Subgroups — C₄₇×#34397 #26074095

Order 12032.

2090 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2383	C₂	1	4	yes	maximal, complemented
3	C₄₇×#2370	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2346	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2343	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2335	C₂	1	4	yes	maximal, complemented
12	C₄₇×#2324	C₂	1	2	yes	maximal
13	C₄₇×#2323	C₂	1	2	yes	maximal, complemented
14	C₄₇×#2319	C₂	1	2	yes	maximal, complemented
15	C₄₇×#2318	C₂	1	2	yes	maximal, complemented
16	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₇×#529	C₄	1	16	yes	complemented
19	C₂×#126×C₄₇	C₂²	1	2	yes	—
20	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
30	C₂×#117×C₄₇	C₂²	1	2	yes	—
31	C₂×#117×C₄₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#391	C₂²	1	2	yes	—
34	C₄₇×#390	C₂²	1	4	yes	—
35	C₄₇×#390	C₂²	1	2	yes	—
36	C₄₇×#389	C₂²	1	4	yes	—
37	C₄₇×#389	C₂²	1	4	yes	—
38	C₄₇×#389	C₂²	1	2	yes	—
39	C₄₇×#389	C₂²	1	2	yes	—
40	C₄₇×#389	C₂²	1	4	yes	—
41	C₄₇×#388	C₂²	1	4	yes	—
42	C₄₇×#388	C₂²	1	4	yes	—
43	C₄₇×#388	C₂²	1	4	yes	—
44	C₄₇×#388	C₂²	1	4	yes	—
45	C₄₇×#388	C₂²	1	4	yes	—
46	C₄₇×#388	C₂²	1	4	yes	—
47	C₄₇×#387	C₂²	1	4	yes	—
48	C₄₇×#387	C₂²	1	4	yes	—
49	C₄₇×#387	C₂²	1	4	yes	—
50	C₄₇×#387	C₂²	1	4	yes	—
51	C₄₇×#386	C₂²	1	4	yes	—
52	C₄₇×#385	C₂²	1	4	yes	—
53	C₄₇×#385	C₂²	1	4	yes	—
54	C₄₇×#385	C₂²	1	4	yes	—
55	C₄₇×#384	C₂²	1	2	yes	—
56	C₄₇×#383	C₂²	1	2	yes	—
57	C₄₇×#383	C₂²	1	2	yes	—
58	C₄₇×#382	C₂²	1	1	yes	characteristic
59	C₄₇×#382	C₂²	1	1	yes	characteristic
60	C₄₇×#382	C₂²	1	1	yes	characteristic
61	C₄₇×#382	C₂²	1	1	yes	characteristic
62	C₄₇×#382	C₂²	1	2	yes	—
63	C₄₇×#381	C₂²	1	2	yes	—
64	C₄₇×#381	C₂²	1	2	yes	—
65	C₄₇×#380	C₂²	1	2	yes	—
66	C₄₇×#380	C₂²	1	1	yes	characteristic
67	C₄₇×#380	C₂²	1	1	yes	characteristic
68	C₄₇×#380	C₂²	1	2	yes	—
69	C₄₇×#380	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
81	C₄₇×#376	C₂²	1	2	yes	—
82	C₄₇×#376	C₂²	1	2	yes	—
83	C₂×#95×C₄₇	C₂²	1	2	yes	—
84	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
92	#126×C₄₇	C₂×C₄	1	16	yes	complemented
93	#125×C₄₇	C₂×C₄	1	8	yes	complemented
94	#124×C₄₇	C₂×C₄	1	8	yes	—
95	#123×C₄₇	C₂×C₄	1	16	yes	complemented
96	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
97	#121×C₄₇	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₄₇	—	4	4	no	—
99	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₄₇	—	4	4	no	—
101	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
103	#117×C₄₇	—	4	4	no	—
104	#117×C₄₇	C₂×C₄	1	16	yes	complemented
105	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
133	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
145	#95×C₄₇	C₂³	1	1	yes	characteristic
146	#95×C₄₇	C₂³	1	2	yes	—
147	#95×C₄₇	C₂³	1	4	yes	—
148	#95×C₄₇	C₂³	1	2	yes	—
149	#95×C₄₇	C₂³	1	1	yes	characteristic
150	#95×C₄₇	C₂³	1	4	yes	—
151	#95×C₄₇	C₂³	1	4	yes	—
152	#95×C₄₇	C₂³	1	1	yes	characteristic
153	#95×C₄₇	C₂³	1	2	yes	—
154	#95×C₄₇	C₂³	1	2	yes	—
155	#95×C₄₇	C₂³	1	2	yes	—
156	#95×C₄₇	C₂³	1	4	yes	—
157	#95×C₄₇	C₂³	1	1	yes	characteristic
158	#95×C₄₇	C₂³	1	2	yes	—
159	#95×C₄₇	C₂³	1	4	yes	—
160	#95×C₄₇	C₂³	1	4	yes	—
161	#95×C₄₇	C₂³	1	4	yes	—
162	#95×C₄₇	C₂³	1	4	yes	—
163	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₄₇	—	2	2	no	—
166	C₂×Q₈×C₄₇	—	2	2	no	—
167	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
168	C₂×D₄×C₄₇	—	2	2	no	—
169	C₂×D₄×C₄₇	—	2	2	no	—
170	C₂×D₄×C₄₇	—	4	4	no	—
171	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₄₇	—	2	2	no	—
174	C₂²×C₄×C₄₇	—	2	2	no	—
175	C₂²×C₄×C₄₇	—	4	2	no	—
176	C₂²×C₄×C₄₇	—	4	4	no	—
177	C₂²×C₄×C₄₇	—	4	2	no	—
178	C₂²×C₄×C₄₇	—	4	4	no	—
179	C₂²×C₄×C₄₇	—	4	4	no	—
180	C₂²×C₄×C₄₇	—	4	4	no	—
181	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
185	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₄₇	—	2	4	no	—
201	C₄⋊C₄×C₄₇	—	2	4	no	—
202	C₄⋊C₄×C₄₇	—	4	4	no	—
203	C₄⋊C₄×C₄₇	—	4	4	no	—
204	C₄⋊C₄×C₄₇	—	4	2	no	—
205	C₄⋊C₄×C₄₇	—	4	2	no	—
206	C₄⋊C₄×C₄₇	—	4	2	no	—
207	C₄⋊C₄×C₄₇	—	4	2	no	—
208	C₄⋊C₄×C₄₇	—	4	2	no	—
209	C₄⋊C₄×C₄₇	—	4	2	no	—
210	C₄⋊C₄×C₄₇	—	4	4	no	—
211	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
217	C₂²⋊C₄×C₄₇	—	4	4	no	—
218	C₂²⋊C₄×C₄₇	—	4	4	no	—
219	C₂²⋊C₄×C₄₇	—	4	4	no	—
220	C₂²⋊C₄×C₄₇	—	4	2	no	—
221	C₂²⋊C₄×C₄₇	—	4	2	no	—
222	C₂²⋊C₄×C₄₇	—	4	4	no	—
223	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
228	C₄²×C₄₇	—	2	4	no	—
229	C₄²×C₄₇	—	2	4	no	—
230	C₄²×C₄₇	—	4	4	no	—
231	C₄²×C₄₇	—	4	4	no	—
232	C₄²×C₄₇	—	4	4	no	—
233	C₄²×C₄₇	—	4	4	no	—
234	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
235	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
236	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
237	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
238	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
239	C₂³×C₄₇	—	2	1	no	—
240	C₂³×C₄₇	—	2	2	no	—
241	C₂³×C₄₇	—	2	1	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	2	no	—
244	C₂³×C₄₇	—	2	4	no	—
245	C₂³×C₄₇	—	2	4	no	—
246	C₂³×C₄₇	—	2	2	no	—
247	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
248	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
249	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
250	Q₈×C₄₇	—	2	8	no	—
251	D₄×C₄₇	—	2	8	no	—
252	D₄×C₄₇	—	4	8	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	1	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	4	no	—
259	C₂×C₄×C₄₇	—	2	4	no	—
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	2	no	—
262	C₂×C₄×C₄₇	—	2	2	no	—
263	C₂×C₄×C₄₇	—	2	8	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	2	no	—
268	C₂×C₄×C₄₇	—	2	4	no	—
269	C₂×C₄×C₄₇	—	2	4	no	—
270	C₂×C₄×C₄₇	—	2	4	no	—
271	C₂×C₄×C₄₇	—	2	2	no	—
272	C₂×C₄×C₄₇	—	2	2	no	—
273	C₂×C₄×C₄₇	—	2	4	no	—
274	C₂×C₄×C₄₇	—	2	4	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	2	no	—
277	C₂×C₄×C₄₇	—	2	4	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	2	no	—
280	C₂×C₄×C₄₇	—	2	2	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	4	4	no	—
283	C₂×C₄×C₄₇	—	4	8	no	—
284	C₂×C₄×C₄₇	—	4	4	no	—
285	C₂×C₄×C₄₇	—	8	8	no	—
286	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
296	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
297	#34397	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	2	4	no	—
300	C₂²×C₄₇	—	2	2	no	—
301	C₂²×C₄₇	—	2	2	no	—
302	C₂²×C₄₇	—	2	4	no	—
303	C₂²×C₄₇	—	2	4	no	—
304	C₂²×C₄₇	—	4	4	no	—
305	C₂²×C₄₇	—	4	2	no	—
306	C₂²×C₄₇	—	4	2	no	—
307	C₂²×C₄₇	—	4	4	no	—
308	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
309	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂²×C₄₇	#585	1	2	yes	—
312	C₂²×C₄₇	#585	1	2	yes	—
313	C₄×C₄₇	—	2	2	no	—
314	C₄×C₄₇	—	2	4	no	—
315	C₄×C₄₇	—	2	2	no	—
316	C₄×C₄₇	—	2	2	no	—
317	C₄×C₄₇	—	2	4	no	—
318	C₄×C₄₇	—	2	2	no	—
319	C₄×C₄₇	—	2	2	no	—
320	C₄×C₄₇	—	2	4	no	—
321	C₄×C₄₇	—	4	2	no	—
322	C₄×C₄₇	—	4	2	no	—
323	C₄×C₄₇	—	4	2	no	—
324	C₄×C₄₇	—	4	4	no	—
325	C₄×C₄₇	—	4	2	no	—
326	C₄×C₄₇	—	4	4	no	—
327	C₄×C₄₇	#520	1	4	yes	—
328	C₂×#529	C₂×C₄₇	1	1	yes	characteristic
329	#2383	C₂×C₄₇	1	4	yes	complemented
330	#2370	C₂×C₄₇	1	2	yes	complemented
331	#2367	C₂×C₄₇	1	2	yes	complemented
332	#2357	C₂×C₄₇	1	1	yes	characteristic, complemented
333	#2356	C₂×C₄₇	1	1	yes	characteristic, complemented
334	#2351	C₂×C₄₇	1	1	yes	characteristic, complemented
335	#2349	C₂×C₄₇	1	1	yes	characteristic, complemented
336	#2346	C₂×C₄₇	1	2	yes	complemented
337	#2343	C₂×C₄₇	1	2	yes	complemented
338	#2335	C₂×C₄₇	1	4	yes	complemented
339	#2324	C₂×C₄₇	1	2	yes	—
340	#2323	C₂×C₄₇	1	2	yes	complemented
341	#2319	C₂×C₄₇	1	2	yes	complemented
342	#2318	C₂×C₄₇	1	2	yes	complemented
343	#2285	C₂×C₄₇	1	1	yes	characteristic, complemented
344	#2283	C₂×C₄₇	1	1	yes	characteristic, complemented
345	C₂×C₄₇	—	4	2	no	—
346	C₂×C₄₇	—	4	4	no	—
347	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
348	C₂×C₄₇	#3428	1	1	yes	characteristic
349	C₂×C₄₇	#3428	1	1	yes	characteristic
350	C₂×C₄₇	#3551	1	2	yes	—
351	C₂×C₄₇	#3557	1	2	yes	—
352	#529	C₄×C₄₇	1	16	yes	complemented
353	C₂×#126	C₂²×C₄₇	1	2	yes	—
354	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
355	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
356	C₂×#123	C₂²×C₄₇	1	2	yes	—
357	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
358	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
360	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
362	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
364	C₂×#117	C₂²×C₄₇	1	2	yes	—
365	C₂×#117	C₂²×C₄₇	1	2	yes	—
366	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
367	#391	C₂²×C₄₇	1	2	yes	—
368	#390	C₂²×C₄₇	1	4	yes	—
369	#390	C₂²×C₄₇	1	2	yes	—
370	#389	C₂²×C₄₇	1	4	yes	—
371	#389	C₂²×C₄₇	1	4	yes	—
372	#389	C₂²×C₄₇	1	2	yes	—
373	#389	C₂²×C₄₇	1	2	yes	—
374	#389	C₂²×C₄₇	1	4	yes	—
375	#388	C₂²×C₄₇	1	4	yes	—
376	#388	C₂²×C₄₇	1	4	yes	—
377	#388	C₂²×C₄₇	1	4	yes	—
378	#388	C₂²×C₄₇	1	4	yes	—
379	#388	C₂²×C₄₇	1	4	yes	—
380	#388	C₂²×C₄₇	1	4	yes	—
381	#387	C₂²×C₄₇	1	4	yes	—
382	#387	C₂²×C₄₇	1	4	yes	—
383	#387	C₂²×C₄₇	1	4	yes	—
384	#387	C₂²×C₄₇	1	4	yes	—
385	#386	C₂²×C₄₇	1	4	yes	—
386	#385	C₂²×C₄₇	1	4	yes	—
387	#385	C₂²×C₄₇	1	4	yes	—
388	#385	C₂²×C₄₇	1	4	yes	—
389	#384	C₂²×C₄₇	1	2	yes	—
390	#383	C₂²×C₄₇	1	2	yes	—
391	#383	C₂²×C₄₇	1	2	yes	—
392	#382	C₂²×C₄₇	1	2	yes	—
393	#382	C₂²×C₄₇	1	1	yes	characteristic
394	#382	C₂²×C₄₇	1	1	yes	characteristic
395	#382	C₂²×C₄₇	1	1	yes	characteristic
396	#382	C₂²×C₄₇	1	1	yes	characteristic
397	#381	C₂²×C₄₇	1	2	yes	—
398	#381	C₂²×C₄₇	1	2	yes	—
399	#380	C₂²×C₄₇	1	1	yes	characteristic
400	#380	C₂²×C₄₇	1	1	yes	characteristic
401	#380	C₂²×C₄₇	1	2	yes	—
402	#380	C₂²×C₄₇	1	2	yes	—
403	#380	C₂²×C₄₇	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
408	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
415	#376	C₂²×C₄₇	1	2	yes	—
416	#376	C₂²×C₄₇	1	2	yes	—
417	C₂×#95	C₂²×C₄₇	1	2	yes	—
418	C₄₇	#34397	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
422	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
424	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
425	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
427	#126	C₂×C₄×C₄₇	1	16	yes	complemented
428	#125	C₂×C₄×C₄₇	1	8	yes	complemented
429	#124	C₂×C₄×C₄₇	1	8	yes	—
430	#123	C₂×C₄×C₄₇	1	16	yes	complemented
431	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
432	#121	C₂×C₄×C₄₇	1	8	yes	—
433	C₄×Q₈	—	4	4	no	—
434	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
435	C₄×D₄	—	4	4	no	—
436	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
437	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
438	#117	—	4	4	no	—
439	#117	C₂×C₄×C₄₇	1	16	yes	complemented
440	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
468	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	complemented
469	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
470	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
471	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
472	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
473	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
474	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
475	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
477	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
480	#95	C₂³×C₄₇	1	1	yes	characteristic
481	#95	C₂³×C₄₇	1	2	yes	—
482	#95	C₂³×C₄₇	1	4	yes	—
483	#95	C₂³×C₄₇	1	2	yes	—
484	#95	C₂³×C₄₇	1	1	yes	characteristic
485	#95	C₂³×C₄₇	1	4	yes	—
486	#95	C₂³×C₄₇	1	4	yes	—
487	#95	C₂³×C₄₇	1	1	yes	characteristic
488	#95	C₂³×C₄₇	1	2	yes	—
489	#95	C₂³×C₄₇	1	2	yes	—
490	#95	C₂³×C₄₇	1	2	yes	—
491	#95	C₂³×C₄₇	1	4	yes	—
492	#95	C₂³×C₄₇	1	1	yes	characteristic
493	#95	C₂³×C₄₇	1	2	yes	—
494	#95	C₂³×C₄₇	1	4	yes	—
495	#95	C₂³×C₄₇	1	4	yes	—
496	#95	C₂³×C₄₇	1	4	yes	—
497	#95	C₂³×C₄₇	1	4	yes	—
498	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
507	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	4	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
517	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
519	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
520	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	4	4	no	—
538	C₄⋊C₄	—	4	4	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
547	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
548	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
549	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
550	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	4	4	no	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
570	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
571	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
572	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
573	C₄²	C₂²×C₄×C₄₇	1	8	yes	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	2	no	—
582	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
583	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
584	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
585	Q₈	—	2	8	no	—
586	D₄	—	2	8	no	—
587	D₄	—	4	8	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	8	8	no	—
621	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
629	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
630	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
631	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
643	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
644	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
645	C₂²	C₄₇×#585	1	2	yes	—
646	C₂²	C₄₇×#585	1	2	yes	—
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	4	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	C₄₇×#520	1	4	yes	—
662	C₂	—	4	2	no	—
663	C₂	—	4	4	no	—
664	C₂	C₂×C₄₇×#520	1	1	yes	characteristic
665	C₂	C₄₇×#3428	1	1	yes	characteristic
666	C₂	C₄₇×#3428	1	1	yes	characteristic
667	C₂	C₄₇×#3551	1	2	yes	—
668	C₂	C₄₇×#3557	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2383	C₂	semidirect
3. C₄₇×#2370	C₂	semidirect
4. C₄₇×#2367	C₂	semidirect
5. C₄₇×#2357	C₂	semidirect
6. C₄₇×#2356	C₂	semidirect
7. C₄₇×#2351	C₂	semidirect
8. C₄₇×#2349	C₂	semidirect
9. C₄₇×#2346	C₂	semidirect
10. C₄₇×#2343	C₂	semidirect
11. C₄₇×#2335	C₂	semidirect
13. C₄₇×#2323	C₂	semidirect
14. C₄₇×#2319	C₂	semidirect
15. C₄₇×#2318	C₂	semidirect
16. C₄₇×#2285	C₂	semidirect
17. C₄₇×#2283	C₂	semidirect
18. C₄₇×#529	C₄	semidirect
92. #126×C₄₇	C₂×C₄	semidirect
93. #125×C₄₇	C₂×C₄	semidirect
95. #123×C₄₇	C₂×C₄	semidirect
96. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
99. C₄×Q₈×C₄₇	C₂×C₄	semidirect
102. C₄×D₄×C₄₇	C₂×C₄	semidirect
104. #117×C₄₇	C₂×C₄	semidirect
133. C₂×C₄²×C₄₇	C₂×C₄	semidirect
297. #34397	C₄₇	direct (N × H)
329. #2383	C₂×C₄₇	semidirect
330. #2370	C₂×C₄₇	semidirect
331. #2367	C₂×C₄₇	semidirect
332. #2357	C₂×C₄₇	semidirect
333. #2356	C₂×C₄₇	semidirect
334. #2351	C₂×C₄₇	semidirect
335. #2349	C₂×C₄₇	semidirect
336. #2346	C₂×C₄₇	semidirect
337. #2343	C₂×C₄₇	semidirect
338. #2335	C₂×C₄₇	semidirect
340. #2323	C₂×C₄₇	semidirect
341. #2319	C₂×C₄₇	semidirect
342. #2318	C₂×C₄₇	semidirect
343. #2285	C₂×C₄₇	semidirect
344. #2283	C₂×C₄₇	semidirect
352. #529	C₄×C₄₇	semidirect
418. C₄₇	#34397	direct (N × H)
427. #126	C₂×C₄×C₄₇	semidirect
428. #125	C₂×C₄×C₄₇	semidirect
430. #123	C₂×C₄×C₄₇	semidirect
431. C₂²⋊Q₈	C₂×C₄×C₄₇	semidirect
434. C₄×Q₈	C₂×C₄×C₄₇	semidirect
437. C₄×D₄	C₂×C₄×C₄₇	semidirect
439. #117	C₂×C₄×C₄₇	semidirect
468. C₂×C₄²	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×C₄₇×#529	2
C₄₇×#2383	2
C₄₇×#2370	2
C₄₇×#2367	2
C₄₇×#2357	2
C₄₇×#2356	2
C₄₇×#2351	2
C₄₇×#2349	2
C₄₇×#2346	2
C₄₇×#2343	2
C₄₇×#2335	2
C₄₇×#2324	2
C₄₇×#2323	2
C₄₇×#2319	2
C₄₇×#2318	2
C₄₇×#2285	2
C₄₇×#2283	2
#34397	47

Subgroups — C47×#34397 #26074095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#34397 #26074095