Subgroups — C₂²×#529×C₈₃ #35290487

Order 21248.

8670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄×C₈₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₃
socle	C₂⁴×C₈₃	C₂⁴
prime radical	C₂²×#121×C₈₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₈₃	C₂	direct (N × H)
2. C₂²×#126×C₈₃	C₂	semidirect
3. C₂²×#125×C₈₃	C₂	semidirect
4. C₂²×#124×C₈₃	C₂	semidirect
5. C₂²×#123×C₈₃	C₂	semidirect
6. C₂²×C₂²⋊Q₈×C₈₃	C₂	semidirect
8. C₂²×C₄×Q₈×C₈₃	C₂	semidirect
9. C₂²×C₄×D₄×C₈₃	C₂	semidirect
10. C₂²×C₄×D₄×C₈₃	C₂	semidirect
11. C₂²×#117×C₈₃	C₂	semidirect
12. C₂³×C₄²×C₈₃	C₂	semidirect
20. #529×C₈₃	C₂²	direct (N × H)
21. C₂×#126×C₈₃	C₂²	semidirect
22. C₂×#125×C₈₃	C₂²	semidirect
23. C₂×#124×C₈₃	C₂²	semidirect
24. C₂×#123×C₈₃	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₈₃	C₂²	semidirect
27. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
28. C₂×C₄×D₄×C₈₃	C₂²	semidirect
29. C₂×C₄×D₄×C₈₃	C₂²	semidirect
30. C₂×#117×C₈₃	C₂²	semidirect
47. C₂²×C₄²×C₈₃	C₂²	semidirect
73. #126×C₈₃	C₂³	semidirect
74. #125×C₈₃	C₂³	semidirect
75. #124×C₈₃	C₂³	semidirect
76. #123×C₈₃	C₂³	semidirect
77. C₂²⋊Q₈×C₈₃	C₂³	semidirect
79. C₄×Q₈×C₈₃	C₂³	semidirect
80. C₄×D₄×C₈₃	C₂³	semidirect
81. C₄×D₄×C₈₃	C₂³	semidirect
82. #117×C₈₃	C₂³	semidirect
99. C₂×C₄²×C₈₃	C₂³	semidirect
203. C₂²×C₈₃	#529	direct (N × H)
218. C₂²×#529	C₈₃	direct (N × H)
221. C₂×C₈₃	C₂×#529	direct (N × H)
225. C₂×#529	C₂×C₈₃	direct (N × H)
226. C₂²×#126	C₂×C₈₃	semidirect
227. C₂²×#125	C₂×C₈₃	semidirect
228. C₂²×#124	C₂×C₈₃	semidirect
229. C₂²×#123	C₂×C₈₃	semidirect
230. C₂²×C₂²⋊Q₈	C₂×C₈₃	semidirect
232. C₂²×C₄×Q₈	C₂×C₈₃	semidirect
233. C₂²×C₄×D₄	C₂×C₈₃	semidirect
234. C₂²×C₄×D₄	C₂×C₈₃	semidirect
235. C₂²×#117	C₂×C₈₃	semidirect
236. C₂³×C₄²	C₂×C₈₃	semidirect
237. C₈₃	C₂²×#529	direct (N × H)
245. #529	C₂²×C₈₃	direct (N × H)
246. C₂×#126	C₂²×C₈₃	semidirect
247. C₂×#125	C₂²×C₈₃	semidirect
248. C₂×#124	C₂²×C₈₃	semidirect
249. C₂×#123	C₂²×C₈₃	semidirect
250. C₂×C₂²⋊Q₈	C₂²×C₈₃	semidirect
252. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
253. C₂×C₄×D₄	C₂²×C₈₃	semidirect
254. C₂×C₄×D₄	C₂²×C₈₃	semidirect
255. C₂×#117	C₂²×C₈₃	semidirect
272. C₂²×C₄²	C₂²×C₈₃	semidirect
298. #126	C₂³×C₈₃	semidirect
299. #125	C₂³×C₈₃	semidirect
300. #124	C₂³×C₈₃	semidirect
301. #123	C₂³×C₈₃	semidirect
302. C₂²⋊Q₈	C₂³×C₈₃	semidirect
304. C₄×Q₈	C₂³×C₈₃	semidirect
305. C₄×D₄	C₂³×C₈₃	semidirect
306. C₄×D₄	C₂³×C₈₃	semidirect
307. #117	C₂³×C₈₃	semidirect
324. C₂×C₄²	C₂³×C₈₃	semidirect
428. C₂²	#529×C₈₃	direct (N × H)
445. C₂	C₂×#529×C₈₃	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×#529×C₈₃	2
C₂²×#126×C₈₃	2
C₂²×#125×C₈₃	2
C₂²×#124×C₈₃	2
C₂²×#123×C₈₃	2
C₂²×C₂²⋊Q₈×C₈₃	2
C₂²×#121×C₈₃	2
C₂²×C₄×Q₈×C₈₃	2
C₂²×C₄×D₄×C₈₃	2
C₂²×#117×C₈₃	2
C₂³×C₄²×C₈₃	2
C₂²×#529	83

Subgroups — C22×#529×C83 #35290487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#529×C₈₃ #35290487