Subgroups — #35310404

Order 21248.

782 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×#19127728	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#19127465	C₂	1	1	yes	maximal, characteristic
4	#24907179	C₂	1	1	yes	maximal, characteristic
5	C₂×#19127461	C₂	1	1	yes	maximal, characteristic
6	#24907161	C₂	1	1	yes	maximal, characteristic
7	C₂×#339×C₈₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×#13050574	C₂²	1	1	yes	characteristic
9	C₂³×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#14581751	C₂²	1	1	yes	characteristic
12	#19127728	—	2	2	no	—
13	#19127728	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
15	C₂×C₄×C₈₃⋊C₈	—	2	2	no	—
16	C₂×C₄×C₈₃⋊C₈	—	2	2	no	—
17	C₂×C₄×C₈₃⋊C₈	—	2	2	no	—
18	#19127465	—	2	2	no	—
19	#19127463	C₄	1	4	yes	complemented
20	#19127461	—	2	2	no	—
21	#19127455	—	2	2	no	—
22	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
25	#339×C₈₃	C₄	1	4	yes	complemented
26	C₂×#13050574	—	2	1	no	—
27	C₂×#13050574	—	2	1	no	—
28	C₂×#13050574	—	2	1	no	—
29	C₂×#13050574	—	2	1	no	—
30	C₂×#13050574	—	2	1	no	—
31	C₂×#13050574	C₂×C₄	1	2	yes	—
32	C₂²×C₈₃⋊C₈	—	2	1	no	—
33	C₂²×C₈₃⋊C₈	—	2	1	no	—
34	C₂²×C₈₃⋊C₈	—	2	1	no	—
35	C₂²×C₈₃⋊C₈	—	2	1	no	—
36	C₂²×C₈₃⋊C₈	—	2	1	no	—
37	C₂²×C₈₃⋊C₈	—	2	1	no	—
38	C₂²×C₈₃⋊C₈	—	2	1	no	—
39	C₂²×C₈₃⋊C₈	—	2	1	no	—
40	C₂²×C₈₃⋊C₈	—	2	1	no	—
41	C₂²×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₈₃⋊C₈	D₄	1	2	yes	—
44	C₂²×C₈₃⋊C₈	D₄	1	2	yes	—
45	C₂²×C₈₃⋊C₈	D₄	1	2	yes	—
46	C₂²×C₈₃⋊C₈	Q₈	1	2	yes	—
47	#14581751	—	2	1	no	—
48	#14581751	—	2	1	no	—
49	#14581751	—	2	1	no	—
50	#14581751	—	2	1	no	—
51	C₂×C₄⋊Dic₈₃	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₈₃	—	2	1	no	—
53	C₂×C₄×Dic₈₃	—	2	1	no	—
54	C₄⋊(C₈₃⋊C₈)	—	2	8	no	—
55	C₄×C₈₃⋊C₈	—	2	8	no	—
56	C₂³×C₄×C₈₃	—	2	1	no	—
57	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₈₃	—	2	1	no	—
59	C₂×M₁₆×C₈₃	—	2	1	no	—
60	C₂×M₁₆×C₈₃	—	2	1	no	—
61	C₂×M₁₆×C₈₃	—	2	1	no	—
62	C₂×M₁₆×C₈₃	—	2	1	no	—
63	C₂×M₁₆×C₈₃	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₈₃	—	2	1	no	—
65	#117×C₈₃	—	2	1	no	—
66	#117×C₈₃	—	2	1	no	—
67	#117×C₈₃	C₂×C₄	1	2	yes	—
68	#117×C₈₃	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
71	C₂×C₄²×C₈₃	—	2	1	no	—
72	C₂×C₄²×C₈₃	—	2	1	no	—
73	C₂×C₄²×C₈₃	—	2	1	no	—
74	C₂×C₄²×C₈₃	—	2	1	no	—
75	C₂×C₄²×C₈₃	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₈₃	D₄	1	2	yes	—
77	C₂×C₄²×C₈₃	Q₈	1	2	yes	—
78	C₂²×Dic₈₃	—	2	2	no	—
79	#13050574	—	2	2	no	—
80	#13050574	—	2	2	no	—
81	#13050574	—	4	1	no	—
82	#13050574	—	4	1	no	—
83	C₂×C₈₃⋊C₈	—	2	2	no	—
84	C₂×C₈₃⋊C₈	—	2	2	no	—
85	C₂×C₈₃⋊C₈	—	2	2	no	—
86	C₂×C₈₃⋊C₈	—	2	2	no	—
87	C₂×C₈₃⋊C₈	—	2	2	no	—
88	C₂×C₈₃⋊C₈	—	2	2	no	—
89	C₂×C₈₃⋊C₈	—	2	2	no	—
90	C₂×C₈₃⋊C₈	—	2	2	no	—
91	C₂×C₈₃⋊C₈	—	2	2	no	—
92	C₂×C₈₃⋊C₈	—	2	2	no	—
93	C₂×C₈₃⋊C₈	—	2	2	no	—
94	C₂×C₈₃⋊C₈	—	2	2	no	—
95	C₂×C₈₃⋊C₈	—	2	2	no	—
96	C₂×C₈₃⋊C₈	—	4	1	no	—
97	C₂×C₈₃⋊C₈	—	4	1	no	—
98	C₂×C₈₃⋊C₈	C₂²⋊C₄	1	4	yes	—
99	C₂×C₈₃⋊C₈	C₄⋊C₄	1	4	yes	—
100	C₄⋊Dic₈₃	—	2	2	no	—
101	C₄⋊Dic₈₃	—	2	2	no	—
102	C₂²⋊Dic₈₃	—	4	1	no	—
103	C₂²⋊Dic₈₃	—	4	1	no	—
104	C₄×Dic₈₃	—	4	1	no	—
105	C₄×Dic₈₃	—	4	1	no	—
106	C₂⁴×C₈₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₈₃	—	2	8	no	—
108	C₂²×C₄×C₈₃	—	2	2	no	—
109	C₂²×C₄×C₈₃	—	2	2	no	—
110	C₂²×C₄×C₈₃	—	2	2	no	—
111	C₂²×C₄×C₈₃	—	2	2	no	—
112	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
126	M₁₆×C₈₃	—	2	2	no	—
127	M₁₆×C₈₃	—	2	2	no	—
128	M₁₆×C₈₃	—	4	1	no	—
129	M₁₆×C₈₃	—	4	1	no	—
130	C₂×C₈×C₈₃	—	2	2	no	—
131	C₂×C₈×C₈₃	—	4	1	no	—
132	C₂×C₈×C₈₃	—	4	1	no	—
133	C₄⋊C₄×C₈₃	—	2	2	no	—
134	C₄⋊C₄×C₈₃	C₄²	1	4	yes	—
135	C₂²⋊C₄×C₈₃	—	2	2	no	—
136	C₂²⋊C₄×C₈₃	—	2	2	no	—
137	C₄²×C₈₃	—	2	2	no	—
138	C₄²×C₈₃	—	2	2	no	—
139	C₄²×C₈₃	—	2	2	no	—
140	C₄²×C₈₃	—	2	2	no	—
141	C₄²×C₈₃	—	2	2	no	—
142	C₄²×C₈₃	C₄⋊C₄	1	4	yes	—
143	C₂³×C₈₃	—	2	4	no	—
144	C₂³×C₈₃	#117	1	1	yes	characteristic
145	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂³×C₈₃	#123	1	1	yes	characteristic
149	C₂³×C₈₃	#125	1	1	yes	characteristic
150	C₂³×C₈₃	#126	1	1	yes	characteristic
151	C₂×C₄×C₈₃	—	2	8	no	—
152	C₂×C₄×C₈₃	—	2	8	no	—
153	C₂×C₄×C₈₃	—	2	8	no	—
154	C₂×C₄×C₈₃	—	2	4	no	—
155	C₂×C₄×C₈₃	—	2	4	no	—
156	C₂×C₄×C₈₃	—	4	4	no	—
157	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
162	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
163	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
174	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
180	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
181	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
182	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
183	C₂×C₄×C₈₃	#126	1	1	yes	characteristic
184	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×Dic₈₃	—	4	2	no	—
186	C₂×Dic₈₃	—	4	4	no	—
187	C₈×C₈₃	—	4	2	no	—
188	C₈₃⋊C₈	—	2	4	no	—
189	C₈₃⋊C₈	—	2	4	no	—
190	C₈₃⋊C₈	—	4	2	no	—
191	C₂²×C₈₃	—	2	2	no	—
192	C₂²×C₈₃	—	2	2	no	—
193	C₂²×C₈₃	—	2	2	no	—
194	C₂²×C₈₃	—	2	2	no	—
195	C₂²×C₈₃	—	2	2	no	—
196	C₂²×C₈₃	—	2	2	no	—
197	C₂²×C₈₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₈₃	#385	1	1	yes	characteristic
199	C₂²×C₈₃	#387	1	1	yes	characteristic
200	C₂²×C₈₃	#387	1	1	yes	characteristic
201	C₂²×C₈₃	#387	1	1	yes	characteristic
202	C₂²×C₈₃	#388	1	1	yes	characteristic
203	C₂²×C₈₃	#389	1	1	yes	characteristic
204	C₂²×C₈₃	#443	1	4	yes	—
205	C₄×C₈₃	—	2	8	no	—
206	C₄×C₈₃	—	4	4	no	—
207	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
208	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₈₃	#385	1	1	yes	characteristic
210	C₄×C₈₃	#386	1	1	yes	characteristic
211	C₄×C₈₃	#387	1	1	yes	characteristic
212	C₄×C₈₃	#388	1	1	yes	characteristic
213	C₄×C₈₃	#389	1	1	yes	characteristic
214	C₄×C₈₃	#391	1	1	yes	characteristic
215	Dic₈₃	—	8	2	no	—
216	#10882	—	83	1	no	maximal, Sylow
217	C₂×C₈₃	—	2	1	no	—
218	C₂×C₈₃	—	2	1	no	—
219	C₂×C₈₃	—	2	1	no	—
220	C₂×C₈₃	—	2	1	no	—
221	C₂×C₈₃	#1436	1	1	yes	characteristic
222	C₂×C₈₃	#1764	1	2	yes	—
223	C₂×C₈₃	#1937	1	2	yes	—
224	C₂×C₈₃	#1945	1	2	yes	—
225	C₂×#424	—	83	1	no	—
226	C₂²×C₄×C₈	—	83	1	no	—
227	C₂×#341	—	83	1	no	—
228	#1735	—	83	1	no	—
229	C₂×#339	—	83	1	no	—
230	C₂×#339	D₈₃	1	1	yes	characteristic
231	#1729	—	83	1	no	—
232	C₈₃	#10882	1	1	yes	characteristic, complemented, Sylow
233	C₂²×M₁₆	—	83	1	no	—
234	C₂²×M₁₆	C₂×D₈₃	1	1	yes	characteristic
235	C₂³×C₈	—	83	1	no	—
236	C₂³×C₈	—	83	1	no	—
237	C₂×#117	—	83	1	no	—
238	C₂×#117	C₂×D₈₃	1	1	yes	characteristic
239	C₂²×C₄²	C₂×D₈₃	1	1	yes	characteristic
240	#424	—	83	4	no	—
241	#424	—	166	2	no	—
242	C₂×C₄⋊C₈	—	166	2	no	—
243	C₂×C₄×C₈	—	166	2	no	—
244	C₂×C₄×C₈	—	166	2	no	—
245	C₂×C₄×C₈	—	166	2	no	—
246	#341	—	166	2	no	—
247	#340	—	83	4	no	—
248	#339	—	166	2	no	—
249	#339	Dic₈₃	1	4	yes	complemented
250	#336	—	166	2	no	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	83	2	no	—
259	C₂×M₁₆	—	166	1	no	—
260	C₂×M₁₆	—	166	1	no	—
261	C₂×M₁₆	—	166	1	no	—
262	C₂×M₁₆	—	166	1	no	—
263	C₂×M₁₆	—	166	1	no	—
264	C₂×M₁₆	C₂×Dic₈₃	1	2	yes	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	83	2	no	—
267	C₂²×C₈	—	83	2	no	—
268	C₂²×C₈	—	83	2	no	—
269	C₂²×C₈	—	83	2	no	—
270	C₂²×C₈	—	83	2	no	—
271	C₂²×C₈	—	83	2	no	—
272	C₂²×C₈	—	166	1	no	—
273	C₂²×C₈	—	166	1	no	—
274	C₂²×C₈	—	166	1	no	—
275	C₂²×C₈	—	166	1	no	—
276	C₂²×C₈	—	166	1	no	—
277	C₂²×C₈	—	166	1	no	—
278	C₂²×C₈	—	166	1	no	—
279	C₂²×C₈	—	166	1	no	—
280	C₂²×C₈	—	166	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	166	1	no	—
284	#117	—	166	1	no	—
285	#117	—	166	1	no	—
286	#117	—	166	1	no	—
287	#117	C₄×D₈₃	1	2	yes	—
288	#117	C₂×Dic₈₃	1	2	yes	—
289	C₂×C₄⋊C₄	—	83	2	no	—
290	C₂×C₄⋊C₄	C₄×D₈₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	166	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	166	1	no	—
298	C₂×C₄²	Dic₁₆₆	1	2	yes	—
299	C₂×C₄²	D₃₃₂	1	2	yes	—
300	C₂×C₄²	C₂×Dic₈₃	1	2	yes	—
301	C₄⋊C₈	—	166	8	no	—
302	C₄×C₈	—	166	8	no	—
303	C₂⁴	#13050589	1	1	yes	characteristic
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	166	2	no	—
310	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
317	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
319	C₂²×C₄	#13050589	1	1	yes	characteristic
320	C₂²×C₄	#13050589	1	1	yes	characteristic
321	C₂²×C₄	#13050590	1	1	yes	characteristic
322	C₂²×C₄	#13050590	1	1	yes	characteristic
323	C₂²×C₄	#13050591	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	332	1	no	—
329	M₁₆	—	332	1	no	—
330	M₁₆	—	166	2	no	—
331	M₁₆	—	166	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	332	1	no	—
336	C₂×C₈	—	332	1	no	—
337	C₂×C₈	—	83	4	no	—
338	C₂×C₈	—	83	4	no	—
339	C₂×C₈	—	166	2	no	—
340	C₂×C₈	—	166	2	no	—
341	C₂×C₈	—	166	2	no	—
342	C₂×C₈	—	166	2	no	—
343	C₂×C₈	—	166	2	no	—
344	C₂×C₈	—	166	2	no	—
345	C₂×C₈	—	166	2	no	—
346	C₂×C₈	—	166	2	no	—
347	C₂×C₈	—	166	2	no	—
348	C₂×C₈	—	166	2	no	—
349	C₂×C₈	—	166	2	no	—
350	C₂×C₈	—	166	2	no	—
351	C₂×C₈	—	166	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	166	2	no	—
354	C₄⋊C₄	—	166	2	no	—
355	C₄⋊C₄	C₄×Dic₈₃	1	4	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	332	1	no	—
359	C₂²⋊C₄	—	332	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	332	1	no	—
366	C₄²	—	332	1	no	—
367	C₄²	C₄⋊Dic₈₃	1	4	yes	—
368	C₂³	—	2	4	no	—
369	C₂³	#14581748	1	1	yes	characteristic
370	C₂³	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
371	C₂³	D₄×Dic₈₃	1	1	yes	characteristic
372	C₂³	#14581769	1	1	yes	characteristic
373	C₂³	#14581776	1	1	yes	characteristic
374	C₂³	#14581782	1	1	yes	characteristic
375	C₂³	#14581787	1	1	yes	characteristic
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	332	4	no	—
383	C₂×C₄	—	332	2	no	—
384	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
385	C₂×C₄	C₂²⋊C₄×D₈₃	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
387	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
388	C₂×C₄	#14581750	1	1	yes	characteristic
389	C₂×C₄	#14581751	1	1	yes	characteristic
390	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	#14581754	1	1	yes	characteristic
392	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
393	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
394	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
395	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
396	C₂×C₄	#14581757	1	1	yes	characteristic
397	C₂×C₄	C₄×Dic₁₆₆	1	1	yes	characteristic
398	C₂×C₄	C₄×Dic₁₆₆	1	1	yes	characteristic
399	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
400	C₂×C₄	#14581762	1	1	yes	characteristic
401	C₂×C₄	#14581765	1	1	yes	characteristic
402	C₂×C₄	#14581767	1	1	yes	characteristic
403	C₂×C₄	#14581769	1	1	yes	characteristic
404	C₂×C₄	#14581770	1	1	yes	characteristic
405	C₂×C₄	#14581772	1	1	yes	characteristic
406	C₂×C₄	#14581774	1	1	yes	characteristic
407	C₂×C₄	#14581777	1	1	yes	characteristic
408	C₂×C₄	#14581778	1	1	yes	characteristic
409	C₂×C₄	#14581783	1	1	yes	characteristic
410	C₂×C₄	#14581785	1	1	yes	characteristic
411	C₂×C₄	#14581791	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	332	2	no	—
414	C₈	—	166	4	no	—
415	C₈	—	166	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₂²⋊C₄×Dic₈₃	1	1	yes	characteristic
423	C₂²	#19127576	1	1	yes	characteristic
424	C₂²	#19127584	1	1	yes	characteristic
425	C₂²	#19127586	1	1	yes	characteristic
426	C₂²	#19127587	1	1	yes	characteristic
427	C₂²	#19127593	1	1	yes	characteristic
428	C₂²	#19127598	1	1	yes	characteristic
429	C₂²	#19127815	1	4	yes	—
430	C₄	—	2	8	no	—
431	C₄	—	4	4	no	—
432	C₄	—	664	2	no	—
433	C₄	C₄×C₄⋊Dic₈₃	1	1	yes	characteristic
434	C₄	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
435	C₄	#19127575	1	1	yes	characteristic
436	C₄	#19127579	1	1	yes	characteristic
437	C₄	#19127588	1	1	yes	characteristic
438	C₄	#19127594	1	1	yes	characteristic
439	C₄	#19127600	1	1	yes	characteristic
440	C₄	#19127605	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	#24905697	1	1	yes	characteristic
446	C₂	#24907301	1	2	yes	—
447	C₂	#24908168	1	2	yes	—
448	C₂	#24908210	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₃
Fitting	C₂×#339×C₈₃	C₂
socle	C₂³×C₈₃	C₄×D₄
prime radical	C₂⁴×C₈₃	#41
cosocle	C₂³×C₄×C₈₃	C₂³
hypercenter	C₂×#339	D₈₃
hypocenter	C₈₃	#10882
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #19127728	C₄	semidirect
19. #19127463	C₄	semidirect
25. #339×C₈₃	C₄	semidirect
232. C₈₃	#10882	semidirect
249. #339	Dic₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19127728	2
C₂²×C₄×C₈₃⋊C₈	2
C₂×#19127465	2
#24907179	2
C₂×#19127461	2
#24907161	2
C₂×#339×C₈₃	2
#10882	83