Subgroups — C₄×#15689195 #26214628

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689195	C₂	1	2	yes	maximal
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243263	C₂	1	2	yes	maximal, complemented
5	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243172	C₂	1	2	yes	maximal, complemented
7	#20243166	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15689195	C₄	1	16	yes	direct product factor
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₄×#10625329	—	2	4	no	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	C₂×#13093935	C₂²	1	2	yes	—
21	C₂×#13093935	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
38	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
39	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄³×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#10625329	—	2	4	no	—
43	C₂×#10625329	—	2	4	no	—
44	C₂×#10625329	C₂×C₄	1	8	yes	complemented
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	4	no	—
47	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
53	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
54	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
55	#13093935	—	2	4	no	—
56	#13093935	—	2	4	no	—
57	#13093935	C₂×C₄	1	8	yes	complemented
58	C₄×C₄₇⋊C₈	—	2	2	no	—
59	C₄×C₄₇⋊C₈	—	2	2	no	—
60	C₄×C₄₇⋊C₈	—	2	2	no	—
61	C₄×C₄₇⋊C₈	—	2	4	no	—
62	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
63	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₇	—	2	8	no	—
69	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	—	2	2	no	—
77	C₂×C₄²×C₄₇	—	2	2	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	#95×C₄₇	C₂×C₄	1	2	yes	—
90	#95×C₄₇	C₂×C₄	1	2	yes	—
91	#95×C₄₇	C₂×C₄	1	2	yes	—
92	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	4	no	—
95	C₂×D₄×C₄₇	C₄²	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	M₁₆	1	8	yes	complemented
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
124	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
125	C₄²×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	—	2	4	no	—
127	C₄²×C₄₇	—	2	4	no	—
128	C₄²×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
135	C₄²×C₄₇	C₂×D₄	1	2	yes	—
136	C₄²×C₄₇	#41	1	2	yes	—
137	#10625329	—	2	16	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	16	no	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
150	C₂×C₄₇⋊C₈	#41	1	4	yes	—
151	C₂³×C₄₇	—	2	1	no	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
159	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
160	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
161	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	D₄×C₄₇	—	2	8	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	16	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	4	8	no	—
183	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
187	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
189	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
190	C₂×C₄×C₄₇	#131	1	4	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₄₇⋊C₈	—	2	4	no	—
196	C₄₇⋊C₈	—	2	4	no	—
197	C₄₇⋊C₈	—	2	4	no	—
198	C₄₇⋊C₈	C₄×D₄	1	8	yes	complemented
199	C₄×#435	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	C₄×M₁₆	1	4	yes	complemented
210	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
213	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
214	C₂²×C₄₇	C₂×#131	1	2	yes	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	2	4	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	#435	1	8	yes	complemented
223	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
224	C₄×C₄₇	C₄×#41	1	2	yes	—
225	C₂×#435	—	47	2	no	—
226	C₂×C₄×M₁₆	—	47	1	no	—
227	C₂²×C₄×C₈	—	47	1	no	—
228	C₄²×D₄	D₄₇	1	1	yes	characteristic
229	#1771	—	47	2	no	—
230	C₄×C₄⋊C₈	—	47	1	no	—
231	#1753	—	47	2	no	—
232	#1752	—	47	2	no	—
233	C₄×C₂²⋊C₈	—	47	1	no	—
234	C₄×C₂²⋊C₈	—	47	1	no	—
235	C₄×#97	—	47	1	no	—
236	C₂×C₄₇	—	2	4	no	—
237	C₂×C₄₇	—	4	2	no	—
238	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
239	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
240	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
241	C₂×C₄₇	C₂×#435	1	2	yes	—
242	C₂×C₄₇	#2965	1	2	yes	—
243	C₂²×M₁₆	—	47	2	no	—
244	C₂³×C₈	—	47	2	no	—
245	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
246	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
247	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
248	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
249	#435	—	47	16	no	—
250	C₂×C₄⋊C₈	—	47	2	no	—
251	C₂×C₂²⋊C₈	—	47	2	no	—
252	C₂×C₂²⋊C₈	—	47	2	no	—
253	C₄×M₁₆	—	94	4	no	—
254	C₂×#97	—	47	2	no	—
255	C₂×#97	—	47	2	no	—
256	C₂×#97	—	47	2	no	—
257	C₂×C₄×C₈	—	47	1	no	—
258	C₂×C₄×C₈	—	47	2	no	—
259	C₂×C₄×C₈	—	47	1	no	—
260	C₂×C₄×C₈	—	47	1	no	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	94	4	no	—
263	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
264	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
266	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
267	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
268	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
269	C₄³	C₂×D₄₇	1	1	yes	characteristic
270	#336	—	47	2	no	—
271	#336	—	47	2	no	—
272	#336	—	47	2	no	—
273	C₄₇	C₄×#435	1	1	yes	characteristic, complemented, Sylow
274	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
276	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
277	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×M₁₆	—	47	8	no	—
280	C₂×M₁₆	—	94	4	no	—
281	C₂×M₁₆	—	94	4	no	—
282	C₂²×C₈	—	47	2	no	—
283	C₂²×C₈	—	47	8	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	94	4	no	—
288	C₂²×C₈	—	94	4	no	—
289	C₄×D₄	—	2	8	no	—
290	C₄×D₄	C₄×D₄₇	1	8	yes	—
291	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
302	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
303	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	C₄⋊C₈	—	47	8	no	—
311	C₂²⋊C₈	—	47	8	no	—
312	C₂²⋊C₈	—	47	8	no	—
313	#97	—	47	8	no	—
314	#97	—	94	4	no	—
315	#97	—	94	4	no	—
316	C₄×C₈	—	47	4	no	—
317	C₄×C₈	—	94	4	no	—
318	C₄×C₈	—	94	2	no	—
319	C₄×C₈	—	94	2	no	—
320	C₄×C₈	—	94	2	no	—
321	#95	C₂×Dic₄₇	1	2	yes	—
322	#95	C₂×Dic₄₇	1	2	yes	—
323	#95	C₂×Dic₄₇	1	2	yes	—
324	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
325	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	#10625329	1	8	yes	complemented
340	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
341	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
342	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
344	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
349	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
350	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
351	M₁₆	—	94	16	no	—
352	C₂×C₈	—	47	4	no	—
353	C₂×C₈	—	47	4	no	—
354	C₂×C₈	—	47	4	no	—
355	C₂×C₈	—	47	4	no	—
356	C₂×C₈	—	47	4	no	—
357	C₂×C₈	—	47	4	no	—
358	C₂×C₈	—	94	16	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
370	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	C₂×C₄×D₄₇	1	4	yes	—
381	C₄²	D₄×D₄₇	1	2	yes	—
382	C₄²	#10625352	1	2	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
391	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
392	C₂³	C₂×#10625329	1	4	yes	—
393	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
394	D₄	—	2	8	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	16	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
416	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
417	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
418	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
419	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
420	C₂×C₄	C₂×#10625329	1	4	yes	—
421	C₂×C₄	C₂×#10625329	1	4	yes	—
422	C₂×C₄	#13094031	1	4	yes	—
423	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	#41×D₄₇	1	2	yes	—
426	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
427	C₈	—	47	8	no	—
428	C₈	—	94	4	no	—
429	C₈	—	94	4	no	—
430	C₈	—	94	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	C₄×#10625329	1	4	yes	complemented
441	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
442	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
443	C₂²	#41×Dic₄₇	1	1	yes	characteristic
444	C₂²	C₂²×#10625329	1	2	yes	—
445	C₂²	C₂×#13094031	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	#15689195	1	8	yes	direct product factor
454	C₄	C₄×D₄×D₄₇	1	2	yes	—
455	C₄	C₄×#10625352	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
459	C₂	C₂×C₄×#10625329	1	1	yes	characteristic
460	C₂	C₄×#13094031	1	1	yes	characteristic
461	C₂	C₂×#15689195	1	2	yes	—
462	C₂	#20252355	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄²×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×D₄	D₄₇
hypocenter	C₄₇	C₄×#435
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625329	C₂	semidirect
3. C₂²×C₄×C₄₇⋊C₈	C₂	semidirect
4. #20243263	C₂	semidirect
5. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
6. #20243172	C₂	semidirect
7. #20243166	C₂	semidirect
8. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
9. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
10. C₄×#13093935	C₂	semidirect
14. #15689195	C₄	direct (N × H)
44. C₂×#10625329	C₂×C₄	semidirect
47. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
52. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
53. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
54. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
57. #13093935	C₂×C₄	semidirect
62. C₄×C₄₇⋊C₈	D₄	semidirect
107. C₂²×C₄×C₄₇	M₁₆	semidirect
198. C₄₇⋊C₈	C₄×D₄	semidirect
209. C₂²×C₄₇	C₄×M₁₆	semidirect
222. C₄×C₄₇	#435	semidirect
273. C₄₇	C₄×#435	semidirect
339. C₂²×C₄	#10625329	semidirect
440. C₂²	C₄×#10625329	semidirect
453. C₄	#15689195	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×#15689195	2
C₂×C₄×#10625329	2
C₂²×C₄×C₄₇⋊C₈	2
#20243263	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243172	2
#20243166	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₄×#13093935	2
C₄²×D₄×C₄₇	2
C₄×#435	47

Subgroups — C4×#15689195 #26214628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689195 #26214628