Subgroups — C₂×C₈₃×#3510 #35290632

Order 21248.

7302 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3510	C₂	1	32	yes	maximal, direct product factor
2	C₂×#559×C₈₃	C₂	1	4	yes	maximal, complemented
3	C₂×#556×C₈₃	C₂	1	4	yes	maximal, complemented
4	C₂×#551×C₈₃	C₂	1	8	yes	maximal, complemented
5	C₂×#542×C₈₃	C₂	1	4	yes	maximal, complemented
6	C₂×#536×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#535×C₈₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#533×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#529×C₈₃	C₂	1	4	yes	maximal, complemented
10	C₂²×#124×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#519×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#518×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×#41×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₈₃	C₂²	1	1	yes	characteristic
17	#559×C₈₃	C₂²	1	64	yes	complemented
18	#556×C₈₃	C₂²	1	64	yes	complemented
19	#551×C₈₃	C₂²	1	128	yes	complemented
20	#542×C₈₃	C₂²	1	64	yes	complemented
21	#536×C₈₃	C₂²	1	16	yes	complemented
22	#535×C₈₃	C₂²	1	16	yes	—
23	#533×C₈₃	C₂²	1	16	yes	complemented
24	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
25	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	complemented
26	C₂×#127×C₈₃	C₂²	1	2	yes	—
27	#529×C₈₃	C₂²	1	64	yes	complemented
28	C₂×#126×C₈₃	C₂²	1	8	yes	complemented
29	C₂×#126×C₈₃	C₂²	1	8	yes	complemented
30	C₂×#125×C₈₃	C₂²	1	2	yes	complemented
31	C₂×#124×C₈₃	C₂²	1	2	yes	—
32	C₂×#124×C₈₃	C₂²	1	2	yes	—
33	C₂×#124×C₈₃	C₂²	1	4	yes	—
34	C₂×#124×C₈₃	C₂²	1	2	yes	—
35	C₂×#124×C₈₃	C₂²	1	16	yes	complemented
36	C₂×#124×C₈₃	C₂²	1	2	yes	complemented
37	C₂×#124×C₈₃	C₂²	1	8	yes	complemented
38	C₂×#123×C₈₃	C₂²	1	4	yes	—
39	C₂×#123×C₈₃	C₂²	1	8	yes	complemented
40	C₂×#123×C₈₃	C₂²	1	8	yes	complemented
41	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	4	yes	—
42	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	4	yes	complemented
43	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	8	yes	complemented
44	C₂×#121×C₈₃	C₂²	1	4	yes	—
45	C₂×#120×C₈₃	C₂²	1	4	yes	—
46	#519×C₈₃	C₂²	1	16	yes	complemented
47	#518×C₈₃	C₂²	1	16	yes	complemented
48	C₄×#41×C₈₃	C₂²	1	16	yes	complemented
49	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
51	C₂×C₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
52	C₂×C₄×Q₈×C₈₃	C₂²	1	4	yes	complemented
53	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
54	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
55	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
56	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₈₃	C₂²	1	8	yes	complemented
58	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
59	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
60	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
61	C₂×#117×C₈₃	C₂²	1	4	yes	—
62	C₂×#117×C₈₃	C₂²	1	2	yes	complemented
63	C₂×#117×C₈₃	C₂²	1	8	yes	complemented
64	C₂²×C₂²⋊C₄×C₈₃	C₂²	1	4	yes	—
65	C₂²×C₂²⋊C₄×C₈₃	C₂²	1	4	yes	—
66	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₈₃	C₂²	1	2	yes	complemented
68	C₂⁵×C₈₃	C₂³	1	2	yes	—
69	C₂×#41×C₈₃	—	2	8	no	—
70	C₂×#41×C₈₃	C₂³	1	8	yes	—
71	C₂²×Q₈×C₈₃	—	2	8	no	—
72	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
73	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₈₃	C₂³	1	8	yes	—
76	C₂²×Q₈×C₈₃	C₂³	1	4	yes	—
77	C₂²×D₄×C₈₃	—	2	8	no	—
78	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
83	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
84	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₈₃	C₂³	1	4	yes	—
88	C₂³×C₄×C₈₃	C₂³	1	8	yes	—
89	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₃	C₂³	1	16	yes	complemented
91	C₄⋊Q₈×C₈₃	C₂³	1	16	yes	complemented
92	#127×C₈₃	C₂³	1	16	yes	—
93	#126×C₈₃	C₂³	1	64	yes	complemented
94	#126×C₈₃	C₂³	1	64	yes	complemented
95	#125×C₈₃	C₂³	1	16	yes	complemented
96	#124×C₈₃	C₂³	1	16	yes	—
97	#124×C₈₃	C₂³	1	16	yes	—
98	#124×C₈₃	C₂³	1	32	yes	—
99	#124×C₈₃	C₂³	1	16	yes	—
100	#124×C₈₃	C₂³	1	16	yes	complemented
101	#124×C₈₃	C₂³	1	64	yes	complemented
102	#123×C₈₃	C₂³	1	32	yes	—
103	#123×C₈₃	C₂³	1	64	yes	complemented
104	#123×C₈₃	C₂³	1	64	yes	complemented
105	C₂²⋊Q₈×C₈₃	C₂³	1	32	yes	—
106	C₂²⋊Q₈×C₈₃	C₂³	1	32	yes	complemented
107	C₂²⋊Q₈×C₈₃	C₂³	1	64	yes	complemented
108	#121×C₈₃	C₂³	1	32	yes	—
109	#120×C₈₃	C₂³	1	32	yes	—
110	C₄×Q₈×C₈₃	C₂³	1	16	yes	complemented
111	C₄×Q₈×C₈₃	C₂³	1	32	yes	complemented
112	C₄×Q₈×C₈₃	C₂³	1	32	yes	complemented
113	C₄×Q₈×C₈₃	C₂³	1	32	yes	complemented
114	C₄×D₄×C₈₃	C₂³	1	32	yes	—
115	C₄×D₄×C₈₃	C₂³	1	32	yes	—
116	C₄×D₄×C₈₃	C₂³	1	32	yes	—
117	C₄×D₄×C₈₃	C₂³	1	16	yes	complemented
118	C₄×D₄×C₈₃	C₂³	1	64	yes	complemented
119	#117×C₈₃	C₂³	1	8	yes	—
120	#117×C₈₃	C₂³	1	8	yes	—
121	#117×C₈₃	C₂³	1	8	yes	—
122	#117×C₈₃	C₂³	1	32	yes	—
123	#117×C₈₃	C₂³	1	16	yes	complemented
124	#117×C₈₃	C₂³	1	64	yes	complemented
125	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
129	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
132	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
137	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₈₃	C₂³	1	32	yes	—
139	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
140	C₂×C₂²⋊C₄×C₈₃	C₂³	1	32	yes	—
141	C₂×C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
144	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
145	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
149	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
152	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₈₃	C₂³	1	16	yes	complemented
155	C₂⁴×C₈₃	—	2	8	no	—
156	C₂⁴×C₈₃	—	4	8	no	—
157	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
158	C₂⁴×C₈₃	C₂⁴	1	2	yes	—
159	C₂⁴×C₈₃	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₈₃	C₂⁴	1	8	yes	—
161	#41×C₈₃	—	2	32	no	—
162	C₂×Q₈×C₈₃	—	2	8	no	—
163	C₂×Q₈×C₈₃	—	2	8	no	—
164	C₂×Q₈×C₈₃	—	2	32	no	—
165	C₂×Q₈×C₈₃	—	2	4	no	—
166	C₂×Q₈×C₈₃	—	4	8	no	—
167	C₂×Q₈×C₈₃	C₂⁴	1	8	yes	—
168	C₂×Q₈×C₈₃	C₂⁴	1	8	yes	—
169	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
170	C₂×Q₈×C₈₃	C₂⁴	1	16	yes	—
171	C₂×D₄×C₈₃	—	2	8	no	—
172	C₂×D₄×C₈₃	—	2	8	no	—
173	C₂×D₄×C₈₃	—	2	8	no	—
174	C₂×D₄×C₈₃	—	2	32	no	—
175	C₂×D₄×C₈₃	—	2	4	no	—
176	C₂×D₄×C₈₃	—	4	16	no	—
177	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
178	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
179	C₂×D₄×C₈₃	C₂⁴	1	8	yes	—
180	C₂×D₄×C₈₃	C₂⁴	1	4	yes	—
181	C₂×D₄×C₈₃	C₂⁴	1	32	yes	—
182	C₂²×C₄×C₈₃	—	2	8	no	—
183	C₂²×C₄×C₈₃	—	2	8	no	—
184	C₂²×C₄×C₈₃	—	4	8	no	—
185	C₂²×C₄×C₈₃	—	4	16	no	—
186	C₂²×C₄×C₈₃	—	4	4	no	—
187	C₂²×C₄×C₈₃	#41	1	8	yes	—
188	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
189	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
190	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
198	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
199	C₂²×C₄×C₈₃	C₂⁴	1	32	yes	—
200	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
203	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
205	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
206	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
207	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
208	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
209	C₄⋊C₄×C₈₃	C₂⁴	1	32	yes	—
210	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
211	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
212	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
213	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
214	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
215	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
216	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
217	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
218	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
219	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
220	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
221	C₄²×C₈₃	C₂⁴	1	4	yes	—
222	C₄²×C₈₃	C₂⁴	1	4	yes	—
223	C₄²×C₈₃	C₂⁴	1	8	yes	—
224	C₄²×C₈₃	C₂⁴	1	8	yes	—
225	C₄²×C₈₃	C₂⁴	1	16	yes	—
226	C₄²×C₈₃	C₂⁴	1	32	yes	—
227	C₄²×C₈₃	C₂⁴	1	8	yes	—
228	C₄²×C₈₃	C₂⁴	1	8	yes	—
229	C₂³×C₈₃	—	2	4	no	—
230	C₂³×C₈₃	—	2	4	no	—
231	C₂³×C₈₃	—	2	8	no	—
232	C₂³×C₈₃	—	2	8	no	—
233	C₂³×C₈₃	—	2	16	no	—
234	C₂³×C₈₃	—	2	16	no	—
235	C₂³×C₈₃	—	4	16	no	—
236	C₂³×C₈₃	—	8	16	no	—
237	C₂³×C₈₃	C₂×#41	1	4	yes	—
238	C₂³×C₈₃	C₂⁵	1	8	yes	—
239	C₂³×C₈₃	C₂⁵	1	4	yes	—
240	C₂³×C₈₃	C₂⁵	1	2	yes	—
241	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
242	Q₈×C₈₃	—	2	16	no	—
243	Q₈×C₈₃	—	2	16	no	—
244	Q₈×C₈₃	—	2	8	no	—
245	Q₈×C₈₃	—	4	16	no	—
246	D₄×C₈₃	—	2	16	no	—
247	D₄×C₈₃	—	2	16	no	—
248	D₄×C₈₃	—	2	16	no	—
249	D₄×C₈₃	—	2	8	no	—
250	D₄×C₈₃	—	4	32	no	—
251	C₂×C₄×C₈₃	—	2	4	no	—
252	C₂×C₄×C₈₃	—	2	16	no	—
253	C₂×C₄×C₈₃	—	2	8	no	—
254	C₂×C₄×C₈₃	—	2	4	no	—
255	C₂×C₄×C₈₃	—	2	8	no	—
256	C₂×C₄×C₈₃	—	2	8	no	—
257	C₂×C₄×C₈₃	—	2	4	no	—
258	C₂×C₄×C₈₃	—	2	8	no	—
259	C₂×C₄×C₈₃	—	2	16	no	—
260	C₂×C₄×C₈₃	—	4	16	no	—
261	C₂×C₄×C₈₃	—	4	32	no	—
262	C₂×C₄×C₈₃	—	4	8	no	—
263	C₂×C₄×C₈₃	C₂×#41	1	4	yes	—
264	C₂×C₄×C₈₃	C₂×#41	1	4	yes	—
265	C₂×C₄×C₈₃	C₂×#41	1	16	yes	—
266	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
267	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
268	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
269	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
270	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
271	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
272	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
273	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
274	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
275	C₂²×C₈₃	—	2	4	no	—
276	C₂²×C₈₃	—	2	8	no	—
277	C₂²×C₈₃	—	2	4	no	—
278	C₂²×C₈₃	—	2	8	no	—
279	C₂²×C₈₃	—	2	8	no	—
280	C₂²×C₈₃	—	2	16	no	—
281	C₂²×C₈₃	—	4	8	no	—
282	C₂²×C₈₃	—	4	16	no	—
283	C₂²×C₈₃	—	8	16	no	—
284	C₂²×C₈₃	C₂²×#41	1	4	yes	—
285	C₂²×C₈₃	C₂²×#41	1	2	yes	—
286	C₂²×C₈₃	#585	1	4	yes	—
287	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
288	C₄×C₈₃	—	2	4	no	—
289	C₄×C₈₃	—	2	8	no	—
290	C₄×C₈₃	—	2	4	no	—
291	C₄×C₈₃	—	2	8	no	—
292	C₄×C₈₃	—	2	8	no	—
293	C₄×C₈₃	—	2	4	no	—
294	C₄×C₈₃	—	2	8	no	—
295	C₄×C₈₃	C₂²×#41	1	4	yes	—
296	C₄×C₈₃	C₂²×#41	1	4	yes	—
297	C₂×#3510	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂×C₈₃	—	2	4	no	—
299	C₂×C₈₃	—	4	4	no	—
300	C₂×C₈₃	—	4	8	no	—
301	C₂×C₈₃	#3510	1	4	yes	direct product factor
302	C₂×C₈₃	C₂³×#41	1	1	yes	characteristic
303	C₂×C₈₃	C₂×#585	1	2	yes	—
304	#3510	C₂×C₈₃	1	32	yes	direct product factor
305	C₂×#559	C₂×C₈₃	1	4	yes	complemented
306	C₂×#556	C₂×C₈₃	1	4	yes	complemented
307	C₂×#551	C₂×C₈₃	1	8	yes	complemented
308	C₂×#542	C₂×C₈₃	1	4	yes	complemented
309	C₂×#536	C₂×C₈₃	1	1	yes	characteristic, complemented
310	C₂×#535	C₂×C₈₃	1	1	yes	characteristic
311	C₂×#533	C₂×C₈₃	1	1	yes	characteristic, complemented
312	C₂×#529	C₂×C₈₃	1	4	yes	complemented
313	C₂²×#124	C₂×C₈₃	1	1	yes	characteristic, complemented
314	C₂×#519	C₂×C₈₃	1	1	yes	characteristic, complemented
315	C₂×#518	C₂×C₈₃	1	1	yes	characteristic, complemented
316	C₂×C₄×#41	C₂×C₈₃	1	1	yes	characteristic, complemented
317	C₈₃	C₂×#3510	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
319	C₂³×Q₈	C₂²×C₈₃	1	1	yes	characteristic
320	C₂³×D₄	C₂²×C₈₃	1	1	yes	characteristic
321	#559	C₂²×C₈₃	1	64	yes	complemented
322	#556	C₂²×C₈₃	1	64	yes	complemented
323	#551	C₂²×C₈₃	1	128	yes	complemented
324	#542	C₂²×C₈₃	1	64	yes	complemented
325	#536	C₂²×C₈₃	1	16	yes	complemented
326	#535	C₂²×C₈₃	1	16	yes	—
327	#533	C₂²×C₈₃	1	16	yes	complemented
328	C₂×C₄⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
329	C₂×C₄⋊Q₈	C₂²×C₈₃	1	2	yes	complemented
330	C₂×#127	C₂²×C₈₃	1	2	yes	—
331	#529	C₂²×C₈₃	1	64	yes	complemented
332	C₂×#126	C₂²×C₈₃	1	8	yes	complemented
333	C₂×#126	C₂²×C₈₃	1	8	yes	complemented
334	C₂×#125	C₂²×C₈₃	1	2	yes	complemented
335	C₂×#124	C₂²×C₈₃	1	2	yes	—
336	C₂×#124	C₂²×C₈₃	1	2	yes	—
337	C₂×#124	C₂²×C₈₃	1	4	yes	—
338	C₂×#124	C₂²×C₈₃	1	2	yes	—
339	C₂×#124	C₂²×C₈₃	1	16	yes	complemented
340	C₂×#124	C₂²×C₈₃	1	2	yes	complemented
341	C₂×#124	C₂²×C₈₃	1	8	yes	complemented
342	C₂×#123	C₂²×C₈₃	1	4	yes	—
343	C₂×#123	C₂²×C₈₃	1	8	yes	complemented
344	C₂×#123	C₂²×C₈₃	1	8	yes	complemented
345	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	4	yes	—
346	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	4	yes	complemented
347	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	8	yes	complemented
348	C₂×#121	C₂²×C₈₃	1	4	yes	—
349	C₂×#120	C₂²×C₈₃	1	4	yes	—
350	#519	C₂²×C₈₃	1	16	yes	complemented
351	#518	C₂²×C₈₃	1	16	yes	complemented
352	C₄×#41	C₂²×C₈₃	1	16	yes	complemented
353	C₂×C₄×Q₈	C₂²×C₈₃	1	2	yes	complemented
354	C₂×C₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
355	C₂×C₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
356	C₂×C₄×Q₈	C₂²×C₈₃	1	4	yes	complemented
357	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
358	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
359	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
360	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	complemented
361	C₂×C₄×D₄	C₂²×C₈₃	1	8	yes	complemented
362	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
363	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
364	C₂×#117	C₂²×C₈₃	1	1	yes	characteristic
365	C₂×#117	C₂²×C₈₃	1	4	yes	—
366	C₂×#117	C₂²×C₈₃	1	2	yes	complemented
367	C₂×#117	C₂²×C₈₃	1	8	yes	complemented
368	C₂²×C₂²⋊C₄	C₂²×C₈₃	1	4	yes	—
369	C₂²×C₂²⋊C₄	C₂²×C₈₃	1	4	yes	—
370	C₂²×C₄²	C₂²×C₈₃	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₈₃	1	2	yes	complemented
372	C₂⁵	C₂³×C₈₃	1	2	yes	—
373	C₂×#41	—	2	8	no	—
374	C₂×#41	C₂³×C₈₃	1	8	yes	—
375	C₂²×Q₈	—	2	8	no	—
376	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
377	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
378	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₈₃	1	8	yes	—
380	C₂²×Q₈	C₂³×C₈₃	1	4	yes	—
381	C₂²×D₄	—	2	8	no	—
382	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
383	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
384	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
385	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
387	C₂²×D₄	C₂³×C₈₃	1	8	yes	—
388	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
389	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₈₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₈₃	1	8	yes	—
392	C₂³×C₄	C₂³×C₈₃	1	4	yes	—
393	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₈₃	1	16	yes	complemented
395	C₄⋊Q₈	C₂³×C₈₃	1	16	yes	complemented
396	#127	C₂³×C₈₃	1	16	yes	—
397	#126	C₂³×C₈₃	1	64	yes	complemented
398	#126	C₂³×C₈₃	1	64	yes	complemented
399	#125	C₂³×C₈₃	1	16	yes	complemented
400	#124	C₂³×C₈₃	1	16	yes	—
401	#124	C₂³×C₈₃	1	16	yes	—
402	#124	C₂³×C₈₃	1	32	yes	—
403	#124	C₂³×C₈₃	1	16	yes	—
404	#124	C₂³×C₈₃	1	16	yes	complemented
405	#124	C₂³×C₈₃	1	64	yes	complemented
406	#123	C₂³×C₈₃	1	32	yes	—
407	#123	C₂³×C₈₃	1	64	yes	complemented
408	#123	C₂³×C₈₃	1	64	yes	complemented
409	C₂²⋊Q₈	C₂³×C₈₃	1	32	yes	—
410	C₂²⋊Q₈	C₂³×C₈₃	1	32	yes	complemented
411	C₂²⋊Q₈	C₂³×C₈₃	1	64	yes	complemented
412	#121	C₂³×C₈₃	1	32	yes	—
413	#120	C₂³×C₈₃	1	32	yes	—
414	C₄×Q₈	C₂³×C₈₃	1	16	yes	complemented
415	C₄×Q₈	C₂³×C₈₃	1	32	yes	complemented
416	C₄×Q₈	C₂³×C₈₃	1	32	yes	complemented
417	C₄×Q₈	C₂³×C₈₃	1	32	yes	complemented
418	C₄×D₄	C₂³×C₈₃	1	32	yes	—
419	C₄×D₄	C₂³×C₈₃	1	32	yes	—
420	C₄×D₄	C₂³×C₈₃	1	32	yes	—
421	C₄×D₄	C₂³×C₈₃	1	16	yes	complemented
422	C₄×D₄	C₂³×C₈₃	1	64	yes	complemented
423	#117	C₂³×C₈₃	1	8	yes	—
424	#117	C₂³×C₈₃	1	8	yes	—
425	#117	C₂³×C₈₃	1	8	yes	—
426	#117	C₂³×C₈₃	1	32	yes	—
427	#117	C₂³×C₈₃	1	16	yes	complemented
428	#117	C₂³×C₈₃	1	64	yes	complemented
429	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
433	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
436	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
437	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₈₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₈₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₈₃	1	32	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₈₃	1	32	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₈₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
449	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
450	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
451	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
454	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
456	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
457	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₈₃	1	16	yes	complemented
459	C₂⁴	—	2	8	no	—
460	C₂⁴	—	4	8	no	—
461	C₂⁴	C₂⁴×C₈₃	1	4	yes	—
462	C₂⁴	C₂⁴×C₈₃	1	2	yes	—
463	C₂⁴	C₂⁴×C₈₃	1	1	yes	characteristic
464	C₂⁴	C₂⁴×C₈₃	1	8	yes	—
465	#41	—	2	32	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	32	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	4	8	no	—
471	C₂×Q₈	C₂⁴×C₈₃	1	8	yes	—
472	C₂×Q₈	C₂⁴×C₈₃	1	8	yes	—
473	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
474	C₂×Q₈	C₂⁴×C₈₃	1	16	yes	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	8	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	32	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	4	16	no	—
481	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
482	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
483	C₂×D₄	C₂⁴×C₈₃	1	8	yes	—
484	C₂×D₄	C₂⁴×C₈₃	1	4	yes	—
485	C₂×D₄	C₂⁴×C₈₃	1	32	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	#41×C₈₃	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₈₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
500	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
502	C₂²×C₄	C₂⁴×C₈₃	1	16	yes	—
503	C₂²×C₄	C₂⁴×C₈₃	1	32	yes	—
504	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
507	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
508	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
509	C₄⋊C₄	C₂⁴×C₈₃	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
511	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
512	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
513	C₄⋊C₄	C₂⁴×C₈₃	1	32	yes	—
514	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
515	C₄⋊C₄	C₂⁴×C₈₃	1	16	yes	—
516	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
518	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
519	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
520	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
521	C₂²⋊C₄	C₂⁴×C₈₃	1	8	yes	—
522	C₂²⋊C₄	C₂⁴×C₈₃	1	16	yes	—
523	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
524	C₂²⋊C₄	C₂⁴×C₈₃	1	32	yes	—
525	C₄²	C₂⁴×C₈₃	1	4	yes	—
526	C₄²	C₂⁴×C₈₃	1	4	yes	—
527	C₄²	C₂⁴×C₈₃	1	8	yes	—
528	C₄²	C₂⁴×C₈₃	1	8	yes	—
529	C₄²	C₂⁴×C₈₃	1	16	yes	—
530	C₄²	C₂⁴×C₈₃	1	32	yes	—
531	C₄²	C₂⁴×C₈₃	1	8	yes	—
532	C₄²	C₂⁴×C₈₃	1	8	yes	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	2	8	no	—
537	C₂³	—	2	16	no	—
538	C₂³	—	2	16	no	—
539	C₂³	—	4	16	no	—
540	C₂³	—	8	16	no	—
541	C₂³	C₂×#41×C₈₃	1	4	yes	—
542	C₂³	C₂⁵×C₈₃	1	8	yes	—
543	C₂³	C₂⁵×C₈₃	1	4	yes	—
544	C₂³	C₂⁵×C₈₃	1	2	yes	—
545	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
546	Q₈	—	2	16	no	—
547	Q₈	—	2	16	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	4	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	16	no	—
552	D₄	—	2	16	no	—
553	D₄	—	2	8	no	—
554	D₄	—	4	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	—	4	32	no	—
566	C₂×C₄	—	4	8	no	—
567	C₂×C₄	C₂×#41×C₈₃	1	4	yes	—
568	C₂×C₄	C₂×#41×C₈₃	1	4	yes	—
569	C₂×C₄	C₂×#41×C₈₃	1	16	yes	—
570	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
571	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
572	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
573	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
574	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
575	C₂×C₄	C₂⁵×C₈₃	1	4	yes	—
576	C₂×C₄	C₂⁵×C₈₃	1	8	yes	—
577	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
578	C₂×C₄	C₂⁵×C₈₃	1	2	yes	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	16	no	—
585	C₂²	—	4	16	no	—
586	C₂²	—	4	8	no	—
587	C₂²	—	8	16	no	—
588	C₂²	C₂²×#41×C₈₃	1	4	yes	—
589	C₂²	C₂²×#41×C₈₃	1	2	yes	—
590	C₂²	#585×C₈₃	1	4	yes	—
591	C₂²	C₂⁶×C₈₃	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	8	no	—
596	C₄	—	2	8	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	8	no	—
599	C₄	C₂²×#41×C₈₃	1	4	yes	—
600	C₄	C₂²×#41×C₈₃	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	4	8	no	—
603	C₂	—	4	4	no	—
604	C₂	C₈₃×#3510	1	4	yes	direct product factor
605	C₂	C₂³×#41×C₈₃	1	1	yes	characteristic
606	C₂	C₂×#585×C₈₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₃
prime radical	C₂×#535×C₈₃	C₂
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×#3510	C₂	direct (N × H)
2. C₂×#559×C₈₃	C₂	semidirect
3. C₂×#556×C₈₃	C₂	semidirect
4. C₂×#551×C₈₃	C₂	semidirect
5. C₂×#542×C₈₃	C₂	semidirect
6. C₂×#536×C₈₃	C₂	semidirect
8. C₂×#533×C₈₃	C₂	semidirect
9. C₂×#529×C₈₃	C₂	semidirect
10. C₂²×#124×C₈₃	C₂	semidirect
11. C₂×#519×C₈₃	C₂	semidirect
12. C₂×#518×C₈₃	C₂	semidirect
13. C₂×C₄×#41×C₈₃	C₂	semidirect
17. #559×C₈₃	C₂²	semidirect
18. #556×C₈₃	C₂²	semidirect
19. #551×C₈₃	C₂²	semidirect
20. #542×C₈₃	C₂²	semidirect
21. #536×C₈₃	C₂²	semidirect
23. #533×C₈₃	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
25. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
27. #529×C₈₃	C₂²	semidirect
28. C₂×#126×C₈₃	C₂²	semidirect
29. C₂×#126×C₈₃	C₂²	semidirect
30. C₂×#125×C₈₃	C₂²	semidirect
35. C₂×#124×C₈₃	C₂²	semidirect
36. C₂×#124×C₈₃	C₂²	semidirect
37. C₂×#124×C₈₃	C₂²	semidirect
39. C₂×#123×C₈₃	C₂²	semidirect
40. C₂×#123×C₈₃	C₂²	semidirect
42. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
43. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
46. #519×C₈₃	C₂²	semidirect
47. #518×C₈₃	C₂²	semidirect
48. C₄×#41×C₈₃	C₂²	semidirect
49. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
50. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
51. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
52. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
56. C₂×C₄×D₄×C₈₃	C₂²	semidirect
57. C₂×C₄×D₄×C₈₃	C₂²	semidirect
62. C₂×#117×C₈₃	C₂²	semidirect
63. C₂×#117×C₈₃	C₂²	semidirect
67. C₂²×C₄²×C₈₃	C₂²	semidirect
90. C₄⋊Q₈×C₈₃	C₂³	semidirect
91. C₄⋊Q₈×C₈₃	C₂³	semidirect
93. #126×C₈₃	C₂³	semidirect
94. #126×C₈₃	C₂³	semidirect
95. #125×C₈₃	C₂³	semidirect
100. #124×C₈₃	C₂³	semidirect
101. #124×C₈₃	C₂³	semidirect
103. #123×C₈₃	C₂³	semidirect
104. #123×C₈₃	C₂³	semidirect
106. C₂²⋊Q₈×C₈₃	C₂³	semidirect
107. C₂²⋊Q₈×C₈₃	C₂³	semidirect
110. C₄×Q₈×C₈₃	C₂³	semidirect
111. C₄×Q₈×C₈₃	C₂³	semidirect
112. C₄×Q₈×C₈₃	C₂³	semidirect
113. C₄×Q₈×C₈₃	C₂³	semidirect
117. C₄×D₄×C₈₃	C₂³	semidirect
118. C₄×D₄×C₈₃	C₂³	semidirect
123. #117×C₈₃	C₂³	semidirect
124. #117×C₈₃	C₂³	semidirect
154. C₂×C₄²×C₈₃	C₂³	semidirect
297. C₂×#3510	C₈₃	direct (N × H)
301. C₂×C₈₃	#3510	direct (N × H)
304. #3510	C₂×C₈₃	direct (N × H)
305. C₂×#559	C₂×C₈₃	semidirect
306. C₂×#556	C₂×C₈₃	semidirect
307. C₂×#551	C₂×C₈₃	semidirect
308. C₂×#542	C₂×C₈₃	semidirect
309. C₂×#536	C₂×C₈₃	semidirect
311. C₂×#533	C₂×C₈₃	semidirect
312. C₂×#529	C₂×C₈₃	semidirect
313. C₂²×#124	C₂×C₈₃	semidirect
314. C₂×#519	C₂×C₈₃	semidirect
315. C₂×#518	C₂×C₈₃	semidirect
316. C₂×C₄×#41	C₂×C₈₃	semidirect
317. C₈₃	C₂×#3510	direct (N × H)
321. #559	C₂²×C₈₃	semidirect
322. #556	C₂²×C₈₃	semidirect
323. #551	C₂²×C₈₃	semidirect
324. #542	C₂²×C₈₃	semidirect
325. #536	C₂²×C₈₃	semidirect
327. #533	C₂²×C₈₃	semidirect
328. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
329. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
331. #529	C₂²×C₈₃	semidirect
332. C₂×#126	C₂²×C₈₃	semidirect
333. C₂×#126	C₂²×C₈₃	semidirect
334. C₂×#125	C₂²×C₈₃	semidirect
339. C₂×#124	C₂²×C₈₃	semidirect
340. C₂×#124	C₂²×C₈₃	semidirect
341. C₂×#124	C₂²×C₈₃	semidirect
343. C₂×#123	C₂²×C₈₃	semidirect
344. C₂×#123	C₂²×C₈₃	semidirect
346. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
347. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
350. #519	C₂²×C₈₃	semidirect
351. #518	C₂²×C₈₃	semidirect
352. C₄×#41	C₂²×C₈₃	semidirect
353. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
354. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
355. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
356. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
360. C₂×C₄×D₄	C₂²×C₈₃	semidirect
361. C₂×C₄×D₄	C₂²×C₈₃	semidirect
366. C₂×#117	C₂²×C₈₃	semidirect
367. C₂×#117	C₂²×C₈₃	semidirect
371. C₂²×C₄²	C₂²×C₈₃	semidirect
394. C₄⋊Q₈	C₂³×C₈₃	semidirect
395. C₄⋊Q₈	C₂³×C₈₃	semidirect
397. #126	C₂³×C₈₃	semidirect
398. #126	C₂³×C₈₃	semidirect
399. #125	C₂³×C₈₃	semidirect
404. #124	C₂³×C₈₃	semidirect
405. #124	C₂³×C₈₃	semidirect
407. #123	C₂³×C₈₃	semidirect
408. #123	C₂³×C₈₃	semidirect
410. C₂²⋊Q₈	C₂³×C₈₃	semidirect
411. C₂²⋊Q₈	C₂³×C₈₃	semidirect
414. C₄×Q₈	C₂³×C₈₃	semidirect
415. C₄×Q₈	C₂³×C₈₃	semidirect
416. C₄×Q₈	C₂³×C₈₃	semidirect
417. C₄×Q₈	C₂³×C₈₃	semidirect
421. C₄×D₄	C₂³×C₈₃	semidirect
422. C₄×D₄	C₂³×C₈₃	semidirect
427. #117	C₂³×C₈₃	semidirect
428. #117	C₂³×C₈₃	semidirect
458. C₂×C₄²	C₂³×C₈₃	semidirect
604. C₂	C₈₃×#3510	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×#3510	2
C₂×#559×C₈₃	2
C₂×#556×C₈₃	2
C₂×#551×C₈₃	2
C₂×#542×C₈₃	2
C₂×#536×C₈₃	2
C₂×#535×C₈₃	2
C₂×#533×C₈₃	2
C₂×#529×C₈₃	2
C₂²×#124×C₈₃	2
C₂×#519×C₈₃	2
C₂×#518×C₈₃	2
C₂×C₄×#41×C₈₃	2
C₂×#3510	83

Subgroups — C2×C83×#3510 #35290632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3510 #35290632