇	1	8	yes	—
308	#117	D₄×C₄₇	1	4	yes	—
309	#117	C₂³×C₄₇	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
325	#107	C₂³×C₄₇	1	8	yes	—
326	#106	C₂³×C₄₇	1	8	yes	—
327	C₄⋊C₈	C₂³×C₄₇	1	8	yes	—
328	C₄⋊C₈	C₂³×C₄₇	1	8	yes	—
329	#103	C₂³×C₄₇	1	8	yes	—
330	#103	C₂³×C₄₇	1	8	yes	—
331	#102	C₂³×C₄₇	1	8	yes	—
332	#102	C₂³×C₄₇	1	8	yes	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	8	4	no	—
345	C₂×D₄	—	8	4	no	—
346	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	8	4	no	—
354	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
360	SD₁₆	—	4	8	no	—
361	SD₁₆	—	4	8	no	—
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
367	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
376	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
382	C₄²	—	2	8	no	—
383	C₄²	C₂×D₄×C₄₇	1	2	yes	—
384	C₄²	C₂×D₄×C₄₇	1	2	yes	—
385	C₄²	C₂⁴×C₄₇	1	2	yes	—
386	C₄²	C₂⁴×C₄₇	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
394	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	4	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	8	8	no	—
402	D₄	—	8	8	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
420	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
421	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
422	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	8	no	—
432	C₂²	C₄₇×#537	1	2	yes	—
433	C₂²	C₄₇×#577	1	4	yes	—
434	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₄₇×#537	1	2	yes	—
442	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
443	C₄	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₄₇×#3260	1	4	yes	direct product factor
447	C₂	C₂×C₄₇×#537	1	1	yes	characteristic
448	C₂	C₂×C₄₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
prime radical	C₂×C₄₇×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#541	C₂	semidirect
3. C₄₇×#3260	C₂	direct (N × H)
4. C₂×C₄₇×#479	C₂	semidirect
5. C₂×C₄₇×#478	C₂	semidirect
6. C₂×C₄₇×#468	C₂	semidirect
7. C₂×C₄₇×#465	C₂	semidirect
8. C₂×C₄₇×#460	C₂	semidirect
9. C₂×C₄₇×#461	C₂	semidirect
10. C₂×C₄₇×#424	C₂	semidirect
16. C₄₇×#541	C₂²	semidirect
32. C₄₇×#479	C₂²	semidirect
33. C₄₇×#478	C₂²	semidirect
34. C₄₇×#468	C₂²	semidirect
35. C₄₇×#465	C₂²	semidirect
36. C₄₇×#461	C₂²	semidirect
37. C₄₇×#460	C₂²	semidirect
40. C₄₇×#424	C₂²	semidirect
200. C₂×#3260	C₄₇	direct (N × H)
220. C₂×#541	C₂×C₄₇	semidirect
222. #3260	C₂×C₄₇	direct (N × H)
223. C₂×#479	C₂×C₄₇	semidirect
224. C₂×#478	C₂×C₄₇	semidirect
225. C₂×#468	C₂×C₄₇	semidirect
226. C₂×#465	C₂×C₄₇	semidirect
227. C₂×#460	C₂×C₄₇	semidirect
228. C₂×#461	C₂×C₄₇	semidirect
229. C₂×#424	C₂×C₄₇	semidirect
232. C₂×C₄₇	#3260	direct (N × H)
240. #541	C₂²×C₄₇	semidirect
256. #479	C₂²×C₄₇	semidirect
257. #478	C₂²×C₄₇	semidirect
258. #468	C₂²×C₄₇	semidirect
259. #465	C₂²×C₄₇	semidirect
260. #461	C₂²×C₄₇	semidirect
261. #460	C₂²×C₄₇	semidirect
264. #424	C₂²×C₄₇	semidirect
271. C₄₇	C₂×#3260	direct (N × H)
446. C₂	C₄₇×#3260	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#541	2
C₂×C₄₇×#540	2
C₄₇×#3260	2
C₂×C₄₇×#479	2
C₂×C₄₇×#478	2
C₂×C₄₇×#468	2
C₂×C₄₇×#465	2
C₂×C₄₇×#460	2
C₂×C₄₇×#461	2
C₂×C₄₇×#424	2
C₂×#3260	47

Subgroups — C2×C47×#3260 #26100609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3260 #26100609