Subgroups — #26234405

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
3	#20246317	C₂	1	2	yes	maximal
4	#20244158	C₂	1	2	yes	maximal, complemented
5	#20243589	C₂	1	2	yes	maximal, complemented
6	#20243583	C₂	1	2	yes	maximal, complemented
7	#20243552	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243417	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	2	yes	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	#15689161	—	2	4	no	—
15	C₂×#13093958	—	2	4	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093958	C₂²	1	2	yes	—
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093958	C₂²	1	1	yes	characteristic
21	C₂×#13093956	C₂²	1	2	yes	—
22	C₂×#13093956	C₂²	1	2	yes	—
23	#15689016	—	2	2	no	—
24	#15689009	—	2	2	no	—
25	#15689003	—	2	2	no	—
26	#15688989	C₂²	1	2	yes	—
27	#15688983	C₂²	1	2	yes	—
28	#15688983	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
30	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
31	#15688886	C₂²	1	2	yes	—
32	#15688886	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₈×D₄×C₄₇	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₇	—	2	2	no	—
43	#13093983	—	2	4	no	—
44	#13093983	—	4	2	no	—
45	C₂×C₄⋊Dic₄₇	—	2	4	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	—	4	2	no	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	#13093958	—	2	2	no	—
58	#13093958	—	2	2	no	—
59	#13093958	—	2	2	no	—
60	#13093958	—	2	4	no	—
61	#13093958	D₄	1	4	yes	complemented
62	#13093956	—	2	4	no	—
63	#13093956	—	4	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	—	2	2	no	—
73	C₂²×C₈×C₄₇	—	2	2	no	—
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	C₂²×C₈×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
83	C₄×D₄×C₄₇	Q₈	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
90	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
91	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
92	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	—	2	2	no	—
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	2	2	no	—
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	—	4	4	no	—
119	C₂²×Dic₄₇	—	4	4	no	—
120	C₂²×Dic₄₇	—	8	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	8	no	—
128	C₂×C₈×C₄₇	—	2	8	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	#41	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
136	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
137	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
140	C₂²⋊Dic₄₇	—	4	4	no	—
141	C₂²⋊Dic₄₇	—	4	4	no	—
142	C₂²⋊Dic₄₇	—	8	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	4	4	no	—
151	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
152	C₄×Dic₄₇	—	4	4	no	—
153	C₄×Dic₄₇	—	8	2	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂³×C₄₇	#135	1	2	yes	—
167	C₂³×C₄₇	#135	1	2	yes	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×Dic₄₇	—	2	4	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	4	2	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	C₂×Dic₄₇	—	4	2	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	C₂×Dic₄₇	—	4	2	no	—
206	C₂×Dic₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	8	8	no	—
209	C₈×C₄₇	—	2	2	no	—
210	C₈×C₄₇	—	2	2	no	—
211	C₈×C₄₇	—	2	2	no	—
212	C₈×C₄₇	C₄×D₄	1	4	yes	—
213	#22656	—	47	1	no	maximal, Sylow
214	C₂²×C₄₇	—	2	2	no	—
215	C₂²×C₄₇	—	2	2	no	—
216	C₂²×C₄₇	—	2	2	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	2	2	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	1	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	—	4	1	no	—
227	C₂²×C₄₇	#427	1	4	yes	complemented
228	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₄₇	D₄²	1	1	yes	characteristic
230	C₂²×C₄₇	#547	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
233	C₂²×C₄₇	#576	1	1	yes	characteristic
234	C₂²×C₄₇	#578	1	1	yes	characteristic
235	C₄×C₄₇	—	2	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₄₇	#520	1	1	yes	characteristic
241	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
242	C₄×C₄₇	#554	1	1	yes	characteristic
243	Dic₄₇	—	4	4	no	—
244	Dic₄₇	—	8	2	no	—
245	Dic₄₇	—	8	2	no	—
246	Dic₄₇	—	8	2	no	—
247	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic
248	C₂×#427	—	47	1	no	—
249	C₂²×#107	—	47	1	no	—
250	#2352	—	47	2	no	—
251	#1949	—	47	2	no	—
252	#1854	—	47	2	no	—
253	#1853	—	47	2	no	—
254	#1846	—	47	1	no	—
255	#1808	—	47	1	no	—
256	#1808	—	47	1	no	—
257	C₄×#107	—	47	1	no	—
258	C₂×C₄₇	—	2	4	no	—
259	C₂×C₄₇	—	4	2	no	—
260	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
262	C₂×C₄₇	#2913	1	1	yes	characteristic
263	C₂×C₄₇	#3280	1	1	yes	characteristic
264	C₂×C₄₇	#3285	1	1	yes	characteristic
265	C₂×C₄₇	#3336	1	1	yes	characteristic
266	C₂×C₄₇	#3339	1	1	yes	characteristic
267	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
268	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
270	C₂×#117	—	47	2	no	—
271	C₂²×C₄⋊C₄	—	47	2	no	—
272	C₈×D₄	Dic₄₇	1	8	yes	complemented
273	#427	—	94	4	no	—
274	C₂×#107	—	47	1	no	—
275	C₂×#107	—	47	1	no	—
276	C₂×#107	—	47	1	no	—
277	C₂×#107	—	47	1	no	—
278	C₂×#107	—	47	2	no	—
279	C₂×#107	—	94	4	no	—
280	C₂×#106	—	47	2	no	—
281	C₂×#106	—	47	2	no	—
282	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
286	#388	—	94	2	no	—
287	#387	—	94	2	no	—
288	#386	—	94	2	no	—
289	#382	—	47	2	no	—
290	#380	—	47	2	no	—
291	#380	—	47	2	no	—
292	C₄×C₄⋊C₄	—	47	2	no	—
293	C₄×C₂²⋊C₄	—	94	2	no	—
294	#340	—	47	2	no	—
295	#340	—	47	2	no	—
296	#340	—	47	2	no	—
297	C₄₇	#22656	1	1	yes	characteristic, complemented, Sylow
298	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
299	C₂³×C₄	—	94	2	no	—
300	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
307	C₂²×C₈	C₂×Dic₄₇	1	4	yes	complemented
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
310	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
311	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄×D₄	Dic₉₄	1	4	yes	—
313	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
314	#117	—	94	4	no	—
315	#117	—	188	2	no	—
316	C₂×C₄⋊C₄	—	47	2	no	—
317	C₂×C₄⋊C₄	—	47	2	no	—
318	C₂×C₄⋊C₄	—	47	2	no	—
319	C₂×C₄⋊C₄	—	47	2	no	—
320	C₂×C₄⋊C₄	—	94	4	no	—
321	C₂×C₄⋊C₄	—	94	2	no	—
322	C₂×C₄⋊C₄	—	188	2	no	—
323	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	94	2	no	—
325	C₂×C₂²⋊C₄	—	94	2	no	—
326	C₂×C₂²⋊C₄	—	94	2	no	—
327	C₂×C₂²⋊C₄	D₁₈₈	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	D₁₈₈	1	1	yes	characteristic
329	C₂×C₄²	—	94	2	no	—
330	C₂×C₄²	—	94	2	no	—
331	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
332	#107	—	47	4	no	—
333	#107	—	94	4	no	—
334	#107	—	94	2	no	—
335	#107	—	94	2	no	—
336	#107	—	94	2	no	—
337	#106	—	94	4	no	—
338	#106	—	188	2	no	—
339	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
340	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
341	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
342	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
343	#95	—	94	2	no	—
344	#95	—	94	2	no	—
345	#95	—	94	2	no	—
346	#95	—	94	2	no	—
347	#95	—	94	2	no	—
348	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
349	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	94	2	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	94	2	no	—
365	C₂²×C₄	—	376	2	no	—
366	C₂²×C₄	—	188	4	no	—
367	C₂²×C₄	—	188	4	no	—
368	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
369	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
370	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
374	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
375	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
376	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	8	no	—
384	C₂×C₈	—	2	8	no	—
385	C₂×C₈	D₄×D₄₇	1	2	yes	—
386	C₂×C₈	#10625352	1	2	yes	—
387	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
388	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
389	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
390	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
391	C₄⋊C₄	—	47	4	no	—
392	C₄⋊C₄	—	94	2	no	—
393	C₄⋊C₄	—	94	2	no	—
394	C₄⋊C₄	—	94	2	no	—
395	C₄⋊C₄	—	94	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	94	2	no	—
398	C₄⋊C₄	—	94	2	no	—
399	C₄⋊C₄	—	188	4	no	—
400	C₄⋊C₄	C₄⋊Dic₄₇	1	4	yes	—
401	C₂²⋊C₄	—	376	2	no	—
402	C₂²⋊C₄	—	188	4	no	—
403	C₂²⋊C₄	—	188	4	no	—
404	C₂²⋊C₄	C₄⋊Dic₄₇	1	4	yes	—
405	C₂²⋊C₄	C₄⋊Dic₄₇	1	4	yes	—
406	C₄²	—	376	2	no	—
407	C₄²	—	188	4	no	—
408	C₄²	C₂×Dic₉₄	1	2	yes	—
409	C₄²	C₂²×Dic₄₇	1	2	yes	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
421	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
422	C₂³	#13094046	1	2	yes	—
423	C₂³	#13094046	1	2	yes	—
424	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
425	D₄	—	2	8	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	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	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	94	4	no	—
443	C₂×C₄	—	376	8	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	—	188	2	no	—
448	C₂×C₄	—	188	2	no	—
449	C₂×C₄	—	188	2	no	—
450	C₂×C₄	—	188	2	no	—
451	C₂×C₄	—	188	2	no	—
452	C₂×C₄	—	188	2	no	—
453	C₂×C₄	—	188	2	no	—
454	C₂×C₄	—	188	2	no	—
455	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
456	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
457	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
458	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
459	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
462	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
463	C₂×C₄	#13094070	1	1	yes	characteristic
464	C₂×C₄	#13094071	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	D₄×Dic₄₇	1	4	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	#15689161	1	4	yes	complemented
483	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
484	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
485	C₂²	#15689777	1	1	yes	characteristic
486	C₂²	C₂×#13094046	1	1	yes	characteristic
487	C₂²	C₂×#13094046	1	1	yes	characteristic
488	C₂²	#15689928	1	1	yes	characteristic
489	C₂²	#15689940	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	376	2	no	—
495	C₄	—	376	2	no	—
496	C₄	—	376	2	no	—
497	C₄	—	188	4	no	—
498	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
499	C₄	#15689606	1	1	yes	characteristic
500	C₄	D₄×Dic₉₄	1	1	yes	characteristic
501	C₄	#15689830	1	1	yes	characteristic
502	C₂	—	2	4	no	—
503	C₂	—	4	2	no	—
504	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
505	C₂	C₂×#15689161	1	1	yes	characteristic
506	C₂	#20251988	1	1	yes	characteristic
507	C₂	#20255075	1	1	yes	characteristic
508	C₂	#20255131	1	1	yes	characteristic
509	C₂	#20255757	1	1	yes	characteristic
510	C₂	#20255791	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	#22656
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689161	C₂	semidirect
2. C₂²×#13093958	C₂	semidirect
4. #20244158	C₂	semidirect
5. #20243589	C₂	semidirect
6. #20243583	C₂	semidirect
7. #20243552	C₂	semidirect
8. #20243417	C₂	semidirect
9. #20243417	C₂	semidirect
10. C₄×#13093958	C₂	semidirect
37. C₈×D₄×C₄₇	C₄	semidirect
61. #13093958	D₄	semidirect
77. C₂²×C₈×C₄₇	C₂×C₄	semidirect
88. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
90. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
91. C₄×C₈×C₄₇	C₂×C₄	semidirect
227. C₂²×C₄₇	#427	semidirect
272. C₈×D₄	Dic₄₇	semidirect
297. C₄₇	#22656	semidirect
307. C₂²×C₈	C₂×Dic₄₇	semidirect
339. C₄⋊C₈	C₂×Dic₄₇	semidirect
341. C₂²⋊C₈	C₂×Dic₄₇	semidirect
342. C₄×C₈	C₂×Dic₄₇	semidirect
482. C₂²	#15689161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689161	2
C₂²×#13093958	2
#20246317	2
#20244158	2
#20243589	2
#20243583	2
#20243552	2
#20243417	2
C₄×#13093958	2
C₂×C₈×D₄×C₄₇	2
#22656	47