Subgroups — #24922015

Order 10624.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128453	C₂	1	2	yes	maximal, complemented
2	#19128442	C₂	1	2	yes	maximal, complemented
3	#19128402	C₂	1	2	yes	maximal, complemented
4	#19128399	C₂	1	2	yes	maximal, complemented
5	#19128376	C₂	1	2	yes	maximal, complemented
6	#19128352	C₂	1	2	yes	maximal, complemented
7	#19128341	C₂	1	2	yes	maximal, complemented
8	#19128341	C₂	1	2	yes	maximal, complemented
9	#19128317	C₂	1	2	yes	maximal, complemented
10	#19128298	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128292	C₂	1	2	yes	maximal, complemented
12	#19128290	C₂	1	2	yes	maximal, complemented
13	#19128290	C₂	1	2	yes	maximal, complemented
14	#19128289	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128282	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128263	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128251	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128235	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#126×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13050590	C₂²	1	2	yes	complemented
21	C₂×#13050590	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₈₃	C₂²	1	2	yes	—
23	#14581792	C₂²	1	1	yes	characteristic, complemented
24	#14581791	C₂²	1	2	yes	complemented
25	#14581789	C₂²	1	1	yes	characteristic, complemented
26	#14581787	C₂²	1	2	yes	complemented
27	#14581787	C₂²	1	2	yes	complemented
28	#14581787	C₂²	1	2	yes	complemented
29	#14581786	C₂²	1	2	yes	complemented
30	#14581785	C₂²	1	2	yes	complemented
31	#14581784	C₂²	1	1	yes	characteristic, complemented
32	#14581783	C₂²	1	2	yes	complemented
33	#14581782	C₂²	1	2	yes	complemented
34	#14581780	C₂²	1	1	yes	characteristic, complemented
35	#14581780	C₂²	1	2	yes	complemented
36	#14581778	C₂²	1	2	yes	—
37	#14581778	C₂²	1	2	yes	—
38	#14581778	C₂²	1	2	yes	complemented
39	#14581777	C₂²	1	2	yes	complemented
40	#14581777	C₂²	1	2	yes	complemented
41	#14581777	C₂²	1	2	yes	complemented
42	#14581777	C₂²	1	2	yes	complemented
43	#14581777	C₂²	1	2	yes	complemented
44	#14581776	C₂²	1	2	yes	—
45	#14581776	C₂²	1	2	yes	—
46	#14581775	C₂²	1	2	yes	complemented
47	#14581775	C₂²	1	2	yes	complemented
48	#14581774	C₂²	1	2	yes	—
49	#14581774	C₂²	1	2	yes	—
50	#14581774	C₂²	1	2	yes	complemented
51	#14581772	C₂²	1	2	yes	complemented
52	#14581772	C₂²	1	2	yes	complemented
53	#14581771	C₂²	1	1	yes	characteristic, complemented
54	#14581770	C₂²	1	2	yes	complemented
55	#14581770	C₂²	1	2	yes	complemented
56	#14581770	C₂²	1	2	yes	complemented
57	#14581769	C₂²	1	2	yes	complemented
58	#14581769	C₂²	1	2	yes	complemented
59	#14581767	C₂²	1	2	yes	complemented
60	#14581767	C₂²	1	2	yes	complemented
61	#14581767	C₂²	1	2	yes	complemented
62	#14581767	C₂²	1	2	yes	complemented
63	#14581766	C₂²	1	2	yes	—
64	#14581766	C₂²	1	1	yes	characteristic
65	#14581766	C₂²	1	1	yes	characteristic
66	#14581766	C₂²	1	2	yes	complemented
67	#14581766	C₂²	1	2	yes	complemented
68	#14581766	C₂²	1	1	yes	characteristic, complemented
69	#14581765	C₂²	1	2	yes	—
70	#14581765	C₂²	1	2	yes	—
71	#14581765	C₂²	1	2	yes	—
72	#14581765	C₂²	1	2	yes	—
73	#14581765	C₂²	1	2	yes	complemented
74	#14581762	C₂²	1	2	yes	—
75	#14581762	C₂²	1	2	yes	—
76	#14581762	C₂²	1	2	yes	complemented
77	#14581762	C₂²	1	2	yes	complemented
78	#14581761	C₂²	1	2	yes	—
79	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₃₃₂	C₂²	1	2	yes	complemented
84	#14581754	C₂²	1	2	yes	complemented
85	#14581754	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
89	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
91	#14581750	C₂²	1	2	yes	complemented
92	#14581749	C₂²	1	2	yes	complemented
93	C₄⋊C₄×D₈₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
96	#126×C₈₃	C₂²	1	2	yes	complemented
97	#126×C₈₃	C₂²	1	2	yes	complemented
98	#126×C₈₃	C₂²	1	2	yes	complemented
99	#126×C₈₃	C₂²	1	2	yes	complemented
100	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
106	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₈₃	C₂³	1	2	yes	—
108	#13050590	—	4	4	no	—
109	#13050590	—	4	4	no	—
110	C₂×Dic₁₆₆	C₂³	1	2	yes	—
111	C₂×Dic₁₆₆	C₂³	1	2	yes	—
112	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
113	C₂×D₃₃₂	C₂³	1	2	yes	—
114	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
115	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
116	C₂×D₃₃₂	C₂³	1	2	yes	—
117	C₂×D₃₃₂	C₂³	1	2	yes	—
118	C₂×D₃₃₂	C₂³	1	2	yes	—
119	C₂×D₃₃₂	C₂³	1	2	yes	—
120	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊D₈₃	—	4	4	no	—
122	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
129	C₂²×Dic₈₃	C₂³	1	2	yes	—
130	C₂×C₄×D₈₃	C₂³	1	2	yes	—
131	C₂×C₄×D₈₃	C₂³	1	2	yes	—
132	C₂×C₄×D₈₃	C₂³	1	2	yes	—
133	C₂×C₄×D₈₃	C₂³	1	2	yes	—
134	C₂×C₄×D₈₃	C₂³	1	2	yes	—
135	C₂×C₄×D₈₃	C₂³	1	2	yes	—
136	C₂×C₄×D₈₃	C₂³	1	2	yes	—
137	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₈₃	C₂³	1	2	yes	—
140	C₄⋊Dic₈₃	C₂³	1	2	yes	—
141	C₄⋊Dic₈₃	C₂³	1	2	yes	—
142	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
144	Dic₈₃⋊C₄	C₂³	1	2	yes	—
145	Dic₈₃⋊C₄	C₂³	1	2	yes	—
146	Dic₈₃⋊C₄	C₂³	1	2	yes	—
147	Dic₈₃⋊C₄	C₂³	1	2	yes	—
148	Dic₈₃⋊C₄	C₂³	1	2	yes	—
149	Dic₈₃⋊C₄	C₂³	1	2	yes	—
150	Dic₈₃⋊C₄	C₂³	1	2	yes	—
151	Dic₈₃⋊C₄	C₂³	1	2	yes	—
152	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
155	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
171	C₄×Dic₈₃	C₂³	1	2	yes	—
172	C₄×Dic₈₃	C₂³	1	2	yes	—
173	C₄×Dic₈₃	C₂³	1	2	yes	—
174	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
182	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
183	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
184	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
185	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
186	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
193	C₄²×C₈₃	C₂³	1	1	yes	characteristic
194	C₄²×C₈₃	C₂³	1	1	yes	characteristic
195	C₄²×C₈₃	C₂³	1	1	yes	characteristic
196	C₄²×C₈₃	C₂³	1	1	yes	characteristic
197	C₂³×C₈₃	—	2	2	no	—
198	C₂³×C₈₃	—	4	1	no	—
199	C₂³×C₈₃	—	4	1	no	—
200	C₂³×C₈₃	C₂⁴	1	2	yes	—
201	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
202	C₂²×D₈₃	—	4	2	no	—
203	C₂²×D₈₃	—	4	2	no	—
204	C₂²×D₈₃	—	4	2	no	—
205	C₂²×D₈₃	C₂⁴	1	2	yes	—
206	C₂²×D₈₃	C₂⁴	1	2	yes	—
207	C₂²×D₈₃	C₂⁴	1	2	yes	—
208	C₂×C₄×C₈₃	—	2	2	no	—
209	C₂×C₄×C₈₃	—	2	2	no	—
210	C₂×C₄×C₈₃	—	4	1	no	—
211	C₂×C₄×C₈₃	—	4	1	no	—
212	C₂×C₄×C₈₃	—	4	1	no	—
213	C₂×C₄×C₈₃	—	4	1	no	—
214	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
221	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
222	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
223	C₂²⋊D₈₃	—	2	4	no	—
224	C₂²⋊D₈₃	—	2	4	no	—
225	C₂²⋊D₈₃	—	2	4	no	—
226	C₂²⋊D₈₃	—	4	2	no	—
227	C₂²⋊D₈₃	—	4	2	no	—
228	C₂²⋊D₈₃	—	4	2	no	—
229	C₂²⋊D₈₃	—	4	2	no	—
230	C₂×Dic₈₃	—	4	2	no	—
231	C₂×Dic₈₃	C₂⁴	1	2	yes	—
232	C₂×Dic₈₃	C₂⁴	1	2	yes	—
233	C₂×Dic₈₃	C₂⁴	1	2	yes	—
234	C₂×Dic₈₃	C₂⁴	1	2	yes	—
235	C₂×Dic₈₃	C₂⁴	1	2	yes	—
236	D₃₃₂	—	4	1	no	—
237	D₃₃₂	—	4	2	no	—
238	D₃₃₂	—	4	2	no	—
239	D₃₃₂	—	4	2	no	—
240	D₃₃₂	—	4	1	no	—
241	D₃₃₂	—	4	1	no	—
242	D₃₃₂	—	4	2	no	—
243	D₃₃₂	—	4	2	no	—
244	C₄×D₈₃	—	4	2	no	—
245	C₄×D₈₃	—	4	2	no	—
246	C₄×D₈₃	—	4	2	no	—
247	C₄×D₈₃	—	4	2	no	—
248	C₄×D₈₃	—	4	2	no	—
249	C₄×D₈₃	—	4	2	no	—
250	C₄×D₈₃	—	4	2	no	—
251	Dic₁₆₆	—	4	1	no	—
252	Dic₁₆₆	—	4	2	no	—
253	Dic₁₆₆	—	4	2	no	—
254	C₂²×C₈₃	—	2	1	no	—
255	C₂²×C₈₃	—	2	1	no	—
256	C₂²×C₈₃	—	2	2	no	—
257	C₂²×C₈₃	—	2	2	no	—
258	C₂²×C₈₃	—	2	2	no	—
259	C₂²×C₈₃	—	8	2	no	—
260	C₂²×C₈₃	H(5,𝔽₂)	1	2	yes	—
261	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
262	C₂×D₈₃	—	2	2	no	—
263	C₂×D₈₃	—	2	2	no	—
264	C₂×D₈₃	—	2	2	no	—
265	C₂×D₈₃	—	2	2	no	—
266	C₂×D₈₃	—	2	2	no	—
267	C₂×D₈₃	—	2	2	no	—
268	C₂×D₈₃	—	2	2	no	—
269	C₂×D₈₃	—	2	2	no	—
270	C₂×D₈₃	—	2	2	no	—
271	C₂×D₈₃	—	8	4	no	—
272	C₄×C₈₃	—	2	1	no	—
273	C₄×C₈₃	—	2	2	no	—
274	C₄×C₈₃	—	2	1	no	—
275	C₄×C₈₃	—	2	1	no	—
276	C₄×C₈₃	—	2	1	no	—
277	C₄×C₈₃	—	2	2	no	—
278	C₄×C₈₃	—	2	2	no	—
279	C₄×C₈₃	—	2	1	no	—
280	C₄×C₈₃	—	2	1	no	—
281	Dic₈₃	—	2	2	no	—
282	Dic₈₃	—	2	2	no	—
283	Dic₈₃	—	2	2	no	—
284	Dic₈₃	—	2	2	no	—
285	Dic₈₃	—	2	2	no	—
286	C₂×C₈₃	—	2	2	no	—
287	C₂×C₈₃	—	4	2	no	—
288	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₈₃	#585	1	1	yes	characteristic
290	C₂×C₈₃	#585	1	1	yes	characteristic
291	D₈₃	—	4	2	no	—
292	D₈₃	—	4	2	no	—
293	D₈₃	—	4	2	no	—
294	#3560	—	83	1	no	maximal, Sylow
295	C₈₃	#3560	1	1	yes	characteristic, complemented, Sylow
296	#563	—	83	2	no	—
297	#560	—	83	2	no	—
298	#553	—	83	2	no	—
299	#553	—	83	2	no	—
300	#551	—	83	2	no	—
301	#547	—	83	2	no	—
302	#546	—	83	2	no	—
303	#546	—	83	2	no	—
304	#542	—	83	2	no	—
305	#539	—	83	2	no	—
306	#539	—	83	1	no	—
307	#538	—	83	2	no	—
308	#538	—	83	2	no	—
309	#538	—	83	1	no	—
310	#537	—	83	1	no	—
311	#534	—	83	1	no	—
312	#532	—	83	1	no	—
313	#529	—	83	1	no	—
314	C₂×#126	D₈₃	1	1	yes	characteristic, complemented
315	C₂×#41	—	83	2	no	—
316	C₂×#41	—	83	2	no	—
317	C₂²×D₄	—	83	2	no	—
318	C₄⋊Q₈	—	83	2	no	—
319	C₄⋊Q₈	—	83	1	no	—
320	#127	—	83	1	no	—
321	#126	—	83	2	no	—
322	#126	—	83	2	no	—
323	#126	—	83	2	no	—
324	#126	—	83	2	no	—
325	#126	—	83	2	no	—
326	#126	C₂×D₈₃	1	2	yes	complemented
327	#126	C₂×D₈₃	1	2	yes	complemented
328	#126	C₂×D₈₃	1	2	yes	complemented
329	#126	C₂×D₈₃	1	2	yes	complemented
330	#125	—	83	2	no	—
331	#125	—	83	2	no	—
332	#125	—	83	1	no	—
333	#124	—	83	2	no	—
334	#124	—	83	2	no	—
335	#124	—	83	2	no	—
336	#124	—	83	1	no	—
337	#124	—	83	2	no	—
338	#123	—	83	2	no	—
339	#123	—	83	2	no	—
340	#123	—	83	2	no	—
341	#123	—	83	2	no	—
342	#123	—	83	2	no	—
343	#123	—	83	2	no	—
344	#123	—	83	2	no	—
345	#123	—	83	2	no	—
346	#123	—	83	2	no	—
347	#123	—	83	2	no	—
348	#123	—	83	2	no	—
349	#123	—	83	2	no	—
350	C₂²⋊Q₈	—	83	1	no	—
351	C₂²⋊Q₈	—	83	2	no	—
352	C₂²⋊Q₈	—	83	2	no	—
353	C₂²⋊Q₈	—	83	2	no	—
354	C₂²⋊Q₈	—	83	2	no	—
355	C₂²⋊Q₈	—	83	2	no	—
356	C₂²⋊Q₈	—	83	2	no	—
357	C₂²⋊Q₈	—	83	2	no	—
358	#121	—	83	1	no	—
359	#121	—	83	1	no	—
360	#121	—	83	2	no	—
361	#121	—	83	1	no	—
362	#121	—	83	2	no	—
363	#121	—	83	2	no	—
364	#121	—	83	2	no	—
365	#121	—	83	2	no	—
366	#121	—	83	2	no	—
367	#121	—	83	2	no	—
368	#121	—	83	2	no	—
369	#121	—	83	2	no	—
370	#121	—	83	2	no	—
371	#121	—	83	2	no	—
372	#121	—	83	2	no	—
373	#120	—	83	2	no	—
374	#120	—	83	2	no	—
375	#120	—	83	2	no	—
376	#120	—	83	2	no	—
377	#120	—	83	2	no	—
378	C₄×Q₈	—	83	1	no	—
379	C₄×D₄	—	83	2	no	—
380	C₄×D₄	—	83	2	no	—
381	C₄×D₄	—	83	2	no	—
382	C₄×D₄	—	83	2	no	—
383	C₄×D₄	—	83	2	no	—
384	C₄×D₄	—	83	2	no	—
385	C₄×D₄	—	83	2	no	—
386	C₄×D₄	—	83	1	no	—
387	C₄×D₄	—	83	2	no	—
388	C₄×D₄	—	83	1	no	—
389	C₄×D₄	—	83	1	no	—
390	#117	—	83	2	no	—
391	#117	—	83	2	no	—
392	C₂×C₄⋊C₄	—	83	2	no	—
393	C₂×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic, complemented
394	C₂×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic, complemented
395	C₂×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic, complemented
396	C₂×C₂²⋊C₄	—	83	2	no	—
397	C₂×C₂²⋊C₄	—	83	2	no	—
398	C₂×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
401	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic, complemented
402	C₂⁴	—	83	2	no	—
403	C₂⁴	C₂²×D₈₃	1	1	yes	characteristic
404	#41	—	332	4	no	—
405	#41	—	332	4	no	—
406	C₂×Q₈	—	83	1	no	—
407	C₂×Q₈	—	83	2	no	—
408	C₂×Q₈	—	83	2	no	—
409	C₂×D₄	—	332	4	no	—
410	C₂×D₄	—	83	2	no	—
411	C₂×D₄	—	83	2	no	—
412	C₂×D₄	—	83	2	no	—
413	C₂×D₄	—	83	2	no	—
414	C₂×D₄	—	83	2	no	—
415	C₂×D₄	—	83	2	no	—
416	C₂×D₄	—	83	2	no	—
417	C₂×D₄	—	83	2	no	—
418	C₂×D₄	—	83	1	no	—
419	C₂×D₄	—	83	1	no	—
420	C₂×D₄	—	83	2	no	—
421	C₂×D₄	—	83	2	no	—
422	C₂×D₄	—	83	1	no	—
423	C₂×D₄	—	83	2	no	—
424	C₂×D₄	—	83	2	no	—
425	C₂²×C₄	—	83	2	no	—
426	C₂²×C₄	—	83	2	no	—
427	C₂²×C₄	—	83	2	no	—
428	C₂²×C₄	—	83	2	no	—
429	C₂²×C₄	—	83	2	no	—
430	C₂²×C₄	—	83	2	no	—
431	C₂²×C₄	—	83	2	no	—
432	C₂²×C₄	—	83	2	no	—
433	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
439	C₄⋊C₄	—	83	2	no	—
440	C₄⋊C₄	—	83	2	no	—
441	C₄⋊C₄	—	83	2	no	—
442	C₄⋊C₄	—	83	2	no	—
443	C₄⋊C₄	—	83	2	no	—
444	C₄⋊C₄	—	83	2	no	—
445	C₄⋊C₄	—	83	1	no	—
446	C₄⋊C₄	—	83	2	no	—
447	C₄⋊C₄	—	83	2	no	—
448	C₄⋊C₄	—	83	1	no	—
449	C₄⋊C₄	—	83	2	no	—
450	C₄⋊C₄	—	83	2	no	—
451	C₄⋊C₄	—	83	1	no	—
452	C₄⋊C₄	—	83	1	no	—
453	C₄⋊C₄	—	83	2	no	—
454	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
455	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
457	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
458	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
460	C₂²⋊C₄	—	83	2	no	—
461	C₂²⋊C₄	—	83	2	no	—
462	C₂²⋊C₄	—	83	2	no	—
463	C₂²⋊C₄	—	83	2	no	—
464	C₂²⋊C₄	—	83	2	no	—
465	C₂²⋊C₄	—	83	2	no	—
466	C₂²⋊C₄	—	83	2	no	—
467	C₂²⋊C₄	—	83	2	no	—
468	C₂²⋊C₄	—	83	2	no	—
469	C₂²⋊C₄	—	83	2	no	—
470	C₂²⋊C₄	—	83	2	no	—
471	C₂²⋊C₄	—	83	2	no	—
472	C₂²⋊C₄	—	83	2	no	—
473	C₂²⋊C₄	—	83	2	no	—
474	C₂²⋊C₄	—	83	2	no	—
475	C₂²⋊C₄	—	83	2	no	—
476	C₂²⋊C₄	—	83	2	no	—
477	C₂²⋊C₄	—	83	2	no	—
478	C₂²⋊C₄	—	83	2	no	—
479	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
485	C₄²	—	83	2	no	—
486	C₄²	—	83	2	no	—
487	C₄²	—	83	2	no	—
488	C₄²	C₂²×D₈₃	1	1	yes	characteristic
489	C₄²	C₂²×D₈₃	1	1	yes	characteristic
490	C₄²	C₂²×D₈₃	1	1	yes	characteristic
491	C₄²	C₂²×D₈₃	1	1	yes	characteristic
492	C₂³	—	2	2	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	332	2	no	—
496	C₂³	—	332	2	no	—
497	C₂³	—	332	2	no	—
498	C₂³	—	83	2	no	—
499	C₂³	—	83	2	no	—
500	C₂³	—	83	2	no	—
501	C₂³	C₂³×D₈₃	1	2	yes	—
502	C₂³	C₂³×D₈₃	1	1	yes	characteristic
503	Q₈	—	332	2	no	—
504	Q₈	—	332	2	no	—
505	Q₈	—	332	1	no	—
506	D₄	—	332	2	no	—
507	D₄	—	332	2	no	—
508	D₄	—	332	2	no	—
509	D₄	—	332	2	no	—
510	D₄	—	332	2	no	—
511	D₄	—	332	1	no	—
512	D₄	—	332	1	no	—
513	D₄	—	332	1	no	—
514	D₄	—	332	2	no	—
515	D₄	—	332	2	no	—
516	D₄	—	332	2	no	—
517	D₄	—	332	2	no	—
518	D₄	—	166	4	no	—
519	D₄	—	166	4	no	—
520	D₄	—	166	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	332	2	no	—
528	C₂×C₄	—	332	2	no	—
529	C₂×C₄	—	332	2	no	—
530	C₂×C₄	—	332	2	no	—
531	C₂×C₄	—	332	2	no	—
532	C₂×C₄	—	332	2	no	—
533	C₂×C₄	—	332	2	no	—
534	C₂×C₄	—	332	2	no	—
535	C₂×C₄	—	83	2	no	—
536	C₂×C₄	—	83	2	no	—
537	C₂×C₄	—	83	2	no	—
538	C₂×C₄	—	83	2	no	—
539	C₂×C₄	—	83	2	no	—
540	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
541	C₂×C₄	C₂³×D₈₃	1	2	yes	—
542	C₂×C₄	C₂³×D₈₃	1	2	yes	—
543	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₈₃	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	664	4	no	—
556	C₂²	—	166	2	no	—
557	C₂²	—	166	2	no	—
558	C₂²	—	166	2	no	—
559	C₂²	—	166	2	no	—
560	C₂²	—	166	2	no	—
561	C₂²	—	166	2	no	—
562	C₂²	—	166	2	no	—
563	C₂²	—	166	2	no	—
564	C₂²	—	166	2	no	—
565	C₂²	#14581838	1	2	yes	—
566	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	166	2	no	—
577	C₄	—	166	2	no	—
578	C₄	—	166	2	no	—
579	C₄	—	166	2	no	—
580	C₄	—	166	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	332	2	no	—
584	C₂	—	332	2	no	—
585	C₂	—	332	2	no	—
586	C₂	C₂×#14581838	1	1	yes	characteristic
587	C₂	#19128537	1	1	yes	characteristic
588	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	C₂×#126×C₈₃	C₂
hypercenter	C₂×#126	D₈₃
hypocenter	C₈₃	#3560
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #19128453	C₂	semidirect
2. #19128442	C₂	semidirect
3. #19128402	C₂	semidirect
4. #19128399	C₂	semidirect
5. #19128376	C₂	semidirect
6. #19128352	C₂	semidirect
7. #19128341	C₂	semidirect
8. #19128341	C₂	semidirect
9. #19128317	C₂	semidirect
10. #19128298	C₂	semidirect
11. #19128292	C₂	semidirect
12. #19128290	C₂	semidirect
13. #19128290	C₂	semidirect
14. #19128289	C₂	semidirect
15. #19128282	C₂	semidirect
16. #19128263	C₂	semidirect
17. #19128251	C₂	semidirect
18. #19128235	C₂	semidirect
19. C₂×#126×C₈₃	C₂	semidirect
20. C₂×#13050590	C₂²	semidirect
21. C₂×#13050590	C₂²	semidirect
23. #14581792	C₂²	semidirect
24. #14581791	C₂²	semidirect
25. #14581789	C₂²	semidirect
26. #14581787	C₂²	semidirect
27. #14581787	C₂²	semidirect
28. #14581787	C₂²	semidirect
29. #14581786	C₂²	semidirect
30. #14581785	C₂²	semidirect
31. #14581784	C₂²	semidirect
32. #14581783	C₂²	semidirect
33. #14581782	C₂²	semidirect
34. #14581780	C₂²	semidirect
35. #14581780	C₂²	semidirect
38. #14581778	C₂²	semidirect
39. #14581777	C₂²	semidirect
40. #14581777	C₂²	semidirect
41. #14581777	C₂²	semidirect
42. #14581777	C₂²	semidirect
43. #14581777	C₂²	semidirect
46. #14581775	C₂²	semidirect
47. #14581775	C₂²	semidirect
50. #14581774	C₂²	semidirect
51. #14581772	C₂²	semidirect
52. #14581772	C₂²	semidirect
53. #14581771	C₂²	semidirect
54. #14581770	C₂²	semidirect
55. #14581770	C₂²	semidirect
56. #14581770	C₂²	semidirect
57. #14581769	C₂²	semidirect
58. #14581769	C₂²	semidirect
59. #14581767	C₂²	semidirect
60. #14581767	C₂²	semidirect
61. #14581767	C₂²	semidirect
62. #14581767	C₂²	semidirect
66. #14581766	C₂²	semidirect
67. #14581766	C₂²	semidirect
68. #14581766	C₂²	semidirect
73. #14581765	C₂²	semidirect
76. #14581762	C₂²	semidirect
77. #14581762	C₂²	semidirect
79. C₄×Dic₁₆₆	C₂²	semidirect
80. C₄×D₃₃₂	C₂²	semidirect
81. C₄×D₃₃₂	C₂²	semidirect
82. C₄×D₃₃₂	C₂²	semidirect
83. C₄×D₃₃₂	C₂²	semidirect
84. #14581754	C₂²	semidirect
85. #14581754	C₂²	semidirect
86. C₄×C₂²⋊D₈₃	C₂²	semidirect
87. C₄×C₂²⋊D₈₃	C₂²	semidirect
88. C₄×C₂²⋊D₈₃	C₂²	semidirect
89. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
91. #14581750	C₂²	semidirect
92. #14581749	C₂²	semidirect
93. C₄⋊C₄×D₈₃	C₂²	semidirect
94. C₂²⋊C₄×D₈₃	C₂²	semidirect
95. C₂²⋊C₄×D₈₃	C₂²	semidirect
96. #126×C₈₃	C₂²	semidirect
97. #126×C₈₃	C₂²	semidirect
98. #126×C₈₃	C₂²	semidirect
99. #126×C₈₃	C₂²	semidirect
100. C₂×C₄⋊C₄×C₈₃	C₂²	semidirect
101. C₂×C₄⋊C₄×C₈₃	C₂²	semidirect
102. C₂×C₄⋊C₄×C₈₃	C₂²	semidirect
106. C₂×C₄²×C₈₃	C₂²	semidirect
295. C₈₃	#3560	semidirect
314. C₂×#126	D₈₃	semidirect
326. #126	C₂×D₈₃	semidirect
327. #126	C₂×D₈₃	semidirect
328. #126	C₂×D₈₃	semidirect
329. #126	C₂×D₈₃	semidirect
393. C₂×C₄⋊C₄	C₂×D₈₃	semidirect
394. C₂×C₄⋊C₄	C₂×D₈₃	semidirect
395. C₂×C₄⋊C₄	C₂×D₈₃	semidirect
401. C₂×C₄²	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128453	2
#19128442	2
#19128402	2
#19128399	2
#19128376	2
#19128352	2
#19128341	2
#19128317	2
#19128298	2
#19128292	2
#19128290	2
#19128289	2
#19128282	2
#19128263	2
#19128251	2
#19128235	2
C₂×#126×C₈₃	2
#3560	83