Subgroups — #24921950

Order 10624.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128453	C₂	1	2	yes	maximal, complemented
2	#19128452	C₂	1	2	yes	maximal, complemented
3	Q₈×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128429	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128427	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128426	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128420	C₂	1	1	yes	maximal, characteristic, complemented
8	#19128420	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128418	C₂	1	2	yes	maximal, complemented
10	#19128410	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128384	C₂	1	2	yes	maximal, complemented
12	#19128330	C₂	1	2	yes	maximal, complemented
13	#19128320	C₂	1	1	yes	maximal, characteristic
14	#19128316	C₂	1	1	yes	maximal, characteristic
15	#19128313	C₂	1	2	yes	maximal, complemented
16	#19128312	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128309	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128308	C₂	1	2	yes	maximal, complemented
19	#19128308	C₂	1	2	yes	maximal, complemented
20	#19128255	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128255	C₂	1	1	yes	maximal, characteristic, complemented
22	#19128230	C₂	1	1	yes	maximal, characteristic
23	#556×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#14581792	C₂²	1	1	yes	characteristic
25	#14581792	C₂²	1	2	yes	—
26	#14581791	C₂²	1	2	yes	—
27	#14581791	C₂²	1	2	yes	—
28	#14581791	C₂²	1	1	yes	characteristic
29	#14581791	C₂²	1	1	yes	characteristic
30	#14581791	C₂²	1	2	yes	—
31	#14581791	C₂²	1	1	yes	characteristic
32	#14581790	C₂²	1	1	yes	characteristic
33	#14581790	C₂²	1	2	yes	—
34	#14581790	C₂²	1	1	yes	characteristic
35	#14581790	C₂²	1	1	yes	characteristic
36	#14581787	C₂²	1	2	yes	—
37	#14581787	C₂²	1	2	yes	—
38	#14581787	C₂²	1	2	yes	—
39	#14581786	C₂²	1	2	yes	—
40	#14581785	C₂²	1	2	yes	—
41	#14581785	C₂²	1	2	yes	—
42	#14581785	C₂²	1	2	yes	—
43	#14581785	C₂²	1	2	yes	—
44	#14581785	C₂²	1	2	yes	—
45	#14581785	C₂²	1	2	yes	—
46	#14581785	C₂²	1	2	yes	—
47	#14581784	C₂²	1	2	yes	—
48	#14581784	C₂²	1	1	yes	characteristic
49	#14581784	C₂²	1	1	yes	characteristic
50	#14581784	C₂²	1	2	yes	—
51	#14581783	C₂²	1	1	yes	characteristic
52	#14581783	C₂²	1	2	yes	—
53	#14581783	C₂²	1	2	yes	—
54	#14581782	C₂²	1	2	yes	—
55	#14581782	C₂²	1	2	yes	—
56	#14581782	C₂²	1	2	yes	—
57	#14581782	C₂²	1	2	yes	—
58	#14581782	C₂²	1	2	yes	—
59	#14581782	C₂²	1	2	yes	—
60	#14581782	C₂²	1	2	yes	—
61	#14581782	C₂²	1	1	yes	characteristic
62	#14581782	C₂²	1	1	yes	characteristic
63	#14581782	C₂²	1	2	yes	—
64	#14581779	C₂²	1	1	yes	characteristic
65	#14581778	C₂²	1	2	yes	—
66	#14581778	C₂²	1	2	yes	—
67	#14581776	C₂²	1	2	yes	—
68	#14581775	C₂²	1	2	yes	—
69	#14581774	C₂²	1	2	yes	—
70	#14581772	C₂²	1	1	yes	characteristic
71	#14581772	C₂²	1	1	yes	characteristic
72	#14581771	C₂²	1	2	yes	—
73	#14581771	C₂²	1	2	yes	—
74	#14581770	C₂²	1	1	yes	characteristic
75	#14581770	C₂²	1	1	yes	characteristic
76	#14581770	C₂²	1	2	yes	—
77	#14581769	C₂²	1	2	yes	—
78	#14581769	C₂²	1	2	yes	—
79	#14581769	C₂²	1	2	yes	—
80	#14581769	C₂²	1	2	yes	—
81	#14581769	C₂²	1	2	yes	—
82	#14581768	C₂²	1	1	yes	characteristic
83	#14581768	C₂²	1	1	yes	characteristic
84	#14581768	C₂²	1	1	yes	characteristic
85	#14581763	C₂²	1	1	yes	characteristic
86	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
87	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
88	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
89	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₆₆	C₂²	1	2	yes	—
91	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₆₆	C₂²	1	2	yes	—
93	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
94	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
95	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
96	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
97	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
98	C₄×Dic₁₆₆	C₂²	1	2	yes	—
99	#14581757	C₂²	1	2	yes	—
100	#14581757	C₂²	1	2	yes	—
101	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
102	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
104	#14581749	C₂²	1	1	yes	characteristic
105	#14581749	C₂²	1	2	yes	—
106	#14581749	C₂²	1	1	yes	characteristic
107	#14581748	C₂²	1	2	yes	—
108	#14581748	C₂²	1	2	yes	—
109	#14581748	C₂²	1	2	yes	—
110	C₂×Dic₈₃⋊C₄	C₂²	1	2	yes	—
111	C₄²×D₈₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	#126×C₈₃	C₂²	1	2	yes	—
114	#126×C₈₃	C₂²	1	2	yes	—
115	#124×C₈₃	C₂²	1	1	yes	characteristic
116	#124×C₈₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
118	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
122	#117×C₈₃	C₂²	1	2	yes	—
123	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
124	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
125	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₆₆	C₂³	1	2	yes	—
128	C₂×Dic₁₆₆	C₂³	1	2	yes	—
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
131	C₂²×Dic₈₃	C₂³	1	2	yes	—
132	C₂²×Dic₈₃	C₂³	1	2	yes	—
133	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₈₃	C₂³	1	2	yes	—
142	C₄⋊Dic₈₃	C₂³	1	2	yes	—
143	C₄⋊Dic₈₃	C₂³	1	2	yes	—
144	C₄⋊Dic₈₃	C₂³	1	2	yes	—
145	C₄⋊Dic₈₃	C₂³	1	2	yes	—
146	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₈₃	C₂³	1	2	yes	—
148	C₄⋊Dic₈₃	C₂³	1	2	yes	—
149	Dic₈₃⋊C₄	C₂³	1	2	yes	—
150	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
151	Dic₈₃⋊C₄	C₂³	1	2	yes	—
152	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
153	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
154	Dic₈₃⋊C₄	C₂³	1	2	yes	—
155	Dic₈₃⋊C₄	C₂³	1	2	yes	—
156	Dic₈₃⋊C₄	C₂³	1	2	yes	—
157	Dic₈₃⋊C₄	C₂³	1	2	yes	—
158	Dic₈₃⋊C₄	C₂³	1	2	yes	—
159	Dic₈₃⋊C₄	C₂³	1	2	yes	—
160	Dic₈₃⋊C₄	C₂³	1	2	yes	—
161	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₈₃⋊C₄	C₂³	1	2	yes	—
163	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₈₃⋊C₄	C₂³	1	2	yes	—
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	2	yes	—
171	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	2	yes	—
174	Dic₈₃⋊C₄	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
180	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
187	C₄×Dic₈₃	C₂³	1	2	yes	—
188	C₄×Dic₈₃	C₂³	1	2	yes	—
189	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
190	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
191	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
192	C₄×Dic₈₃	C₂³	1	2	yes	—
193	C₄×Dic₈₃	C₂³	1	2	yes	—
194	C₄×Dic₈₃	C₂³	1	2	yes	—
195	C₄×Dic₈₃	C₂³	1	2	yes	—
196	C₄×Dic₈₃	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
199	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
200	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
201	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
204	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
217	C₄²×C₈₃	C₂³	1	2	yes	—
218	C₄²×C₈₃	C₂³	1	2	yes	—
219	C₄²×C₈₃	C₂³	1	1	yes	characteristic
220	C₄²×C₈₃	C₂³	1	1	yes	characteristic
221	C₄²×C₈₃	C₂³	1	1	yes	characteristic
222	C₂³×C₈₃	C₂⁴	1	2	yes	—
223	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
224	Q₈×C₈₃	—	2	2	no	—
225	Q₈×C₈₃	—	2	2	no	—
226	Q₈×C₈₃	—	4	1	no	—
227	D₄×C₈₃	—	2	2	no	—
228	C₂×C₄×C₈₃	—	4	2	no	—
229	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₈₃	—	4	2	no	—
240	C₂×Dic₈₃	—	2	4	no	—
241	C₂×Dic₈₃	—	4	2	no	—
242	C₂×Dic₈₃	C₂⁴	1	2	yes	—
243	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₈₃	C₂⁴	1	2	yes	—
247	C₂×Dic₈₃	C₂⁴	1	2	yes	—
248	C₂×Dic₈₃	C₂⁴	1	2	yes	—
249	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
253	C₄×D₈₃	—	2	2	no	—
254	C₄×D₈₃	—	2	2	no	—
255	C₄×D₈₃	—	4	1	no	—
256	Dic₁₆₆	—	2	2	no	—
257	Dic₁₆₆	—	2	2	no	—
258	Dic₁₆₆	—	2	2	no	—
259	Dic₁₆₆	—	4	2	no	—
260	Dic₁₆₆	—	4	1	no	—
261	Dic₁₆₆	—	4	2	no	—
262	Dic₁₆₆	—	4	2	no	—
263	C₂²×C₈₃	—	2	2	no	—
264	C₂²×C₈₃	—	2	2	no	—
265	C₂²×C₈₃	—	2	2	no	—
266	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
267	C₂×D₈₃	—	2	1	no	—
268	C₂×D₈₃	—	2	1	no	—
269	C₂×D₈₃	—	2	1	no	—
270	C₄×C₈₃	—	2	1	no	—
271	C₄×C₈₃	—	2	1	no	—
272	C₄×C₈₃	—	2	1	no	—
273	C₄×C₈₃	—	2	2	no	—
274	C₄×C₈₃	—	2	2	no	—
275	C₄×C₈₃	—	2	2	no	—
276	C₄×C₈₃	—	2	1	no	—
277	C₄×C₈₃	—	2	1	no	—
278	C₄×C₈₃	—	2	1	no	—
279	C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
280	Dic₈₃	—	2	1	no	—
281	Dic₈₃	—	2	1	no	—
282	Dic₈₃	—	2	2	no	—
283	Dic₈₃	—	2	1	no	—
284	Dic₈₃	—	2	2	no	—
285	Dic₈₃	—	2	1	no	—
286	Dic₈₃	—	2	1	no	—
287	Dic₈₃	—	2	2	no	—
288	Dic₈₃	—	2	2	no	—
289	Dic₈₃	—	2	1	no	—
290	Dic₈₃	2₋¹⁺⁴	1	2	yes	—
291	C₂×C₈₃	—	4	2	no	—
292	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
293	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
294	C₂×C₈₃	#585	1	1	yes	characteristic
295	D₈₃	—	4	1	no	—
296	#3555	—	83	1	no	maximal, Sylow
297	C₈₃	#3555	1	1	yes	characteristic, complemented, Sylow
298	#563	—	83	2	no	—
299	#563	—	83	2	no	—
300	Q₈²	—	83	1	no	—
301	#557	—	83	1	no	—
302	#557	—	83	1	no	—
303	#557	—	83	1	no	—
304	#556	—	83	2	no	—
305	#556	—	83	1	no	—
306	#556	—	83	1	no	—
307	#556	D₈₃	1	1	yes	characteristic, complemented
308	#554	—	83	1	no	—
309	#552	—	83	2	no	—
310	#544	—	83	2	no	—
311	#542	—	83	1	no	—
312	#542	—	83	1	no	—
313	#541	—	83	1	no	—
314	#541	—	83	2	no	—
315	#541	—	83	2	no	—
316	#541	—	83	1	no	—
317	#541	—	83	2	no	—
318	#533	—	83	1	no	—
319	#533	—	83	1	no	—
320	#529	—	83	1	no	—
321	C₄⋊Q₈	—	83	1	no	—
322	C₄⋊Q₈	—	83	1	no	—
323	C₄⋊Q₈	—	83	1	no	—
324	C₄⋊Q₈	—	83	2	no	—
325	C₄⋊Q₈	—	83	1	no	—
326	C₄⋊Q₈	—	83	1	no	—
327	C₄⋊Q₈	—	83	2	no	—
328	C₄⋊Q₈	—	83	1	no	—
329	C₄⋊Q₈	—	83	2	no	—
330	C₄⋊Q₈	—	83	2	no	—
331	C₄⋊Q₈	—	83	2	no	—
332	C₄⋊Q₈	—	83	1	no	—
333	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
334	#126	—	83	2	no	—
335	#126	—	83	2	no	—
336	#126	—	83	2	no	—
337	#126	—	83	2	no	—
338	#126	—	83	2	no	—
339	#126	—	83	2	no	—
340	#126	—	83	2	no	—
341	#126	—	83	2	no	—
342	#126	—	83	2	no	—
343	#126	—	83	2	no	—
344	#126	—	83	2	no	—
345	#126	C₂×D₈₃	1	2	yes	—
346	#126	C₂×D₈₃	1	2	yes	—
347	#125	—	83	1	no	—
348	#125	—	83	1	no	—
349	#125	—	83	2	no	—
350	#125	—	83	2	no	—
351	#125	—	83	2	no	—
352	#125	—	83	2	no	—
353	#125	—	83	2	no	—
354	#125	—	83	2	no	—
355	#125	—	83	2	no	—
356	#125	—	83	2	no	—
357	#125	—	83	1	no	—
358	#125	—	83	2	no	—
359	#125	—	83	2	no	—
360	#125	—	83	1	no	—
361	#125	—	83	2	no	—
362	#125	—	83	2	no	—
363	#125	—	83	1	no	—
364	#124	—	83	1	no	—
365	#124	—	83	2	no	—
366	#124	—	83	2	no	—
367	#124	C₂×D₈₃	1	1	yes	characteristic
368	#124	C₂×D₈₃	1	1	yes	characteristic
369	#123	—	83	2	no	—
370	#123	—	83	2	no	—
371	#123	—	83	2	no	—
372	C₂²⋊Q₈	—	83	1	no	—
373	C₂²⋊Q₈	—	83	1	no	—
374	C₂²⋊Q₈	—	83	1	no	—
375	C₂²⋊Q₈	—	83	2	no	—
376	C₂²⋊Q₈	—	83	2	no	—
377	C₂²⋊Q₈	—	83	1	no	—
378	C₂²⋊Q₈	—	83	1	no	—
379	C₂²⋊Q₈	—	83	2	no	—
380	C₂²⋊Q₈	—	83	1	no	—
381	C₂²⋊Q₈	—	83	1	no	—
382	C₂²⋊Q₈	—	83	2	no	—
383	C₂²⋊Q₈	—	83	2	no	—
384	C₂²⋊Q₈	—	83	2	no	—
385	C₂²⋊Q₈	—	83	2	no	—
386	C₂²⋊Q₈	—	83	2	no	—
387	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	—
388	#121	—	83	1	no	—
389	C₄×Q₈	—	83	1	no	—
390	C₄×Q₈	—	83	1	no	—
391	C₄×Q₈	—	83	1	no	—
392	C₄×Q₈	—	83	1	no	—
393	C₄×Q₈	—	83	2	no	—
394	C₄×Q₈	—	83	2	no	—
395	C₄×Q₈	—	83	2	no	—
396	C₄×Q₈	—	83	1	no	—
397	C₄×Q₈	—	83	1	no	—
398	C₄×Q₈	—	83	1	no	—
399	C₄×Q₈	—	83	1	no	—
400	C₄×Q₈	—	83	2	no	—
401	C₄×Q₈	—	83	1	no	—
402	C₄×Q₈	—	83	2	no	—
403	C₄×Q₈	—	83	1	no	—
404	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
405	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
407	C₄×D₄	—	83	1	no	—
408	C₄×D₄	—	83	1	no	—
409	C₄×D₄	—	83	2	no	—
410	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
411	#117	—	83	2	no	—
412	#117	—	83	2	no	—
413	#117	—	83	2	no	—
414	#117	—	83	1	no	—
415	#117	—	83	1	no	—
416	#117	—	83	2	no	—
417	#117	C₂×D₈₃	1	2	yes	—
418	C₂×C₄⋊C₄	—	83	2	no	—
419	C₂×C₄²	—	83	1	no	—
420	C₂×Q₈	—	83	1	no	—
421	C₂×Q₈	—	83	2	no	—
422	C₂×Q₈	—	83	2	no	—
423	C₂×Q₈	—	83	2	no	—
424	C₂×Q₈	—	83	1	no	—
425	C₂×Q₈	—	83	1	no	—
426	C₂×Q₈	—	83	1	no	—
427	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
429	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
430	C₂×D₄	—	83	2	no	—
431	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
432	C₂²×C₄	—	83	2	no	—
433	C₂²×C₄	—	83	1	no	—
434	C₂²×C₄	—	83	2	no	—
435	C₂²×C₄	—	83	1	no	—
436	C₂²×C₄	—	83	1	no	—
437	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
438	C₄⋊C₄	—	83	1	no	—
439	C₄⋊C₄	—	83	2	no	—
440	C₄⋊C₄	—	83	2	no	—
441	C₄⋊C₄	—	83	2	no	—
442	C₄⋊C₄	—	83	1	no	—
443	C₄⋊C₄	—	83	2	no	—
444	C₄⋊C₄	—	83	1	no	—
445	C₄⋊C₄	—	83	1	no	—
446	C₄⋊C₄	—	83	1	no	—
447	C₄⋊C₄	—	83	2	no	—
448	C₄⋊C₄	—	83	2	no	—
449	C₄⋊C₄	—	83	2	no	—
450	C₄⋊C₄	—	83	1	no	—
451	C₄⋊C₄	—	83	1	no	—
452	C₄⋊C₄	—	83	1	no	—
453	C₄⋊C₄	—	83	1	no	—
454	C₄⋊C₄	—	83	2	no	—
455	C₄⋊C₄	—	83	1	no	—
456	C₄⋊C₄	—	83	1	no	—
457	C₄⋊C₄	—	83	1	no	—
458	C₄⋊C₄	—	83	1	no	—
459	C₄⋊C₄	—	83	2	no	—
460	C₄⋊C₄	—	83	2	no	—
461	C₄⋊C₄	—	83	2	no	—
462	C₄⋊C₄	—	83	2	no	—
463	C₄⋊C₄	—	83	2	no	—
464	C₄⋊C₄	—	83	2	no	—
465	C₄⋊C₄	—	83	2	no	—
466	C₄⋊C₄	—	83	2	no	—
467	C₄⋊C₄	—	83	2	no	—
468	C₄⋊C₄	—	83	2	no	—
469	C₄⋊C₄	—	83	1	no	—
470	C₄⋊C₄	—	83	1	no	—
471	C₄⋊C₄	—	83	2	no	—
472	C₄⋊C₄	—	83	1	no	—
473	C₄⋊C₄	—	83	2	no	—
474	C₄⋊C₄	—	83	2	no	—
475	C₄⋊C₄	—	83	2	no	—
476	C₄⋊C₄	—	83	2	no	—
477	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
483	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
485	C₂²⋊C₄	—	83	2	no	—
486	C₂²⋊C₄	—	83	2	no	—
487	C₂²⋊C₄	—	83	2	no	—
488	C₂²⋊C₄	—	83	2	no	—
489	C₂²⋊C₄	—	83	2	no	—
490	C₂²⋊C₄	—	83	1	no	—
491	C₂²⋊C₄	—	83	1	no	—
492	C₂²⋊C₄	—	83	2	no	—
493	C₂²⋊C₄	—	83	2	no	—
494	C₂²⋊C₄	—	83	1	no	—
495	C₂²⋊C₄	—	83	1	no	—
496	C₂²⋊C₄	—	83	2	no	—
497	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
502	C₄²	—	83	1	no	—
503	C₄²	—	83	1	no	—
504	C₄²	—	83	1	no	—
505	C₄²	—	83	2	no	—
506	C₄²	—	83	2	no	—
507	C₄²	—	83	1	no	—
508	C₄²	—	83	1	no	—
509	C₄²	—	83	2	no	—
510	C₄²	—	83	2	no	—
511	C₄²	—	83	2	no	—
512	C₄²	—	83	2	no	—
513	C₄²	—	83	2	no	—
514	C₄²	C₂²×D₈₃	1	1	yes	characteristic
515	C₄²	C₂²×D₈₃	1	2	yes	—
516	C₄²	C₂²×D₈₃	1	1	yes	characteristic
517	C₄²	C₂²×D₈₃	1	1	yes	characteristic
518	C₄²	C₂²×D₈₃	1	2	yes	—
519	C₂³	—	83	1	no	—
520	C₂³	C₂³×D₈₃	1	2	yes	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	332	2	no	—
525	Q₈	—	332	2	no	—
526	Q₈	—	332	1	no	—
527	Q₈	—	332	2	no	—
528	Q₈	—	166	2	no	—
529	Q₈	—	166	2	no	—
530	Q₈	—	166	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	332	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	332	1	no	—
535	C₂×C₄	—	332	2	no	—
536	C₂×C₄	—	83	1	no	—
537	C₂×C₄	—	83	1	no	—
538	C₂×C₄	—	83	1	no	—
539	C₂×C₄	—	83	2	no	—
540	C₂×C₄	—	83	1	no	—
541	C₂×C₄	—	83	2	no	—
542	C₂×C₄	—	83	2	no	—
543	C₂×C₄	—	83	1	no	—
544	C₂×C₄	—	83	1	no	—
545	C₂×C₄	—	83	2	no	—
546	C₂×C₄	—	83	1	no	—
547	C₂×C₄	—	166	2	no	—
548	C₂×C₄	—	166	4	no	—
549	C₂×C₄	—	166	2	no	—
550	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
551	C₂×C₄	C₂³×D₈₃	1	2	yes	—
552	C₂×C₄	C₂³×D₈₃	1	2	yes	—
553	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₈₃	1	2	yes	—
558	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	166	1	no	—
564	C₂²	—	166	1	no	—
565	C₂²	—	166	1	no	—
566	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	83	2	no	—
577	C₄	—	166	2	no	—
578	C₄	—	166	1	no	—
579	C₄	—	166	1	no	—
580	C₄	—	166	1	no	—
581	C₄	—	166	2	no	—
582	C₄	—	166	1	no	—
583	C₄	—	166	1	no	—
584	C₄	—	166	2	no	—
585	C₄	—	166	2	no	—
586	C₄	—	166	1	no	—
587	C₄	#14581839	1	2	yes	—
588	C₂	—	4	2	no	—
589	C₂	—	332	1	no	—
590	C₂	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic
591	C₂	C₂×#14581839	1	1	yes	characteristic
592	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#556×C₈₃	C₂
prime radical	#14581763	C₂²
hypercenter	#556	D₈₃
hypocenter	C₈₃	#3555
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #19128453	C₂	semidirect
2. #19128452	C₂	semidirect
3. Q₈×Dic₁₆₆	C₂	semidirect
4. #19128429	C₂	semidirect
5. #19128427	C₂	semidirect
6. #19128426	C₂	semidirect
7. #19128420	C₂	semidirect
8. #19128420	C₂	semidirect
9. #19128418	C₂	semidirect
10. #19128410	C₂	semidirect
11. #19128384	C₂	semidirect
12. #19128330	C₂	semidirect
15. #19128313	C₂	semidirect
16. #19128312	C₂	semidirect
17. #19128309	C₂	semidirect
18. #19128308	C₂	semidirect
19. #19128308	C₂	semidirect
20. #19128255	C₂	semidirect
21. #19128255	C₂	semidirect
23. #556×C₈₃	C₂	semidirect
297. C₈₃	#3555	semidirect
307. #556	D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128453	2
#19128452	2
Q₈×Dic₁₆₆	2
#19128429	2
#19128427	2
#19128426	2
#19128420	2
#19128418	2
#19128410	2
#19128384	2
#19128330	2
#19128320	2
#19128316	2
#19128313	2
#19128312	2
#19128309	2
#19128308	2
#19128255	2
#19128230	2
#556×C₈₃	2
#3555	83