Subgroups — #35415053

Order 21248.

930 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24908071	C₂	1	2	yes	maximal, complemented
2	#24908022	C₂	1	2	yes	maximal, complemented
3	#24907756	C₂	1	2	yes	maximal
4	#24907643	C₂	1	2	yes	maximal, complemented
5	#24907606	C₂	1	1	yes	maximal, characteristic, complemented
6	#24907580	C₂	1	1	yes	maximal, characteristic, complemented
7	#24907531	C₂	1	1	yes	maximal, characteristic, complemented
8	#24907443	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19127456	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₈₃	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄×C₈₃⋊C₈	C₂²	1	2	yes	—
19	#19127456	C₂²	1	1	yes	characteristic
20	#19127456	C₂²	1	1	yes	characteristic
21	#19127456	C₂²	1	2	yes	—
22	#19127456	C₂²	1	2	yes	—
23	#19127456	C₂²	1	2	yes	—
24	#19127456	C₂²	1	1	yes	characteristic
25	#19127456	C₂²	1	2	yes	—
26	#19127456	C₂²	1	1	yes	characteristic
27	#19127456	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₃	C₄	1	1	yes	characteristic
29	C₂×C₄×D₄×C₈₃	C₄	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₃	C₄	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₈₃	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₈₃	C₄	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₈₃	C₄	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₈₃	C₄	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₈₃	C₄	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
42	C₄³×C₈₃	C₂²	1	1	yes	characteristic
43	C₂²×C₈₃⋊C₈	—	2	4	no	—
44	C₂²×C₈₃⋊C₈	—	4	2	no	—
45	C₂²×C₈₃⋊C₈	—	4	2	no	—
46	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
50	C₄⋊(C₈₃⋊C₈)	—	4	2	no	—
51	C₄⋊(C₈₃⋊C₈)	—	4	2	no	—
52	C₂²⋊(C₈₃⋊C₈)	—	2	4	no	—
53	C₂²⋊(C₈₃⋊C₈)	—	4	2	no	—
54	C₂²⋊(C₈₃⋊C₈)	—	4	2	no	—
55	C₄×C₈₃⋊C₈	—	4	2	no	—
56	C₂²×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₈₃	—	2	4	no	—
64	C₄×D₄×C₈₃	—	2	4	no	—
65	C₄×D₄×C₈₃	C₈	1	8	yes	complemented
66	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₃	—	4	2	no	—
76	C₂×C₄²×C₈₃	—	4	2	no	—
77	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
90	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
91	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
92	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
93	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
94	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
95	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₈₃⋊C₈	—	2	2	no	—
97	C₂×C₈₃⋊C₈	—	2	2	no	—
98	C₂×C₈₃⋊C₈	—	2	2	no	—
99	C₂×C₈₃⋊C₈	—	2	2	no	—
100	C₂×C₈₃⋊C₈	—	2	2	no	—
101	C₂×C₈₃⋊C₈	—	2	2	no	—
102	C₂×C₈₃⋊C₈	—	2	2	no	—
103	C₂×C₈₃⋊C₈	—	2	2	no	—
104	C₂×C₈₃⋊C₈	—	2	2	no	—
105	C₂×C₈₃⋊C₈	—	2	2	no	—
106	C₂×C₈₃⋊C₈	—	2	2	no	—
107	C₂×C₈₃⋊C₈	—	2	2	no	—
108	C₂×C₈₃⋊C₈	—	4	8	no	—
109	C₂⁴×C₈₃	C₂²×C₄	1	1	yes	characteristic
110	C₂⁴×C₈₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₈₃	—	2	2	no	—
112	C₂×D₄×C₈₃	—	2	2	no	—
113	C₂×D₄×C₈₃	C₂×C₈	1	4	yes	—
114	C₂²×C₄×C₈₃	—	2	1	no	—
115	C₂²×C₄×C₈₃	—	2	2	no	—
116	C₂²×C₄×C₈₃	—	2	1	no	—
117	C₂²×C₄×C₈₃	—	2	2	no	—
118	C₂²×C₄×C₈₃	—	2	2	no	—
119	C₂²×C₄×C₈₃	—	2	2	no	—
120	C₂²×C₄×C₈₃	—	2	1	no	—
121	C₂²×C₄×C₈₃	—	2	1	no	—
122	C₂²×C₄×C₈₃	—	4	1	no	—
123	C₂²×C₄×C₈₃	—	4	1	no	—
124	C₂²×C₄×C₈₃	—	4	1	no	—
125	C₂²×C₄×C₈₃	—	4	1	no	—
126	C₂²×C₄×C₈₃	—	4	1	no	—
127	C₂²×C₄×C₈₃	—	4	1	no	—
128	C₂²×C₄×C₈₃	—	4	1	no	—
129	C₂²×C₄×C₈₃	—	4	1	no	—
130	C₂²×C₄×C₈₃	C₂×C₈	1	4	yes	—
131	C₂²×C₄×C₈₃	C₂×C₈	1	4	yes	complemented
132	C₂²×C₄×C₈₃	M₁₆	1	4	yes	—
133	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₃	#41	1	4	yes	—
146	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₈₃	—	2	2	no	—
148	C₄⋊C₄×C₈₃	—	2	2	no	—
149	C₄⋊C₄×C₈₃	C₂×C₈	1	4	yes	complemented
150	C₂²⋊C₄×C₈₃	—	2	2	no	—
151	C₂²⋊C₄×C₈₃	—	2	2	no	—
152	C₂²⋊C₄×C₈₃	—	2	2	no	—
153	C₂²⋊C₄×C₈₃	—	2	2	no	—
154	C₂²⋊C₄×C₈₃	C₂×C₈	1	4	yes	—
155	C₂²⋊C₄×C₈₃	C₂×C₈	1	4	yes	complemented
156	C₄²×C₈₃	—	2	2	no	—
157	C₄²×C₈₃	—	2	2	no	—
158	C₄²×C₈₃	—	2	2	no	—
159	C₄²×C₈₃	—	2	2	no	—
160	C₄²×C₈₃	—	2	2	no	—
161	C₄²×C₈₃	—	2	1	no	—
162	C₄²×C₈₃	—	2	1	no	—
163	C₄²×C₈₃	—	4	1	no	—
164	C₄²×C₈₃	—	4	1	no	—
165	C₄²×C₈₃	—	4	1	no	—
166	C₄²×C₈₃	—	4	1	no	—
167	C₄²×C₈₃	—	4	1	no	—
168	C₄²×C₈₃	—	4	1	no	—
169	C₄²×C₈₃	C₂×C₈	1	4	yes	complemented
170	C₂³×C₈₃	—	2	1	no	—
171	C₂³×C₈₃	—	2	1	no	—
172	C₂³×C₈₃	—	2	1	no	—
173	C₂³×C₈₃	—	2	1	no	—
174	C₂³×C₈₃	—	2	1	no	—
175	C₂³×C₈₃	—	2	1	no	—
176	C₂³×C₈₃	—	2	1	no	—
177	C₂³×C₈₃	—	2	1	no	—
178	C₂³×C₈₃	—	2	1	no	—
179	C₂³×C₈₃	—	2	1	no	—
180	C₂³×C₈₃	#117	1	2	yes	—
181	C₂³×C₈₃	C₂²×C₈	1	2	yes	—
182	C₂³×C₈₃	C₂²×C₈	1	2	yes	—
183	C₂³×C₈₃	C₂×M₁₆	1	2	yes	—
184	C₂³×C₈₃	C₂³×C₄	1	1	yes	characteristic
185	D₄×C₈₃	—	2	8	no	—
186	C₂×C₄×C₈₃	—	2	1	no	—
187	C₂×C₄×C₈₃	—	2	1	no	—
188	C₂×C₄×C₈₃	—	2	1	no	—
189	C₂×C₄×C₈₃	—	2	1	no	—
190	C₂×C₄×C₈₃	—	2	1	no	—
191	C₂×C₄×C₈₃	—	2	1	no	—
192	C₂×C₄×C₈₃	—	2	1	no	—
193	C₂×C₄×C₈₃	—	2	1	no	—
194	C₂×C₄×C₈₃	—	2	1	no	—
195	C₂×C₄×C₈₃	—	2	1	no	—
196	C₂×C₄×C₈₃	—	2	1	no	—
197	C₂×C₄×C₈₃	—	2	1	no	—
198	C₂×C₄×C₈₃	—	2	1	no	—
199	C₂×C₄×C₈₃	—	2	1	no	—
200	C₂×C₄×C₈₃	—	2	1	no	—
201	C₂×C₄×C₈₃	—	2	1	no	—
202	C₂×C₄×C₈₃	—	2	4	no	—
203	C₂×C₄×C₈₃	—	2	4	no	—
204	C₂×C₄×C₈₃	—	2	1	no	—
205	C₂×C₄×C₈₃	—	2	1	no	—
206	C₂×C₄×C₈₃	—	2	1	no	—
207	C₂×C₄×C₈₃	—	2	1	no	—
208	C₂×C₄×C₈₃	—	2	1	no	—
209	C₂×C₄×C₈₃	—	2	1	no	—
210	C₂×C₄×C₈₃	—	2	1	no	—
211	C₂×C₄×C₈₃	—	2	1	no	—
212	C₂×C₄×C₈₃	—	2	1	no	—
213	C₂×C₄×C₈₃	—	2	1	no	—
214	C₂×C₄×C₈₃	—	2	1	no	—
215	C₂×C₄×C₈₃	—	2	1	no	—
216	C₂×C₄×C₈₃	—	4	4	no	—
217	C₂×C₄×C₈₃	—	4	4	no	—
218	C₂×C₄×C₈₃	—	4	4	no	—
219	C₂×C₄×C₈₃	—	4	4	no	—
220	C₂×C₄×C₈₃	—	4	2	no	—
221	C₂×C₄×C₈₃	—	4	2	no	—
222	C₂×C₄×C₈₃	#117	1	2	yes	—
223	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
224	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
225	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
226	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
227	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
228	C₂×C₄×C₈₃	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₈₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈₃⋊C₈	—	4	2	no	—
235	C₈₃⋊C₈	—	4	2	no	—
236	C₈₃⋊C₈	—	4	2	no	—
237	C₈₃⋊C₈	—	4	2	no	—
238	C₂²×C₈₃	—	2	2	no	—
239	C₂²×C₈₃	—	2	2	no	—
240	C₂²×C₈₃	—	2	2	no	—
241	C₂²×C₈₃	—	2	2	no	—
242	C₂²×C₈₃	—	2	2	no	—
243	C₂²×C₈₃	—	2	2	no	—
244	C₂²×C₈₃	—	2	2	no	—
245	C₂²×C₈₃	—	2	2	no	—
246	C₂²×C₈₃	—	2	2	no	—
247	C₂²×C₈₃	—	4	1	no	—
248	C₂²×C₈₃	—	4	1	no	—
249	C₂²×C₈₃	—	4	1	no	—
250	C₂²×C₈₃	—	4	1	no	—
251	C₂²×C₈₃	#431	1	4	yes	—
252	C₂²×C₈₃	C₂×#117	1	1	yes	characteristic
253	C₂²×C₈₃	#518	1	1	yes	characteristic
254	C₂²×C₈₃	#520	1	1	yes	characteristic
255	C₂²×C₈₃	C₂³×C₈	1	1	yes	characteristic
256	C₂²×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
257	C₂²×C₈₃	#568	1	1	yes	characteristic
258	C₂²×C₈₃	#568	1	1	yes	characteristic
259	C₄×C₈₃	—	2	2	no	—
260	C₄×C₈₃	—	2	2	no	—
261	C₄×C₈₃	—	2	2	no	—
262	C₄×C₈₃	—	2	2	no	—
263	C₄×C₈₃	—	2	2	no	—
264	C₄×C₈₃	—	2	2	no	—
265	C₄×C₈₃	—	2	2	no	—
266	C₄×C₈₃	—	2	2	no	—
267	C₄×C₈₃	—	4	1	no	—
268	C₄×C₈₃	—	4	1	no	—
269	C₄×C₈₃	—	4	1	no	—
270	C₄×C₈₃	—	4	1	no	—
271	C₄×C₈₃	#538	1	2	yes	—
272	C₄×C₈₃	#539	1	2	yes	—
273	#21996	—	83	1	no	maximal, Sylow
274	C₂×C₈₃	—	2	4	no	—
275	C₂×C₈₃	—	4	2	no	—
276	C₂×C₈₃	#2318	1	1	yes	characteristic
277	C₂×C₈₃	C₂×#431	1	1	yes	characteristic
278	C₂×C₈₃	#2923	1	1	yes	characteristic
279	C₂×C₈₃	#2972	1	1	yes	characteristic
280	C₂×C₈₃	#2973	1	1	yes	characteristic
281	C₂×C₈₃	#2988	1	1	yes	characteristic
282	C₂×C₈₃	#2989	1	1	yes	characteristic
283	C₄²×D₄	D₈₃	1	1	yes	characteristic
284	#1923	—	83	2	no	—
285	#1916	—	83	2	no	—
286	#1869	—	83	2	no	—
287	#1850	—	83	2	no	—
288	#1839	—	83	1	no	—
289	#1831	—	83	1	no	—
290	#1817	—	83	1	no	—
291	#1797	—	83	1	no	—
292	C₄×C₂²⋊C₈	—	83	1	no	—
293	C₂×#336	—	83	1	no	—
294	C₈₃	#21996	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₈	—	83	2	no	—
296	C₂×C₄×D₄	Dic₈₃	1	1	yes	characteristic
297	C₂×C₄×D₄	Dic₈₃	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
299	C₂²×C₄²	C₂×D₈₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂×D₈₃	1	1	yes	characteristic
301	C₂×C₄⋊C₈	—	83	2	no	—
302	C₂×C₄⋊C₈	—	83	2	no	—
303	C₂×C₂²⋊C₈	—	83	2	no	—
304	C₂×C₂²⋊C₈	—	83	2	no	—
305	C₂×C₂²⋊C₈	—	83	2	no	—
306	C₂×C₄×C₈	—	83	2	no	—
307	C₄×C₄⋊C₄	Dic₈₃	1	1	yes	characteristic
308	C₄×C₄⋊C₄	Dic₈₃	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	Dic₈₃	1	1	yes	characteristic
311	C₄×C₂²⋊C₄	Dic₈₃	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	Dic₈₃	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	Dic₈₃	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
316	C₄³	C₂×D₈₃	1	1	yes	characteristic
317	#336	—	83	1	no	—
318	#336	—	83	1	no	—
319	#336	—	83	1	no	—
320	#336	—	83	1	no	—
321	#336	—	83	2	no	—
322	#336	—	83	2	no	—
323	#336	—	83	2	no	—
324	#336	—	83	2	no	—
325	#336	—	83	2	no	—
326	C₂²×D₄	C₂×Dic₈₃	1	1	yes	characteristic
327	C₂³×C₄	C₂×Dic₈₃	1	1	yes	characteristic
328	C₂³×C₄	C₂×Dic₈₃	1	1	yes	characteristic
329	C₂³×C₄	C₂×Dic₈₃	1	1	yes	characteristic
330	C₂³×C₄	C₂×Dic₈₃	1	1	yes	characteristic
331	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
332	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
333	C₂²×C₈	—	332	2	no	—
334	C₂²×C₈	—	332	2	no	—
335	C₂²×C₈	—	83	2	no	—
336	C₂²×C₈	—	83	2	no	—
337	C₂²×C₈	—	83	2	no	—
338	C₂²×C₈	—	83	2	no	—
339	C₂²×C₈	—	166	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	C₈₃⋊C₈	1	8	yes	complemented
343	C₂×C₄⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
352	C₂×C₄²	—	4	2	no	—
353	C₂×C₄²	—	4	2	no	—
354	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
355	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
356	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
357	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
358	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
359	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
360	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
361	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
367	C₄⋊C₈	—	332	2	no	—
368	C₄⋊C₈	—	332	2	no	—
369	C₂²⋊C₈	—	332	2	no	—
370	C₂²⋊C₈	—	332	2	no	—
371	C₂²⋊C₈	—	166	4	no	—
372	C₄×C₈	—	332	2	no	—
373	#95	C₂×Dic₈₃	1	1	yes	characteristic
374	#95	C₂×Dic₈₃	1	1	yes	characteristic
375	#95	C₂×Dic₈₃	1	1	yes	characteristic
376	#95	C₂×Dic₈₃	1	1	yes	characteristic
377	#95	C₂×Dic₈₃	1	1	yes	characteristic
378	#95	C₂×Dic₈₃	1	1	yes	characteristic
379	C₂⁴	C₂²×Dic₈₃	1	1	yes	characteristic
380	C₂⁴	C₂²×Dic₈₃	1	1	yes	characteristic
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	C₂×C₈₃⋊C₈	1	4	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂×C₈₃⋊C₈	1	4	yes	—
401	C₂²×C₄	C₂×C₈₃⋊C₈	1	4	yes	complemented
402	C₂²×C₄	#13050574	1	4	yes	—
403	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
404	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
405	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
406	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
407	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
408	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
411	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
412	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
413	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
414	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
415	C₂²×C₄	#13050590	1	4	yes	—
416	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
417	C₂×C₈	—	332	8	no	—
418	C₂×C₈	—	166	2	no	—
419	C₂×C₈	—	166	2	no	—
420	C₂×C₈	—	166	2	no	—
421	C₂×C₈	—	166	2	no	—
422	C₂×C₈	—	166	2	no	—
423	C₂×C₈	—	166	2	no	—
424	C₂×C₈	—	166	2	no	—
425	C₂×C₈	—	166	2	no	—
426	C₂×C₈	—	166	2	no	—
427	C₂×C₈	—	166	2	no	—
428	C₂×C₈	—	166	2	no	—
429	C₂×C₈	—	166	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×C₈₃⋊C₈	1	4	yes	complemented
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	C₂×C₈₃⋊C₈	1	4	yes	—
438	C₂²⋊C₄	C₂×C₈₃⋊C₈	1	4	yes	complemented
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	4	1	no	—
447	C₄²	—	4	1	no	—
448	C₄²	—	4	1	no	—
449	C₄²	—	4	1	no	—
450	C₄²	—	4	1	no	—
451	C₄²	—	4	1	no	—
452	C₄²	C₂×C₈₃⋊C₈	1	4	yes	complemented
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	#14581751	1	2	yes	—
464	C₂³	C₂²×C₈₃⋊C₈	1	2	yes	—
465	C₂³	C₂²×C₈₃⋊C₈	1	2	yes	—
466	C₂³	C₂×#13050574	1	2	yes	—
467	C₂³	C₂³×Dic₈₃	1	1	yes	characteristic
468	D₄	—	2	8	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	#14581751	1	2	yes	—
506	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
507	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
508	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
509	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
510	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
511	C₂×C₄	C₂×#13050574	1	2	yes	—
512	C₂×C₄	C₂×#13050574	1	2	yes	—
513	C₂×C₄	C₂×#13050590	1	2	yes	—
514	C₂×C₄	#14581837	1	2	yes	—
515	C₂×C₄	#14581838	1	1	yes	characteristic
516	C₂×C₄	#14581839	1	1	yes	characteristic
517	C₈	—	332	2	no	—
518	C₈	—	332	2	no	—
519	C₈	—	332	2	no	—
520	C₈	—	332	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	#19127754	1	4	yes	—
535	C₂²	C₂×#14581751	1	1	yes	characteristic
536	C₂²	#19128176	1	1	yes	characteristic
537	C₂²	#19128184	1	1	yes	characteristic
538	C₂²	C₂³×C₈₃⋊C₈	1	1	yes	characteristic
539	C₂²	C₂²×#13050574	1	1	yes	characteristic
540	C₂²	#19128468	1	1	yes	characteristic
541	C₂²	#19128468	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	#19128284	1	2	yes	—
555	C₄	#19128293	1	2	yes	—
556	C₂	—	2	4	no	—
557	C₂	—	4	2	no	—
558	C₂	#24910096	1	1	yes	characteristic
559	C₂	C₂×#19127754	1	1	yes	characteristic
560	C₂	#24916114	1	1	yes	characteristic
561	C₂	#24916487	1	1	yes	characteristic
562	C₂	#24916492	1	1	yes	characteristic
563	C₂	#24916574	1	1	yes	characteristic
564	C₂	#24916580	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₃
commutator	C₂²×C₈₃	C₂³×C₈
Fitting	C₄²×D₄×C₈₃	C₂
socle	C₂³×C₈₃	C₂³×C₄
prime radical	C₂²×D₄×C₈₃	C₂×C₄
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	C₄²×D₄	D₈₃
hypocenter	C₈₃	#21996
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. #24908071	C₂	semidirect
2. #24908022	C₂	semidirect
4. #24907643	C₂	semidirect
5. #24907606	C₂	semidirect
6. #24907580	C₂	semidirect
7. #24907531	C₂	semidirect
8. #24907443	C₂	semidirect
9. C₄×C₂²⋊(C₈₃⋊C₈)	C₂	semidirect
10. C₂×#19127456	C₂	semidirect
65. C₄×D₄×C₈₃	C₈	semidirect
131. C₂²×C₄×C₈₃	C₂×C₈	semidirect
149. C₄⋊C₄×C₈₃	C₂×C₈	semidirect
155. C₂²⋊C₄×C₈₃	C₂×C₈	semidirect
169. C₄²×C₈₃	C₂×C₈	semidirect
294. C₈₃	#21996	semidirect
342. C₄×D₄	C₈₃⋊C₈	semidirect
401. C₂²×C₄	C₂×C₈₃⋊C₈	semidirect
432. C₄⋊C₄	C₂×C₈₃⋊C₈	semidirect
438. C₂²⋊C₄	C₂×C₈₃⋊C₈	semidirect
452. C₄²	C₂×C₈₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#24908071	2
#24908022	2
#24907756	2
#24907643	2
#24907606	2
#24907580	2
#24907531	2
#24907443	2
C₄×C₂²⋊(C₈₃⋊C₈)	2
C₂×#19127456	2
C₄²×D₄×C₈₃	2
#21996	83