Subgroups — #26214365

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689160	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
4	#20245742	C₂	1	2	yes	maximal
5	#20243286	C₂	1	2	yes	maximal, complemented
6	#20243284	C₂	1	2	yes	maximal, complemented
7	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243106	C₂	1	2	yes	maximal
11	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₂²	1	2	yes	—
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	#15689160	C₄	1	8	yes	complemented
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093957	C₂²	1	2	yes	—
21	#107×D₄₇	C₄	1	8	yes	complemented
22	C₂×#13093955	C₂²	1	2	yes	—
23	#15689077	C₄	1	8	yes	complemented
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₄×Dic₄₇⋊C₄	—	2	2	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	#15688974	—	2	2	no	—
32	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
33	#15688970	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625324	—	2	2	no	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
52	#13093982	—	2	4	no	—
53	#13093982	C₂×C₄	1	8	yes	—
54	#13093981	C₂×C₄	1	4	yes	—
55	#13093981	Q₈	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
61	C₄⋊C₄×D₄₇	—	2	4	no	—
62	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
65	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	2	no	—
68	C₂×C₄×Dic₄₇	—	2	2	no	—
69	C₂×C₄×Dic₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	#13093958	C₂×C₄	1	4	yes	—
72	#13093958	C₂×C₄	1	4	yes	complemented
73	#13093957	C₂×C₄	1	8	yes	—
74	#13093955	C₂×C₄	1	8	yes	complemented
75	#13093935	C₂×C₄	1	4	yes	complemented
76	#13093934	C₂×C₄	1	4	yes	complemented
77	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#107×C₄₇	C₂×C₄	1	4	yes	—
88	#107×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
90	#95×C₄₇	—	2	2	no	—
91	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	—	2	8	no	—
103	C₂×C₄×D₄₇	—	8	2	no	—
104	C₂×C₄×D₄₇	—	8	2	no	—
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
109	C₂×C₄×D₄₇	#41	1	2	yes	—
110	C₂×C₄×D₄₇	#41	1	2	yes	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₄²×C₄₇	—	8	2	no	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	—	2	8	no	—
125	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
131	Dic₄₇⋊C₄	—	2	8	no	—
132	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
133	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
134	C₄×Dic₄₇	—	2	8	no	—
135	C₄×Dic₄₇	—	8	2	no	—
136	C₄×Dic₄₇	—	8	2	no	—
137	C₄×Dic₄₇	—	8	2	no	—
138	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
139	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	#10625324	—	2	8	no	—
147	C₈×D₄₇	C₄²	1	16	yes	complemented
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	1	no	—
150	C₂²×D₄₇	—	2	1	no	—
151	C₂²×D₄₇	—	2	1	no	—
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂²×D₄₇	C₄×D₄	1	2	yes	—
155	C₂²×D₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
186	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
188	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
189	C₄×D₄₇	—	8	8	no	—
190	C₄×D₄₇	C₂×C₄²	1	4	yes	—
191	C₄×D₄₇	#117	1	4	yes	—
192	C₄×D₄₇	C₄×Q₈	1	4	yes	—
193	C₄×D₄₇	C₄×Q₈	1	4	yes	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	C₂×C₄²	1	4	yes	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	C₂×C₄²	1	4	yes	—
198	#20455	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₄₇	#576	1	1	yes	characteristic
203	C₂²×C₄₇	#576	1	1	yes	characteristic
204	C₂²×C₄₇	#578	1	1	yes	characteristic
205	C₂²×C₄₇	#578	1	1	yes	characteristic
206	C₂×D₄₇	—	2	2	no	—
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	4	4	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
218	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
219	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
221	Dic₄₇	—	2	2	no	—
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	4	4	no	—
224	Dic₄₇	—	4	4	no	—
225	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
226	C₂×#427	—	47	1	no	—
227	C₂²×#107	—	47	1	no	—
228	C₂×#405	—	47	1	no	—
229	#2274	—	47	2	no	—
230	#1776	—	47	2	no	—
231	#1776	—	47	2	no	—
232	C₄×#107	—	47	1	no	—
233	C₄×#107	—	47	1	no	—
234	C₄×#107	—	47	1	no	—
235	C₄×#107	D₄₇	1	1	yes	characteristic, complemented
236	#1736	—	47	2	no	—
237	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄₇	#2913	1	1	yes	characteristic
239	C₂×C₄₇	#2913	1	1	yes	characteristic
240	C₂×C₄₇	#2948	1	1	yes	characteristic
241	C₂×C₄₇	#2950	1	1	yes	characteristic
242	C₂×C₄₇	#2951	1	1	yes	characteristic
243	C₂×C₄₇	#2951	1	1	yes	characteristic
244	D₄₇	—	2	4	no	—
245	C₂²×M₁₆	—	47	1	no	—
246	C₂³×C₈	—	47	1	no	—
247	C₂×#117	—	47	1	no	—
248	C₂×#117	—	47	2	no	—
249	C₂²×C₄⋊C₄	—	47	2	no	—
250	#427	—	47	8	no	—
251	C₂×#107	—	47	1	no	—
252	C₂×#107	—	47	1	no	—
253	C₂×#107	—	47	2	no	—
254	C₂×#107	—	47	8	no	—
255	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
256	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
257	C₂×#106	—	47	2	no	—
258	#405	—	47	8	no	—
259	C₂×#97	—	47	1	no	—
260	C₂×#97	—	47	1	no	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
263	C₄×C₄⋊C₄	—	47	2	no	—
264	C₄×C₄⋊C₄	—	47	2	no	—
265	C₄×C₄⋊C₄	—	47	2	no	—
266	C₄×C₄⋊C₄	—	94	2	no	—
267	C₄×C₄⋊C₄	—	94	2	no	—
268	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
269	C₄×C₂²⋊C₄	—	94	2	no	—
270	C₄×C₂²⋊C₄	—	94	2	no	—
271	#340	—	47	2	no	—
272	#340	—	47	2	no	—
273	#340	—	47	2	no	—
274	#340	C₂×D₄₇	1	2	yes	—
275	C₄₇	#20455	1	1	yes	characteristic, complemented, Sylow
276	C₂³×C₄	—	47	1	no	—
277	C₂³×C₄	—	94	2	no	—
278	C₂×M₁₆	—	47	4	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	—	94	2	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	47	4	no	—
283	C₂²×C₈	—	47	4	no	—
284	C₂²×C₈	—	47	4	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
288	#117	—	47	4	no	—
289	#117	—	47	4	no	—
290	#117	—	47	8	no	—
291	#117	—	94	4	no	—
292	C₂×C₄⋊C₄	—	47	1	no	—
293	C₂×C₄⋊C₄	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄⋊C₄	—	47	2	no	—
296	C₂×C₄⋊C₄	—	47	8	no	—
297	C₂×C₄⋊C₄	—	94	4	no	—
298	C₂×C₄⋊C₄	—	94	2	no	—
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
301	C₂×C₂²⋊C₄	—	47	1	no	—
302	C₂×C₂²⋊C₄	—	47	1	no	—
303	C₂×C₂²⋊C₄	—	94	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	94	2	no	—
307	C₂×C₄²	—	94	2	no	—
308	C₂×C₄²	—	94	2	no	—
309	C₂×C₄²	—	94	2	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#107	—	47	4	no	—
312	#107	—	47	4	no	—
313	#107	—	47	8	no	—
314	#107	C₄×D₄₇	1	4	yes	—
315	#107	C₄×D₄₇	1	4	yes	complemented
316	#106	—	47	8	no	—
317	#97	—	47	4	no	—
318	#97	—	47	4	no	—
319	C₄×C₈	—	47	4	no	—
320	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
321	#95	—	2	2	no	—
322	#95	—	94	2	no	—
323	#95	—	94	2	no	—
324	#95	—	94	2	no	—
325	C₂⁴	—	47	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	2	no	—
330	C₂²×C₄	—	47	2	no	—
331	C₂²×C₄	—	47	2	no	—
332	C₂²×C₄	—	47	2	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	2	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	47	1	no	—
337	C₂²×C₄	—	94	8	no	—
338	C₂²×C₄	—	94	2	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	—	376	2	no	—
341	C₂²×C₄	—	376	2	no	—
342	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	M₁₆	—	94	8	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	47	2	no	—
350	C₂×C₈	—	47	2	no	—
351	C₂×C₈	—	47	16	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
356	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
357	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
358	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	47	4	no	—
362	C₄⋊C₄	—	47	4	no	—
363	C₄⋊C₄	—	47	4	no	—
364	C₄⋊C₄	—	47	4	no	—
365	C₄⋊C₄	—	94	8	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
369	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
370	C₂²⋊C₄	—	47	4	no	—
371	C₂²⋊C₄	—	47	4	no	—
372	C₂²⋊C₄	—	94	8	no	—
373	C₄²	—	8	2	no	—
374	C₄²	—	47	2	no	—
375	C₄²	—	47	2	no	—
376	C₄²	—	94	8	no	—
377	C₄²	—	376	2	no	—
378	C₄²	—	376	2	no	—
379	C₄²	—	376	2	no	—
380	C₄²	C₂×C₄×D₄₇	1	2	yes	—
381	C₄²	Q₈×D₄₇	1	2	yes	—
382	C₂³	—	47	2	no	—
383	C₂³	—	47	2	no	—
384	C₂³	—	47	2	no	—
385	C₂³	—	94	1	no	—
386	C₂³	—	94	1	no	—
387	C₂³	—	94	1	no	—
388	C₂³	—	94	1	no	—
389	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	47	2	no	—
402	C₂×C₄	—	47	2	no	—
403	C₂×C₄	—	47	4	no	—
404	C₂×C₄	—	47	4	no	—
405	C₂×C₄	—	47	4	no	—
406	C₂×C₄	—	47	4	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	2	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	4	no	—
415	C₂×C₄	—	376	8	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	2	no	—
418	C₂×C₄	—	188	2	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
421	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
426	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
427	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	47	4	no	—
430	C₈	—	94	2	no	—
431	C₈	C₄²×D₄₇	1	4	yes	—
432	C₂²	—	47	4	no	—
433	C₂²	—	94	2	no	—
434	C₂²	—	94	2	no	—
435	C₂²	—	94	2	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	94	2	no	—
438	C₂²	—	94	2	no	—
439	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
440	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
441	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
442	C₂²	#15689924	1	1	yes	characteristic
443	C₂²	#15689925	1	1	yes	characteristic
444	C₂²	#15689936	1	1	yes	characteristic
445	C₂²	#15689937	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	47	4	no	—
451	C₄	—	94	2	no	—
452	C₄	—	94	2	no	—
453	C₄	—	188	4	no	—
454	C₄	—	188	4	no	—
455	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
456	C₄	#117×D₄₇	1	1	yes	characteristic
457	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
458	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
459	C₂	—	94	4	no	—
460	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
461	C₂	#20251984	1	1	yes	characteristic
462	C₂	#20251985	1	1	yes	characteristic
463	C₂	#20252235	1	1	yes	characteristic
464	C₂	#20252251	1	1	yes	characteristic
465	C₂	#20252258	1	1	yes	characteristic
466	C₂	#20252263	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#107	D₄₇
hypocenter	C₄₇	#20455
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
5. #20243286	C₂	semidirect
6. #20243284	C₂	semidirect
7. #107×Dic₄₇	C₂	semidirect
8. #107×Dic₄₇	C₂	semidirect
9. C₄×#13093958	C₂	semidirect
11. C₄×#107×C₄₇	C₂	semidirect
17. #15689160	C₄	semidirect
21. #107×D₄₇	C₄	semidirect
23. #15689077	C₄	semidirect
72. #13093958	C₂×C₄	semidirect
74. #13093955	C₂×C₄	semidirect
75. #13093935	C₂×C₄	semidirect
76. #13093934	C₂×C₄	semidirect
77. C₈×Dic₄₇	C₂×C₄	semidirect
88. #107×C₄₇	C₂×C₄	semidirect
89. C₄×C₈×C₄₇	C₂×C₄	semidirect
147. C₈×D₄₇	C₄²	semidirect
235. C₄×#107	D₄₇	semidirect
275. C₄₇	#20455	semidirect
315. #107	C₄×D₄₇	semidirect
320. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689160	2
C₂×#107×D₄₇	2
C₂×#15689077	2
#20245742	2
#20243286	2
#20243284	2
#107×Dic₄₇	2
C₄×#13093958	2
#20243106	2
C₄×#107×C₄₇	2
#20455	47