Subgroups — C₂×#20252115 #27080169

Order 12032.

2926 conjugacy classes of subgroups.

The subgroup lattice has 638 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	C₂³×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252115	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689201	C₂	1	2	yes	maximal, complemented
5	C₂×#15689195	C₂	1	2	yes	maximal, complemented
6	C₂×#15689195	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₂×#15689150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689090	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
13	C₂×#13094031	—	2	8	no	—
14	C₂×#13094031	C₂²	1	8	yes	complemented
15	C₂²×#10625329	—	2	8	no	—
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	2	yes	—
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×#10625329	C₂²	1	8	yes	complemented
20	C₂²×#10625329	C₂²	1	2	yes	complemented
21	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	complemented
25	#15689201	C₂²	1	16	yes	complemented
26	#15689195	C₂²	1	16	yes	complemented
27	#15689195	C₂²	1	16	yes	complemented
28	D₄×C₄₇⋊C₈	C₂²	1	16	yes	complemented
29	#15689150	C₂²	1	8	yes	complemented
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
31	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
32	#15689090	C₂²	1	8	yes	complemented
33	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	8	yes	complemented
38	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
40	#15689079	C₂²	1	8	yes	complemented
41	C₂×#13093935	C₂²	1	2	yes	complemented
42	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
43	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
44	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#525	C₄	1	8	yes	—
46	C₄₇×#525	C₂²	1	8	yes	—
47	C₂×#123×C₄₇	C₄	1	2	yes	—
48	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
49	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
50	C₂×#121×C₄₇	C₄	1	1	yes	characteristic
51	C₂×#121×C₄₇	C₄	1	1	yes	characteristic
52	C₂×#120×C₄₇	C₄	1	2	yes	—
53	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
54	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
55	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
56	#13094031	—	2	32	no	—
57	C₂×#10625329	—	2	4	no	—
58	C₂×#10625329	—	2	32	no	—
59	C₂×#10625329	—	2	8	no	—
60	C₂×#10625329	—	2	8	no	—
61	C₂×#10625329	D₄	1	8	yes	complemented
62	C₂×#10625329	C₂³	1	4	yes	—
63	C₂×#10625329	C₂³	1	8	yes	—
64	C₂×#10625329	C₂³	1	4	yes	—
65	C₂×#10625329	C₂³	1	8	yes	complemented
66	C₂²×C₄₇⋊C₈	—	2	4	no	—
67	C₂²×C₄₇⋊C₈	—	2	4	no	—
68	C₂²×C₄₇⋊C₈	—	2	8	no	—
69	C₂²×C₄₇⋊C₈	—	2	8	no	—
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
73	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
76	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
77	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
78	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	complemented
80	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	complemented
81	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	complemented
82	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
83	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
84	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
85	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
86	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	complemented
87	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	complemented
88	#13093935	C₂³	1	8	yes	complemented
89	C₄×C₄₇⋊C₈	C₂³	1	8	yes	complemented
90	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×#41×C₄₇	—	2	4	no	—
92	C₂×#41×C₄₇	—	2	4	no	—
93	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
94	C₂×#41×C₄₇	C₂³	1	4	yes	—
95	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
97	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
98	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
100	C₂³×C₄×C₄₇	—	2	4	no	—
101	C₂³×C₄×C₄₇	—	2	4	no	—
102	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
111	#123×C₄₇	C₂×C₄	1	16	yes	—
112	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
113	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
114	#121×C₄₇	C₂×C₄	1	8	yes	—
115	#121×C₄₇	C₂×C₄	1	8	yes	—
116	#120×C₄₇	C₂×C₄	1	16	yes	—
117	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
118	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
119	C₄×D₄×C₄₇	C₂³	1	8	yes	—
120	C₄×D₄×C₄₇	C₂³	1	8	yes	—
121	#117×C₄₇	C₂×C₄	1	4	yes	—
122	#117×C₄₇	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
126	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
127	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
128	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
129	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
130	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
131	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
132	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
133	C₂⁴×C₄₇	—	2	4	no	—
134	C₂⁴×C₄₇	—	2	4	no	—
135	C₂⁴×C₄₇	—	4	2	no	—
136	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
139	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	#41×C₄₇	—	2	16	no	—
142	#41×C₄₇	—	2	8	no	—
143	#41×C₄₇	—	2	8	no	—
144	C₂×Q₈×C₄₇	—	2	4	no	—
145	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
146	C₂×D₄×C₄₇	—	2	8	no	—
147	C₂×D₄×C₄₇	—	2	8	no	—
148	C₂×D₄×C₄₇	—	2	4	no	—
149	C₂×D₄×C₄₇	—	4	4	no	—
150	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
151	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
152	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
153	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
154	C₂²×C₄×C₄₇	—	2	4	no	—
155	C₂²×C₄×C₄₇	—	2	4	no	—
156	C₂²×C₄×C₄₇	—	2	4	no	—
157	C₂²×C₄×C₄₇	—	2	16	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	2	8	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	4	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	8	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
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	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₇	#41	1	4	yes	—
181	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
187	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
188	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
189	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
190	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
191	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
192	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
193	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
194	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
195	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
196	C₄²×C₄₇	C₂⁴	1	4	yes	—
197	#10625329	—	2	8	no	—
198	#10625329	—	2	16	no	—
199	#10625329	—	2	16	no	—
200	#10625329	C₂×D₄	1	16	yes	complemented
201	C₂×C₄₇⋊C₈	—	2	2	no	—
202	C₂×C₄₇⋊C₈	—	2	2	no	—
203	C₂×C₄₇⋊C₈	—	2	4	no	—
204	C₂×C₄₇⋊C₈	—	2	8	no	—
205	C₂×C₄₇⋊C₈	—	2	2	no	—
206	C₂×C₄₇⋊C₈	—	2	2	no	—
207	C₂×C₄₇⋊C₈	—	2	8	no	—
208	C₂×C₄₇⋊C₈	—	2	16	no	—
209	C₂×C₄₇⋊C₈	—	2	16	no	—
210	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
211	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
212	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
213	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
214	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
215	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
216	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
217	C₂³×C₄₇	—	2	2	no	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	2	2	no	—
220	C₂³×C₄₇	—	2	2	no	—
221	C₂³×C₄₇	—	2	8	no	—
222	C₂³×C₄₇	—	2	2	no	—
223	C₂³×C₄₇	—	2	4	no	—
224	C₂³×C₄₇	—	2	4	no	—
225	C₂³×C₄₇	—	2	2	no	—
226	C₂³×C₄₇	—	2	8	no	—
227	C₂³×C₄₇	—	2	2	no	—
228	C₂³×C₄₇	—	2	4	no	—
229	C₂³×C₄₇	—	4	4	no	—
230	C₂³×C₄₇	—	4	16	no	—
231	C₂³×C₄₇	C₄×D₄	1	4	yes	—
232	C₂³×C₄₇	#131	1	4	yes	complemented
233	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
234	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
235	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
236	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
237	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
238	Q₈×C₄₇	—	2	8	no	—
239	D₄×C₄₇	—	2	16	no	—
240	D₄×C₄₇	—	2	16	no	—
241	D₄×C₄₇	—	2	8	no	—
242	D₄×C₄₇	—	4	8	no	—
243	C₂×C₄×C₄₇	—	2	8	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	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	8	no	—
252	C₂×C₄×C₄₇	—	2	8	no	—
253	C₂×C₄×C₄₇	—	2	8	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	4	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	4	no	—
260	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
261	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
262	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
263	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
264	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
265	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
266	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
272	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
273	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
274	C₄₇⋊C₈	—	2	2	no	—
275	C₄₇⋊C₈	—	2	2	no	—
276	C₄₇⋊C₈	—	2	4	no	—
277	C₄₇⋊C₈	—	2	2	no	—
278	C₄₇⋊C₈	—	2	2	no	—
279	C₄₇⋊C₈	C₂²×D₄	1	8	yes	—
280	C₂×#2933	—	47	1	no	maximal, Sylow
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	8	no	—
283	C₂²×C₄₇	—	2	8	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	2	no	—
287	C₂²×C₄₇	—	2	2	no	—
288	C₂²×C₄₇	—	2	4	no	—
289	C₂²×C₄₇	—	2	4	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	2	no	—
292	C₂²×C₄₇	—	2	4	no	—
293	C₂²×C₄₇	—	4	16	no	—
294	C₂²×C₄₇	—	4	8	no	—
295	C₂²×C₄₇	—	4	4	no	—
296	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
297	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
298	C₂²×C₄₇	C₂×#131	1	2	yes	—
299	C₂²×C₄₇	C₂×#131	1	4	yes	complemented
300	C₂²×C₄₇	#568	1	2	yes	—
301	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
302	C₄×C₄₇	—	2	2	no	—
303	C₄×C₄₇	—	2	2	no	—
304	C₄×C₄₇	—	2	4	no	—
305	C₄×C₄₇	—	2	4	no	—
306	C₄×C₄₇	—	2	4	no	—
307	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
308	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
309	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
310	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
311	C₂²×#131	—	47	1	no	—
312	C₂³×M₁₆	—	47	1	no	—
313	C₂×#525	D₄₇	1	1	yes	characteristic
314	#2933	—	47	16	no	—
315	C₂×#436	—	47	2	no	—
316	C₂×#435	—	47	2	no	—
317	C₂×#435	—	47	2	no	—
318	C₂×C₈×D₄	—	47	2	no	—
319	C₂×#424	—	47	1	no	—
320	C₂×#408	—	47	1	no	—
321	C₂²×C₂²⋊C₈	—	47	1	no	—
322	C₂×#405	—	47	1	no	—
323	C₂×C₄₇	—	2	4	no	—
324	C₂×C₄₇	—	2	4	no	—
325	C₂×C₄₇	—	4	4	no	—
326	C₂×C₄₇	—	4	2	no	—
327	C₂×C₄₇	#2933	1	4	yes	complemented
328	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
329	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
330	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
331	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
332	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
333	C₂×#131	—	47	8	no	—
334	C₂×#131	—	94	8	no	—
335	C₂²×M₁₆	—	47	1	no	—
336	C₂²×M₁₆	—	47	1	no	—
337	C₂²×M₁₆	—	47	2	no	—
338	C₂²×M₁₆	—	47	2	no	—
339	C₂²×M₁₆	—	47	8	no	—
340	C₂²×M₁₆	—	94	8	no	—
341	C₂³×C₈	—	47	1	no	—
342	C₂³×C₈	—	47	1	no	—
343	C₂³×C₈	—	47	2	no	—
344	C₂³×C₈	—	47	2	no	—
345	#525	Dic₄₇	1	8	yes	—
346	#525	C₂×D₄₇	1	8	yes	—
347	C₂×#123	Dic₄₇	1	2	yes	—
348	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
350	C₂×#121	Dic₄₇	1	1	yes	characteristic
351	C₂×#121	Dic₄₇	1	1	yes	characteristic
352	C₂×#120	Dic₄₇	1	2	yes	—
353	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
354	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
355	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
356	#436	—	47	16	no	—
357	#435	—	47	16	no	—
358	#435	—	47	16	no	—
359	C₈×D₄	—	47	16	no	—
360	#424	—	47	8	no	—
361	C₂×C₄⋊C₈	—	47	2	no	—
362	C₂×C₄⋊C₈	—	47	2	no	—
363	#408	—	47	8	no	—
364	C₂×C₂²⋊C₈	—	47	1	no	—
365	C₂×C₂²⋊C₈	—	47	1	no	—
366	C₂×C₂²⋊C₈	—	47	1	no	—
367	C₂×C₂²⋊C₈	—	47	1	no	—
368	C₂×C₂²⋊C₈	—	47	8	no	—
369	C₂×C₂²⋊C₈	—	47	2	no	—
370	C₂×C₂²⋊C₈	—	47	2	no	—
371	#405	—	47	8	no	—
372	C₂×#97	—	47	2	no	—
373	C₂×C₄×C₈	—	47	2	no	—
374	C₄₇	C₂×#2933	1	1	yes	characteristic, complemented, Sylow
375	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
376	C₂×#41	—	2	4	no	—
377	C₂×#41	—	2	4	no	—
378	C₂×#41	C₂×Dic₄₇	1	4	yes	—
379	C₂×#41	C₂²×D₄₇	1	4	yes	—
380	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
381	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
382	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
383	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
384	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
388	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
389	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
390	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
391	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
392	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
393	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
394	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
395	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
396	#131	—	94	32	no	—
397	C₂×M₁₆	—	47	8	no	—
398	C₂×M₁₆	—	47	4	no	—
399	C₂×M₁₆	—	47	4	no	—
400	C₂×M₁₆	—	47	8	no	—
401	C₂×M₁₆	—	47	8	no	—
402	C₂×M₁₆	—	94	8	no	—
403	C₂×M₁₆	—	94	8	no	—
404	C₂×M₁₆	—	94	32	no	—
405	C₂×M₁₆	—	94	4	no	—
406	C₂²×C₈	—	47	2	no	—
407	C₂²×C₈	—	47	8	no	—
408	C₂²×C₈	—	47	4	no	—
409	C₂²×C₈	—	47	8	no	—
410	C₂²×C₈	—	47	4	no	—
411	C₂²×C₈	—	47	1	no	—
412	C₂²×C₈	—	47	1	no	—
413	C₂²×C₈	—	47	2	no	—
414	C₂²×C₈	—	47	1	no	—
415	C₂²×C₈	—	47	1	no	—
416	C₂²×C₈	—	94	8	no	—
417	C₂²×C₈	—	94	8	no	—
418	C₂²×C₈	—	94	4	no	—
419	C₂²×C₈	—	94	4	no	—
420	#123	C₂×Dic₄₇	1	16	yes	—
421	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
422	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
423	#121	C₂×Dic₄₇	1	8	yes	—
424	#121	C₂×Dic₄₇	1	8	yes	—
425	#120	C₂×Dic₄₇	1	16	yes	—
426	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
427	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
428	C₄×D₄	C₂²×D₄₇	1	8	yes	—
429	C₄×D₄	C₂²×D₄₇	1	8	yes	—
430	#117	C₂×Dic₄₇	1	4	yes	—
431	#117	C₂²×D₄₇	1	4	yes	—
432	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
435	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
441	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
442	C₄⋊C₈	—	47	8	no	—
443	C₄⋊C₈	—	47	8	no	—
444	C₂²⋊C₈	—	47	4	no	—
445	C₂²⋊C₈	—	47	4	no	—
446	C₂²⋊C₈	—	47	4	no	—
447	C₂²⋊C₈	—	47	4	no	—
448	C₂²⋊C₈	—	47	8	no	—
449	C₂²⋊C₈	—	47	8	no	—
450	#97	—	47	8	no	—
451	C₄×C₈	—	47	8	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	4	2	no	—
455	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
456	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
457	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
458	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
459	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
460	#41	—	2	16	no	—
461	#41	—	2	8	no	—
462	#41	—	2	8	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
470	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
471	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
472	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	16	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	D₄×D₄₇	1	4	yes	—
486	C₂²×C₄	#10625352	1	4	yes	—
487	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
488	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
489	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
492	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
493	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
494	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
495	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
496	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
497	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
498	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
499	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
500	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
501	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
502	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
503	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
504	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
505	M₁₆	—	47	16	no	—
506	M₁₆	—	94	16	no	—
507	M₁₆	—	94	16	no	—
508	M₁₆	—	94	8	no	—
509	C₂×C₈	—	47	8	no	—
510	C₂×C₈	—	47	4	no	—
511	C₂×C₈	—	47	2	no	—
512	C₂×C₈	—	47	2	no	—
513	C₂×C₈	—	47	2	no	—
514	C₂×C₈	—	47	2	no	—
515	C₂×C₈	—	47	4	no	—
516	C₂×C₈	—	94	16	no	—
517	C₂×C₈	—	94	16	no	—
518	C₂×C₈	—	94	2	no	—
519	C₂×C₈	—	94	4	no	—
520	C₂×C₈	—	94	2	no	—
521	C₂×C₈	—	94	8	no	—
522	C₂×C₈	—	94	2	no	—
523	C₂×C₈	—	94	2	no	—
524	C₂×C₈	—	94	8	no	—
525	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
526	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
527	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
528	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
529	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
530	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
531	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
532	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
533	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
534	C₄²	C₂²×Dic₄₇	1	4	yes	—
535	C₄²	C₂³×D₄₇	1	4	yes	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	16	no	—
550	C₂³	D₄×Dic₄₇	1	4	yes	—
551	C₂³	#13094031	1	4	yes	complemented
552	C₂³	C₂³×Dic₄₇	1	2	yes	—
553	C₂³	C₂³×Dic₄₇	1	4	yes	—
554	C₂³	C₂³×Dic₄₇	1	2	yes	—
555	C₂³	C₂³×Dic₄₇	1	2	yes	—
556	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
557	Q₈	—	2	8	no	—
558	D₄	—	2	16	no	—
559	D₄	—	2	16	no	—
560	D₄	—	2	8	no	—
561	D₄	—	4	8	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
580	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
581	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
582	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
583	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
584	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
585	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
586	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
587	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
588	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
589	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
590	C₂×C₄	C₂×#10625352	1	2	yes	—
591	C₂×C₄	C₂×#10625352	1	4	yes	—
592	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
593	C₈	—	47	8	no	—
594	C₈	—	94	2	no	—
595	C₈	—	94	4	no	—
596	C₈	—	94	2	no	—
597	C₈	—	94	2	no	—
598	C₈	—	94	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	4	16	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	8	no	—
614	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
615	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
616	C₂²	C₂×#13094031	1	2	yes	—
617	C₂²	C₂×#13094031	1	4	yes	complemented
618	C₂²	#15689890	1	2	yes	—
619	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
620	C₄	—	2	4	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
626	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
627	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
628	C₄	C₂²×#10625352	1	1	yes	characteristic
629	C₂	—	2	4	no	—
630	C₂	—	2	4	no	—
631	C₂	—	4	2	no	—
632	C₂	—	4	4	no	—
633	C₂	#20252115	1	4	yes	direct product factor
634	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
635	C₂	C₂²×#13094031	1	1	yes	characteristic
636	C₂	C₂×#15689890	1	1	yes	characteristic

	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×#2933
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. C₂³×#10625329	C₂	semidirect
3. #20252115	C₂	direct (N × H)
4. C₂×#15689201	C₂	semidirect
5. C₂×#15689195	C₂	semidirect
6. C₂×#15689195	C₂	semidirect
7. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
8. C₂×#15689150	C₂	semidirect
9. C₂×#15689090	C₂	semidirect
10. C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
11. C₂×#15689079	C₂	semidirect
14. C₂×#13094031	C₂²	semidirect
19. C₂²×#10625329	C₂²	semidirect
20. C₂²×#10625329	C₂²	semidirect
24. C₂³×C₄₇⋊C₈	C₂²	semidirect
25. #15689201	C₂²	semidirect
26. #15689195	C₂²	semidirect
27. #15689195	C₂²	semidirect
28. D₄×C₄₇⋊C₈	C₂²	semidirect
29. #15689150	C₂²	semidirect
30. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
31. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
32. #15689090	C₂²	semidirect
37. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
38. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
39. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
40. #15689079	C₂²	semidirect
41. C₂×#13093935	C₂²	semidirect
42. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
61. C₂×#10625329	D₄	semidirect
65. C₂×#10625329	C₂³	semidirect
79. C₂²×C₄₇⋊C₈	C₂³	semidirect
80. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
81. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
86. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
87. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
88. #13093935	C₂³	semidirect
89. C₄×C₄₇⋊C₈	C₂³	semidirect
200. #10625329	C₂×D₄	semidirect
232. C₂³×C₄₇	#131	semidirect
299. C₂²×C₄₇	C₂×#131	semidirect
327. C₂×C₄₇	#2933	semidirect
374. C₄₇	C₂×#2933	semidirect
551. C₂³	#13094031	semidirect
617. C₂²	C₂×#13094031	semidirect
633. C₂	#20252115	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
C₂³×#10625329	2
#20252115	2
C₂×#15689201	2
C₂×#15689195	2
C₂×D₄×C₄₇⋊C₈	2
C₂×#15689150	2
C₂×#15689090	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15689079	2
C₂×C₄₇×#525	2
C₂×#2933	47

Subgroups — C2×#20252115 #27080169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252115 #27080169