Subgroups — #26234540

Order 12032.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10625329	C₂	1	2	yes	maximal
2	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244164	C₂	1	2	yes	maximal, complemented
5	#20243595	C₂	1	2	yes	maximal, complemented
6	#20243595	C₂	1	2	yes	maximal, complemented
7	#20243563	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243430	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243426	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	2	yes	—
14	#15689201	—	2	2	no	—
15	#15689195	—	2	2	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	2	no	—
18	#15689172	—	2	4	no	—
19	C₂×#13093960	—	2	4	no	—
20	C₂×#13093960	C₂²	1	1	yes	characteristic
21	C₂×#13093960	C₂²	1	2	yes	—
22	C₂×#13093960	C₂²	1	1	yes	characteristic
23	C₂×#13093960	C₂²	1	2	yes	—
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	C₂×#13093960	C₂²	1	2	yes	—
26	C₂×#13093960	C₂²	1	1	yes	characteristic
27	#15689147	C₂²	1	2	yes	—
28	#15689087	C₂²	1	2	yes	—
29	#15689087	C₂²	1	2	yes	—
30	C₄×#10625329	C₂²	1	2	yes	—
31	#15688888	C₂²	1	2	yes	—
32	#15688888	C₂²	1	2	yes	—
33	#15688888	C₂²	1	2	yes	—
34	C₂²×M₁₆×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	C₄₇×#435	C₄	1	4	yes	—
38	C₄₇×#435	C₄	1	4	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	4	2	no	—
48	C₂×#10625329	—	4	2	no	—
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	#13093960	—	2	2	no	—
56	#13093960	—	2	2	no	—
57	#13093960	—	2	2	no	—
58	#13093960	—	2	4	no	—
59	#13093960	—	2	4	no	—
60	#13093960	—	4	2	no	—
61	#13093960	D₄	1	4	yes	complemented
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093935	—	2	2	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₄₇	D₄	1	2	yes	—
87	C₄×D₄×C₄₇	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
93	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
94	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
96	#97×C₄₇	C₂×C₄	1	4	yes	—
97	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
98	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
99	C₂×D₄×C₄₇	—	4	2	no	—
100	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
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	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₄₇	—	2	8	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	1	no	—
128	C₂×C₈×C₄₇	—	2	4	no	—
129	C₂×C₈×C₄₇	—	2	4	no	—
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	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₇	#41	1	2	yes	—
136	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
137	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
139	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
141	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
142	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₇	C₂×D₄	1	2	yes	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	#10625329	—	2	2	no	—
147	#10625329	—	2	2	no	—
148	#10625329	—	2	2	no	—
149	#10625329	—	2	2	no	—
150	#10625329	—	2	2	no	—
151	#10625329	—	4	4	no	—
152	#10625329	—	4	4	no	—
153	#10625329	C₂×D₄	1	4	yes	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	4	4	no	—
159	C₂×C₄₇⋊C₈	—	4	4	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	1	no	—
167	C₂³×C₄₇	—	4	1	no	—
168	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	4	2	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	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₄₇	—	2	2	no	—
204	C₈×C₄₇	—	2	2	no	—
205	C₈×C₄₇	—	2	2	no	—
206	C₈×C₄₇	C₄×D₄	1	4	yes	—
207	C₄₇⋊C₈	—	2	4	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	C₄₇⋊C₈	—	4	2	no	—
211	#22668	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	1	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	8	1	no	—
225	C₂²×C₄₇	—	8	1	no	—
226	C₂²×C₄₇	#430	1	2	yes	complemented
227	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
229	C₂²×C₄₇	#554	1	1	yes	characteristic
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₇	#520	1	1	yes	characteristic
237	C₄×C₄₇	D₄²	1	1	yes	characteristic
238	C₄×C₄₇	#547	1	1	yes	characteristic
239	D₄×M₁₆	—	47	2	no	—
240	C₂×#435	D₄₇	1	1	yes	characteristic
241	C₂×#430	—	47	1	no	—
242	C₂²×#108	—	47	1	no	—
243	#1950	—	47	2	no	—
244	#1855	—	47	2	no	—
245	#1855	—	47	2	no	—
246	#1849	—	47	1	no	—
247	#1811	—	47	1	no	—
248	#1810	—	47	1	no	—
249	#1778	—	47	1	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	2	1	no	—
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	—	4	1	no	—
254	C₂×C₄₇	—	4	2	no	—
255	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
256	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
257	C₂×C₄₇	#2916	1	1	yes	characteristic
258	C₂²×M₁₆	—	47	2	no	—
259	C₂²×M₁₆	—	47	2	no	—
260	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
261	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
263	#436	—	94	2	no	—
264	#435	—	94	2	no	—
265	#435	—	94	2	no	—
266	#435	Dic₄₇	1	4	yes	—
267	#435	Dic₄₇	1	4	yes	—
268	C₈×D₄	—	94	2	no	—
269	#430	—	94	4	no	—
270	C₂×#108	—	47	1	no	—
271	C₂×#108	—	47	1	no	—
272	C₂×#108	—	47	1	no	—
273	C₂×#108	—	47	1	no	—
274	C₂×#108	—	47	2	no	—
275	C₂×#108	—	47	2	no	—
276	C₂×#108	—	47	2	no	—
277	C₂×#108	—	94	4	no	—
278	#423	—	47	2	no	—
279	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
280	#407	—	47	2	no	—
281	#407	—	47	2	no	—
282	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
284	C₄×M₁₆	—	47	2	no	—
285	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
286	#341	—	47	2	no	—
287	#341	—	47	2	no	—
288	#341	—	47	2	no	—
289	C₄₇	#22668	1	1	yes	characteristic, complemented, Sylow
290	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
291	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	47	2	no	—
296	C₂×M₁₆	—	47	2	no	—
297	C₂×M₁₆	—	47	2	no	—
298	C₂×M₁₆	—	47	2	no	—
299	C₂×M₁₆	—	94	2	no	—
300	C₂×M₁₆	—	94	2	no	—
301	C₂×M₁₆	—	94	4	no	—
302	C₂×M₁₆	—	94	4	no	—
303	C₂×M₁₆	—	188	2	no	—
304	C₂×M₁₆	—	188	2	no	—
305	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	94	2	no	—
309	C₂²×C₈	—	94	2	no	—
310	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
311	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
312	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
314	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₄×D₄	D₁₈₈	1	2	yes	—
317	C₄×D₄	D₁₈₈	1	2	yes	—
318	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
319	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
320	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	Dic₉₄	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	Dic₉₄	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
324	#108	—	47	4	no	—
325	#108	—	94	4	no	—
326	#108	—	94	4	no	—
327	#108	—	94	2	no	—
328	#108	—	94	2	no	—
329	#108	—	94	2	no	—
330	#108	—	188	2	no	—
331	C₄⋊C₈	—	94	2	no	—
332	C₄⋊C₈	—	94	2	no	—
333	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
334	C₂²⋊C₈	—	94	2	no	—
335	C₂²⋊C₈	—	94	2	no	—
336	C₂²⋊C₈	—	94	2	no	—
337	C₂²⋊C₈	—	94	2	no	—
338	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
339	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
340	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
341	#97	—	94	2	no	—
342	#97	C₂×Dic₄₇	1	4	yes	—
343	C₄×C₈	—	94	2	no	—
344	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
345	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
348	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
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	C₂×Dic₉₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
363	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
367	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
368	M₁₆	—	2	8	no	—
369	M₁₆	—	47	4	no	—
370	M₁₆	—	94	2	no	—
371	M₁₆	—	94	2	no	—
372	M₁₆	—	94	2	no	—
373	M₁₆	—	94	2	no	—
374	M₁₆	—	94	2	no	—
375	M₁₆	—	94	2	no	—
376	M₁₆	—	94	2	no	—
377	M₁₆	—	188	4	no	—
378	M₁₆	—	188	4	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	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	—	94	2	no	—
390	C₂×C₈	—	94	2	no	—
391	C₂×C₈	—	188	4	no	—
392	C₂×C₈	—	188	4	no	—
393	C₂×C₈	D₄×D₄₇	1	2	yes	—
394	C₂×C₈	#10625352	1	2	yes	—
395	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
396	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
397	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
398	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
399	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
400	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
401	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
402	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
403	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
404	C₂²⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
405	C₄²	C₂×D₁₈₈	1	2	yes	—
406	C₄²	C₂²×Dic₄₇	1	2	yes	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
416	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
417	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
418	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
419	D₄	—	2	4	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
440	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
441	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
443	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
444	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
447	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
448	C₂×C₄	#13094070	1	1	yes	characteristic
449	C₂×C₄	#13094071	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	94	4	no	—
454	C₈	—	188	2	no	—
455	C₈	—	188	2	no	—
456	C₈	—	188	2	no	—
457	C₈	D₄×Dic₄₇	1	4	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	#15689172	1	2	yes	complemented
473	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
474	C₂²	D₄×Dic₉₄	1	1	yes	characteristic
475	C₂²	#15689830	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
482	C₄	#15689606	1	1	yes	characteristic
483	C₄	D₄×D₁₈₈	1	1	yes	characteristic
484	C₄	#15689777	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
491	C₂	C₂×#15689172	1	1	yes	characteristic
492	C₂	#20251999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#435	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	#22668
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. C₂×#15689172	C₂	semidirect
3. C₂²×#13093960	C₂	semidirect
4. #20244164	C₂	semidirect
5. #20243595	C₂	semidirect
6. #20243595	C₂	semidirect
7. #20243563	C₂	semidirect
8. #20243430	C₂	semidirect
9. #20243426	C₂	semidirect
10. #20243294	C₂	semidirect
61. #13093960	D₄	semidirect
226. C₂²×C₄₇	#430	semidirect
289. C₄₇	#22668	semidirect
472. C₂²	#15689172	semidirect

Maximal subgroups

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

subgroup	index
D₄×#10625329	2
C₂×#15689172	2
C₂²×#13093960	2
#20244164	2
#20243595	2
#20243563	2
#20243430	2
#20243426	2
#20243294	2
C₂×C₄₇×#435	2
#22668	47