Subgroups — #24921951

Order 10624.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128452	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128430	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128429	C₂	1	2	yes	maximal, complemented
5	#19128424	C₂	1	2	yes	maximal, complemented
6	#19128424	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128422	C₂	1	2	yes	maximal, complemented
8	#19128411	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128385	C₂	1	2	yes	maximal, complemented
10	#19128328	C₂	1	2	yes	maximal, complemented
11	#19128322	C₂	1	2	yes	maximal
12	#19128313	C₂	1	2	yes	maximal, complemented
13	#19128312	C₂	1	2	yes	maximal, complemented
14	#19128310	C₂	1	4	yes	maximal, complemented
15	#19128258	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128235	C₂	1	1	yes	maximal, characteristic
17	#533×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#14581792	C₂²	1	2	yes	—
19	#14581792	C₂²	1	1	yes	characteristic
20	#14581792	C₂²	1	1	yes	characteristic
21	#14581792	C₂²	1	2	yes	—
22	#14581791	C₂²	1	2	yes	—
23	#14581791	C₂²	1	4	yes	—
24	#14581790	C₂²	1	4	yes	—
25	#14581787	C₂²	1	4	yes	—
26	#14581787	C₂²	1	4	yes	—
27	#14581787	C₂²	1	4	yes	—
28	#14581787	C₂²	1	4	yes	—
29	#14581786	C₂²	1	2	yes	—
30	#14581785	C₂²	1	4	yes	—
31	#14581785	C₂²	1	4	yes	—
32	#14581784	C₂²	1	2	yes	—
33	#14581784	C₂²	1	2	yes	—
34	#14581784	C₂²	1	1	yes	characteristic
35	#14581783	C₂²	1	2	yes	—
36	#14581783	C₂²	1	4	yes	—
37	#14581782	C₂²	1	4	yes	—
38	#14581782	C₂²	1	4	yes	—
39	#14581782	C₂²	1	4	yes	—
40	#14581782	C₂²	1	4	yes	—
41	#14581780	C₂²	1	2	yes	—
42	#14581780	C₂²	1	1	yes	characteristic
43	#14581778	C₂²	1	4	yes	—
44	#14581775	C₂²	1	2	yes	—
45	#14581774	C₂²	1	4	yes	—
46	#14581771	C₂²	1	2	yes	—
47	#14581771	C₂²	1	2	yes	—
48	#14581771	C₂²	1	1	yes	characteristic
49	#14581770	C₂²	1	4	yes	—
50	#14581770	C₂²	1	4	yes	—
51	#14581768	C₂²	1	4	yes	—
52	#14581768	C₂²	1	2	yes	—
53	#14581768	C₂²	1	2	yes	—
54	#14581766	C₂²	1	1	yes	characteristic
55	Q₈×Dic₈₃	C₂²	1	2	yes	—
56	Q₈×Dic₈₃	C₂²	1	2	yes	—
57	C₄×Dic₁₆₆	C₂²	1	2	yes	—
58	C₄×Dic₁₆₆	C₂²	1	2	yes	—
59	C₄×Dic₁₆₆	C₂²	1	2	yes	—
60	C₄×Dic₁₆₆	C₂²	1	2	yes	—
61	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
62	C₄×Dic₁₆₆	C₂²	1	2	yes	—
63	#14581757	C₂²	1	4	yes	—
64	C₄×D₃₃₂	C₂²	1	2	yes	—
65	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	—
67	#14581751	C₂²	1	2	yes	—
68	#14581750	C₂²	1	2	yes	—
69	#14581750	C₂²	1	4	yes	—
70	#14581749	C₂²	1	2	yes	—
71	C₄⋊C₄×D₈₃	C₂²	1	2	yes	—
72	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
73	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
74	#125×C₈₃	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
77	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
78	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
79	C₄×Q₈×C₈₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
81	#117×C₈₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
83	C₂×Dic₁₆₆	C₂³	1	2	yes	—
84	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
85	C₂×Dic₁₆₆	C₂³	1	2	yes	—
86	C₂×Dic₁₆₆	C₂³	1	4	yes	—
87	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
89	C₂×C₄×D₈₃	C₂³	1	2	yes	—
90	C₂×C₄×D₈₃	C₂³	1	4	yes	—
91	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
92	C₄⋊Dic₈₃	C₂³	1	4	yes	—
93	C₄⋊Dic₈₃	C₂³	1	2	yes	—
94	C₄⋊Dic₈₃	C₂³	1	2	yes	—
95	C₄⋊Dic₈₃	C₂³	1	2	yes	—
96	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₈₃	C₂³	1	2	yes	—
98	C₄⋊Dic₈₃	C₂³	1	4	yes	—
99	C₄⋊Dic₈₃	C₂³	1	4	yes	—
100	Dic₈₃⋊C₄	C₂³	1	4	yes	—
101	Dic₈₃⋊C₄	C₂³	1	4	yes	—
102	Dic₈₃⋊C₄	C₂³	1	4	yes	—
103	Dic₈₃⋊C₄	C₂³	1	4	yes	—
104	Dic₈₃⋊C₄	C₂³	1	4	yes	—
105	Dic₈₃⋊C₄	C₂³	1	4	yes	—
106	Dic₈₃⋊C₄	C₂³	1	4	yes	—
107	Dic₈₃⋊C₄	C₂³	1	2	yes	—
108	Dic₈₃⋊C₄	C₂³	1	2	yes	—
109	Dic₈₃⋊C₄	C₂³	1	2	yes	—
110	Dic₈₃⋊C₄	C₂³	1	2	yes	—
111	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
112	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
113	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
119	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
120	C₄×Dic₈₃	C₂³	1	4	yes	—
121	C₄×Dic₈₃	C₂³	1	4	yes	—
122	C₄×Dic₈₃	C₂³	1	4	yes	—
123	C₄×Dic₈₃	C₂³	1	4	yes	—
124	C₄×Dic₈₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
128	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
132	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
133	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
134	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
135	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
136	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
138	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
139	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
140	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
142	C₄²×C₈₃	C₂³	1	1	yes	characteristic
143	C₄²×C₈₃	C₂³	1	2	yes	—
144	C₄²×C₈₃	C₂³	1	1	yes	characteristic
145	C₄²×C₈₃	C₂³	1	2	yes	—
146	C₄²×C₈₃	C₂³	1	1	yes	characteristic
147	C₄²×C₈₃	C₂³	1	1	yes	characteristic
148	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
149	C₂²×D₈₃	C₂⁴	1	2	yes	—
150	Q₈×C₈₃	—	2	2	no	—
151	Q₈×C₈₃	—	2	2	no	—
152	Q₈×C₈₃	—	4	2	no	—
153	C₂×C₄×C₈₃	—	2	2	no	—
154	C₂×C₄×C₈₃	—	2	2	no	—
155	C₂×C₄×C₈₃	—	4	1	no	—
156	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₈₃	—	4	2	no	—
167	C₂×Dic₈₃	C₂⁴	1	4	yes	—
168	C₂×Dic₈₃	C₂⁴	1	2	yes	—
169	C₂×Dic₈₃	C₂⁴	1	2	yes	—
170	C₂×Dic₈₃	C₂⁴	1	2	yes	—
171	C₂×Dic₈₃	C₂⁴	1	4	yes	—
172	D₃₃₂	—	2	2	no	—
173	C₄×D₈₃	—	2	4	no	—
174	C₄×D₈₃	—	4	4	no	—
175	Dic₁₆₆	—	2	4	no	—
176	Dic₁₆₆	—	2	2	no	—
177	Dic₁₆₆	—	4	2	no	—
178	Dic₁₆₆	—	4	4	no	—
179	C₂²×C₈₃	—	2	1	no	—
180	C₂²×C₈₃	—	2	1	no	—
181	C₂²×C₈₃	—	2	1	no	—
182	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
183	C₂×D₈₃	—	2	2	no	—
184	C₂×D₈₃	—	2	2	no	—
185	C₂×D₈₃	—	2	2	no	—
186	C₄×C₈₃	—	2	1	no	—
187	C₄×C₈₃	—	2	1	no	—
188	C₄×C₈₃	—	2	2	no	—
189	C₄×C₈₃	—	2	2	no	—
190	C₄×C₈₃	—	2	1	no	—
191	C₄×C₈₃	—	2	2	no	—
192	C₄×C₈₃	—	2	2	no	—
193	C₄×C₈₃	—	2	1	no	—
194	C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
195	C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
196	Dic₈₃	—	2	4	no	—
197	Dic₈₃	—	2	2	no	—
198	Dic₈₃	—	2	2	no	—
199	Dic₈₃	—	2	4	no	—
200	Dic₈₃	—	2	2	no	—
201	C₂×C₈₃	—	4	1	no	—
202	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₈₃	#585	1	1	yes	characteristic
205	D₈₃	—	4	2	no	—
206	#3555	—	83	1	no	maximal, Sylow
207	C₈₃	#3555	1	1	yes	characteristic, complemented, Sylow
208	#563	—	83	4	no	—
209	Q₈²	—	83	1	no	—
210	#557	—	83	2	no	—
211	#557	—	83	1	no	—
212	#556	—	83	2	no	—
213	#556	—	83	2	no	—
214	#556	—	83	1	no	—
215	#554	—	83	1	no	—
216	#552	—	83	2	no	—
217	#544	—	83	2	no	—
218	#542	—	83	2	no	—
219	#541	—	83	2	no	—
220	#541	—	83	4	no	—
221	#541	—	83	2	no	—
222	#533	—	83	1	no	—
223	#533	D₈₃	1	1	yes	characteristic, complemented
224	#529	—	83	1	no	—
225	C₄⋊Q₈	—	83	4	no	—
226	C₄⋊Q₈	—	83	4	no	—
227	C₄⋊Q₈	—	83	2	no	—
228	C₄⋊Q₈	—	83	1	no	—
229	C₄⋊Q₈	—	83	1	no	—
230	C₄⋊Q₈	—	83	2	no	—
231	C₄⋊Q₈	—	83	2	no	—
232	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
234	#126	—	83	4	no	—
235	#126	—	83	4	no	—
236	#126	—	83	4	no	—
237	#126	—	83	4	no	—
238	#126	—	83	4	no	—
239	#126	—	83	4	no	—
240	#126	—	83	2	no	—
241	#125	—	83	4	no	—
242	#125	—	83	4	no	—
243	#125	—	83	4	no	—
244	#125	—	83	4	no	—
245	#125	—	83	4	no	—
246	#125	—	83	2	no	—
247	#125	—	83	1	no	—
248	#125	—	83	2	no	—
249	#125	—	83	2	no	—
250	#125	C₂×D₈₃	1	2	yes	—
251	#124	—	83	4	no	—
252	#124	—	83	1	no	—
253	#124	—	83	2	no	—
254	#123	—	83	2	no	—
255	#123	—	83	4	no	—
256	C₂²⋊Q₈	—	83	2	no	—
257	C₂²⋊Q₈	—	83	2	no	—
258	C₂²⋊Q₈	—	83	4	no	—
259	C₂²⋊Q₈	—	83	1	no	—
260	C₂²⋊Q₈	—	83	2	no	—
261	C₂²⋊Q₈	—	83	2	no	—
262	C₂²⋊Q₈	—	83	4	no	—
263	C₂²⋊Q₈	—	83	4	no	—
264	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
265	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
266	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	—
267	#121	—	83	1	no	—
268	C₄×Q₈	—	83	2	no	—
269	C₄×Q₈	—	83	2	no	—
270	C₄×Q₈	—	83	4	no	—
271	C₄×Q₈	—	83	1	no	—
272	C₄×Q₈	—	83	2	no	—
273	C₄×Q₈	—	83	2	no	—
274	C₄×Q₈	—	83	2	no	—
275	C₄×Q₈	—	83	2	no	—
276	C₄×Q₈	—	83	2	no	—
277	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
278	C₄×Q₈	C₂×D₈₃	1	2	yes	—
279	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
280	C₄×D₄	—	83	2	no	—
281	C₄×D₄	—	83	1	no	—
282	C₄×D₄	—	83	2	no	—
283	#117	—	83	2	no	—
284	#117	—	83	4	no	—
285	#117	—	83	2	no	—
286	#117	—	83	2	no	—
287	#117	C₂×D₈₃	1	2	yes	—
288	C₂×C₄⋊C₄	—	83	2	no	—
289	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
290	C₂×Q₈	—	83	2	no	—
291	C₂×Q₈	—	83	4	no	—
292	C₂×Q₈	—	83	1	no	—
293	C₂×Q₈	—	83	2	no	—
294	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
295	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
296	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
297	C₂×D₄	—	83	2	no	—
298	C₂×D₄	—	83	1	no	—
299	C₂²×C₄	—	83	4	no	—
300	C₂²×C₄	—	83	2	no	—
301	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
304	C₄⋊C₄	—	83	2	no	—
305	C₄⋊C₄	—	83	4	no	—
306	C₄⋊C₄	—	83	2	no	—
307	C₄⋊C₄	—	83	2	no	—
308	C₄⋊C₄	—	83	4	no	—
309	C₄⋊C₄	—	83	2	no	—
310	C₄⋊C₄	—	83	1	no	—
311	C₄⋊C₄	—	83	2	no	—
312	C₄⋊C₄	—	83	2	no	—
313	C₄⋊C₄	—	83	1	no	—
314	C₄⋊C₄	—	83	4	no	—
315	C₄⋊C₄	—	83	4	no	—
316	C₄⋊C₄	—	83	4	no	—
317	C₄⋊C₄	—	83	4	no	—
318	C₄⋊C₄	—	83	4	no	—
319	C₄⋊C₄	—	83	2	no	—
320	C₄⋊C₄	—	83	4	no	—
321	C₄⋊C₄	—	83	2	no	—
322	C₄⋊C₄	—	83	4	no	—
323	C₄⋊C₄	—	83	4	no	—
324	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
326	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
327	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
328	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
329	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
330	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
331	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
332	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
333	C₂²⋊C₄	—	83	4	no	—
334	C₂²⋊C₄	—	83	2	no	—
335	C₂²⋊C₄	—	83	2	no	—
336	C₂²⋊C₄	—	83	2	no	—
337	C₂²⋊C₄	—	83	2	no	—
338	C₂²⋊C₄	—	83	4	no	—
339	C₂²⋊C₄	—	83	4	no	—
340	C₂²⋊C₄	—	83	2	no	—
341	C₂²⋊C₄	—	83	4	no	—
342	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
344	C₄²	—	83	4	no	—
345	C₄²	—	83	2	no	—
346	C₄²	—	83	4	no	—
347	C₄²	—	83	4	no	—
348	C₄²	—	83	4	no	—
349	C₄²	C₂²×D₈₃	1	1	yes	characteristic
350	C₄²	C₂²×D₈₃	1	1	yes	characteristic
351	C₄²	C₂²×D₈₃	1	1	yes	characteristic
352	C₄²	C₂²×D₈₃	1	1	yes	characteristic
353	C₄²	C₂²×D₈₃	1	2	yes	—
354	C₄²	C₂²×D₈₃	1	2	yes	—
355	C₂³	—	83	2	no	—
356	C₂³	C₂³×D₈₃	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	332	2	no	—
361	Q₈	—	332	4	no	—
362	Q₈	—	166	2	no	—
363	Q₈	—	166	4	no	—
364	D₄	—	332	2	no	—
365	D₄	—	166	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	332	4	no	—
370	C₂×C₄	—	83	4	no	—
371	C₂×C₄	—	83	2	no	—
372	C₂×C₄	—	83	2	no	—
373	C₂×C₄	—	83	2	no	—
374	C₂×C₄	—	83	4	no	—
375	C₂×C₄	—	166	4	no	—
376	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₈₃	1	2	yes	—
378	C₂×C₄	C₂³×D₈₃	1	2	yes	—
379	C₂×C₄	C₂³×D₈₃	1	2	yes	—
380	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₈₃	1	2	yes	—
384	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	166	2	no	—
390	C₂²	—	166	2	no	—
391	C₂²	—	166	2	no	—
392	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	166	2	no	—
402	C₄	—	166	4	no	—
403	C₄	—	166	2	no	—
404	C₄	—	166	4	no	—
405	C₄	—	166	2	no	—
406	C₄	#14581839	1	2	yes	—
407	C₄	#14581840	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	332	2	no	—
410	C₂	C₂×#14581839	1	1	yes	characteristic
411	C₂	C₂×#14581840	1	1	yes	characteristic
412	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#533×C₈₃	C₂
prime radical	#14581766	C₂²
hypercenter	#533	D₈₃
hypocenter	C₈₃	#3555
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #19128452	C₂	semidirect
2. Q₈×Dic₁₆₆	C₂	semidirect
3. #19128430	C₂	semidirect
4. #19128429	C₂	semidirect
5. #19128424	C₂	semidirect
6. #19128424	C₂	semidirect
7. #19128422	C₂	semidirect
8. #19128411	C₂	semidirect
9. #19128385	C₂	semidirect
10. #19128328	C₂	semidirect
12. #19128313	C₂	semidirect
13. #19128312	C₂	semidirect
14. #19128310	C₂	semidirect
15. #19128258	C₂	semidirect
17. #533×C₈₃	C₂	semidirect
207. C₈₃	#3555	semidirect
223. #533	D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128452	2
Q₈×Dic₁₆₆	2
#19128430	2
#19128429	2
#19128424	2
#19128422	2
#19128411	2
#19128385	2
#19128328	2
#19128322	2
#19128313	2
#19128312	2
#19128310	2
#19128258	2
#19128235	2
#533×C₈₃	2
#3555	83