Subgroups — C₄₇×#22509 #26062207

Order 12032.

1064 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1985	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1984	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1798	C₂	1	2	yes	maximal
9	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1750	C₂	1	2	yes	maximal
11	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₄₇×#533	—	2	4	no	—
13	C₄₇×#533	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
16	C₂×#125×C₄₇	C₄	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
20	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#446	—	2	4	no	—
26	C₈×Q₈×C₄₇	—	2	4	no	—
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#336	C₂²	1	2	yes	—
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₇	—	2	4	no	—
58	C₄⋊Q₈×C₄₇	—	2	4	no	—
59	#125×C₄₇	—	2	8	no	—
60	C₂²⋊Q₈×C₄₇	—	2	4	no	—
61	C₂²⋊Q₈×C₄₇	—	2	4	no	—
62	C₂²⋊Q₈×C₄₇	—	2	8	no	—
63	C₄×Q₈×C₄₇	—	2	4	no	—
64	C₄×Q₈×C₄₇	—	2	4	no	—
65	C₄×Q₈×C₄₇	—	2	2	no	—
66	C₄×Q₈×C₄₇	—	2	2	no	—
67	C₄×Q₈×C₄₇	D₄	1	4	yes	—
68	C₄×Q₈×C₄₇	D₄	1	4	yes	—
69	#117×C₄₇	—	2	4	no	—
70	#117×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₄⋊C₈×C₄₇	—	2	2	no	—
91	C₄⋊C₈×C₄₇	—	2	4	no	—
92	C₄⋊C₈×C₄₇	—	2	2	no	—
93	C₄⋊C₈×C₄₇	—	2	4	no	—
94	C₂²⋊C₈×C₄₇	—	2	4	no	—
95	C₂²⋊C₈×C₄₇	—	2	2	no	—
96	C₂²⋊C₈×C₄₇	Q₈	1	4	yes	complemented
97	#97×C₄₇	—	2	4	no	—
98	C₄×C₈×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	—	2	4	no	—
100	C₄×C₈×C₄₇	—	2	2	no	—
101	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×Q₈×C₄₇	—	2	4	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	4	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	—	4	2	no	—
110	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	4	1	no	—
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	2	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₄₇	#41	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	1	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
150	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
151	C₄⋊C₄×C₄₇	—	2	4	no	—
152	C₄⋊C₄×C₄₇	—	2	4	no	—
153	C₄⋊C₄×C₄₇	—	2	4	no	—
154	C₄⋊C₄×C₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	2	4	no	—
156	C₄⋊C₄×C₄₇	—	2	4	no	—
157	C₄⋊C₄×C₄₇	—	2	2	no	—
158	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
159	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
160	C₂²⋊C₄×C₄₇	—	2	4	no	—
161	C₂²⋊C₄×C₄₇	—	2	4	no	—
162	C₄²×C₄₇	—	2	2	no	—
163	C₄²×C₄₇	—	2	2	no	—
164	C₄²×C₄₇	—	2	1	no	—
165	C₄²×C₄₇	—	2	1	no	—
166	C₄²×C₄₇	—	2	2	no	—
167	C₄²×C₄₇	—	2	2	no	—
168	C₄²×C₄₇	C₂×D₄	1	2	yes	—
169	C₄²×C₄₇	C₂×D₄	1	2	yes	—
170	C₄²×C₄₇	C₂×D₄	1	4	yes	—
171	C₄²×C₄₇	C₂×D₄	1	4	yes	—
172	C₂³×C₄₇	—	2	1	no	—
173	C₂³×C₄₇	—	2	1	no	—
174	C₂³×C₄₇	—	2	1	no	—
175	C₂³×C₄₇	—	2	1	no	—
176	C₂³×C₄₇	—	2	1	no	—
177	C₂³×C₄₇	—	2	1	no	—
178	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
179	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	8	no	—
181	Q₈×C₄₇	—	4	8	no	—
182	Q₈×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	4	4	no	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
213	C₂×C₄×C₄₇	#131	1	2	yes	—
214	C₂×C₄×C₄₇	#131	1	2	yes	—
215	C₂×C₄×C₄₇	#131	1	2	yes	—
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₄₇	—	2	2	no	—
223	C₈×C₄₇	—	2	2	no	—
224	C₈×C₄₇	—	4	2	no	—
225	C₈×C₄₇	—	4	1	no	—
226	C₈×C₄₇	—	4	1	no	—
227	C₈×C₄₇	—	4	2	no	—
228	#22509	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	4	1	no	—
233	C₂²×C₄₇	—	4	1	no	—
234	C₂²×C₄₇	—	4	1	no	—
235	C₂²×C₄₇	—	4	1	no	—
236	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
238	C₂²×C₄₇	#519	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
242	C₂²×C₄₇	#568	1	1	yes	characteristic
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	2	4	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	4	no	—
248	C₄×C₄₇	—	4	1	no	—
249	C₄×C₄₇	—	4	2	no	—
250	C₄×C₄₇	—	4	2	no	—
251	C₄×C₄₇	#408	1	4	yes	—
252	C₄×C₄₇	#548	1	1	yes	characteristic
253	C₄×C₄₇	#548	1	1	yes	characteristic
254	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
255	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
256	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
257	C₂×#446	C₂×C₄₇	1	1	yes	characteristic, complemented
258	C₂×C₈×Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
259	#1985	C₂×C₄₇	1	2	yes	complemented
260	#1984	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#1984	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#1984	C₂×C₄₇	1	2	yes	complemented
263	#1798	C₂×C₄₇	1	2	yes	—
264	#1797	C₂×C₄₇	1	1	yes	characteristic
265	#1750	C₂×C₄₇	1	2	yes	—
266	C₄×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
267	C₂×C₄₇	—	4	2	no	—
268	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
270	C₂×C₄₇	#2880	1	1	yes	characteristic
271	C₂×C₄₇	#2960	1	1	yes	characteristic
272	C₂×C₄₇	#2962	1	1	yes	characteristic
273	C₂×C₄₇	#2985	1	1	yes	characteristic
274	C₂×C₄₇	#2986	1	1	yes	characteristic
275	#533	—	2	4	no	—
276	#533	—	2	4	no	—
277	C₂×C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic
279	C₂×#125	C₄×C₄₇	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₄×C₄₇	1	1	yes	characteristic
281	C₂×C₂²⋊Q₈	C₄×C₄₇	1	1	yes	characteristic
282	C₂×C₂²⋊Q₈	C₄×C₄₇	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
284	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
286	C₂×#117	C₂²×C₄₇	1	2	yes	—
287	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
288	#446	—	2	4	no	—
289	C₈×Q₈	—	2	4	no	—
290	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
293	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
294	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
297	C₂×#97	C₂²×C₄₇	1	2	yes	—
298	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
301	#336	C₂²×C₄₇	1	2	yes	—
302	#336	C₂²×C₄₇	1	2	yes	—
303	#336	C₂²×C₄₇	1	2	yes	—
304	#336	C₂²×C₄₇	1	1	yes	characteristic
305	#336	C₂²×C₄₇	1	2	yes	—
306	#336	C₂²×C₄₇	1	2	yes	—
307	#336	C₂²×C₄₇	1	1	yes	characteristic
308	C₄₇	#22509	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
310	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
311	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
312	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
313	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
316	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
319	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
321	C₄⋊Q₈	—	2	4	no	—
322	C₄⋊Q₈	—	2	4	no	—
323	#125	—	2	8	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	D₄×C₄₇	1	4	yes	—
332	C₄×Q₈	D₄×C₄₇	1	4	yes	—
333	#117	—	2	4	no	—
334	#117	—	2	4	no	—
335	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
336	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
337	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
340	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
342	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
343	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
351	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
353	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	2	4	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	4	no	—
358	C₂²⋊C₈	—	2	4	no	—
359	C₂²⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	Q₈×C₄₇	1	4	yes	complemented
361	#97	—	2	4	no	—
362	C₄×C₈	—	2	2	no	—
363	C₄×C₈	—	2	4	no	—
364	C₄×C₈	—	2	2	no	—
365	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
388	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
391	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
394	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
395	C₂²×C₄	#41×C₄₇	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	C₂×Q₈×C₄₇	1	2	yes	—
414	C₂×C₈	C₂×Q₈×C₄₇	1	2	yes	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
423	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₂×D₄×C₄₇	1	2	yes	—
433	C₄²	C₂×D₄×C₄₇	1	2	yes	—
434	C₄²	C₂×D₄×C₄₇	1	4	yes	—
435	C₄²	C₂×D₄×C₄₇	1	4	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	C₄×Q₈×C₄₇	1	2	yes	—
443	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
444	Q₈	—	2	8	no	—
445	Q₈	—	4	8	no	—
446	Q₈	—	4	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
473	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
474	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
475	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
476	C₂×C₄	C₄×Q₈×C₄₇	1	2	yes	—
477	C₂×C₄	#131×C₄₇	1	2	yes	—
478	C₂×C₄	#131×C₄₇	1	2	yes	—
479	C₂×C₄	#131×C₄₇	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
484	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
485	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
500	C₂²	C₂×C₄×Q₈×C₄₇	1	1	yes	characteristic
501	C₂²	C₄₇×#519	1	1	yes	characteristic
502	C₂²	C₂×#131×C₄₇	1	1	yes	characteristic
503	C₂²	C₂×#131×C₄₇	1	1	yes	characteristic
504	C₂²	C₂×#131×C₄₇	1	1	yes	characteristic
505	C₂²	C₄₇×#568	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	C₄₇×#408	1	4	yes	—
515	C₄	C₄₇×#548	1	1	yes	characteristic
516	C₄	C₄₇×#548	1	1	yes	characteristic
517	C₄	D₄×Q₈×C₄₇	1	1	yes	characteristic
518	C₄	D₄×Q₈×C₄₇	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	Q₈×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
521	C₂	C₂×C₄₇×#408	1	1	yes	characteristic
522	C₂	C₄₇×#2880	1	1	yes	characteristic
523	C₂	C₄₇×#2960	1	1	yes	characteristic
524	C₂	C₄₇×#2962	1	1	yes	characteristic
525	C₂	C₄₇×#2985	1	1	yes	characteristic
526	C₂	C₄₇×#2986	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#446	C₂	semidirect
3. C₂×C₈×Q₈×C₄₇	C₂	semidirect
4. C₄₇×#1985	C₂	semidirect
5. C₄₇×#1984	C₂	semidirect
6. C₄₇×#1984	C₂	semidirect
7. C₄₇×#1984	C₂	semidirect
96. C₂²⋊C₈×C₄₇	Q₈	semidirect
228. #22509	C₄₇	direct (N × H)
257. C₂×#446	C₂×C₄₇	semidirect
258. C₂×C₈×Q₈	C₂×C₄₇	semidirect
259. #1985	C₂×C₄₇	semidirect
260. #1984	C₂×C₄₇	semidirect
261. #1984	C₂×C₄₇	semidirect
262. #1984	C₂×C₄₇	semidirect
308. C₄₇	#22509	direct (N × H)
360. C₂²⋊C₈	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#533	2
C₂×C₄₇×#446	2
C₂×C₈×Q₈×C₄₇	2
C₄₇×#1985	2
C₄₇×#1984	2
C₄₇×#1798	2
C₄₇×#1797	2
C₄₇×#1750	2
C₄×C₂²⋊C₈×C₄₇	2
#22509	47

Subgroups — C47×#22509 #26062207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22509 #26062207