Subgroups — C₂×#20246021 #26374916

Order 12032.

3262 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246021	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689016	C₂	1	2	yes	maximal, complemented
3	C₂×#15689009	C₂	1	2	yes	maximal, complemented
4	C₂×#15689003	C₂	1	2	yes	maximal
5	C₂×#15688998	C₂	1	2	yes	maximal, complemented
6	C₂×#15688991	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15688986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
20	#15689016	C₂²	1	16	yes	complemented
21	#15689009	C₂²	1	16	yes	complemented
22	#15689003	C₂²	1	16	yes	—
23	#15688998	C₂²	1	16	yes	complemented
24	#15688991	C₂²	1	8	yes	complemented
25	#15688989	C₂²	1	8	yes	complemented
26	#15688986	C₂²	1	8	yes	complemented
27	#15688983	C₂²	1	8	yes	complemented
28	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
29	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
30	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
31	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
32	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
33	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
34	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
35	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
36	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
37	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
38	C₂×C₄₇⋊#95	C₂²	1	8	yes	complemented
39	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
43	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	—
44	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂³×Dic₄₇	—	2	8	no	—
49	C₂³×Dic₄₇	—	4	4	no	—
50	C₂³×Dic₄₇	—	4	4	no	—
51	C₂³×Dic₄₇	C₂³	1	2	yes	—
52	C₂³×Dic₄₇	C₂³	1	2	yes	—
53	C₂³×Dic₄₇	C₂³	1	2	yes	—
54	C₂³×Dic₄₇	C₂³	1	2	yes	—
55	C₂³×Dic₄₇	C₂³	1	8	yes	—
56	C₂×C₄⋊Dic₄₇	—	4	4	no	—
57	C₂×C₄⋊Dic₄₇	—	4	4	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
60	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
61	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
62	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
63	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
64	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
65	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
66	C₂×C₄×Dic₄₇	—	4	4	no	—
67	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
68	C₄₇⋊#95	C₂³	1	4	yes	—
69	C₄₇⋊#95	C₂³	1	4	yes	—
70	C₄₇⋊#95	C₂³	1	8	yes	—
71	C₄₇⋊#95	C₂³	1	4	yes	—
72	C₄₇⋊#95	C₂³	1	4	yes	—
73	C₄₇⋊#95	C₂³	1	8	yes	—
74	C₄₇⋊#95	C₂³	1	8	yes	—
75	C₄₇⋊#95	C₂³	1	8	yes	—
76	C₄₇⋊#95	C₂³	1	8	yes	—
77	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₄₇	—	2	8	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
81	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
82	C₂³×C₄×C₄₇	—	4	4	no	—
83	C₂³×C₄×C₄₇	—	4	4	no	—
84	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
85	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
93	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
94	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
97	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
98	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
100	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
101	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
102	C₂⁴×C₄₇	—	2	4	no	—
103	C₂⁴×C₄₇	—	2	2	no	—
104	C₂⁴×C₄₇	—	2	2	no	—
105	C₂⁴×C₄₇	—	2	4	no	—
106	C₂⁴×C₄₇	—	2	4	no	—
107	C₂⁴×C₄₇	—	2	2	no	—
108	C₂⁴×C₄₇	—	2	2	no	—
109	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂⁴×C₄₇	#41	1	8	yes	—
112	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
113	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
114	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂×D₄×C₄₇	—	2	32	no	—
116	C₂×D₄×C₄₇	—	2	16	no	—
117	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	4	16	no	—
125	C₂²×C₄×C₄₇	—	4	16	no	—
126	C₂²×C₄×C₄₇	—	4	8	no	—
127	C₂²×C₄×C₄₇	—	4	8	no	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
135	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
140	C₂²×Dic₄₇	—	2	4	no	—
141	C₂²×Dic₄₇	—	2	4	no	—
142	C₂²×Dic₄₇	—	2	16	no	—
143	C₂²×Dic₄₇	—	2	4	no	—
144	C₂²×Dic₄₇	—	2	4	no	—
145	C₂²×Dic₄₇	—	2	4	no	—
146	C₂²×Dic₄₇	—	2	4	no	—
147	C₂²×Dic₄₇	—	2	4	no	—
148	C₂²×Dic₄₇	—	2	4	no	—
149	C₂²×Dic₄₇	—	2	4	no	—
150	C₂²×Dic₄₇	—	2	4	no	—
151	C₂²×Dic₄₇	—	2	4	no	—
152	C₂²×Dic₄₇	—	2	4	no	—
153	C₂²×Dic₄₇	—	4	8	no	—
154	C₂²×Dic₄₇	—	4	8	no	—
155	C₂²×Dic₄₇	—	4	32	no	—
156	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
157	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
158	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
159	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
161	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
162	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
163	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
164	C₂²⋊Dic₄₇	—	2	16	no	—
165	C₂²⋊Dic₄₇	—	4	8	no	—
166	C₂²⋊Dic₄₇	—	4	8	no	—
167	C₄⋊Dic₄₇	—	4	8	no	—
168	C₄⋊Dic₄₇	—	4	8	no	—
169	C₄×Dic₄₇	—	4	8	no	—
170	C₂³×C₄₇	—	2	8	no	—
171	C₂³×C₄₇	—	2	8	no	—
172	C₂³×C₄₇	—	2	16	no	—
173	C₂³×C₄₇	—	2	16	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	8	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	—	2	8	no	—
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	4	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	4	8	no	—
185	C₂³×C₄₇	—	4	8	no	—
186	C₂³×C₄₇	#117	1	16	yes	—
187	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
188	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
189	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
190	C₂³×C₄₇	C₂×#41	1	8	yes	—
191	C₂³×C₄₇	C₂×#41	1	4	yes	—
192	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
193	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
194	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
195	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
196	D₄×C₄₇	—	2	32	no	—
197	C₂×C₄×C₄₇	—	2	8	no	—
198	C₂×C₄×C₄₇	—	2	8	no	—
199	C₂×C₄×C₄₇	—	2	8	no	—
200	C₂×C₄×C₄₇	—	2	8	no	—
201	C₂×C₄×C₄₇	—	2	8	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	4	16	no	—
209	C₂×C₄×C₄₇	—	4	16	no	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
215	C₂×Dic₄₇	—	2	4	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	2	4	no	—
224	C₂×Dic₄₇	—	2	4	no	—
225	C₂×Dic₄₇	—	2	4	no	—
226	C₂×Dic₄₇	—	2	4	no	—
227	C₂×Dic₄₇	—	4	32	no	—
228	C₂×Dic₄₇	—	4	8	no	—
229	C₂×Dic₄₇	—	4	8	no	—
230	C₂×Dic₄₇	—	4	8	no	—
231	C₂×Dic₄₇	—	4	8	no	—
232	C₂×#2318	—	47	1	no	maximal, Sylow
233	C₂²×C₄₇	—	2	32	no	—
234	C₂²×C₄₇	—	2	4	no	—
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	2	8	no	—
237	C₂²×C₄₇	—	2	8	no	—
238	C₂²×C₄₇	—	2	4	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	4	16	no	—
242	C₂²×C₄₇	—	4	4	no	—
243	C₂²×C₄₇	—	4	4	no	—
244	C₂²×C₄₇	C₂×#117	1	8	yes	—
245	C₂²×C₄₇	C₂×#117	1	4	yes	—
246	C₂²×C₄₇	#518	1	4	yes	—
247	C₂²×C₄₇	#520	1	4	yes	—
248	C₂²×C₄₇	#538	1	8	yes	—
249	C₂²×C₄₇	#539	1	8	yes	—
250	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
251	C₂²×C₄₇	C₂²×#41	1	2	yes	—
252	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
253	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
254	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
255	C₄×C₄₇	—	2	4	no	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	2	4	no	—
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	—	2	4	no	—
260	Dic₄₇	—	4	4	no	—
261	Dic₄₇	—	4	4	no	—
262	Dic₄₇	—	4	4	no	—
263	Dic₄₇	—	4	4	no	—
264	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
265	#2318	—	47	16	no	—
266	C₂×#388	—	47	2	no	—
267	C₂×#387	—	47	2	no	—
268	C₂×#386	—	47	2	no	—
269	C₂×#385	—	47	2	no	—
270	C₂×#383	—	47	1	no	—
271	C₂×#382	—	47	1	no	—
272	C₂×#381	—	47	1	no	—
273	C₂×#380	—	47	1	no	—
274	C₂×C₄×C₂²⋊C₄	—	47	1	no	—
275	C₂²×#95	—	47	1	no	—
276	C₂×C₄₇	—	2	8	no	—
277	C₂×C₄₇	—	4	4	no	—
278	C₂×C₄₇	#2318	1	8	yes	complemented
279	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
280	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
282	C₂×C₄₇	C₂×#538	1	2	yes	—
283	C₂×C₄₇	C₂×#539	1	2	yes	—
284	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
285	C₂⁴×C₄	—	47	2	no	—
286	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
287	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
288	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
289	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
290	C₂²×C₄⋊C₄	—	47	2	no	—
291	C₂²×C₄⋊C₄	—	47	2	no	—
292	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	—	47	2	no	—
294	C₂²×C₂²⋊C₄	—	47	2	no	—
295	C₂²×C₂²⋊C₄	—	47	2	no	—
296	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
298	C₂²×C₄²	—	47	2	no	—
299	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
300	#388	—	47	16	no	—
301	#387	—	47	16	no	—
302	#386	—	47	16	no	—
303	#385	—	47	16	no	—
304	#383	—	47	8	no	—
305	#382	—	47	8	no	—
306	#381	—	47	8	no	—
307	#380	—	47	8	no	—
308	C₄×C₂²⋊C₄	—	47	8	no	—
309	C₂×#95	—	47	1	no	—
310	C₂×#95	—	47	1	no	—
311	C₂×#95	—	47	2	no	—
312	C₂×#95	—	47	1	no	—
313	C₂×#95	—	47	1	no	—
314	C₂×#95	—	47	2	no	—
315	C₂×#95	—	47	2	no	—
316	C₂×#95	—	47	2	no	—
317	C₂×#95	—	47	2	no	—
318	C₂×#95	—	47	8	no	—
319	C₄₇	C₂×#2318	1	1	yes	characteristic, complemented, Sylow
320	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
321	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
322	C₂²×D₄	—	2	8	no	—
323	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
324	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
325	C₂³×C₄	—	4	4	no	—
326	C₂³×C₄	—	4	4	no	—
327	C₂³×C₄	—	47	2	no	—
328	C₂³×C₄	—	47	2	no	—
329	C₂³×C₄	—	47	2	no	—
330	C₂³×C₄	—	47	2	no	—
331	C₂³×C₄	—	47	8	no	—
332	C₂³×C₄	—	94	8	no	—
333	C₂³×C₄	—	188	4	no	—
334	C₂³×C₄	—	188	4	no	—
335	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
336	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
337	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
339	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
340	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
341	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
342	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
343	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
344	C₄×D₄	C₂×Dic₄₇	1	64	yes	complemented
345	C₂×C₄⋊C₄	—	47	8	no	—
346	C₂×C₄⋊C₄	—	47	8	no	—
347	C₂×C₄⋊C₄	—	188	4	no	—
348	C₂×C₄⋊C₄	—	188	4	no	—
349	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
350	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
351	C₂×C₂²⋊C₄	—	47	8	no	—
352	C₂×C₂²⋊C₄	—	47	8	no	—
353	C₂×C₂²⋊C₄	—	47	8	no	—
354	C₂×C₂²⋊C₄	—	94	8	no	—
355	C₂×C₂²⋊C₄	—	188	4	no	—
356	C₂×C₂²⋊C₄	—	188	4	no	—
357	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
359	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
361	C₂×C₄²	—	47	8	no	—
362	C₂×C₄²	—	188	4	no	—
363	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
364	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
365	#95	—	47	4	no	—
366	#95	—	47	4	no	—
367	#95	—	47	8	no	—
368	#95	—	47	4	no	—
369	#95	—	47	4	no	—
370	#95	—	47	8	no	—
371	#95	—	47	8	no	—
372	#95	—	47	8	no	—
373	#95	—	47	8	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	#10625350	1	8	yes	—
382	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
383	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
384	C₂⁴	C₂³×D₄₇	1	2	yes	—
385	C₂⁴	C₂³×D₄₇	1	2	yes	—
386	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
387	C₂×D₄	—	2	32	no	—
388	C₂×D₄	—	2	16	no	—
389	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	16	no	—
397	C₂²×C₄	—	4	16	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	—	4	8	no	—
400	C₂²×C₄	—	47	4	no	—
401	C₂²×C₄	—	47	4	no	—
402	C₂²×C₄	—	47	4	no	—
403	C₂²×C₄	—	47	4	no	—
404	C₂²×C₄	—	94	4	no	—
405	C₂²×C₄	—	94	4	no	—
406	C₂²×C₄	—	94	16	no	—
407	C₂²×C₄	—	94	4	no	—
408	C₂²×C₄	—	94	4	no	—
409	C₂²×C₄	—	94	4	no	—
410	C₂²×C₄	—	94	4	no	—
411	C₂²×C₄	—	94	4	no	—
412	C₂²×C₄	—	94	4	no	—
413	C₂²×C₄	—	94	4	no	—
414	C₂²×C₄	—	94	4	no	—
415	C₂²×C₄	—	94	4	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	—	188	8	no	—
418	C₂²×C₄	—	188	8	no	—
419	C₂²×C₄	—	188	32	no	—
420	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
421	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
422	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
423	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
424	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
425	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
426	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	complemented
427	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
428	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
429	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
430	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
431	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
432	C₄⋊C₄	—	188	8	no	—
433	C₄⋊C₄	—	188	8	no	—
434	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
435	C₂²⋊C₄	—	94	16	no	—
436	C₂²⋊C₄	—	188	8	no	—
437	C₂²⋊C₄	—	188	8	no	—
438	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
439	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
440	C₄²	—	188	8	no	—
441	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
442	C₂³	—	2	8	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	16	no	—
448	C₂³	—	2	16	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	8	no	—
458	C₂³	#13093983	1	16	yes	—
459	C₂³	C₂³×Dic₄₇	1	4	yes	—
460	C₂³	C₂³×Dic₄₇	1	4	yes	—
461	C₂³	C₂³×Dic₄₇	1	2	yes	—
462	C₂³	C₂×#10625350	1	8	yes	—
463	C₂³	C₂×#10625350	1	4	yes	—
464	C₂³	#13094069	1	4	yes	—
465	C₂³	#13094070	1	2	yes	—
466	C₂³	#13094071	1	2	yes	—
467	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
468	D₄	—	2	32	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	16	no	—
481	C₂×C₄	—	4	16	no	—
482	C₂×C₄	—	94	4	no	—
483	C₂×C₄	—	94	4	no	—
484	C₂×C₄	—	94	4	no	—
485	C₂×C₄	—	94	4	no	—
486	C₂×C₄	—	94	4	no	—
487	C₂×C₄	—	94	4	no	—
488	C₂×C₄	—	94	4	no	—
489	C₂×C₄	—	94	4	no	—
490	C₂×C₄	—	94	4	no	—
491	C₂×C₄	—	94	4	no	—
492	C₂×C₄	—	94	4	no	—
493	C₂×C₄	—	94	4	no	—
494	C₂×C₄	—	188	32	no	—
495	C₂×C₄	—	188	8	no	—
496	C₂×C₄	—	188	8	no	—
497	C₂×C₄	—	188	8	no	—
498	C₂×C₄	—	188	8	no	—
499	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
500	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
501	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
502	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
503	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
504	C₂²	—	2	32	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	C₂×#13093983	1	8	yes	—
516	C₂²	C₂×#13093983	1	4	yes	—
517	C₂²	#15689598	1	4	yes	—
518	C₂²	#15689606	1	4	yes	—
519	C₂²	#15689706	1	8	yes	—
520	C₂²	#15689715	1	8	yes	—
521	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
522	C₂²	C₂²×#10625350	1	2	yes	—
523	C₂²	C₂×#13094069	1	2	yes	—
524	C₂²	C₂×#13094070	1	1	yes	characteristic
525	C₂²	C₂×#13094071	1	1	yes	characteristic
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	4	no	—
531	C₄	—	188	4	no	—
532	C₄	—	188	4	no	—
533	C₄	—	188	4	no	—
534	C₄	—	188	4	no	—
535	C₂	—	2	8	no	—
536	C₂	—	4	4	no	—
537	C₂	#20246021	1	8	yes	direct product factor
538	C₂	C₂²×#13093983	1	1	yes	characteristic
539	C₂	C₂×#15689598	1	1	yes	characteristic
540	C₂	C₂×#15689606	1	1	yes	characteristic
541	C₂	C₂×#15689706	1	2	yes	—
542	C₂	C₂×#15689715	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#2318
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20246021	C₂	direct (N × H)
2. C₂×#15689016	C₂	semidirect
3. C₂×#15689009	C₂	semidirect
5. C₂×#15688998	C₂	semidirect
6. C₂×#15688991	C₂	semidirect
7. C₂×#15688989	C₂	semidirect
8. C₂×#15688986	C₂	semidirect
9. C₂×#15688983	C₂	semidirect
10. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
11. C₂²×C₄₇⋊#95	C₂	semidirect
20. #15689016	C₂²	semidirect
21. #15689009	C₂²	semidirect
23. #15688998	C₂²	semidirect
24. #15688991	C₂²	semidirect
25. #15688989	C₂²	semidirect
26. #15688986	C₂²	semidirect
27. #15688983	C₂²	semidirect
28. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
38. C₂×C₄₇⋊#95	C₂²	semidirect
42. C₂×C₄×D₄×C₄₇	C₄	semidirect
85. C₂³×C₄×C₄₇	C₂×C₄	semidirect
93. C₄×D₄×C₄₇	C₂×C₄	semidirect
94. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
97. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
100. C₂×C₄²×C₄₇	C₂×C₄	semidirect
134. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
160. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
162. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
163. C₄²×C₄₇	C₂²×C₄	semidirect
278. C₂×C₄₇	#2318	semidirect
288. C₂×C₄×D₄	Dic₄₇	semidirect
319. C₄₇	C₂×#2318	semidirect
336. C₂³×C₄	C₂×Dic₄₇	semidirect
344. C₄×D₄	C₂×Dic₄₇	semidirect
349. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
358. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
363. C₂×C₄²	C₂×Dic₄₇	semidirect
426. C₂²×C₄	C₂²×Dic₄₇	semidirect
434. C₄⋊C₄	C₂²×Dic₄₇	semidirect
439. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
441. C₄²	C₂²×Dic₄₇	semidirect
537. C₂	#20246021	direct (N × H)

Maximal subgroups

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

subgroup	index
#20246021	2
C₂×#15689016	2
C₂×#15689009	2
C₂×#15689003	2
C₂×#15688998	2
C₂×#15688991	2
C₂×#15688989	2
C₂×#15688986	2
C₂×#15688983	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂²×C₄₇⋊#95	2
C₂²×C₄×D₄×C₄₇	2
C₂×#2318	47

Subgroups — C2×#20246021 #26374916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246021 #26374916