Subgroups — #24921485

Order 10624.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128414	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128410	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128401	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128400	C₂	1	2	yes	maximal, complemented
5	#19128395	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128372	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128347	C₂	1	2	yes	maximal, complemented
8	#19128341	C₂	1	2	yes	maximal, complemented
9	#19128341	C₂	1	2	yes	maximal, complemented
10	D₄×D₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128306	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128302	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128289	C₂	1	2	yes	maximal, complemented
16	#19128284	C₂	1	2	yes	maximal, complemented
17	#19128248	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128229	C₂	1	1	yes	maximal, characteristic, complemented
19	#19128210	C₂	1	2	yes	maximal, complemented
20	C₂×#14581765	C₂	1	2	yes	maximal, complemented
21	#19128173	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#518×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050590	C₂²	1	2	yes	complemented
25	C₂×#13050590	C₂²	1	2	yes	complemented
26	C₂²×D₃₃₂	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
29	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₈₃	C₂²	1	2	yes	complemented
32	#14581791	C₂²	1	1	yes	characteristic, complemented
33	#14581789	C₂²	1	1	yes	characteristic, complemented
34	#14581788	C₂²	1	1	yes	characteristic, complemented
35	#14581788	C₂²	1	1	yes	characteristic, complemented
36	#14581787	C₂²	1	1	yes	characteristic, complemented
37	#14581786	C₂²	1	2	yes	complemented
38	#14581785	C₂²	1	2	yes	complemented
39	#14581785	C₂²	1	1	yes	characteristic, complemented
40	#14581784	C₂²	1	1	yes	characteristic, complemented
41	#14581783	C₂²	1	1	yes	characteristic, complemented
42	#14581782	C₂²	1	1	yes	characteristic, complemented
43	#14581780	C₂²	1	2	yes	complemented
44	#14581778	C₂²	1	1	yes	characteristic, complemented
45	#14581778	C₂²	1	2	yes	complemented
46	#14581778	C₂²	1	2	yes	complemented
47	#14581777	C₂²	1	1	yes	characteristic, complemented
48	#14581777	C₂²	1	2	yes	complemented
49	#14581777	C₂²	1	2	yes	complemented
50	#14581775	C₂²	1	2	yes	complemented
51	#14581775	C₂²	1	2	yes	complemented
52	#14581774	C₂²	1	1	yes	characteristic, complemented
53	#14581774	C₂²	1	2	yes	complemented
54	#14581774	C₂²	1	2	yes	complemented
55	#14581771	C₂²	1	2	yes	complemented
56	#14581770	C₂²	1	1	yes	characteristic, complemented
57	#14581769	C₂²	1	2	yes	complemented
58	#14581769	C₂²	1	2	yes	complemented
59	#14581767	C₂²	1	1	yes	characteristic, complemented
60	#14581767	C₂²	1	1	yes	characteristic, complemented
61	#14581766	C₂²	1	1	yes	characteristic, complemented
62	#14581766	C₂²	1	1	yes	characteristic, complemented
63	#14581766	C₂²	1	2	yes	complemented
64	#14581766	C₂²	1	2	yes	complemented
65	#14581766	C₂²	1	2	yes	complemented
66	#14581765	C₂²	1	1	yes	characteristic
67	#14581765	C₂²	1	2	yes	complemented
68	#14581765	C₂²	1	2	yes	complemented
69	#14581765	C₂²	1	2	yes	complemented
70	#14581765	C₂²	1	2	yes	complemented
71	#14581765	C₂²	1	2	yes	complemented
72	#14581765	C₂²	1	2	yes	complemented
73	#14581765	C₂²	1	2	yes	complemented
74	#14581765	C₂²	1	2	yes	complemented
75	#14581765	C₂²	1	2	yes	complemented
76	#14581764	C₂²	1	2	yes	complemented
77	#14581764	C₂²	1	2	yes	complemented
78	#14581763	C₂²	1	1	yes	characteristic, complemented
79	#14581763	C₂²	1	1	yes	characteristic, complemented
80	#14581762	C₂²	1	2	yes	complemented
81	#14581762	C₂²	1	2	yes	complemented
82	#14581761	C₂²	1	2	yes	complemented
83	#14581761	C₂²	1	2	yes	complemented
84	#14581760	C₂²	1	2	yes	complemented
85	#14581760	C₂²	1	2	yes	complemented
86	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₃₃₂	C₂²	1	2	yes	complemented
89	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
90	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
91	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
92	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
93	#14581754	C₂²	1	1	yes	characteristic, complemented
94	#14581754	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
101	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
103	#14581750	C₂²	1	1	yes	characteristic, complemented
104	#14581749	C₂²	1	2	yes	complemented
105	#14581749	C₂²	1	1	yes	characteristic, complemented
106	C₂×Dic₈₃⋊C₄	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
111	C₄²×D₈₃	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
113	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
114	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
116	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
118	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
119	#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
120	#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₈₃	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₈₃	C₂²	1	2	yes	complemented
123	C₂³×D₈₃	C₂³	1	2	yes	—
124	C₂³×D₈₃	C₂³	1	2	yes	—
125	#13050590	—	4	4	no	—
126	#13050590	—	4	4	no	—
127	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₆₆	C₂³	1	2	yes	—
129	C₂×D₃₃₂	—	4	4	no	—
130	C₂×D₃₃₂	C₂³	1	2	yes	—
131	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
132	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
133	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
134	C₂×D₃₃₂	C₂³	1	2	yes	—
135	C₂×D₃₃₂	C₂³	1	2	yes	—
136	C₂×D₃₃₂	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₃	—	4	4	no	—
138	C₂×C₂²⋊D₈₃	—	4	4	no	—
139	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
151	D₄×D₈₃	—	2	4	no	—
152	D₄×D₈₃	—	2	4	no	—
153	C₂²×Dic₈₃	C₂³	1	2	yes	—
154	C₂²×Dic₈₃	C₂³	1	2	yes	—
155	C₂×C₄×D₈₃	—	4	4	no	—
156	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₈₃	C₂³	1	2	yes	—
160	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₈₃	C₂³	1	2	yes	—
162	C₂×C₄×D₈₃	C₂³	1	2	yes	—
163	C₂×C₄×D₈₃	C₂³	1	2	yes	—
164	C₂×C₄×D₈₃	C₂³	1	2	yes	—
165	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₈₃	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	2	yes	—
174	Dic₈₃⋊C₄	C₂³	1	2	yes	—
175	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₈₃⋊C₄	C₂³	1	2	yes	—
177	Dic₈₃⋊C₄	C₂³	1	2	yes	—
178	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₈₃⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
187	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₃	C₂³	1	2	yes	—
205	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
206	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
207	C₂⁴×C₈₃	C₂³	1	2	yes	—
208	C₂×D₄×C₈₃	—	2	4	no	—
209	C₂×D₄×C₈₃	C₂³	1	2	yes	—
210	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
214	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
215	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
216	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
228	C₄²×C₈₃	C₂³	1	2	yes	—
229	C₄²×C₈₃	C₂³	1	1	yes	characteristic
230	C₄²×C₈₃	C₂³	1	1	yes	characteristic
231	C₂³×C₈₃	—	2	4	no	—
232	C₂³×C₈₃	—	4	2	no	—
233	C₂³×C₈₃	—	4	2	no	—
234	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₈₃	C₂⁴	1	2	yes	—
236	C₂³×C₈₃	C₂⁴	1	2	yes	—
237	C₂²×D₈₃	—	2	4	no	—
238	C₂²×D₈₃	—	2	4	no	—
239	C₂²×D₈₃	—	2	4	no	—
240	C₂²×D₈₃	—	4	2	no	—
241	C₂²×D₈₃	—	4	2	no	—
242	C₂²×D₈₃	—	4	2	no	—
243	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₈₃	C₂⁴	1	2	yes	—
245	C₂²×D₈₃	C₂⁴	1	2	yes	—
246	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
247	D₄×C₈₃	—	2	4	no	—
248	D₄×C₈₃	—	2	2	no	—
249	D₄×C₈₃	#41	1	4	yes	complemented
250	C₂×C₄×C₈₃	—	2	2	no	—
251	C₂×C₄×C₈₃	—	4	2	no	—
252	C₂×C₄×C₈₃	—	4	2	no	—
253	C₂×C₄×C₈₃	—	4	2	no	—
254	C₂×C₄×C₈₃	—	4	2	no	—
255	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₈₃	—	2	4	no	—
264	C₂²⋊D₈₃	—	2	4	no	—
265	C₂²⋊D₈₃	—	2	2	no	—
266	C₂²⋊D₈₃	—	2	4	no	—
267	C₂²⋊D₈₃	—	2	2	no	—
268	C₂²⋊D₈₃	—	2	4	no	—
269	C₂²⋊D₈₃	—	4	2	no	—
270	C₂²⋊D₈₃	—	4	2	no	—
271	C₂²⋊D₈₃	—	4	2	no	—
272	C₂²⋊D₈₃	—	4	2	no	—
273	C₂²⋊D₈₃	—	4	2	no	—
274	C₂²⋊D₈₃	—	4	2	no	—
275	C₂×Dic₈₃	—	2	4	no	—
276	C₂×Dic₈₃	—	4	2	no	—
277	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₈₃	C₂⁴	1	2	yes	—
281	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₈₃	C₂⁴	1	2	yes	—
284	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
285	D₃₃₂	—	2	2	no	—
286	D₃₃₂	—	2	4	no	—
287	D₃₃₂	—	2	2	no	—
288	D₃₃₂	—	2	2	no	—
289	D₃₃₂	—	4	2	no	—
290	D₃₃₂	—	4	2	no	—
291	D₃₃₂	—	4	2	no	—
292	C₄×D₈₃	—	2	2	no	—
293	C₄×D₈₃	—	2	2	no	—
294	C₄×D₈₃	—	2	2	no	—
295	C₄×D₈₃	—	2	2	no	—
296	C₄×D₈₃	—	2	4	no	—
297	C₄×D₈₃	—	4	2	no	—
298	C₄×D₈₃	—	4	2	no	—
299	C₄×D₈₃	—	4	2	no	—
300	C₄×D₈₃	—	4	2	no	—
301	Dic₁₆₆	—	2	2	no	—
302	Dic₁₆₆	—	4	2	no	—
303	C₂²×C₈₃	—	2	2	no	—
304	C₂²×C₈₃	—	2	2	no	—
305	C₂²×C₈₃	—	2	1	no	—
306	C₂²×C₈₃	—	2	2	no	—
307	C₂²×C₈₃	—	2	2	no	—
308	C₂²×C₈₃	—	2	2	no	—
309	C₂²×C₈₃	—	2	1	no	—
310	C₂²×C₈₃	—	2	1	no	—
311	C₂²×C₈₃	—	8	4	no	—
312	C₂²×C₈₃	C₂×#41	1	4	yes	—
313	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
314	C₂×D₈₃	—	2	1	no	—
315	C₂×D₈₃	—	2	1	no	—
316	C₂×D₈₃	—	2	1	no	—
317	C₂×D₈₃	—	2	2	no	—
318	C₂×D₈₃	—	2	2	no	—
319	C₂×D₈₃	—	2	2	no	—
320	C₂×D₈₃	—	2	2	no	—
321	C₂×D₈₃	—	2	2	no	—
322	C₂×D₈₃	—	2	1	no	—
323	C₂×D₈₃	—	2	2	no	—
324	C₂×D₈₃	—	2	1	no	—
325	C₂×D₈₃	—	4	8	no	—
326	C₂×D₈₃	—	8	4	no	—
327	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
328	C₄×C₈₃	—	2	1	no	—
329	C₄×C₈₃	—	2	1	no	—
330	C₄×C₈₃	—	2	2	no	—
331	C₄×C₈₃	—	2	1	no	—
332	C₄×C₈₃	—	2	1	no	—
333	C₄×C₈₃	—	2	2	no	—
334	C₄×C₈₃	—	2	1	no	—
335	C₄×C₈₃	C₂×#41	1	2	yes	—
336	Dic₈₃	—	2	1	no	—
337	Dic₈₃	—	2	1	no	—
338	Dic₈₃	—	2	1	no	—
339	Dic₈₃	—	2	1	no	—
340	Dic₈₃	—	2	2	no	—
341	Dic₈₃	—	2	2	no	—
342	Dic₈₃	—	2	1	no	—
343	Dic₈₃	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₈₃	—	2	4	no	—
345	C₂×C₈₃	—	4	2	no	—
346	C₂×C₈₃	—	4	1	no	—
347	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
348	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	D₈₃	—	2	2	no	—
351	D₈₃	—	4	2	no	—
352	D₈₃	—	4	2	no	—
353	D₈₃	—	4	1	no	—
354	#3519	—	83	1	no	maximal, Sylow
355	C₈₃	#3519	1	1	yes	characteristic, complemented, Sylow
356	#555	—	83	1	no	—
357	#554	—	83	1	no	—
358	#553	—	83	2	no	—
359	#553	—	83	1	no	—
360	#553	—	83	1	no	—
361	#550	—	83	1	no	—
362	#546	—	83	2	no	—
363	#546	—	83	2	no	—
364	#546	—	83	2	no	—
365	D₄²	—	83	1	no	—
366	D₄²	—	83	1	no	—
367	D₄²	—	83	1	no	—
368	#540	—	83	1	no	—
369	#540	—	83	1	no	—
370	#538	—	83	2	no	—
371	#538	—	83	2	no	—
372	#532	—	83	1	no	—
373	#529	—	83	1	no	—
374	#525	—	83	2	no	—
375	C₂×#121	—	83	2	no	—
376	#518	—	83	1	no	—
377	#518	D₈₃	1	1	yes	characteristic, complemented
378	C₂×C₄×D₄	—	83	1	no	—
379	C₂×#41	—	83	2	no	—
380	C₂×#41	—	83	2	no	—
381	C₂²×D₄	—	83	2	no	—
382	C₂²×D₄	—	83	2	no	—
383	C₂²×D₄	—	83	1	no	—
384	C₂²×D₄	—	83	1	no	—
385	C₂²×D₄	—	83	2	no	—
386	C₂²×D₄	C₂×D₈₃	1	1	yes	characteristic
387	C₂³×C₄	—	83	2	no	—
388	C₄⋊Q₈	—	83	1	no	—
389	#127	—	83	1	no	—
390	#127	—	83	1	no	—
391	#127	—	83	1	no	—
392	#126	—	83	1	no	—
393	#126	—	83	1	no	—
394	#126	—	83	2	no	—
395	#126	—	83	2	no	—
396	#125	—	83	1	no	—
397	#125	—	83	1	no	—
398	#125	—	83	1	no	—
399	#124	—	83	1	no	—
400	#124	—	83	2	no	—
401	#124	—	83	2	no	—
402	#124	—	83	2	no	—
403	#123	—	83	2	no	—
404	#123	—	83	2	no	—
405	#123	—	83	2	no	—
406	#123	—	83	1	no	—
407	#123	—	83	2	no	—
408	#123	—	83	2	no	—
409	#123	—	83	1	no	—
410	#123	—	83	2	no	—
411	C₂²⋊Q₈	—	83	2	no	—
412	C₂²⋊Q₈	—	83	1	no	—
413	C₂²⋊Q₈	—	83	2	no	—
414	C₂²⋊Q₈	—	83	2	no	—
415	#121	—	83	1	no	—
416	#121	—	83	1	no	—
417	#121	—	83	2	no	—
418	#121	—	83	2	no	—
419	#121	—	83	2	no	—
420	#121	—	83	2	no	—
421	#121	—	83	1	no	—
422	#121	—	83	1	no	—
423	#121	—	83	2	no	—
424	#121	—	83	1	no	—
425	#121	—	83	1	no	—
426	#121	—	83	1	no	—
427	#121	—	83	2	no	—
428	#121	—	83	2	no	—
429	#121	—	83	2	no	—
430	#121	—	83	2	no	—
431	#121	—	83	2	no	—
432	#121	—	83	2	no	—
433	#121	—	83	2	no	—
434	#121	—	83	2	no	—
435	#121	—	83	2	no	—
436	#120	—	83	2	no	—
437	#120	—	83	2	no	—
438	#120	—	83	2	no	—
439	#120	—	83	2	no	—
440	#120	—	83	2	no	—
441	#120	—	83	2	no	—
442	C₄×Q₈	—	83	1	no	—
443	C₄×D₄	—	83	1	no	—
444	C₄×D₄	—	83	1	no	—
445	C₄×D₄	—	83	2	no	—
446	C₄×D₄	—	83	2	no	—
447	C₄×D₄	—	83	2	no	—
448	C₄×D₄	—	83	1	no	—
449	C₄×D₄	—	83	1	no	—
450	C₄×D₄	—	83	2	no	—
451	C₄×D₄	—	83	1	no	—
452	C₄×D₄	—	83	1	no	—
453	C₄×D₄	—	83	2	no	—
454	C₄×D₄	—	83	2	no	—
455	C₄×D₄	—	83	1	no	—
456	C₄×D₄	—	83	1	no	—
457	C₄×D₄	—	83	2	no	—
458	C₄×D₄	—	83	1	no	—
459	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
460	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
461	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
462	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
463	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
464	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
465	#117	—	83	1	no	—
466	#117	—	83	1	no	—
467	#117	—	83	2	no	—
468	#117	C₂×D₈₃	1	1	yes	characteristic, complemented
469	#117	C₂×D₈₃	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	—	83	2	no	—
471	C₂×C₄⋊C₄	—	83	1	no	—
472	C₂×C₂²⋊C₄	—	83	2	no	—
473	C₂×C₂²⋊C₄	—	83	2	no	—
474	C₂×C₂²⋊C₄	—	83	2	no	—
475	C₂×C₂²⋊C₄	C₂×D₈₃	1	2	yes	complemented
476	C₂×C₂²⋊C₄	C₂×D₈₃	1	2	yes	complemented
477	C₂×C₄²	—	83	1	no	—
478	C₂⁴	—	83	2	no	—
479	C₂⁴	—	83	2	no	—
480	C₂⁴	C₂²×D₈₃	1	2	yes	—
481	#41	—	332	4	no	—
482	#41	—	332	4	no	—
483	C₂×Q₈	—	83	2	no	—
484	C₂×Q₈	—	83	1	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	332	4	no	—
487	C₂×D₄	—	332	4	no	—
488	C₂×D₄	—	332	4	no	—
489	C₂×D₄	—	83	2	no	—
490	C₂×D₄	—	83	2	no	—
491	C₂×D₄	—	83	2	no	—
492	C₂×D₄	—	83	2	no	—
493	C₂×D₄	—	83	2	no	—
494	C₂×D₄	—	83	2	no	—
495	C₂×D₄	—	83	2	no	—
496	C₂×D₄	—	83	2	no	—
497	C₂×D₄	—	83	2	no	—
498	C₂×D₄	—	83	1	no	—
499	C₂×D₄	—	83	1	no	—
500	C₂×D₄	—	83	2	no	—
501	C₂×D₄	—	83	2	no	—
502	C₂×D₄	—	83	2	no	—
503	C₂×D₄	—	83	2	no	—
504	C₂×D₄	—	83	1	no	—
505	C₂×D₄	—	83	1	no	—
506	C₂×D₄	—	83	2	no	—
507	C₂×D₄	—	83	1	no	—
508	C₂×D₄	—	166	4	no	—
509	C₂×D₄	—	166	4	no	—
510	C₂×D₄	C₂²×D₈₃	1	2	yes	—
511	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
512	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
513	C₂²×C₄	—	332	4	no	—
514	C₂²×C₄	—	83	2	no	—
515	C₂²×C₄	—	83	2	no	—
516	C₂²×C₄	—	83	2	no	—
517	C₂²×C₄	—	83	2	no	—
518	C₂²×C₄	—	83	2	no	—
519	C₂²×C₄	—	83	2	no	—
520	C₂²×C₄	—	83	1	no	—
521	C₂²×C₄	—	83	1	no	—
522	C₂²×C₄	—	83	1	no	—
523	C₂²×C₄	—	83	1	no	—
524	C₂²×C₄	—	83	2	no	—
525	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
527	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
528	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
529	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
530	C₄⋊C₄	—	83	1	no	—
531	C₄⋊C₄	—	83	2	no	—
532	C₄⋊C₄	—	83	1	no	—
533	C₄⋊C₄	—	83	2	no	—
534	C₄⋊C₄	—	83	2	no	—
535	C₄⋊C₄	—	83	2	no	—
536	C₄⋊C₄	—	83	1	no	—
537	C₄⋊C₄	—	83	1	no	—
538	C₄⋊C₄	—	83	1	no	—
539	C₄⋊C₄	—	83	1	no	—
540	C₄⋊C₄	—	83	1	no	—
541	C₄⋊C₄	—	83	1	no	—
542	C₄⋊C₄	—	83	2	no	—
543	C₄⋊C₄	—	83	2	no	—
544	C₄⋊C₄	—	83	1	no	—
545	C₄⋊C₄	—	83	1	no	—
546	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
550	C₂²⋊C₄	—	83	2	no	—
551	C₂²⋊C₄	—	83	2	no	—
552	C₂²⋊C₄	—	83	1	no	—
553	C₂²⋊C₄	—	83	1	no	—
554	C₂²⋊C₄	—	83	2	no	—
555	C₂²⋊C₄	—	83	2	no	—
556	C₂²⋊C₄	—	83	1	no	—
557	C₂²⋊C₄	—	83	2	no	—
558	C₂²⋊C₄	—	83	1	no	—
559	C₂²⋊C₄	—	83	2	no	—
560	C₂²⋊C₄	—	83	2	no	—
561	C₂²⋊C₄	—	83	2	no	—
562	C₂²⋊C₄	—	83	2	no	—
563	C₂²⋊C₄	—	83	2	no	—
564	C₂²⋊C₄	—	83	2	no	—
565	C₂²⋊C₄	—	83	1	no	—
566	C₂²⋊C₄	—	83	1	no	—
567	C₂²⋊C₄	—	83	1	no	—
568	C₂²⋊C₄	—	83	1	no	—
569	C₂²⋊C₄	—	83	2	no	—
570	C₂²⋊C₄	—	83	2	no	—
571	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
578	C₄²	—	83	1	no	—
579	C₄²	—	83	1	no	—
580	C₄²	—	83	1	no	—
581	C₄²	—	83	2	no	—
582	C₄²	—	83	1	no	—
583	C₄²	C₂²×D₈₃	1	1	yes	characteristic
584	C₄²	C₂²×D₈₃	1	2	yes	—
585	C₄²	C₂²×D₈₃	1	1	yes	characteristic
586	C₂³	—	2	4	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	332	2	no	—
590	C₂³	—	332	2	no	—
591	C₂³	—	332	2	no	—
592	C₂³	—	83	1	no	—
593	C₂³	—	83	1	no	—
594	C₂³	—	83	2	no	—
595	C₂³	—	83	2	no	—
596	C₂³	—	166	4	no	—
597	C₂³	—	166	4	no	—
598	C₂³	—	166	4	no	—
599	C₂³	C₂³×D₈₃	1	1	yes	characteristic
600	C₂³	C₂³×D₈₃	1	2	yes	—
601	C₂³	C₂³×D₈₃	1	2	yes	—
602	Q₈	—	332	2	no	—
603	Q₈	—	166	2	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	332	2	no	—
607	D₄	—	332	2	no	—
608	D₄	—	332	2	no	—
609	D₄	—	332	2	no	—
610	D₄	—	332	2	no	—
611	D₄	—	332	2	no	—
612	D₄	—	332	2	no	—
613	D₄	—	332	2	no	—
614	D₄	—	332	2	no	—
615	D₄	—	166	2	no	—
616	D₄	—	166	4	no	—
617	D₄	—	166	2	no	—
618	D₄	—	166	4	no	—
619	D₄	—	166	2	no	—
620	D₄	—	166	4	no	—
621	D₄	—	166	4	no	—
622	D₄	—	166	4	no	—
623	D₄	—	166	2	no	—
624	D₄	—	166	2	no	—
625	D₄	#13050590	1	4	yes	complemented
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	332	2	no	—
632	C₂×C₄	—	332	2	no	—
633	C₂×C₄	—	332	2	no	—
634	C₂×C₄	—	332	2	no	—
635	C₂×C₄	—	332	2	no	—
636	C₂×C₄	—	83	1	no	—
637	C₂×C₄	—	83	1	no	—
638	C₂×C₄	—	83	1	no	—
639	C₂×C₄	—	83	1	no	—
640	C₂×C₄	—	83	1	no	—
641	C₂×C₄	—	83	2	no	—
642	C₂×C₄	—	83	1	no	—
643	C₂×C₄	—	83	2	no	—
644	C₂×C₄	—	166	2	no	—
645	C₂×C₄	—	166	4	no	—
646	C₂×C₄	—	166	2	no	—
647	C₂×C₄	—	166	4	no	—
648	C₂×C₄	—	166	2	no	—
649	C₂×C₄	—	166	2	no	—
650	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₈₃	1	2	yes	—
653	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₈₃	1	2	yes	—
656	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
657	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	8	4	no	—
667	C₂²	—	332	8	no	—
668	C₂²	—	83	2	no	—
669	C₂²	—	664	4	no	—
670	C₂²	—	166	1	no	—
671	C₂²	—	166	2	no	—
672	C₂²	—	166	2	no	—
673	C₂²	—	166	2	no	—
674	C₂²	—	166	2	no	—
675	C₂²	—	166	2	no	—
676	C₂²	—	166	2	no	—
677	C₂²	—	166	1	no	—
678	C₂²	—	166	1	no	—
679	C₂²	—	166	1	no	—
680	C₂²	—	166	1	no	—
681	C₂²	C₂×#13050590	1	4	yes	—
682	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	2	no	—
690	C₄	—	83	2	no	—
691	C₄	—	166	1	no	—
692	C₄	—	166	1	no	—
693	C₄	—	166	2	no	—
694	C₄	—	166	1	no	—
695	C₄	—	166	1	no	—
696	C₄	—	166	2	no	—
697	C₄	—	166	1	no	—
698	C₄	C₂×#13050590	1	2	yes	—
699	C₂	—	2	4	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	332	2	no	—
703	C₂	—	332	1	no	—
704	C₂	—	332	2	no	—
705	C₂	—	166	2	no	—
706	C₂	C₂²×#13050590	1	1	yes	characteristic
707	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
708	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#518×C₈₃	C₂
hypercenter	#518	D₈₃
hypocenter	C₈₃	#3519
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #19128414	C₂	semidirect
2. #19128410	C₂	semidirect
3. #19128401	C₂	semidirect
4. #19128400	C₂	semidirect
5. #19128395	C₂	semidirect
6. #19128372	C₂	semidirect
7. #19128347	C₂	semidirect
8. #19128341	C₂	semidirect
9. #19128341	C₂	semidirect
10. D₄×D₃₃₂	C₂	semidirect
11. D₄×C₂²⋊D₈₃	C₂	semidirect
12. D₄×C₂²⋊D₈₃	C₂	semidirect
13. #19128306	C₂	semidirect
14. #19128302	C₂	semidirect
15. #19128289	C₂	semidirect
16. #19128284	C₂	semidirect
17. #19128248	C₂	semidirect
18. #19128229	C₂	semidirect
19. #19128210	C₂	semidirect
20. C₂×#14581765	C₂	semidirect
21. #19128173	C₂	semidirect
22. C₄×D₄×D₈₃	C₂	semidirect
23. #518×C₈₃	C₂	semidirect
24. C₂×#13050590	C₂²	semidirect
25. C₂×#13050590	C₂²	semidirect
26. C₂²×D₃₃₂	C₂²	semidirect
27. C₂²×C₂²⋊D₈₃	C₂²	semidirect
28. C₂²×C₂²⋊D₈₃	C₂²	semidirect
31. C₂²×C₄×D₈₃	C₂²	semidirect
32. #14581791	C₂²	semidirect
33. #14581789	C₂²	semidirect
34. #14581788	C₂²	semidirect
35. #14581788	C₂²	semidirect
36. #14581787	C₂²	semidirect
37. #14581786	C₂²	semidirect
38. #14581785	C₂²	semidirect
39. #14581785	C₂²	semidirect
40. #14581784	C₂²	semidirect
41. #14581783	C₂²	semidirect
42. #14581782	C₂²	semidirect
43. #14581780	C₂²	semidirect
44. #14581778	C₂²	semidirect
45. #14581778	C₂²	semidirect
46. #14581778	C₂²	semidirect
47. #14581777	C₂²	semidirect
48. #14581777	C₂²	semidirect
49. #14581777	C₂²	semidirect
50. #14581775	C₂²	semidirect
51. #14581775	C₂²	semidirect
52. #14581774	C₂²	semidirect
53. #14581774	C₂²	semidirect
54. #14581774	C₂²	semidirect
55. #14581771	C₂²	semidirect
56. #14581770	C₂²	semidirect
57. #14581769	C₂²	semidirect
58. #14581769	C₂²	semidirect
59. #14581767	C₂²	semidirect
60. #14581767	C₂²	semidirect
61. #14581766	C₂²	semidirect
62. #14581766	C₂²	semidirect
63. #14581766	C₂²	semidirect
64. #14581766	C₂²	semidirect
65. #14581766	C₂²	semidirect
67. #14581765	C₂²	semidirect
68. #14581765	C₂²	semidirect
69. #14581765	C₂²	semidirect
70. #14581765	C₂²	semidirect
71. #14581765	C₂²	semidirect
72. #14581765	C₂²	semidirect
73. #14581765	C₂²	semidirect
74. #14581765	C₂²	semidirect
75. #14581765	C₂²	semidirect
76. #14581764	C₂²	semidirect
77. #14581764	C₂²	semidirect
78. #14581763	C₂²	semidirect
79. #14581763	C₂²	semidirect
80. #14581762	C₂²	semidirect
81. #14581762	C₂²	semidirect
82. #14581761	C₂²	semidirect
83. #14581761	C₂²	semidirect
84. #14581760	C₂²	semidirect
85. #14581760	C₂²	semidirect
86. C₄×Dic₁₆₆	C₂²	semidirect
87. C₄×D₃₃₂	C₂²	semidirect
88. C₄×D₃₃₂	C₂²	semidirect
89. C₄×D₃₃₂	C₂²	semidirect
90. C₄×D₃₃₂	C₂²	semidirect
93. #14581754	C₂²	semidirect
94. #14581754	C₂²	semidirect
95. C₄×C₂²⋊D₈₃	C₂²	semidirect
96. C₄×C₂²⋊D₈₃	C₂²	semidirect
97. C₄×C₂²⋊D₈₃	C₂²	semidirect
98. C₄×C₂²⋊D₈₃	C₂²	semidirect
99. C₄×C₂²⋊D₈₃	C₂²	semidirect
100. C₄×C₂²⋊D₈₃	C₂²	semidirect
101. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
103. #14581750	C₂²	semidirect
104. #14581749	C₂²	semidirect
105. #14581749	C₂²	semidirect
106. C₂×Dic₈₃⋊C₄	C₂²	semidirect
107. C₄⋊C₄×D₈₃	C₂²	semidirect
108. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
109. C₂²⋊C₄×D₈₃	C₂²	semidirect
110. C₂²⋊C₄×D₈₃	C₂²	semidirect
111. C₄²×D₈₃	C₂²	semidirect
115. C₄×D₄×C₈₃	C₂²	semidirect
116. C₄×D₄×C₈₃	C₂²	semidirect
117. C₄×D₄×C₈₃	C₂²	semidirect
118. C₄×D₄×C₈₃	C₂²	semidirect
119. #117×C₈₃	C₂²	semidirect
120. #117×C₈₃	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₈₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₈₃	C₂²	semidirect
249. D₄×C₈₃	#41	semidirect
355. C₈₃	#3519	semidirect
377. #518	D₈₃	semidirect
461. C₄×D₄	C₂×D₈₃	semidirect
462. C₄×D₄	C₂×D₈₃	semidirect
463. C₄×D₄	C₂×D₈₃	semidirect
464. C₄×D₄	C₂×D₈₃	semidirect
468. #117	C₂×D₈₃	semidirect
469. #117	C₂×D₈₃	semidirect
475. C₂×C₂²⋊C₄	C₂×D₈₃	semidirect
476. C₂×C₂²⋊C₄	C₂×D₈₃	semidirect
625. D₄	#13050590	semidirect

Maximal subgroups

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

subgroup	index
#19128414	2
#19128410	2
#19128401	2
#19128400	2
#19128395	2
#19128372	2
#19128347	2
#19128341	2
D₄×D₃₃₂	2
D₄×C₂²⋊D₈₃	2
#19128306	2
#19128302	2
#19128289	2
#19128284	2
#19128248	2
#19128229	2
#19128210	2
C₂×#14581765	2
#19128173	2
C₄×D₄×D₈₃	2
#518×C₈₃	2
#3519	83