Subgroups — C₂×C₄₇×#3038 #26100110

Order 12032.

3478 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₇	C₂	1	2	yes	maximal, complemented
2	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3038	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₇×#460	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₇×#459	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#418	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₇	—	2	2	no	—
11	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
13	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	16	yes	complemented
14	C₂²×SD₁₆×C₄₇	C₂²	1	4	yes	complemented
15	C₂²×D₈×C₄₇	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂×#127×C₄₇	—	2	1	no	—
18	C₂×#127×C₄₇	—	2	1	no	—
19	C₂×#127×C₄₇	—	2	4	no	—
20	C₂×#127×C₄₇	C₂²	1	4	yes	—
21	C₂×#127×C₄₇	C₂²	1	8	yes	complemented
22	C₄×#41×C₄₇	—	2	4	no	—
23	C₄×#41×C₄₇	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
25	C₂×C₄×D₄×C₄₇	—	2	2	no	—
26	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
27	C₂×#117×C₄₇	—	2	1	no	—
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	—	2	1	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#460	C₂²	1	32	yes	complemented
32	C₄₇×#459	C₂²	1	32	yes	complemented
33	C₄₇×#423	C₂²	1	8	yes	complemented
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	complemented
35	C₄₇×#418	C₂²	1	16	yes	complemented
36	C₂×#102×C₄₇	C₂²	1	8	yes	complemented
37	C₂⁵×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	—	2	4	no	—
40	C₂×#41×C₄₇	D₄	1	8	yes	complemented
41	C₂×#41×C₄₇	C₂³	1	4	yes	—
42	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	—	2	8	no	—
45	C₂²×D₄×C₄₇	—	2	4	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	4	no	—
48	C₂²×D₄×C₄₇	—	2	4	no	—
49	C₂²×D₄×C₄₇	—	2	16	no	—
50	C₂²×D₄×C₄₇	—	2	8	no	—
51	C₂²×D₄×C₄₇	—	4	16	no	—
52	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
53	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
54	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂³×C₄×C₄₇	—	2	2	no	—
57	C₂³×C₄×C₄₇	D₄	1	2	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	AGL(1,ℤ/8)×C₄₇	—	2	64	no	—
60	C₂×SD₁₆×C₄₇	—	2	16	no	—
61	C₂×SD₁₆×C₄₇	C₂³	1	16	yes	complemented
62	C₂×D₈×C₄₇	—	2	16	no	—
63	C₂×D₈×C₄₇	C₂³	1	16	yes	complemented
64	C₂×M₁₆×C₄₇	—	2	8	no	—
65	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
66	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
67	#127×C₄₇	—	2	8	no	—
68	#127×C₄₇	—	2	8	no	—
69	#127×C₄₇	—	2	8	no	—
70	#127×C₄₇	C₂³	1	16	yes	—
71	C₄×Q₈×C₄₇	—	2	4	no	—
72	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
73	C₄×D₄×C₄₇	—	2	16	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₄×D₄×C₄₇	C₂³	1	8	yes	complemented
76	#117×C₄₇	—	2	2	no	—
77	#117×C₄₇	—	2	8	no	—
78	#117×C₄₇	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	1	no	—
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	—	2	8	no	—
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	4	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
91	C₄⋊C₈×C₄₇	C₂³	1	16	yes	complemented
92	#102×C₄₇	C₂³	1	32	yes	complemented
93	C₂⁴×C₄₇	—	2	1	no	—
94	C₂⁴×C₄₇	—	2	8	no	—
95	C₂⁴×C₄₇	—	2	4	no	—
96	C₂⁴×C₄₇	—	4	16	no	—
97	C₂⁴×C₄₇	—	4	8	no	—
98	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
99	#41×C₄₇	—	2	16	no	—
100	#41×C₄₇	—	2	8	no	—
101	#41×C₄₇	C₂×D₄	1	16	yes	complemented
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	complemented
105	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
106	C₂×D₄×C₄₇	—	2	8	no	—
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	8	no	—
110	C₂×D₄×C₄₇	—	2	16	no	—
111	C₂×D₄×C₄₇	—	2	8	no	—
112	C₂×D₄×C₄₇	—	2	4	no	—
113	C₂×D₄×C₄₇	—	2	16	no	—
114	C₂×D₄×C₄₇	—	2	16	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	8	no	—
117	C₂×D₄×C₄₇	—	2	16	no	—
118	C₂×D₄×C₄₇	—	4	16	no	—
119	C₂×D₄×C₄₇	—	4	64	no	—
120	C₂×D₄×C₄₇	—	4	8	no	—
121	C₂×D₄×C₄₇	—	4	16	no	—
122	C₂×D₄×C₄₇	—	4	16	no	—
123	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	complemented
124	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
125	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	8	no	—
128	C₂²×C₄×C₄₇	—	2	8	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	8	no	—
132	C₂²×C₄×C₄₇	—	4	8	no	—
133	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₇	#41	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₄₇	—	2	32	no	—
143	D₈×C₄₇	—	2	32	no	—
144	M₁₆×C₄₇	—	2	16	no	—
145	C₂×C₈×C₄₇	—	2	8	no	—
146	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
147	C₄⋊C₄×C₄₇	—	2	8	no	—
148	C₄⋊C₄×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₄₇	—	2	4	no	—
151	C₂²⋊C₄×C₄₇	—	2	8	no	—
152	C₄²×C₄₇	—	2	4	no	—
153	C₄²×C₄₇	—	2	8	no	—
154	C₄²×C₄₇	C₂×D₄	1	4	yes	—
155	C₄²×C₄₇	C₂×D₄	1	4	yes	—
156	C₄²×C₄₇	C₂×D₄	1	4	yes	—
157	C₄²×C₄₇	C₂⁴	1	4	yes	—
158	C₂³×C₄₇	—	2	4	no	—
159	C₂³×C₄₇	—	2	4	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	8	no	—
162	C₂³×C₄₇	—	4	32	no	—
163	C₂³×C₄₇	—	4	4	no	—
164	C₂³×C₄₇	—	4	16	no	—
165	C₂³×C₄₇	—	4	8	no	—
166	C₂³×C₄₇	—	4	16	no	—
167	C₂³×C₄₇	—	8	32	no	—
168	C₂³×C₄₇	#121	1	4	yes	—
169	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
170	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₇	—	2	4	no	—
172	Q₈×C₄₇	—	2	2	no	—
173	Q₈×C₄₇	C₂²×D₄	1	4	yes	complemented
174	D₄×C₄₇	—	2	16	no	—
175	D₄×C₄₇	—	2	4	no	—
176	D₄×C₄₇	—	2	8	no	—
177	D₄×C₄₇	—	2	2	no	—
178	D₄×C₄₇	—	2	8	no	—
179	D₄×C₄₇	—	4	32	no	—
180	D₄×C₄₇	—	4	16	no	—
181	D₄×C₄₇	—	4	8	no	—
182	D₄×C₄₇	—	4	32	no	—
183	D₄×C₄₇	C₂²×D₄	1	4	yes	complemented
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	16	no	—
188	C₂×C₄×C₄₇	—	2	16	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	—	4	16	no	—
192	C₂×C₄×C₄₇	#121	1	4	yes	—
193	C₂×C₄×C₄₇	#121	1	8	yes	—
194	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	8	yes	complemented
195	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
203	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
204	C₈×C₄₇	—	2	8	no	—
205	C₂×#3038	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₇	—	2	8	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	4	8	no	—
210	C₂²×C₄₇	—	4	4	no	—
211	C₂²×C₄₇	—	4	8	no	—
212	C₂²×C₄₇	—	4	16	no	—
213	C₂²×C₄₇	—	8	32	no	—
214	C₂²×C₄₇	—	8	16	no	—
215	C₂²×C₄₇	C₂×#121	1	4	yes	—
216	C₂²×C₄₇	C₂×#121	1	2	yes	—
217	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
218	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
219	C₄×C₄₇	—	2	4	no	—
220	C₄×C₄₇	—	2	4	no	—
221	C₄×C₄₇	—	4	4	no	—
222	C₄×C₄₇	C₂×#121	1	4	yes	—
223	C₄×C₄₇	C₂×#121	1	2	yes	—
224	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
225	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
227	C₂²×AGL(1,ℤ/8)	C₂×C₄₇	1	2	yes	complemented
228	C₂²×#127	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#3038	C₂×C₄₇	1	16	yes	direct product factor
231	C₂×#460	C₂×C₄₇	1	4	yes	complemented
232	C₂×#459	C₂×C₄₇	1	4	yes	complemented
233	C₂×#423	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂×#418	C₂×C₄₇	1	2	yes	complemented
235	C₂×C₄₇	—	2	4	no	—
236	C₂×C₄₇	—	4	4	no	—
237	C₂×C₄₇	—	8	8	no	—
238	C₂×C₄₇	#3038	1	4	yes	direct product factor
239	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
240	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	2	yes	—
241	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
242	C₂³×D₄	—	2	2	no	—
243	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
244	C₂×AGL(1,ℤ/8)	—	2	16	no	—
245	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	16	yes	complemented
246	C₂²×SD₁₆	C₂²×C₄₇	1	4	yes	complemented
247	C₂²×D₈	C₂²×C₄₇	1	4	yes	complemented
248	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
249	C₂×#127	—	2	1	no	—
250	C₂×#127	—	2	4	no	—
251	C₂×#127	—	2	1	no	—
252	C₂×#127	C₂²×C₄₇	1	4	yes	—
253	C₂×#127	C₂²×C₄₇	1	8	yes	complemented
254	C₄×#41	—	2	4	no	—
255	C₄×#41	C₂²×C₄₇	1	8	yes	complemented
256	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	complemented
257	C₂×C₄×D₄	—	2	2	no	—
258	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	complemented
259	C₂×#117	—	2	1	no	—
260	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
261	C₂²×C₄²	—	2	1	no	—
262	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
263	#460	C₂²×C₄₇	1	32	yes	complemented
264	#459	C₂²×C₄₇	1	32	yes	complemented
265	#423	C₂²×C₄₇	1	8	yes	complemented
266	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
267	#418	C₂²×C₄₇	1	16	yes	complemented
268	C₂×#102	C₂²×C₄₇	1	8	yes	complemented
269	C₄₇	C₂×#3038	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁵	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	D₄×C₄₇	1	8	yes	complemented
274	C₂×#41	C₂³×C₄₇	1	4	yes	—
275	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	8	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	4	no	—
280	C₂²×D₄	—	2	4	no	—
281	C₂²×D₄	—	2	4	no	—
282	C₂²×D₄	—	2	16	no	—
283	C₂²×D₄	—	2	8	no	—
284	C₂²×D₄	—	4	16	no	—
285	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
286	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
287	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	D₄×C₄₇	1	2	yes	—
291	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
292	AGL(1,ℤ/8)	—	2	64	no	—
293	C₂×SD₁₆	—	2	16	no	—
294	C₂×SD₁₆	C₂³×C₄₇	1	16	yes	complemented
295	C₂×D₈	—	2	16	no	—
296	C₂×D₈	C₂³×C₄₇	1	16	yes	complemented
297	C₂×M₁₆	—	2	8	no	—
298	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
299	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
300	#127	—	2	8	no	—
301	#127	—	2	8	no	—
302	#127	—	2	8	no	—
303	#127	C₂³×C₄₇	1	16	yes	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	C₂³×C₄₇	1	8	yes	complemented
306	C₄×D₄	—	2	16	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	C₂³×C₄₇	1	8	yes	complemented
309	#117	—	2	2	no	—
310	#117	—	2	8	no	—
311	#117	C₂³×C₄₇	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	8	no	—
319	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₄₇	1	4	yes	—
321	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
323	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
324	C₄⋊C₈	C₂³×C₄₇	1	16	yes	complemented
325	#102	C₂³×C₄₇	1	32	yes	complemented
326	C₂⁴	—	2	1	no	—
327	C₂⁴	—	2	8	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	4	16	no	—
330	C₂⁴	—	4	8	no	—
331	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
332	#41	—	2	16	no	—
333	#41	—	2	8	no	—
334	#41	C₂×D₄×C₄₇	1	16	yes	complemented
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	complemented
338	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	16	no	—
347	C₂×D₄	—	2	16	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	16	no	—
351	C₂×D₄	—	4	16	no	—
352	C₂×D₄	—	4	64	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	4	16	no	—
355	C₂×D₄	—	4	16	no	—
356	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	complemented
357	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
358	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
368	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
372	C₂²×C₄	#41×C₄₇	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
375	SD₁₆	—	2	32	no	—
376	D₈	—	2	32	no	—
377	M₁₆	—	2	16	no	—
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	C₂⁴×C₄₇	1	8	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	8	no	—
387	C₄²	C₂×D₄×C₄₇	1	4	yes	—
388	C₄²	C₂×D₄×C₄₇	1	4	yes	—
389	C₄²	C₂×D₄×C₄₇	1	4	yes	—
390	C₄²	C₂⁴×C₄₇	1	4	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	8	no	—
395	C₂³	—	4	32	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	16	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	16	no	—
400	C₂³	—	8	32	no	—
401	C₂³	#121×C₄₇	1	4	yes	—
402	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
403	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	C₂²×D₄×C₄₇	1	4	yes	complemented
407	D₄	—	2	16	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	8	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	8	no	—
412	D₄	—	4	32	no	—
413	D₄	—	4	16	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	32	no	—
416	D₄	C₂²×D₄×C₄₇	1	4	yes	complemented
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	16	no	—
421	C₂×C₄	—	2	16	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	#121×C₄₇	1	4	yes	—
426	C₂×C₄	#121×C₄₇	1	8	yes	—
427	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	8	yes	complemented
428	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
434	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
435	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
436	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
437	C₈	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	16	no	—
444	C₂²	—	4	8	no	—
445	C₂²	—	8	32	no	—
446	C₂²	—	8	16	no	—
447	C₂²	C₂×#121×C₄₇	1	4	yes	—
448	C₂²	C₂×#121×C₄₇	1	2	yes	—
449	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	4	yes	—
450	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	4	no	—
454	C₄	C₂×#121×C₄₇	1	4	yes	—
455	C₄	C₂×#121×C₄₇	1	2	yes	—
456	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	8	yes	complemented
457	C₄	C₂³×D₄×C₄₇	1	1	yes	characteristic
458	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	4	4	no	—
461	C₂	—	8	8	no	—
462	C₂	C₄₇×#3038	1	4	yes	direct product factor
463	C₂	C₂²×#121×C₄₇	1	1	yes	characteristic
464	C₂	C₂²×AGL(1,ℤ/8)×C₄₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
2. C₂²×#127×C₄₇	C₂	semidirect
3. C₂×C₄×#41×C₄₇	C₂	semidirect
4. C₄₇×#3038	C₂	direct (N × H)
5. C₂×C₄₇×#460	C₂	semidirect
6. C₂×C₄₇×#459	C₂	semidirect
7. C₂×C₄₇×#423	C₂	semidirect
8. C₂×C₄₇×#418	C₂	semidirect
13. C₂×AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
14. C₂²×SD₁₆×C₄₇	C₂²	semidirect
15. C₂²×D₈×C₄₇	C₂²	semidirect
21. C₂×#127×C₄₇	C₂²	semidirect
23. C₄×#41×C₄₇	C₂²	semidirect
24. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
26. C₂×C₄×D₄×C₄₇	C₂²	semidirect
31. C₄₇×#460	C₂²	semidirect
32. C₄₇×#459	C₂²	semidirect
33. C₄₇×#423	C₂²	semidirect
34. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
35. C₄₇×#418	C₂²	semidirect
36. C₂×#102×C₄₇	C₂²	semidirect
40. C₂×#41×C₄₇	D₄	semidirect
61. C₂×SD₁₆×C₄₇	C₂³	semidirect
63. C₂×D₈×C₄₇	C₂³	semidirect
72. C₄×Q₈×C₄₇	C₂³	semidirect
75. C₄×D₄×C₄₇	C₂³	semidirect
91. C₄⋊C₈×C₄₇	C₂³	semidirect
92. #102×C₄₇	C₂³	semidirect
101. #41×C₄₇	C₂×D₄	semidirect
104. C₂×Q₈×C₄₇	C₂×D₄	semidirect
123. C₂×D₄×C₄₇	C₂×D₄	semidirect
173. Q₈×C₄₇	C₂²×D₄	semidirect
183. D₄×C₄₇	C₂²×D₄	semidirect
194. C₂×C₄×C₄₇	AGL(1,ℤ/8)	semidirect
205. C₂×#3038	C₄₇	direct (N × H)
224. C₄×C₄₇	C₂×AGL(1,ℤ/8)	semidirect
227. C₂²×AGL(1,ℤ/8)	C₂×C₄₇	semidirect
228. C₂²×#127	C₂×C₄₇	semidirect
229. C₂×C₄×#41	C₂×C₄₇	semidirect
230. #3038	C₂×C₄₇	direct (N × H)
231. C₂×#460	C₂×C₄₇	semidirect
232. C₂×#459	C₂×C₄₇	semidirect
233. C₂×#423	C₂×C₄₇	semidirect
234. C₂×#418	C₂×C₄₇	semidirect
238. C₂×C₄₇	#3038	direct (N × H)
245. C₂×AGL(1,ℤ/8)	C₂²×C₄₇	semidirect
246. C₂²×SD₁₆	C₂²×C₄₇	semidirect
247. C₂²×D₈	C₂²×C₄₇	semidirect
253. C₂×#127	C₂²×C₄₇	semidirect
255. C₄×#41	C₂²×C₄₇	semidirect
256. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
258. C₂×C₄×D₄	C₂²×C₄₇	semidirect
263. #460	C₂²×C₄₇	semidirect
264. #459	C₂²×C₄₇	semidirect
265. #423	C₂²×C₄₇	semidirect
266. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
267. #418	C₂²×C₄₇	semidirect
268. C₂×#102	C₂²×C₄₇	semidirect
269. C₄₇	C₂×#3038	direct (N × H)
273. C₂×#41	D₄×C₄₇	semidirect
294. C₂×SD₁₆	C₂³×C₄₇	semidirect
296. C₂×D₈	C₂³×C₄₇	semidirect
305. C₄×Q₈	C₂³×C₄₇	semidirect
308. C₄×D₄	C₂³×C₄₇	semidirect
324. C₄⋊C₈	C₂³×C₄₇	semidirect
325. #102	C₂³×C₄₇	semidirect
334. #41	C₂×D₄×C₄₇	semidirect
337. C₂×Q₈	C₂×D₄×C₄₇	semidirect
356. C₂×D₄	C₂×D₄×C₄₇	semidirect
406. Q₈	C₂²×D₄×C₄₇	semidirect
416. D₄	C₂²×D₄×C₄₇	semidirect
427. C₂×C₄	AGL(1,ℤ/8)×C₄₇	semidirect
456. C₄	C₂×AGL(1,ℤ/8)×C₄₇	semidirect
462. C₂	C₄₇×#3038	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×AGL(1,ℤ/8)×C₄₇	2
C₂²×#127×C₄₇	2
C₂×C₄×#41×C₄₇	2
C₄₇×#3038	2
C₂×C₄₇×#460	2
C₂×C₄₇×#459	2
C₂×C₄₇×#423	2
C₂×C₄₇×#418	2
C₂×#3038	47

Subgroups — C2×C47×#3038 #26100110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3038 #26100110