Subgroups — C₂×#20256989 #27123355

Order 12032.

8722 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256989	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689830	C₂	1	2	yes	maximal, complemented
4	C₂×#15689825	C₂	1	4	yes	maximal, complemented
5	C₂×#15689804	C₂	1	4	yes	maximal, complemented
6	C₂×#15689767	C₂	1	4	yes	maximal, complemented
7	C₂×#15689671	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689654	C₂	1	4	yes	maximal, complemented
9	C₂×#15689629	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×#10625352	C₂	1	2	yes	maximal, complemented
11	C₂²×D₄×Dic₄₇	C₂	1	4	yes	maximal, complemented
12	C₂×D₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625352	C₂²	1	2	yes	—
14	C₂²×#10625352	C₂²	1	2	yes	complemented
15	C₂⁴×Dic₄₇	C₂²	1	4	yes	complemented
16	#15689859	C₂²	1	16	yes	complemented
17	#15689830	C₂²	1	32	yes	complemented
18	#15689825	C₂²	1	64	yes	complemented
19	#15689804	C₂²	1	64	yes	complemented
20	#15689767	C₂²	1	64	yes	complemented
21	#15689671	C₂²	1	16	yes	complemented
22	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
23	#15689654	C₂²	1	64	yes	complemented
24	C₂×#13094017	C₂²	1	8	yes	complemented
25	C₂×#13094015	C₂²	1	4	yes	complemented
26	C₂×#13094011	C₂²	1	4	yes	complemented
27	C₂×#13094011	C₂²	1	2	yes	complemented
28	#15689629	C₂²	1	64	yes	complemented
29	C₂×#13094008	C₂²	1	4	yes	complemented
30	C₂×#13094005	C₂²	1	8	yes	complemented
31	C₂×#13094005	C₂²	1	4	yes	complemented
32	C₂×#13094003	C₂²	1	4	yes	complemented
33	C₂×#13094001	C₂²	1	8	yes	complemented
34	C₂×#13093996	C₂²	1	8	yes	complemented
35	C₂×#13093995	C₂²	1	4	yes	complemented
36	C₂×#13093993	C₂²	1	4	yes	complemented
37	C₄×#10625352	C₂²	1	32	yes	complemented
38	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
39	C₂×#13093989	C₂²	1	2	yes	complemented
40	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
41	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
42	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
43	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
44	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
45	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
46	C₂×D₄×Dic₄₇	C₂²	1	64	yes	complemented
47	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
48	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
49	C₂×#13093982	C₂²	1	2	yes	complemented
50	C₂×#13093980	C₂²	1	4	yes	complemented
51	C₂×#13093980	C₂²	1	4	yes	complemented
52	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
53	C₂²×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
54	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	complemented
55	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
57	D₄²×C₄₇	C₂²	1	16	yes	complemented
58	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×#121×C₄₇	C₂²	1	4	yes	—
60	C₂×#120×C₄₇	C₂²	1	4	yes	—
61	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
62	C₂×#10625352	—	2	16	no	—
63	C₂×#10625352	—	4	8	no	—
64	C₂×#10625352	C₂³	1	16	yes	—
65	C₂×#10625352	C₂³	1	16	yes	complemented
66	C₂²×Dic₉₄	C₂³	1	2	yes	—
67	C₂²×Dic₉₄	C₂³	1	2	yes	—
68	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
69	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
70	C₂³×Dic₄₇	—	4	16	no	—
71	C₂³×Dic₄₇	C₂³	1	4	yes	—
72	C₂³×Dic₄₇	C₂³	1	4	yes	—
73	C₂³×Dic₄₇	C₂³	1	4	yes	—
74	C₂³×Dic₄₇	C₂³	1	8	yes	—
75	C₂³×Dic₄₇	C₂³	1	4	yes	—
76	C₂³×Dic₄₇	C₂³	1	32	yes	complemented
77	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
78	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
79	#13094024	C₂³	1	8	yes	complemented
80	#13094017	C₂³	1	64	yes	complemented
81	#13094015	C₂³	1	32	yes	complemented
82	#13094011	C₂³	1	32	yes	complemented
83	#13094011	C₂³	1	16	yes	complemented
84	#13094008	C₂³	1	32	yes	complemented
85	#13094005	C₂³	1	64	yes	complemented
86	#13094005	C₂³	1	32	yes	complemented
87	#13094003	C₂³	1	32	yes	complemented
88	#13094001	C₂³	1	64	yes	complemented
89	#13093996	C₂³	1	64	yes	complemented
90	#13093995	C₂³	1	32	yes	complemented
91	#13093993	C₂³	1	32	yes	complemented
92	C₄×Dic₉₄	C₂³	1	16	yes	complemented
93	#13093989	C₂³	1	16	yes	complemented
94	D₄×Dic₄₇	C₂³	1	32	yes	—
95	D₄×Dic₄₇	C₂³	1	16	yes	—
96	D₄×Dic₄₇	C₂³	1	64	yes	complemented
97	D₄×Dic₄₇	C₂³	1	32	yes	complemented
98	D₄×Dic₄₇	C₂³	1	64	yes	complemented
99	D₄×Dic₄₇	C₂³	1	32	yes	complemented
100	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
101	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
102	#13093982	C₂³	1	16	yes	complemented
103	#13093980	C₂³	1	32	yes	complemented
104	#13093980	C₂³	1	32	yes	complemented
105	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
108	C₂×C₄⋊Dic₄₇	C₂³	1	32	yes	complemented
109	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
110	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
111	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
112	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
114	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
116	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
117	C₂×C₂²⋊Dic₄₇	C₂³	1	64	yes	complemented
118	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
119	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
120	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
122	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
123	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
124	C₂×C₄×Dic₄₇	C₂³	1	32	yes	complemented
125	C₄²×D₄₇	C₂³	1	8	yes	complemented
126	C₂⁵×C₄₇	C₂³	1	4	yes	—
127	C₂²×D₄×C₄₇	—	2	32	no	—
128	C₂²×D₄×C₄₇	C₂³	1	32	yes	—
129	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
130	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
131	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
134	#127×C₄₇	C₂³	1	8	yes	—
135	#121×C₄₇	C₂³	1	32	yes	—
136	#120×C₄₇	C₂³	1	32	yes	—
137	C₄×D₄×C₄₇	C₂³	1	16	yes	—
138	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	C₂⁴×C₄₇	—	2	32	no	—
143	C₂⁴×C₄₇	—	4	8	no	—
144	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
145	C₂⁴×C₄₇	C₂⁴	1	16	yes	—
146	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
147	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
148	C₂×D₄×C₄₇	—	2	32	no	—
149	C₂×D₄×C₄₇	—	2	128	no	—
150	C₂×D₄×C₄₇	—	2	16	no	—
151	C₂×D₄×C₄₇	—	4	4	no	—
152	C₂×D₄×C₄₇	#41	1	16	yes	complemented
153	C₂×D₄×C₄₇	C₂⁴	1	32	yes	—
154	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
155	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
156	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₄₇	—	2	16	no	—
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
161	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
162	C₂×C₂²⋊D₄₇	—	2	16	no	—
163	C₂×C₂²⋊D₄₇	—	4	8	no	—
164	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
165	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
166	C₂²×Dic₄₇	—	2	16	no	—
167	C₂²×Dic₄₇	—	2	16	no	—
168	C₂²×Dic₄₇	—	2	16	no	—
169	C₂²×Dic₄₇	—	4	64	no	—
170	C₂²×Dic₄₇	—	4	16	no	—
171	C₂²×Dic₄₇	—	4	8	no	—
172	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
173	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
174	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
175	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
176	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
177	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
178	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
179	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
180	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
181	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
182	#10625352	—	2	64	no	—
183	#10625352	—	4	32	no	—
184	C₂×C₄×D₄₇	—	2	8	no	—
185	C₂×C₄×D₄₇	—	2	4	no	—
186	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
187	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
188	C₂×Dic₉₄	—	2	8	no	—
189	C₂×Dic₉₄	—	4	4	no	—
190	C₂×Dic₉₄	C₂⁴	1	8	yes	—
191	C₂×Dic₉₄	C₂⁴	1	8	yes	—
192	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
193	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
194	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
195	C₄²×C₄₇	C₂⁴	1	4	yes	—
196	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
197	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
198	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
199	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
200	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
201	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
202	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
203	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
204	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
205	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
206	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
207	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
208	C₄×Dic₄₇	C₂⁴	1	8	yes	—
209	C₄×Dic₄₇	C₂⁴	1	4	yes	—
210	C₄×Dic₄₇	C₂⁴	1	16	yes	—
211	C₄×Dic₄₇	C₂⁴	1	16	yes	—
212	C₄×Dic₄₇	C₂⁴	1	16	yes	—
213	C₂³×C₄₇	—	2	8	no	—
214	C₂³×C₄₇	—	2	8	no	—
215	C₂³×C₄₇	—	2	64	no	—
216	C₂³×C₄₇	—	2	16	no	—
217	C₂³×C₄₇	—	2	8	no	—
218	C₂³×C₄₇	—	4	16	no	—
219	C₂³×C₄₇	—	4	64	no	—
220	C₂³×C₄₇	C₂×#41	1	16	yes	—
221	C₂³×C₄₇	C₂⁵	1	8	yes	—
222	C₂³×C₄₇	C₂⁵	1	8	yes	—
223	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
224	C₂²×D₄₇	—	2	4	no	—
225	C₂²×D₄₇	—	2	2	no	—
226	C₂²×D₄₇	C₂⁵	1	2	yes	—
227	D₄×C₄₇	—	2	64	no	—
228	D₄×C₄₇	—	2	32	no	—
229	D₄×C₄₇	—	4	8	no	—
230	D₄×C₄₇	C₂×#41	1	32	yes	complemented
231	C₂×C₄×C₄₇	—	2	8	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	32	no	—
234	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
235	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
236	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
237	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
238	C₂²⋊D₄₇	—	2	32	no	—
239	C₂²⋊D₄₇	—	4	16	no	—
240	C₂×Dic₄₇	—	2	8	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	2	32	no	—
243	C₂×Dic₄₇	—	2	8	no	—
244	C₂×Dic₄₇	—	2	8	no	—
245	C₂×Dic₄₇	—	2	32	no	—
246	C₂×Dic₄₇	—	2	32	no	—
247	C₂×Dic₄₇	—	4	32	no	—
248	C₂×Dic₄₇	—	4	16	no	—
249	C₂×Dic₄₇	H(5,𝔽₂)	1	4	yes	—
250	C₂×Dic₄₇	C₂⁵	1	4	yes	—
251	C₂×Dic₄₇	C₂⁵	1	8	yes	—
252	C₂×Dic₄₇	C₂⁵	1	8	yes	—
253	C₂×Dic₄₇	C₂⁵	1	8	yes	—
254	C₂×Dic₄₇	C₂⁵	1	2	yes	—
255	C₄×D₄₇	—	2	16	no	—
256	C₄×D₄₇	—	2	8	no	—
257	Dic₉₄	—	2	16	no	—
258	Dic₉₄	—	4	8	no	—
259	C₂×#3481	—	47	1	no	maximal, Sylow
260	C₂²×C₄₇	—	2	8	no	—
261	C₂²×C₄₇	—	2	8	no	—
262	C₂²×C₄₇	—	2	32	no	—
263	C₂²×C₄₇	—	2	16	no	—
264	C₂²×C₄₇	—	2	8	no	—
265	C₂²×C₄₇	—	4	64	no	—
266	C₂²×C₄₇	—	4	16	no	—
267	C₂²×C₄₇	C₂²×#41	1	16	yes	—
268	C₂²×C₄₇	C₂²×#41	1	4	yes	—
269	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
270	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
271	C₂×D₄₇	—	2	4	no	—
272	C₂×D₄₇	—	2	2	no	—
273	C₂×D₄₇	—	4	4	no	—
274	C₄×C₄₇	—	2	8	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	C₂²×#41	1	8	yes	—
277	Dic₄₇	—	2	8	no	—
278	Dic₄₇	—	2	4	no	—
279	Dic₄₇	—	2	8	no	—
280	Dic₄₇	—	2	8	no	—
281	Dic₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
282	#3481	—	47	32	no	—
283	C₂×#559	—	47	1	no	—
284	C₂×#554	—	47	2	no	—
285	C₂×#553	—	47	4	no	—
286	C₂×#551	—	47	4	no	—
287	C₂×#546	—	47	4	no	—
288	C₂×D₄²	D₄₇	1	1	yes	characteristic, complemented
289	C₂×#532	—	47	1	no	—
290	C₂×#529	—	47	4	no	—
291	C₂×#525	—	47	4	no	—
292	C₂×C₄×#41	—	47	2	no	—
293	C₂²×C₄×D₄	—	47	4	no	—
294	C₂×C₄₇	—	2	16	no	—
295	C₂×C₄₇	—	4	8	no	—
296	C₂×C₄₇	#3481	1	4	yes	complemented
297	C₂×C₄₇	C₂³×#41	1	2	yes	—
298	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
299	D₄₇	—	4	2	no	—
300	C₂²×#41	—	47	2	no	—
301	C₂²×#41	—	47	2	no	—
302	C₂³×D₄	C₂×D₄₇	1	4	yes	—
303	C₂⁴×C₄	—	47	4	no	—
304	#559	—	47	16	no	—
305	#554	—	47	32	no	—
306	#553	—	47	64	no	—
307	#551	—	47	64	no	—
308	#546	—	47	64	no	—
309	D₄²	C₂×D₄₇	1	16	yes	complemented
310	#532	—	47	16	no	—
311	C₂×C₄⋊Q₈	—	47	1	no	—
312	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
313	#529	—	47	64	no	—
314	C₂×#126	—	47	8	no	—
315	C₂×#125	—	47	4	no	—
316	C₂×#124	—	47	4	no	—
317	C₂×#124	—	47	2	no	—
318	#525	—	47	64	no	—
319	C₂×#123	—	47	4	no	—
320	C₂×#123	—	47	8	no	—
321	C₂×#123	—	47	4	no	—
322	C₂×C₂²⋊Q₈	—	47	4	no	—
323	C₂×C₂²⋊Q₈	—	47	8	no	—
324	C₂×#121	—	47	8	no	—
325	C₂×#121	—	47	4	no	—
326	C₂×#121	C₂×D₄₇	1	4	yes	—
327	C₂×#120	—	47	4	no	—
328	C₂×#120	C₂×D₄₇	1	4	yes	—
329	C₄×#41	—	47	32	no	—
330	C₂×C₄×Q₈	—	47	2	no	—
331	C₂×C₄×Q₈	—	47	2	no	—
332	C₂×C₄×D₄	—	47	2	no	—
333	C₂×C₄×D₄	—	47	8	no	—
334	C₂×C₄×D₄	—	47	4	no	—
335	C₂×C₄×D₄	—	47	4	no	—
336	C₂×C₄×D₄	—	47	8	no	—
337	C₂×C₄×D₄	—	47	4	no	—
338	C₂×C₄×D₄	—	47	64	no	—
339	C₂×C₄×D₄	—	47	4	no	—
340	C₂×C₄×D₄	—	47	4	no	—
341	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
342	C₂×#117	—	47	2	no	—
343	C₂×#117	—	47	4	no	—
344	C₂×#117	—	47	4	no	—
345	C₂²×C₄⋊C₄	—	47	4	no	—
346	C₂²×C₂²⋊C₄	—	47	8	no	—
347	C₂²×C₄²	—	47	4	no	—
348	C₂²×C₄²	—	47	1	no	—
349	C₄₇	C₂×#3481	1	1	yes	characteristic, complemented, Sylow
350	C₂⁵	C₂²×D₄₇	1	4	yes	—
351	C₂×#41	—	47	16	no	—
352	C₂×#41	—	47	16	no	—
353	C₂×#41	—	94	16	no	—
354	C₂×#41	—	188	8	no	—
355	C₂²×Q₈	—	47	2	no	—
356	C₂²×Q₈	—	47	2	no	—
357	C₂²×D₄	—	2	32	no	—
358	C₂²×D₄	—	47	4	no	—
359	C₂²×D₄	—	47	4	no	—
360	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
361	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
362	C₂²×D₄	C₂²×D₄₇	1	32	yes	—
363	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
364	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
365	C₂³×C₄	—	47	4	no	—
366	C₂³×C₄	—	47	4	no	—
367	C₂³×C₄	—	47	4	no	—
368	C₂³×C₄	—	47	8	no	—
369	C₂³×C₄	—	47	4	no	—
370	C₂³×C₄	—	47	32	no	—
371	C₂³×C₄	—	47	2	no	—
372	C₂³×C₄	—	47	1	no	—
373	C₂³×C₄	—	188	16	no	—
374	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
375	C₄⋊Q₈	—	47	8	no	—
376	#127	C₂²×D₄₇	1	8	yes	—
377	#126	—	47	64	no	—
378	#125	—	47	32	no	—
379	#124	—	47	32	no	—
380	#124	—	47	16	no	—
381	#123	—	47	32	no	—
382	#123	—	47	64	no	—
383	#123	—	47	32	no	—
384	C₂²⋊Q₈	—	47	32	no	—
385	C₂²⋊Q₈	—	47	64	no	—
386	#121	—	47	64	no	—
387	#121	—	47	32	no	—
388	#121	C₂²×D₄₇	1	32	yes	—
389	#120	—	47	32	no	—
390	#120	C₂²×D₄₇	1	32	yes	—
391	C₄×Q₈	—	47	16	no	—
392	C₄×Q₈	—	47	16	no	—
393	C₄×D₄	—	47	16	no	—
394	C₄×D₄	—	47	64	no	—
395	C₄×D₄	—	47	32	no	—
396	C₄×D₄	—	47	32	no	—
397	C₄×D₄	—	47	64	no	—
398	C₄×D₄	—	47	32	no	—
399	C₄×D₄	—	47	32	no	—
400	C₄×D₄	—	47	32	no	—
401	C₄×D₄	C₂²×D₄₇	1	16	yes	—
402	#117	—	47	16	no	—
403	#117	—	47	32	no	—
404	#117	—	47	32	no	—
405	C₂×C₄⋊C₄	—	47	2	no	—
406	C₂×C₄⋊C₄	—	47	4	no	—
407	C₂×C₄⋊C₄	—	47	8	no	—
408	C₂×C₄⋊C₄	—	47	32	no	—
409	C₂×C₄⋊C₄	—	47	4	no	—
410	C₂×C₄⋊C₄	—	47	4	no	—
411	C₂×C₄⋊C₄	—	47	8	no	—
412	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
413	C₂×C₂²⋊C₄	—	47	4	no	—
414	C₂×C₂²⋊C₄	—	47	8	no	—
415	C₂×C₂²⋊C₄	—	47	8	no	—
416	C₂×C₂²⋊C₄	—	47	8	no	—
417	C₂×C₂²⋊C₄	—	47	64	no	—
418	C₂×C₂²⋊C₄	—	47	4	no	—
419	C₂×C₂²⋊C₄	—	47	4	no	—
420	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
422	C₂×C₄²	—	47	1	no	—
423	C₂×C₄²	—	47	4	no	—
424	C₂×C₄²	—	47	4	no	—
425	C₂×C₄²	—	47	4	no	—
426	C₂×C₄²	—	47	2	no	—
427	C₂×C₄²	—	47	32	no	—
428	C₂×C₄²	—	47	8	no	—
429	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
430	C₂⁴	—	2	32	no	—
431	C₂⁴	—	4	8	no	—
432	C₂⁴	—	47	1	no	—
433	C₂⁴	C₂³×D₄₇	1	4	yes	—
434	C₂⁴	C₂³×D₄₇	1	16	yes	—
435	C₂⁴	C₂³×D₄₇	1	4	yes	—
436	#41	—	94	64	no	—
437	#41	—	188	32	no	—
438	C₂×Q₈	—	47	8	no	—
439	C₂×Q₈	—	47	8	no	—
440	C₂×Q₈	—	94	8	no	—
441	C₂×Q₈	—	188	4	no	—
442	C₂×D₄	—	2	32	no	—
443	C₂×D₄	—	2	128	no	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	47	16	no	—
447	C₂×D₄	—	47	16	no	—
448	C₂×D₄	—	94	16	no	—
449	C₂×D₄	—	188	8	no	—
450	C₂×D₄	#10625352	1	16	yes	complemented
451	C₂×D₄	C₂³×D₄₇	1	32	yes	—
452	C₂×D₄	C₂³×D₄₇	1	16	yes	—
453	C₂×D₄	C₂³×D₄₇	1	8	yes	—
454	C₂×D₄	C₂³×D₄₇	1	8	yes	—
455	C₂²×C₄	—	2	16	no	—
456	C₂²×C₄	—	47	1	no	—
457	C₂²×C₄	—	47	16	no	—
458	C₂²×C₄	—	47	16	no	—
459	C₂²×C₄	—	47	16	no	—
460	C₂²×C₄	—	47	2	no	—
461	C₂²×C₄	—	47	4	no	—
462	C₂²×C₄	—	47	4	no	—
463	C₂²×C₄	—	47	4	no	—
464	C₂²×C₄	—	47	32	no	—
465	C₂²×C₄	—	47	16	no	—
466	C₂²×C₄	—	47	8	no	—
467	C₂²×C₄	—	47	4	no	—
468	C₂²×C₄	—	94	4	no	—
469	C₂²×C₄	—	94	16	no	—
470	C₂²×C₄	—	94	16	no	—
471	C₂²×C₄	—	94	16	no	—
472	C₂²×C₄	—	94	8	no	—
473	C₂²×C₄	—	188	64	no	—
474	C₂²×C₄	—	188	8	no	—
475	C₂²×C₄	—	188	16	no	—
476	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
477	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
478	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
480	C₄⋊C₄	—	47	16	no	—
481	C₄⋊C₄	—	47	16	no	—
482	C₄⋊C₄	—	47	32	no	—
483	C₄⋊C₄	—	47	8	no	—
484	C₄⋊C₄	—	47	16	no	—
485	C₄⋊C₄	—	47	32	no	—
486	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
487	C₂²⋊C₄	—	47	16	no	—
488	C₂²⋊C₄	—	47	32	no	—
489	C₂²⋊C₄	—	47	32	no	—
490	C₂²⋊C₄	—	47	32	no	—
491	C₂²⋊C₄	—	47	16	no	—
492	C₂²⋊C₄	—	47	16	no	—
493	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
494	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
495	C₄²	—	47	8	no	—
496	C₄²	—	47	4	no	—
497	C₄²	—	47	16	no	—
498	C₄²	—	47	16	no	—
499	C₄²	—	47	16	no	—
500	C₄²	C₂³×D₄₇	1	4	yes	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	64	no	—
504	C₂³	—	2	16	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	4	16	no	—
507	C₂³	—	4	64	no	—
508	C₂³	—	47	2	no	—
509	C₂³	—	94	4	no	—
510	C₂³	—	94	2	no	—
511	C₂³	C₂×#10625352	1	16	yes	—
512	C₂³	C₂⁴×D₄₇	1	8	yes	—
513	C₂³	C₂⁴×D₄₇	1	8	yes	—
514	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
515	Q₈	—	94	16	no	—
516	Q₈	—	188	8	no	—
517	D₄	—	2	64	no	—
518	D₄	—	2	32	no	—
519	D₄	—	4	8	no	—
520	D₄	—	94	32	no	—
521	D₄	—	188	16	no	—
522	D₄	C₂×#10625352	1	32	yes	complemented
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	32	no	—
526	C₂×C₄	—	47	4	no	—
527	C₂×C₄	—	47	2	no	—
528	C₂×C₄	—	47	4	no	—
529	C₂×C₄	—	47	8	no	—
530	C₂×C₄	—	47	8	no	—
531	C₂×C₄	—	47	8	no	—
532	C₂×C₄	—	94	8	no	—
533	C₂×C₄	—	94	32	no	—
534	C₂×C₄	—	94	32	no	—
535	C₂×C₄	—	94	4	no	—
536	C₂×C₄	—	94	8	no	—
537	C₂×C₄	—	94	32	no	—
538	C₂×C₄	—	94	8	no	—
539	C₂×C₄	—	94	8	no	—
540	C₂×C₄	—	94	16	no	—
541	C₂×C₄	—	188	16	no	—
542	C₂×C₄	—	188	32	no	—
543	C₂×C₄	C₂×#10625352	1	8	yes	—
544	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
545	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
546	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	32	no	—
550	C₂²	—	2	16	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	4	64	no	—
553	C₂²	—	4	16	no	—
554	C₂²	—	94	4	no	—
555	C₂²	—	94	2	no	—
556	C₂²	—	188	4	no	—
557	C₂²	C₂²×#10625352	1	16	yes	—
558	C₂²	C₂²×#10625352	1	4	yes	—
559	C₂²	H(5,𝔽₂)×D₄₇	1	2	yes	—
560	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
561	C₄	—	2	8	no	—
562	C₄	—	2	2	no	—
563	C₄	—	47	4	no	—
564	C₄	—	94	4	no	—
565	C₄	—	94	8	no	—
566	C₄	—	94	8	no	—
567	C₄	—	94	8	no	—
568	C₄	C₂²×#10625352	1	8	yes	—
569	C₂	—	2	16	no	—
570	C₂	—	4	8	no	—
571	C₂	—	188	2	no	—
572	C₂	#20256989	1	4	yes	direct product factor
573	C₂	C₂³×#10625352	1	2	yes	—
574	C₂	C₂×H(5,𝔽₂)×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×D₄²×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×D₄²	D₄₇
hypocenter	C₄₇	C₂×#3481
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×D₄²

Complements

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

N	H ≅ G/N	type
1. #20256989	C₂	direct (N × H)
2. C₂×#15689859	C₂	semidirect
3. C₂×#15689830	C₂	semidirect
4. C₂×#15689825	C₂	semidirect
5. C₂×#15689804	C₂	semidirect
6. C₂×#15689767	C₂	semidirect
7. C₂×#15689671	C₂	semidirect
8. C₂×#15689654	C₂	semidirect
9. C₂×#15689629	C₂	semidirect
10. C₂×C₄×#10625352	C₂	semidirect
11. C₂²×D₄×Dic₄₇	C₂	semidirect
12. C₂×D₄²×C₄₇	C₂	semidirect
14. C₂²×#10625352	C₂²	semidirect
15. C₂⁴×Dic₄₇	C₂²	semidirect
16. #15689859	C₂²	semidirect
17. #15689830	C₂²	semidirect
18. #15689825	C₂²	semidirect
19. #15689804	C₂²	semidirect
20. #15689767	C₂²	semidirect
21. #15689671	C₂²	semidirect
22. C₂×#13094024	C₂²	semidirect
23. #15689654	C₂²	semidirect
24. C₂×#13094017	C₂²	semidirect
25. C₂×#13094015	C₂²	semidirect
26. C₂×#13094011	C₂²	semidirect
27. C₂×#13094011	C₂²	semidirect
28. #15689629	C₂²	semidirect
29. C₂×#13094008	C₂²	semidirect
30. C₂×#13094005	C₂²	semidirect
31. C₂×#13094005	C₂²	semidirect
32. C₂×#13094003	C₂²	semidirect
33. C₂×#13094001	C₂²	semidirect
34. C₂×#13093996	C₂²	semidirect
35. C₂×#13093995	C₂²	semidirect
36. C₂×#13093993	C₂²	semidirect
37. C₄×#10625352	C₂²	semidirect
38. C₂×C₄×Dic₉₄	C₂²	semidirect
39. C₂×#13093989	C₂²	semidirect
42. C₂×D₄×Dic₄₇	C₂²	semidirect
43. C₂×D₄×Dic₄₇	C₂²	semidirect
44. C₂×D₄×Dic₄₇	C₂²	semidirect
45. C₂×D₄×Dic₄₇	C₂²	semidirect
46. C₂×D₄×Dic₄₇	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
48. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
49. C₂×#13093982	C₂²	semidirect
50. C₂×#13093980	C₂²	semidirect
51. C₂×#13093980	C₂²	semidirect
52. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
53. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
54. C₂²×C₄×Dic₄₇	C₂²	semidirect
55. C₂×C₄²×D₄₇	C₂²	semidirect
57. D₄²×C₄₇	C₂²	semidirect
65. C₂×#10625352	C₂³	semidirect
76. C₂³×Dic₄₇	C₂³	semidirect
79. #13094024	C₂³	semidirect
80. #13094017	C₂³	semidirect
81. #13094015	C₂³	semidirect
82. #13094011	C₂³	semidirect
83. #13094011	C₂³	semidirect
84. #13094008	C₂³	semidirect
85. #13094005	C₂³	semidirect
86. #13094005	C₂³	semidirect
87. #13094003	C₂³	semidirect
88. #13094001	C₂³	semidirect
89. #13093996	C₂³	semidirect
90. #13093995	C₂³	semidirect
91. #13093993	C₂³	semidirect
92. C₄×Dic₉₄	C₂³	semidirect
93. #13093989	C₂³	semidirect
96. D₄×Dic₄₇	C₂³	semidirect
97. D₄×Dic₄₇	C₂³	semidirect
98. D₄×Dic₄₇	C₂³	semidirect
99. D₄×Dic₄₇	C₂³	semidirect
100. C₄×C₂²⋊D₄₇	C₂³	semidirect
101. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
102. #13093982	C₂³	semidirect
103. #13093980	C₂³	semidirect
104. #13093980	C₂³	semidirect
108. C₂×C₄⋊Dic₄₇	C₂³	semidirect
117. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
124. C₂×C₄×Dic₄₇	C₂³	semidirect
125. C₄²×D₄₇	C₂³	semidirect
152. C₂×D₄×C₄₇	#41	semidirect
230. D₄×C₄₇	C₂×#41	semidirect
288. C₂×D₄²	D₄₇	semidirect
296. C₂×C₄₇	#3481	semidirect
309. D₄²	C₂×D₄₇	semidirect
349. C₄₇	C₂×#3481	semidirect
450. C₂×D₄	#10625352	semidirect
522. D₄	C₂×#10625352	semidirect
572. C₂	#20256989	direct (N × H)

Maximal subgroups

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

subgroup	index
#20256989	2
C₂×#15689859	2
C₂×#15689830	2
C₂×#15689825	2
C₂×#15689804	2
C₂×#15689767	2
C₂×#15689671	2
C₂×#15689654	2
C₂×#15689629	2
C₂×C₄×#10625352	2
C₂²×D₄×Dic₄₇	2
C₂×D₄²×C₄₇	2
C₂×#3481	47

Subgroups — C2×#20256989 #27123355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256989 #27123355