Subgroups — C₄₇×#20378 #26060076

Order 12032.

1626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#408	C₂	1	2	yes	maximal
3	C₂×C₄₇×#405	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1750	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1749	C₂	1	2	yes	maximal, complemented
6	C₄×C₂²⋊C₈×C₄₇	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
12	C₄×#41×C₄₇	—	2	8	no	—
13	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	—
16	C₂×#117×C₄₇	C₂²	1	2	yes	—
17	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#408	C₄	1	16	yes	complemented
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
23	C₄₇×#405	—	2	8	no	—
24	C₂×#97×C₄₇	C₂²	1	4	yes	—
25	C₂×C₄×C₈×C₄₇	C₂²	1	4	yes	—
26	C₄₇×#336	C₂²	1	2	yes	—
27	C₄₇×#336	C₂²	1	2	yes	—
28	C₄₇×#336	C₂²	1	1	yes	characteristic
29	C₄₇×#336	C₂²	1	1	yes	characteristic
30	C₄₇×#336	C₂²	1	2	yes	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	—	2	2	no	—
33	C₂×#41×C₄₇	—	2	2	no	—
34	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₄₇	—	2	4	no	—
43	C₂×M₁₆×C₄₇	—	2	4	no	—
44	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	—	2	4	no	—
47	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
48	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
51	C₄×Q₈×C₄₇	—	2	8	no	—
52	C₄×D₄×C₄₇	—	2	8	no	—
53	C₄×D₄×C₄₇	—	2	16	no	—
54	#117×C₄₇	—	2	8	no	—
55	#117×C₄₇	D₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	2	8	no	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
67	C₂²⋊C₈×C₄₇	C₂×C₄	1	16	yes	complemented
68	C₂²⋊C₈×C₄₇	C₂×C₄	1	16	yes	complemented
69	#97×C₄₇	—	2	8	no	—
70	C₄×C₈×C₄₇	—	2	8	no	—
71	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	#41×C₄₇	—	2	16	no	—
74	#41×C₄₇	—	2	16	no	—
75	C₂×Q₈×C₄₇	—	2	2	no	—
76	C₂×Q₈×C₄₇	—	2	2	no	—
77	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
78	C₂×D₄×C₄₇	—	2	4	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	C₄²	1	8	yes	—
83	C₂×D₄×C₄₇	C₄²	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	4	4	no	—
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₄₇	—	2	16	no	—
105	C₂×C₈×C₄₇	—	2	16	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
115	C₄⋊C₄×C₄₇	—	2	8	no	—
116	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
117	C₂²⋊C₄×C₄₇	—	2	8	no	—
118	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
119	C₄²×C₄₇	—	2	8	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₂×D₄	1	8	yes	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
131	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₄₇	#117	1	2	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	2	8	no	—
136	D₄×C₄₇	—	2	16	no	—
137	D₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	2	8	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	4	16	no	—
150	C₂×C₄×C₄₇	—	4	8	no	—
151	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
152	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	#117	1	2	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
158	C₂×C₄×C₄₇	#131	1	4	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₈×C₄₇	—	2	4	no	—
164	C₈×C₄₇	—	2	4	no	—
165	C₈×C₄₇	—	2	8	no	—
166	#20378	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	4	4	no	—
175	C₂²×C₄₇	—	4	4	no	—
176	C₂²×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
177	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
178	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#131	1	2	yes	—
181	C₂²×C₄₇	#568	1	2	yes	—
182	C₄×C₄₇	—	2	4	no	—
183	C₄×C₄₇	—	2	8	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	4	2	no	—
186	C₄×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
187	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
188	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
189	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
190	C₂×#408	C₂×C₄₇	1	2	yes	—
191	C₂×#405	C₂×C₄₇	1	2	yes	complemented
192	#1750	C₂×C₄₇	1	4	yes	complemented
193	#1749	C₂×C₄₇	1	2	yes	complemented
194	C₄×C₂²⋊C₈	C₂×C₄₇	1	2	yes	complemented
195	#1728	C₂×C₄₇	1	1	yes	characteristic, complemented
196	C₂×#336	C₂×C₄₇	1	1	yes	characteristic, complemented
197	C₂×C₄₇	—	2	4	no	—
198	C₂×C₄₇	—	4	4	no	—
199	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
201	C₂×C₄₇	#2875	1	1	yes	characteristic
202	C₂×C₄₇	#2880	1	2	yes	—
203	C₂×C₄₇	#2925	1	2	yes	—
204	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
206	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
207	C₄×#41	—	2	8	no	—
208	C₂×C₄×Q₈	C₄×C₄₇	1	2	yes	—
209	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
210	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	—
211	C₂×#117	C₂²×C₄₇	1	2	yes	—
212	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
215	#408	C₄×C₄₇	1	16	yes	complemented
216	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
218	#405	—	2	8	no	—
219	C₂×#97	C₂²×C₄₇	1	4	yes	—
220	C₂×C₄×C₈	C₂²×C₄₇	1	4	yes	—
221	#336	C₂²×C₄₇	1	1	yes	characteristic
222	#336	C₂²×C₄₇	1	1	yes	characteristic
223	#336	C₂²×C₄₇	1	2	yes	—
224	#336	C₂²×C₄₇	1	2	yes	—
225	#336	C₂²×C₄₇	1	2	yes	—
226	C₄₇	#20378	1	1	yes	characteristic, direct product factor, Sylow
227	C₂×#41	—	2	4	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	C₂×C₄×C₄₇	1	8	yes	—
231	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
232	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
233	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
235	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
236	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	C₂×C₄×C₄₇	1	8	yes	complemented
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	C₂×C₄×C₄₇	1	8	yes	complemented
244	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
245	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
246	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
247	C₄×Q₈	—	2	8	no	—
248	C₄×D₄	—	2	8	no	—
249	C₄×D₄	—	2	16	no	—
250	#117	—	2	8	no	—
251	#117	D₄×C₄₇	1	8	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	—	2	8	no	—
258	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
259	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
260	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
263	C₂²⋊C₈	C₂×C₄×C₄₇	1	16	yes	complemented
264	C₂²⋊C₈	C₂×C₄×C₄₇	1	16	yes	complemented
265	#97	—	2	8	no	—
266	C₄×C₈	—	2	8	no	—
267	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
268	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
269	#41	—	2	16	no	—
270	#41	—	2	16	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₄²×C₄₇	1	4	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₄²×C₄₇	1	8	yes	—
279	C₂×D₄	C₄²×C₄₇	1	4	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
292	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
293	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
297	C₂²×C₄	#41×C₄₇	1	2	yes	—
298	C₂²×C₄	#41×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
300	M₁₆	—	2	16	no	—
301	C₂×C₈	—	2	16	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
309	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
310	C₂×C₈	C₂²×C₄×C₄₇	1	8	yes	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
315	C₄²	—	2	8	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂×D₄×C₄₇	1	8	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	C₂×C₄²×C₄₇	1	4	yes	—
327	C₂³	C₂×C₄²×C₄₇	1	2	yes	—
328	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
329	C₂³	#117×C₄₇	1	2	yes	—
330	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
331	Q₈	—	2	8	no	—
332	D₄	—	2	16	no	—
333	D₄	—	2	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	16	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
348	C₂×C₄	C₂×C₄²×C₄₇	1	2	yes	—
349	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
351	C₂×C₄	#117×C₄₇	1	2	yes	—
352	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
353	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
354	C₂×C₄	#131×C₄₇	1	4	yes	—
355	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
357	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	4	no	—
361	C₈	—	2	8	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	C₄×C₂²⋊C₄×C₄₇	1	4	yes	—
372	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
373	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
374	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
375	C₂²	C₂×#131×C₄₇	1	2	yes	—
376	C₂²	C₄₇×#568	1	2	yes	—
377	C₄	—	2	4	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	8	no	—
380	C₄	—	4	2	no	—
381	C₄	C₄×C₂²⋊C₄×C₄₇	1	4	yes	—
382	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
383	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
384	C₂	—	2	4	no	—
385	C₂	—	4	4	no	—
386	C₂	C₂×C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
387	C₂	C₄×#131×C₄₇	1	1	yes	characteristic
388	C₂	C₄₇×#2875	1	1	yes	characteristic
389	C₂	C₄₇×#2880	1	2	yes	—
390	C₂	C₄₇×#2925	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₇×#405	C₂	semidirect
4. C₄₇×#1750	C₂	semidirect
5. C₄₇×#1749	C₂	semidirect
6. C₄×C₂²⋊C₈×C₄₇	C₂	semidirect
7. C₄₇×#1728	C₂	semidirect
8. C₂×C₄₇×#336	C₂	semidirect
20. C₄₇×#408	C₄	semidirect
44. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
47. C₂²×C₈×C₄₇	C₂×C₄	semidirect
67. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
68. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
166. #20378	C₄₇	direct (N × H)
191. C₂×#405	C₂×C₄₇	semidirect
192. #1750	C₂×C₄₇	semidirect
193. #1749	C₂×C₄₇	semidirect
194. C₄×C₂²⋊C₈	C₂×C₄₇	semidirect
195. #1728	C₂×C₄₇	semidirect
196. C₂×#336	C₂×C₄₇	semidirect
215. #408	C₄×C₄₇	semidirect
226. C₄₇	#20378	direct (N × H)
240. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
243. C₂²×C₈	C₂×C₄×C₄₇	semidirect
263. C₂²⋊C₈	C₂×C₄×C₄₇	semidirect
264. C₂²⋊C₈	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₇	2
C₂×C₄₇×#408	2
C₂×C₄₇×#405	2
C₄₇×#1750	2
C₄₇×#1749	2
C₄×C₂²⋊C₈×C₄₇	2
C₄₇×#1728	2
C₂×C₄₇×#336	2
#20378	47

Subgroups — C47×#20378 #26060076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20378 #26060076