Subgroups — C₂×#20252083 #27080133

Order 12032.

3046 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252083	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689195	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×C₄₇⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂×#15689150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689090	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689087	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
11	C₂×#13094031	—	2	8	no	—
12	C₂×#13094031	C₂²	1	8	yes	complemented
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	C₂²×#10625329	C₂²	1	2	yes	complemented
16	C₂³×C₄₇⋊C₈	—	2	8	no	—
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂³×C₄₇⋊C₈	C₂²	1	8	yes	complemented
22	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	complemented
23	#15689195	C₂²	1	32	yes	complemented
24	D₄×C₄₇⋊C₈	C₂²	1	32	yes	complemented
25	#15689150	C₂²	1	8	yes	complemented
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
27	#15689090	C₂²	1	8	yes	complemented
28	#15689087	C₂²	1	8	yes	complemented
29	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
30	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
31	#15689079	C₂²	1	8	yes	complemented
32	C₂×#13093935	C₂²	1	2	yes	complemented
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
34	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
35	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#525	C₄	1	8	yes	—
37	C₄₇×#525	C₂²	1	8	yes	—
38	C₂×#123×C₄₇	C₄	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
40	C₂×#121×C₄₇	C₄	1	2	yes	—
41	C₂×#120×C₄₇	C₄	1	2	yes	—
42	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
43	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
44	#13094031	—	2	32	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	2	8	no	—
48	C₂×#10625329	C₂³	1	4	yes	—
49	C₂×#10625329	C₂³	1	4	yes	—
50	C₂×#10625329	C₂³	1	8	yes	complemented
51	C₂²×C₄₇⋊C₈	—	2	4	no	—
52	C₂²×C₄₇⋊C₈	—	2	8	no	—
53	C₂²×C₄₇⋊C₈	—	2	8	no	—
54	C₂²×C₄₇⋊C₈	—	2	8	no	—
55	C₂²×C₄₇⋊C₈	—	2	32	no	—
56	C₂²×C₄₇⋊C₈	D₄	1	8	yes	complemented
57	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
58	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
59	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
61	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
62	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
66	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	complemented
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
68	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	—
69	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
70	#13093935	C₂³	1	8	yes	complemented
71	C₄×C₄₇⋊C₈	C₂³	1	8	yes	complemented
72	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×#41×C₄₇	—	2	4	no	—
74	C₂×#41×C₄₇	—	2	4	no	—
75	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×#41×C₄₇	C₂³	1	4	yes	—
77	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
79	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	—	2	4	no	—
82	C₂³×C₄×C₄₇	—	2	4	no	—
83	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
86	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	#123×C₄₇	C₂×C₄	1	16	yes	—
91	C₂²⋊Q₈×C₄₇	C₂×C₄	1	16	yes	—
92	#121×C₄₇	C₂×C₄	1	16	yes	—
93	#120×C₄₇	C₂×C₄	1	16	yes	—
94	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	—
95	C₄×D₄×C₄₇	C₂³	1	16	yes	—
96	#117×C₄₇	C₂×C₄	1	4	yes	—
97	#117×C₄₇	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
100	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
102	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
103	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
104	C₂⁴×C₄₇	—	2	4	no	—
105	C₂⁴×C₄₇	—	2	8	no	—
106	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
110	#41×C₄₇	—	2	16	no	—
111	#41×C₄₇	—	2	8	no	—
112	#41×C₄₇	—	2	8	no	—
113	C₂×Q₈×C₄₇	—	2	4	no	—
114	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂×D₄×C₄₇	—	2	8	no	—
116	C₂×D₄×C₄₇	—	2	16	no	—
117	C₂×D₄×C₄₇	—	2	4	no	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
119	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
120	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	8	no	—
123	C₂²×C₄×C₄₇	—	2	16	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	2	8	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	8	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₄₇	#41	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
146	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
147	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
148	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
149	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
150	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
151	C₄²×C₄₇	C₂⁴	1	4	yes	—
152	#10625329	—	2	8	no	—
153	#10625329	—	2	8	no	—
154	#10625329	—	2	16	no	—
155	C₂×C₄₇⋊C₈	—	2	4	no	—
156	C₂×C₄₇⋊C₈	—	2	8	no	—
157	C₂×C₄₇⋊C₈	—	2	4	no	—
158	C₂×C₄₇⋊C₈	—	2	4	no	—
159	C₂×C₄₇⋊C₈	—	2	16	no	—
160	C₂×C₄₇⋊C₈	—	2	16	no	—
161	C₂×C₄₇⋊C₈	—	2	16	no	—
162	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
163	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
164	C₂×C₄₇⋊C₈	C₂×D₄	1	16	yes	complemented
165	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
166	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
167	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
168	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
169	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
170	C₂³×C₄₇	—	2	32	no	—
171	C₂³×C₄₇	—	2	8	no	—
172	C₂³×C₄₇	—	2	4	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	2	16	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	2	8	no	—
178	C₂³×C₄₇	C₄×D₄	1	4	yes	—
179	C₂³×C₄₇	#131	1	8	yes	complemented
180	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
181	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
182	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
183	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
184	Q₈×C₄₇	—	2	8	no	—
185	D₄×C₄₇	—	2	16	no	—
186	D₄×C₄₇	—	2	32	no	—
187	D₄×C₄₇	—	2	8	no	—
188	C₂×C₄×C₄₇	—	2	8	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	8	no	—
192	C₂×C₄×C₄₇	—	2	8	no	—
193	C₂×C₄×C₄₇	—	2	16	no	—
194	C₂×C₄×C₄₇	—	2	8	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
200	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
201	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
203	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
204	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
206	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
210	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
211	C₄₇⋊C₈	—	2	4	no	—
212	C₄₇⋊C₈	—	2	4	no	—
213	C₄₇⋊C₈	—	2	4	no	—
214	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
215	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
216	C₂×#2929	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	2	32	no	—
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	8	no	—
220	C₂²×C₄₇	—	2	16	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	2	4	no	—
223	C₂²×C₄₇	—	2	4	no	—
224	C₂²×C₄₇	—	2	8	no	—
225	C₂²×C₄₇	—	4	8	no	—
226	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
227	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
228	C₂²×C₄₇	C₂×#131	1	4	yes	—
229	C₂²×C₄₇	C₂×#131	1	8	yes	complemented
230	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	2	8	no	—
234	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
235	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
236	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
237	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
238	C₂²×#131	—	47	1	no	—
239	C₂⁴×C₈	—	47	1	no	—
240	C₂×#525	D₄₇	1	1	yes	characteristic
241	#2929	—	47	16	no	—
242	C₂×#435	—	47	4	no	—
243	C₂×C₈×D₄	—	47	4	no	—
244	C₂×#424	—	47	1	no	—
245	C₂×#408	—	47	1	no	—
246	C₂×#407	—	47	1	no	—
247	C₂×#405	—	47	1	no	—
248	C₂×C₄₇	—	2	4	no	—
249	C₂×C₄₇	—	2	8	no	—
250	C₂×C₄₇	—	4	4	no	—
251	C₂×C₄₇	#2929	1	4	yes	complemented
252	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
253	C₂×C₄₇	C₂²×#131	1	2	yes	—
254	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
255	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
256	C₂×#131	—	47	8	no	—
257	C₂×#131	—	94	8	no	—
258	C₂²×M₁₆	—	47	1	no	—
259	C₂²×M₁₆	—	47	1	no	—
260	C₂²×M₁₆	—	47	2	no	—
261	C₂³×C₈	—	47	1	no	—
262	C₂³×C₈	—	47	1	no	—
263	C₂³×C₈	—	47	2	no	—
264	C₂³×C₈	—	47	2	no	—
265	C₂³×C₈	—	47	2	no	—
266	C₂³×C₈	—	47	8	no	—
267	C₂³×C₈	—	94	8	no	—
268	#525	Dic₄₇	1	8	yes	—
269	#525	C₂×D₄₇	1	8	yes	—
270	C₂×#123	Dic₄₇	1	2	yes	—
271	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
272	C₂×#121	Dic₄₇	1	2	yes	—
273	C₂×#120	Dic₄₇	1	2	yes	—
274	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	—
275	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
276	#435	—	47	32	no	—
277	C₈×D₄	—	47	32	no	—
278	#424	—	47	8	no	—
279	C₂×C₄⋊C₈	—	47	4	no	—
280	#408	—	47	8	no	—
281	#407	—	47	8	no	—
282	C₂×C₂²⋊C₈	—	47	4	no	—
283	C₂×C₂²⋊C₈	—	47	4	no	—
284	#405	—	47	8	no	—
285	C₂×#97	—	47	2	no	—
286	C₂×C₄×C₈	—	47	2	no	—
287	C₄₇	C₂×#2929	1	1	yes	characteristic, complemented, Sylow
288	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	C₂×Dic₄₇	1	4	yes	—
292	C₂×#41	C₂²×D₄₇	1	4	yes	—
293	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
294	C₂²×D₄	C₂×Dic₄₇	1	4	yes	—
295	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
296	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	4	no	—
298	C₂³×C₄	—	2	4	no	—
299	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
300	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
302	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
303	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
304	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
305	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
306	#131	—	94	32	no	—
307	C₂×M₁₆	—	47	4	no	—
308	C₂×M₁₆	—	47	8	no	—
309	C₂×M₁₆	—	47	4	no	—
310	C₂×M₁₆	—	94	8	no	—
311	C₂×M₁₆	—	94	4	no	—
312	C₂×M₁₆	—	94	4	no	—
313	C₂²×C₈	—	47	8	no	—
314	C₂²×C₈	—	47	4	no	—
315	C₂²×C₈	—	47	1	no	—
316	C₂²×C₈	—	47	1	no	—
317	C₂²×C₈	—	47	4	no	—
318	C₂²×C₈	—	47	8	no	—
319	C₂²×C₈	—	47	8	no	—
320	C₂²×C₈	—	47	8	no	—
321	C₂²×C₈	—	47	2	no	—
322	C₂²×C₈	—	47	2	no	—
323	C₂²×C₈	—	47	2	no	—
324	C₂²×C₈	—	94	8	no	—
325	C₂²×C₈	—	94	8	no	—
326	C₂²×C₈	—	94	32	no	—
327	C₂²×C₈	—	94	8	no	—
328	C₂²×C₈	—	94	4	no	—
329	#123	C₂×Dic₄₇	1	16	yes	—
330	C₂²⋊Q₈	C₂×Dic₄₇	1	16	yes	—
331	#121	C₂×Dic₄₇	1	16	yes	—
332	#120	C₂×Dic₄₇	1	16	yes	—
333	C₄×D₄	C₂×Dic₄₇	1	16	yes	—
334	C₄×D₄	C₂²×D₄₇	1	16	yes	—
335	#117	C₂×Dic₄₇	1	4	yes	—
336	#117	C₂²×D₄₇	1	4	yes	—
337	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
340	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
342	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
343	C₄⋊C₈	—	47	16	no	—
344	C₂²⋊C₈	—	47	16	no	—
345	C₂²⋊C₈	—	47	16	no	—
346	#97	—	47	8	no	—
347	C₄×C₈	—	47	8	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	8	no	—
350	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
351	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
352	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
353	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
354	#41	—	2	16	no	—
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	16	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
363	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
364	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	16	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	D₄×D₄₇	1	4	yes	—
375	C₂²×C₄	#10625352	1	4	yes	—
376	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
377	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
378	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
379	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
380	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
381	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
382	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
383	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
385	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
386	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
387	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
388	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
389	M₁₆	—	94	16	no	—
390	M₁₆	—	94	8	no	—
391	M₁₆	—	94	8	no	—
392	C₂×C₈	—	47	4	no	—
393	C₂×C₈	—	47	4	no	—
394	C₂×C₈	—	47	16	no	—
395	C₂×C₈	—	47	2	no	—
396	C₂×C₈	—	47	2	no	—
397	C₂×C₈	—	47	4	no	—
398	C₂×C₈	—	47	4	no	—
399	C₂×C₈	—	47	4	no	—
400	C₂×C₈	—	94	16	no	—
401	C₂×C₈	—	94	16	no	—
402	C₂×C₈	—	94	16	no	—
403	C₂×C₈	—	94	4	no	—
404	C₂×C₈	—	94	8	no	—
405	C₂×C₈	—	94	4	no	—
406	C₂×C₈	—	94	4	no	—
407	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
408	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
409	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
410	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
411	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
412	C₄²	C₂²×Dic₄₇	1	4	yes	—
413	C₄²	C₂³×D₄₇	1	4	yes	—
414	C₂³	—	2	32	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	16	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	8	no	—
422	C₂³	D₄×Dic₄₇	1	4	yes	—
423	C₂³	#13094031	1	8	yes	complemented
424	C₂³	C₂³×Dic₄₇	1	4	yes	—
425	C₂³	C₂³×Dic₄₇	1	2	yes	—
426	C₂³	C₂³×Dic₄₇	1	4	yes	—
427	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
428	Q₈	—	2	8	no	—
429	D₄	—	2	16	no	—
430	D₄	—	2	32	no	—
431	D₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	16	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
444	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
445	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
446	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
447	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
448	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
450	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
451	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
452	C₂×C₄	C₂×#10625352	1	2	yes	—
453	C₂×C₄	C₂×#10625352	1	4	yes	—
454	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
455	C₈	—	47	4	no	—
456	C₈	—	47	4	no	—
457	C₈	—	94	4	no	—
458	C₈	—	94	4	no	—
459	C₈	—	94	4	no	—
460	C₂²	—	2	32	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	16	no	—
466	C₂²	—	2	8	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
470	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
471	C₂²	C₂×#13094031	1	4	yes	—
472	C₂²	C₂×#13094031	1	8	yes	complemented
473	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
474	C₄	—	2	8	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
478	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
479	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
480	C₄	C₂²×#10625352	1	1	yes	characteristic
481	C₂	—	2	4	no	—
482	C₂	—	2	8	no	—
483	C₂	—	4	4	no	—
484	C₂	#20252083	1	4	yes	direct product factor
485	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
486	C₂	C₂²×#13094031	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂×C₄₇×#525	C₂
socle	C₂³×C₄₇	C₂³×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#525	D₄₇
hypocenter	C₄₇	C₂×#2929
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂²×#13094031	C₂	semidirect
2. C₂⁴×C₄₇⋊C₈	C₂	semidirect
3. #20252083	C₂	direct (N × H)
4. C₂×#15689195	C₂	semidirect
5. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
6. C₂×#15689150	C₂	semidirect
7. C₂×#15689090	C₂	semidirect
8. C₂×#15689087	C₂	semidirect
9. C₂×#15689079	C₂	semidirect
12. C₂×#13094031	C₂²	semidirect
15. C₂²×#10625329	C₂²	semidirect
21. C₂³×C₄₇⋊C₈	C₂²	semidirect
22. C₂³×C₄₇⋊C₈	C₂²	semidirect
23. #15689195	C₂²	semidirect
24. D₄×C₄₇⋊C₈	C₂²	semidirect
25. #15689150	C₂²	semidirect
26. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
27. #15689090	C₂²	semidirect
28. #15689087	C₂²	semidirect
30. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
31. #15689079	C₂²	semidirect
32. C₂×#13093935	C₂²	semidirect
33. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
50. C₂×#10625329	C₂³	semidirect
56. C₂²×C₄₇⋊C₈	D₄	semidirect
66. C₂²×C₄₇⋊C₈	C₂³	semidirect
67. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
69. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
70. #13093935	C₂³	semidirect
71. C₄×C₄₇⋊C₈	C₂³	semidirect
164. C₂×C₄₇⋊C₈	C₂×D₄	semidirect
179. C₂³×C₄₇	#131	semidirect
229. C₂²×C₄₇	C₂×#131	semidirect
251. C₂×C₄₇	#2929	semidirect
287. C₄₇	C₂×#2929	semidirect
423. C₂³	#13094031	semidirect
472. C₂²	C₂×#13094031	semidirect
484. C₂	#20252083	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094031	2
C₂⁴×C₄₇⋊C₈	2
#20252083	2
C₂×#15689195	2
C₂×D₄×C₄₇⋊C₈	2
C₂×#15689150	2
C₂×#15689090	2
C₂×#15689087	2
C₂×#15689079	2
C₂×C₄₇×#525	2
C₂×#2929	47

Subgroups — C2×#20252083 #27080133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252083 #27080133