Subgroups — #35299014

Order 21248.

560 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13050577	C₂	1	1	yes	maximal, characteristic
2	#24908257	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19127428	C₂	1	1	yes	maximal, characteristic
5	#24905297	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#446×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13050577	C₄	1	1	yes	characteristic
9	C₂×C₄×D₃₃₂	C₂²	1	1	yes	characteristic
10	C₄×#13050577	—	2	2	no	—
11	C₄×#13050577	—	2	2	no	—
12	C₂×#14581723	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14581716	C₄	1	1	yes	characteristic
15	C₂×#14581712	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₈₃)⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₈₃)⋊C₈	—	2	1	no	—
18	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
20	Q₈⋊(C₈₃⋊C₈)	—	2	2	no	—
21	#19127428	—	2	2	no	—
22	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
23	#446×C₈₃	—	2	2	no	—
24	#446×C₈₃	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₃	—	2	1	no	—
26	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
27	C₂×#97×C₈₃	—	2	1	no	—
28	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
29	C₂²×D₃₃₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₈₃	—	2	1	no	—
31	C₂×#13050577	—	2	2	no	—
32	C₂×#13050577	—	2	2	no	—
33	C₂×#13050577	—	2	2	no	—
34	C₂²×C₈₃⋊C₈	—	2	1	no	—
35	C₂²×C₈₃⋊C₈	—	2	1	no	—
36	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₄×D₃₃₂	—	2	1	no	—
39	C₄×D₃₃₂	—	2	1	no	—
40	C₄×D₃₃₂	—	2	1	no	—
41	C₄×D₃₃₂	—	2	1	no	—
42	C₂×C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
43	C₂×(C₂×D₈₃)⋊C₄	—	2	1	no	—
44	#14581723	—	2	2	no	—
45	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
46	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
47	#14581716	—	2	2	no	—
48	#14581712	—	2	2	no	—
49	(C₂×D₈₃)⋊C₈	—	4	2	no	—
50	(C₂×D₈₃)⋊C₈	—	4	2	no	—
51	C₄×C₈₃⋊C₈	—	2	1	no	—
52	C₄×C₈₃⋊C₈	—	2	1	no	—
53	C₄×C₈₃⋊C₈	—	2	1	no	—
54	C₄×C₈₃⋊C₈	—	2	1	no	—
55	C₂²×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₃	—	2	1	no	—
57	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
59	C₄×Q₈×C₈₃	—	2	1	no	—
60	C₄×Q₈×C₈₃	—	2	1	no	—
61	C₄×Q₈×C₈₃	D₄	1	2	yes	—
62	C₄×Q₈×C₈₃	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₃	—	2	1	no	—
66	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₈₃	—	2	4	no	—
68	C₄⋊C₈×C₈₃	—	2	1	no	—
69	C₄⋊C₈×C₈₃	D₄	1	2	yes	—
70	#97×C₈₃	—	2	4	no	—
71	C₄×C₈×C₈₃	—	2	1	no	—
72	C₄×C₈×C₈₃	—	2	1	no	—
73	C₂³×D₈₃	—	2	1	no	—
74	C₂×D₃₃₂	—	2	1	no	—
75	C₂×D₃₃₂	—	2	1	no	—
76	C₂×D₃₃₂	—	2	1	no	—
77	C₂×D₃₃₂	—	2	1	no	—
78	C₂×D₃₃₂	—	2	1	no	—
79	C₂×D₃₃₂	M₁₆	1	2	yes	—
80	C₂²×Dic₈₃	—	2	1	no	—
81	C₂×C₄×D₈₃	—	4	1	no	—
82	C₂×C₄×D₈₃	—	4	1	no	—
83	C₂×C₄×D₈₃	—	4	1	no	—
84	C₂×C₄×D₈₃	—	4	1	no	—
85	C₂×C₄×D₈₃	—	4	1	no	—
86	C₂×C₄×D₈₃	—	4	1	no	—
87	#13050577	—	2	8	no	—
88	C₂×C₈₃⋊C₈	—	2	1	no	—
89	C₂×C₈₃⋊C₈	—	2	1	no	—
90	C₂×C₈₃⋊C₈	—	2	2	no	—
91	C₂×C₈₃⋊C₈	—	2	1	no	—
92	C₂×C₈₃⋊C₈	—	2	1	no	—
93	C₂×C₈₃⋊C₈	—	2	1	no	—
94	C₂×C₈₃⋊C₈	—	4	1	no	—
95	C₂×C₈₃⋊C₈	—	4	1	no	—
96	C₂×C₈₃⋊C₈	—	4	1	no	—
97	C₂×C₈₃⋊C₈	—	4	1	no	—
98	C₂×C₈₃⋊C₈	—	4	1	no	—
99	C₂×C₈₃⋊C₈	M₁₆	1	2	yes	—
100	C₄⋊Dic₈₃	—	2	1	no	—
101	C₄⋊Dic₈₃	—	2	1	no	—
102	(C₂×D₈₃)⋊C₄	—	4	1	no	—
103	(C₂×D₈₃)⋊C₄	—	4	1	no	—
104	C₂×Q₈×C₈₃	—	2	1	no	—
105	C₂×Q₈×C₈₃	—	2	1	no	—
106	C₂×Q₈×C₈₃	—	2	1	no	—
107	C₂×Q₈×C₈₃	—	2	1	no	—
108	C₂×Q₈×C₈₃	—	2	1	no	—
109	C₂×Q₈×C₈₃	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₈₃	—	2	1	no	—
111	C₂²×C₄×C₈₃	—	2	1	no	—
112	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
115	C₂×C₈×C₈₃	—	2	1	no	—
116	C₂×C₈×C₈₃	—	2	1	no	—
117	C₂×C₈×C₈₃	—	2	1	no	—
118	C₂×C₈×C₈₃	—	2	2	no	—
119	C₂×C₈×C₈₃	—	2	1	no	—
120	C₂×C₈×C₈₃	—	2	1	no	—
121	C₂×C₈×C₈₃	—	4	1	no	—
122	C₂×C₈×C₈₃	—	4	1	no	—
123	C₂×C₈×C₈₃	SD₁₆	1	2	yes	complemented
124	C₄⋊C₄×C₈₃	—	2	1	no	—
125	C₄⋊C₄×C₈₃	—	2	2	no	—
126	C₄⋊C₄×C₈₃	—	2	2	no	—
127	C₄⋊C₄×C₈₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₈₃	—	2	2	no	—
129	C₄²×C₈₃	—	2	2	no	—
130	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₃	#41	1	1	yes	characteristic
134	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
135	C₂²×D₈₃	—	2	2	no	—
136	C₂²×D₈₃	—	4	1	no	—
137	C₂²×D₈₃	—	4	1	no	—
138	C₂²×D₈₃	—	4	1	no	—
139	C₂²×D₈₃	—	4	1	no	—
140	C₂²×D₈₃	—	4	1	no	—
141	C₂²×D₈₃	—	4	1	no	—
142	Q₈×C₈₃	—	2	2	no	—
143	Q₈×C₈₃	—	2	2	no	—
144	Q₈×C₈₃	—	4	1	no	—
145	Q₈×C₈₃	—	4	1	no	—
146	C₂×C₄×C₈₃	—	2	1	no	—
147	C₂×C₄×C₈₃	—	2	1	no	—
148	C₂×C₄×C₈₃	—	2	2	no	—
149	C₂×C₄×C₈₃	—	2	2	no	—
150	C₂×C₄×C₈₃	—	4	1	no	—
151	C₂×C₄×C₈₃	—	4	1	no	—
152	C₂×C₄×C₈₃	—	4	1	no	—
153	C₂×C₄×C₈₃	—	4	1	no	—
154	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
157	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
160	C₂×C₄×C₈₃	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₈₃	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₈₃	#131	1	1	yes	characteristic
163	C₂×C₄×C₈₃	#131	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₈₃	#137	1	1	yes	characteristic
168	C₂×Dic₈₃	—	4	1	no	—
169	C₂×Dic₈₃	—	4	1	no	—
170	C₂×Dic₈₃	—	4	1	no	—
171	D₃₃₂	—	2	2	no	—
172	D₃₃₂	—	2	2	no	—
173	D₃₃₂	—	4	1	no	—
174	D₃₃₂	—	4	1	no	—
175	C₄×D₈₃	—	8	1	no	—
176	C₄×D₈₃	—	8	1	no	—
177	C₄×D₈₃	—	8	1	no	—
178	C₄×D₈₃	—	8	1	no	—
179	C₈×C₈₃	—	2	2	no	—
180	C₈×C₈₃	—	4	1	no	—
181	C₈×C₈₃	—	4	2	no	—
182	C₈₃⋊C₈	—	2	2	no	—
183	C₈₃⋊C₈	—	4	2	no	—
184	C₈₃⋊C₈	—	4	1	no	—
185	C₈₃⋊C₈	—	8	1	no	—
186	C₂²×C₈₃	#386	1	1	yes	characteristic
187	C₂²×C₈₃	#435	1	1	yes	characteristic
188	C₂²×C₈₃	#436	1	1	yes	characteristic
189	C₂²×C₈₃	C₄×SD₁₆	1	1	yes	characteristic
190	C₂²×C₈₃	#440	1	1	yes	characteristic
191	C₂²×C₈₃	#443	1	1	yes	characteristic
192	C₂²×C₈₃	#444	1	1	yes	characteristic
193	C₂×D₈₃	—	4	2	no	—
194	C₂×D₈₃	—	4	2	no	—
195	C₂×D₈₃	—	4	2	no	—
196	C₂×D₈₃	—	8	1	no	—
197	C₂×D₈₃	—	8	1	no	—
198	C₂×D₈₃	—	8	1	no	—
199	C₂×D₈₃	—	8	1	no	—
200	C₄×C₈₃	—	2	1	no	—
201	C₄×C₈₃	—	2	1	no	—
202	C₄×C₈₃	—	4	2	no	—
203	C₄×C₈₃	—	4	2	no	—
204	C₄×C₈₃	#407	1	1	yes	characteristic
205	C₄×C₈₃	#408	1	1	yes	characteristic
206	C₄×C₈₃	#435	1	1	yes	characteristic
207	C₄×C₈₃	#436	1	1	yes	characteristic
208	C₄×C₈₃	#448	1	1	yes	characteristic
209	C₄×C₈₃	#449	1	1	yes	characteristic
210	C₄×C₈₃	#460	1	1	yes	characteristic
211	C₄×C₈₃	#464	1	1	yes	characteristic
212	Dic₈₃	—	8	1	no	—
213	#8952	—	83	1	no	maximal, Sylow
214	C₂×C₈₃	#1582	1	1	yes	characteristic
215	C₂×C₈₃	#1585	1	1	yes	characteristic
216	C₂×C₈₃	#1590	1	1	yes	characteristic
217	C₂×C₈₃	#1592	1	1	yes	characteristic
218	C₂×C₈₃	#1870	1	1	yes	characteristic
219	C₂×C₈₃	#1876	1	1	yes	characteristic
220	C₂×C₈₃	#1880	1	1	yes	characteristic
221	D₈₃	—	8	2	no	—
222	C₂×#446	D₈₃	1	1	yes	characteristic, complemented
223	C₂×C₄×SD₁₆	—	83	1	no	—
224	#1954	—	83	1	no	—
225	C₂×Q₈⋊C₈	—	83	1	no	—
226	C₂×D₄⋊C₈	—	83	1	no	—
227	#1277	—	83	1	no	—
228	#1273	—	83	1	no	—
229	C₈₃	#8952	1	1	yes	characteristic, complemented, Sylow
230	C₂²×SD₁₆	—	83	1	no	—
231	C₂×C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	83	1	no	—
233	#446	—	2	2	no	—
234	#446	—	2	2	no	—
235	C₄×SD₁₆	—	166	2	no	—
236	C₄×SD₁₆	—	166	2	no	—
237	C₂×#106	—	83	1	no	—
238	C₂×C₄⋊C₈	—	2	1	no	—
239	C₂×C₄⋊C₈	—	83	1	no	—
240	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
241	C₂×#103	—	83	1	no	—
242	C₂×#102	—	83	1	no	—
243	C₂×C₂²⋊C₈	—	166	1	no	—
244	C₂×C₂²⋊C₈	—	166	1	no	—
245	C₂×#97	—	2	1	no	—
246	C₂×C₄×C₈	—	83	1	no	—
247	C₂×C₄×C₈	—	83	1	no	—
248	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
249	Q₈⋊C₈	—	166	2	no	—
250	D₄⋊C₈	—	166	2	no	—
251	C₂²×Q₈	C₄×D₈₃	1	1	yes	characteristic
252	C₂²×D₄	—	83	1	no	—
253	C₂³×C₄	—	166	1	no	—
254	C₂×SD₁₆	—	166	2	no	—
255	C₂×SD₁₆	—	166	2	no	—
256	C₂×SD₁₆	—	166	2	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	83	1	no	—
259	C₂²×C₈	—	83	1	no	—
260	C₂²×C₈	—	166	1	no	—
261	C₂²×C₈	—	166	1	no	—
262	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	D₃₃₂	1	2	yes	—
267	C₄×Q₈	C₂²⋊D₈₃	1	2	yes	—
268	C₄×D₄	—	166	1	no	—
269	C₄×D₄	—	166	1	no	—
270	C₄×D₄	—	166	1	no	—
271	C₄×D₄	—	166	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	83	1	no	—
274	C₂×C₄⋊C₄	C₄×D₈₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	166	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
278	#106	—	166	2	no	—
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	166	1	no	—
282	C₄⋊C₈	—	166	1	no	—
283	C₄⋊C₈	C₂²⋊D₈₃	1	2	yes	—
284	#103	—	166	2	no	—
285	#102	—	166	2	no	—
286	C₂²⋊C₈	—	332	2	no	—
287	C₂²⋊C₈	—	332	2	no	—
288	#97	—	2	4	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	166	1	no	—
292	C₄×C₈	—	166	1	no	—
293	C₄×C₈	—	166	1	no	—
294	C₄×C₈	—	166	1	no	—
295	C₂⁴	—	166	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
302	C₂×D₄	—	83	2	no	—
303	C₂×D₄	—	166	1	no	—
304	C₂×D₄	—	166	1	no	—
305	C₂×D₄	—	166	1	no	—
306	C₂×D₄	—	166	1	no	—
307	C₂×D₄	—	166	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	332	1	no	—
311	C₂²×C₄	—	332	1	no	—
312	C₂²×C₄	—	332	1	no	—
313	C₂²×C₄	—	332	1	no	—
314	C₂²×C₄	—	332	1	no	—
315	C₂²×C₄	—	332	1	no	—
316	C₂²×C₄	—	166	1	no	—
317	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
319	C₂²×C₄	#13050590	1	1	yes	characteristic
320	SD₁₆	—	166	8	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	332	1	no	—
330	C₂×C₈	—	332	1	no	—
331	C₂×C₈	—	332	1	no	—
332	C₂×C₈	—	332	1	no	—
333	C₂×C₈	—	332	1	no	—
334	C₂×C₈	—	83	2	no	—
335	C₂×C₈	—	166	2	no	—
336	C₂×C₈	—	166	1	no	—
337	C₂×C₈	—	166	1	no	—
338	C₂×C₈	—	166	1	no	—
339	C₂×C₈	—	166	1	no	—
340	C₂×C₈	—	166	1	no	—
341	C₂×C₈	#13050577	1	2	yes	complemented
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	166	1	no	—
346	C₄⋊C₄	—	166	1	no	—
347	C₄⋊C₄	(C₂×D₈₃)⋊C₄	1	2	yes	—
348	C₂²⋊C₄	—	332	1	no	—
349	C₂²⋊C₄	—	332	1	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
354	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
355	C₄²	#13050590	1	1	yes	characteristic
356	C₂³	—	332	1	no	—
357	C₂³	—	332	1	no	—
358	C₂³	—	332	1	no	—
359	C₂³	—	332	1	no	—
360	C₂³	—	332	1	no	—
361	C₂³	—	332	1	no	—
362	C₂³	—	166	2	no	—
363	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	D₄	—	332	1	no	—
369	D₄	—	332	1	no	—
370	D₄	—	166	2	no	—
371	D₄	—	166	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	332	1	no	—
381	C₂×C₄	—	332	1	no	—
382	C₂×C₄	—	332	1	no	—
383	C₂×C₄	—	664	1	no	—
384	C₂×C₄	—	664	1	no	—
385	C₂×C₄	—	664	1	no	—
386	C₂×C₄	—	664	1	no	—
387	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
389	C₂×C₄	#14581761	1	1	yes	characteristic
390	C₂×C₄	#14581766	1	1	yes	characteristic
391	C₂×C₄	#14581766	1	1	yes	characteristic
392	C₂×C₄	#14581775	1	1	yes	characteristic
393	C₂×C₄	M₁₆×D₈₃	1	1	yes	characteristic
394	C₂×C₄	M₁₆×D₈₃	1	1	yes	characteristic
395	C₂×C₄	#14581800	1	1	yes	characteristic
396	C₂×C₄	#14581800	1	1	yes	characteristic
397	C₂×C₄	C₂×#13050577	1	1	yes	characteristic
398	C₂×C₄	#14581812	1	1	yes	characteristic
399	C₂×C₄	#14581817	1	1	yes	characteristic
400	C₂×C₄	#14581823	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	2	no	—
404	C₈	—	332	2	no	—
405	C₈	—	332	1	no	—
406	C₈	—	664	1	no	—
407	C₈	—	166	2	no	—
408	C₂²	—	332	2	no	—
409	C₂²	—	332	2	no	—
410	C₂²	—	332	2	no	—
411	C₂²	—	664	1	no	—
412	C₂²	—	664	1	no	—
413	C₂²	—	664	1	no	—
414	C₂²	—	664	1	no	—
415	C₂²	#19127580	1	1	yes	characteristic
416	C₂²	#19127770	1	1	yes	characteristic
417	C₂²	#19127777	1	1	yes	characteristic
418	C₂²	C₄×#13050577	1	1	yes	characteristic
419	C₂²	#19127799	1	1	yes	characteristic
420	C₂²	#19127816	1	1	yes	characteristic
421	C₂²	#19127821	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	664	1	no	—
427	C₄	#19127664	1	1	yes	characteristic
428	C₄	#19127669	1	1	yes	characteristic
429	C₄	#19127770	1	1	yes	characteristic
430	C₄	#19127777	1	1	yes	characteristic
431	C₄	#19127840	1	1	yes	characteristic
432	C₄	#19127846	1	1	yes	characteristic
433	C₄	#19127901	1	1	yes	characteristic
434	C₄	#19127923	1	1	yes	characteristic
435	C₂	—	664	2	no	—
436	C₂	#24906297	1	1	yes	characteristic
437	C₂	#24906318	1	1	yes	characteristic
438	C₂	#24906353	1	1	yes	characteristic
439	C₂	#24906363	1	1	yes	characteristic
440	C₂	#24907760	1	1	yes	characteristic
441	C₂	#24907790	1	1	yes	characteristic
442	C₂	#24907818	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₈₃
commutator	C₂²×C₄×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₂×#446×C₈₃	C₂
socle	C₂³×C₈₃	C₄×D₄
prime radical	C₂²×D₃₃₂	C₂×C₄
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	C₂×#446	D₈₃
hypocenter	C₈₃	#8952
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₈₃⋊C₈)	C₂	semidirect
5. #24905297	C₂	semidirect
6. C₈₃⋊#1273	C₂	semidirect
7. C₂×#446×C₈₃	C₂	semidirect
123. C₂×C₈×C₈₃	SD₁₆	semidirect
222. C₂×#446	D₈₃	semidirect
229. C₈₃	#8952	semidirect
341. C₂×C₈	#13050577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#13050577	2
#24908257	2
C₂×Q₈⋊(C₈₃⋊C₈)	2
C₂×#19127428	2
#24905297	2
C₈₃⋊#1273	2
C₂×#446×C₈₃	2
#8952	83