Subgroups — #35375414

Order 21248.

662 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	Q₈×#13050574	C₂	1	1	yes	maximal, characteristic, complemented
2	#24916207	C₂	1	1	yes	maximal, characteristic
3	#24906366	C₂	1	2	yes	maximal, complemented
4	#24906342	C₂	1	2	yes	maximal, complemented
5	#24906321	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊(C₈₃⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#24906238	C₂	1	1	yes	maximal, characteristic, complemented
8	#24905914	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#24905753	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3103	C₂	1	1	yes	maximal, characteristic
12	C₂×#14581799	—	2	1	no	—
13	#19127832	—	2	2	no	—
14	#19127832	C₂²	1	2	yes	—
15	Q₈×C₈₃⋊C₈	C₂²	1	2	yes	—
16	#19127779	C₂²	1	2	yes	—
17	#19127773	—	2	2	no	—
18	D₄×C₈₃⋊C₈	C₂²	1	2	yes	—
19	#19127725	—	2	1	no	—
20	#19127725	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
22	#19127668	—	2	1	no	—
23	C₄×#13050574	—	2	1	no	—
24	C₄×#13050574	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
26	#19127454	C₂²	1	2	yes	—
27	#19127454	C₂²	1	2	yes	—
28	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
29	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
30	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
31	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
34	#19127423	C₂²	1	2	yes	—
35	#19127422	C₂²	1	2	yes	—
36	#532×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
38	#481×C₈₃	C₄	1	2	yes	—
39	#475×C₈₃	C₄	1	1	yes	characteristic
40	#475×C₈₃	C₄	1	1	yes	characteristic
41	#460×C₈₃	C₄	1	1	yes	characteristic
42	#460×C₈₃	C₄	1	1	yes	characteristic
43	#448×C₈₃	C₄	1	2	yes	—
44	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
46	#431×C₈₃	C₂²	1	1	yes	characteristic
47	#14581799	—	4	4	no	—
48	C₂×#13050574	—	2	2	no	—
49	C₂×#13050574	—	2	1	no	—
50	C₂×#13050574	D₄	1	1	yes	characteristic
51	C₂×#13050574	D₄	1	1	yes	characteristic
52	C₂²×C₈₃⋊C₈	—	2	2	no	—
53	C₂²×C₈₃⋊C₈	—	2	1	no	—
54	C₂²×C₈₃⋊C₈	—	2	1	no	—
55	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
56	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
57	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
58	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
59	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
61	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
64	#14581703	—	2	2	no	—
65	#14581703	D₄	1	2	yes	—
66	C₄×C₈₃⋊C₈	—	2	2	no	—
67	C₄×C₈₃⋊C₈	—	2	1	no	—
68	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
71	C₂×#41×C₈₃	—	2	1	no	—
72	C₂²×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
74	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
75	C₄⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
76	#127×C₈₃	C₂×C₄	1	1	yes	characteristic
77	#124×C₈₃	—	2	1	no	—
78	#121×C₈₃	—	2	1	no	—
79	#121×C₈₃	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₈₃	—	2	1	no	—
81	C₄×Q₈×C₈₃	—	2	1	no	—
82	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₈₃	—	2	1	no	—
87	C₄×D₄×C₈₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₃	—	2	1	no	—
91	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
92	#106×C₈₃	C₂×C₄	1	2	yes	—
93	#106×C₈₃	C₂×C₄	1	2	yes	—
94	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
95	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
96	#103×C₈₃	C₂×C₄	1	2	yes	—
97	#103×C₈₃	C₂×C₄	1	2	yes	—
98	#102×C₈₃	C₂×C₄	1	2	yes	—
99	#102×C₈₃	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₈₃	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₈₃	C₂³	1	2	yes	—
102	#13050574	—	2	2	no	—
103	#13050574	—	2	2	no	—
104	#13050574	—	4	4	no	—
105	#13050574	—	4	2	no	—
106	C₂×C₈₃⋊C₈	—	2	1	no	—
107	C₂×C₈₃⋊C₈	—	2	1	no	—
108	C₂×C₈₃⋊C₈	—	2	1	no	—
109	C₂×C₈₃⋊C₈	—	2	2	no	—
110	C₂×C₈₃⋊C₈	—	2	1	no	—
111	C₂×C₈₃⋊C₈	—	4	2	no	—
112	C₂×C₈₃⋊C₈	—	4	4	no	—
113	C₂×C₈₃⋊C₈	—	4	2	no	—
114	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
115	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
116	#41×C₈₃	—	4	2	no	—
117	#41×C₈₃	—	4	2	no	—
118	C₂×Q₈×C₈₃	—	2	1	no	—
119	C₂×Q₈×C₈₃	—	2	1	no	—
120	C₂×Q₈×C₈₃	—	2	2	no	—
121	C₂×Q₈×C₈₃	—	4	1	no	—
122	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₈₃	—	2	2	no	—
125	C₂×D₄×C₈₃	—	2	1	no	—
126	C₂×D₄×C₈₃	—	2	1	no	—
127	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₈₃	—	2	1	no	—
129	C₂²×C₄×C₈₃	—	2	1	no	—
130	C₂²×C₄×C₈₃	—	2	2	no	—
131	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
134	SD₁₆×C₈₃	—	2	4	no	—
135	SD₁₆×C₈₃	—	4	2	no	—
136	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₈₃	—	2	1	no	—
139	C₄⋊C₄×C₈₃	—	2	1	no	—
140	C₄⋊C₄×C₈₃	—	2	1	no	—
141	C₄⋊C₄×C₈₃	—	2	1	no	—
142	C₄⋊C₄×C₈₃	—	2	1	no	—
143	C₄⋊C₄×C₈₃	—	2	1	no	—
144	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₈₃	—	2	2	no	—
148	C₂²⋊C₄×C₈₃	—	2	2	no	—
149	C₄²×C₈₃	—	2	1	no	—
150	C₄²×C₈₃	—	2	1	no	—
151	C₄²×C₈₃	—	2	1	no	—
152	C₄²×C₈₃	—	2	1	no	—
153	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₃	#41	1	1	yes	characteristic
156	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₃	—	2	2	no	—
158	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
159	Q₈×C₈₃	—	2	1	no	—
160	Q₈×C₈₃	—	2	1	no	—
161	Q₈×C₈₃	—	2	1	no	—
162	Q₈×C₈₃	—	4	2	no	—
163	Q₈×C₈₃	—	4	2	no	—
164	Q₈×C₈₃	#131	1	2	yes	complemented
165	D₄×C₈₃	—	2	2	no	—
166	D₄×C₈₃	—	2	2	no	—
167	D₄×C₈₃	—	4	4	no	—
168	D₄×C₈₃	—	4	2	no	—
169	D₄×C₈₃	—	8	1	no	—
170	C₂×C₄×C₈₃	—	2	1	no	—
171	C₂×C₄×C₈₃	—	2	1	no	—
172	C₂×C₄×C₈₃	—	2	1	no	—
173	C₂×C₄×C₈₃	—	2	1	no	—
174	C₂×C₄×C₈₃	—	2	1	no	—
175	C₂×C₄×C₈₃	—	2	1	no	—
176	C₂×C₄×C₈₃	—	2	2	no	—
177	C₂×C₄×C₈₃	—	4	1	no	—
178	C₂×C₄×C₈₃	—	4	2	no	—
179	C₂×C₄×C₈₃	—	4	2	no	—
180	C₂×C₄×C₈₃	—	4	2	no	—
181	C₂×C₄×C₈₃	—	8	1	no	—
182	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₈₃	#137	1	2	yes	—
187	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
190	C₈×C₈₃	—	2	2	no	—
191	C₈×C₈₃	—	2	2	no	—
192	C₈₃⋊C₈	—	2	2	no	—
193	C₈₃⋊C₈	—	2	2	no	—
194	C₈₃⋊C₈	—	2	2	no	—
195	C₈₃⋊C₈	—	4	1	no	—
196	C₈₃⋊C₈	—	4	1	no	—
197	C₈₃⋊C₈	—	4	1	no	—
198	C₈₃⋊C₈	—	4	2	no	—
199	C₂²×C₈₃	—	2	1	no	—
200	C₂²×C₈₃	—	2	1	no	—
201	C₂²×C₈₃	—	4	2	no	—
202	C₂²×C₈₃	—	4	2	no	—
203	C₂²×C₈₃	—	4	2	no	—
204	C₂²×C₈₃	#440	1	2	yes	—
205	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₈₃	—	2	1	no	—
207	C₄×C₈₃	—	2	2	no	—
208	C₄×C₈₃	—	2	1	no	—
209	C₄×C₈₃	—	2	1	no	—
210	C₄×C₈₃	—	4	1	no	—
211	C₄×C₈₃	—	4	2	no	—
212	C₄×C₈₃	—	4	1	no	—
213	C₄×C₈₃	—	4	1	no	—
214	C₄×C₈₃	#440	1	2	yes	—
215	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
216	C₄×C₈₃	#568	1	1	yes	characteristic
217	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
219	#18004	—	83	1	no	maximal, Sylow
220	C₂×C₈₃	—	2	2	no	—
221	C₂×C₈₃	—	8	2	no	—
222	C₂×C₈₃	#2933	1	1	yes	characteristic
223	C₂×C₈₃	C₂×#440	1	1	yes	characteristic
224	C₂×C₈₃	#2956	1	1	yes	characteristic
225	#3103	D₈₃	1	1	yes	characteristic
226	Q₈×M₁₆	—	83	1	no	—
227	#2935	—	83	1	no	—
228	#1592	—	83	2	no	—
229	#1588	—	83	2	no	—
230	#1585	—	83	2	no	—
231	SD₁₆⋊C₈	—	83	2	no	—
232	#1571	—	83	1	no	—
233	#1492	—	83	1	no	—
234	C₂×Q₈⋊C₈	—	83	1	no	—
235	#1451	—	83	1	no	—
236	C₈₃	#18004	1	1	yes	characteristic, complemented, Sylow
237	C₂×#131	—	166	1	no	—
238	#532	C₂×D₈₃	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
240	#481	Dic₈₃	1	2	yes	—
241	#475	Dic₈₃	1	1	yes	characteristic
242	#475	Dic₈₃	1	1	yes	characteristic
243	#460	Dic₈₃	1	1	yes	characteristic
244	#460	Dic₈₃	1	1	yes	characteristic
245	#448	Dic₈₃	1	2	yes	—
246	#446	—	83	2	no	—
247	#446	—	166	2	no	—
248	C₈×Q₈	—	83	2	no	—
249	C₄×SD₁₆	C₂×D₈₃	1	2	yes	—
250	C₄×SD₁₆	C₂×D₈₃	1	2	yes	—
251	#436	—	83	2	no	—
252	#435	—	166	2	no	—
253	C₈×D₄	—	83	2	no	—
254	#431	C₂×D₈₃	1	1	yes	characteristic
255	#423	—	83	1	no	—
256	#423	—	166	1	no	—
257	C₂×C₄⋊C₈	—	83	1	no	—
258	#408	—	166	1	no	—
259	C₄×M₁₆	—	83	1	no	—
260	C₄×M₁₆	—	166	1	no	—
261	C₂×C₄×C₈	—	83	1	no	—
262	#335	—	83	2	no	—
263	#335	—	83	2	no	—
264	Q₈⋊C₈	—	83	1	no	—
265	Q₈⋊C₈	—	83	1	no	—
266	Q₈⋊C₈	—	83	1	no	—
267	Q₈⋊C₈	—	83	1	no	—
268	D₄⋊C₈	—	83	2	no	—
269	D₄⋊C₈	—	83	2	no	—
270	#322	—	83	2	no	—
271	#322	—	83	2	no	—
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	C₂×Dic₈₃	1	1	yes	characteristic
274	C₂×SD₁₆	C₂×Dic₈₃	1	2	yes	—
275	C₂×SD₁₆	C₂×Dic₈₃	1	2	yes	—
276	#131	—	332	4	no	—
277	C₂×M₁₆	—	83	1	no	—
278	C₂×M₁₆	—	83	1	no	—
279	C₂×M₁₆	—	166	2	no	—
280	C₂×M₁₆	—	166	1	no	—
281	C₂²×C₈	—	166	2	no	—
282	C₂²×C₈	—	166	1	no	—
283	C₂²×C₈	—	166	1	no	—
284	C₄⋊Q₈	C₂×Dic₈₃	1	1	yes	characteristic
285	#127	C₂×Dic₈₃	1	1	yes	characteristic
286	#124	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	C₂×Dic₈₃	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₂×Dic₈₃	1	1	yes	characteristic
292	C₄×Q₈	C₂×Dic₈₃	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²×D₈₃	1	2	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂×Dic₈₃	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
301	#106	C₂×Dic₈₃	1	2	yes	—
302	#106	C₂×Dic₈₃	1	2	yes	—
303	C₄⋊C₈	—	83	2	no	—
304	C₄⋊C₈	—	83	1	no	—
305	C₄⋊C₈	—	83	1	no	—
306	C₄⋊C₈	—	166	2	no	—
307	C₄⋊C₈	—	166	2	no	—
308	C₄⋊C₈	—	166	1	no	—
309	C₄⋊C₈	—	166	1	no	—
310	C₄⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂×Dic₈₃	1	1	yes	characteristic
312	#103	C₂×Dic₈₃	1	2	yes	—
313	#103	C₂×Dic₈₃	1	2	yes	—
314	#102	C₂×Dic₈₃	1	2	yes	—
315	#102	C₂×Dic₈₃	1	2	yes	—
316	C₂²⋊C₈	—	166	2	no	—
317	C₂²⋊C₈	—	166	2	no	—
318	C₂²⋊C₈	C₂×Dic₈₃	1	2	yes	—
319	#97	—	83	2	no	—
320	#97	—	166	2	no	—
321	C₄×C₈	—	83	2	no	—
322	C₄×C₈	—	83	1	no	—
323	C₄×C₈	—	83	1	no	—
324	C₄×C₈	—	166	2	no	—
325	C₄×C₈	—	166	1	no	—
326	C₄×C₈	C₂²×D₈₃	1	2	yes	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	C₂²×Dic₈₃	1	1	yes	characteristic
334	C₂×Q₈	C₂²×Dic₈₃	1	1	yes	characteristic
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×Dic₈₃	1	2	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
344	C₂²×C₄	#13050589	1	1	yes	characteristic
345	SD₁₆	—	2	4	no	—
346	SD₁₆	—	4	2	no	—
347	M₁₆	—	332	2	no	—
348	M₁₆	—	332	4	no	—
349	M₁₆	—	166	2	no	—
350	M₁₆	—	166	2	no	—
351	C₂×C₈	—	332	2	no	—
352	C₂×C₈	—	332	4	no	—
353	C₂×C₈	—	332	2	no	—
354	C₂×C₈	—	83	2	no	—
355	C₂×C₈	—	83	2	no	—
356	C₂×C₈	—	166	2	no	—
357	C₂×C₈	—	166	1	no	—
358	C₂×C₈	—	166	1	no	—
359	C₂×C₈	—	166	1	no	—
360	C₂×C₈	—	166	1	no	—
361	C₂×C₈	C₂²×Dic₈₃	1	2	yes	—
362	C₂×C₈	C₂²×Dic₈₃	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×Dic₈₃	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×Dic₈₃	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
379	C₄²	D₄×D₈₃	1	1	yes	characteristic
380	C₄²	#13050589	1	1	yes	characteristic
381	C₄²	C₂³×D₈₃	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	D₄×Dic₈₃	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	#14581799	1	2	yes	complemented
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
408	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
409	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
410	C₂×C₄	#14581819	1	2	yes	—
411	C₂×C₄	#14581821	1	2	yes	—
412	C₂×C₄	C₂³×Dic₈₃	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	332	1	no	—
418	C₈	—	332	1	no	—
419	C₈	—	332	1	no	—
420	C₈	—	332	2	no	—
421	C₈	—	166	2	no	—
422	C₈	—	166	2	no	—
423	C₈	—	166	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	#19127802	1	2	yes	—
430	C₂²	C₂×D₄×Dic₈₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	#19127802	1	2	yes	—
440	C₄	C₂×#14581799	1	1	yes	characteristic
441	C₄	#19128468	1	1	yes	characteristic
442	C₄	C₂×#14581819	1	1	yes	characteristic
443	C₄	C₂×#14581821	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	#24916190	1	1	yes	characteristic
447	C₂	C₂×#19127802	1	1	yes	characteristic
448	C₂	#24916373	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#3103	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#532×C₈₃	C₂²
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#3103	D₈₃
hypocenter	C₈₃	#18004
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3103

Complements

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

N	H ≅ G/N	type
1. Q₈×#13050574	C₂	semidirect
3. #24906366	C₂	semidirect
4. #24906342	C₂	semidirect
5. #24906321	C₂	semidirect
6. SD₁₆⋊(C₈₃⋊C₈)	C₂	semidirect
7. #24906238	C₂	semidirect
9. C₂×Q₈⋊(C₈₃⋊C₈)	C₂	semidirect
10. #24905753	C₂	semidirect
164. Q₈×C₈₃	#131	semidirect
236. C₈₃	#18004	semidirect
389. Q₈	#14581799	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#13050574	2
#24916207	2
#24906366	2
#24906342	2
#24906321	2
SD₁₆⋊(C₈₃⋊C₈)	2
#24906238	2
#24905914	2
C₂×Q₈⋊(C₈₃⋊C₈)	2
#24905753	2
C₈₃×#3103	2
#18004	83