Subgroups — C₄×C₄₇×#388 #26053461

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#388	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄³×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1437	C₂	1	2	yes	maximal
8	C₄₇×#1436	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1434	C₂	1	2	yes	maximal, complemented
10	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#388	C₄	1	16	yes	direct product factor
27	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
28	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
29	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
30	C₄×C₂²⋊C₄×C₄₇	C₄	1	8	yes	complemented
31	C₂×#95×C₄₇	C₂²	1	2	yes	—
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	2	yes	—
34	C₂×#95×C₄₇	C₂²	1	2	yes	—
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₄³×C₄₇	—	2	4	no	—
41	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	—	2	2	no	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	—	2	2	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
62	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
72	C₂×C₄²×C₄₇	—	2	4	no	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	4	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	—	2	2	no	—
77	C₂×C₄²×C₄₇	—	2	4	no	—
78	C₂×C₄²×C₄₇	—	2	4	no	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	—	2	4	no	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
93	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₂×C₄²×C₄₇	D₄	1	4	yes	—
95	C₂×C₄²×C₄₇	D₄	1	4	yes	—
96	#95×C₄₇	—	2	4	no	—
97	#95×C₄₇	—	2	4	no	—
98	#95×C₄₇	—	2	4	no	—
99	#95×C₄₇	—	2	4	no	—
100	#95×C₄₇	—	2	4	no	—
101	#95×C₄₇	C₂×C₄	1	4	yes	—
102	#95×C₄₇	C₂×C₄	1	4	yes	—
103	#95×C₄₇	C₂×C₄	1	8	yes	complemented
104	#95×C₄₇	C₂×C₄	1	8	yes	complemented
105	C₂⁴×C₄₇	—	2	1	no	—
106	C₂⁴×C₄₇	—	2	1	no	—
107	C₂⁴×C₄₇	—	2	2	no	—
108	C₂⁴×C₄₇	—	2	2	no	—
109	C₂⁴×C₄₇	—	2	2	no	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	1	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	8	no	—
157	C₂²×C₄×C₄₇	—	2	8	no	—
158	C₂²×C₄×C₄₇	—	2	8	no	—
159	C₂²×C₄×C₄₇	—	4	4	no	—
160	C₂²×C₄×C₄₇	—	4	4	no	—
161	C₂²×C₄×C₄₇	—	4	4	no	—
162	C₂²×C₄×C₄₇	—	4	4	no	—
163	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₇	#41	1	4	yes	—
180	C₂²×C₄×C₄₇	#41	1	4	yes	—
181	C₂²×C₄×C₄₇	#41	1	4	yes	—
182	C₂²×C₄×C₄₇	#41	1	2	yes	—
183	C₂²×C₄×C₄₇	#41	1	2	yes	—
184	C₂²×C₄×C₄₇	#41	1	2	yes	—
185	C₂²×C₄×C₄₇	#41	1	2	yes	—
186	C₄⋊C₄×C₄₇	—	2	16	no	—
187	C₂²⋊C₄×C₄₇	—	2	8	no	—
188	C₂²⋊C₄×C₄₇	—	2	16	no	—
189	C₂²⋊C₄×C₄₇	—	2	16	no	—
190	C₂²⋊C₄×C₄₇	C₄²	1	16	yes	complemented
191	C₄²×C₄₇	—	2	16	no	—
192	C₄²×C₄₇	—	2	8	no	—
193	C₄²×C₄₇	—	2	8	no	—
194	C₄²×C₄₇	—	2	16	no	—
195	C₄²×C₄₇	—	2	8	no	—
196	C₄²×C₄₇	—	2	8	no	—
197	C₄²×C₄₇	—	4	4	no	—
198	C₄²×C₄₇	—	4	4	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	2	4	no	—
202	C₂³×C₄₇	—	2	4	no	—
203	C₂³×C₄₇	—	2	2	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	4	no	—
206	C₂³×C₄₇	—	2	4	no	—
207	C₂³×C₄₇	—	2	4	no	—
208	C₂³×C₄₇	—	2	4	no	—
209	C₂³×C₄₇	—	2	2	no	—
210	C₂³×C₄₇	—	2	2	no	—
211	C₂³×C₄₇	—	4	1	no	—
212	C₂³×C₄₇	—	4	1	no	—
213	C₂³×C₄₇	—	4	2	no	—
214	C₂³×C₄₇	—	4	1	no	—
215	C₂³×C₄₇	—	4	1	no	—
216	C₂³×C₄₇	—	4	2	no	—
217	C₂³×C₄₇	—	4	2	no	—
218	C₂³×C₄₇	—	4	2	no	—
219	C₂³×C₄₇	—	4	2	no	—
220	C₂³×C₄₇	—	4	2	no	—
221	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
222	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
224	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
227	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
228	C₂³×C₄₇	C₂×#41	1	2	yes	—
229	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
230	C₂³×C₄₇	C₂×#41	1	2	yes	—
231	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
232	C₂³×C₄₇	C₂×#41	1	2	yes	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	4	no	—
245	C₂×C₄×C₄₇	—	2	4	no	—
246	C₂×C₄×C₄₇	—	2	4	no	—
247	C₂×C₄×C₄₇	—	2	4	no	—
248	C₂×C₄×C₄₇	—	2	4	no	—
249	C₂×C₄×C₄₇	—	2	4	no	—
250	C₂×C₄×C₄₇	—	2	4	no	—
251	C₂×C₄×C₄₇	—	2	4	no	—
252	C₂×C₄×C₄₇	—	2	4	no	—
253	C₂×C₄×C₄₇	—	2	4	no	—
254	C₂×C₄×C₄₇	—	2	4	no	—
255	C₂×C₄×C₄₇	—	2	4	no	—
256	C₂×C₄×C₄₇	—	2	4	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	2	no	—
260	C₂×C₄×C₄₇	—	2	4	no	—
261	C₂×C₄×C₄₇	—	2	4	no	—
262	C₂×C₄×C₄₇	—	2	4	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	4	no	—
267	C₂×C₄×C₄₇	—	2	4	no	—
268	C₂×C₄×C₄₇	—	2	4	no	—
269	C₂×C₄×C₄₇	—	4	2	no	—
270	C₂×C₄×C₄₇	—	4	1	no	—
271	C₂×C₄×C₄₇	—	4	1	no	—
272	C₂×C₄×C₄₇	—	4	2	no	—
273	C₂×C₄×C₄₇	—	4	2	no	—
274	C₂×C₄×C₄₇	—	4	1	no	—
275	C₂×C₄×C₄₇	—	4	1	no	—
276	C₂×C₄×C₄₇	—	4	2	no	—
277	C₂×C₄×C₄₇	—	4	2	no	—
278	C₂×C₄×C₄₇	—	4	2	no	—
279	C₂×C₄×C₄₇	—	4	2	no	—
280	C₂×C₄×C₄₇	—	4	2	no	—
281	C₂×C₄×C₄₇	—	4	2	no	—
282	C₂×C₄×C₄₇	—	4	2	no	—
283	C₂×C₄×C₄₇	—	4	16	no	—
284	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
285	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
286	C₂×C₄×C₄₇	#117	1	4	yes	—
287	C₂×C₄×C₄₇	#117	1	4	yes	—
288	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
289	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
290	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
291	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
292	C₂×C₄×C₄₇	#121	1	4	yes	—
293	C₂×C₄×C₄₇	#123	1	4	yes	—
294	C₂×C₄×C₄₇	#124	1	4	yes	—
295	C₂×C₄×C₄₇	#126	1	4	yes	—
296	C₄×#388	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂²×C₄₇	—	2	4	no	—
298	C₂²×C₄₇	—	2	4	no	—
299	C₂²×C₄₇	—	2	4	no	—
300	C₂²×C₄₇	—	4	4	no	—
301	C₂²×C₄₇	—	4	2	no	—
302	C₂²×C₄₇	—	4	2	no	—
303	C₂²×C₄₇	—	4	2	no	—
304	C₂²×C₄₇	—	4	2	no	—
305	C₂²×C₄₇	—	4	4	no	—
306	C₂²×C₄₇	—	4	4	no	—
307	C₂²×C₄₇	—	4	4	no	—
308	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
309	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
310	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
311	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
314	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
315	C₂²×C₄₇	C₄×#41	1	2	yes	—
316	C₂²×C₄₇	C₄×#41	1	2	yes	—
317	C₂²×C₄₇	C₄×#41	1	2	yes	—
318	C₂²×C₄₇	C₄×#41	1	2	yes	—
319	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
320	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
321	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
322	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
323	C₂²×C₄₇	#525	1	2	yes	—
324	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
325	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
326	C₂²×C₄₇	#529	1	2	yes	—
327	C₂²×C₄₇	#529	1	2	yes	—
328	C₂²×C₄₇	#529	1	2	yes	—
329	C₂²×C₄₇	#529	1	2	yes	—
330	C₂²×C₄₇	#532	1	2	yes	—
331	C₄×C₄₇	—	2	4	no	—
332	C₄×C₄₇	—	2	4	no	—
333	C₄×C₄₇	—	2	4	no	—
334	C₄×C₄₇	—	2	8	no	—
335	C₄×C₄₇	—	2	8	no	—
336	C₄×C₄₇	—	4	2	no	—
337	C₄×C₄₇	—	4	2	no	—
338	C₄×C₄₇	—	4	4	no	—
339	C₄×C₄₇	—	4	4	no	—
340	C₄×C₄₇	#388	1	8	yes	direct product factor
341	C₂×#388	C₂×C₄₇	1	2	yes	—
342	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
343	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
344	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
345	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
346	C₂×C₄³	C₂×C₄₇	1	1	yes	characteristic, complemented
347	#1437	C₂×C₄₇	1	2	yes	—
348	#1436	C₂×C₄₇	1	2	yes	complemented
349	#1434	C₂×C₄₇	1	2	yes	complemented
350	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
351	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
352	C₂×C₄₇	—	4	4	no	—
353	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
354	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
355	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
356	C₂×C₄₇	C₂×#388	1	1	yes	characteristic
357	C₂×C₄₇	#2290	1	1	yes	characteristic
358	C₂×C₄₇	#2293	1	1	yes	characteristic
359	C₂×C₄₇	#2298	1	1	yes	characteristic
360	C₂×C₄₇	C₄×#121	1	2	yes	—
361	C₂×C₄₇	C₄×#123	1	2	yes	—
362	C₂×C₄₇	C₄×#124	1	2	yes	—
363	C₂×C₄₇	C₄×#126	1	2	yes	—
364	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
365	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
366	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
368	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
369	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
373	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
374	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
375	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
376	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
378	#388	C₄×C₄₇	1	16	yes	direct product factor
379	C₄×C₄⋊C₄	—	2	4	no	—
380	C₄×C₂²⋊C₄	—	2	4	no	—
381	C₄×C₂²⋊C₄	—	2	4	no	—
382	C₄×C₂²⋊C₄	C₄×C₄₇	1	8	yes	complemented
383	C₂×#95	C₂²×C₄₇	1	2	yes	—
384	C₂×#95	C₂²×C₄₇	1	2	yes	—
385	C₂×#95	C₂²×C₄₇	1	2	yes	—
386	C₂×#95	C₂²×C₄₇	1	2	yes	—
387	C₂×#95	C₂²×C₄₇	1	2	yes	—
388	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
389	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
390	C₂×#95	C₂²×C₄₇	1	2	yes	—
391	C₂×#95	C₂²×C₄₇	1	2	yes	—
392	C₄³	—	2	4	no	—
393	C₄₇	C₄×#388	1	1	yes	characteristic, direct product factor, Sylow
394	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	2	2	no	—
397	C₂³×C₄	—	2	2	no	—
398	C₂³×C₄	—	2	2	no	—
399	C₂³×C₄	—	2	2	no	—
400	C₂³×C₄	—	2	2	no	—
401	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
402	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
405	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
409	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
410	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	—	2	4	no	—
413	C₂×C₄⋊C₄	—	2	4	no	—
414	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₂²⋊C₄	—	2	4	no	—
417	C₂×C₂²⋊C₄	—	2	4	no	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	—	2	4	no	—
420	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
425	C₂×C₄²	—	2	4	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	—	2	4	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	—	2	4	no	—
431	C₂×C₄²	—	2	4	no	—
432	C₂×C₄²	—	2	2	no	—
433	C₂×C₄²	—	2	2	no	—
434	C₂×C₄²	—	2	4	no	—
435	C₂×C₄²	—	2	2	no	—
436	C₂×C₄²	—	2	2	no	—
437	C₂×C₄²	—	2	2	no	—
438	C₂×C₄²	—	2	2	no	—
439	C₂×C₄²	—	2	2	no	—
440	C₂×C₄²	—	2	2	no	—
441	C₂×C₄²	—	2	2	no	—
442	C₂×C₄²	—	2	2	no	—
443	C₂×C₄²	—	2	2	no	—
444	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
445	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
446	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	complemented
447	C₂×C₄²	D₄×C₄₇	1	4	yes	—
448	C₂×C₄²	D₄×C₄₇	1	4	yes	—
449	#95	—	2	4	no	—
450	#95	—	2	4	no	—
451	#95	—	2	4	no	—
452	#95	—	2	4	no	—
453	#95	—	2	4	no	—
454	#95	C₂×C₄×C₄₇	1	4	yes	—
455	#95	C₂×C₄×C₄₇	1	4	yes	—
456	#95	C₂×C₄×C₄₇	1	8	yes	complemented
457	#95	C₂×C₄×C₄₇	1	8	yes	complemented
458	C₂⁴	—	2	1	no	—
459	C₂⁴	—	2	1	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	—	2	2	no	—
462	C₂⁴	—	2	2	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	1	no	—
465	C₂⁴	—	2	1	no	—
466	C₂⁴	—	2	1	no	—
467	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
468	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
469	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	4	4	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	2	yes	—
517	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
518	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
519	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
520	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
521	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
522	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
525	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
526	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
528	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
529	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
531	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
532	C₂²×C₄	#41×C₄₇	1	4	yes	—
533	C₂²×C₄	#41×C₄₇	1	4	yes	—
534	C₂²×C₄	#41×C₄₇	1	4	yes	—
535	C₂²×C₄	#41×C₄₇	1	2	yes	—
536	C₂²×C₄	#41×C₄₇	1	2	yes	—
537	C₂²×C₄	#41×C₄₇	1	2	yes	—
538	C₂²×C₄	#41×C₄₇	1	2	yes	—
539	C₄⋊C₄	—	2	16	no	—
540	C₂²⋊C₄	—	2	8	no	—
541	C₂²⋊C₄	—	2	16	no	—
542	C₂²⋊C₄	—	2	16	no	—
543	C₂²⋊C₄	C₄²×C₄₇	1	16	yes	complemented
544	C₄²	—	2	16	no	—
545	C₄²	—	2	8	no	—
546	C₄²	—	2	8	no	—
547	C₄²	—	2	16	no	—
548	C₄²	—	2	8	no	—
549	C₄²	—	2	8	no	—
550	C₄²	—	4	4	no	—
551	C₄²	—	4	4	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	C₂×C₄²×C₄₇	1	4	yes	—
575	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
576	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
577	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
578	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
579	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
580	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
581	C₂³	C₂×#41×C₄₇	1	2	yes	—
582	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
583	C₂³	C₂×#41×C₄₇	1	2	yes	—
584	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
585	C₂³	C₂×#41×C₄₇	1	2	yes	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	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	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	16	no	—
637	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
638	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
639	C₂×C₄	#117×C₄₇	1	4	yes	—
640	C₂×C₄	#117×C₄₇	1	4	yes	—
641	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
642	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
643	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
644	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
645	C₂×C₄	#121×C₄₇	1	4	yes	—
646	C₂×C₄	#123×C₄₇	1	4	yes	—
647	C₂×C₄	#124×C₄₇	1	4	yes	—
648	C₂×C₄	#126×C₄₇	1	4	yes	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	4	4	no	—
660	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
661	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
662	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
663	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
664	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
665	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
666	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
667	C₂²	C₄×#41×C₄₇	1	2	yes	—
668	C₂²	C₄×#41×C₄₇	1	2	yes	—
669	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
670	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
671	C₂²	C₄×#41×C₄₇	1	2	yes	—
672	C₂²	C₄×#41×C₄₇	1	2	yes	—
673	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
674	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
675	C₂²	C₄₇×#525	1	2	yes	—
676	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
677	C₂²	C₂×#126×C₄₇	1	1	yes	characteristic
678	C₂²	C₄₇×#529	1	2	yes	—
679	C₂²	C₄₇×#529	1	2	yes	—
680	C₂²	C₄₇×#529	1	2	yes	—
681	C₂²	C₄₇×#529	1	2	yes	—
682	C₂²	C₄₇×#532	1	2	yes	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	8	no	—
687	C₄	—	2	8	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	4	no	—
692	C₄	C₄₇×#388	1	8	yes	direct product factor
693	C₂	—	4	4	no	—
694	C₂	C₄×#117×C₄₇	1	1	yes	characteristic
695	C₂	C₄²×D₄×C₄₇	1	1	yes	characteristic
696	C₂	C₄²×D₄×C₄₇	1	1	yes	characteristic
697	C₂	C₂×C₄₇×#388	1	1	yes	characteristic
698	C₂	C₄₇×#2290	1	1	yes	characteristic
699	C₂	C₄₇×#2293	1	1	yes	characteristic
700	C₂	C₄₇×#2298	1	1	yes	characteristic
701	C₂	C₄×#121×C₄₇	1	2	yes	—
702	C₂	C₄×#123×C₄₇	1	2	yes	—
703	C₂	C₄×#124×C₄₇	1	2	yes	—
704	C₂	C₄×#126×C₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₇	C₂³
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
6. C₂×C₄³×C₄₇	C₂	semidirect
8. C₄₇×#1436	C₂	semidirect
9. C₄₇×#1434	C₂	semidirect
10. C₄×#95×C₄₇	C₂	semidirect
11. C₄×#95×C₄₇	C₂	semidirect
26. C₄₇×#388	C₄	direct (N × H)
30. C₄×C₂²⋊C₄×C₄₇	C₄	semidirect
61. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
93. C₂×C₄²×C₄₇	C₂×C₄	semidirect
103. #95×C₄₇	C₂×C₄	semidirect
104. #95×C₄₇	C₂×C₄	semidirect
190. C₂²⋊C₄×C₄₇	C₄²	semidirect
296. C₄×#388	C₄₇	direct (N × H)
340. C₄×C₄₇	#388	direct (N × H)
342. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
346. C₂×C₄³	C₂×C₄₇	semidirect
348. #1436	C₂×C₄₇	semidirect
349. #1434	C₂×C₄₇	semidirect
350. C₄×#95	C₂×C₄₇	semidirect
351. C₄×#95	C₂×C₄₇	semidirect
378. #388	C₄×C₄₇	direct (N × H)
382. C₄×C₂²⋊C₄	C₄×C₄₇	semidirect
393. C₄₇	C₄×#388	direct (N × H)
414. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
446. C₂×C₄²	C₂×C₄×C₄₇	semidirect
456. #95	C₂×C₄×C₄₇	semidirect
457. #95	C₂×C₄×C₄₇	semidirect
543. C₂²⋊C₄	C₄²×C₄₇	semidirect
692. C₄	C₄₇×#388	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#388	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×C₄³×C₄₇	2
C₄₇×#1437	2
C₄₇×#1436	2
C₄₇×#1434	2
C₄×#95×C₄₇	2
C₄×#388	47

Subgroups — C4×C47×#388 #26053461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₇×#388 #26053461