Subgroups — Q₁₆×#10621898 #25978067

Order 11008.

1826 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10621898	C₂	1	2	yes	maximal
2	#19147600	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147271	C₂	1	2	yes	maximal, complemented
5	#19146989	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146985	C₂	1	2	yes	maximal, complemented
7	#19146473	C₂	1	2	yes	maximal, complemented
8	#19146467	C₂	1	4	yes	maximal, complemented
9	Q₁₆×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₁₆×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
11	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145178	C₂	1	2	yes	maximal, complemented
13	#19144634	C₂	1	2	yes	maximal, complemented
14	#19144632	C₂	1	4	yes	maximal, complemented
15	C₈×#10621898	C₂	1	1	yes	maximal, characteristic
16	C₄×Q₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₁₆×D₄₃	C₂²	1	2	yes	—
19	Q₈×Dic₈₆	C₂²	1	2	yes	—
20	#14583627	—	2	2	no	—
21	#14583627	C₂²	1	2	yes	—
22	#14583609	—	2	2	no	—
23	#14583609	C₂²	1	2	yes	—
24	#14583604	—	2	4	no	—
25	#14583604	C₂²	1	4	yes	—
26	Q₈×D₁₇₂	C₂²	1	2	yes	—
27	Q₈×C₂²⋊D₄₃	C₂²	1	4	yes	—
28	#14583456	—	2	2	no	—
29	#14583456	C₂²	1	2	yes	—
30	#14583453	—	2	4	no	—
31	#14583453	C₂²	1	4	yes	—
32	C₄×#10621898	—	2	2	no	—
33	C₄×#10621898	C₂²	1	1	yes	characteristic
34	C₄×Q₈×D₄₃	C₂²	1	4	yes	—
35	#14583304	C₂²	1	1	yes	characteristic
36	#14583303	C₂²	1	2	yes	—
37	#14583279	C₂²	1	1	yes	characteristic
38	#14583277	C₂²	1	2	yes	—
39	#14583250	C₂²	1	2	yes	—
40	#14583248	C₂²	1	4	yes	—
41	#14583236	C₂²	1	4	yes	—
42	#14583234	C₂²	1	4	yes	—
43	#14583233	C₂²	1	4	yes	—
44	#14583194	C₂²	1	2	yes	—
45	#14583194	C₂²	1	2	yes	—
46	#14583193	C₂²	1	4	yes	—
47	#14583192	C₂²	1	4	yes	—
48	#14583141	C₂²	1	2	yes	—
49	#14583140	C₂²	1	2	yes	—
50	#14583140	C₂²	1	2	yes	—
51	#14583139	C₂²	1	4	yes	—
52	#14583137	C₂²	1	2	yes	—
53	#14583109	C₂²	1	2	yes	—
54	#14583109	C₂²	1	2	yes	—
55	#14583108	C₂²	1	4	yes	—
56	#14583107	C₂²	1	4	yes	—
57	#14583056	C₂²	1	4	yes	—
58	#14583055	C₂²	1	4	yes	—
59	#14583053	C₂²	1	4	yes	—
60	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
61	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
62	C₄×Dic₁₇₂	C₂²	1	2	yes	—
63	C₄×Dic₁₇₂	C₂²	1	2	yes	—
64	Q₁₆×Dic₄₃	C₂²	1	2	yes	—
65	#14582993	C₂²	1	2	yes	—
66	C₄×#10621885	C₂²	1	4	yes	—
67	C₄×#10621885	C₂²	1	4	yes	—
68	#14582991	C₂²	1	4	yes	—
69	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
70	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
71	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
72	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
73	#14582952	C₂²	1	1	yes	characteristic
74	#14582950	C₂²	1	2	yes	—
75	#107×D₄₃	C₂²	1	2	yes	—
76	#103×D₄₃	C₂²	1	4	yes	—
77	C₄×C₈×D₄₃	C₂²	1	2	yes	—
78	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
82	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
83	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
84	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
85	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
86	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
87	C₂×#103×C₄₃	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
89	C₂×#10621898	D₄	1	1	yes	characteristic
90	C₂×Q₈×D₄₃	C₂³	1	4	yes	—
91	C₂×Dic₁₇₂	C₂³	1	2	yes	—
92	C₂×Dic₁₇₂	C₂³	1	2	yes	—
93	C₂×#10621885	C₂³	1	4	yes	—
94	C₂×#10621885	C₂³	1	4	yes	—
95	Q₁₆×D₄₃	—	2	8	no	—
96	C₂×C₈×D₄₃	C₂³	1	2	yes	—
97	C₂×C₈×D₄₃	C₂³	1	2	yes	—
98	#13063325	—	2	2	no	—
99	#13063325	—	2	2	no	—
100	#13063325	C₂³	1	2	yes	—
101	#13063325	C₂³	1	2	yes	—
102	#13063324	—	2	4	no	—
103	#13063324	C₂³	1	4	yes	—
104	#13063323	—	2	4	no	—
105	#13063323	C₂³	1	4	yes	—
106	#13063317	—	2	2	no	—
107	#13063317	—	2	2	no	—
108	#13063317	—	2	2	no	—
109	#13063315	—	2	4	no	—
110	#13063315	—	2	4	no	—
111	#13063315	—	2	4	no	—
112	#13063305	—	2	4	no	—
113	#13063305	C₂³	1	4	yes	—
114	#13063304	—	2	2	no	—
115	#13063304	—	2	4	no	—
116	#13063304	—	2	4	no	—
117	#13063304	C₂³	1	4	yes	—
118	#13063303	—	2	4	no	—
119	#13063303	—	2	4	no	—
120	#13063303	—	2	4	no	—
121	#13063301	—	2	4	no	—
122	#13063301	C₂³	1	4	yes	—
123	Q₈×Dic₄₃	C₂³	1	4	yes	—
124	C₄×Dic₈₆	—	2	2	no	—
125	C₄×Dic₈₆	—	2	2	no	—
126	C₄×Dic₈₆	—	2	2	no	—
127	C₄×Dic₈₆	—	2	4	no	—
128	C₄×Dic₈₆	—	2	4	no	—
129	C₄×Dic₈₆	D₄	1	1	yes	characteristic
130	C₄×Dic₈₆	C₂³	1	4	yes	—
131	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
132	#13063290	—	2	4	no	—
133	#13063290	C₂³	1	4	yes	—
134	C₄×D₁₇₂	—	2	2	no	—
135	C₄×D₁₇₂	—	2	2	no	—
136	C₄×D₁₇₂	D₄	1	1	yes	characteristic
137	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₄×C₂²⋊D₄₃	—	2	4	no	—
139	C₄×C₂²⋊D₄₃	—	2	4	no	—
140	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
141	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
142	#13063284	—	2	2	no	—
143	#13063284	D₄	1	1	yes	characteristic
144	#13063282	—	2	4	no	—
145	#13063282	D₄	1	2	yes	—
146	C₄⋊C₄×D₄₃	—	2	4	no	—
147	C₄⋊C₄×D₄₃	C₂³	1	4	yes	—
148	C₄²×D₄₃	—	2	4	no	—
149	C₄²×D₄₃	C₂³	1	2	yes	—
150	#13063259	C₂³	1	2	yes	—
151	#13063259	C₂³	1	2	yes	—
152	#13063258	C₂³	1	4	yes	—
153	#13063258	C₂³	1	4	yes	—
154	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
155	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
156	Dic₄₃⋊C₈	C₂³	1	2	yes	—
157	Dic₄₃⋊C₈	C₂³	1	2	yes	—
158	#13063250	C₂³	1	4	yes	—
159	#13063250	C₂³	1	4	yes	—
160	#13063249	C₂³	1	4	yes	—
161	#13063249	C₂³	1	4	yes	—
162	#13063248	C₂³	1	4	yes	—
163	#13063248	C₂³	1	4	yes	—
164	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
165	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
166	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
167	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
168	C₈×Dic₄₃	C₂³	1	2	yes	—
169	C₈×Dic₄₃	C₂³	1	2	yes	—
170	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
171	C₂×Q₁₆×C₄₃	—	2	4	no	—
172	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
173	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
174	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₄₃	—	2	2	no	—
178	C₄×Q₈×C₄₃	—	2	2	no	—
179	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
182	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
184	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₄₃	—	2	2	no	—
186	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
187	#107×C₄₃	C₂³	1	1	yes	characteristic
188	#107×C₄₃	C₂³	1	1	yes	characteristic
189	#107×C₄₃	C₂³	1	2	yes	—
190	#103×C₄₃	C₂³	1	2	yes	—
191	#103×C₄₃	C₂³	1	2	yes	—
192	#103×C₄₃	C₂³	1	2	yes	—
193	#103×C₄₃	C₂³	1	2	yes	—
194	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
198	C₂×Q₈×C₄₃	—	2	2	no	—
199	C₂×Q₈×C₄₃	—	2	4	no	—
200	C₂×Q₈×C₄₃	—	4	2	no	—
201	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₄₃	—	2	2	no	—
204	C₂²×C₄×C₄₃	—	2	2	no	—
205	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
209	Q₈×D₄₃	—	2	8	no	—
210	Q₈×D₄₃	—	4	4	no	—
211	#10621898	Q₁₆	1	8	yes	direct product factor
212	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
213	C₂×C₄×D₄₃	—	2	4	no	—
214	C₂×C₄×D₄₃	—	2	4	no	—
215	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
216	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
217	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
218	C₂×Dic₈₆	—	2	4	no	—
219	C₂×Dic₈₆	—	2	2	no	—
220	C₂×Dic₈₆	—	2	4	no	—
221	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
222	C₂×Dic₈₆	C₂⁴	1	4	yes	—
223	Q₁₆×C₄₃	—	2	4	no	—
224	Q₁₆×C₄₃	—	2	2	no	—
225	Q₁₆×C₄₃	#41	1	4	yes	complemented
226	C₂×C₈×C₄₃	—	2	2	no	—
227	C₂×C₈×C₄₃	—	4	1	no	—
228	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₄₃	—	2	2	no	—
233	C₄⋊C₄×C₄₃	—	2	2	no	—
234	C₄⋊C₄×C₄₃	—	2	2	no	—
235	C₄⋊C₄×C₄₃	—	2	2	no	—
236	C₄⋊C₄×C₄₃	—	2	2	no	—
237	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
238	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
239	C₄²×C₄₃	—	2	2	no	—
240	C₄²×C₄₃	—	2	2	no	—
241	C₄²×C₄₃	—	2	2	no	—
242	C₄²×C₄₃	—	2	2	no	—
243	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
244	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
245	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
247	C₂²⋊Dic₄₃	—	2	4	no	—
248	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
249	#10621885	—	2	8	no	—
250	#10621885	—	4	4	no	—
251	(C₂×D₄₃)⋊C₄	—	2	4	no	—
252	(C₂×D₄₃)⋊C₄	—	2	4	no	—
253	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
254	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
255	C₄⋊Dic₄₃	—	2	2	no	—
256	C₄⋊Dic₄₃	—	2	2	no	—
257	C₄⋊Dic₄₃	—	2	2	no	—
258	C₄⋊Dic₄₃	—	2	4	no	—
259	C₄⋊Dic₄₃	—	2	4	no	—
260	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
261	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
262	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
263	Dic₄₃⋊C₄	—	2	4	no	—
264	Dic₄₃⋊C₄	—	2	4	no	—
265	Dic₄₃⋊C₄	—	2	4	no	—
266	Dic₄₃⋊C₄	—	2	4	no	—
267	Dic₄₃⋊C₄	—	2	4	no	—
268	Dic₄₃⋊C₄	—	2	4	no	—
269	Dic₄₃⋊C₄	—	2	4	no	—
270	Dic₄₃⋊C₄	—	2	4	no	—
271	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
272	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
273	C₄×Dic₄₃	—	2	4	no	—
274	C₄×Dic₄₃	—	2	4	no	—
275	C₄×Dic₄₃	—	2	4	no	—
276	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
277	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
278	C₄×Dic₄₃	C₂⁴	1	2	yes	—
279	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
280	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
281	Dic₁₇₂	—	2	4	no	—
282	Dic₁₇₂	—	4	2	no	—
283	C₈×D₄₃	—	2	4	no	—
284	C₈×D₄₃	—	4	2	no	—
285	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
286	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
287	Q₈×C₄₃	—	2	2	no	—
288	Q₈×C₄₃	—	2	2	no	—
289	Q₈×C₄₃	—	2	2	no	—
290	Q₈×C₄₃	—	4	4	no	—
291	Q₈×C₄₃	C₂×#41	1	4	yes	—
292	C₂×C₄×C₄₃	—	2	2	no	—
293	C₂×C₄×C₄₃	—	2	1	no	—
294	C₂×C₄×C₄₃	—	2	1	no	—
295	C₂×C₄×C₄₃	—	2	2	no	—
296	C₂×C₄×C₄₃	—	2	2	no	—
297	C₂×C₄×C₄₃	—	2	2	no	—
298	C₂×C₄×C₄₃	—	4	1	no	—
299	C₂×C₄×C₄₃	—	4	4	no	—
300	C₂×C₄×C₄₃	—	8	2	no	—
301	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	complemented
302	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
308	C₂²⋊D₄₃	C₂×Q₁₆	1	8	yes	complemented
309	C₂×Dic₄₃	—	2	4	no	—
310	C₂×Dic₄₃	—	2	4	no	—
311	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
312	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
313	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
314	D₁₇₂	C₂×Q₁₆	1	4	yes	complemented
315	C₄×D₄₃	—	2	2	no	—
316	C₄×D₄₃	—	2	2	no	—
317	C₄×D₄₃	—	4	2	no	—
318	C₄×D₄₃	—	4	8	no	—
319	C₄×D₄₃	—	8	4	no	—
320	C₄×D₄₃	C₂×Q₁₆	1	8	yes	complemented
321	Dic₈₆	—	2	4	no	—
322	Dic₈₆	—	2	4	no	—
323	Dic₈₆	—	4	8	no	—
324	Dic₈₆	—	8	4	no	—
325	Dic₈₆	—	8	2	no	—
326	Dic₈₆	C₂×Q₁₆	1	4	yes	complemented
327	C₈×C₄₃	—	2	1	no	—
328	C₈×C₄₃	—	2	1	no	—
329	C₈×C₄₃	—	2	1	no	—
330	C₈×C₄₃	C₂×#41	1	2	yes	—
331	C₄₃⋊C₈	—	2	2	no	—
332	C₄₃⋊C₈	—	2	2	no	—
333	Q₁₆×#41	—	43	1	no	maximal, Sylow
334	C₂²×C₄₃	—	2	1	no	—
335	C₂²×C₄₃	—	2	1	no	—
336	C₂²×C₄₃	C₂²×Q₁₆	1	2	yes	—
337	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
338	C₂×D₄₃	—	2	2	no	—
339	C₂×D₄₃	—	2	2	no	—
340	C₂×D₄₃	C₂²×Q₁₆	1	4	yes	—
341	C₄×C₄₃	—	2	1	no	—
342	C₄×C₄₃	—	2	1	no	—
343	C₄×C₄₃	—	2	4	no	—
344	C₄×C₄₃	—	2	1	no	—
345	C₄×C₄₃	—	4	2	no	—
346	C₄×C₄₃	—	4	2	no	—
347	C₄×C₄₃	—	4	2	no	—
348	C₄×C₄₃	C₂²×Q₁₆	1	2	yes	—
349	C₄×C₄₃	C₂²×Q₁₆	1	2	yes	—
350	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
351	C₄×C₄₃	#585	1	1	yes	characteristic
352	Dic₄₃	—	2	2	no	—
353	Dic₄₃	—	2	2	no	—
354	Dic₄₃	—	4	4	no	—
355	Dic₄₃	—	4	4	no	—
356	Dic₄₃	C₂²×Q₁₆	1	4	yes	—
357	Q₈×#41	—	43	2	no	—
358	#3395	—	43	1	no	—
359	Q₈×Q₁₆	—	43	1	no	—
360	#3363	—	43	2	no	—
361	#3338	—	43	1	no	—
362	#3338	—	43	2	no	—
363	#3299	—	43	2	no	—
364	#3299	—	43	4	no	—
365	D₄×Q₁₆	—	43	1	no	—
366	D₄×Q₁₆	—	43	2	no	—
367	#3170	—	43	2	no	—
368	#3170	—	43	1	no	—
369	#3104	—	43	4	no	—
370	#3104	—	43	2	no	—
371	C₈×#41	—	43	1	no	—
372	C₂×C₄×Q₁₆	—	43	2	no	—
373	C₂×C₄×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
374	C₂×C₄₃	—	2	2	no	—
375	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
376	C₂×C₄₃	C₂³×Q₁₆	1	1	yes	characteristic
377	C₂×C₄₃	#3584	1	1	yes	characteristic
378	D₄₃	—	2	4	no	—
379	C₂²×Q₁₆	—	43	2	no	—
380	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
381	Q₈²	—	43	2	no	—
382	#557	—	43	2	no	—
383	#557	—	86	2	no	—
384	#554	—	43	2	no	—
385	#554	—	43	4	no	—
386	#554	—	86	4	no	—
387	#554	—	86	2	no	—
388	D₄×Q₈	—	43	4	no	—
389	D₄×Q₈	—	43	2	no	—
390	#533	—	43	4	no	—
391	#533	—	43	2	no	—
392	#533	—	86	2	no	—
393	#533	—	86	4	no	—
394	C₄×#41	—	43	1	no	—
395	C₄×#41	—	86	2	no	—
396	C₂×C₄×Q₈	—	43	4	no	—
397	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
398	#500	—	43	2	no	—
399	#500	—	43	1	no	—
400	#494	—	43	2	no	—
401	#494	—	43	1	no	—
402	#487	—	43	4	no	—
403	#487	—	43	2	no	—
404	#484	—	43	4	no	—
405	#484	—	43	4	no	—
406	#484	—	43	4	no	—
407	#477	—	43	2	no	—
408	#477	—	43	2	no	—
409	#477	—	43	4	no	—
410	#477	—	43	4	no	—
411	#467	—	43	2	no	—
412	#467	—	43	2	no	—
413	#467	—	43	2	no	—
414	#467	—	43	2	no	—
415	#467	—	43	4	no	—
416	#462	—	43	4	no	—
417	#462	—	43	2	no	—
418	#462	—	43	2	no	—
419	#462	—	43	4	no	—
420	#451	—	43	4	no	—
421	#451	—	43	4	no	—
422	#451	—	43	4	no	—
423	C₈×Q₈	—	43	1	no	—
424	C₈×Q₈	—	43	1	no	—
425	C₄×Q₁₆	—	43	2	no	—
426	C₄×Q₁₆	—	43	4	no	—
427	C₄×Q₁₆	—	43	4	no	—
428	C₄×Q₁₆	—	43	2	no	—
429	C₄×Q₁₆	—	43	4	no	—
430	C₄×Q₁₆	—	43	2	no	—
431	C₄×Q₁₆	—	43	2	no	—
432	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
433	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
434	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
435	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
436	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
437	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
438	C₈×D₄	—	43	2	no	—
439	C₈×D₄	—	43	2	no	—
440	C₈×D₄	—	43	1	no	—
441	C₈×D₄	—	43	1	no	—
442	#431	—	43	1	no	—
443	#431	—	43	2	no	—
444	C₂×#107	—	43	2	no	—
445	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
446	C₂×#103	—	43	4	no	—
447	C₂×#103	C₂×D₄₃	1	2	yes	—
448	C₂×C₄×C₈	—	43	2	no	—
449	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
450	C₄₃	Q₁₆×#41	1	1	yes	characteristic, complemented, Sylow
451	C₂×#41	—	43	1	no	—
452	C₂²×Q₈	—	43	4	no	—
453	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
454	C₂×Q₁₆	—	2	4	no	—
455	C₂×Q₁₆	—	43	4	no	—
456	C₂×Q₁₆	—	43	4	no	—
457	C₂×Q₁₆	—	43	2	no	—
458	C₂×Q₁₆	—	43	2	no	—
459	C₂×Q₁₆	—	86	8	no	—
460	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
461	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
462	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
463	C₂²×C₈	—	43	2	no	—
464	C₂²×C₈	—	43	2	no	—
465	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
466	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
467	C₄⋊Q₈	—	43	4	no	—
468	C₄⋊Q₈	—	43	4	no	—
469	C₄⋊Q₈	—	43	2	no	—
470	C₄⋊Q₈	—	43	2	no	—
471	C₄⋊Q₈	—	86	2	no	—
472	C₄⋊Q₈	—	86	2	no	—
473	C₄⋊Q₈	—	86	4	no	—
474	C₄⋊Q₈	—	86	4	no	—
475	#125	—	86	2	no	—
476	#125	—	86	2	no	—
477	#125	—	86	4	no	—
478	#125	—	86	4	no	—
479	#125	—	86	4	no	—
480	#125	—	86	2	no	—
481	C₂²⋊Q₈	—	43	4	no	—
482	C₂²⋊Q₈	—	43	4	no	—
483	C₂²⋊Q₈	—	43	4	no	—
484	C₂²⋊Q₈	—	86	4	no	—
485	C₂²⋊Q₈	—	86	4	no	—
486	C₂²⋊Q₈	—	86	4	no	—
487	C₂²⋊Q₈	—	86	4	no	—
488	C₂²⋊Q₈	—	86	4	no	—
489	C₂²⋊Q₈	—	86	4	no	—
490	C₂²⋊Q₈	—	86	4	no	—
491	C₂²⋊Q₈	—	86	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	43	1	no	—
495	C₄×Q₈	—	43	1	no	—
496	C₄×Q₈	—	43	4	no	—
497	C₄×Q₈	—	43	4	no	—
498	C₄×Q₈	—	43	4	no	—
499	C₄×Q₈	—	86	4	no	—
500	C₄×Q₈	—	86	4	no	—
501	C₄×Q₈	—	86	2	no	—
502	C₄×Q₈	—	86	2	no	—
503	C₄×Q₈	—	86	4	no	—
504	C₄×Q₈	—	86	2	no	—
505	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
506	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
507	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
508	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
509	C₄×D₄	—	43	2	no	—
510	C₄×D₄	—	43	2	no	—
511	C₄×D₄	—	43	1	no	—
512	C₄×D₄	—	43	1	no	—
513	C₄×D₄	—	86	2	no	—
514	C₄×D₄	—	86	2	no	—
515	C₄×D₄	—	86	4	no	—
516	C₄×D₄	—	86	4	no	—
517	#117	—	43	1	no	—
518	#117	—	43	2	no	—
519	#117	—	86	4	no	—
520	#117	—	86	2	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	43	4	no	—
523	C₂×C₄⋊C₄	—	86	4	no	—
524	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
525	C₂×C₄²	—	2	2	no	—
526	C₂×C₄²	—	43	2	no	—
527	C₂×C₄²	—	86	4	no	—
528	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
529	#107	—	43	2	no	—
530	#107	—	43	2	no	—
531	#107	—	43	4	no	—
532	#107	—	43	4	no	—
533	#107	C₂²×D₄₃	1	1	yes	characteristic
534	#107	C₂²×D₄₃	1	1	yes	characteristic
535	#107	C₂²×D₄₃	1	2	yes	—
536	C₄⋊C₈	—	43	2	no	—
537	C₄⋊C₈	—	43	2	no	—
538	C₄⋊C₈	—	43	1	no	—
539	C₄⋊C₈	—	43	1	no	—
540	#103	—	43	4	no	—
541	#103	—	43	4	no	—
542	#103	—	43	4	no	—
543	#103	—	43	4	no	—
544	#103	—	43	4	no	—
545	#103	—	43	4	no	—
546	#103	C₂²×D₄₃	1	2	yes	—
547	#103	C₂²×D₄₃	1	2	yes	—
548	#103	C₂²×D₄₃	1	2	yes	—
549	#103	C₂²×D₄₃	1	2	yes	—
550	C₂²⋊C₈	—	43	2	no	—
551	C₂²⋊C₈	—	43	2	no	—
552	C₂²⋊C₈	—	43	2	no	—
553	C₄×C₈	—	43	2	no	—
554	C₄×C₈	—	43	2	no	—
555	C₄×C₈	—	43	2	no	—
556	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
557	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
558	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
559	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
560	#41	—	43	8	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	4	2	no	—
564	C₂×Q₈	—	43	1	no	—
565	C₂×Q₈	—	43	4	no	—
566	C₂×Q₈	—	86	4	no	—
567	C₂×Q₈	—	86	4	no	—
568	C₂×Q₈	—	86	2	no	—
569	C₂×Q₈	—	86	8	no	—
570	C₂×Q₈	—	172	4	no	—
571	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
572	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
573	C₂×D₄	—	43	2	no	—
574	C₂×D₄	—	43	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	43	2	no	—
578	C₂²×C₄	—	43	2	no	—
579	C₂²×C₄	—	43	2	no	—
580	C₂²×C₄	—	86	4	no	—
581	C₂²×C₄	—	86	4	no	—
582	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
583	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
584	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	2	2	no	—
587	Q₁₆	—	86	8	no	—
588	Q₁₆	—	86	4	no	—
589	Q₁₆	—	172	2	no	—
590	Q₁₆	—	172	4	no	—
591	Q₁₆	#10621898	1	4	yes	direct product factor
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	4	1	no	—
594	C₂×C₈	—	43	2	no	—
595	C₂×C₈	—	43	2	no	—
596	C₂×C₈	—	86	4	no	—
597	C₂×C₈	—	172	2	no	—
598	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
599	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
600	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
601	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	43	2	no	—
608	C₄⋊C₄	—	43	2	no	—
609	C₄⋊C₄	—	43	1	no	—
610	C₄⋊C₄	—	43	1	no	—
611	C₄⋊C₄	—	43	4	no	—
612	C₄⋊C₄	—	86	4	no	—
613	C₄⋊C₄	—	86	4	no	—
614	C₄⋊C₄	—	86	4	no	—
615	C₄⋊C₄	—	86	4	no	—
616	C₄⋊C₄	—	86	4	no	—
617	C₄⋊C₄	—	86	4	no	—
618	C₄⋊C₄	—	86	4	no	—
619	C₄⋊C₄	—	86	4	no	—
620	C₄⋊C₄	—	86	4	no	—
621	C₄⋊C₄	—	86	2	no	—
622	C₄⋊C₄	—	86	2	no	—
623	C₄⋊C₄	—	86	4	no	—
624	C₄⋊C₄	—	86	2	no	—
625	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
626	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
627	C₂²⋊C₄	—	43	2	no	—
628	C₂²⋊C₄	—	43	2	no	—
629	C₂²⋊C₄	—	43	2	no	—
630	C₂²⋊C₄	—	86	4	no	—
631	C₂²⋊C₄	—	86	4	no	—
632	C₂²⋊C₄	—	86	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	43	2	no	—
638	C₄²	—	43	2	no	—
639	C₄²	—	43	2	no	—
640	C₄²	—	86	4	no	—
641	C₄²	—	86	4	no	—
642	C₄²	—	86	4	no	—
643	C₄²	D₄×D₄₃	1	1	yes	characteristic
644	C₄²	D₄×D₄₃	1	1	yes	characteristic
645	C₄²	C₂³×D₄₃	1	1	yes	characteristic
646	C₄²	C₂³×D₄₃	1	1	yes	characteristic
647	C₂³	—	43	2	no	—
648	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	4	4	no	—
653	Q₈	—	43	4	no	—
654	Q₈	—	86	4	no	—
655	Q₈	—	86	4	no	—
656	Q₈	—	344	2	no	—
657	Q₈	—	344	4	no	—
658	Q₈	—	172	8	no	—
659	Q₈	C₂×#10621898	1	4	yes	—
660	D₄	—	43	8	no	—
661	D₄	—	43	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	—	43	2	no	—
672	C₂×C₄	—	43	8	no	—
673	C₂×C₄	—	43	2	no	—
674	C₂×C₄	—	43	2	no	—
675	C₂×C₄	—	86	2	no	—
676	C₂×C₄	—	86	2	no	—
677	C₂×C₄	—	86	4	no	—
678	C₂×C₄	—	86	4	no	—
679	C₂×C₄	—	344	4	no	—
680	C₂×C₄	—	172	2	no	—
681	C₂×C₄	—	172	8	no	—
682	C₂×C₄	Q₁₆×D₄₃	1	4	yes	complemented
683	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
684	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
685	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
686	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
687	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
688	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	1	no	—
692	C₈	—	86	2	no	—
693	C₈	—	86	2	no	—
694	C₈	C₂×#10621898	1	2	yes	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	43	4	no	—
698	C₂²	—	86	2	no	—
699	C₂²	—	86	2	no	—
700	C₂²	C₂×Q₁₆×D₄₃	1	2	yes	—
701	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
702	C₄	—	2	1	no	—
703	C₄	—	2	4	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	43	4	no	—
710	C₄	—	86	2	no	—
711	C₄	—	86	2	no	—
712	C₄	—	172	4	no	—
713	C₄	—	172	4	no	—
714	C₄	C₂×Q₁₆×D₄₃	1	2	yes	—
715	C₄	C₂×Q₁₆×D₄₃	1	2	yes	—
716	C₄	C₂²×#10621898	1	1	yes	characteristic
717	C₄	#14583735	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	86	4	no	—
720	C₂	D₄×#10621898	1	1	yes	characteristic
721	C₂	C₂²×Q₁₆×D₄₃	1	1	yes	characteristic
722	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×#10621898	D₄
hypercenter	C₂×C₄×Q₁₆	D₄₃
hypocenter	C₄₃	Q₁₆×#41
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #19147600	C₂	semidirect
3. Q₁₆×Dic₈₆	C₂	semidirect
4. #19147271	C₂	semidirect
5. #19146989	C₂	semidirect
6. #19146985	C₂	semidirect
7. #19146473	C₂	semidirect
8. #19146467	C₂	semidirect
9. Q₁₆×D₁₇₂	C₂	semidirect
10. Q₁₆×C₂²⋊D₄₃	C₂	semidirect
11. #19145181	C₂	semidirect
12. #19145178	C₂	semidirect
13. #19144634	C₂	semidirect
14. #19144632	C₂	semidirect
16. C₄×Q₁₆×D₄₃	C₂	semidirect
17. C₂×C₄×Q₁₆×C₄₃	C₂	semidirect
211. #10621898	Q₁₆	direct (N × H)
225. Q₁₆×C₄₃	#41	semidirect
301. C₂×C₄×C₄₃	C₂×Q₁₆	semidirect
308. C₂²⋊D₄₃	C₂×Q₁₆	semidirect
314. D₁₇₂	C₂×Q₁₆	semidirect
320. C₄×D₄₃	C₂×Q₁₆	semidirect
326. Dic₈₆	C₂×Q₁₆	semidirect
373. C₂×C₄×Q₁₆	D₄₃	semidirect
450. C₄₃	Q₁₆×#41	semidirect
591. Q₁₆	#10621898	direct (N × H)
682. C₂×C₄	Q₁₆×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10621898	2
#19147600	2
Q₁₆×Dic₈₆	2
#19147271	2
#19146989	2
#19146985	2
#19146473	2
#19146467	2
Q₁₆×D₁₇₂	2
Q₁₆×C₂²⋊D₄₃	2
#19145181	2
#19145178	2
#19144634	2
#19144632	2
C₈×#10621898	2
C₄×Q₁₆×D₄₃	2
C₂×C₄×Q₁₆×C₄₃	2
Q₁₆×#41	43

Subgroups — Q16×#10621898 #25978067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#10621898 #25978067