Subgroups — C₂×#20246248 #26375504

Order 12032.

3006 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246248	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689009	C₂	1	2	yes	maximal, complemented
3	C₂×#15689009	C₂	1	2	yes	maximal, complemented
4	C₂×#15688998	C₂	1	2	yes	maximal
5	C₂×#15688991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688986	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊C₄×Dic₄₇	C₂	1	2	yes	maximal
10	C₂×#15688969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
12	C₂²×#117×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×C₄×Dic₄₇	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
19	#15689009	C₂²	1	16	yes	complemented
20	#15689009	C₂²	1	16	yes	complemented
21	#15688998	C₂²	1	16	yes	—
22	#15688991	C₂²	1	8	yes	complemented
23	#15688989	C₂²	1	8	yes	complemented
24	#15688986	C₂²	1	8	yes	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
26	C₂²⋊C₄×Dic₄₇	C₂²	1	16	yes	—
27	#15688969	C₂²	1	8	yes	complemented
28	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
29	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
30	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
31	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
32	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
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	1	yes	characteristic
38	C₂×C₄₇⋊#95	C₂²	1	8	yes	—
39	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₄₇	C₄	1	16	yes	complemented
41	C₂×#117×C₄₇	C₂²	1	8	yes	—
42	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂³×Dic₄₇	—	2	8	no	—
49	C₂³×Dic₄₇	—	2	8	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	8	yes	—
55	C₂³×Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	—	2	8	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	C₂³	1	8	yes	—
62	C₂×C₄×Dic₄₇	—	2	8	no	—
63	C₂×C₄×Dic₄₇	—	4	4	no	—
64	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
65	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
66	C₄₇⋊#95	C₂³	1	4	yes	—
67	C₄₇⋊#95	C₂³	1	4	yes	—
68	C₄₇⋊#95	C₂³	1	8	yes	—
69	C₄₇⋊#95	C₂³	1	4	yes	—
70	C₄₇⋊#95	C₂³	1	8	yes	—
71	C₄₇⋊#95	C₂³	1	8	yes	—
72	C₄₇⋊#95	C₂³	1	8	yes	—
73	C₄₇⋊#95	C₂³	1	4	yes	—
74	C₄₇⋊#95	C₂³	1	8	yes	—
75	C₄₇⋊#95	C₂³	1	8	yes	—
76	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₇	—	2	8	no	—
78	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	#117×C₄₇	C₂×C₄	1	64	yes	complemented
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
89	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
93	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
95	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
96	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
97	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
98	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	2	2	no	—
101	C₂⁴×C₄₇	—	2	2	no	—
102	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂⁴×C₄₇	#41	1	8	yes	—
104	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
105	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	—	2	32	no	—
107	C₂²×C₄×C₄₇	—	2	16	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
129	C₂²×Dic₄₇	—	2	4	no	—
130	C₂²×Dic₄₇	—	2	4	no	—
131	C₂²×Dic₄₇	—	2	4	no	—
132	C₂²×Dic₄₇	—	2	4	no	—
133	C₂²×Dic₄₇	—	2	4	no	—
134	C₂²×Dic₄₇	—	2	4	no	—
135	C₂²×Dic₄₇	—	2	16	no	—
136	C₂²×Dic₄₇	—	2	4	no	—
137	C₂²×Dic₄₇	—	2	4	no	—
138	C₂²×Dic₄₇	—	2	4	no	—
139	C₂²×Dic₄₇	—	2	4	no	—
140	C₂²×Dic₄₇	—	2	4	no	—
141	C₂²×Dic₄₇	—	2	16	no	—
142	C₂²×Dic₄₇	—	4	8	no	—
143	C₂²×Dic₄₇	—	4	32	no	—
144	C₂²×Dic₄₇	#41	1	8	yes	—
145	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
146	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
147	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
148	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
150	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
151	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
152	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
153	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
154	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
155	C₂²⋊Dic₄₇	—	2	16	no	—
156	C₄⋊Dic₄₇	—	2	16	no	—
157	C₄⋊Dic₄₇	—	4	8	no	—
158	C₄×Dic₄₇	—	2	16	no	—
159	C₄×Dic₄₇	—	4	8	no	—
160	C₂³×C₄₇	—	2	8	no	—
161	C₂³×C₄₇	—	2	8	no	—
162	C₂³×C₄₇	—	2	16	no	—
163	C₂³×C₄₇	—	2	16	no	—
164	C₂³×C₄₇	—	2	4	no	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	#117	1	16	yes	—
168	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
169	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
170	C₂³×C₄₇	C₂×#41	1	4	yes	—
171	C₂³×C₄₇	C₂×#41	1	8	yes	—
172	C₂³×C₄₇	C₂×#41	1	4	yes	—
173	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
174	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
175	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
176	C₂×C₄×C₄₇	—	2	32	no	—
177	C₂×C₄×C₄₇	—	2	8	no	—
178	C₂×C₄×C₄₇	—	2	8	no	—
179	C₂×C₄×C₄₇	—	2	8	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	—	2	8	no	—
182	C₂×C₄×C₄₇	—	2	8	no	—
183	C₂×C₄×C₄₇	—	2	4	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
196	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
197	C₂×Dic₄₇	—	2	16	no	—
198	C₂×Dic₄₇	—	2	4	no	—
199	C₂×Dic₄₇	—	2	4	no	—
200	C₂×Dic₄₇	—	2	4	no	—
201	C₂×Dic₄₇	—	2	4	no	—
202	C₂×Dic₄₇	—	2	4	no	—
203	C₂×Dic₄₇	—	2	4	no	—
204	C₂×Dic₄₇	—	2	4	no	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	2	4	no	—
207	C₂×Dic₄₇	—	2	4	no	—
208	C₂×Dic₄₇	—	2	4	no	—
209	C₂×Dic₄₇	—	4	32	no	—
210	C₂×Dic₄₇	—	4	8	no	—
211	C₂×Dic₄₇	—	4	8	no	—
212	C₂×Dic₄₇	—	4	8	no	—
213	C₂×Dic₄₇	C₂×#41	1	8	yes	—
214	C₂×#2343	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	—	2	32	no	—
216	C₂²×C₄₇	—	2	4	no	—
217	C₂²×C₄₇	—	2	4	no	—
218	C₂²×C₄₇	—	2	8	no	—
219	C₂²×C₄₇	—	2	8	no	—
220	C₂²×C₄₇	C₂×#117	1	8	yes	—
221	C₂²×C₄₇	C₂×#117	1	4	yes	—
222	C₂²×C₄₇	C₄×#41	1	4	yes	—
223	C₂²×C₄₇	#520	1	4	yes	—
224	C₂²×C₄₇	#551	1	8	yes	—
225	C₂²×C₄₇	#552	1	8	yes	—
226	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
227	C₂²×C₄₇	C₂²×#41	1	2	yes	—
228	C₂²×C₄₇	C₂²×#41	1	2	yes	—
229	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	2	4	no	—
235	C₄×C₄₇	—	2	4	no	—
236	C₄×C₄₇	—	2	4	no	—
237	Dic₄₇	—	2	8	no	—
238	Dic₄₇	—	4	4	no	—
239	Dic₄₇	—	4	4	no	—
240	Dic₄₇	—	4	4	no	—
241	C₂²×#117	D₄₇	1	1	yes	characteristic
242	#2343	—	47	16	no	—
243	C₂×#387	—	47	2	no	—
244	C₂×#387	—	47	2	no	—
245	C₂×#385	—	47	2	no	—
246	C₂×#383	—	47	1	no	—
247	C₂×#382	—	47	1	no	—
248	C₂×#381	—	47	1	no	—
249	C₂×C₄×C₄⋊C₄	—	47	1	no	—
250	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
251	C₂×#376	—	47	1	no	—
252	C₂²×#95	—	47	1	no	—
253	C₂×C₄₇	—	2	8	no	—
254	C₂×C₄₇	#2343	1	8	yes	complemented
255	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
256	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
257	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
258	C₂×C₄₇	C₂×#551	1	2	yes	—
259	C₂×C₄₇	C₂×#552	1	2	yes	—
260	C₂⁴×C₄	—	47	2	no	—
261	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
262	C₂×#117	Dic₄₇	1	16	yes	complemented
263	C₂×#117	C₂×D₄₇	1	8	yes	—
264	C₂²×C₄⋊C₄	—	47	2	no	—
265	C₂²×C₄⋊C₄	—	47	2	no	—
266	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	—	47	2	no	—
269	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
271	C₂²×C₄²	—	47	2	no	—
272	C₂²×C₄²	—	47	2	no	—
273	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
274	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
275	#387	—	47	16	no	—
276	#387	—	47	16	no	—
277	#385	—	47	16	no	—
278	#383	—	47	8	no	—
279	#382	—	47	8	no	—
280	#381	—	47	8	no	—
281	C₄×C₄⋊C₄	—	47	8	no	—
282	C₄×C₂²⋊C₄	—	47	16	no	—
283	#376	—	47	8	no	—
284	C₂×#95	—	47	8	no	—
285	C₂×#95	—	47	1	no	—
286	C₂×#95	—	47	1	no	—
287	C₂×#95	—	47	2	no	—
288	C₂×#95	—	47	1	no	—
289	C₂×#95	—	47	2	no	—
290	C₂×#95	—	47	2	no	—
291	C₂×#95	—	47	2	no	—
292	C₂×#95	—	47	1	no	—
293	C₂×#95	—	47	2	no	—
294	C₂×#95	—	47	2	no	—
295	C₄₇	C₂×#2343	1	1	yes	characteristic, complemented, Sylow
296	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	8	no	—
298	C₂³×C₄	—	47	2	no	—
299	C₂³×C₄	—	47	2	no	—
300	C₂³×C₄	—	47	2	no	—
301	C₂³×C₄	—	47	2	no	—
302	C₂³×C₄	—	47	8	no	—
303	C₂³×C₄	—	94	8	no	—
304	C₂³×C₄	—	94	8	no	—
305	C₂³×C₄	—	188	4	no	—
306	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
307	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
308	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
310	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
312	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
313	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
314	#117	C₂×Dic₄₇	1	64	yes	complemented
315	C₂×C₄⋊C₄	—	47	8	no	—
316	C₂×C₄⋊C₄	—	47	8	no	—
317	C₂×C₄⋊C₄	—	94	8	no	—
318	C₂×C₄⋊C₄	—	188	4	no	—
319	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
320	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
321	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
322	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
323	C₂×C₂²⋊C₄	—	47	8	no	—
324	C₂×C₂²⋊C₄	—	94	8	no	—
325	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
327	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
329	C₂×C₄²	—	47	8	no	—
330	C₂×C₄²	—	47	8	no	—
331	C₂×C₄²	—	94	8	no	—
332	C₂×C₄²	—	188	4	no	—
333	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
334	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
335	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
336	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
337	#95	—	47	4	no	—
338	#95	—	47	4	no	—
339	#95	—	47	8	no	—
340	#95	—	47	4	no	—
341	#95	—	47	8	no	—
342	#95	—	47	8	no	—
343	#95	—	47	8	no	—
344	#95	—	47	4	no	—
345	#95	—	47	8	no	—
346	#95	—	47	8	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	#10625350	1	8	yes	—
351	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
352	C₂⁴	C₂³×D₄₇	1	2	yes	—
353	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	—	2	32	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	16	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	47	8	no	—
365	C₂²×C₄	—	47	4	no	—
366	C₂²×C₄	—	47	4	no	—
367	C₂²×C₄	—	47	4	no	—
368	C₂²×C₄	—	47	4	no	—
369	C₂²×C₄	—	94	16	no	—
370	C₂²×C₄	—	94	4	no	—
371	C₂²×C₄	—	94	4	no	—
372	C₂²×C₄	—	94	4	no	—
373	C₂²×C₄	—	94	4	no	—
374	C₂²×C₄	—	94	4	no	—
375	C₂²×C₄	—	94	4	no	—
376	C₂²×C₄	—	94	4	no	—
377	C₂²×C₄	—	94	16	no	—
378	C₂²×C₄	—	94	4	no	—
379	C₂²×C₄	—	94	4	no	—
380	C₂²×C₄	—	94	4	no	—
381	C₂²×C₄	—	94	4	no	—
382	C₂²×C₄	—	188	8	no	—
383	C₂²×C₄	—	188	32	no	—
384	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
385	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
386	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
387	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
388	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
389	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
390	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
391	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
392	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
393	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
394	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
395	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
396	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
397	C₄⋊C₄	—	94	16	no	—
398	C₄⋊C₄	—	188	8	no	—
399	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
400	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
401	C₂²⋊C₄	—	94	16	no	—
402	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
403	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
404	C₄²	—	94	16	no	—
405	C₄²	—	188	8	no	—
406	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
407	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
408	C₂³	—	2	16	no	—
409	C₂³	—	2	16	no	—
410	C₂³	—	2	8	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	#13093983	1	16	yes	—
416	C₂³	C₂³×Dic₄₇	1	4	yes	—
417	C₂³	C₂³×Dic₄₇	1	2	yes	—
418	C₂³	#41×D₄₇	1	4	yes	—
419	C₂³	C₂×#10625350	1	8	yes	—
420	C₂³	C₂×#10625350	1	4	yes	—
421	C₂³	#13094070	1	2	yes	—
422	C₂³	#13094071	1	2	yes	—
423	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
424	C₂×C₄	—	2	32	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	47	8	no	—
440	C₂×C₄	—	94	16	no	—
441	C₂×C₄	—	94	4	no	—
442	C₂×C₄	—	94	4	no	—
443	C₂×C₄	—	94	4	no	—
444	C₂×C₄	—	94	4	no	—
445	C₂×C₄	—	94	4	no	—
446	C₂×C₄	—	94	4	no	—
447	C₂×C₄	—	94	4	no	—
448	C₂×C₄	—	94	4	no	—
449	C₂×C₄	—	94	4	no	—
450	C₂×C₄	—	94	4	no	—
451	C₂×C₄	—	94	4	no	—
452	C₂×C₄	—	188	32	no	—
453	C₂×C₄	—	188	8	no	—
454	C₂×C₄	—	188	8	no	—
455	C₂×C₄	—	188	8	no	—
456	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
457	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
458	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
459	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
460	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
461	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	32	no	—
467	C₂²	C₂×#13093983	1	8	yes	—
468	C₂²	C₂×#13093983	1	4	yes	—
469	C₂²	#41×Dic₄₇	1	4	yes	—
470	C₂²	#15689606	1	4	yes	—
471	C₂²	#15689797	1	8	yes	—
472	C₂²	#15689806	1	8	yes	—
473	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
474	C₂²	C₂×#41×D₄₇	1	2	yes	—
475	C₂²	C₂²×#10625350	1	2	yes	—
476	C₂²	C₂×#13094070	1	1	yes	characteristic
477	C₂²	C₂×#13094071	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	4	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	4	no	—
483	C₄	—	2	4	no	—
484	C₄	—	94	8	no	—
485	C₄	—	188	4	no	—
486	C₄	—	188	4	no	—
487	C₄	—	188	4	no	—
488	C₂	—	2	8	no	—
489	C₂	#20246248	1	8	yes	direct product factor
490	C₂	C₂²×#13093983	1	1	yes	characteristic
491	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
492	C₂	C₂×#15689606	1	1	yes	characteristic
493	C₂	C₂×#15689797	1	2	yes	—
494	C₂	C₂×#15689806	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂×#2343
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #20246248	C₂	direct (N × H)
2. C₂×#15689009	C₂	semidirect
3. C₂×#15689009	C₂	semidirect
5. C₂×#15688991	C₂	semidirect
6. C₂×#15688989	C₂	semidirect
8. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
10. C₂×#15688969	C₂	semidirect
19. #15689009	C₂²	semidirect
20. #15689009	C₂²	semidirect
22. #15688991	C₂²	semidirect
23. #15688989	C₂²	semidirect
25. C₄×C₄⋊Dic₄₇	C₂²	semidirect
27. #15688969	C₂²	semidirect
40. C₂×#117×C₄₇	C₄	semidirect
86. #117×C₄₇	C₂×C₄	semidirect
87. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
88. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
95. C₂×C₄²×C₄₇	C₂×C₄	semidirect
96. C₂×C₄²×C₄₇	C₂×C₄	semidirect
149. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
150. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
153. C₄²×C₄₇	C₂²×C₄	semidirect
154. C₄²×C₄₇	C₂²×C₄	semidirect
254. C₂×C₄₇	#2343	semidirect
262. C₂×#117	Dic₄₇	semidirect
295. C₄₇	C₂×#2343	semidirect
314. #117	C₂×Dic₄₇	semidirect
319. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
320. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
333. C₂×C₄²	C₂×Dic₄₇	semidirect
334. C₂×C₄²	C₂×Dic₄₇	semidirect
399. C₄⋊C₄	C₂²×Dic₄₇	semidirect
400. C₄⋊C₄	C₂²×Dic₄₇	semidirect
406. C₄²	C₂²×Dic₄₇	semidirect
407. C₄²	C₂²×Dic₄₇	semidirect
489. C₂	#20246248	direct (N × H)

Maximal subgroups

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

subgroup	index
#20246248	2
C₂×#15689009	2
C₂×#15688998	2
C₂×#15688991	2
C₂×#15688989	2
C₂×#15688986	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₂²⋊C₄×Dic₄₇	2
C₂×#15688969	2
C₂²×C₄₇⋊#95	2
C₂²×#117×C₄₇	2
C₂×#2343	47

Subgroups — C2×#20246248 #26375504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246248 #26375504