Subgroups — C₂×C₄₇×#3044 #26100117

Order 12032.

2666 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#3044	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₇×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#462	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#416	C₂	1	1	yes	maximal, characteristic
11	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₇	—	2	8	no	—
15	C₂×#137×C₄₇	C₂²	1	8	yes	—
16	C₂²×Q₁₆×C₄₇	—	2	8	no	—
17	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₄₇	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₄₇	C₂²	1	8	yes	complemented
20	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#536	—	2	4	no	—
24	C₄₇×#536	C₂²	1	8	yes	—
25	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
26	C₂×#124×C₄₇	C₂²	1	2	yes	—
27	C₂×#123×C₄₇	—	2	2	no	—
28	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
29	C₄₇×#519	—	2	4	no	—
30	C₄₇×#519	C₂²	1	8	yes	complemented
31	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
32	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	—
33	C₂×#117×C₄₇	—	2	2	no	—
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#464	C₂²	1	32	yes	complemented
37	C₄₇×#462	C₂²	1	32	yes	complemented
38	C₄₇×#424	C₂²	1	8	yes	complemented
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
40	C₄₇×#419	C₂²	1	8	yes	complemented
41	C₄₇×#416	C₂²	1	8	yes	—
42	C₂×#103×C₄₇	C₂²	1	2	yes	—
43	C₂×#103×C₄₇	C₂²	1	4	yes	—
44	C₂×#102×C₄₇	C₂²	1	2	yes	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	4	no	—
47	C₂×#41×C₄₇	—	2	4	no	—
48	C₂×#41×C₄₇	C₂³	1	4	yes	—
49	C₂²×Q₈×C₄₇	—	2	1	no	—
50	C₂²×Q₈×C₄₇	—	2	2	no	—
51	C₂²×Q₈×C₄₇	—	2	1	no	—
52	C₂²×Q₈×C₄₇	—	2	2	no	—
53	C₂²×Q₈×C₄₇	—	2	4	no	—
54	C₂²×Q₈×C₄₇	—	2	4	no	—
55	C₂²×Q₈×C₄₇	—	2	4	no	—
56	C₂²×Q₈×C₄₇	D₄	1	8	yes	—
57	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
58	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
60	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂³×C₄×C₄₇	—	2	1	no	—
66	C₂³×C₄×C₄₇	—	2	1	no	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	#137×C₄₇	—	2	32	no	—
69	C₂×Q₁₆×C₄₇	—	2	16	no	—
70	C₂×Q₁₆×C₄₇	—	2	32	no	—
71	C₂×Q₁₆×C₄₇	—	2	8	no	—
72	C₂×Q₁₆×C₄₇	C₂³	1	8	yes	—
73	C₂×Q₁₆×C₄₇	C₂³	1	16	yes	—
74	C₂×SD₁₆×C₄₇	—	2	8	no	—
75	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
76	C₂×M₁₆×C₄₇	—	2	4	no	—
77	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
78	C₂²×C₈×C₄₇	—	2	4	no	—
79	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₄₇	—	2	4	no	—
83	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	—
84	#124×C₄₇	—	2	4	no	—
85	#124×C₄₇	C₂³	1	8	yes	—
86	#123×C₄₇	—	2	16	no	—
87	C₂²⋊Q₈×C₄₇	—	2	16	no	—
88	C₄×Q₈×C₄₇	—	2	16	no	—
89	C₄×Q₈×C₄₇	—	2	8	no	—
90	C₄×Q₈×C₄₇	C₂³	1	16	yes	—
91	#117×C₄₇	—	2	2	no	—
92	#117×C₄₇	—	2	16	no	—
93	#117×C₄₇	D₄	1	4	yes	—
94	#117×C₄₇	C₂³	1	4	yes	—
95	#117×C₄₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
103	C₂×C₄²×C₄₇	—	2	4	no	—
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
106	C₄⋊C₈×C₄₇	C₂³	1	16	yes	—
107	#103×C₄₇	C₂³	1	8	yes	—
108	#103×C₄₇	C₂³	1	16	yes	—
109	#102×C₄₇	C₂³	1	8	yes	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
112	#41×C₄₇	—	2	8	no	—
113	#41×C₄₇	—	2	8	no	—
114	#41×C₄₇	—	4	8	no	—
115	C₂×Q₈×C₄₇	—	2	8	no	—
116	C₂×Q₈×C₄₇	—	2	16	no	—
117	C₂×Q₈×C₄₇	—	2	4	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	4	no	—
120	C₂×Q₈×C₄₇	—	2	2	no	—
121	C₂×Q₈×C₄₇	—	2	1	no	—
122	C₂×Q₈×C₄₇	—	2	4	no	—
123	C₂×Q₈×C₄₇	—	2	8	no	—
124	C₂×Q₈×C₄₇	—	2	4	no	—
125	C₂×Q₈×C₄₇	—	2	8	no	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	—	2	4	no	—
128	C₂×Q₈×C₄₇	—	2	8	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	—	4	4	no	—
131	C₂×Q₈×C₄₇	—	4	8	no	—
132	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
133	C₂×Q₈×C₄₇	C₂×D₄	1	16	yes	—
134	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
135	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
137	C₂×D₄×C₄₇	—	2	4	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	4	4	no	—
142	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₄₇	—	2	8	no	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	4	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	4	no	—
151	C₂²×C₄×C₄₇	—	4	4	no	—
152	C₂²×C₄×C₄₇	—	4	4	no	—
153	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₄₇	#41	1	4	yes	—
158	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₄₇	—	2	32	no	—
161	Q₁₆×C₄₇	—	2	16	no	—
162	SD₁₆×C₄₇	—	2	16	no	—
163	M₁₆×C₄₇	—	2	8	no	—
164	C₂×C₈×C₄₇	—	2	4	no	—
165	C₂×C₈×C₄₇	—	2	8	no	—
166	C₂×C₈×C₄₇	—	2	4	no	—
167	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
168	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
169	C₄⋊C₄×C₄₇	—	2	16	no	—
170	C₄⋊C₄×C₄₇	—	2	16	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
173	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
174	C₂²⋊C₄×C₄₇	—	2	4	no	—
175	C₂²⋊C₄×C₄₇	—	2	16	no	—
176	C₂²⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
177	C₄²×C₄₇	—	2	16	no	—
178	C₄²×C₄₇	—	2	4	no	—
179	C₄²×C₄₇	C₂×D₄	1	4	yes	—
180	C₄²×C₄₇	C₂⁴	1	4	yes	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	4	no	—
185	C₂³×C₄₇	#121	1	4	yes	—
186	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
187	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₄₇	—	2	16	no	—
189	Q₈×C₄₇	—	2	8	no	—
190	Q₈×C₄₇	—	2	4	no	—
191	Q₈×C₄₇	—	2	4	no	—
192	Q₈×C₄₇	—	2	2	no	—
193	Q₈×C₄₇	—	2	4	no	—
194	Q₈×C₄₇	—	2	2	no	—
195	Q₈×C₄₇	—	4	8	no	—
196	Q₈×C₄₇	—	4	4	no	—
197	Q₈×C₄₇	—	4	2	no	—
198	Q₈×C₄₇	C₂²×D₄	1	8	yes	—
199	D₄×C₄₇	—	2	2	no	—
200	D₄×C₄₇	—	2	2	no	—
201	D₄×C₄₇	—	4	8	no	—
202	D₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	2	16	no	—
204	C₂×C₄×C₄₇	—	2	8	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	8	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	4	8	no	—
215	C₂×C₄×C₄₇	#121	1	4	yes	—
216	C₂×C₄×C₄₇	#121	1	8	yes	—
217	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
218	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
224	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
225	C₈×C₄₇	—	2	4	no	—
226	C₈×C₄₇	—	2	4	no	—
227	C₂×#3044	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₇	—	2	8	no	—
229	C₂²×C₄₇	—	2	4	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	4	no	—
232	C₂²×C₄₇	—	8	4	no	—
233	C₂²×C₄₇	C₂×#121	1	4	yes	—
234	C₂²×C₄₇	C₂×#121	1	2	yes	—
235	C₂²×C₄₇	#578	1	4	yes	—
236	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
237	C₄×C₄₇	—	2	8	no	—
238	C₄×C₄₇	—	2	8	no	—
239	C₄×C₄₇	—	4	2	no	—
240	C₄×C₄₇	—	4	4	no	—
241	C₄×C₄₇	—	4	4	no	—
242	C₄×C₄₇	C₂×#121	1	4	yes	—
243	C₄×C₄₇	C₂×#121	1	2	yes	—
244	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
246	C₂²×#137	C₂×C₄₇	1	1	yes	characteristic
247	C₂³×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
248	C₂×#536	C₂×C₄₇	1	1	yes	characteristic
249	C₂×#519	C₂×C₄₇	1	1	yes	characteristic, complemented
250	#3044	C₂×C₄₇	1	16	yes	direct product factor
251	C₂×#464	C₂×C₄₇	1	4	yes	complemented
252	C₂×#462	C₂×C₄₇	1	4	yes	complemented
253	C₂×#424	C₂×C₄₇	1	1	yes	characteristic, complemented
254	C₂×#419	C₂×C₄₇	1	1	yes	characteristic, complemented
255	C₂×#416	C₂×C₄₇	1	1	yes	characteristic
256	C₂×C₄₇	—	2	4	no	—
257	C₂×C₄₇	—	8	2	no	—
258	C₂×C₄₇	#3044	1	4	yes	direct product factor
259	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
260	C₂×C₄₇	C₂×#578	1	2	yes	—
261	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
262	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×#137	—	2	8	no	—
265	C₂×#137	C₂²×C₄₇	1	8	yes	—
266	C₂²×Q₁₆	—	2	8	no	—
267	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
268	C₂²×Q₁₆	C₂²×C₄₇	1	4	yes	—
269	C₂²×Q₁₆	C₂²×C₄₇	1	8	yes	complemented
270	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
271	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
273	#536	—	2	4	no	—
274	#536	C₂²×C₄₇	1	8	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
276	C₂×#124	C₂²×C₄₇	1	2	yes	—
277	C₂×#123	—	2	2	no	—
278	C₂×C₂²⋊Q₈	—	2	2	no	—
279	#519	—	2	4	no	—
280	#519	C₂²×C₄₇	1	8	yes	complemented
281	C₂×C₄×Q₈	—	2	2	no	—
282	C₂×C₄×Q₈	C₂²×C₄₇	1	4	yes	—
283	C₂×#117	—	2	2	no	—
284	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
285	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
286	#464	C₂²×C₄₇	1	32	yes	complemented
287	#462	C₂²×C₄₇	1	32	yes	complemented
288	#424	C₂²×C₄₇	1	8	yes	complemented
289	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	—
290	#419	C₂²×C₄₇	1	8	yes	complemented
291	#416	C₂²×C₄₇	1	8	yes	—
292	C₂×#103	C₂²×C₄₇	1	2	yes	—
293	C₂×#103	C₂²×C₄₇	1	4	yes	—
294	C₂×#102	C₂²×C₄₇	1	2	yes	—
295	C₄₇	C₂×#3044	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	4	no	—
299	C₂×#41	C₂³×C₄₇	1	4	yes	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	—	2	2	no	—
304	C₂²×Q₈	—	2	4	no	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	—	2	4	no	—
307	C₂²×Q₈	D₄×C₄₇	1	8	yes	—
308	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
309	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
311	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
312	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
319	#137	—	2	32	no	—
320	C₂×Q₁₆	—	2	16	no	—
321	C₂×Q₁₆	—	2	32	no	—
322	C₂×Q₁₆	—	2	8	no	—
323	C₂×Q₁₆	C₂³×C₄₇	1	16	yes	—
324	C₂×Q₁₆	C₂³×C₄₇	1	8	yes	—
325	C₂×SD₁₆	—	2	8	no	—
326	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
327	C₂×M₁₆	—	2	4	no	—
328	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
331	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
332	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
333	C₄⋊Q₈	—	2	4	no	—
334	C₄⋊Q₈	C₂³×C₄₇	1	8	yes	—
335	#124	—	2	4	no	—
336	#124	C₂³×C₄₇	1	8	yes	—
337	#123	—	2	16	no	—
338	C₂²⋊Q₈	—	2	16	no	—
339	C₄×Q₈	—	2	16	no	—
340	C₄×Q₈	—	2	8	no	—
341	C₄×Q₈	C₂³×C₄₇	1	16	yes	—
342	#117	—	2	2	no	—
343	#117	—	2	16	no	—
344	#117	D₄×C₄₇	1	4	yes	—
345	#117	C₂³×C₄₇	1	4	yes	—
346	#117	C₂³×C₄₇	1	4	yes	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	4	no	—
353	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
357	C₄⋊C₈	C₂³×C₄₇	1	16	yes	—
358	#103	C₂³×C₄₇	1	8	yes	—
359	#103	C₂³×C₄₇	1	16	yes	—
360	#102	C₂³×C₄₇	1	8	yes	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	4	8	no	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	2	16	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	8	no	—
383	C₂×Q₈	C₂×D₄×C₄₇	1	8	yes	—
384	C₂×Q₈	C₂×D₄×C₄₇	1	16	yes	—
385	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
386	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
387	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
408	C₂²×C₄	#41×C₄₇	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
411	Q₁₆	—	2	32	no	—
412	Q₁₆	—	2	16	no	—
413	SD₁₆	—	2	16	no	—
414	M₁₆	—	2	8	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
419	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
420	C₄⋊C₄	—	2	16	no	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
424	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
428	C₄²	—	2	16	no	—
429	C₄²	—	2	4	no	—
430	C₄²	C₂×D₄×C₄₇	1	4	yes	—
431	C₄²	C₂⁴×C₄₇	1	4	yes	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	4	no	—
436	C₂³	#121×C₄₇	1	4	yes	—
437	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
438	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
439	Q₈	—	2	16	no	—
440	Q₈	—	2	8	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	2	4	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	2	4	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	8	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	C₂²×D₄×C₄₇	1	8	yes	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	8	no	—
453	D₄	—	4	2	no	—
454	C₂×C₄	—	2	16	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	#121×C₄₇	1	4	yes	—
467	C₂×C₄	#121×C₄₇	1	8	yes	—
468	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
469	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
473	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
474	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
475	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	2	4	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	4	no	—
483	C₂²	C₂×#121×C₄₇	1	4	yes	—
484	C₂²	C₂×#121×C₄₇	1	2	yes	—
485	C₂²	C₄₇×#578	1	4	yes	—
486	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
487	C₄	—	2	8	no	—
488	C₄	—	2	8	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	C₂×#121×C₄₇	1	4	yes	—
493	C₄	C₂×#121×C₄₇	1	2	yes	—
494	C₄	C₂³×D₄×C₄₇	1	1	yes	characteristic
495	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
496	C₂	—	2	4	no	—
497	C₂	—	8	2	no	—
498	C₂	C₄₇×#3044	1	4	yes	direct product factor
499	C₂	C₂²×#121×C₄₇	1	1	yes	characteristic
500	C₂	C₂×C₄₇×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
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
2. C₂³×Q₁₆×C₄₇	C₂	semidirect
4. C₂×C₄₇×#519	C₂	semidirect
5. C₄₇×#3044	C₂	direct (N × H)
6. C₂×C₄₇×#464	C₂	semidirect
7. C₂×C₄₇×#462	C₂	semidirect
8. C₂×C₄₇×#424	C₂	semidirect
9. C₂×C₄₇×#419	C₂	semidirect
19. C₂²×Q₁₆×C₄₇	C₂²	semidirect
30. C₄₇×#519	C₂²	semidirect
36. C₄₇×#464	C₂²	semidirect
37. C₄₇×#462	C₂²	semidirect
38. C₄₇×#424	C₂²	semidirect
40. C₄₇×#419	C₂²	semidirect
227. C₂×#3044	C₄₇	direct (N × H)
247. C₂³×Q₁₆	C₂×C₄₇	semidirect
249. C₂×#519	C₂×C₄₇	semidirect
250. #3044	C₂×C₄₇	direct (N × H)
251. C₂×#464	C₂×C₄₇	semidirect
252. C₂×#462	C₂×C₄₇	semidirect
253. C₂×#424	C₂×C₄₇	semidirect
254. C₂×#419	C₂×C₄₇	semidirect
258. C₂×C₄₇	#3044	direct (N × H)
269. C₂²×Q₁₆	C₂²×C₄₇	semidirect
280. #519	C₂²×C₄₇	semidirect
286. #464	C₂²×C₄₇	semidirect
287. #462	C₂²×C₄₇	semidirect
288. #424	C₂²×C₄₇	semidirect
290. #419	C₂²×C₄₇	semidirect
295. C₄₇	C₂×#3044	direct (N × H)
498. C₂	C₄₇×#3044	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×#137×C₄₇	2
C₂³×Q₁₆×C₄₇	2
C₂×C₄₇×#536	2
C₂×C₄₇×#519	2
C₄₇×#3044	2
C₂×C₄₇×#464	2
C₂×C₄₇×#462	2
C₂×C₄₇×#424	2
C₂×C₄₇×#419	2
C₂×C₄₇×#416	2
C₂×#3044	47

Subgroups — C2×C47×#3044 #26100117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3044 #26100117