Subgroups — C₂×C₈₃×#3512 #35290633

Order 21248.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3512	C₂	1	32	yes	maximal, direct product factor
2	C₂×#553×C₈₃	C₂	1	4	yes	maximal, complemented
3	C₂×#553×C₈₃	C₂	1	8	yes	maximal, complemented
4	C₂×#552×C₈₃	C₂	1	4	yes	maximal, complemented
5	C₂×#541×C₈₃	C₂	1	2	yes	maximal, complemented
6	C₂×#540×C₈₃	C₂	1	2	yes	maximal, complemented
7	C₂×#537×C₈₃	C₂	1	2	yes	maximal, complemented
8	C₂×#532×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#529×C₈₃	C₂	1	4	yes	maximal, complemented
10	C₂²×#125×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#520×C₈₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×#41×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₈₃	C₂²	1	2	yes	—
15	#553×C₈₃	C₂²	1	64	yes	complemented
16	#553×C₈₃	C₂²	1	128	yes	complemented
17	#552×C₈₃	C₂²	1	64	yes	complemented
18	#541×C₈₃	C₂²	1	32	yes	complemented
19	#540×C₈₃	C₂²	1	32	yes	complemented
20	#537×C₈₃	C₂²	1	32	yes	complemented
21	#532×C₈₃	C₂²	1	16	yes	complemented
22	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
23	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
24	#529×C₈₃	C₂²	1	64	yes	complemented
25	C₂×#126×C₈₃	C₂²	1	8	yes	—
26	C₂×#126×C₈₃	C₂²	1	8	yes	—
27	C₂×#125×C₈₃	C₂²	1	2	yes	—
28	C₂×#125×C₈₃	C₂²	1	2	yes	—
29	C₂×#125×C₈₃	C₂²	1	4	yes	—
30	C₂×#125×C₈₃	C₂²	1	8	yes	—
31	C₂×#125×C₈₃	C₂²	1	16	yes	complemented
32	C₂×#124×C₈₃	C₂²	1	2	yes	—
33	C₂×#123×C₈₃	C₂²	1	8	yes	—
34	C₂×#123×C₈₃	C₂²	1	8	yes	—
35	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	4	yes	—
36	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	4	yes	—
37	C₂×#121×C₈₃	C₂²	1	4	yes	—
38	C₂×#121×C₈₃	C₂²	1	4	yes	—
39	C₂×#121×C₈₃	C₂²	1	8	yes	—
40	C₂×#121×C₈₃	C₂²	1	4	yes	—
41	C₂×#121×C₈₃	C₂²	1	8	yes	—
42	#520×C₈₃	C₂²	1	32	yes	complemented
43	C₄×#41×C₈₃	C₂²	1	16	yes	complemented
44	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₈₃	C₂²	1	4	yes	—
46	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
47	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₈₃	C₂²	1	8	yes	—
50	C₂×C₄×D₄×C₈₃	C₂²	1	8	yes	—
51	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
52	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
53	C₂×#117×C₈₃	C₂²	1	2	yes	—
54	C₂×#117×C₈₃	C₂²	1	4	yes	—
55	C₂×#117×C₈₃	C₂²	1	8	yes	—
56	C₂²×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
57	C₂²×C₄⋊C₄×C₈₃	C₂²	1	4	yes	—
58	C₂²×C₄⋊C₄×C₈₃	C₂²	1	4	yes	—
59	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₈₃	C₂²	1	2	yes	—
61	C₂×#41×C₈₃	—	2	8	no	—
62	C₂×#41×C₈₃	—	2	16	no	—
63	C₂×#41×C₈₃	C₂³	1	8	yes	—
64	C₂×#41×C₈₃	C₂³	1	16	yes	—
65	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
72	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
73	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₈₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₈₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₈₃	C₂³	1	8	yes	—
79	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₈₃	C₂³	1	8	yes	—
81	#127×C₈₃	C₂³	1	8	yes	—
82	#126×C₈₃	C₂³	1	64	yes	—
83	#126×C₈₃	C₂³	1	64	yes	—
84	#125×C₈₃	C₂³	1	16	yes	—
85	#125×C₈₃	C₂³	1	16	yes	—
86	#125×C₈₃	C₂³	1	32	yes	—
87	#125×C₈₃	C₂³	1	64	yes	—
88	#124×C₈₃	C₂³	1	16	yes	—
89	#123×C₈₃	C₂³	1	64	yes	—
90	#123×C₈₃	C₂³	1	64	yes	—
91	C₂²⋊Q₈×C₈₃	C₂³	1	32	yes	—
92	C₂²⋊Q₈×C₈₃	C₂³	1	32	yes	—
93	#121×C₈₃	C₂³	1	32	yes	—
94	#121×C₈₃	C₂³	1	32	yes	—
95	#121×C₈₃	C₂³	1	64	yes	—
96	#121×C₈₃	C₂³	1	32	yes	—
97	#121×C₈₃	C₂³	1	64	yes	—
98	C₄×Q₈×C₈₃	C₂³	1	16	yes	—
99	C₄×Q₈×C₈₃	C₂³	1	32	yes	—
100	C₄×D₄×C₈₃	C₂³	1	32	yes	—
101	C₄×D₄×C₈₃	C₂³	1	16	yes	—
102	C₄×D₄×C₈₃	C₂³	1	32	yes	—
103	C₄×D₄×C₈₃	C₂³	1	64	yes	—
104	C₄×D₄×C₈₃	C₂³	1	64	yes	—
105	C₄×D₄×C₈₃	C₂³	1	32	yes	—
106	#117×C₈₃	C₂³	1	8	yes	—
107	#117×C₈₃	C₂³	1	16	yes	—
108	#117×C₈₃	C₂³	1	32	yes	—
109	#117×C₈₃	C₂³	1	64	yes	—
110	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
113	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
115	C₂×C₄⋊C₄×C₈₃	C₂³	1	16	yes	—
116	C₂×C₄⋊C₄×C₈₃	C₂³	1	32	yes	—
117	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
118	C₂×C₄⋊C₄×C₈₃	C₂³	1	32	yes	—
119	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
121	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
129	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
135	C₂×C₄²×C₈₃	C₂³	1	16	yes	—
136	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
137	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
138	C₂⁴×C₈₃	C₂⁴	1	2	yes	—
139	C₂⁴×C₈₃	C₂⁴	1	1	yes	characteristic
140	#41×C₈₃	—	2	32	no	—
141	#41×C₈₃	—	2	64	no	—
142	C₂×Q₈×C₈₃	—	2	4	no	—
143	C₂×Q₈×C₈₃	—	2	8	no	—
144	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
145	C₂×Q₈×C₈₃	C₂⁴	1	8	yes	—
146	C₂×D₄×C₈₃	—	2	8	no	—
147	C₂×D₄×C₈₃	—	2	16	no	—
148	C₂×D₄×C₈₃	—	2	4	no	—
149	C₂×D₄×C₈₃	—	2	8	no	—
150	C₂×D₄×C₈₃	—	4	16	no	—
151	C₂×D₄×C₈₃	—	4	8	no	—
152	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
153	C₂×D₄×C₈₃	C₂⁴	1	16	yes	—
154	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
155	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
156	C₂×D₄×C₈₃	C₂⁴	1	32	yes	—
157	C₂×D₄×C₈₃	C₂⁴	1	16	yes	—
158	C₂²×C₄×C₈₃	—	2	16	no	—
159	C₂²×C₄×C₈₃	—	2	8	no	—
160	C₂²×C₄×C₈₃	—	4	8	no	—
161	C₂²×C₄×C₈₃	—	4	16	no	—
162	C₂²×C₄×C₈₃	—	4	4	no	—
163	C₂²×C₄×C₈₃	—	4	8	no	—
164	C₂²×C₄×C₈₃	#41	1	8	yes	—
165	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
166	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
173	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
176	C₂²×C₄×C₈₃	C₂⁴	1	32	yes	—
177	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
180	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
182	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
183	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
184	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
185	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
186	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
187	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
188	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
189	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
190	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
191	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
192	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
193	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
194	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
195	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
196	C₄²×C₈₃	C₂⁴	1	4	yes	—
197	C₄²×C₈₃	C₂⁴	1	8	yes	—
198	C₄²×C₈₃	C₂⁴	1	16	yes	—
199	C₄²×C₈₃	C₂⁴	1	4	yes	—
200	C₄²×C₈₃	C₂⁴	1	8	yes	—
201	C₄²×C₈₃	C₂⁴	1	32	yes	—
202	C₂³×C₈₃	—	2	4	no	—
203	C₂³×C₈₃	—	2	8	no	—
204	C₂³×C₈₃	—	2	4	no	—
205	C₂³×C₈₃	—	2	8	no	—
206	C₂³×C₈₃	—	2	8	no	—
207	C₂³×C₈₃	—	2	8	no	—
208	C₂³×C₈₃	C₂×#41	1	4	yes	—
209	C₂³×C₈₃	C₂⁵	1	8	yes	—
210	C₂³×C₈₃	C₂⁵	1	4	yes	—
211	C₂³×C₈₃	C₂⁵	1	2	yes	—
212	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
213	Q₈×C₈₃	—	2	8	no	—
214	Q₈×C₈₃	—	2	16	no	—
215	D₄×C₈₃	—	2	16	no	—
216	D₄×C₈₃	—	2	32	no	—
217	D₄×C₈₃	—	2	8	no	—
218	D₄×C₈₃	—	2	16	no	—
219	D₄×C₈₃	—	4	32	no	—
220	D₄×C₈₃	—	4	16	no	—
221	C₂×C₄×C₈₃	—	2	8	no	—
222	C₂×C₄×C₈₃	—	2	4	no	—
223	C₂×C₄×C₈₃	—	2	4	no	—
224	C₂×C₄×C₈₃	—	2	8	no	—
225	C₂×C₄×C₈₃	—	2	16	no	—
226	C₂×C₄×C₈₃	—	2	4	no	—
227	C₂×C₄×C₈₃	—	2	32	no	—
228	C₂×C₄×C₈₃	—	2	16	no	—
229	C₂×C₄×C₈₃	—	4	16	no	—
230	C₂×C₄×C₈₃	—	4	32	no	—
231	C₂×C₄×C₈₃	—	4	8	no	—
232	C₂×C₄×C₈₃	—	4	16	no	—
233	C₂×C₄×C₈₃	C₂×#41	1	4	yes	—
234	C₂×C₄×C₈₃	C₂×#41	1	4	yes	—
235	C₂×C₄×C₈₃	C₂×#41	1	16	yes	—
236	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
237	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
238	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
239	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
240	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
241	C₂×C₄×C₈₃	C₂⁵	1	16	yes	—
242	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
243	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
244	C₂²×C₈₃	—	2	4	no	—
245	C₂²×C₈₃	—	2	8	no	—
246	C₂²×C₈₃	—	2	8	no	—
247	C₂²×C₈₃	—	2	4	no	—
248	C₂²×C₈₃	—	2	8	no	—
249	C₂²×C₈₃	—	2	8	no	—
250	C₂²×C₈₃	—	2	8	no	—
251	C₂²×C₈₃	—	4	16	no	—
252	C₂²×C₈₃	—	4	8	no	—
253	C₂²×C₈₃	C₂²×#41	1	4	yes	—
254	C₂²×C₈₃	C₂²×#41	1	2	yes	—
255	C₂²×C₈₃	#585	1	4	yes	—
256	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
257	C₄×C₈₃	—	2	8	no	—
258	C₄×C₈₃	—	2	4	no	—
259	C₄×C₈₃	—	2	4	no	—
260	C₄×C₈₃	—	2	8	no	—
261	C₄×C₈₃	—	2	16	no	—
262	C₄×C₈₃	—	2	4	no	—
263	C₄×C₈₃	C₂²×#41	1	4	yes	—
264	C₄×C₈₃	C₂²×#41	1	4	yes	—
265	C₂×#3512	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂×C₈₃	—	2	4	no	—
267	C₂×C₈₃	—	4	8	no	—
268	C₂×C₈₃	—	4	4	no	—
269	C₂×C₈₃	#3512	1	4	yes	direct product factor
270	C₂×C₈₃	C₂³×#41	1	1	yes	characteristic
271	C₂×C₈₃	C₂×#585	1	2	yes	—
272	#3512	C₂×C₈₃	1	32	yes	direct product factor
273	C₂×#553	C₂×C₈₃	1	4	yes	complemented
274	C₂×#553	C₂×C₈₃	1	8	yes	complemented
275	C₂×#552	C₂×C₈₃	1	4	yes	complemented
276	C₂×#541	C₂×C₈₃	1	2	yes	complemented
277	C₂×#540	C₂×C₈₃	1	2	yes	complemented
278	C₂×#537	C₂×C₈₃	1	2	yes	complemented
279	C₂×#532	C₂×C₈₃	1	1	yes	characteristic, complemented
280	C₂×#529	C₂×C₈₃	1	4	yes	complemented
281	C₂²×#125	C₂×C₈₃	1	1	yes	characteristic, complemented
282	C₂×#520	C₂×C₈₃	1	2	yes	complemented
283	C₂×C₄×#41	C₂×C₈₃	1	1	yes	characteristic, complemented
284	C₈₃	C₂×#3512	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
286	C₂²×#41	C₂²×C₈₃	1	2	yes	—
287	#553	C₂²×C₈₃	1	64	yes	complemented
288	#553	C₂²×C₈₃	1	128	yes	complemented
289	#552	C₂²×C₈₃	1	64	yes	complemented
290	#541	C₂²×C₈₃	1	32	yes	complemented
291	#540	C₂²×C₈₃	1	32	yes	complemented
292	#537	C₂²×C₈₃	1	32	yes	complemented
293	#532	C₂²×C₈₃	1	16	yes	complemented
294	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
295	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
296	#529	C₂²×C₈₃	1	64	yes	complemented
297	C₂×#126	C₂²×C₈₃	1	8	yes	—
298	C₂×#126	C₂²×C₈₃	1	8	yes	—
299	C₂×#125	C₂²×C₈₃	1	2	yes	—
300	C₂×#125	C₂²×C₈₃	1	2	yes	—
301	C₂×#125	C₂²×C₈₃	1	4	yes	—
302	C₂×#125	C₂²×C₈₃	1	8	yes	—
303	C₂×#125	C₂²×C₈₃	1	16	yes	complemented
304	C₂×#124	C₂²×C₈₃	1	2	yes	—
305	C₂×#123	C₂²×C₈₃	1	8	yes	—
306	C₂×#123	C₂²×C₈₃	1	8	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	4	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	4	yes	—
309	C₂×#121	C₂²×C₈₃	1	4	yes	—
310	C₂×#121	C₂²×C₈₃	1	4	yes	—
311	C₂×#121	C₂²×C₈₃	1	8	yes	—
312	C₂×#121	C₂²×C₈₃	1	4	yes	—
313	C₂×#121	C₂²×C₈₃	1	8	yes	—
314	#520	C₂²×C₈₃	1	32	yes	complemented
315	C₄×#41	C₂²×C₈₃	1	16	yes	complemented
316	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	—
317	C₂×C₄×Q₈	C₂²×C₈₃	1	4	yes	—
318	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
319	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
320	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
321	C₂×C₄×D₄	C₂²×C₈₃	1	8	yes	—
322	C₂×C₄×D₄	C₂²×C₈₃	1	8	yes	—
323	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
324	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
325	C₂×#117	C₂²×C₈₃	1	2	yes	—
326	C₂×#117	C₂²×C₈₃	1	4	yes	—
327	C₂×#117	C₂²×C₈₃	1	8	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₈₃	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₈₃	1	4	yes	—
330	C₂²×C₄⋊C₄	C₂²×C₈₃	1	4	yes	—
331	C₂²×C₄²	C₂²×C₈₃	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×C₈₃	1	2	yes	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	—	2	16	no	—
335	C₂×#41	C₂³×C₈₃	1	8	yes	—
336	C₂×#41	C₂³×C₈₃	1	16	yes	—
337	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
339	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
341	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
343	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
344	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
345	C₂³×C₄	C₂³×C₈₃	1	4	yes	—
346	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₈₃	1	4	yes	—
348	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
349	C₂³×C₄	C₂³×C₈₃	1	8	yes	—
350	C₂³×C₄	C₂³×C₈₃	1	4	yes	—
351	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₈₃	1	8	yes	—
353	#127	C₂³×C₈₃	1	8	yes	—
354	#126	C₂³×C₈₃	1	64	yes	—
355	#126	C₂³×C₈₃	1	64	yes	—
356	#125	C₂³×C₈₃	1	16	yes	—
357	#125	C₂³×C₈₃	1	16	yes	—
358	#125	C₂³×C₈₃	1	32	yes	—
359	#125	C₂³×C₈₃	1	64	yes	—
360	#124	C₂³×C₈₃	1	16	yes	—
361	#123	C₂³×C₈₃	1	64	yes	—
362	#123	C₂³×C₈₃	1	64	yes	—
363	C₂²⋊Q₈	C₂³×C₈₃	1	32	yes	—
364	C₂²⋊Q₈	C₂³×C₈₃	1	32	yes	—
365	#121	C₂³×C₈₃	1	32	yes	—
366	#121	C₂³×C₈₃	1	32	yes	—
367	#121	C₂³×C₈₃	1	64	yes	—
368	#121	C₂³×C₈₃	1	32	yes	—
369	#121	C₂³×C₈₃	1	64	yes	—
370	C₄×Q₈	C₂³×C₈₃	1	16	yes	—
371	C₄×Q₈	C₂³×C₈₃	1	32	yes	—
372	C₄×D₄	C₂³×C₈₃	1	32	yes	—
373	C₄×D₄	C₂³×C₈₃	1	16	yes	—
374	C₄×D₄	C₂³×C₈₃	1	32	yes	—
375	C₄×D₄	C₂³×C₈₃	1	64	yes	—
376	C₄×D₄	C₂³×C₈₃	1	64	yes	—
377	C₄×D₄	C₂³×C₈₃	1	32	yes	—
378	#117	C₂³×C₈₃	1	8	yes	—
379	#117	C₂³×C₈₃	1	16	yes	—
380	#117	C₂³×C₈₃	1	32	yes	—
381	#117	C₂³×C₈₃	1	64	yes	—
382	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
385	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
387	C₂×C₄⋊C₄	C₂³×C₈₃	1	16	yes	—
388	C₂×C₄⋊C₄	C₂³×C₈₃	1	32	yes	—
389	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
390	C₂×C₄⋊C₄	C₂³×C₈₃	1	32	yes	—
391	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
393	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₈₃	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
401	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
403	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
404	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
407	C₂×C₄²	C₂³×C₈₃	1	16	yes	—
408	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
409	C₂⁴	C₂⁴×C₈₃	1	4	yes	—
410	C₂⁴	C₂⁴×C₈₃	1	2	yes	—
411	C₂⁴	C₂⁴×C₈₃	1	1	yes	characteristic
412	#41	—	2	32	no	—
413	#41	—	2	64	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
417	C₂×Q₈	C₂⁴×C₈₃	1	8	yes	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	16	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	4	16	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
425	C₂×D₄	C₂⁴×C₈₃	1	16	yes	—
426	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
427	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
428	C₂×D₄	C₂⁴×C₈₃	1	32	yes	—
429	C₂×D₄	C₂⁴×C₈₃	1	16	yes	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	4	8	no	—
433	C₂²×C₄	—	4	16	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	#41×C₈₃	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
443	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
444	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
445	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
446	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
447	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
448	C₂²×C₄	C₂⁴×C₈₃	1	32	yes	—
449	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
452	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
453	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
454	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
455	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
456	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
457	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
458	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
459	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
460	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
461	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
462	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
463	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
464	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
465	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
466	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
467	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
468	C₄²	C₂⁴×C₈₃	1	4	yes	—
469	C₄²	C₂⁴×C₈₃	1	8	yes	—
470	C₄²	C₂⁴×C₈₃	1	16	yes	—
471	C₄²	C₂⁴×C₈₃	1	4	yes	—
472	C₄²	C₂⁴×C₈₃	1	8	yes	—
473	C₄²	C₂⁴×C₈₃	1	32	yes	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	8	no	—
480	C₂³	C₂×#41×C₈₃	1	4	yes	—
481	C₂³	C₂⁵×C₈₃	1	8	yes	—
482	C₂³	C₂⁵×C₈₃	1	4	yes	—
483	C₂³	C₂⁵×C₈₃	1	2	yes	—
484	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
485	Q₈	—	2	8	no	—
486	Q₈	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	32	no	—
489	D₄	—	2	8	no	—
490	D₄	—	2	16	no	—
491	D₄	—	4	32	no	—
492	D₄	—	4	16	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	16	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	32	no	—
500	C₂×C₄	—	2	16	no	—
501	C₂×C₄	—	4	16	no	—
502	C₂×C₄	—	4	32	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	16	no	—
505	C₂×C₄	C₂×#41×C₈₃	1	4	yes	—
506	C₂×C₄	C₂×#41×C₈₃	1	4	yes	—
507	C₂×C₄	C₂×#41×C₈₃	1	16	yes	—
508	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
509	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
510	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
511	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
512	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
513	C₂×C₄	C₂⁵×C₈₃	1	16	yes	—
514	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
515	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂²×#41×C₈₃	1	4	yes	—
526	C₂²	C₂²×#41×C₈₃	1	2	yes	—
527	C₂²	#585×C₈₃	1	4	yes	—
528	C₂²	C₂⁶×C₈₃	1	1	yes	characteristic
529	C₄	—	2	8	no	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	2	16	no	—
534	C₄	—	2	4	no	—
535	C₄	C₂²×#41×C₈₃	1	4	yes	—
536	C₄	C₂²×#41×C₈₃	1	4	yes	—
537	C₂	—	2	4	no	—
538	C₂	—	4	8	no	—
539	C₂	—	4	4	no	—
540	C₂	C₈₃×#3512	1	4	yes	direct product factor
541	C₂	C₂³×#41×C₈₃	1	1	yes	characteristic
542	C₂	C₂×#585×C₈₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3512	C₂	direct (N × H)
2. C₂×#553×C₈₃	C₂	semidirect
3. C₂×#553×C₈₃	C₂	semidirect
4. C₂×#552×C₈₃	C₂	semidirect
5. C₂×#541×C₈₃	C₂	semidirect
6. C₂×#540×C₈₃	C₂	semidirect
7. C₂×#537×C₈₃	C₂	semidirect
8. C₂×#532×C₈₃	C₂	semidirect
9. C₂×#529×C₈₃	C₂	semidirect
10. C₂²×#125×C₈₃	C₂	semidirect
11. C₂×#520×C₈₃	C₂	semidirect
12. C₂×C₄×#41×C₈₃	C₂	semidirect
15. #553×C₈₃	C₂²	semidirect
16. #553×C₈₃	C₂²	semidirect
17. #552×C₈₃	C₂²	semidirect
18. #541×C₈₃	C₂²	semidirect
19. #540×C₈₃	C₂²	semidirect
20. #537×C₈₃	C₂²	semidirect
21. #532×C₈₃	C₂²	semidirect
24. #529×C₈₃	C₂²	semidirect
31. C₂×#125×C₈₃	C₂²	semidirect
42. #520×C₈₃	C₂²	semidirect
43. C₄×#41×C₈₃	C₂²	semidirect
265. C₂×#3512	C₈₃	direct (N × H)
269. C₂×C₈₃	#3512	direct (N × H)
272. #3512	C₂×C₈₃	direct (N × H)
273. C₂×#553	C₂×C₈₃	semidirect
274. C₂×#553	C₂×C₈₃	semidirect
275. C₂×#552	C₂×C₈₃	semidirect
276. C₂×#541	C₂×C₈₃	semidirect
277. C₂×#540	C₂×C₈₃	semidirect
278. C₂×#537	C₂×C₈₃	semidirect
279. C₂×#532	C₂×C₈₃	semidirect
280. C₂×#529	C₂×C₈₃	semidirect
281. C₂²×#125	C₂×C₈₃	semidirect
282. C₂×#520	C₂×C₈₃	semidirect
283. C₂×C₄×#41	C₂×C₈₃	semidirect
284. C₈₃	C₂×#3512	direct (N × H)
287. #553	C₂²×C₈₃	semidirect
288. #553	C₂²×C₈₃	semidirect
289. #552	C₂²×C₈₃	semidirect
290. #541	C₂²×C₈₃	semidirect
291. #540	C₂²×C₈₃	semidirect
292. #537	C₂²×C₈₃	semidirect
293. #532	C₂²×C₈₃	semidirect
296. #529	C₂²×C₈₃	semidirect
303. C₂×#125	C₂²×C₈₃	semidirect
314. #520	C₂²×C₈₃	semidirect
315. C₄×#41	C₂²×C₈₃	semidirect
540. C₂	C₈₃×#3512	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₃×#3512	2
C₂×#553×C₈₃	2
C₂×#552×C₈₃	2
C₂×#541×C₈₃	2
C₂×#540×C₈₃	2
C₂×#537×C₈₃	2
C₂×#532×C₈₃	2
C₂×#529×C₈₃	2
C₂²×#125×C₈₃	2
C₂×#520×C₈₃	2
C₂×C₄×#41×C₈₃	2
C₂×#3512	83

Subgroups — C2×C83×#3512 #35290633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3512 #35290633