Subgroups — #36312945

Order 21248.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19128537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#24921144	C₂	1	8	yes	maximal, complemented
4	#24921133	C₂	1	8	yes	maximal, complemented
5	#24921122	C₂	1	2	yes	maximal, complemented
6	#24921115	C₂	1	2	yes	maximal, complemented
7	#24921108	C₂	1	6	yes	maximal, complemented
8	#24921099	C₂	1	6	yes	maximal, complemented
9	#41×D₃₃₂	C₂	1	16	yes	maximal, complemented
10	#24920796	C₂	1	6	yes	maximal, complemented
11	C₂×#19128213	C₂	1	6	yes	maximal, complemented
12	C₈₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128537	—	2	16	no	—
14	C₂×#14581840	C₂²	1	2	yes	complemented
15	C₂×#14581839	C₂²	1	4	yes	complemented
16	C₂×#14581838	C₂²	1	4	yes	complemented
17	C₂×#14581837	C₂²	1	6	yes	complemented
18	C₂²×#13050591	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#13050590	C₂²	1	3	yes	complemented
20	C₂²×#13050590	C₂²	1	6	yes	complemented
21	C₂²×#13050589	C₂²	1	3	yes	complemented
22	C₂×#41×D₈₃	—	2	16	no	—
23	C₂×#41×D₈₃	C₂²	1	8	yes	complemented
24	C₂×#41×D₈₃	C₂²	1	8	yes	complemented
25	C₂×#41×D₈₃	C₂²	1	8	yes	complemented
26	C₂²×Q₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₄×D₈₃	C₂²	1	3	yes	complemented
28	C₂³×C₄×D₈₃	C₂²	1	3	yes	complemented
29	#19128373	C₂²	1	16	yes	complemented
30	Q₈×D₃₃₂	C₂²	1	16	yes	complemented
31	#19128363	C₂²	1	16	yes	complemented
32	#19128363	C₂²	1	16	yes	complemented
33	#19128355	C₂²	1	48	yes	complemented
34	#19128346	C₂²	1	48	yes	complemented
35	#19128346	C₂²	1	48	yes	complemented
36	D₄×D₃₃₂	C₂²	1	48	yes	complemented
37	#19128282	C₂²	1	24	yes	complemented
38	#19128277	C₂²	1	12	yes	complemented
39	#19128277	C₂²	1	12	yes	complemented
40	#19128270	C₂²	1	12	yes	complemented
41	#19128270	C₂²	1	12	yes	complemented
42	#19128263	C₂²	1	24	yes	complemented
43	#19128251	C₂²	1	24	yes	complemented
44	#19128213	C₂²	1	12	yes	complemented
45	#19128213	C₂²	1	4	yes	complemented
46	#19128213	C₂²	1	24	yes	complemented
47	#19128213	C₂²	1	24	yes	complemented
48	#19128213	C₂²	1	12	yes	complemented
49	#19128213	C₂²	1	12	yes	complemented
50	#19128213	C₂²	1	24	yes	complemented
51	C₂×#14581776	C₂²	1	12	yes	complemented
52	C₂×#14581772	C₂²	1	12	yes	complemented
53	C₂×#14581767	C₂²	1	12	yes	complemented
54	C₂×#14581762	C₂²	1	12	yes	complemented
55	C₂×C₄×D₃₃₂	C₂²	1	24	yes	complemented
56	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
57	#520×C₈₃	C₂²	1	8	yes	complemented
58	#519×C₈₃	C₂²	1	2	yes	complemented
59	#518×C₈₃	C₂²	1	6	yes	complemented
60	C₄×#41×C₈₃	C₂²	1	8	yes	complemented
61	C₂×#117×C₈₃	C₂²	1	6	yes	complemented
62	C₂⁴×D₈₃	C₂³	1	3	yes	—
63	#14581840	—	2	16	no	—
64	#14581839	—	2	32	no	—
65	#14581838	—	2	32	no	—
66	#14581837	—	2	48	no	—
67	C₂×#13050591	—	2	8	no	—
68	C₂×#13050591	C₂³	1	8	yes	—
69	C₂×#13050591	C₂³	1	8	yes	complemented
70	C₂×#13050590	—	2	24	no	—
71	C₂×#13050590	—	2	48	no	—
72	C₂×#13050590	C₂³	1	4	yes	—
73	C₂×#13050590	C₂³	1	12	yes	—
74	C₂×#13050590	C₂³	1	12	yes	—
75	C₂×#13050590	C₂³	1	12	yes	—
76	C₂×#13050590	C₂³	1	12	yes	complemented
77	C₂×#13050590	C₂³	1	12	yes	complemented
78	C₂×#13050589	—	2	24	no	—
79	C₂×#13050589	C₂³	1	24	yes	—
80	C₂×#13050589	C₂³	1	24	yes	complemented
81	#41×D₈₃	—	2	64	no	—
82	#41×D₈₃	—	2	64	no	—
83	#41×D₈₃	—	2	64	no	—
84	C₂²×Dic₁₆₆	C₂³	1	3	yes	—
85	C₂²×Dic₁₆₆	C₂³	1	6	yes	complemented
86	C₂×Q₈×D₈₃	—	2	8	no	—
87	C₂×Q₈×D₈₃	C₂³	1	8	yes	—
88	C₂×Q₈×D₈₃	C₂³	1	8	yes	complemented
89	C₂²×D₃₃₂	C₂³	1	3	yes	—
90	C₂²×D₃₃₂	C₂³	1	24	yes	—
91	C₂²×D₃₃₂	C₂³	1	6	yes	complemented
92	C₂²×C₂²⋊D₈₃	C₂³	1	12	yes	—
93	C₂²×C₂²⋊D₈₃	C₂³	1	6	yes	—
94	C₂×D₄×D₈₃	—	2	24	no	—
95	C₂×D₄×D₈₃	C₂³	1	24	yes	—
96	C₂×D₄×D₈₃	C₂³	1	24	yes	complemented
97	C₂³×Dic₈₃	C₂³	1	3	yes	—
98	C₂²×C₄×D₈₃	—	2	24	no	—
99	C₂²×C₄×D₈₃	C₂³	1	12	yes	—
100	C₂²×C₄×D₈₃	C₂³	1	12	yes	—
101	C₂²×C₄×D₈₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×D₈₃	C₂³	1	3	yes	—
103	C₂²×C₄×D₈₃	C₂³	1	3	yes	—
104	C₂²×C₄×D₈₃	C₂³	1	3	yes	—
105	C₂²×C₄×D₈₃	C₂³	1	12	yes	complemented
106	#14581792	C₂³	1	24	yes	complemented
107	#14581789	C₂³	1	24	yes	complemented
108	#14581780	C₂³	1	24	yes	complemented
109	#14581780	C₂³	1	24	yes	complemented
110	#14581776	C₂³	1	8	yes	—
111	#14581776	C₂³	1	24	yes	—
112	#14581776	C₂³	1	48	yes	complemented
113	#14581776	C₂³	1	48	yes	complemented
114	#14581772	C₂³	1	24	yes	—
115	#14581772	C₂³	1	8	yes	—
116	#14581772	C₂³	1	48	yes	complemented
117	#14581772	C₂³	1	24	yes	complemented
118	#14581772	C₂³	1	24	yes	complemented
119	#14581767	C₂³	1	24	yes	—
120	#14581767	C₂³	1	8	yes	—
121	#14581767	C₂³	1	48	yes	complemented
122	#14581767	C₂³	1	24	yes	complemented
123	#14581767	C₂³	1	24	yes	complemented
124	#14581766	C₂³	1	96	yes	complemented
125	#14581762	C₂³	1	48	yes	—
126	#14581762	C₂³	1	8	yes	—
127	#14581762	C₂³	1	24	yes	—
128	#14581762	C₂³	1	48	yes	complemented
129	C₄×D₃₃₂	C₂³	1	48	yes	—
130	C₄×D₃₃₂	C₂³	1	16	yes	—
131	C₄×D₃₃₂	C₂³	1	48	yes	complemented
132	C₄×D₃₃₂	C₂³	1	48	yes	complemented
133	C₂×C₄⋊Dic₈₃	C₂³	1	24	yes	complemented
134	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	24	yes	—
135	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	24	yes	complemented
136	C₂×#41×C₈₃	D₄	1	16	yes	complemented
137	C₂×#41×C₈₃	C₂³	1	4	yes	—
138	C₂×#41×C₈₃	C₂³	1	4	yes	—
139	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₈₃	C₂³	1	3	yes	—
141	C₂³×C₄×C₈₃	C₂³	1	3	yes	—
142	C₄×Q₈×C₈₃	C₂³	1	16	yes	complemented
143	C₄×D₄×C₈₃	C₂³	1	48	yes	complemented
144	#117×C₈₃	C₂³	1	4	yes	—
145	#117×C₈₃	C₂³	1	12	yes	—
146	#117×C₈₃	C₂³	1	12	yes	complemented
147	#117×C₈₃	C₂³	1	12	yes	complemented
148	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	complemented
149	C₂×C₂²⋊C₄×C₈₃	C₂³	1	12	yes	—
150	C₂×C₄²×C₈₃	C₂³	1	12	yes	complemented
151	C₂³×D₈₃	—	2	12	no	—
152	C₂³×D₈₃	—	4	12	no	—
153	C₂³×D₈₃	C₂⁴	1	1	yes	characteristic
154	C₂³×D₈₃	C₂⁴	1	12	yes	—
155	C₂³×D₈₃	C₂⁴	1	3	yes	—
156	C₂³×D₈₃	C₂⁴	1	12	yes	—
157	#13050591	—	2	32	no	—
158	#13050591	—	2	32	no	—
159	#13050590	—	2	48	no	—
160	#13050590	—	2	48	no	—
161	#13050590	—	2	48	no	—
162	#13050590	—	2	16	no	—
163	#13050590	—	2	48	no	—
164	#13050590	—	2	48	no	—
165	#13050589	—	2	96	no	—
166	#13050589	—	2	96	no	—
167	C₂×Dic₁₆₆	—	2	12	no	—
168	C₂×Dic₁₆₆	—	2	24	no	—
169	C₂×Dic₁₆₆	C₂⁴	1	4	yes	—
170	C₂×Dic₁₆₆	C₂⁴	1	12	yes	—
171	C₂×Dic₁₆₆	C₂⁴	1	12	yes	—
172	Q₈×D₈₃	—	2	32	no	—
173	Q₈×D₈₃	—	2	32	no	—
174	C₂×D₃₃₂	—	2	12	no	—
175	C₂×D₃₃₂	—	2	24	no	—
176	C₂×D₃₃₂	—	4	48	no	—
177	C₂×D₃₃₂	C₂⁴	1	16	yes	—
178	C₂×D₃₃₂	C₂⁴	1	4	yes	—
179	C₂×D₃₃₂	C₂⁴	1	12	yes	—
180	C₂×D₃₃₂	C₂⁴	1	12	yes	—
181	C₂×D₃₃₂	C₂⁴	1	48	yes	—
182	C₂×C₂²⋊D₈₃	—	2	24	no	—
183	C₂×C₂²⋊D₈₃	—	2	48	no	—
184	C₂×C₂²⋊D₈₃	C₂⁴	1	8	yes	—
185	C₂×C₂²⋊D₈₃	C₂⁴	1	24	yes	—
186	C₂×C₂²⋊D₈₃	C₂⁴	1	24	yes	—
187	D₄×D₈₃	—	2	96	no	—
188	D₄×D₈₃	—	2	96	no	—
189	C₂²×Dic₈₃	—	2	12	no	—
190	C₂²×Dic₈₃	C₂⁴	1	1	yes	characteristic
191	C₂²×Dic₈₃	C₂⁴	1	3	yes	—
192	C₂²×Dic₈₃	C₂⁴	1	12	yes	—
193	C₂²×Dic₈₃	C₂⁴	1	12	yes	—
194	C₂×C₄×D₈₃	—	2	4	no	—
195	C₂×C₄×D₈₃	—	2	12	no	—
196	C₂×C₄×D₈₃	—	2	48	no	—
197	C₂×C₄×D₈₃	—	2	48	no	—
198	C₂×C₄×D₈₃	—	2	12	no	—
199	C₂×C₄×D₈₃	—	2	12	no	—
200	C₂×C₄×D₈₃	—	2	48	no	—
201	C₂×C₄×D₈₃	C₂⁴	1	2	yes	—
202	C₂×C₄×D₈₃	C₂⁴	1	12	yes	—
203	C₂×C₄×D₈₃	C₂⁴	1	6	yes	—
204	C₂×C₄×D₈₃	C₂⁴	1	12	yes	—
205	C₂×C₄×D₈₃	C₂⁴	1	24	yes	—
206	C₂×C₄×D₈₃	C₂⁴	1	2	yes	—
207	C₂×C₄×D₈₃	C₂⁴	1	6	yes	—
208	C₂×C₄×D₈₃	C₂⁴	1	8	yes	—
209	C₄⋊Dic₈₃	C₂⁴	1	48	yes	—
210	C₄⋊Dic₈₃	C₂⁴	1	16	yes	—
211	(C₂×D₈₃)⋊C₄	C₂⁴	1	16	yes	—
212	(C₂×D₈₃)⋊C₄	C₂⁴	1	48	yes	—
213	(C₂×D₈₃)⋊C₄	C₂⁴	1	48	yes	—
214	(C₂×D₈₃)⋊C₄	C₂⁴	1	16	yes	—
215	C₂⁴×C₈₃	C₂⁴	1	3	yes	—
216	#41×C₈₃	C₂×D₄	1	32	yes	complemented
217	#41×C₈₃	C₂×D₄	1	32	yes	complemented
218	C₂×Q₈×C₈₃	C₂×D₄	1	8	yes	complemented
219	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
220	C₂×D₄×C₈₃	C₂×D₄	1	24	yes	complemented
221	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
222	C₂²×C₄×C₈₃	C₂×D₄	1	24	yes	complemented
223	C₂²×C₄×C₈₃	C₂⁴	1	24	yes	—
224	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
226	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
227	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
228	C₄⋊C₄×C₈₃	C₂⁴	1	8	yes	—
229	C₄⋊C₄×C₈₃	C₂⁴	1	24	yes	—
230	C₂²⋊C₄×C₈₃	C₂⁴	1	8	yes	—
231	C₂²⋊C₄×C₈₃	C₂⁴	1	24	yes	—
232	C₄²×C₈₃	C₂⁴	1	24	yes	—
233	C₄²×C₈₃	C₂⁴	1	8	yes	—
234	C₂³×C₈₃	—	4	6	no	—
235	C₂³×C₈₃	C₂²×D₄	1	12	yes	—
236	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
237	C₂³×C₈₃	C₂⁵	1	6	yes	—
238	C₂²×D₈₃	—	2	2	no	—
239	C₂²×D₈₃	—	2	4	no	—
240	C₂²×D₈₃	—	2	24	no	—
241	C₂²×D₈₃	—	2	6	no	—
242	C₂²×D₈₃	—	2	24	no	—
243	C₂²×D₈₃	—	2	24	no	—
244	C₂²×D₈₃	—	4	12	no	—
245	C₂²×D₈₃	—	4	6	no	—
246	C₂²×D₈₃	—	4	24	no	—
247	C₂²×D₈₃	—	4	48	no	—
248	C₂²×D₈₃	C₂⁵	1	8	yes	—
249	C₂²×D₈₃	C₂⁵	1	6	yes	—
250	C₂²×D₈₃	C₂⁵	1	2	yes	—
251	Q₈×C₈₃	C₂²×D₄	1	16	yes	—
252	D₄×C₈₃	C₂²×D₄	1	48	yes	—
253	C₂×C₄×C₈₃	—	4	24	no	—
254	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₈₃	C₂²×D₄	1	12	yes	—
256	C₂×C₄×C₈₃	C₂²×D₄	1	24	yes	—
257	C₂×C₄×C₈₃	C₂²×D₄	1	24	yes	—
258	C₂×C₄×C₈₃	C₂⁵	1	16	yes	—
259	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
260	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
261	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
262	C₂²⋊D₈₃	—	2	48	no	—
263	C₂²⋊D₈₃	—	2	48	no	—
264	C₂²⋊D₈₃	—	2	16	no	—
265	C₂×Dic₈₃	—	2	2	no	—
266	C₂×Dic₈₃	—	2	6	no	—
267	C₂×Dic₈₃	—	2	24	no	—
268	C₂×Dic₈₃	—	2	24	no	—
269	C₂×Dic₈₃	C₂⁵	1	2	yes	—
270	C₂×Dic₈₃	C₂⁵	1	8	yes	—
271	C₂×Dic₈₃	C₂⁵	1	6	yes	—
272	D₃₃₂	—	2	32	no	—
273	D₃₃₂	—	2	24	no	—
274	D₃₃₂	—	2	24	no	—
275	D₃₃₂	—	2	8	no	—
276	D₃₃₂	—	4	48	no	—
277	C₄×D₈₃	—	2	4	no	—
278	C₄×D₈₃	—	2	4	no	—
279	C₄×D₈₃	—	2	24	no	—
280	C₄×D₈₃	—	2	24	no	—
281	C₄×D₈₃	—	2	12	no	—
282	C₄×D₈₃	—	2	12	no	—
283	C₄×D₈₃	—	2	16	no	—
284	C₄×D₈₃	—	2	48	no	—
285	Dic₁₆₆	—	2	24	no	—
286	Dic₁₆₆	—	2	24	no	—
287	Dic₁₆₆	—	2	8	no	—
288	C₂²×C₈₃	—	2	12	no	—
289	C₂²×C₈₃	—	2	2	no	—
290	C₂²×C₈₃	—	4	12	no	—
291	C₂²×C₈₃	C₂³×D₄	1	2	yes	—
292	C₂²×C₈₃	C₂³×D₄	1	12	yes	—
293	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
294	C₂×D₈₃	—	2	8	no	—
295	C₂×D₈₃	—	2	2	no	—
296	C₂×D₈₃	—	2	2	no	—
297	C₂×D₈₃	—	2	6	no	—
298	C₂×D₈₃	—	2	8	no	—
299	C₂×D₈₃	—	2	16	no	—
300	C₂×D₈₃	—	2	12	no	—
301	C₂×D₈₃	—	4	48	no	—
302	C₂×D₈₃	—	4	12	no	—
303	C₂×D₈₃	—	8	24	no	—
304	C₂×D₈₃	#585	1	4	yes	complemented
305	C₄×C₈₃	—	2	16	no	—
306	C₄×C₈₃	C₂³×D₄	1	2	yes	—
307	C₄×C₈₃	C₂³×D₄	1	12	yes	—
308	C₄×C₈₃	C₂³×D₄	1	2	yes	—
309	Dic₈₃	—	2	6	no	—
310	Dic₈₃	—	2	8	no	—
311	Dic₈₃	—	2	2	no	—
312	#62811	—	83	1	no	maximal, Sylow
313	C₂×C₈₃	—	2	2	no	—
314	C₂×C₈₃	—	2	12	no	—
315	C₂×C₈₃	C₂⁴×D₄	1	1	yes	characteristic
316	C₂×C₈₃	C₂×#585	1	2	yes	—
317	D₈₃	—	2	4	no	—
318	D₈₃	—	4	6	no	—
319	D₈₃	—	4	8	no	—
320	C₂×#585	—	83	1	no	—
321	C₂³×#41	—	83	1	no	—
322	#3489	—	83	8	no	—
323	#3488	—	83	8	no	—
324	#3487	—	83	2	no	—
325	#3486	—	83	2	no	—
326	#3485	—	83	6	no	—
327	#3484	—	83	6	no	—
328	D₄×#41	—	83	16	no	—
329	#3449	—	83	6	no	—
330	C₂×#525	—	83	6	no	—
331	#3428	D₈₃	1	1	yes	characteristic, complemented
332	C₈₃	#62811	1	1	yes	characteristic, complemented, Sylow
333	#585	—	166	16	no	—
334	C₂×2₋¹⁺⁴	—	83	4	no	—
335	C₂×2₋¹⁺⁴	—	83	2	no	—
336	C₂×H(5,𝔽₂)	—	83	4	no	—
337	C₂×H(5,𝔽₂)	—	83	6	no	—
338	C₂²×#41	—	83	8	no	—
339	C₂²×#41	—	83	8	no	—
340	C₂²×#41	—	83	8	no	—
341	C₂²×#41	—	83	1	no	—
342	C₂²×#41	—	83	3	no	—
343	C₂²×#41	—	83	3	no	—
344	C₂²×#41	—	83	6	no	—
345	C₂²×#41	—	166	16	no	—
346	C₂²×#41	C₂×D₈₃	1	1	yes	characteristic
347	C₂³×Q₈	—	83	1	no	—
348	C₂³×D₄	—	83	3	no	—
349	C₂⁴×C₄	—	83	3	no	—
350	#550	—	83	16	no	—
351	D₄×Q₈	—	83	16	no	—
352	#548	—	83	16	no	—
353	#548	—	83	16	no	—
354	#547	—	83	48	no	—
355	#546	—	83	48	no	—
356	#546	—	83	48	no	—
357	D₄²	—	83	48	no	—
358	#537	—	83	24	no	—
359	#536	—	83	12	no	—
360	#536	—	83	12	no	—
361	#535	—	83	12	no	—
362	#535	—	83	12	no	—
363	#534	—	83	24	no	—
364	#532	—	83	24	no	—
365	#525	—	83	4	no	—
366	#525	—	83	12	no	—
367	#525	—	83	12	no	—
368	#525	—	83	12	no	—
369	#525	—	83	24	no	—
370	#525	—	83	24	no	—
371	#525	—	83	24	no	—
372	C₂×#123	—	83	12	no	—
373	C₂×C₂²⋊Q₈	—	83	12	no	—
374	C₂×#121	—	83	12	no	—
375	C₂×#120	—	83	12	no	—
376	#520	C₂×D₈₃	1	8	yes	complemented
377	#519	C₂×D₈₃	1	2	yes	complemented
378	#518	C₂×D₈₃	1	6	yes	complemented
379	C₄×#41	C₂×D₈₃	1	8	yes	complemented
380	C₂×C₄×D₄	—	83	24	no	—
381	C₂×#117	C₂×D₈₃	1	6	yes	complemented
382	C₂⁵	—	83	3	no	—
383	2₋¹⁺⁴	—	166	32	no	—
384	2₋¹⁺⁴	—	166	16	no	—
385	H(5,𝔽₂)	—	166	32	no	—
386	H(5,𝔽₂)	—	166	48	no	—
387	C₂×#41	—	83	8	no	—
388	C₂×#41	—	83	8	no	—
389	C₂×#41	—	83	24	no	—
390	C₂×#41	—	83	24	no	—
391	C₂×#41	—	83	4	no	—
392	C₂×#41	—	83	12	no	—
393	C₂×#41	—	83	12	no	—
394	C₂×#41	—	83	12	no	—
395	C₂×#41	—	83	12	no	—
396	C₂×#41	—	83	12	no	—
397	C₂×#41	—	166	64	no	—
398	C₂×#41	—	166	64	no	—
399	C₂×#41	—	166	64	no	—
400	C₂×#41	—	166	8	no	—
401	C₂×#41	—	166	24	no	—
402	C₂×#41	—	166	24	no	—
403	C₂×#41	—	166	48	no	—
404	C₂×#41	D₃₃₂	1	16	yes	complemented
405	C₂×#41	C₂²×D₈₃	1	4	yes	—
406	C₂×#41	C₂²×D₈₃	1	4	yes	—
407	C₂²×Q₈	—	83	8	no	—
408	C₂²×Q₈	—	83	8	no	—
409	C₂²×Q₈	—	83	6	no	—
410	C₂²×Q₈	—	83	3	no	—
411	C₂²×Q₈	—	166	8	no	—
412	C₂²×Q₈	C₂²×D₈₃	1	1	yes	characteristic
413	C₂²×D₄	—	83	12	no	—
414	C₂²×D₄	—	83	6	no	—
415	C₂²×D₄	—	83	24	no	—
416	C₂²×D₄	—	83	24	no	—
417	C₂²×D₄	—	83	24	no	—
418	C₂²×D₄	—	83	6	no	—
419	C₂²×D₄	—	83	3	no	—
420	C₂²×D₄	—	166	24	no	—
421	C₂²×D₄	C₂²×D₈₃	1	3	yes	—
422	C₂³×C₄	—	83	3	no	—
423	C₂³×C₄	—	83	12	no	—
424	C₂³×C₄	—	83	12	no	—
425	C₂³×C₄	—	83	12	no	—
426	C₂³×C₄	—	83	1	no	—
427	C₂³×C₄	—	83	3	no	—
428	C₂³×C₄	—	83	3	no	—
429	C₂³×C₄	—	83	3	no	—
430	C₂³×C₄	—	166	24	no	—
431	C₂³×C₄	C₂²×D₈₃	1	3	yes	—
432	C₄⋊Q₈	—	83	24	no	—
433	#127	—	83	24	no	—
434	#124	—	83	24	no	—
435	#124	—	83	24	no	—
436	#123	—	83	8	no	—
437	#123	—	83	24	no	—
438	#123	—	83	48	no	—
439	#123	—	83	48	no	—
440	C₂²⋊Q₈	—	83	8	no	—
441	C₂²⋊Q₈	—	83	24	no	—
442	C₂²⋊Q₈	—	83	24	no	—
443	C₂²⋊Q₈	—	83	24	no	—
444	C₂²⋊Q₈	—	83	48	no	—
445	#121	—	83	96	no	—
446	#121	—	83	8	no	—
447	#121	—	83	24	no	—
448	#121	—	83	24	no	—
449	#121	—	83	24	no	—
450	#121	—	83	48	no	—
451	#120	—	83	8	no	—
452	#120	—	83	24	no	—
453	#120	—	83	48	no	—
454	#120	—	83	48	no	—
455	C₄×Q₈	C₂²×D₈₃	1	16	yes	complemented
456	C₄×D₄	—	83	16	no	—
457	C₄×D₄	—	83	48	no	—
458	C₄×D₄	—	83	48	no	—
459	C₄×D₄	—	83	48	no	—
460	C₄×D₄	C₂²×D₈₃	1	48	yes	complemented
461	#117	C₂²×D₈₃	1	4	yes	—
462	#117	C₂²×D₈₃	1	12	yes	—
463	#117	C₂²×D₈₃	1	12	yes	complemented
464	#117	C₂²×D₈₃	1	12	yes	complemented
465	C₂×C₄⋊C₄	—	83	24	no	—
466	C₂×C₄⋊C₄	C₂²×D₈₃	1	12	yes	complemented
467	C₂×C₂²⋊C₄	—	83	24	no	—
468	C₂×C₂²⋊C₄	—	83	24	no	—
469	C₂×C₂²⋊C₄	C₂²×D₈₃	1	12	yes	—
470	C₂×C₄²	C₂²×D₈₃	1	12	yes	complemented
471	C₂⁴	—	332	12	no	—
472	C₂⁴	—	83	12	no	—
473	C₂⁴	—	83	3	no	—
474	C₂⁴	—	83	12	no	—
475	C₂⁴	—	83	1	no	—
476	C₂⁴	—	166	12	no	—
477	C₂⁴	C₂³×D₈₃	1	3	yes	—
478	#41	—	166	32	no	—
479	#41	—	166	32	no	—
480	#41	—	166	96	no	—
481	#41	—	166	96	no	—
482	#41	—	166	16	no	—
483	#41	—	166	48	no	—
484	#41	—	166	48	no	—
485	#41	—	166	48	no	—
486	#41	—	166	48	no	—
487	#41	—	166	48	no	—
488	#41	C₂×D₃₃₂	1	32	yes	complemented
489	#41	C₂×D₃₃₂	1	32	yes	complemented
490	C₂×Q₈	—	83	4	no	—
491	C₂×Q₈	—	83	12	no	—
492	C₂×Q₈	—	83	12	no	—
493	C₂×Q₈	—	166	32	no	—
494	C₂×Q₈	—	166	32	no	—
495	C₂×Q₈	—	166	12	no	—
496	C₂×Q₈	—	166	24	no	—
497	C₂×Q₈	C₂×D₃₃₂	1	8	yes	complemented
498	C₂×Q₈	C₂³×D₈₃	1	4	yes	—
499	C₂×D₄	—	332	48	no	—
500	C₂×D₄	—	83	8	no	—
501	C₂×D₄	—	83	24	no	—
502	C₂×D₄	—	83	24	no	—
503	C₂×D₄	—	83	48	no	—
504	C₂×D₄	—	83	16	no	—
505	C₂×D₄	—	83	4	no	—
506	C₂×D₄	—	83	12	no	—
507	C₂×D₄	—	83	12	no	—
508	C₂×D₄	—	166	24	no	—
509	C₂×D₄	—	166	48	no	—
510	C₂×D₄	—	166	96	no	—
511	C₂×D₄	—	166	96	no	—
512	C₂×D₄	—	166	12	no	—
513	C₂×D₄	—	166	24	no	—
514	C₂×D₄	C₂×D₃₃₂	1	24	yes	complemented
515	C₂×D₄	C₂³×D₈₃	1	12	yes	—
516	C₂²×C₄	—	83	12	no	—
517	C₂²×C₄	—	83	12	no	—
518	C₂²×C₄	—	83	1	no	—
519	C₂²×C₄	—	83	3	no	—
520	C₂²×C₄	—	83	12	no	—
521	C₂²×C₄	—	83	12	no	—
522	C₂²×C₄	—	83	24	no	—
523	C₂²×C₄	—	83	2	no	—
524	C₂²×C₄	—	83	6	no	—
525	C₂²×C₄	—	83	2	no	—
526	C₂²×C₄	—	83	8	no	—
527	C₂²×C₄	—	83	6	no	—
528	C₂²×C₄	—	166	12	no	—
529	C₂²×C₄	—	166	4	no	—
530	C₂²×C₄	—	166	12	no	—
531	C₂²×C₄	—	166	12	no	—
532	C₂²×C₄	—	166	12	no	—
533	C₂²×C₄	—	166	48	no	—
534	C₂²×C₄	—	166	48	no	—
535	C₂²×C₄	—	166	48	no	—
536	C₂²×C₄	C₂×D₃₃₂	1	24	yes	complemented
537	C₂²×C₄	C₂³×D₈₃	1	24	yes	—
538	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
539	C₂²×C₄	C₂³×D₈₃	1	3	yes	—
540	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
541	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
542	C₄⋊C₄	—	83	16	no	—
543	C₄⋊C₄	—	83	48	no	—
544	C₄⋊C₄	C₂³×D₈₃	1	8	yes	—
545	C₄⋊C₄	C₂³×D₈₃	1	24	yes	—
546	C₂²⋊C₄	—	83	16	no	—
547	C₂²⋊C₄	—	83	16	no	—
548	C₂²⋊C₄	—	83	48	no	—
549	C₂²⋊C₄	—	83	48	no	—
550	C₂²⋊C₄	C₂³×D₈₃	1	8	yes	—
551	C₂²⋊C₄	C₂³×D₈₃	1	24	yes	—
552	C₄²	C₂³×D₈₃	1	24	yes	—
553	C₄²	C₂³×D₈₃	1	8	yes	—
554	C₂³	—	4	6	no	—
555	C₂³	—	332	12	no	—
556	C₂³	—	332	6	no	—
557	C₂³	—	332	24	no	—
558	C₂³	—	332	48	no	—
559	C₂³	—	83	2	no	—
560	C₂³	—	83	6	no	—
561	C₂³	—	83	8	no	—
562	C₂³	—	166	24	no	—
563	C₂³	—	166	4	no	—
564	C₂³	—	166	6	no	—
565	C₂³	—	166	24	no	—
566	C₂³	—	166	24	no	—
567	C₂³	—	166	2	no	—
568	C₂³	C₂²×D₃₃₂	1	12	yes	—
569	C₂³	C₂⁴×D₈₃	1	1	yes	characteristic
570	C₂³	C₂⁴×D₈₃	1	6	yes	—
571	Q₈	—	166	8	no	—
572	Q₈	—	166	24	no	—
573	Q₈	—	166	24	no	—
574	Q₈	C₂²×D₃₃₂	1	16	yes	—
575	D₄	—	332	48	no	—
576	D₄	—	166	32	no	—
577	D₄	—	166	16	no	—
578	D₄	—	166	48	no	—
579	D₄	—	166	48	no	—
580	D₄	—	166	8	no	—
581	D₄	—	166	24	no	—
582	D₄	—	166	24	no	—
583	D₄	C₂²×D₃₃₂	1	48	yes	—
584	C₂×C₄	—	4	24	no	—
585	C₂×C₄	—	83	2	no	—
586	C₂×C₄	—	83	8	no	—
587	C₂×C₄	—	83	6	no	—
588	C₂×C₄	—	166	2	no	—
589	C₂×C₄	—	166	6	no	—
590	C₂×C₄	—	166	24	no	—
591	C₂×C₄	—	166	24	no	—
592	C₂×C₄	—	166	4	no	—
593	C₂×C₄	—	166	4	no	—
594	C₂×C₄	—	166	24	no	—
595	C₂×C₄	—	166	24	no	—
596	C₂×C₄	—	166	12	no	—
597	C₂×C₄	—	166	16	no	—
598	C₂×C₄	—	166	12	no	—
599	C₂×C₄	—	166	48	no	—
600	C₂×C₄	C₂²×D₃₃₂	1	4	yes	—
601	C₂×C₄	C₂²×D₃₃₂	1	24	yes	—
602	C₂×C₄	C₂²×D₃₃₂	1	12	yes	—
603	C₂×C₄	C₂²×D₃₃₂	1	24	yes	—
604	C₂×C₄	C₂⁴×D₈₃	1	16	yes	—
605	C₂×C₄	C₂⁴×D₈₃	1	6	yes	—
606	C₂×C₄	C₂⁴×D₈₃	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₈₃	1	1	yes	characteristic
608	C₂²	—	2	12	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	4	12	no	—
611	C₂²	—	332	12	no	—
612	C₂²	—	332	48	no	—
613	C₂²	—	83	4	no	—
614	C₂²	—	664	24	no	—
615	C₂²	—	166	8	no	—
616	C₂²	—	166	6	no	—
617	C₂²	—	166	8	no	—
618	C₂²	—	166	12	no	—
619	C₂²	—	166	16	no	—
620	C₂²	—	166	2	no	—
621	C₂²	—	166	2	no	—
622	C₂²	C₂³×D₃₃₂	1	2	yes	—
623	C₂²	C₂³×D₃₃₂	1	12	yes	—
624	C₂²	C₂⁵×D₈₃	1	1	yes	characteristic
625	C₄	—	2	16	no	—
626	C₄	—	166	2	no	—
627	C₄	—	166	6	no	—
628	C₄	—	166	8	no	—
629	C₄	C₂³×D₃₃₂	1	2	yes	—
630	C₄	C₂³×D₃₃₂	1	2	yes	—
631	C₄	C₂³×D₃₃₂	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	12	no	—
634	C₂	—	332	6	no	—
635	C₂	—	332	8	no	—
636	C₂	—	166	4	no	—
637	C₂	C₂⁴×D₃₃₂	1	1	yes	characteristic
638	C₂	#585×D₈₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁶
Frattini	C₂²	C₂⁵×D₈₃
Fitting	C₈₃×#3428	C₂
hypercenter	#3428	D₈₃
hypocenter	C₈₃	#62811
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #3428

Complements

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

N	H ≅ G/N	type
1. C₂×#19128537	C₂	semidirect
2. C₂²×#41×D₈₃	C₂	semidirect
3. #24921144	C₂	semidirect
4. #24921133	C₂	semidirect
5. #24921122	C₂	semidirect
6. #24921115	C₂	semidirect
7. #24921108	C₂	semidirect
8. #24921099	C₂	semidirect
9. #41×D₃₃₂	C₂	semidirect
10. #24920796	C₂	semidirect
11. C₂×#19128213	C₂	semidirect
12. C₈₃×#3428	C₂	semidirect
14. C₂×#14581840	C₂²	semidirect
15. C₂×#14581839	C₂²	semidirect
16. C₂×#14581838	C₂²	semidirect
17. C₂×#14581837	C₂²	semidirect
18. C₂²×#13050591	C₂²	semidirect
19. C₂²×#13050590	C₂²	semidirect
20. C₂²×#13050590	C₂²	semidirect
21. C₂²×#13050589	C₂²	semidirect
23. C₂×#41×D₈₃	C₂²	semidirect
24. C₂×#41×D₈₃	C₂²	semidirect
25. C₂×#41×D₈₃	C₂²	semidirect
26. C₂²×Q₈×D₈₃	C₂²	semidirect
27. C₂²×D₄×D₈₃	C₂²	semidirect
28. C₂³×C₄×D₈₃	C₂²	semidirect
29. #19128373	C₂²	semidirect
30. Q₈×D₃₃₂	C₂²	semidirect
31. #19128363	C₂²	semidirect
32. #19128363	C₂²	semidirect
33. #19128355	C₂²	semidirect
34. #19128346	C₂²	semidirect
35. #19128346	C₂²	semidirect
36. D₄×D₃₃₂	C₂²	semidirect
37. #19128282	C₂²	semidirect
38. #19128277	C₂²	semidirect
39. #19128277	C₂²	semidirect
40. #19128270	C₂²	semidirect
41. #19128270	C₂²	semidirect
42. #19128263	C₂²	semidirect
43. #19128251	C₂²	semidirect
44. #19128213	C₂²	semidirect
45. #19128213	C₂²	semidirect
46. #19128213	C₂²	semidirect
47. #19128213	C₂²	semidirect
48. #19128213	C₂²	semidirect
49. #19128213	C₂²	semidirect
50. #19128213	C₂²	semidirect
51. C₂×#14581776	C₂²	semidirect
52. C₂×#14581772	C₂²	semidirect
53. C₂×#14581767	C₂²	semidirect
54. C₂×#14581762	C₂²	semidirect
55. C₂×C₄×D₃₃₂	C₂²	semidirect
57. #520×C₈₃	C₂²	semidirect
58. #519×C₈₃	C₂²	semidirect
59. #518×C₈₃	C₂²	semidirect
60. C₄×#41×C₈₃	C₂²	semidirect
61. C₂×#117×C₈₃	C₂²	semidirect
69. C₂×#13050591	C₂³	semidirect
76. C₂×#13050590	C₂³	semidirect
77. C₂×#13050590	C₂³	semidirect
80. C₂×#13050589	C₂³	semidirect
85. C₂²×Dic₁₆₆	C₂³	semidirect
88. C₂×Q₈×D₈₃	C₂³	semidirect
91. C₂²×D₃₃₂	C₂³	semidirect
96. C₂×D₄×D₈₃	C₂³	semidirect
105. C₂²×C₄×D₈₃	C₂³	semidirect
106. #14581792	C₂³	semidirect
107. #14581789	C₂³	semidirect
108. #14581780	C₂³	semidirect
109. #14581780	C₂³	semidirect
112. #14581776	C₂³	semidirect
113. #14581776	C₂³	semidirect
116. #14581772	C₂³	semidirect
117. #14581772	C₂³	semidirect
118. #14581772	C₂³	semidirect
121. #14581767	C₂³	semidirect
122. #14581767	C₂³	semidirect
123. #14581767	C₂³	semidirect
124. #14581766	C₂³	semidirect
128. #14581762	C₂³	semidirect
131. C₄×D₃₃₂	C₂³	semidirect
132. C₄×D₃₃₂	C₂³	semidirect
133. C₂×C₄⋊Dic₈₃	C₂³	semidirect
135. C₂×(C₂×D₈₃)⋊C₄	C₂³	semidirect
136. C₂×#41×C₈₃	D₄	semidirect
142. C₄×Q₈×C₈₃	C₂³	semidirect
143. C₄×D₄×C₈₃	C₂³	semidirect
146. #117×C₈₃	C₂³	semidirect
147. #117×C₈₃	C₂³	semidirect
148. C₂×C₄⋊C₄×C₈₃	C₂³	semidirect
150. C₂×C₄²×C₈₃	C₂³	semidirect
216. #41×C₈₃	C₂×D₄	semidirect
217. #41×C₈₃	C₂×D₄	semidirect
218. C₂×Q₈×C₈₃	C₂×D₄	semidirect
220. C₂×D₄×C₈₃	C₂×D₄	semidirect
222. C₂²×C₄×C₈₃	C₂×D₄	semidirect
304. C₂×D₈₃	#585	semidirect
331. #3428	D₈₃	semidirect
332. C₈₃	#62811	semidirect
376. #520	C₂×D₈₃	semidirect
377. #519	C₂×D₈₃	semidirect
378. #518	C₂×D₈₃	semidirect
379. C₄×#41	C₂×D₈₃	semidirect
381. C₂×#117	C₂×D₈₃	semidirect
404. C₂×#41	D₃₃₂	semidirect
455. C₄×Q₈	C₂²×D₈₃	semidirect
460. C₄×D₄	C₂²×D₈₃	semidirect
463. #117	C₂²×D₈₃	semidirect
464. #117	C₂²×D₈₃	semidirect
466. C₂×C₄⋊C₄	C₂²×D₈₃	semidirect
470. C₂×C₄²	C₂²×D₈₃	semidirect
488. #41	C₂×D₃₃₂	semidirect
489. #41	C₂×D₃₃₂	semidirect
497. C₂×Q₈	C₂×D₃₃₂	semidirect
514. C₂×D₄	C₂×D₃₃₂	semidirect
536. C₂²×C₄	C₂×D₃₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19128537	2
C₂²×#41×D₈₃	2
#24921144	2
#24921133	2
#24921122	2
#24921115	2
#24921108	2
#24921099	2
#41×D₃₃₂	2
#24920796	2
C₂×#19128213	2
C₈₃×#3428	2
#62811	83