Subgroups — C₂×C₈₃×#3208 #35288599

Order 21248.

2822 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#127×C₈₃	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#3208	C₂	1	16	yes	maximal, direct product factor
4	C₂×#492×C₈₃	C₂	1	2	yes	maximal, complemented
5	C₂×#486×C₈₃	C₂	1	2	yes	maximal, complemented
6	C₂×#460×C₈₃	C₂	1	4	yes	maximal, complemented
7	C₂×#450×C₈₃	C₂	1	4	yes	maximal, complemented
8	C₂×#431×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₈₃	—	2	1	no	—
10	C₂³×D₄×C₈₃	—	2	1	no	—
11	C₂³×D₄×C₈₃	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₈₃	C₂²	1	8	yes	complemented
13	#533×C₈₃	—	2	4	no	—
14	#533×C₈₃	C₂²	1	8	yes	complemented
15	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₈₃	—	2	1	no	—
18	C₂×#127×C₈₃	—	2	1	no	—
19	C₂×#127×C₈₃	—	2	4	no	—
20	C₂×#127×C₈₃	C₂²	1	2	yes	—
21	C₂×#127×C₈₃	C₂²	1	2	yes	—
22	C₂×#127×C₈₃	C₂²	1	8	yes	—
23	C₂×#125×C₈₃	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₈₃	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	complemented
28	C₂×#117×C₈₃	—	2	1	no	—
29	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
30	#492×C₈₃	C₂²	1	16	yes	complemented
31	#486×C₈₃	C₂²	1	16	yes	complemented
32	#460×C₈₃	C₂²	1	32	yes	complemented
33	#450×C₈₃	C₂²	1	32	yes	complemented
34	#431×C₈₃	C₂²	1	8	yes	complemented
35	C₂×C₄⋊C₈×C₈₃	C₂²	1	2	yes	complemented
36	C₂×#102×C₈₃	C₂²	1	8	yes	complemented
37	C₂×C₂²⋊C₈×C₈₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₈₃	C₂²	1	2	yes	complemented
39	C₂⁵×C₈₃	—	2	2	no	—
40	C₂²×Q₈×C₈₃	—	2	1	no	—
41	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₈₃	—	2	4	no	—
43	C₂²×D₄×C₈₃	—	2	2	no	—
44	C₂²×D₄×C₈₃	—	2	8	no	—
45	C₂²×D₄×C₈₃	—	2	2	no	—
46	C₂²×D₄×C₈₃	—	2	2	no	—
47	C₂²×D₄×C₈₃	—	2	2	no	—
48	C₂²×D₄×C₈₃	—	2	8	no	—
49	C₂²×D₄×C₈₃	—	2	2	no	—
50	C₂²×D₄×C₈₃	—	4	8	no	—
51	C₂²×D₄×C₈₃	—	4	8	no	—
52	C₂²×D₄×C₈₃	—	4	8	no	—
53	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
54	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
55	C₂³×C₄×C₈₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₈₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₈₃	—	4	16	no	—
59	C₂×SD₁₆×C₈₃	C₂³	1	32	yes	complemented
60	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
61	C₄⋊Q₈×C₈₃	—	2	2	no	—
62	C₄⋊Q₈×C₈₃	—	2	2	no	—
63	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	complemented
64	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	complemented
65	#127×C₈₃	—	2	4	no	—
66	#127×C₈₃	—	2	8	no	—
67	#127×C₈₃	—	2	8	no	—
68	#127×C₈₃	—	2	4	no	—
69	#127×C₈₃	C₂³	1	8	yes	—
70	#127×C₈₃	C₂³	1	8	yes	—
71	#125×C₈₃	—	2	8	no	—
72	C₂²⋊Q₈×C₈₃	—	2	8	no	—
73	C₂²⋊Q₈×C₈₃	—	2	4	no	—
74	C₂²⋊Q₈×C₈₃	C₂³	1	8	yes	—
75	C₄×Q₈×C₈₃	—	2	8	no	—
76	C₄×Q₈×C₈₃	—	2	4	no	—
77	C₄×Q₈×C₈₃	C₂³	1	8	yes	complemented
78	#117×C₈₃	—	2	8	no	—
79	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
86	C₂×C₄²×C₈₃	—	2	2	no	—
87	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₈₃	D₄	1	4	yes	—
90	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
93	C₄⋊C₈×C₈₃	C₂³	1	8	yes	complemented
94	#102×C₈₃	C₂³	1	32	yes	complemented
95	C₂²⋊C₈×C₈₃	C₂³	1	8	yes	—
96	C₄×C₈×C₈₃	C₂³	1	8	yes	complemented
97	C₂⁴×C₈₃	—	2	8	no	—
98	C₂⁴×C₈₃	—	2	4	no	—
99	C₂⁴×C₈₃	—	4	8	no	—
100	C₂⁴×C₈₃	—	4	8	no	—
101	C₂⁴×C₈₃	—	4	8	no	—
102	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₈₃	—	2	2	no	—
104	C₂×Q₈×C₈₃	—	2	4	no	—
105	C₂×Q₈×C₈₃	—	2	8	no	—
106	C₂×Q₈×C₈₃	—	4	4	no	—
107	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
108	C₂×D₄×C₈₃	—	2	8	no	—
109	C₂×D₄×C₈₃	—	2	4	no	—
110	C₂×D₄×C₈₃	—	2	8	no	—
111	C₂×D₄×C₈₃	—	2	8	no	—
112	C₂×D₄×C₈₃	—	2	8	no	—
113	C₂×D₄×C₈₃	—	2	8	no	—
114	C₂×D₄×C₈₃	—	2	16	no	—
115	C₂×D₄×C₈₃	—	4	16	no	—
116	C₂×D₄×C₈₃	—	4	8	no	—
117	C₂×D₄×C₈₃	—	4	8	no	—
118	C₂×D₄×C₈₃	—	4	16	no	—
119	C₂×D₄×C₈₃	—	4	32	no	—
120	C₂×D₄×C₈₃	—	4	8	no	—
121	C₂×D₄×C₈₃	—	4	8	no	—
122	C₂×D₄×C₈₃	—	4	32	no	—
123	C₂×D₄×C₈₃	—	4	8	no	—
124	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₈₃	—	2	4	no	—
126	C₂²×C₄×C₈₃	—	2	4	no	—
127	C₂²×C₄×C₈₃	—	2	2	no	—
128	C₂²×C₄×C₈₃	—	2	2	no	—
129	C₂²×C₄×C₈₃	SD₁₆	1	8	yes	complemented
130	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₈₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₃	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₈₃	—	4	32	no	—
141	C₂×C₈×C₈₃	—	2	8	no	—
142	C₂×C₈×C₈₃	C₂⁴	1	8	yes	—
143	C₄⋊C₄×C₈₃	—	2	4	no	—
144	C₄⋊C₄×C₈₃	—	2	4	no	—
145	C₄⋊C₄×C₈₃	—	2	4	no	—
146	C₄⋊C₄×C₈₃	—	2	8	no	—
147	C₄⋊C₄×C₈₃	—	2	8	no	—
148	C₄⋊C₄×C₈₃	—	2	2	no	—
149	C₄⋊C₄×C₈₃	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₈₃	—	2	8	no	—
151	C₄²×C₈₃	—	2	8	no	—
152	C₄²×C₈₃	C₂×D₄	1	4	yes	—
153	C₄²×C₈₃	C₂×D₄	1	2	yes	—
154	C₄²×C₈₃	C₂×D₄	1	4	yes	—
155	C₄²×C₈₃	C₂×D₄	1	2	yes	—
156	C₄²×C₈₃	C₂⁴	1	2	yes	—
157	C₄²×C₈₃	C₂⁴	1	2	yes	—
158	C₂³×C₈₃	—	2	2	no	—
159	C₂³×C₈₃	—	2	2	no	—
160	C₂³×C₈₃	—	2	8	no	—
161	C₂³×C₈₃	—	4	16	no	—
162	C₂³×C₈₃	—	4	16	no	—
163	C₂³×C₈₃	—	4	8	no	—
164	C₂³×C₈₃	—	4	16	no	—
165	C₂³×C₈₃	—	4	8	no	—
166	C₂³×C₈₃	—	4	8	no	—
167	C₂³×C₈₃	—	8	32	no	—
168	C₂³×C₈₃	C₂×SD₁₆	1	4	yes	—
169	C₂³×C₈₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₈₃	—	2	8	no	—
172	Q₈×C₈₃	—	4	4	no	—
173	Q₈×C₈₃	—	4	8	no	—
174	D₄×C₈₃	—	2	16	no	—
175	D₄×C₈₃	—	4	16	no	—
176	D₄×C₈₃	—	4	16	no	—
177	D₄×C₈₃	—	4	8	no	—
178	D₄×C₈₃	—	4	16	no	—
179	D₄×C₈₃	—	4	16	no	—
180	D₄×C₈₃	—	4	16	no	—
181	C₂×C₄×C₈₃	—	2	2	no	—
182	C₂×C₄×C₈₃	—	2	2	no	—
183	C₂×C₄×C₈₃	—	2	4	no	—
184	C₂×C₄×C₈₃	—	2	8	no	—
185	C₂×C₄×C₈₃	—	2	4	no	—
186	C₂×C₄×C₈₃	—	2	4	no	—
187	C₂×C₄×C₈₃	—	2	4	no	—
188	C₂×C₄×C₈₃	—	4	4	no	—
189	C₂×C₄×C₈₃	—	4	4	no	—
190	C₂×C₄×C₈₃	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₈₃	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₈₃	C₂×SD₁₆	1	16	yes	complemented
193	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	4	yes	—
194	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₈₃	H(5,𝔽₂)	1	4	yes	—
201	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
202	C₈×C₈₃	—	2	8	no	—
203	C₂²×C₈₃	—	2	2	no	—
204	C₂²×C₈₃	—	2	8	no	—
205	C₂²×C₈₃	—	2	2	no	—
206	C₂²×C₈₃	—	4	8	no	—
207	C₂²×C₈₃	—	4	8	no	—
208	C₂²×C₈₃	—	4	8	no	—
209	C₂²×C₈₃	—	8	32	no	—
210	C₂²×C₈₃	—	8	16	no	—
211	C₂²×C₈₃	#535	1	2	yes	—
212	C₂²×C₈₃	C₂²×SD₁₆	1	4	yes	—
213	C₂²×C₈₃	C₂²×SD₁₆	1	2	yes	—
214	C₂²×C₈₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
216	C₄×C₈₃	—	2	2	no	—
217	C₄×C₈₃	—	2	2	no	—
218	C₄×C₈₃	—	4	4	no	—
219	C₄×C₈₃	—	4	4	no	—
220	C₄×C₈₃	#535	1	2	yes	—
221	C₄×C₈₃	C₂²×SD₁₆	1	4	yes	—
222	C₄×C₈₃	C₂²×SD₁₆	1	4	yes	—
223	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
224	C₄×C₈₃	C₂×H(5,𝔽₂)	1	2	yes	—
225	C₂×#3208	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂×C₈₃	—	2	4	no	—
227	C₂×C₈₃	—	8	8	no	—
228	C₂×C₈₃	#3208	1	4	yes	direct product factor
229	C₂×C₈₃	C₂×#535	1	1	yes	characteristic
230	C₂×C₈₃	C₂³×SD₁₆	1	1	yes	characteristic
231	C₂×C₈₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂×#533	C₂×C₈₃	1	1	yes	characteristic, complemented
233	C₂²×#127	C₂×C₈₃	1	1	yes	characteristic
234	#3208	C₂×C₈₃	1	16	yes	direct product factor
235	C₂×#492	C₂×C₈₃	1	2	yes	complemented
236	C₂×#486	C₂×C₈₃	1	2	yes	complemented
237	C₂×#460	C₂×C₈₃	1	4	yes	complemented
238	C₂×#450	C₂×C₈₃	1	4	yes	complemented
239	C₂×#431	C₂×C₈₃	1	1	yes	characteristic, complemented
240	C₈₃	C₂×#3208	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³×D₄	—	2	1	no	—
242	C₂³×D₄	—	2	1	no	—
243	C₂³×D₄	C₂²×C₈₃	1	2	yes	—
244	C₂²×SD₁₆	C₂²×C₈₃	1	8	yes	complemented
245	#533	—	2	4	no	—
246	#533	C₂²×C₈₃	1	8	yes	complemented
247	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
248	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
249	C₂×#127	—	2	1	no	—
250	C₂×#127	—	2	1	no	—
251	C₂×#127	—	2	4	no	—
252	C₂×#127	C₂²×C₈₃	1	2	yes	—
253	C₂×#127	C₂²×C₈₃	1	8	yes	—
254	C₂×#127	C₂²×C₈₃	1	2	yes	—
255	C₂×#125	—	2	1	no	—
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	2	yes	—
258	C₂×C₄×Q₈	—	2	1	no	—
259	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	complemented
260	C₂×#117	—	2	1	no	—
261	C₂²×C₄²	C₂²×C₈₃	1	1	yes	characteristic
262	#492	C₂²×C₈₃	1	16	yes	complemented
263	#486	C₂²×C₈₃	1	16	yes	complemented
264	#460	C₂²×C₈₃	1	32	yes	complemented
265	#450	C₂²×C₈₃	1	32	yes	complemented
266	#431	C₂²×C₈₃	1	8	yes	complemented
267	C₂×C₄⋊C₈	C₂²×C₈₃	1	2	yes	complemented
268	C₂×#102	C₂²×C₈₃	1	8	yes	complemented
269	C₂×C₂²⋊C₈	C₂²×C₈₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₈₃	1	2	yes	complemented
271	C₂⁵	—	2	2	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	8	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	8	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	4	8	no	—
283	C₂²×D₄	—	4	8	no	—
284	C₂²×D₄	—	4	8	no	—
285	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
286	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
287	C₂³×C₄	D₄×C₈₃	1	1	yes	characteristic
288	C₂³×C₄	D₄×C₈₃	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
290	C₂×SD₁₆	—	4	16	no	—
291	C₂×SD₁₆	C₂³×C₈₃	1	32	yes	complemented
292	C₂²×C₈	C₂³×C₈₃	1	4	yes	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	complemented
296	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	complemented
297	#127	—	2	8	no	—
298	#127	—	2	4	no	—
299	#127	—	2	8	no	—
300	#127	—	2	4	no	—
301	#127	C₂³×C₈₃	1	8	yes	—
302	#127	C₂³×C₈₃	1	8	yes	—
303	#125	—	2	8	no	—
304	C₂²⋊Q₈	—	2	8	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	C₂³×C₈₃	1	8	yes	—
307	C₄×Q₈	—	2	8	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	C₂³×C₈₃	1	8	yes	complemented
310	#117	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₈₃	1	4	yes	—
322	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
325	C₄⋊C₈	C₂³×C₈₃	1	8	yes	complemented
326	#102	C₂³×C₈₃	1	32	yes	complemented
327	C₂²⋊C₈	C₂³×C₈₃	1	8	yes	—
328	C₄×C₈	C₂³×C₈₃	1	8	yes	complemented
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	4	8	no	—
332	C₂⁴	—	4	8	no	—
333	C₂⁴	—	4	8	no	—
334	C₂⁴	C₂×D₄×C₈₃	1	1	yes	characteristic
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	16	no	—
347	C₂×D₄	—	4	16	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	4	16	no	—
351	C₂×D₄	—	4	32	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	4	32	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	SD₁₆×C₈₃	1	8	yes	complemented
362	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₈₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₈₃	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₈₃	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
372	SD₁₆	—	4	32	no	—
373	C₂×C₈	—	2	8	no	—
374	C₂×C₈	C₂⁴×C₈₃	1	8	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	C₂⁴×C₈₃	1	4	yes	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	C₂×D₄×C₈₃	1	4	yes	—
385	C₄²	C₂×D₄×C₈₃	1	2	yes	—
386	C₄²	C₂×D₄×C₈₃	1	4	yes	—
387	C₄²	C₂×D₄×C₈₃	1	2	yes	—
388	C₄²	C₂⁴×C₈₃	1	2	yes	—
389	C₄²	C₂⁴×C₈₃	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	4	16	no	—
394	C₂³	—	4	16	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	16	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	8	32	no	—
400	C₂³	C₂×SD₁₆×C₈₃	1	4	yes	—
401	C₂³	C₂²×D₄×C₈₃	1	2	yes	—
402	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
403	Q₈	—	2	8	no	—
404	Q₈	—	4	4	no	—
405	Q₈	—	4	8	no	—
406	D₄	—	2	16	no	—
407	D₄	—	4	16	no	—
408	D₄	—	4	16	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	16	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	C₂×SD₁₆×C₈₃	1	4	yes	—
423	C₂×C₄	C₂×SD₁₆×C₈₃	1	4	yes	—
424	C₂×C₄	C₂×SD₁₆×C₈₃	1	16	yes	complemented
425	C₂×C₄	AGL(1,ℤ/8)×C₈₃	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
432	C₂×C₄	H(5,𝔽₂)×C₈₃	1	4	yes	—
433	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
434	C₈	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	32	no	—
442	C₂²	—	8	16	no	—
443	C₂²	#535×C₈₃	1	2	yes	—
444	C₂²	C₂²×SD₁₆×C₈₃	1	4	yes	—
445	C₂²	C₂²×SD₁₆×C₈₃	1	2	yes	—
446	C₂²	C₂×AGL(1,ℤ/8)×C₈₃	1	2	yes	—
447	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	#535×C₈₃	1	2	yes	—
453	C₄	C₂²×SD₁₆×C₈₃	1	4	yes	—
454	C₄	C₂²×SD₁₆×C₈₃	1	4	yes	—
455	C₄	C₂×AGL(1,ℤ/8)×C₈₃	1	4	yes	—
456	C₄	C₂×H(5,𝔽₂)×C₈₃	1	2	yes	—
457	C₂	—	2	4	no	—
458	C₂	—	8	8	no	—
459	C₂	C₈₃×#3208	1	4	yes	direct product factor
460	C₂	C₂×#535×C₈₃	1	1	yes	characteristic
461	C₂	C₂³×SD₁₆×C₈₃	1	1	yes	characteristic
462	C₂	C₂²×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₂²×#127×C₈₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂²×C₄²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₃	C₂	semidirect
3. C₈₃×#3208	C₂	direct (N × H)
4. C₂×#492×C₈₃	C₂	semidirect
5. C₂×#486×C₈₃	C₂	semidirect
6. C₂×#460×C₈₃	C₂	semidirect
7. C₂×#450×C₈₃	C₂	semidirect
8. C₂×#431×C₈₃	C₂	semidirect
12. C₂²×SD₁₆×C₈₃	C₂²	semidirect
14. #533×C₈₃	C₂²	semidirect
15. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
27. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
30. #492×C₈₃	C₂²	semidirect
31. #486×C₈₃	C₂²	semidirect
32. #460×C₈₃	C₂²	semidirect
33. #450×C₈₃	C₂²	semidirect
34. #431×C₈₃	C₂²	semidirect
35. C₂×C₄⋊C₈×C₈₃	C₂²	semidirect
36. C₂×#102×C₈₃	C₂²	semidirect
38. C₂×C₄×C₈×C₈₃	C₂²	semidirect
59. C₂×SD₁₆×C₈₃	C₂³	semidirect
63. C₄⋊Q₈×C₈₃	C₂³	semidirect
64. C₄⋊Q₈×C₈₃	C₂³	semidirect
77. C₄×Q₈×C₈₃	C₂³	semidirect
93. C₄⋊C₈×C₈₃	C₂³	semidirect
94. #102×C₈₃	C₂³	semidirect
96. C₄×C₈×C₈₃	C₂³	semidirect
129. C₂²×C₄×C₈₃	SD₁₆	semidirect
192. C₂×C₄×C₈₃	C₂×SD₁₆	semidirect
225. C₂×#3208	C₈₃	direct (N × H)
228. C₂×C₈₃	#3208	direct (N × H)
232. C₂×#533	C₂×C₈₃	semidirect
234. #3208	C₂×C₈₃	direct (N × H)
235. C₂×#492	C₂×C₈₃	semidirect
236. C₂×#486	C₂×C₈₃	semidirect
237. C₂×#460	C₂×C₈₃	semidirect
238. C₂×#450	C₂×C₈₃	semidirect
239. C₂×#431	C₂×C₈₃	semidirect
240. C₈₃	C₂×#3208	direct (N × H)
244. C₂²×SD₁₆	C₂²×C₈₃	semidirect
246. #533	C₂²×C₈₃	semidirect
247. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
248. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
259. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
262. #492	C₂²×C₈₃	semidirect
263. #486	C₂²×C₈₃	semidirect
264. #460	C₂²×C₈₃	semidirect
265. #450	C₂²×C₈₃	semidirect
266. #431	C₂²×C₈₃	semidirect
267. C₂×C₄⋊C₈	C₂²×C₈₃	semidirect
268. C₂×#102	C₂²×C₈₃	semidirect
270. C₂×C₄×C₈	C₂²×C₈₃	semidirect
291. C₂×SD₁₆	C₂³×C₈₃	semidirect
295. C₄⋊Q₈	C₂³×C₈₃	semidirect
296. C₄⋊Q₈	C₂³×C₈₃	semidirect
309. C₄×Q₈	C₂³×C₈₃	semidirect
325. C₄⋊C₈	C₂³×C₈₃	semidirect
326. #102	C₂³×C₈₃	semidirect
328. C₄×C₈	C₂³×C₈₃	semidirect
361. C₂²×C₄	SD₁₆×C₈₃	semidirect
424. C₂×C₄	C₂×SD₁₆×C₈₃	semidirect
459. C₂	C₈₃×#3208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₃	2
C₂²×#127×C₈₃	2
C₈₃×#3208	2
C₂×#492×C₈₃	2
C₂×#486×C₈₃	2
C₂×#460×C₈₃	2
C₂×#450×C₈₃	2
C₂×#431×C₈₃	2
C₂×#3208	83

Subgroups — C2×C83×#3208 #35288599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3208 #35288599