Subgroups — #24921972

Order 10624.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128448	C₂	1	2	yes	maximal, complemented
2	#19128444	C₂	1	2	yes	maximal, complemented
3	#19128434	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128433	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128361	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128358	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128348	C₂	1	2	yes	maximal, complemented
8	#19128347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128341	C₂	1	2	yes	maximal, complemented
10	#19128335	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128324	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128318	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128289	C₂	1	2	yes	maximal, complemented
15	#19128287	C₂	1	2	yes	maximal, complemented
16	#19128283	C₂	1	2	yes	maximal, complemented
17	#19128268	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128265	C₂	1	1	yes	maximal, characteristic, complemented
19	#19128261	C₂	1	2	yes	maximal, complemented
20	#19128248	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128233	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050590	C₂²	1	2	yes	complemented
25	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
31	#14581791	C₂²	1	1	yes	characteristic, complemented
32	#14581788	C₂²	1	1	yes	characteristic
33	#14581788	C₂²	1	1	yes	characteristic
34	#14581788	C₂²	1	1	yes	characteristic, complemented
35	#14581787	C₂²	1	2	yes	complemented
36	#14581785	C₂²	1	1	yes	characteristic, complemented
37	#14581785	C₂²	1	1	yes	characteristic, complemented
38	#14581785	C₂²	1	2	yes	complemented
39	#14581783	C₂²	1	1	yes	characteristic, complemented
40	#14581781	C₂²	1	1	yes	characteristic, complemented
41	#14581781	C₂²	1	1	yes	characteristic, complemented
42	#14581780	C₂²	1	1	yes	characteristic, complemented
43	#14581779	C₂²	1	2	yes	complemented
44	#14581779	C₂²	1	1	yes	characteristic, complemented
45	#14581779	C₂²	1	2	yes	complemented
46	#14581779	C₂²	1	1	yes	characteristic, complemented
47	#14581779	C₂²	1	1	yes	characteristic, complemented
48	#14581778	C₂²	1	2	yes	complemented
49	#14581778	C₂²	1	2	yes	complemented
50	#14581778	C₂²	1	2	yes	complemented
51	#14581778	C₂²	1	2	yes	complemented
52	#14581778	C₂²	1	2	yes	complemented
53	#14581778	C₂²	1	2	yes	complemented
54	#14581778	C₂²	1	2	yes	complemented
55	#14581777	C₂²	1	2	yes	complemented
56	#14581776	C₂²	1	2	yes	complemented
57	#14581775	C₂²	1	2	yes	complemented
58	#14581774	C₂²	1	2	yes	complemented
59	#14581774	C₂²	1	1	yes	characteristic, complemented
60	#14581774	C₂²	1	1	yes	characteristic, complemented
61	#14581774	C₂²	1	2	yes	complemented
62	#14581774	C₂²	1	2	yes	complemented
63	#14581773	C₂²	1	2	yes	complemented
64	#14581772	C₂²	1	2	yes	complemented
65	#14581772	C₂²	1	1	yes	characteristic, complemented
66	#14581771	C₂²	1	1	yes	characteristic, complemented
67	#14581771	C₂²	1	2	yes	complemented
68	#14581770	C₂²	1	2	yes	complemented
69	#14581769	C₂²	1	2	yes	complemented
70	#14581767	C₂²	1	1	yes	characteristic, complemented
71	#14581766	C₂²	1	1	yes	characteristic
72	#14581766	C₂²	1	2	yes	complemented
73	#14581766	C₂²	1	2	yes	complemented
74	#14581765	C₂²	1	2	yes	complemented
75	#14581765	C₂²	1	2	yes	complemented
76	#14581765	C₂²	1	2	yes	complemented
77	#14581765	C₂²	1	2	yes	complemented
78	#14581764	C₂²	1	2	yes	complemented
79	#14581763	C₂²	1	1	yes	characteristic
80	#14581763	C₂²	1	1	yes	characteristic, complemented
81	#14581763	C₂²	1	2	yes	complemented
82	#14581763	C₂²	1	2	yes	complemented
83	#14581763	C₂²	1	2	yes	complemented
84	#14581762	C₂²	1	2	yes	complemented
85	#14581761	C₂²	1	2	yes	complemented
86	#14581761	C₂²	1	2	yes	complemented
87	#14581761	C₂²	1	2	yes	complemented
88	#14581760	C₂²	1	2	yes	complemented
89	#14581760	C₂²	1	2	yes	complemented
90	#14581760	C₂²	1	2	yes	complemented
91	#14581760	C₂²	1	2	yes	complemented
92	#14581760	C₂²	1	2	yes	complemented
93	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
95	#14581757	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
98	#14581754	C₂²	1	1	yes	characteristic, complemented
99	#14581754	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
105	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
106	#14581751	C₂²	1	1	yes	characteristic, complemented
107	#14581751	C₂²	1	1	yes	characteristic, complemented
108	C₂²⋊C₄×D₈₃	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	C₂×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₈₃	C₂²	1	1	yes	characteristic, complemented
115	#123×C₈₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₃	C₂²	1	1	yes	characteristic
118	#121×C₈₃	C₂²	1	2	yes	complemented
119	#120×C₈₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, 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	2	no	—
126	#13050590	—	4	4	no	—
127	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₆₆	C₂³	1	2	yes	—
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
131	Q₈×D₈₃	—	4	2	no	—
132	C₂×D₃₃₂	—	4	2	no	—
133	C₂×D₃₃₂	C₂³	1	2	yes	—
134	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
135	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
136	C₂×D₃₃₂	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₃	—	4	4	no	—
138	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
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	D₄×D₈₃	—	4	2	no	—
151	D₄×D₈₃	—	4	4	no	—
152	C₂²×Dic₈₃	C₂³	1	2	yes	—
153	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₈₃	C₂³	1	2	yes	—
157	C₂×C₄×D₈₃	C₂³	1	2	yes	—
158	C₂×C₄×D₈₃	C₂³	1	2	yes	—
159	C₂×C₄×D₈₃	C₂³	1	2	yes	—
160	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₈₃	C₂³	1	2	yes	—
165	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
167	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₈₃⋊C₄	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	2	yes	—
171	Dic₈₃⋊C₄	C₂³	1	2	yes	—
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
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	2	yes	—
189	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
199	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₃	C₂³	1	2	yes	—
201	C₄×Dic₈₃	C₂³	1	2	yes	—
202	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
205	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
206	C₂⁴×C₈₃	C₂³	1	2	yes	—
207	#41×C₈₃	—	4	2	no	—
208	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₈₃	—	4	2	no	—
210	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₈₃	C₂³	1	2	yes	—
214	C₂×D₄×C₈₃	C₂³	1	2	yes	—
215	C₂×D₄×C₈₃	C₂³	1	2	yes	—
216	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
219	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
220	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
222	C₄⋊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	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
230	C₄²×C₈₃	C₂³	1	1	yes	characteristic
231	C₂³×C₈₃	—	4	2	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	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₈₃	—	2	4	no	—
239	C₂²×D₈₃	—	4	2	no	—
240	C₂²×D₈₃	—	4	2	no	—
241	C₂²×D₈₃	—	4	2	no	—
242	C₂²×D₈₃	—	4	2	no	—
243	C₂²×D₈₃	—	4	2	no	—
244	C₂²×D₈₃	C₂⁴	1	2	yes	—
245	C₂²×D₈₃	C₂⁴	1	2	yes	—
246	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
247	Q₈×C₈₃	—	2	2	no	—
248	D₄×C₈₃	—	2	2	no	—
249	D₄×C₈₃	—	2	2	no	—
250	D₄×C₈₃	—	4	2	no	—
251	D₄×C₈₃	—	4	1	no	—
252	D₄×C₈₃	—	4	2	no	—
253	D₄×C₈₃	—	4	2	no	—
254	C₂×C₄×C₈₃	—	2	2	no	—
255	C₂×C₄×C₈₃	—	2	2	no	—
256	C₂×C₄×C₈₃	—	4	2	no	—
257	C₂×C₄×C₈₃	—	4	2	no	—
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	2	yes	—
263	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₈₃	—	2	2	no	—
266	C₂²⋊D₈₃	—	2	2	no	—
267	C₂²⋊D₈₃	—	2	4	no	—
268	C₂²⋊D₈₃	—	4	2	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	C₂²⋊D₈₃	—	4	2	no	—
276	C₂²⋊D₈₃	—	4	2	no	—
277	C₂×Dic₈₃	—	4	2	no	—
278	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
285	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
287	D₃₃₂	—	2	4	no	—
288	D₃₃₂	—	2	2	no	—
289	D₃₃₂	—	2	2	no	—
290	D₃₃₂	—	4	2	no	—
291	C₄×D₈₃	—	2	2	no	—
292	C₄×D₈₃	—	2	2	no	—
293	C₄×D₈₃	—	4	1	no	—
294	C₄×D₈₃	—	4	2	no	—
295	C₄×D₈₃	—	4	2	no	—
296	C₄×D₈₃	—	4	2	no	—
297	C₄×D₈₃	—	4	2	no	—
298	Dic₁₆₆	—	2	2	no	—
299	Dic₁₆₆	—	4	2	no	—
300	Dic₁₆₆	—	4	1	no	—
301	Dic₁₆₆	—	4	2	no	—
302	C₂²×C₈₃	—	2	2	no	—
303	C₂²×C₈₃	—	2	2	no	—
304	C₂²×C₈₃	—	2	1	no	—
305	C₂²×C₈₃	—	2	1	no	—
306	C₂²×C₈₃	—	2	1	no	—
307	C₂²×C₈₃	—	2	2	no	—
308	C₂²×C₈₃	—	2	1	no	—
309	C₂²×C₈₃	—	2	2	no	—
310	C₂²×C₈₃	—	2	2	no	—
311	C₂²×C₈₃	—	2	2	no	—
312	C₂²×C₈₃	—	2	1	no	—
313	C₂²×C₈₃	—	2	1	no	—
314	C₂²×C₈₃	—	8	4	no	—
315	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
316	C₂×D₈₃	—	2	1	no	—
317	C₂×D₈₃	—	2	1	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	2	no	—
323	C₂×D₈₃	—	2	2	no	—
324	C₂×D₈₃	—	8	4	no	—
325	C₂×D₈₃	—	8	4	no	—
326	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
327	C₄×C₈₃	—	2	2	no	—
328	C₄×C₈₃	—	2	2	no	—
329	C₄×C₈₃	—	2	1	no	—
330	C₄×C₈₃	—	2	1	no	—
331	C₄×C₈₃	—	2	1	no	—
332	C₄×C₈₃	—	2	1	no	—
333	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
334	Dic₈₃	—	2	2	no	—
335	Dic₈₃	—	2	1	no	—
336	Dic₈₃	—	2	1	no	—
337	Dic₈₃	—	2	2	no	—
338	Dic₈₃	—	2	1	no	—
339	Dic₈₃	—	2	1	no	—
340	Dic₈₃	—	2	1	no	—
341	Dic₈₃	—	2	1	no	—
342	Dic₈₃	—	2	1	no	—
343	C₂×C₈₃	—	4	1	no	—
344	C₂×C₈₃	—	4	2	no	—
345	C₂×C₈₃	—	4	2	no	—
346	C₂×C₈₃	—	4	1	no	—
347	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₈₃	#585	1	1	yes	characteristic
350	D₈₃	—	2	2	no	—
351	D₈₃	—	4	2	no	—
352	D₈₃	—	4	2	no	—
353	#3558	—	83	1	no	maximal, Sylow
354	C₈₃	#3558	1	1	yes	characteristic, complemented, Sylow
355	#562	—	83	2	no	—
356	H(3,𝔽₄)	—	83	2	no	—
357	#559	—	83	1	no	—
358	#559	—	83	1	no	—
359	#548	—	83	1	no	—
360	#548	—	83	1	no	—
361	#546	—	83	2	no	—
362	#546	—	83	1	no	—
363	#546	—	83	2	no	—
364	#546	D₈₃	1	1	yes	characteristic, complemented
365	D₄²	—	83	1	no	—
366	D₄²	—	83	1	no	—
367	#542	—	83	1	no	—
368	#542	—	83	1	no	—
369	#538	—	83	2	no	—
370	#538	—	83	2	no	—
371	#538	—	83	2	no	—
372	#535	—	83	1	no	—
373	#535	—	83	1	no	—
374	#534	—	83	2	no	—
375	#532	—	83	1	no	—
376	#529	—	83	1	no	—
377	C₂×#124	—	83	1	no	—
378	C₂×#41	—	83	2	no	—
379	C₂×#41	—	83	1	no	—
380	C₂×#41	C₂×D₈₃	1	1	yes	characteristic, complemented
381	C₂²×Q₈	—	83	1	no	—
382	C₂²×D₄	—	83	2	no	—
383	C₂²×D₄	—	83	1	no	—
384	C₂²×D₄	—	83	2	no	—
385	C₂²×D₄	—	83	1	no	—
386	C₂²×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
387	C₄⋊Q₈	—	83	1	no	—
388	#127	—	83	1	no	—
389	#127	—	83	1	no	—
390	#127	—	83	1	no	—
391	#126	—	83	2	no	—
392	#126	—	83	1	no	—
393	#126	—	83	1	no	—
394	#126	—	83	2	no	—
395	#125	—	83	1	no	—
396	#124	—	83	1	no	—
397	#124	—	83	1	no	—
398	#124	—	83	1	no	—
399	#124	—	83	1	no	—
400	#124	—	83	1	no	—
401	#124	—	83	2	no	—
402	#124	—	83	2	no	—
403	#124	—	83	2	no	—
404	#124	—	83	2	no	—
405	#124	—	83	2	no	—
406	#124	—	83	2	no	—
407	#124	—	83	2	no	—
408	#124	—	83	2	no	—
409	#124	—	83	2	no	—
410	#124	—	83	1	no	—
411	#124	C₂×D₈₃	1	1	yes	characteristic, complemented
412	#123	—	83	2	no	—
413	#123	—	83	2	no	—
414	#123	—	83	2	no	—
415	#123	—	83	1	no	—
416	#123	—	83	1	no	—
417	#123	—	83	2	no	—
418	#123	—	83	2	no	—
419	#123	—	83	2	no	—
420	#123	—	83	2	no	—
421	#123	C₂×D₈₃	1	2	yes	complemented
422	C₂²⋊Q₈	—	83	2	no	—
423	C₂²⋊Q₈	—	83	1	no	—
424	C₂²⋊Q₈	—	83	2	no	—
425	C₂²⋊Q₈	—	83	1	no	—
426	C₂²⋊Q₈	—	83	2	no	—
427	C₂²⋊Q₈	—	83	2	no	—
428	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
429	#121	—	83	1	no	—
430	#121	—	83	1	no	—
431	#121	—	83	2	no	—
432	#121	—	83	2	no	—
433	#121	—	83	2	no	—
434	#121	—	83	2	no	—
435	#121	—	83	1	no	—
436	#121	—	83	2	no	—
437	#121	—	83	2	no	—
438	#121	—	83	1	no	—
439	#121	—	83	2	no	—
440	#121	—	83	2	no	—
441	#121	—	83	2	no	—
442	#121	—	83	2	no	—
443	#121	C₂×D₈₃	1	1	yes	characteristic
444	#121	C₂×D₈₃	1	2	yes	complemented
445	#120	—	83	2	no	—
446	#120	—	83	2	no	—
447	#120	—	83	2	no	—
448	#120	—	83	2	no	—
449	#120	—	83	2	no	—
450	#120	—	83	2	no	—
451	#120	—	83	2	no	—
452	#120	—	83	2	no	—
453	#120	—	83	2	no	—
454	#120	C₂×D₈₃	1	2	yes	complemented
455	C₄×Q₈	—	83	1	no	—
456	C₄×Q₈	—	83	1	no	—
457	C₄×Q₈	—	83	1	no	—
458	C₄×D₄	—	83	1	no	—
459	C₄×D₄	—	83	1	no	—
460	C₄×D₄	—	83	1	no	—
461	C₄×D₄	—	83	2	no	—
462	C₄×D₄	—	83	2	no	—
463	C₄×D₄	—	83	2	no	—
464	C₄×D₄	—	83	2	no	—
465	C₄×D₄	—	83	1	no	—
466	C₄×D₄	—	83	2	no	—
467	C₄×D₄	—	83	1	no	—
468	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
469	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
470	#117	—	83	1	no	—
471	#117	—	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×C₄²	—	83	1	no	—
477	C₂⁴	—	83	2	no	—
478	C₂⁴	—	83	2	no	—
479	C₂⁴	C₂²×D₈₃	1	2	yes	—
480	#41	—	4	2	no	—
481	#41	—	332	2	no	—
482	#41	—	332	4	no	—
483	C₂×Q₈	—	332	2	no	—
484	C₂×Q₈	—	83	1	no	—
485	C₂×Q₈	—	83	2	no	—
486	C₂×Q₈	—	83	2	no	—
487	C₂×Q₈	—	83	1	no	—
488	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	332	2	no	—
491	C₂×D₄	—	332	4	no	—
492	C₂×D₄	—	332	4	no	—
493	C₂×D₄	—	332	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	2	no	—
499	C₂×D₄	—	83	2	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	2	no	—
508	C₂×D₄	—	83	1	no	—
509	C₂×D₄	—	83	1	no	—
510	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
511	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
512	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
513	C₂×D₄	C₂²×D₈₃	1	2	yes	—
514	C₂×D₄	C₂²×D₈₃	1	2	yes	—
515	C₂×D₄	C₂²×D₈₃	1	2	yes	—
516	C₂²×C₄	—	83	2	no	—
517	C₂²×C₄	—	83	1	no	—
518	C₂²×C₄	—	83	2	no	—
519	C₂²×C₄	—	83	2	no	—
520	C₂²×C₄	—	83	2	no	—
521	C₂²×C₄	—	83	2	no	—
522	C₂²×C₄	—	83	1	no	—
523	C₂²×C₄	—	83	1	no	—
524	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
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	C₄⋊C₄	—	83	1	no	—
529	C₄⋊C₄	—	83	1	no	—
530	C₄⋊C₄	—	83	1	no	—
531	C₄⋊C₄	—	83	1	no	—
532	C₄⋊C₄	—	83	1	no	—
533	C₄⋊C₄	—	83	1	no	—
534	C₄⋊C₄	—	83	1	no	—
535	C₄⋊C₄	—	83	1	no	—
536	C₄⋊C₄	—	83	1	no	—
537	C₄⋊C₄	—	83	2	no	—
538	C₄⋊C₄	—	83	2	no	—
539	C₄⋊C₄	—	83	2	no	—
540	C₄⋊C₄	—	83	2	no	—
541	C₄⋊C₄	—	83	1	no	—
542	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
544	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
545	C₂²⋊C₄	—	83	2	no	—
546	C₂²⋊C₄	—	83	2	no	—
547	C₂²⋊C₄	—	83	2	no	—
548	C₂²⋊C₄	—	83	1	no	—
549	C₂²⋊C₄	—	83	1	no	—
550	C₂²⋊C₄	—	83	1	no	—
551	C₂²⋊C₄	—	83	1	no	—
552	C₂²⋊C₄	—	83	2	no	—
553	C₂²⋊C₄	—	83	1	no	—
554	C₂²⋊C₄	—	83	1	no	—
555	C₂²⋊C₄	—	83	2	no	—
556	C₂²⋊C₄	—	83	2	no	—
557	C₂²⋊C₄	—	83	2	no	—
558	C₂²⋊C₄	—	83	2	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	1	no	—
564	C₂²⋊C₄	—	83	1	no	—
565	C₂²⋊C₄	—	83	2	no	—
566	C₂²⋊C₄	—	83	2	no	—
567	C₂²⋊C₄	—	83	2	no	—
568	C₂²⋊C₄	—	83	2	no	—
569	C₂²⋊C₄	—	83	2	no	—
570	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
577	C₄²	—	83	1	no	—
578	C₄²	—	83	1	no	—
579	C₄²	—	83	1	no	—
580	C₄²	—	83	1	no	—
581	C₄²	—	83	1	no	—
582	C₄²	—	83	2	no	—
583	C₄²	—	83	2	no	—
584	C₄²	C₂²×D₈₃	1	1	yes	characteristic
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	332	2	no	—
589	C₂³	—	332	2	no	—
590	C₂³	—	332	2	no	—
591	C₂³	—	332	2	no	—
592	C₂³	—	332	2	no	—
593	C₂³	—	83	1	no	—
594	C₂³	—	83	2	no	—
595	C₂³	—	83	2	no	—
596	C₂³	—	166	4	no	—
597	C₂³	C₂³×D₈₃	1	1	yes	characteristic
598	C₂³	C₂³×D₈₃	1	2	yes	—
599	C₂³	C₂³×D₈₃	1	1	yes	characteristic
600	C₂³	C₂³×D₈₃	1	2	yes	—
601	Q₈	—	2	2	no	—
602	Q₈	—	332	2	no	—
603	Q₈	—	332	2	no	—
604	Q₈	—	332	1	no	—
605	Q₈	—	166	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	332	2	no	—
613	D₄	—	332	2	no	—
614	D₄	—	332	2	no	—
615	D₄	—	332	2	no	—
616	D₄	—	332	2	no	—
617	D₄	—	332	2	no	—
618	D₄	—	332	2	no	—
619	D₄	—	332	2	no	—
620	D₄	—	332	2	no	—
621	D₄	—	332	2	no	—
622	D₄	—	166	4	no	—
623	D₄	—	166	2	no	—
624	D₄	—	166	2	no	—
625	D₄	—	166	4	no	—
626	D₄	—	166	2	no	—
627	D₄	—	166	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	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	—	332	1	no	—
637	C₂×C₄	—	332	2	no	—
638	C₂×C₄	—	83	1	no	—
639	C₂×C₄	—	83	1	no	—
640	C₂×C₄	—	83	1	no	—
641	C₂×C₄	—	83	1	no	—
642	C₂×C₄	—	83	1	no	—
643	C₂×C₄	—	83	2	no	—
644	C₂×C₄	—	83	2	no	—
645	C₂×C₄	—	83	1	no	—
646	C₂×C₄	—	83	1	no	—
647	C₂×C₄	—	166	2	no	—
648	C₂×C₄	—	166	2	no	—
649	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₈₃	1	2	yes	—
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	1	yes	characteristic
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	83	2	no	—
670	C₂²	—	664	4	no	—
671	C₂²	—	664	4	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	2	no	—
678	C₂²	—	166	1	no	—
679	C₂²	—	166	1	no	—
680	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	166	1	no	—
688	C₄	—	166	1	no	—
689	C₄	—	166	2	no	—
690	C₄	—	166	1	no	—
691	C₄	—	166	2	no	—
692	C₄	—	166	1	no	—
693	C₄	—	166	1	no	—
694	C₄	—	166	1	no	—
695	C₄	—	166	1	no	—
696	C₄	#14581837	1	2	yes	—
697	C₂	—	4	1	no	—
698	C₂	—	4	2	no	—
699	C₂	—	4	2	no	—
700	C₂	—	4	1	no	—
701	C₂	—	332	2	no	—
702	C₂	—	332	2	no	—
703	C₂	—	166	2	no	—
704	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
705	C₂	C₂×#14581837	1	1	yes	characteristic
706	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#546×C₈₃	C₂
hypercenter	#546	D₈₃
hypocenter	C₈₃	#3558
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #19128448	C₂	semidirect
2. #19128444	C₂	semidirect
3. #19128434	C₂	semidirect
4. #19128433	C₂	semidirect
5. #19128361	C₂	semidirect
6. #19128358	C₂	semidirect
7. #19128348	C₂	semidirect
8. #19128347	C₂	semidirect
9. #19128341	C₂	semidirect
10. #19128335	C₂	semidirect
11. D₄×C₂²⋊D₈₃	C₂	semidirect
12. #19128324	C₂	semidirect
13. #19128318	C₂	semidirect
14. #19128289	C₂	semidirect
15. #19128287	C₂	semidirect
16. #19128283	C₂	semidirect
17. #19128268	C₂	semidirect
18. #19128265	C₂	semidirect
19. #19128261	C₂	semidirect
20. #19128248	C₂	semidirect
21. #19128233	C₂	semidirect
22. #124×D₈₃	C₂	semidirect
23. #546×C₈₃	C₂	semidirect
24. C₂×#13050590	C₂²	semidirect
25. C₂×#13050590	C₂²	semidirect
26. C₂×Q₈×D₈₃	C₂²	semidirect
27. C₂²×D₃₃₂	C₂²	semidirect
28. C₂²×C₂²⋊D₈₃	C₂²	semidirect
30. C₂×D₄×D₈₃	C₂²	semidirect
31. #14581791	C₂²	semidirect
34. #14581788	C₂²	semidirect
35. #14581787	C₂²	semidirect
36. #14581785	C₂²	semidirect
37. #14581785	C₂²	semidirect
38. #14581785	C₂²	semidirect
39. #14581783	C₂²	semidirect
40. #14581781	C₂²	semidirect
41. #14581781	C₂²	semidirect
42. #14581780	C₂²	semidirect
43. #14581779	C₂²	semidirect
44. #14581779	C₂²	semidirect
45. #14581779	C₂²	semidirect
46. #14581779	C₂²	semidirect
47. #14581779	C₂²	semidirect
48. #14581778	C₂²	semidirect
49. #14581778	C₂²	semidirect
50. #14581778	C₂²	semidirect
51. #14581778	C₂²	semidirect
52. #14581778	C₂²	semidirect
53. #14581778	C₂²	semidirect
54. #14581778	C₂²	semidirect
55. #14581777	C₂²	semidirect
56. #14581776	C₂²	semidirect
57. #14581775	C₂²	semidirect
58. #14581774	C₂²	semidirect
59. #14581774	C₂²	semidirect
60. #14581774	C₂²	semidirect
61. #14581774	C₂²	semidirect
62. #14581774	C₂²	semidirect
63. #14581773	C₂²	semidirect
64. #14581772	C₂²	semidirect
65. #14581772	C₂²	semidirect
66. #14581771	C₂²	semidirect
67. #14581771	C₂²	semidirect
68. #14581770	C₂²	semidirect
69. #14581769	C₂²	semidirect
70. #14581767	C₂²	semidirect
72. #14581766	C₂²	semidirect
73. #14581766	C₂²	semidirect
74. #14581765	C₂²	semidirect
75. #14581765	C₂²	semidirect
76. #14581765	C₂²	semidirect
77. #14581765	C₂²	semidirect
78. #14581764	C₂²	semidirect
80. #14581763	C₂²	semidirect
81. #14581763	C₂²	semidirect
82. #14581763	C₂²	semidirect
83. #14581763	C₂²	semidirect
84. #14581762	C₂²	semidirect
85. #14581761	C₂²	semidirect
86. #14581761	C₂²	semidirect
87. #14581761	C₂²	semidirect
88. #14581760	C₂²	semidirect
89. #14581760	C₂²	semidirect
90. #14581760	C₂²	semidirect
91. #14581760	C₂²	semidirect
92. #14581760	C₂²	semidirect
93. Q₈×Dic₈₃	C₂²	semidirect
94. C₄×Dic₁₆₆	C₂²	semidirect
95. #14581757	C₂²	semidirect
96. C₄×D₃₃₂	C₂²	semidirect
97. D₄×Dic₈₃	C₂²	semidirect
98. #14581754	C₂²	semidirect
99. #14581754	C₂²	semidirect
100. C₄×C₂²⋊D₈₃	C₂²	semidirect
101. C₄×C₂²⋊D₈₃	C₂²	semidirect
102. C₄×C₂²⋊D₈₃	C₂²	semidirect
103. C₄×C₂²⋊D₈₃	C₂²	semidirect
104. C₄×C₂²⋊D₈₃	C₂²	semidirect
105. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
106. #14581751	C₂²	semidirect
107. #14581751	C₂²	semidirect
108. C₂²⋊C₄×D₈₃	C₂²	semidirect
109. C₂²⋊C₄×D₈₃	C₂²	semidirect
110. C₂²⋊C₄×D₈₃	C₂²	semidirect
111. C₄²×D₈₃	C₂²	semidirect
112. C₂×#41×C₈₃	C₂²	semidirect
113. C₂²×D₄×C₈₃	C₂²	semidirect
114. #124×C₈₃	C₂²	semidirect
115. #123×C₈₃	C₂²	semidirect
116. C₂²⋊Q₈×C₈₃	C₂²	semidirect
118. #121×C₈₃	C₂²	semidirect
119. #120×C₈₃	C₂²	semidirect
120. C₄×D₄×C₈₃	C₂²	semidirect
121. C₄×D₄×C₈₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₈₃	C₂²	semidirect
354. C₈₃	#3558	semidirect
364. #546	D₈₃	semidirect
380. C₂×#41	C₂×D₈₃	semidirect
386. C₂²×D₄	C₂×D₈₃	semidirect
411. #124	C₂×D₈₃	semidirect
421. #123	C₂×D₈₃	semidirect
428. C₂²⋊Q₈	C₂×D₈₃	semidirect
444. #121	C₂×D₈₃	semidirect
454. #120	C₂×D₈₃	semidirect
468. C₄×D₄	C₂×D₈₃	semidirect
469. C₄×D₄	C₂×D₈₃	semidirect
475. C₂×C₂²⋊C₄	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128448	2
#19128444	2
#19128434	2
#19128433	2
#19128361	2
#19128358	2
#19128348	2
#19128347	2
#19128341	2
#19128335	2
D₄×C₂²⋊D₈₃	2
#19128324	2
#19128318	2
#19128289	2
#19128287	2
#19128283	2
#19128268	2
#19128265	2
#19128261	2
#19128248	2
#19128233	2
#124×D₈₃	2
#546×C₈₃	2
#3558	83