Subgroups — #24921417

Order 10624.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128433	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128423	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128413	C₂	1	2	yes	maximal, complemented
4	#19128380	C₂	1	2	yes	maximal, complemented
5	#19128378	C₂	1	2	yes	maximal, complemented
6	Q₈×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128361	C₂	1	1	yes	maximal, characteristic, complemented
8	#19128347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128340	C₂	1	2	yes	maximal, complemented
10	#19128339	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128335	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128321	C₂	1	2	yes	maximal, complemented
13	#19128288	C₂	1	2	yes	maximal, complemented
14	#19128285	C₂	1	2	yes	maximal, complemented
15	#19128247	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128238	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128237	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128232	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#14581781	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128173	C₂	1	2	yes	maximal, complemented
22	C₄×#13050589	C₂	1	1	yes	maximal, characteristic, complemented
23	#548×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050589	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₈₃	C₂²	1	2	yes	—
29	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
30	#14581790	C₂²	1	2	yes	complemented
31	#14581790	C₂²	1	1	yes	characteristic, complemented
32	#14581788	C₂²	1	1	yes	characteristic
33	#14581787	C₂²	1	2	yes	complemented
34	#14581787	C₂²	1	2	yes	complemented
35	#14581787	C₂²	1	2	yes	complemented
36	#14581786	C₂²	1	2	yes	complemented
37	#14581785	C₂²	1	2	yes	complemented
38	#14581783	C₂²	1	1	yes	characteristic, complemented
39	#14581781	C₂²	1	1	yes	characteristic
40	#14581781	C₂²	1	1	yes	characteristic
41	#14581781	C₂²	1	2	yes	complemented
42	#14581781	C₂²	1	1	yes	characteristic, complemented
43	#14581781	C₂²	1	2	yes	complemented
44	#14581781	C₂²	1	1	yes	characteristic, complemented
45	#14581780	C₂²	1	1	yes	characteristic
46	#14581779	C₂²	1	1	yes	characteristic, complemented
47	#14581778	C₂²	1	2	yes	complemented
48	#14581778	C₂²	1	2	yes	complemented
49	#14581778	C₂²	1	2	yes	complemented
50	#14581778	C₂²	1	2	yes	complemented
51	#14581777	C₂²	1	2	yes	complemented
52	#14581777	C₂²	1	2	yes	complemented
53	#14581776	C₂²	1	2	yes	complemented
54	#14581776	C₂²	1	2	yes	complemented
55	#14581775	C₂²	1	2	yes	complemented
56	#14581774	C₂²	1	2	yes	complemented
57	#14581773	C₂²	1	2	yes	complemented
58	#14581771	C₂²	1	1	yes	characteristic, complemented
59	#14581771	C₂²	1	2	yes	complemented
60	#14581770	C₂²	1	2	yes	complemented
61	#14581770	C₂²	1	2	yes	complemented
62	#14581768	C₂²	1	1	yes	characteristic, complemented
63	#14581768	C₂²	1	2	yes	complemented
64	#14581767	C₂²	1	1	yes	characteristic
65	#14581766	C₂²	1	1	yes	characteristic
66	#14581765	C₂²	1	2	yes	—
67	#14581765	C₂²	1	2	yes	complemented
68	#14581765	C₂²	1	2	yes	complemented
69	#14581764	C₂²	1	2	yes	complemented
70	#14581764	C₂²	1	2	yes	complemented
71	#14581764	C₂²	1	2	yes	complemented
72	#14581762	C₂²	1	2	yes	—
73	#14581760	C₂²	1	2	yes	—
74	#14581760	C₂²	1	2	yes	complemented
75	#14581760	C₂²	1	2	yes	complemented
76	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
78	#14581757	C₂²	1	1	yes	characteristic, complemented
79	#14581757	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₃₃₂	C₂²	1	2	yes	complemented
82	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₈₃	C₂²	1	2	yes	complemented
85	#14581754	C₂²	1	1	yes	characteristic
86	#14581754	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
92	(C₂²⋊D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
93	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
94	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
95	(C₂²⋊D₈₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	#14581750	C₂²	1	2	yes	complemented
97	#14581750	C₂²	1	1	yes	characteristic, complemented
98	#14581749	C₂²	1	2	yes	complemented
99	#14581749	C₂²	1	2	yes	complemented
100	#14581748	C₂²	1	2	yes	complemented
101	#14581748	C₂²	1	1	yes	characteristic, complemented
102	#14581748	C₂²	1	1	yes	characteristic, complemented
103	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
104	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
105	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₈₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₈₃	C₂²	1	2	yes	complemented
115	#124×C₈₃	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
118	#121×C₈₃	C₂²	1	1	yes	characteristic
119	#121×C₈₃	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×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	#13050589	—	2	4	no	—
127	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	Q₈×D₈₃	—	4	2	no	—
131	C₂×D₃₃₂	—	4	2	no	—
132	C₂×D₃₃₂	C₂³	1	2	yes	—
133	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
134	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
135	C₂×D₃₃₂	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
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	1	yes	characteristic
143	D₄×D₈₃	—	2	8	no	—
144	D₄×D₈₃	—	4	2	no	—
145	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
148	C₂²×Dic₈₃	C₂³	1	2	yes	—
149	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₃	C₂³	1	2	yes	—
151	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₈₃	C₂³	1	2	yes	—
154	C₂×C₄×D₈₃	C₂³	1	2	yes	—
155	C₂×C₄×D₈₃	C₂³	1	2	yes	—
156	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₃	C₂³	1	2	yes	—
159	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₃	C₂³	1	2	yes	—
161	Dic₈₃⋊C₄	C₂³	1	2	yes	—
162	Dic₈₃⋊C₄	C₂³	1	2	yes	—
163	Dic₈₃⋊C₄	C₂³	1	2	yes	—
164	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₈₃⋊C₄	C₂³	1	2	yes	—
166	Dic₈₃⋊C₄	C₂³	1	2	yes	—
167	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
177	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
194	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₃	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	2	yes	—
198	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₃	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	1	yes	characteristic
205	#41×C₈₃	—	4	2	no	—
206	C₂×Q₈×C₈₃	—	4	2	no	—
207	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
210	C₂×D₄×C₈₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
217	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
218	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
220	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
221	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
228	C₄²×C₈₃	C₂³	1	1	yes	characteristic
229	C₄²×C₈₃	C₂³	1	2	yes	—
230	C₂³×C₈₃	C₂⁴	1	2	yes	—
231	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₈₃	—	2	4	no	—
234	C₂²×D₈₃	—	2	4	no	—
235	C₂²×D₈₃	—	4	2	no	—
236	C₂²×D₈₃	—	4	2	no	—
237	C₂²×D₈₃	—	4	2	no	—
238	C₂²×D₈₃	—	4	2	no	—
239	C₂²×D₈₃	C₂⁴	1	2	yes	—
240	C₂²×D₈₃	C₂⁴	1	2	yes	—
241	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
242	Q₈×C₈₃	—	2	2	no	—
243	Q₈×C₈₃	—	2	2	no	—
244	Q₈×C₈₃	—	4	2	no	—
245	D₄×C₈₃	—	2	4	no	—
246	D₄×C₈₃	—	2	2	no	—
247	D₄×C₈₃	—	2	2	no	—
248	D₄×C₈₃	—	4	2	no	—
249	C₂×C₄×C₈₃	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₈₃	—	2	2	no	—
262	C₂²⋊D₈₃	—	2	4	no	—
263	C₂²⋊D₈₃	—	4	2	no	—
264	C₂²⋊D₈₃	—	4	2	no	—
265	C₂²⋊D₈₃	—	4	2	no	—
266	C₂²⋊D₈₃	—	4	2	no	—
267	C₂²⋊D₈₃	#41	1	4	yes	complemented
268	C₂×Dic₈₃	—	2	2	no	—
269	C₂×Dic₈₃	—	2	2	no	—
270	C₂×Dic₈₃	—	4	1	no	—
271	C₂×Dic₈₃	—	4	1	no	—
272	C₂×Dic₈₃	—	4	2	no	—
273	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₈₃	C₂⁴	1	2	yes	—
280	C₂×Dic₈₃	C₂⁴	1	2	yes	—
281	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
282	D₃₃₂	—	2	4	no	—
283	D₃₃₂	—	2	2	no	—
284	D₃₃₂	—	2	2	no	—
285	D₃₃₂	—	4	2	no	—
286	C₄×D₈₃	—	2	2	no	—
287	C₄×D₈₃	—	2	2	no	—
288	C₄×D₈₃	—	2	4	no	—
289	C₄×D₈₃	—	4	1	no	—
290	C₄×D₈₃	—	4	2	no	—
291	C₄×D₈₃	—	4	2	no	—
292	C₄×D₈₃	—	4	2	no	—
293	Dic₁₆₆	—	2	2	no	—
294	Dic₁₆₆	—	2	2	no	—
295	Dic₁₆₆	—	4	2	no	—
296	C₂²×C₈₃	—	2	1	no	—
297	C₂²×C₈₃	—	2	1	no	—
298	C₂²×C₈₃	—	2	1	no	—
299	C₂²×C₈₃	—	2	2	no	—
300	C₂²×C₈₃	—	2	1	no	—
301	C₂²×C₈₃	—	2	2	no	—
302	C₂²×C₈₃	—	2	1	no	—
303	C₂²×C₈₃	—	2	2	no	—
304	C₂²×C₈₃	C₂×#41	1	2	yes	—
305	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
306	C₂×D₈₃	—	2	1	no	—
307	C₂×D₈₃	—	2	1	no	—
308	C₂×D₈₃	—	2	2	no	—
309	C₂×D₈₃	—	2	2	no	—
310	C₂×D₈₃	—	2	2	no	—
311	C₂×D₈₃	—	2	2	no	—
312	C₂×D₈₃	—	2	2	no	—
313	C₂×D₈₃	—	2	2	no	—
314	C₂×D₈₃	—	8	4	no	—
315	C₂×D₈₃	—	8	4	no	—
316	C₂×D₈₃	C₂×#41	1	2	yes	—
317	C₄×C₈₃	—	2	1	no	—
318	C₄×C₈₃	—	2	2	no	—
319	C₄×C₈₃	—	2	2	no	—
320	C₄×C₈₃	—	2	1	no	—
321	C₄×C₈₃	—	2	1	no	—
322	C₄×C₈₃	—	2	2	no	—
323	C₄×C₈₃	—	2	1	no	—
324	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
325	Dic₈₃	—	2	1	no	—
326	Dic₈₃	—	2	1	no	—
327	Dic₈₃	—	2	2	no	—
328	Dic₈₃	—	2	1	no	—
329	Dic₈₃	—	2	1	no	—
330	Dic₈₃	—	2	2	no	—
331	Dic₈₃	—	2	1	no	—
332	Dic₈₃	—	2	1	no	—
333	Dic₈₃	C₂×#41	1	2	yes	—
334	C₂×C₈₃	—	2	2	no	—
335	C₂×C₈₃	—	4	2	no	—
336	C₂×C₈₃	—	4	1	no	—
337	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
338	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₈₃	#585	1	1	yes	characteristic
340	D₈₃	—	2	2	no	—
341	D₈₃	—	4	2	no	—
342	D₈₃	—	4	2	no	—
343	#3514	—	83	1	no	maximal, Sylow
344	C₈₃	#3514	1	1	yes	characteristic, complemented, Sylow
345	#559	—	83	1	no	—
346	#556	—	83	1	no	—
347	#555	—	83	2	no	—
348	#551	—	83	2	no	—
349	#551	—	83	2	no	—
350	D₄×Q₈	—	83	1	no	—
351	#548	—	83	1	no	—
352	#548	D₈₃	1	1	yes	characteristic, complemented
353	#546	—	83	1	no	—
354	#546	—	83	2	no	—
355	#546	—	83	1	no	—
356	D₄²	—	83	1	no	—
357	#542	—	83	2	no	—
358	#538	—	83	2	no	—
359	#538	—	83	2	no	—
360	#532	—	83	1	no	—
361	#529	—	83	1	no	—
362	#529	—	83	1	no	—
363	#529	—	83	1	no	—
364	C₂×#124	—	83	1	no	—
365	C₂×#124	—	83	1	no	—
366	#518	—	83	2	no	—
367	C₄×#41	—	83	1	no	—
368	C₂×#41	—	83	1	no	—
369	C₂×#41	—	83	1	no	—
370	C₂×#41	C₂×D₈₃	1	1	yes	characteristic, complemented
371	C₂²×Q₈	—	83	1	no	—
372	C₂²×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
373	C₂²×D₄	—	83	1	no	—
374	C₂²×D₄	—	83	2	no	—
375	C₂²×D₄	—	83	1	no	—
376	C₄⋊Q₈	—	83	1	no	—
377	C₄⋊Q₈	—	83	2	no	—
378	#127	—	83	1	no	—
379	#126	—	83	2	no	—
380	#126	—	83	2	no	—
381	#126	—	83	2	no	—
382	#126	—	83	2	no	—
383	#126	—	83	2	no	—
384	#125	—	83	1	no	—
385	#124	—	83	1	no	—
386	#124	—	83	1	no	—
387	#124	—	83	1	no	—
388	#124	—	83	2	no	—
389	#124	—	83	1	no	—
390	#124	—	83	2	no	—
391	#124	—	83	1	no	—
392	#124	—	83	2	no	—
393	#124	—	83	2	no	—
394	#124	—	83	2	no	—
395	#124	—	83	2	no	—
396	#124	—	83	1	no	—
397	#124	C₂×D₈₃	1	1	yes	characteristic, complemented
398	#124	C₂×D₈₃	1	2	yes	complemented
399	#123	—	83	2	no	—
400	#123	—	83	2	no	—
401	#123	—	83	2	no	—
402	#123	—	83	2	no	—
403	#123	—	83	2	no	—
404	#123	—	83	2	no	—
405	#123	—	83	2	no	—
406	C₂²⋊Q₈	—	83	1	no	—
407	C₂²⋊Q₈	—	83	2	no	—
408	C₂²⋊Q₈	—	83	1	no	—
409	C₂²⋊Q₈	—	83	2	no	—
410	C₂²⋊Q₈	—	83	2	no	—
411	C₂²⋊Q₈	—	83	2	no	—
412	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
413	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	complemented
414	#121	—	83	2	no	—
415	#121	—	83	2	no	—
416	#121	—	83	2	no	—
417	#121	—	83	1	no	—
418	#121	—	83	1	no	—
419	#121	—	83	2	no	—
420	#121	—	83	2	no	—
421	#121	—	83	2	no	—
422	#121	C₂×D₈₃	1	1	yes	characteristic
423	#121	C₂×D₈₃	1	2	yes	complemented
424	#120	—	83	2	no	—
425	#120	—	83	2	no	—
426	#120	—	83	2	no	—
427	#120	—	83	2	no	—
428	C₄×Q₈	—	83	1	no	—
429	C₄×Q₈	—	83	1	no	—
430	C₄×Q₈	—	83	1	no	—
431	C₄×Q₈	—	83	1	no	—
432	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
433	C₄×D₄	—	83	1	no	—
434	C₄×D₄	—	83	2	no	—
435	C₄×D₄	—	83	1	no	—
436	C₄×D₄	—	83	1	no	—
437	C₄×D₄	—	83	1	no	—
438	C₄×D₄	—	83	2	no	—
439	C₄×D₄	—	83	2	no	—
440	C₄×D₄	—	83	2	no	—
441	C₄×D₄	—	83	2	no	—
442	C₄×D₄	—	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	C₂×D₈₃	1	1	yes	characteristic, complemented
450	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
451	#117	—	83	1	no	—
452	#117	—	83	2	no	—
453	#117	—	83	1	no	—
454	#117	—	83	1	no	—
455	#117	—	83	2	no	—
456	#117	—	83	2	no	—
457	#117	—	83	2	no	—
458	C₂×C₂²⋊C₄	—	83	2	no	—
459	C₂×C₂²⋊C₄	—	83	2	no	—
460	C₂×C₂²⋊C₄	—	83	2	no	—
461	C₂×C₂²⋊C₄	—	83	2	no	—
462	C₂×C₂²⋊C₄	—	83	2	no	—
463	C₂×C₂²⋊C₄	—	83	2	no	—
464	C₂×C₄²	—	83	1	no	—
465	C₂×C₄²	—	83	1	no	—
466	C₂×C₄²	—	83	1	no	—
467	C₂⁴	—	83	2	no	—
468	C₂⁴	—	83	2	no	—
469	#41	—	4	2	no	—
470	#41	—	332	2	no	—
471	#41	—	166	4	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	332	2	no	—
474	C₂×Q₈	—	83	2	no	—
475	C₂×Q₈	—	83	1	no	—
476	C₂×Q₈	—	83	1	no	—
477	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
480	C₂×D₄	—	332	2	no	—
481	C₂×D₄	—	332	2	no	—
482	C₂×D₄	—	83	2	no	—
483	C₂×D₄	—	83	2	no	—
484	C₂×D₄	—	83	2	no	—
485	C₂×D₄	—	83	2	no	—
486	C₂×D₄	—	83	1	no	—
487	C₂×D₄	—	83	1	no	—
488	C₂×D₄	—	83	2	no	—
489	C₂×D₄	—	83	2	no	—
490	C₂×D₄	—	83	2	no	—
491	C₂×D₄	—	83	1	no	—
492	C₂×D₄	—	83	1	no	—
493	C₂×D₄	—	166	8	no	—
494	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₈₃	1	2	yes	—
496	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₈₃	1	2	yes	—
498	C₂²×C₄	—	83	1	no	—
499	C₂²×C₄	—	83	1	no	—
500	C₂²×C₄	—	83	2	no	—
501	C₂²×C₄	—	83	1	no	—
502	C₂²×C₄	—	83	2	no	—
503	C₂²×C₄	—	83	2	no	—
504	C₂²×C₄	—	83	2	no	—
505	C₂²×C₄	—	83	1	no	—
506	C₂²×C₄	—	83	1	no	—
507	C₂²×C₄	—	83	1	no	—
508	C₂²×C₄	—	83	1	no	—
509	C₂²×C₄	—	83	2	no	—
510	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
513	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
514	C₄⋊C₄	—	83	1	no	—
515	C₄⋊C₄	—	83	2	no	—
516	C₄⋊C₄	—	83	2	no	—
517	C₄⋊C₄	—	83	2	no	—
518	C₄⋊C₄	—	83	1	no	—
519	C₄⋊C₄	—	83	1	no	—
520	C₄⋊C₄	—	83	1	no	—
521	C₄⋊C₄	—	83	1	no	—
522	C₄⋊C₄	—	83	2	no	—
523	C₄⋊C₄	—	83	2	no	—
524	C₄⋊C₄	—	83	1	no	—
525	C₄⋊C₄	—	83	2	no	—
526	C₄⋊C₄	—	83	2	no	—
527	C₄⋊C₄	—	83	2	no	—
528	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
529	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
532	C₂²⋊C₄	—	83	2	no	—
533	C₂²⋊C₄	—	83	2	no	—
534	C₂²⋊C₄	—	83	2	no	—
535	C₂²⋊C₄	—	83	1	no	—
536	C₂²⋊C₄	—	83	1	no	—
537	C₂²⋊C₄	—	83	2	no	—
538	C₂²⋊C₄	—	83	1	no	—
539	C₂²⋊C₄	—	83	2	no	—
540	C₂²⋊C₄	—	83	2	no	—
541	C₂²⋊C₄	—	83	2	no	—
542	C₂²⋊C₄	—	83	2	no	—
543	C₂²⋊C₄	—	83	2	no	—
544	C₂²⋊C₄	—	83	2	no	—
545	C₂²⋊C₄	—	83	2	no	—
546	C₂²⋊C₄	—	83	2	no	—
547	C₂²⋊C₄	—	83	2	no	—
548	C₂²⋊C₄	—	83	2	no	—
549	C₂²⋊C₄	—	83	2	no	—
550	C₂²⋊C₄	—	83	2	no	—
551	C₂²⋊C₄	—	83	1	no	—
552	C₂²⋊C₄	—	83	2	no	—
553	C₂²⋊C₄	—	83	2	no	—
554	C₂²⋊C₄	—	83	2	no	—
555	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
559	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
561	C₄²	—	83	1	no	—
562	C₄²	—	83	1	no	—
563	C₄²	—	83	1	no	—
564	C₄²	—	83	1	no	—
565	C₄²	—	83	1	no	—
566	C₄²	—	83	1	no	—
567	C₄²	—	83	1	no	—
568	C₄²	—	83	1	no	—
569	C₄²	—	83	1	no	—
570	C₄²	—	83	2	no	—
571	C₄²	—	83	2	no	—
572	C₄²	C₂²×D₈₃	1	1	yes	characteristic
573	C₄²	C₂²×D₈₃	1	2	yes	—
574	C₂³	—	332	2	no	—
575	C₂³	—	332	2	no	—
576	C₂³	—	332	2	no	—
577	C₂³	—	332	2	no	—
578	C₂³	—	83	1	no	—
579	C₂³	—	83	2	no	—
580	C₂³	—	83	2	no	—
581	C₂³	—	166	4	no	—
582	C₂³	—	166	4	no	—
583	C₂³	C₂³×D₈₃	1	2	yes	—
584	C₂³	C₂³×D₈₃	1	1	yes	characteristic
585	C₂³	C₂³×D₈₃	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	332	2	no	—
590	Q₈	—	166	2	no	—
591	Q₈	—	166	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	332	2	no	—
597	D₄	—	332	2	no	—
598	D₄	—	332	2	no	—
599	D₄	—	332	2	no	—
600	D₄	—	332	2	no	—
601	D₄	—	83	4	no	—
602	D₄	—	166	4	no	—
603	D₄	—	166	4	no	—
604	D₄	—	166	2	no	—
605	D₄	—	166	2	no	—
606	D₄	—	166	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	332	2	no	—
612	C₂×C₄	—	332	2	no	—
613	C₂×C₄	—	332	1	no	—
614	C₂×C₄	—	332	2	no	—
615	C₂×C₄	—	332	1	no	—
616	C₂×C₄	—	332	2	no	—
617	C₂×C₄	—	332	1	no	—
618	C₂×C₄	—	83	1	no	—
619	C₂×C₄	—	83	1	no	—
620	C₂×C₄	—	83	1	no	—
621	C₂×C₄	—	83	1	no	—
622	C₂×C₄	—	83	1	no	—
623	C₂×C₄	—	83	1	no	—
624	C₂×C₄	—	83	1	no	—
625	C₂×C₄	—	83	2	no	—
626	C₂×C₄	—	83	2	no	—
627	C₂×C₄	—	166	4	no	—
628	C₂×C₄	—	166	2	no	—
629	C₂×C₄	—	166	2	no	—
630	C₂×C₄	—	166	2	no	—
631	C₂×C₄	—	166	2	no	—
632	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₈₃	1	2	yes	—
637	C₂×C₄	C₂³×D₈₃	1	2	yes	—
638	C₂×C₄	C₂³×D₈₃	1	2	yes	—
639	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	83	2	no	—
649	C₂²	—	664	4	no	—
650	C₂²	—	664	4	no	—
651	C₂²	—	166	2	no	—
652	C₂²	—	166	2	no	—
653	C₂²	—	166	2	no	—
654	C₂²	—	166	2	no	—
655	C₂²	—	166	2	no	—
656	C₂²	—	166	2	no	—
657	C₂²	—	166	1	no	—
658	C₂²	—	166	1	no	—
659	C₂²	#41×D₈₃	1	2	yes	—
660	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	83	2	no	—
669	C₄	—	166	1	no	—
670	C₄	—	166	1	no	—
671	C₄	—	166	2	no	—
672	C₄	—	166	1	no	—
673	C₄	—	166	1	no	—
674	C₄	—	166	1	no	—
675	C₄	—	166	2	no	—
676	C₄	—	166	1	no	—
677	C₄	#14581837	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	332	2	no	—
682	C₂	—	332	2	no	—
683	C₂	—	166	2	no	—
684	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
685	C₂	C₂×#14581837	1	1	yes	characteristic
686	C₂	#19128538	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#548×C₈₃	C₂
hypercenter	#548	D₈₃
hypocenter	C₈₃	#3514
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #19128433	C₂	semidirect
2. #19128423	C₂	semidirect
3. #19128413	C₂	semidirect
4. #19128380	C₂	semidirect
5. #19128378	C₂	semidirect
6. Q₈×C₂²⋊D₈₃	C₂	semidirect
7. #19128361	C₂	semidirect
8. #19128347	C₂	semidirect
9. #19128340	C₂	semidirect
10. #19128339	C₂	semidirect
11. #19128335	C₂	semidirect
12. #19128321	C₂	semidirect
13. #19128288	C₂	semidirect
14. #19128285	C₂	semidirect
15. #19128247	C₂	semidirect
16. #19128238	C₂	semidirect
17. #19128237	C₂	semidirect
18. #19128232	C₂	semidirect
19. C₂×#14581781	C₂	semidirect
20. #124×D₈₃	C₂	semidirect
21. #19128173	C₂	semidirect
22. C₄×#13050589	C₂	semidirect
23. #548×C₈₃	C₂	semidirect
24. C₂×#13050590	C₂²	semidirect
26. C₂×Q₈×D₈₃	C₂²	semidirect
30. #14581790	C₂²	semidirect
31. #14581790	C₂²	semidirect
33. #14581787	C₂²	semidirect
34. #14581787	C₂²	semidirect
35. #14581787	C₂²	semidirect
36. #14581786	C₂²	semidirect
37. #14581785	C₂²	semidirect
38. #14581783	C₂²	semidirect
41. #14581781	C₂²	semidirect
42. #14581781	C₂²	semidirect
43. #14581781	C₂²	semidirect
44. #14581781	C₂²	semidirect
46. #14581779	C₂²	semidirect
47. #14581778	C₂²	semidirect
48. #14581778	C₂²	semidirect
49. #14581778	C₂²	semidirect
50. #14581778	C₂²	semidirect
51. #14581777	C₂²	semidirect
52. #14581777	C₂²	semidirect
53. #14581776	C₂²	semidirect
54. #14581776	C₂²	semidirect
55. #14581775	C₂²	semidirect
56. #14581774	C₂²	semidirect
57. #14581773	C₂²	semidirect
58. #14581771	C₂²	semidirect
59. #14581771	C₂²	semidirect
60. #14581770	C₂²	semidirect
61. #14581770	C₂²	semidirect
62. #14581768	C₂²	semidirect
63. #14581768	C₂²	semidirect
67. #14581765	C₂²	semidirect
68. #14581765	C₂²	semidirect
69. #14581764	C₂²	semidirect
70. #14581764	C₂²	semidirect
71. #14581764	C₂²	semidirect
74. #14581760	C₂²	semidirect
75. #14581760	C₂²	semidirect
76. Q₈×Dic₈₃	C₂²	semidirect
77. C₄×Dic₁₆₆	C₂²	semidirect
78. #14581757	C₂²	semidirect
79. #14581757	C₂²	semidirect
80. C₄×D₃₃₂	C₂²	semidirect
81. C₄×D₃₃₂	C₂²	semidirect
82. D₄×Dic₈₃	C₂²	semidirect
83. D₄×Dic₈₃	C₂²	semidirect
84. D₄×Dic₈₃	C₂²	semidirect
86. #14581754	C₂²	semidirect
89. C₄×C₂²⋊D₈₃	C₂²	semidirect
90. C₄×C₂²⋊D₈₃	C₂²	semidirect
91. C₄×C₂²⋊D₈₃	C₂²	semidirect
93. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
95. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
96. #14581750	C₂²	semidirect
97. #14581750	C₂²	semidirect
98. #14581749	C₂²	semidirect
99. #14581749	C₂²	semidirect
100. #14581748	C₂²	semidirect
101. #14581748	C₂²	semidirect
102. #14581748	C₂²	semidirect
103. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
104. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
105. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
106. C₂²⋊C₄×D₈₃	C₂²	semidirect
107. C₂²⋊C₄×D₈₃	C₂²	semidirect
108. C₂²⋊C₄×D₈₃	C₂²	semidirect
109. C₂×C₄×Dic₈₃	C₂²	semidirect
110. C₂×C₄×Dic₈₃	C₂²	semidirect
111. C₄²×D₈₃	C₂²	semidirect
112. C₂×#41×C₈₃	C₂²	semidirect
113. C₂²×Q₈×C₈₃	C₂²	semidirect
114. #124×C₈₃	C₂²	semidirect
115. #124×C₈₃	C₂²	semidirect
116. C₂²⋊Q₈×C₈₃	C₂²	semidirect
117. C₂²⋊Q₈×C₈₃	C₂²	semidirect
119. #121×C₈₃	C₂²	semidirect
120. C₄×Q₈×C₈₃	C₂²	semidirect
121. C₄×D₄×C₈₃	C₂²	semidirect
122. C₄×D₄×C₈₃	C₂²	semidirect
267. C₂²⋊D₈₃	#41	semidirect
344. C₈₃	#3514	semidirect
352. #548	D₈₃	semidirect
370. C₂×#41	C₂×D₈₃	semidirect
372. C₂²×Q₈	C₂×D₈₃	semidirect
397. #124	C₂×D₈₃	semidirect
398. #124	C₂×D₈₃	semidirect
412. C₂²⋊Q₈	C₂×D₈₃	semidirect
413. C₂²⋊Q₈	C₂×D₈₃	semidirect
423. #121	C₂×D₈₃	semidirect
432. C₄×Q₈	C₂×D₈₃	semidirect
449. C₄×D₄	C₂×D₈₃	semidirect
450. C₄×D₄	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128433	2
#19128423	2
#19128413	2
#19128380	2
#19128378	2
Q₈×C₂²⋊D₈₃	2
#19128361	2
#19128347	2
#19128340	2
#19128339	2
#19128335	2
#19128321	2
#19128288	2
#19128285	2
#19128247	2
#19128238	2
#19128237	2
#19128232	2
C₂×#14581781	2
#124×D₈₃	2
#19128173	2
C₄×#13050589	2
#548×C₈₃	2
#3514	83