Subgroups — C₂×#20257237 #27124226

Order 12032.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257237	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689855	C₂	1	4	yes	maximal, complemented
3	C₂×#15689847	C₂	1	2	yes	maximal, complemented
4	C₂×#15689838	C₂	1	2	yes	maximal, complemented
5	C₂×#15689819	C₂	1	4	yes	maximal, complemented
6	C₂×#15689793	C₂	1	2	yes	maximal, complemented
7	C₂×#15689777	C₂	1	2	yes	maximal, complemented
8	C₂×#15689710	C₂	1	4	yes	maximal, complemented
9	C₂×#15689687	C₂	1	2	yes	maximal, complemented
10	C₂×#15689680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689633	C₂	1	4	yes	maximal, complemented
12	C₂×#15689606	C₂	1	2	yes	maximal, complemented
13	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#10625352	C₂²	1	4	yes	complemented
16	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
18	#15689855	C₂²	1	64	yes	complemented
19	#15689847	C₂²	1	32	yes	complemented
20	#15689838	C₂²	1	32	yes	complemented
21	#15689819	C₂²	1	64	yes	complemented
22	#15689793	C₂²	1	32	yes	complemented
23	#15689777	C₂²	1	32	yes	complemented
24	#15689710	C₂²	1	64	yes	complemented
25	#15689687	C₂²	1	32	yes	complemented
26	#15689680	C₂²	1	16	yes	complemented
27	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13094020	C₂²	1	4	yes	—
30	C₂×#13094019	C₂²	1	8	yes	complemented
31	C₂×#13094016	C₂²	1	2	yes	complemented
32	C₂×#13094013	C₂²	1	4	yes	—
33	C₂×#13094010	C₂²	1	8	yes	complemented
34	#15689633	C₂²	1	64	yes	complemented
35	C₂×#13094008	C₂²	1	8	yes	complemented
36	C₂×#13094006	C₂²	1	8	yes	complemented
37	C₂×#13094004	C₂²	1	4	yes	complemented
38	C₂×#13094003	C₂²	1	2	yes	—
39	C₂×#13094003	C₂²	1	2	yes	—
40	C₂×#13093998	C₂²	1	4	yes	—
41	C₂×#13093998	C₂²	1	4	yes	—
42	C₂×#13093996	C₂²	1	8	yes	complemented
43	C₂×#13093995	C₂²	1	4	yes	complemented
44	C₂×#13093992	C₂²	1	8	yes	—
45	#15689606	C₂²	1	32	yes	complemented
46	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
47	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
48	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
49	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
50	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
51	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
52	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
53	C₂×C₄×D₁₈₈	C₂²	1	16	yes	complemented
54	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
55	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
56	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	8	yes	complemented
57	C₂×#13093983	C₂²	1	2	yes	—
58	C₂×#13093983	C₂²	1	4	yes	complemented
59	C₂×#13093982	C₂²	1	4	yes	complemented
60	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
62	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
63	C₂²×#41×C₄₇	C₂²	1	2	yes	—
64	C₄₇×#532	C₂²	1	16	yes	complemented
65	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
68	C₂×#121×C₄₇	C₂²	1	2	yes	—
69	C₂×#121×C₄₇	C₂²	1	2	yes	—
70	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
72	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
73	C₂⁴×D₄₇	C₂³	1	2	yes	—
74	C₂×#10625352	—	4	16	no	—
75	C₂×#10625352	C₂³	1	32	yes	complemented
76	C₂²×Dic₉₄	C₂³	1	2	yes	—
77	C₂²×Dic₉₄	C₂³	1	2	yes	—
78	C₂²×D₁₈₈	—	2	8	no	—
79	C₂²×D₁₈₈	C₂³	1	2	yes	—
80	C₂²×D₁₈₈	C₂³	1	2	yes	—
81	C₂²×D₁₈₈	C₂³	1	8	yes	—
82	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
83	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
84	C₂³×Dic₄₇	C₂³	1	2	yes	—
85	C₂³×Dic₄₇	C₂³	1	8	yes	—
86	C₂²×C₄×D₄₇	—	4	8	no	—
87	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
88	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
89	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
90	#13094024	C₂³	1	8	yes	complemented
91	#13094024	C₂³	1	8	yes	complemented
92	#13094020	C₂³	1	32	yes	—
93	#13094019	C₂³	1	64	yes	complemented
94	#13094016	C₂³	1	16	yes	complemented
95	#13094013	C₂³	1	32	yes	—
96	#13094010	C₂³	1	64	yes	complemented
97	#13094008	C₂³	1	64	yes	complemented
98	#13094006	C₂³	1	64	yes	complemented
99	#13094004	C₂³	1	32	yes	complemented
100	#13094003	C₂³	1	16	yes	—
101	#13094003	C₂³	1	16	yes	—
102	#13093998	C₂³	1	32	yes	—
103	#13093998	C₂³	1	32	yes	—
104	#13093996	C₂³	1	64	yes	complemented
105	#13093995	C₂³	1	32	yes	complemented
106	#13093992	C₂³	1	64	yes	—
107	Q₈×Dic₄₇	C₂³	1	32	yes	complemented
108	C₄×Dic₉₄	C₂³	1	16	yes	complemented
109	C₄×Dic₉₄	C₂³	1	16	yes	complemented
110	C₄×D₁₈₈	C₂³	1	16	yes	—
111	C₄×D₁₈₈	C₂³	1	16	yes	—
112	C₄×D₁₈₈	C₂³	1	16	yes	—
113	C₄×D₁₈₈	C₂³	1	16	yes	—
114	D₄×Dic₄₇	C₂³	1	64	yes	—
115	D₄×Dic₄₇	C₂³	1	32	yes	complemented
116	(C₂²⋊D₄₇)⋊C₄	C₂³	1	64	yes	complemented
117	#13093983	C₂³	1	16	yes	—
118	#13093983	C₂³	1	32	yes	complemented
119	#13093982	C₂³	1	32	yes	complemented
120	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
121	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
123	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
124	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
125	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
126	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
127	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
128	C₂×C₄⋊Dic₄₇	C₂³	1	32	yes	complemented
129	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
130	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
131	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
133	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
134	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
135	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
136	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
137	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
138	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
139	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
140	C₂×#41×C₄₇	—	2	16	no	—
141	C₂×#41×C₄₇	C₂³	1	16	yes	—
142	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
143	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
144	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
145	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
149	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
152	#127×C₄₇	C₂³	1	8	yes	complemented
153	#124×C₄₇	C₂³	1	16	yes	complemented
154	#121×C₄₇	C₂³	1	16	yes	—
155	#121×C₄₇	C₂³	1	16	yes	—
156	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
157	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
158	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
162	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
167	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
168	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂³×D₄₇	—	2	8	no	—
170	C₂³×D₄₇	—	4	4	no	—
171	C₂³×D₄₇	—	4	4	no	—
172	C₂³×D₄₇	C₂⁴	1	4	yes	—
173	C₂³×D₄₇	C₂⁴	1	8	yes	—
174	#41×C₄₇	—	2	64	no	—
175	C₂×Q₈×C₄₇	—	2	8	no	—
176	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
177	C₂×D₄×C₄₇	—	2	16	no	—
178	C₂×D₄×C₄₇	—	2	8	no	—
179	C₂×D₄×C₄₇	—	2	8	no	—
180	C₂×D₄×C₄₇	—	4	4	no	—
181	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
182	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
183	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
184	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₄₇	—	2	16	no	—
186	C₂²×C₄×C₄₇	—	2	4	no	—
187	C₂²×C₄×C₄₇	—	4	2	no	—
188	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
195	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
200	C₂×C₂²⋊D₄₇	—	4	16	no	—
201	C₂×C₂²⋊D₄₇	—	4	16	no	—
202	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
203	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
204	C₂²×Dic₄₇	—	4	4	no	—
205	C₂²×Dic₄₇	—	4	16	no	—
206	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
207	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
208	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
209	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
210	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
211	#10625352	—	4	64	no	—
212	C₂×D₁₈₈	—	2	8	no	—
213	C₂×D₁₈₈	—	2	8	no	—
214	C₂×D₁₈₈	—	2	32	no	—
215	C₂×D₁₈₈	C₂⁴	1	8	yes	—
216	C₂×D₁₈₈	C₂⁴	1	8	yes	—
217	C₂×C₄×D₄₇	—	2	16	no	—
218	C₂×C₄×D₄₇	—	4	32	no	—
219	C₂×C₄×D₄₇	—	4	8	no	—
220	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
221	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
222	C₂×Dic₉₄	—	2	8	no	—
223	C₂×Dic₉₄	—	4	4	no	—
224	C₂×Dic₉₄	C₂⁴	1	8	yes	—
225	C₂×Dic₉₄	C₂⁴	1	8	yes	—
226	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
227	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
228	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
229	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
230	C₄²×C₄₇	C₂⁴	1	4	yes	—
231	C₄²×C₄₇	C₂⁴	1	4	yes	—
232	C₄²×C₄₇	C₂⁴	1	4	yes	—
233	C₄²×C₄₇	C₂⁴	1	4	yes	—
234	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
235	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
236	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
237	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
238	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
239	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
240	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
241	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
242	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
243	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
244	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
245	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
246	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
247	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
248	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
249	C₄×Dic₄₇	C₂⁴	1	32	yes	—
250	C₄×Dic₄₇	C₂⁴	1	16	yes	—
251	C₂³×C₄₇	—	2	2	no	—
252	C₂³×C₄₇	—	2	2	no	—
253	C₂³×C₄₇	—	2	8	no	—
254	C₂³×C₄₇	—	2	8	no	—
255	C₂³×C₄₇	—	2	8	no	—
256	C₂³×C₄₇	C₂×#41	1	4	yes	—
257	C₂³×C₄₇	C₂⁵	1	8	yes	—
258	C₂³×C₄₇	C₂⁵	1	2	yes	—
259	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
260	C₂²×D₄₇	—	2	16	no	—
261	C₂²×D₄₇	—	2	8	no	—
262	C₂²×D₄₇	—	2	8	no	—
263	C₂²×D₄₇	—	2	8	no	—
264	C₂²×D₄₇	—	4	8	no	—
265	C₂²×D₄₇	—	4	8	no	—
266	C₂²×D₄₇	—	4	32	no	—
267	C₂²×D₄₇	C₂⁵	1	8	yes	—
268	Q₈×C₄₇	—	2	16	no	—
269	D₄×C₄₇	—	2	32	no	—
270	D₄×C₄₇	—	2	16	no	—
271	D₄×C₄₇	—	2	16	no	—
272	D₄×C₄₇	—	4	8	no	—
273	C₂×C₄×C₄₇	—	2	8	no	—
274	C₂×C₄×C₄₇	—	2	2	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	2	no	—
277	C₂×C₄×C₄₇	—	2	32	no	—
278	C₂×C₄×C₄₇	—	2	8	no	—
279	C₂×C₄×C₄₇	—	4	4	no	—
280	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
281	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
282	C₂×C₄×C₄₇	C₂×#41	1	16	yes	complemented
283	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
284	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
285	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
286	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
287	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
288	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
289	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
290	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
291	C₂²⋊D₄₇	—	4	32	no	—
292	C₂²⋊D₄₇	—	4	32	no	—
293	C₂×Dic₄₇	—	2	8	no	—
294	C₂×Dic₄₇	—	2	8	no	—
295	C₂×Dic₄₇	—	2	8	no	—
296	C₂×Dic₄₇	—	4	8	no	—
297	C₂×Dic₄₇	—	4	32	no	—
298	C₂×Dic₄₇	C₂⁵	1	8	yes	—
299	C₂×Dic₄₇	C₂⁵	1	8	yes	—
300	C₂×Dic₄₇	C₂⁵	1	8	yes	—
301	D₁₈₈	—	2	16	no	—
302	D₁₈₈	—	2	16	no	—
303	C₄×D₄₇	—	2	32	no	—
304	C₄×D₄₇	—	4	16	no	—
305	Dic₉₄	—	2	16	no	—
306	Dic₉₄	—	4	8	no	—
307	C₂×#3506	—	47	1	no	maximal, Sylow
308	C₂²×C₄₇	—	2	2	no	—
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	8	no	—
311	C₂²×C₄₇	—	2	8	no	—
312	C₂²×C₄₇	—	2	8	no	—
313	C₂²×C₄₇	—	2	8	no	—
314	C₂²×C₄₇	—	4	16	no	—
315	C₂²×C₄₇	C₂²×#41	1	4	yes	—
316	C₂²×C₄₇	C₂²×#41	1	2	yes	—
317	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₄₇	#585	1	2	yes	—
319	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
320	C₂×D₄₇	—	2	8	no	—
321	C₂×D₄₇	—	2	8	no	—
322	C₂×D₄₇	—	2	8	no	—
323	C₂×D₄₇	—	4	32	no	—
324	C₂×D₄₇	—	4	16	no	—
325	C₄×C₄₇	—	2	8	no	—
326	C₄×C₄₇	—	2	2	no	—
327	C₄×C₄₇	—	2	2	no	—
328	C₄×C₄₇	—	2	2	no	—
329	C₄×C₄₇	C₂²×#41	1	4	yes	—
330	C₄×C₄₇	C₂²×#41	1	4	yes	—
331	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
332	Dic₄₇	—	2	8	no	—
333	Dic₄₇	—	2	8	no	—
334	Dic₄₇	—	2	8	no	—
335	#3506	—	47	32	no	—
336	C₂×#559	—	47	4	no	—
337	C₂×#556	—	47	2	no	—
338	C₂×#555	—	47	2	no	—
339	C₂×#553	—	47	4	no	—
340	C₂×#550	—	47	2	no	—
341	C₂×#547	—	47	2	no	—
342	C₂×#538	—	47	4	no	—
343	C₂×#535	—	47	2	no	—
344	C₂×#533	—	47	1	no	—
345	C₂×#532	D₄₇	1	1	yes	characteristic, complemented
346	C₂×#525	—	47	4	no	—
347	C₂×#520	—	47	2	no	—
348	C₂²×C₄×D₄	—	47	1	no	—
349	C₂×C₄₇	—	2	4	no	—
350	C₂×C₄₇	—	4	8	no	—
351	C₂×C₄₇	#3506	1	4	yes	complemented
352	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
353	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
355	D₄₇	—	4	8	no	—
356	C₂²×#41	—	47	4	no	—
357	C₂²×#41	C₂×D₄₇	1	2	yes	—
358	C₂³×D₄	—	47	1	no	—
359	C₂⁴×C₄	—	47	2	no	—
360	#559	—	47	64	no	—
361	#556	—	47	32	no	—
362	#555	—	47	32	no	—
363	#553	—	47	64	no	—
364	#550	—	47	32	no	—
365	#547	—	47	32	no	—
366	#538	—	47	64	no	—
367	#535	—	47	32	no	—
368	#533	—	47	16	no	—
369	#532	C₂×D₄₇	1	16	yes	complemented
370	C₂×C₄⋊Q₈	—	47	1	no	—
371	C₂×C₄⋊Q₈	—	47	1	no	—
372	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
373	C₂×#127	—	47	4	no	—
374	C₂×#127	C₂×D₄₇	1	1	yes	characteristic, complemented
375	C₂×#126	—	47	8	no	—
376	C₂×#125	—	47	2	no	—
377	C₂×#124	—	47	4	no	—
378	C₂×#124	—	47	8	no	—
379	C₂×#124	C₂×D₄₇	1	2	yes	complemented
380	#525	—	47	64	no	—
381	C₂×#123	—	47	8	no	—
382	C₂×#123	—	47	8	no	—
383	C₂×C₂²⋊Q₈	—	47	2	no	—
384	C₂×C₂²⋊Q₈	—	47	2	no	—
385	C₂×C₂²⋊Q₈	—	47	4	no	—
386	C₂×#121	—	47	4	no	—
387	C₂×#121	—	47	8	no	—
388	C₂×#121	—	47	4	no	—
389	C₂×#121	—	47	4	no	—
390	C₂×#121	C₂×D₄₇	1	2	yes	—
391	C₂×#121	C₂×D₄₇	1	2	yes	—
392	C₂×#120	—	47	8	no	—
393	#520	—	47	32	no	—
394	C₂×C₄×Q₈	—	47	4	no	—
395	C₂×C₄×Q₈	—	47	2	no	—
396	C₂×C₄×Q₈	—	47	2	no	—
397	C₂×C₄×D₄	—	47	8	no	—
398	C₂×C₄×D₄	—	47	4	no	—
399	C₂×C₄×D₄	—	47	8	no	—
400	C₂×C₄×D₄	—	47	2	no	—
401	C₂×C₄×D₄	—	47	2	no	—
402	C₂×C₄×D₄	—	47	2	no	—
403	C₂×C₄×D₄	—	47	2	no	—
404	C₂×C₄×D₄	—	47	16	no	—
405	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
406	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
407	C₂×#117	—	47	2	no	—
408	C₂×#117	—	47	4	no	—
409	C₂×#117	—	47	4	no	—
410	C₂²×C₄⋊C₄	—	47	1	no	—
411	C₂²×C₄⋊C₄	—	47	4	no	—
412	C₂²×C₂²⋊C₄	—	47	2	no	—
413	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
414	C₄₇	C₂×#3506	1	1	yes	characteristic, complemented, Sylow
415	C₂⁵	—	47	2	no	—
416	C₂×#41	—	2	16	no	—
417	C₂×#41	—	47	32	no	—
418	C₂×#41	—	188	16	no	—
419	C₂×#41	C₂²×D₄₇	1	16	yes	—
420	C₂²×Q₈	—	47	2	no	—
421	C₂²×Q₈	—	47	2	no	—
422	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
423	C₂²×D₄	—	47	8	no	—
424	C₂²×D₄	—	47	8	no	—
425	C₂²×D₄	—	47	2	no	—
426	C₂²×D₄	—	47	2	no	—
427	C₂²×D₄	—	47	8	no	—
428	C₂²×D₄	—	94	8	no	—
429	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
430	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
431	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
432	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
433	C₂³×C₄	—	47	2	no	—
434	C₂³×C₄	—	47	8	no	—
435	C₂³×C₄	—	47	4	no	—
436	C₂³×C₄	—	47	4	no	—
437	C₂³×C₄	—	47	16	no	—
438	C₂³×C₄	—	188	8	no	—
439	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
440	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
441	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
442	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
443	C₄⋊Q₈	—	47	8	no	—
444	C₄⋊Q₈	—	47	8	no	—
445	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
446	#127	—	47	32	no	—
447	#127	C₂²×D₄₇	1	8	yes	complemented
448	#126	—	47	64	no	—
449	#125	—	47	16	no	—
450	#124	—	47	32	no	—
451	#124	—	47	64	no	—
452	#124	C₂²×D₄₇	1	16	yes	complemented
453	#123	—	47	64	no	—
454	#123	—	47	64	no	—
455	C₂²⋊Q₈	—	47	16	no	—
456	C₂²⋊Q₈	—	47	16	no	—
457	C₂²⋊Q₈	—	47	32	no	—
458	#121	—	47	32	no	—
459	#121	—	47	64	no	—
460	#121	—	47	32	no	—
461	#121	—	47	32	no	—
462	#121	C₂²×D₄₇	1	16	yes	—
463	#121	C₂²×D₄₇	1	16	yes	—
464	#120	—	47	64	no	—
465	C₄×Q₈	—	47	32	no	—
466	C₄×Q₈	—	47	16	no	—
467	C₄×Q₈	—	47	16	no	—
468	C₄×D₄	—	47	64	no	—
469	C₄×D₄	—	47	32	no	—
470	C₄×D₄	—	47	64	no	—
471	C₄×D₄	—	47	16	no	—
472	C₄×D₄	—	47	16	no	—
473	C₄×D₄	—	47	16	no	—
474	C₄×D₄	—	47	16	no	—
475	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
476	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
477	#117	—	47	16	no	—
478	#117	—	47	32	no	—
479	#117	—	47	32	no	—
480	C₂×C₄⋊C₄	—	47	2	no	—
481	C₂×C₄⋊C₄	—	47	2	no	—
482	C₂×C₄⋊C₄	—	47	2	no	—
483	C₂×C₄⋊C₄	—	47	8	no	—
484	C₂×C₄⋊C₄	—	47	8	no	—
485	C₂×C₄⋊C₄	—	47	32	no	—
486	C₂×C₄⋊C₄	—	47	2	no	—
487	C₂×C₄⋊C₄	—	47	2	no	—
488	C₂×C₄⋊C₄	—	47	4	no	—
489	C₂×C₄⋊C₄	—	47	4	no	—
490	C₂×C₄⋊C₄	—	47	2	no	—
491	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
493	C₂×C₂²⋊C₄	—	47	4	no	—
494	C₂×C₂²⋊C₄	—	47	8	no	—
495	C₂×C₂²⋊C₄	—	47	4	no	—
496	C₂×C₂²⋊C₄	—	47	4	no	—
497	C₂×C₂²⋊C₄	—	47	16	no	—
498	C₂×C₂²⋊C₄	—	47	8	no	—
499	C₂×C₂²⋊C₄	—	47	8	no	—
500	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
502	C₂×C₄²	—	47	8	no	—
503	C₂×C₄²	—	47	4	no	—
504	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
505	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
506	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
507	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
508	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
509	C₂⁴	—	47	4	no	—
510	C₂⁴	—	47	8	no	—
511	C₂⁴	—	94	8	no	—
512	C₂⁴	—	188	4	no	—
513	C₂⁴	—	188	4	no	—
514	C₂⁴	C₂³×D₄₇	1	4	yes	—
515	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
516	#41	—	2	64	no	—
517	#41	—	188	64	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	47	8	no	—
520	C₂×Q₈	—	47	8	no	—
521	C₂×Q₈	—	94	8	no	—
522	C₂×Q₈	—	188	4	no	—
523	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
524	C₂×D₄	—	2	16	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	47	32	no	—
529	C₂×D₄	—	47	32	no	—
530	C₂×D₄	—	47	8	no	—
531	C₂×D₄	—	47	8	no	—
532	C₂×D₄	—	94	8	no	—
533	C₂×D₄	—	94	8	no	—
534	C₂×D₄	—	94	32	no	—
535	C₂×D₄	—	188	16	no	—
536	C₂×D₄	—	188	16	no	—
537	C₂×D₄	C₂³×D₄₇	1	16	yes	—
538	C₂×D₄	C₂³×D₄₇	1	8	yes	—
539	C₂×D₄	C₂³×D₄₇	1	8	yes	—
540	C₂×D₄	C₂³×D₄₇	1	8	yes	—
541	C₂²×C₄	—	2	16	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	47	4	no	—
545	C₂²×C₄	—	47	4	no	—
546	C₂²×C₄	—	47	4	no	—
547	C₂²×C₄	—	47	8	no	—
548	C₂²×C₄	—	47	32	no	—
549	C₂²×C₄	—	47	16	no	—
550	C₂²×C₄	—	47	16	no	—
551	C₂²×C₄	—	94	16	no	—
552	C₂²×C₄	—	188	32	no	—
553	C₂²×C₄	—	188	8	no	—
554	C₂²×C₄	—	188	4	no	—
555	C₂²×C₄	—	188	16	no	—
556	C₂²×C₄	#10625352	1	8	yes	complemented
557	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
558	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
559	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
560	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
561	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
562	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
563	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
564	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
565	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
566	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
567	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
568	C₄⋊C₄	—	47	16	no	—
569	C₄⋊C₄	—	47	16	no	—
570	C₄⋊C₄	—	47	8	no	—
571	C₄⋊C₄	—	47	8	no	—
572	C₄⋊C₄	—	47	8	no	—
573	C₄⋊C₄	—	47	32	no	—
574	C₄⋊C₄	—	47	8	no	—
575	C₄⋊C₄	—	47	8	no	—
576	C₄⋊C₄	—	47	8	no	—
577	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
578	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
579	C₂²⋊C₄	—	47	16	no	—
580	C₂²⋊C₄	—	47	32	no	—
581	C₂²⋊C₄	—	47	16	no	—
582	C₂²⋊C₄	—	47	16	no	—
583	C₂²⋊C₄	—	47	32	no	—
584	C₂²⋊C₄	—	47	32	no	—
585	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
586	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
587	C₄²	—	47	32	no	—
588	C₄²	—	47	16	no	—
589	C₄²	C₂³×D₄₇	1	4	yes	—
590	C₄²	C₂³×D₄₇	1	4	yes	—
591	C₄²	C₂³×D₄₇	1	4	yes	—
592	C₄²	C₂³×D₄₇	1	4	yes	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	8	no	—
596	C₂³	—	2	8	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	47	8	no	—
599	C₂³	—	94	16	no	—
600	C₂³	—	94	8	no	—
601	C₂³	—	94	8	no	—
602	C₂³	—	94	8	no	—
603	C₂³	—	188	8	no	—
604	C₂³	—	188	8	no	—
605	C₂³	—	188	32	no	—
606	C₂³	C₂×#10625352	1	4	yes	—
607	C₂³	C₂⁴×D₄₇	1	8	yes	—
608	C₂³	C₂⁴×D₄₇	1	2	yes	—
609	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
610	Q₈	—	2	16	no	—
611	Q₈	—	94	16	no	—
612	Q₈	—	188	8	no	—
613	D₄	—	2	32	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	16	no	—
616	D₄	—	4	8	no	—
617	D₄	—	94	16	no	—
618	D₄	—	94	16	no	—
619	D₄	—	188	32	no	—
620	D₄	—	188	32	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	32	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	47	8	no	—
629	C₂×C₄	—	47	8	no	—
630	C₂×C₄	—	47	8	no	—
631	C₂×C₄	—	94	8	no	—
632	C₂×C₄	—	94	8	no	—
633	C₂×C₄	—	94	8	no	—
634	C₂×C₄	—	94	32	no	—
635	C₂×C₄	—	188	16	no	—
636	C₂×C₄	—	188	8	no	—
637	C₂×C₄	—	188	32	no	—
638	C₂×C₄	C₂×#10625352	1	4	yes	—
639	C₂×C₄	C₂×#10625352	1	4	yes	—
640	C₂×C₄	C₂×#10625352	1	16	yes	complemented
641	C₂×C₄	#13094070	1	4	yes	—
642	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
643	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
644	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
645	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
646	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
647	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
648	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	4	16	no	—
656	C₂²	—	94	8	no	—
657	C₂²	—	94	8	no	—
658	C₂²	—	94	8	no	—
659	C₂²	—	188	32	no	—
660	C₂²	—	188	16	no	—
661	C₂²	C₂²×#10625352	1	4	yes	—
662	C₂²	C₂²×#10625352	1	2	yes	—
663	C₂²	C₂×#13094070	1	2	yes	—
664	C₂²	#15689959	1	2	yes	—
665	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	94	8	no	—
671	C₄	—	94	8	no	—
672	C₄	—	94	8	no	—
673	C₄	C₂²×#10625352	1	4	yes	—
674	C₄	C₂²×#10625352	1	4	yes	—
675	C₄	C₂×#13094070	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	8	no	—
678	C₂	—	188	8	no	—
679	C₂	#20257237	1	4	yes	direct product factor
680	C₂	C₂³×#10625352	1	1	yes	characteristic
681	C₂	C₂²×#13094070	1	1	yes	characteristic
682	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#3506
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20257237	C₂	direct (N × H)
2. C₂×#15689855	C₂	semidirect
3. C₂×#15689847	C₂	semidirect
4. C₂×#15689838	C₂	semidirect
5. C₂×#15689819	C₂	semidirect
6. C₂×#15689793	C₂	semidirect
7. C₂×#15689777	C₂	semidirect
8. C₂×#15689710	C₂	semidirect
9. C₂×#15689687	C₂	semidirect
10. C₂×#15689680	C₂	semidirect
11. C₂×#15689633	C₂	semidirect
12. C₂×#15689606	C₂	semidirect
13. C₂²×C₄×D₁₈₈	C₂	semidirect
14. C₂×C₄₇×#532	C₂	semidirect
15. C₂²×#10625352	C₂²	semidirect
18. #15689855	C₂²	semidirect
19. #15689847	C₂²	semidirect
20. #15689838	C₂²	semidirect
21. #15689819	C₂²	semidirect
22. #15689793	C₂²	semidirect
23. #15689777	C₂²	semidirect
24. #15689710	C₂²	semidirect
25. #15689687	C₂²	semidirect
26. #15689680	C₂²	semidirect
27. C₂×#13094024	C₂²	semidirect
28. C₂×#13094024	C₂²	semidirect
30. C₂×#13094019	C₂²	semidirect
31. C₂×#13094016	C₂²	semidirect
33. C₂×#13094010	C₂²	semidirect
34. #15689633	C₂²	semidirect
35. C₂×#13094008	C₂²	semidirect
36. C₂×#13094006	C₂²	semidirect
37. C₂×#13094004	C₂²	semidirect
42. C₂×#13093996	C₂²	semidirect
43. C₂×#13093995	C₂²	semidirect
45. #15689606	C₂²	semidirect
46. C₂×Q₈×Dic₄₇	C₂²	semidirect
47. C₂×C₄×Dic₉₄	C₂²	semidirect
48. C₂×C₄×Dic₉₄	C₂²	semidirect
53. C₂×C₄×D₁₈₈	C₂²	semidirect
55. C₂×D₄×Dic₄₇	C₂²	semidirect
56. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
58. C₂×#13093983	C₂²	semidirect
59. C₂×#13093982	C₂²	semidirect
61. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
64. C₄₇×#532	C₂²	semidirect
65. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
66. C₂×#127×C₄₇	C₂²	semidirect
67. C₂×#124×C₄₇	C₂²	semidirect
70. C₂×C₄×D₄×C₄₇	C₂²	semidirect
71. C₂×C₄×D₄×C₄₇	C₂²	semidirect
75. C₂×#10625352	C₂³	semidirect
90. #13094024	C₂³	semidirect
91. #13094024	C₂³	semidirect
93. #13094019	C₂³	semidirect
94. #13094016	C₂³	semidirect
96. #13094010	C₂³	semidirect
97. #13094008	C₂³	semidirect
98. #13094006	C₂³	semidirect
99. #13094004	C₂³	semidirect
104. #13093996	C₂³	semidirect
105. #13093995	C₂³	semidirect
107. Q₈×Dic₄₇	C₂³	semidirect
108. C₄×Dic₉₄	C₂³	semidirect
109. C₄×Dic₉₄	C₂³	semidirect
115. D₄×Dic₄₇	C₂³	semidirect
116. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
118. #13093983	C₂³	semidirect
119. #13093982	C₂³	semidirect
128. C₂×C₄⋊Dic₄₇	C₂³	semidirect
151. C₄⋊Q₈×C₄₇	C₂³	semidirect
152. #127×C₄₇	C₂³	semidirect
153. #124×C₄₇	C₂³	semidirect
156. C₄×D₄×C₄₇	C₂³	semidirect
157. C₄×D₄×C₄₇	C₂³	semidirect
188. C₂²×C₄×C₄₇	#41	semidirect
282. C₂×C₄×C₄₇	C₂×#41	semidirect
345. C₂×#532	D₄₇	semidirect
351. C₂×C₄₇	#3506	semidirect
369. #532	C₂×D₄₇	semidirect
372. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
374. C₂×#127	C₂×D₄₇	semidirect
379. C₂×#124	C₂×D₄₇	semidirect
405. C₂×C₄×D₄	C₂×D₄₇	semidirect
406. C₂×C₄×D₄	C₂×D₄₇	semidirect
414. C₄₇	C₂×#3506	semidirect
445. C₄⋊Q₈	C₂²×D₄₇	semidirect
447. #127	C₂²×D₄₇	semidirect
452. #124	C₂²×D₄₇	semidirect
475. C₄×D₄	C₂²×D₄₇	semidirect
476. C₄×D₄	C₂²×D₄₇	semidirect
556. C₂²×C₄	#10625352	semidirect
640. C₂×C₄	C₂×#10625352	semidirect
679. C₂	#20257237	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257237	2
C₂×#15689855	2
C₂×#15689847	2
C₂×#15689838	2
C₂×#15689819	2
C₂×#15689793	2
C₂×#15689777	2
C₂×#15689710	2
C₂×#15689687	2
C₂×#15689680	2
C₂×#15689633	2
C₂×#15689606	2
C₂²×C₄×D₁₈₈	2
C₂×C₄₇×#532	2
C₂×#3506	47

Subgroups — C2×#20257237 #27124226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257237 #27124226