Subgroups — #26375285

Order 12032.

2638 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246203	C₂	1	4	yes	maximal, complemented
2	#20246155	C₂	1	4	yes	maximal, complemented
3	#20246137	C₂	1	2	yes	maximal, complemented
4	#20246114	C₂	1	2	yes	maximal, complemented
5	#20246083	C₂	1	4	yes	maximal, complemented
6	#20245879	C₂	1	4	yes	maximal, complemented
7	#20245853	C₂	1	2	yes	maximal, complemented
8	#20245833	C₂	1	4	yes	maximal, complemented
9	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
13	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
14	C₂×#13093983	C₂²	1	2	yes	—
15	C₂×#13093983	C₂²	1	4	yes	—
16	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
17	#15689030	C₂²	1	8	yes	—
18	#15689026	C₂²	1	4	yes	—
19	#15689026	C₂²	1	8	yes	—
20	#15689022	C₂²	1	4	yes	—
21	#15689016	C₂²	1	8	yes	—
22	#15689016	C₂²	1	8	yes	—
23	#15689009	C₂²	1	8	yes	—
24	#15689003	C₂²	1	8	yes	—
25	#15689003	C₂²	1	8	yes	—
26	#15689003	C₂²	1	8	yes	—
27	#15688998	C₂²	1	8	yes	—
28	#15688991	C₂²	1	2	yes	—
29	#15688989	C₂²	1	2	yes	—
30	#15688986	C₂²	1	2	yes	—
31	#15688983	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
34	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
36	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
37	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
38	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
39	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
40	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
41	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
42	#15688969	C₂²	1	2	yes	—
43	#15688969	C₂²	1	2	yes	—
44	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
45	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
46	C₂²×#41×C₄₇	C₂²	1	2	yes	—
47	C₄₇×#532	C₄	1	16	yes	complemented
48	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×#124×C₄₇	C₂²	1	2	yes	—
51	C₂×#121×C₄₇	C₂²	1	2	yes	—
52	C₂×#121×C₄₇	C₂²	1	2	yes	—
53	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
54	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
55	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
56	C₂³×Dic₄₇	C₂³	1	8	yes	—
57	D₄×Dic₄₇	—	2	16	no	—
58	#13093983	—	2	8	no	—
59	#13093983	—	4	8	no	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
63	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
64	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
65	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
68	C₂×C₄×Dic₄₇	—	4	8	no	—
69	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
71	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
73	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
75	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
77	C₄₇⋊#95	C₂³	1	4	yes	—
78	C₄₇⋊#95	C₂³	1	4	yes	—
79	C₄₇⋊#95	C₂³	1	4	yes	—
80	C₄₇⋊#95	C₂³	1	4	yes	—
81	C₄₇⋊#95	C₂³	1	8	yes	—
82	C₄₇⋊#95	C₂³	1	4	yes	—
83	C₄₇⋊#95	C₂³	1	8	yes	—
84	C₄₇⋊#95	C₂³	1	4	yes	—
85	C₂×#41×C₄₇	—	4	8	no	—
86	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
97	#127×C₄₇	C₂×C₄	1	8	yes	—
98	#124×C₄₇	C₂×C₄	1	16	yes	complemented
99	#121×C₄₇	C₂×C₄	1	16	yes	complemented
100	#121×C₄₇	C₂×C₄	1	16	yes	complemented
101	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
102	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
112	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
113	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
114	#41×C₄₇	—	4	32	no	—
115	C₂×Q₈×C₄₇	—	4	4	no	—
116	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₄₇	—	2	8	no	—
118	C₂×D₄×C₄₇	—	4	4	no	—
119	C₂×D₄×C₄₇	—	4	4	no	—
120	C₂×D₄×C₄₇	—	4	4	no	—
121	C₂×D₄×C₄₇	—	4	4	no	—
122	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
123	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
125	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	8	no	—
129	C₂²×C₄×C₄₇	—	2	8	no	—
130	C₂²×C₄×C₄₇	—	4	2	no	—
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	4	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×Dic₄₇	—	2	16	no	—
143	C₂²×Dic₄₇	—	4	8	no	—
144	C₂²×Dic₄₇	—	4	8	no	—
145	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
146	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
147	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
150	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
151	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
152	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
153	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
154	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
156	C₂²⋊Dic₄₇	—	2	8	no	—
157	C₂²⋊Dic₄₇	—	2	16	no	—
158	C₂²⋊Dic₄₇	—	4	8	no	—
159	C₂²⋊Dic₄₇	—	4	4	no	—
160	C₂²⋊Dic₄₇	—	4	8	no	—
161	C₄⋊Dic₄₇	—	2	8	no	—
162	C₄⋊Dic₄₇	—	2	8	no	—
163	C₄⋊Dic₄₇	—	4	8	no	—
164	C₄×Dic₄₇	—	2	4	no	—
165	C₄×Dic₄₇	—	2	4	no	—
166	C₄×Dic₄₇	—	2	8	no	—
167	C₄×Dic₄₇	—	2	4	no	—
168	C₄×Dic₄₇	—	4	8	no	—
169	C₄×Dic₄₇	—	4	2	no	—
170	C₄×Dic₄₇	—	4	2	no	—
171	C₄×Dic₄₇	#41	1	8	yes	complemented
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	8	no	—
174	C₂³×C₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
180	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
181	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
182	Q₈×C₄₇	—	4	8	no	—
183	D₄×C₄₇	—	2	16	no	—
184	D₄×C₄₇	—	4	8	no	—
185	D₄×C₄₇	—	4	8	no	—
186	D₄×C₄₇	—	4	16	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	8	no	—
194	C₂×C₄×C₄₇	—	2	32	no	—
195	C₂×C₄×C₄₇	—	2	8	no	—
196	C₂×C₄×C₄₇	—	4	4	no	—
197	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
206	C₂×Dic₄₇	—	2	4	no	—
207	C₂×Dic₄₇	—	2	4	no	—
208	C₂×Dic₄₇	—	2	4	no	—
209	C₂×Dic₄₇	—	2	8	no	—
210	C₂×Dic₄₇	—	2	8	no	—
211	C₂×Dic₄₇	—	2	4	no	—
212	C₂×Dic₄₇	—	2	4	no	—
213	C₂×Dic₄₇	—	2	8	no	—
214	C₂×Dic₄₇	—	4	32	no	—
215	C₂×Dic₄₇	C₂×#41	1	8	yes	—
216	#34086	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	8	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	8	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	2	8	no	—
223	C₂²×C₄₇	—	4	8	no	—
224	C₂²×C₄₇	—	4	4	no	—
225	C₂²×C₄₇	—	4	8	no	—
226	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
227	C₂²×C₄₇	C₂²×#41	1	2	yes	—
228	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
229	C₂²×C₄₇	#585	1	2	yes	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	8	no	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	C₄×#41	1	4	yes	—
236	C₄×C₄₇	#518	1	4	yes	—
237	Dic₄₇	—	2	8	no	—
238	Dic₄₇	—	4	4	no	—
239	Dic₄₇	—	4	8	no	—
240	C₂×#532	D₄₇	1	1	yes	characteristic
241	#2337	—	47	4	no	—
242	#2333	—	47	4	no	—
243	#2331	—	47	2	no	—
244	#2328	—	47	2	no	—
245	#2324	—	47	4	no	—
246	#2297	—	47	4	no	—
247	#2293	—	47	2	no	—
248	#2290	—	47	4	no	—
249	#2283	—	47	1	no	—
250	C₄²×D₄	—	47	2	no	—
251	C₄×#117	—	47	1	no	—
252	C₂×C₄₇	—	4	2	no	—
253	C₂×C₄₇	—	4	8	no	—
254	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
255	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
256	C₂×C₄₇	#3428	1	1	yes	characteristic
257	C₂×C₄₇	#3460	1	4	yes	—
258	C₂²×#41	C₂×D₄₇	1	2	yes	—
259	#532	Dic₄₇	1	16	yes	complemented
260	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
262	C₂×#124	C₂×D₄₇	1	2	yes	—
263	C₂×#121	C₂×D₄₇	1	2	yes	—
264	C₂×#121	C₂×D₄₇	1	2	yes	—
265	C₂×C₄×D₄	—	47	4	no	—
266	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
267	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
268	C₂×#117	—	47	2	no	—
269	C₂×#117	—	47	4	no	—
270	C₂²×C₄²	—	47	4	no	—
271	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
272	#391	—	47	8	no	—
273	#390	—	47	4	no	—
274	#390	—	47	8	no	—
275	#389	—	47	4	no	—
276	#388	—	47	8	no	—
277	#388	—	47	8	no	—
278	#387	—	47	8	no	—
279	#386	—	47	8	no	—
280	#386	—	47	8	no	—
281	#386	—	47	8	no	—
282	#385	—	47	8	no	—
283	#383	—	47	2	no	—
284	#382	—	47	2	no	—
285	#381	—	47	2	no	—
286	#380	—	47	2	no	—
287	C₄×C₄⋊C₄	—	47	4	no	—
288	C₄×C₄⋊C₄	—	47	2	no	—
289	C₄×C₄⋊C₄	—	47	2	no	—
290	C₄×C₄⋊C₄	—	47	2	no	—
291	C₄×C₂²⋊C₄	—	47	2	no	—
292	C₄×C₂²⋊C₄	—	47	2	no	—
293	C₄×C₂²⋊C₄	—	47	4	no	—
294	C₄×C₂²⋊C₄	—	47	2	no	—
295	C₄×C₂²⋊C₄	—	47	4	no	—
296	C₄×C₂²⋊C₄	—	47	8	no	—
297	#376	—	47	2	no	—
298	#376	—	47	2	no	—
299	C₄³	—	47	1	no	—
300	C₄³	—	47	1	no	—
301	C₄₇	#34086	1	1	yes	characteristic, complemented, Sylow
302	C₂×#41	—	4	8	no	—
303	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
304	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
305	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
306	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
307	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
308	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
309	C₂³×C₄	—	47	8	no	—
310	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
312	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
313	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
314	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
315	#127	C₂×Dic₄₇	1	8	yes	—
316	#124	C₂×Dic₄₇	1	16	yes	complemented
317	#121	C₂×Dic₄₇	1	16	yes	complemented
318	#121	C₂×Dic₄₇	1	16	yes	complemented
319	C₄×D₄	—	94	16	no	—
320	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
321	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
322	#117	—	94	8	no	—
323	#117	—	188	8	no	—
324	C₂×C₄⋊C₄	—	47	4	no	—
325	C₂×C₄⋊C₄	—	47	4	no	—
326	C₂×C₄⋊C₄	—	47	8	no	—
327	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
328	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
329	C₂×C₂²⋊C₄	—	47	4	no	—
330	C₂×C₂²⋊C₄	—	47	8	no	—
331	C₂×C₂²⋊C₄	—	47	8	no	—
332	C₂×C₂²⋊C₄	—	47	4	no	—
333	C₂×C₂²⋊C₄	—	47	8	no	—
334	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
336	C₂×C₄²	—	47	2	no	—
337	C₂×C₄²	—	47	2	no	—
338	C₂×C₄²	—	47	2	no	—
339	C₂×C₄²	—	47	4	no	—
340	C₂×C₄²	—	47	2	no	—
341	C₂×C₄²	—	47	2	no	—
342	C₂×C₄²	—	47	2	no	—
343	C₂×C₄²	—	47	8	no	—
344	C₂×C₄²	—	188	8	no	—
345	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
346	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
347	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
350	#95	—	47	4	no	—
351	#95	—	47	4	no	—
352	#95	—	47	4	no	—
353	#95	—	47	4	no	—
354	#95	—	47	4	no	—
355	#95	—	47	8	no	—
356	#95	—	47	4	no	—
357	#95	—	47	8	no	—
358	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
359	C₂⁴	C₂³×D₄₇	1	4	yes	—
360	#41	—	4	32	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	4	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
369	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
370	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
371	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	47	4	no	—
378	C₂²×C₄	—	47	8	no	—
379	C₂²×C₄	—	47	4	no	—
380	C₂²×C₄	—	94	16	no	—
381	C₂²×C₄	—	188	8	no	—
382	C₂²×C₄	—	188	8	no	—
383	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
384	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
385	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
386	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
387	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
394	C₄⋊C₄	—	94	8	no	—
395	C₄⋊C₄	—	94	8	no	—
396	C₄⋊C₄	—	188	8	no	—
397	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
398	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
399	C₂²⋊C₄	—	94	8	no	—
400	C₂²⋊C₄	—	94	16	no	—
401	C₂²⋊C₄	—	188	8	no	—
402	C₂²⋊C₄	—	188	4	no	—
403	C₂²⋊C₄	—	188	8	no	—
404	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
405	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
406	C₄²	—	47	8	no	—
407	C₄²	—	94	4	no	—
408	C₄²	—	94	4	no	—
409	C₄²	—	94	8	no	—
410	C₄²	—	94	4	no	—
411	C₄²	—	188	2	no	—
412	C₄²	—	188	2	no	—
413	C₄²	—	188	8	no	—
414	C₄²	C₂²×Dic₄₇	1	4	yes	—
415	C₄²	C₂²×Dic₄₇	1	4	yes	—
416	C₄²	C₂²×Dic₄₇	1	4	yes	—
417	C₄²	C₂²×Dic₄₇	1	4	yes	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	8	no	—
425	C₂³	C₂³×Dic₄₇	1	8	yes	—
426	C₂³	C₂³×Dic₄₇	1	2	yes	—
427	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
428	Q₈	—	4	8	no	—
429	D₄	—	2	16	no	—
430	D₄	—	4	8	no	—
431	D₄	—	4	8	no	—
432	D₄	—	4	16	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	32	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	47	8	no	—
444	C₂×C₄	—	94	4	no	—
445	C₂×C₄	—	94	4	no	—
446	C₂×C₄	—	94	4	no	—
447	C₂×C₄	—	94	8	no	—
448	C₂×C₄	—	94	8	no	—
449	C₂×C₄	—	94	4	no	—
450	C₂×C₄	—	94	4	no	—
451	C₂×C₄	—	94	8	no	—
452	C₂×C₄	—	188	32	no	—
453	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
454	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
455	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
456	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
457	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
458	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
459	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
460	C₂×C₄	#41×D₄₇	1	4	yes	—
461	C₂×C₄	#13094069	1	4	yes	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	8	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	8	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
472	C₂²	C₂×#41×D₄₇	1	2	yes	—
473	C₂²	C₂×#13094069	1	2	yes	—
474	C₂²	#15689959	1	2	yes	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	8	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	94	8	no	—
481	C₄	—	188	8	no	—
482	C₄	—	188	4	no	—
483	C₄	#41×Dic₄₇	1	4	yes	—
484	C₄	#15689598	1	4	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	8	no	—
487	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
488	C₂	C₂×#15689598	1	1	yes	characteristic
489	C₂	#20256591	1	1	yes	characteristic
490	C₂	#20256802	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#34086
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20246203	C₂	semidirect
2. #20246155	C₂	semidirect
3. #20246137	C₂	semidirect
4. #20246114	C₂	semidirect
5. #20246083	C₂	semidirect
6. #20245879	C₂	semidirect
7. #20245853	C₂	semidirect
8. #20245833	C₂	semidirect
9. #20245786	C₂	semidirect
10. C₄×D₄×Dic₄₇	C₂	semidirect
11. C₄×#13093983	C₂	semidirect
47. C₄₇×#532	C₄	semidirect
86. C₂×#41×C₄₇	C₂×C₄	semidirect
96. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
98. #124×C₄₇	C₂×C₄	semidirect
99. #121×C₄₇	C₂×C₄	semidirect
100. #121×C₄₇	C₂×C₄	semidirect
101. C₄×D₄×C₄₇	C₂×C₄	semidirect
102. C₄×D₄×C₄₇	C₂×C₄	semidirect
107. C₂×C₄²×C₄₇	C₂×C₄	semidirect
171. C₄×Dic₄₇	#41	semidirect
259. #532	Dic₄₇	semidirect
301. C₄₇	#34086	semidirect
303. C₂×#41	C₂×Dic₄₇	semidirect
314. C₄⋊Q₈	C₂×Dic₄₇	semidirect
316. #124	C₂×Dic₄₇	semidirect
317. #121	C₂×Dic₄₇	semidirect
318. #121	C₂×Dic₄₇	semidirect
320. C₄×D₄	C₂×Dic₄₇	semidirect
321. C₄×D₄	C₂×Dic₄₇	semidirect
345. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246203	2
#20246155	2
#20246137	2
#20246114	2
#20246083	2
#20245879	2
#20245853	2
#20245833	2
#20245786	2
C₄×D₄×Dic₄₇	2
C₄×#13093983	2
C₂×C₄₇×#532	2
#34086	47