Subgroups — #36525907

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#13083558	C₂	1	1	yes	maximal, characteristic
3	#26019155	C₂	1	2	yes	maximal, complemented
4	#26019131	C₂	1	2	yes	maximal, complemented
5	#26019110	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#10623494	C₂	1	2	yes	maximal, complemented
7	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018681	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018677	C₂	1	1	yes	maximal, characteristic
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#13083558	—	2	1	no	—
13	#19151729	—	2	2	no	—
14	#19151729	C₂²	1	2	yes	complemented
15	Q₈×#10623494	C₂²	1	2	yes	complemented
16	#19151676	C₂²	1	2	yes	—
17	#19151670	—	2	2	no	—
18	D₄×#10623494	C₂²	1	2	yes	—
19	#19151651	C₂²	1	1	yes	characteristic
20	#19151622	—	2	1	no	—
21	#19151622	C₂²	1	1	yes	characteristic
22	#19151622	C₂²	1	1	yes	characteristic
23	#19151562	—	2	1	no	—
24	C₄×#13083558	—	2	1	no	—
25	C₄×#13083558	C₂²	1	1	yes	characteristic
26	#19151351	C₂²	1	2	yes	complemented
27	#19151351	C₂²	1	2	yes	complemented
28	Q₈⋊#10623494	C₂²	1	2	yes	complemented
29	Q₈⋊#10623494	C₂²	1	2	yes	complemented
30	D₄⋊#10623494	C₂²	1	2	yes	—
31	D₄⋊#10623494	C₂²	1	2	yes	—
32	#19151320	C₂²	1	2	yes	complemented
33	#19151319	C₂²	1	2	yes	complemented
34	C₂²×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
38	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
39	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
40	C₄×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
41	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#106×C₈₉	C₄	1	1	yes	characteristic
46	C₂×#103×C₈₉	C₄	1	1	yes	characteristic
47	C₂×#102×C₈₉	C₄	1	1	yes	characteristic
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083558	—	2	2	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	—	4	4	no	—
53	C₂×#13083558	D₄	1	1	yes	characteristic
54	C₂×#13083558	D₄	1	1	yes	characteristic
55	C₂²×#10623494	—	2	2	no	—
56	C₄⋊#10623494	—	2	2	no	—
57	C₄⋊#10623494	—	2	2	no	—
58	C₄⋊#10623494	—	2	1	no	—
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	—	2	1	no	—
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₄⋊#10623494	C₂³	1	2	yes	—
63	C₂²⋊#10623494	—	2	2	no	—
64	C₂²⋊#10623494	—	2	2	no	—
65	C₂²⋊#10623494	—	2	1	no	—
66	#15667923	—	2	2	no	—
67	#15667923	D₄	1	2	yes	—
68	C₄×#10623494	—	2	2	no	—
69	C₄×#10623494	C₂³	1	2	yes	—
70	C₄×#10623494	C₂³	1	2	yes	—
71	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	—	2	1	no	—
74	C₂×SD₁₆×C₈₉	—	2	4	no	—
75	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₈₉	—	2	1	no	—
82	C₄×Q₈×C₈₉	—	2	1	no	—
83	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₈₉	—	2	1	no	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	—	2	1	no	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
100	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
101	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
102	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
103	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
104	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
105	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
107	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
108	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
109	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
110	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	#13083558	—	2	2	no	—
116	#13083558	—	2	2	no	—
117	#13083558	—	4	4	no	—
118	#13083558	—	4	2	no	—
119	#13083558	—	4	2	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	4	4	no	—
124	C₂×#10623494	C₂×D₄	1	2	yes	—
125	C₂×#10623494	C₂×D₄	1	2	yes	—
126	C₂⁴×C₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂×Q₈×C₈₉	—	4	1	no	—
130	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₈₉	—	2	2	no	—
133	C₂×D₄×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	4	1	no	—
135	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	—	2	1	no	—
140	C₂²×C₄×C₈₉	—	2	1	no	—
141	C₂²×C₄×C₈₉	—	2	1	no	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	4	2	no	—
145	C₂²×C₄×C₈₉	—	4	2	no	—
146	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	SD₁₆×C₈₉	—	2	2	no	—
150	SD₁₆×C₈₉	—	2	2	no	—
151	SD₁₆×C₈₉	—	2	2	no	—
152	SD₁₆×C₈₉	M₁₆	1	4	yes	complemented
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	4	1	no	—
155	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	1	no	—
165	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₈₉	—	2	1	no	—
170	C₂²⋊C₄×C₈₉	—	2	1	no	—
171	C₂²⋊C₄×C₈₉	—	2	1	no	—
172	C₂²⋊C₄×C₈₉	—	2	1	no	—
173	C₄²×C₈₉	—	2	1	no	—
174	C₄²×C₈₉	—	2	1	no	—
175	C₄²×C₈₉	—	2	1	no	—
176	C₄²×C₈₉	—	2	1	no	—
177	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₈₉	#41	1	1	yes	characteristic
180	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂³×C₈₉	—	2	1	no	—
182	C₂³×C₈₉	—	2	1	no	—
183	C₂³×C₈₉	—	4	2	no	—
184	C₂³×C₈₉	—	4	2	no	—
185	C₂³×C₈₉	—	8	1	no	—
186	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
187	Q₈×C₈₉	—	2	1	no	—
188	Q₈×C₈₉	—	2	1	no	—
189	Q₈×C₈₉	—	2	1	no	—
190	Q₈×C₈₉	—	4	2	no	—
191	Q₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
192	D₄×C₈₉	—	2	1	no	—
193	D₄×C₈₉	—	2	1	no	—
194	D₄×C₈₉	—	2	1	no	—
195	D₄×C₈₉	—	4	2	no	—
196	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
197	C₂×C₄×C₈₉	—	2	1	no	—
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	2	1	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	—	4	2	no	—
207	C₂×C₄×C₈₉	—	4	2	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	—	4	1	no	—
210	C₂×C₄×C₈₉	—	4	1	no	—
211	C₂×C₄×C₈₉	—	4	1	no	—
212	C₂×C₄×C₈₉	—	4	2	no	—
213	C₂×C₄×C₈₉	—	4	2	no	—
214	C₂×C₄×C₈₉	—	8	1	no	—
215	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₈₉	#137	1	2	yes	—
220	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
223	C₈×C₈₉	—	2	1	no	—
224	C₈×C₈₉	—	2	1	no	—
225	C₈×C₈₉	—	2	1	no	—
226	C₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
227	#10623494	—	2	2	no	—
228	#10623494	—	2	2	no	—
229	#10623494	—	4	2	no	—
230	#10623494	—	4	2	no	—
231	#10623494	—	4	2	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	4	1	no	—
236	C₂²×C₈₉	—	4	1	no	—
237	C₂²×C₈₉	—	4	1	no	—
238	C₂²×C₈₉	—	4	1	no	—
239	C₂²×C₈₉	—	4	1	no	—
240	C₂²×C₈₉	—	8	4	no	—
241	C₂²×C₈₉	#440	1	2	yes	—
242	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₈₉	—	2	1	no	—
244	C₄×C₈₉	—	2	2	no	—
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	4	1	no	—
248	C₄×C₈₉	—	4	1	no	—
249	C₄×C₈₉	—	4	1	no	—
250	C₄×C₈₉	—	4	1	no	—
251	C₄×C₈₉	—	4	1	no	—
252	C₄×C₈₉	#440	1	2	yes	—
253	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
254	C₄×C₈₉	#568	1	1	yes	characteristic
255	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
257	#18040	—	89	1	no	maximal, Sylow
258	C₂×C₈₉	—	2	2	no	—
259	C₂×C₈₉	—	4	2	no	—
260	C₂×C₈₉	—	8	1	no	—
261	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
262	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
263	C₂×C₈₉	#2957	1	1	yes	characteristic
264	Q₈×M₁₆	—	89	1	no	—
265	C₂×C₄×SD₁₆	D₈₉	1	1	yes	characteristic
266	D₄×M₁₆	—	89	1	no	—
267	#1592	—	89	2	no	—
268	#1588	—	89	2	no	—
269	#1585	—	89	2	no	—
270	SD₁₆⋊C₈	—	89	2	no	—
271	#1567	—	89	1	no	—
272	#1487	—	89	1	no	—
273	#1486	—	89	1	no	—
274	#1451	—	89	1	no	—
275	C₈₉	#18040	1	1	yes	characteristic, complemented, Sylow
276	C₂²×SD₁₆	Dic₈₉	1	1	yes	characteristic
277	C₂²×M₁₆	—	178	1	no	—
278	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
280	#446	—	89	2	no	—
281	#446	—	178	2	no	—
282	C₈×Q₈	—	89	2	no	—
283	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic
284	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic
285	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic
286	C₄×SD₁₆	Dic₈₉	1	1	yes	characteristic
287	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
288	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
289	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
290	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
291	#436	—	89	2	no	—
292	#435	—	178	2	no	—
293	C₈×D₄	—	89	2	no	—
294	#431	—	89	1	no	—
295	C₂×#106	Dic₈₉	1	1	yes	characteristic
296	#423	—	89	1	no	—
297	#423	—	89	1	no	—
298	#423	—	178	1	no	—
299	C₂×#103	Dic₈₉	1	1	yes	characteristic
300	C₂×#102	Dic₈₉	1	1	yes	characteristic
301	#407	—	178	1	no	—
302	C₄×M₁₆	—	89	1	no	—
303	C₄×M₁₆	—	178	1	no	—
304	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
305	#335	—	89	2	no	—
306	#335	—	89	2	no	—
307	Q₈⋊C₈	—	89	2	no	—
308	Q₈⋊C₈	—	89	2	no	—
309	D₄⋊C₈	—	89	2	no	—
310	D₄⋊C₈	—	89	2	no	—
311	#322	—	89	2	no	—
312	#322	—	89	2	no	—
313	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
314	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
318	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
319	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
320	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
321	C₂×M₁₆	—	89	1	no	—
322	C₂×M₁₆	—	89	1	no	—
323	C₂×M₁₆	—	356	4	no	—
324	C₂×M₁₆	—	178	2	no	—
325	C₂×M₁₆	—	178	1	no	—
326	C₂×M₁₆	—	178	1	no	—
327	C₂²×C₈	—	178	2	no	—
328	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
329	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
333	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
334	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
335	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
339	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
340	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
341	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
348	#106	C₂×Dic₈₉	1	1	yes	characteristic
349	#106	C₂×Dic₈₉	1	1	yes	characteristic
350	#106	C₂×Dic₈₉	1	1	yes	characteristic
351	#106	C₂×Dic₈₉	1	1	yes	characteristic
352	C₄⋊C₈	—	89	2	no	—
353	C₄⋊C₈	—	89	2	no	—
354	C₄⋊C₈	—	178	2	no	—
355	C₄⋊C₈	—	178	2	no	—
356	C₄⋊C₈	—	178	1	no	—
357	C₄⋊C₈	—	178	1	no	—
358	C₄⋊C₈	—	178	1	no	—
359	#103	C₂×Dic₈₉	1	1	yes	characteristic
360	#103	C₂×Dic₈₉	1	1	yes	characteristic
361	#103	C₂×Dic₈₉	1	1	yes	characteristic
362	#103	C₂×Dic₈₉	1	1	yes	characteristic
363	#102	C₂×Dic₈₉	1	1	yes	characteristic
364	#102	C₂×Dic₈₉	1	1	yes	characteristic
365	#102	C₂×Dic₈₉	1	1	yes	characteristic
366	#102	C₂×Dic₈₉	1	1	yes	characteristic
367	C₂²⋊C₈	—	178	2	no	—
368	C₂²⋊C₈	—	178	2	no	—
369	C₂²⋊C₈	—	178	1	no	—
370	#97	—	89	2	no	—
371	#97	—	178	2	no	—
372	C₄×C₈	—	89	2	no	—
373	C₄×C₈	—	89	2	no	—
374	C₄×C₈	—	178	2	no	—
375	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
376	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
377	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
379	C₂⁴	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
384	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
389	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
400	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
401	C₂²×C₄	#13083573	1	1	yes	characteristic
402	SD₁₆	—	2	2	no	—
403	SD₁₆	—	2	2	no	—
404	SD₁₆	—	2	2	no	—
405	SD₁₆	#13083558	1	4	yes	complemented
406	M₁₆	—	356	2	no	—
407	M₁₆	—	356	2	no	—
408	M₁₆	—	356	4	no	—
409	M₁₆	—	178	2	no	—
410	M₁₆	—	178	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	4	1	no	—
413	C₂×C₈	—	89	2	no	—
414	C₂×C₈	—	89	2	no	—
415	C₂×C₈	—	356	4	no	—
416	C₂×C₈	—	178	2	no	—
417	C₂×C₈	—	178	2	no	—
418	C₂×C₈	—	178	2	no	—
419	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
420	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
421	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
422	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
430	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
442	C₄²	D₄×D₈₉	1	1	yes	characteristic
443	C₄²	#13083573	1	1	yes	characteristic
444	C₄²	C₂³×D₈₉	1	1	yes	characteristic
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	8	1	no	—
450	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
451	Q₈	—	2	1	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	1	no	—
454	Q₈	—	4	2	no	—
455	Q₈	C₂×#13083558	1	2	yes	complemented
456	D₄	—	2	1	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	4	2	no	—
460	D₄	C₂×#13083558	1	2	yes	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
480	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
481	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
482	C₂×C₄	#15668039	1	2	yes	—
483	C₂×C₄	#15668041	1	2	yes	—
484	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
485	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
486	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	356	2	no	—
491	C₈	—	356	2	no	—
492	C₈	—	356	2	no	—
493	C₈	—	178	2	no	—
494	C₈	—	178	2	no	—
495	C₈	C₂×#13083558	1	2	yes	complemented
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	8	4	no	—
505	C₂²	#19151699	1	2	yes	—
506	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	#19151699	1	2	yes	—
517	C₄	C₂²×#13083558	1	1	yes	characteristic
518	C₄	#19152365	1	1	yes	characteristic
519	C₄	C₂×#15668039	1	1	yes	characteristic
520	C₄	C₂×#15668041	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	4	2	no	—
523	C₂	—	8	1	no	—
524	C₂	D₄×#13083558	1	1	yes	characteristic
525	C₂	C₂×#19151699	1	1	yes	characteristic
526	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×C₄×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₈₉
hypocenter	C₈₉	#18040
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×#13083558	C₂	semidirect
3. #26019155	C₂	semidirect
4. #26019131	C₂	semidirect
5. #26019110	C₂	semidirect
6. SD₁₆⋊#10623494	C₂	semidirect
7. #26019011	C₂	semidirect
8. #26018681	C₂	semidirect
10. #26018541	C₂	semidirect
14. #19151729	C₂²	semidirect
15. Q₈×#10623494	C₂²	semidirect
26. #19151351	C₂²	semidirect
27. #19151351	C₂²	semidirect
28. Q₈⋊#10623494	C₂²	semidirect
29. Q₈⋊#10623494	C₂²	semidirect
32. #19151320	C₂²	semidirect
33. #19151319	C₂²	semidirect
152. SD₁₆×C₈₉	M₁₆	semidirect
191. Q₈×C₈₉	C₂×M₁₆	semidirect
226. C₈×C₈₉	C₂×M₁₆	semidirect
275. C₈₉	#18040	semidirect
405. SD₁₆	#13083558	semidirect
455. Q₈	C₂×#13083558	semidirect
495. C₈	C₂×#13083558	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#13083558	2
D₄×#13083558	2
#26019155	2
#26019131	2
#26019110	2
SD₁₆⋊#10623494	2
#26019011	2
#26018681	2
#26018677	2
#26018541	2
C₂×C₄×SD₁₆×C₈₉	2
#18040	89