Subgroups — #36525962

Order 22784.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029266	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019155	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019143	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019117	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019110	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019089	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019082	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019076	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018695	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018691	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018555	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#13083558	—	2	1	no	—
17	#19151729	C₂²	1	1	yes	characteristic, complemented
18	#19151729	C₂²	1	1	yes	characteristic, complemented
19	#19151676	C₂²	1	1	yes	characteristic
20	#19151676	C₂²	1	1	yes	characteristic
21	#19151670	—	2	1	no	—
22	#19151670	—	2	1	no	—
23	#19151670	—	2	1	no	—
24	#19151670	—	2	1	no	—
25	D₄×#10623494	C₂²	1	1	yes	characteristic
26	D₄×#10623494	C₂²	1	1	yes	characteristic
27	D₄×#10623494	C₂²	1	1	yes	characteristic, complemented
28	D₄×#10623494	C₂²	1	1	yes	characteristic, complemented
29	#19151655	—	2	1	no	—
30	#19151655	C₂²	1	1	yes	characteristic
31	#19151622	C₂²	1	1	yes	characteristic
32	#19151562	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	C₄×#13083558	C₂²	1	1	yes	characteristic
35	C₂×#15667923	—	2	1	no	—
36	#19151351	C₂²	1	1	yes	characteristic, complemented
37	#19151351	C₂²	1	1	yes	characteristic, complemented
38	#19151349	C₂²	1	1	yes	characteristic, complemented
39	#19151349	C₂²	1	1	yes	characteristic, complemented
40	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
41	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊#10623494	C₂²	1	1	yes	characteristic
43	D₄⋊#10623494	C₂²	1	1	yes	characteristic
44	D₄⋊#10623494	C₂²	1	1	yes	characteristic
45	D₄⋊#10623494	C₂²	1	1	yes	characteristic
46	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
47	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
48	#19151320	C₂²	1	1	yes	characteristic, complemented
49	#19151320	C₂²	1	1	yes	characteristic, complemented
50	#19151319	C₂²	1	1	yes	characteristic, complemented
51	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
52	C₂×AGL(1,ℤ/8)×C₈₉	C₄	1	1	yes	characteristic
53	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	#442×C₈₉	C₄	1	1	yes	characteristic
56	#442×C₈₉	C₄	1	1	yes	characteristic
57	#440×C₈₉	C₄	1	1	yes	characteristic
58	#440×C₈₉	C₄	1	1	yes	characteristic
59	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
60	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
63	#428×C₈₉	C₄	1	1	yes	characteristic
64	#418×C₈₉	C₄	1	1	yes	characteristic
65	#417×C₈₉	C₄	1	1	yes	characteristic
66	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083558	—	2	1	no	—
68	C₂×#13083558	—	2	1	no	—
69	C₂×#13083558	—	2	1	no	—
70	C₂×#13083558	—	2	1	no	—
71	C₂×#13083558	—	4	4	no	—
72	C₂×#13083558	D₄	1	1	yes	characteristic
73	C₂×#13083558	D₄	1	1	yes	characteristic
74	C₂²×#10623494	—	2	1	no	—
75	C₂²×#10623494	—	2	1	no	—
76	C₂²×#10623494	—	2	1	no	—
77	C₂²×#10623494	—	2	1	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	—	2	1	no	—
80	C₄⋊#10623494	—	2	1	no	—
81	C₄⋊#10623494	C₂³	1	1	yes	characteristic
82	C₄⋊#10623494	C₂³	1	1	yes	characteristic
83	C₄⋊#10623494	C₂³	1	1	yes	characteristic
84	C₄⋊#10623494	C₂³	1	1	yes	characteristic
85	C₂²⋊#10623494	—	2	1	no	—
86	C₂²⋊#10623494	—	2	1	no	—
87	C₂²⋊#10623494	—	2	1	no	—
88	C₂²⋊#10623494	—	2	1	no	—
89	C₂²⋊#10623494	—	2	1	no	—
90	C₂²⋊#10623494	—	2	1	no	—
91	C₂²⋊#10623494	—	2	1	no	—
92	#15667923	—	2	1	no	—
93	#15667923	—	2	1	no	—
94	#15667923	—	2	1	no	—
95	#15667923	—	2	1	no	—
96	#15667923	D₄	1	1	yes	characteristic
97	#15667923	D₄	1	1	yes	characteristic
98	C₄×#10623494	C₂³	1	1	yes	characteristic
99	C₄×#10623494	C₂³	1	1	yes	characteristic
100	C₄×#10623494	C₂³	1	1	yes	characteristic
101	C₄×#10623494	C₂³	1	1	yes	characteristic
102	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₈₉	—	2	1	no	—
105	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
106	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
108	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
109	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
110	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
111	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₈₉	—	2	1	no	—
115	C₄×D₄×C₈₉	—	2	1	no	—
116	C₄×D₄×C₈₉	—	2	1	no	—
117	C₄×D₄×C₈₉	—	2	1	no	—
118	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
124	#117×C₈₉	—	2	1	no	—
125	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
131	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
132	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
133	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
135	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
141	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
142	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
143	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
146	#13083558	—	2	2	no	—
147	#13083558	—	4	1	no	—
148	#13083558	—	4	2	no	—
149	#13083558	—	4	2	no	—
150	#13083558	—	4	2	no	—
151	#13083558	—	4	2	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	4	2	no	—
159	C₂×#10623494	—	4	2	no	—
160	C₂×#10623494	—	4	2	no	—
161	C₂×#10623494	—	4	2	no	—
162	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
163	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
164	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
165	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×C₈₉	—	2	1	no	—
167	#41×C₈₉	—	2	2	no	—
168	#41×C₈₉	—	4	1	no	—
169	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×D₄×C₈₉	—	2	2	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	4	1	no	—
174	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	1	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	1	no	—
184	C₂²×C₄×C₈₉	—	2	1	no	—
185	C₂²×C₄×C₈₉	—	4	2	no	—
186	C₂²×C₄×C₈₉	—	4	2	no	—
187	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
190	SD₁₆×C₈₉	—	2	2	no	—
191	SD₁₆×C₈₉	—	2	2	no	—
192	D₈×C₈₉	—	2	2	no	—
193	D₈×C₈₉	M₁₆	1	4	yes	complemented
194	M₁₆×C₈₉	—	2	2	no	—
195	M₁₆×C₈₉	—	4	1	no	—
196	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₈₉	—	2	1	no	—
208	C₂²⋊C₄×C₈₉	—	2	1	no	—
209	C₂²⋊C₄×C₈₉	—	2	1	no	—
210	C₂²⋊C₄×C₈₉	—	2	1	no	—
211	C₂²⋊C₄×C₈₉	—	2	1	no	—
212	C₂²⋊C₄×C₈₉	—	2	1	no	—
213	C₂²⋊C₄×C₈₉	—	2	1	no	—
214	C₄²×C₈₉	—	2	1	no	—
215	C₄²×C₈₉	—	2	1	no	—
216	C₄²×C₈₉	—	2	1	no	—
217	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₈₉	#41	1	1	yes	characteristic
220	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂³×C₈₉	—	2	1	no	—
222	C₂³×C₈₉	—	2	1	no	—
223	C₂³×C₈₉	—	2	1	no	—
224	C₂³×C₈₉	—	4	2	no	—
225	C₂³×C₈₉	—	4	2	no	—
226	C₂³×C₈₉	—	8	1	no	—
227	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
228	Q₈×C₈₉	—	2	1	no	—
229	Q₈×C₈₉	—	2	1	no	—
230	D₄×C₈₉	—	2	1	no	—
231	D₄×C₈₉	—	2	1	no	—
232	D₄×C₈₉	—	2	1	no	—
233	D₄×C₈₉	—	2	1	no	—
234	D₄×C₈₉	—	4	2	no	—
235	D₄×C₈₉	—	4	2	no	—
236	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
237	D₄×C₈₉	C₂×M₁₆	1	2	yes	complemented
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	1	no	—
242	C₂×C₄×C₈₉	—	2	1	no	—
243	C₂×C₄×C₈₉	—	2	1	no	—
244	C₂×C₄×C₈₉	—	2	1	no	—
245	C₂×C₄×C₈₉	—	2	1	no	—
246	C₂×C₄×C₈₉	—	2	1	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	2	no	—
249	C₂×C₄×C₈₉	—	4	2	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	—	4	2	no	—
252	C₂×C₄×C₈₉	—	4	1	no	—
253	C₂×C₄×C₈₉	—	4	1	no	—
254	C₂×C₄×C₈₉	—	4	1	no	—
255	C₂×C₄×C₈₉	—	4	1	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	1	no	—
258	C₂×C₄×C₈₉	—	8	1	no	—
259	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
265	C₈×C₈₉	—	2	1	no	—
266	C₈×C₈₉	—	2	1	no	—
267	C₈×C₈₉	—	2	1	no	—
268	C₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
269	#10623494	—	2	2	no	—
270	#10623494	—	2	1	no	—
271	#10623494	—	2	1	no	—
272	#10623494	—	2	1	no	—
273	#10623494	—	4	1	no	—
274	#10623494	—	4	1	no	—
275	#10623494	—	4	1	no	—
276	#10623494	—	4	1	no	—
277	#10623494	—	4	1	no	—
278	#10623494	AGL(1,ℤ/8)	1	2	yes	complemented
279	C₂²×C₈₉	—	2	1	no	—
280	C₂²×C₈₉	—	2	2	no	—
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	—	2	1	no	—
283	C₂²×C₈₉	—	2	1	no	—
284	C₂²×C₈₉	—	4	1	no	—
285	C₂²×C₈₉	—	4	1	no	—
286	C₂²×C₈₉	—	4	1	no	—
287	C₂²×C₈₉	—	4	1	no	—
288	C₂²×C₈₉	—	4	1	no	—
289	C₂²×C₈₉	—	4	1	no	—
290	C₂²×C₈₉	—	4	1	no	—
291	C₂²×C₈₉	—	8	4	no	—
292	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₈₉	—	2	1	no	—
294	C₄×C₈₉	—	2	1	no	—
295	C₄×C₈₉	—	2	1	no	—
296	C₄×C₈₉	—	2	1	no	—
297	C₄×C₈₉	—	4	1	no	—
298	C₄×C₈₉	—	4	1	no	—
299	C₄×C₈₉	—	4	1	no	—
300	C₄×C₈₉	—	4	1	no	—
301	C₄×C₈₉	—	4	1	no	—
302	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
303	C₄×C₈₉	#568	1	1	yes	characteristic
304	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₄×C₈₉	#575	1	1	yes	characteristic
306	#18046	—	89	1	no	maximal, Sylow
307	C₂×C₈₉	—	4	1	no	—
308	C₂×C₈₉	—	4	2	no	—
309	C₂×C₈₉	—	4	2	no	—
310	C₂×C₈₉	—	8	1	no	—
311	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
312	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₂×C₈₉	#2956	1	1	yes	characteristic
314	#2970	—	89	1	no	—
315	C₄×AGL(1,ℤ/8)	D₈₉	1	1	yes	characteristic
316	D₄×M₁₆	—	89	1	no	—
317	#1592	—	89	1	no	—
318	#1590	—	89	1	no	—
319	#1586	—	89	1	no	—
320	#1585	—	89	1	no	—
321	#1582	—	89	1	no	—
322	#1581	—	89	1	no	—
323	#1580	—	89	1	no	—
324	C₈×D₈	—	89	1	no	—
325	#1569	—	89	1	no	—
326	#1490	—	89	1	no	—
327	#1489	—	89	1	no	—
328	#1455	—	89	1	no	—
329	C₈₉	#18046	1	1	yes	characteristic, complemented, Sylow
330	C₂×AGL(1,ℤ/8)	Dic₈₉	1	1	yes	characteristic
331	C₂²×M₁₆	—	178	1	no	—
332	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
334	#446	—	89	1	no	—
335	#446	—	89	1	no	—
336	#442	Dic₈₉	1	1	yes	characteristic
337	#442	Dic₈₉	1	1	yes	characteristic
338	#440	Dic₈₉	1	1	yes	characteristic
339	#440	Dic₈₉	1	1	yes	characteristic
340	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
341	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
342	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
343	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
344	#436	—	89	1	no	—
345	#436	—	89	1	no	—
346	#435	—	178	1	no	—
347	#435	—	178	1	no	—
348	#435	—	178	1	no	—
349	#435	—	178	1	no	—
350	C₈×D₄	—	89	1	no	—
351	C₈×D₄	—	89	1	no	—
352	C₈×D₄	—	89	1	no	—
353	C₈×D₄	—	89	1	no	—
354	#432	—	89	1	no	—
355	#432	—	178	1	no	—
356	#428	Dic₈₉	1	1	yes	characteristic
357	#423	—	89	1	no	—
358	#418	Dic₈₉	1	1	yes	characteristic
359	#417	Dic₈₉	1	1	yes	characteristic
360	#407	—	178	1	no	—
361	C₄×M₁₆	—	89	1	no	—
362	C₄×M₁₆	—	89	1	no	—
363	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
364	C₂×#97	—	178	1	no	—
365	#335	—	89	1	no	—
366	#335	—	89	1	no	—
367	#334	—	89	1	no	—
368	#334	—	89	1	no	—
369	Q₈⋊C₈	—	89	1	no	—
370	Q₈⋊C₈	—	89	1	no	—
371	D₄⋊C₈	—	89	1	no	—
372	D₄⋊C₈	—	89	1	no	—
373	D₄⋊C₈	—	89	1	no	—
374	D₄⋊C₈	—	89	1	no	—
375	D₄⋊C₈	—	89	1	no	—
376	D₄⋊C₈	—	89	1	no	—
377	#322	—	89	1	no	—
378	#322	—	89	1	no	—
379	#322	—	89	1	no	—
380	C₈²	—	89	1	no	—
381	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
382	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	AGL(1,ℤ/8)	—	2	4	no	—
385	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
386	C₂×SD₁₆	C₂×Dic₈₉	1	1	yes	characteristic
387	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
388	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
389	C₂×M₁₆	—	89	1	no	—
390	C₂×M₁₆	—	89	1	no	—
391	C₂×M₁₆	—	356	4	no	—
392	C₂×M₁₆	—	178	1	no	—
393	C₂×M₁₆	—	178	1	no	—
394	C₂×M₁₆	—	178	1	no	—
395	C₂×M₁₆	—	178	1	no	—
396	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
397	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
398	C₂²×C₈	—	178	1	no	—
399	C₂²×C₈	—	178	1	no	—
400	C₂²×C₈	—	178	1	no	—
401	C₂²×C₈	—	178	1	no	—
402	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
403	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
409	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
410	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
411	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
412	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
413	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
414	#117	—	2	1	no	—
415	#117	C₂×Dic₈₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
420	#107	C₂×Dic₈₉	1	1	yes	characteristic
421	#107	C₂×Dic₈₉	1	1	yes	characteristic
422	#106	C₂×Dic₈₉	1	1	yes	characteristic
423	#106	C₂×Dic₈₉	1	1	yes	characteristic
424	C₄⋊C₈	—	89	1	no	—
425	C₄⋊C₈	—	89	1	no	—
426	C₄⋊C₈	—	89	1	no	—
427	C₄⋊C₈	—	89	1	no	—
428	C₄⋊C₈	—	178	1	no	—
429	C₄⋊C₈	—	178	1	no	—
430	C₄⋊C₈	—	178	1	no	—
431	#103	C₂×Dic₈₉	1	1	yes	characteristic
432	#103	C₂×Dic₈₉	1	1	yes	characteristic
433	#102	C₂×Dic₈₉	1	1	yes	characteristic
434	#102	C₂×Dic₈₉	1	1	yes	characteristic
435	#102	C₂×Dic₈₉	1	1	yes	characteristic
436	#102	C₂×Dic₈₉	1	1	yes	characteristic
437	#102	C₂×Dic₈₉	1	1	yes	characteristic
438	#102	C₂×Dic₈₉	1	1	yes	characteristic
439	C₂²⋊C₈	—	178	1	no	—
440	C₂²⋊C₈	—	178	1	no	—
441	C₂²⋊C₈	—	178	1	no	—
442	C₂²⋊C₈	—	178	1	no	—
443	C₂²⋊C₈	—	178	1	no	—
444	C₂²⋊C₈	—	178	1	no	—
445	C₂²⋊C₈	—	178	1	no	—
446	#97	—	89	1	no	—
447	#97	—	89	1	no	—
448	#97	—	178	1	no	—
449	#97	—	178	1	no	—
450	#97	—	178	1	no	—
451	#97	—	178	1	no	—
452	#97	C₂×Dic₈₉	1	1	yes	characteristic
453	#97	C₂×Dic₈₉	1	1	yes	characteristic
454	C₄×C₈	—	89	1	no	—
455	C₄×C₈	—	89	1	no	—
456	C₄×C₈	—	89	1	no	—
457	C₄×C₈	—	89	1	no	—
458	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
459	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
460	C₂⁴	—	2	1	no	—
461	#41	—	2	2	no	—
462	#41	—	4	1	no	—
463	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
469	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
470	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
482	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
483	C₂²×C₄	#13083573	1	1	yes	characteristic
484	SD₁₆	—	2	2	no	—
485	SD₁₆	—	2	2	no	—
486	D₈	—	2	2	no	—
487	D₈	#13083558	1	4	yes	complemented
488	M₁₆	—	2	2	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	356	2	no	—
491	M₁₆	—	356	2	no	—
492	M₁₆	—	356	2	no	—
493	M₁₆	—	356	2	no	—
494	M₁₆	—	356	1	no	—
495	M₁₆	—	178	2	no	—
496	C₂×C₈	—	89	1	no	—
497	C₂×C₈	—	89	1	no	—
498	C₂×C₈	—	89	1	no	—
499	C₂×C₈	—	89	1	no	—
500	C₂×C₈	—	356	2	no	—
501	C₂×C₈	—	356	2	no	—
502	C₂×C₈	—	356	2	no	—
503	C₂×C₈	—	356	2	no	—
504	C₂×C₈	—	178	1	no	—
505	C₂×C₈	—	178	1	no	—
506	C₂×C₈	—	178	1	no	—
507	C₂×C₈	—	178	1	no	—
508	C₂×C₈	—	178	1	no	—
509	C₂×C₈	—	178	1	no	—
510	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
511	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
512	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
513	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
532	C₄²	D₄×D₈₉	1	1	yes	characteristic
533	C₄²	#13083573	1	1	yes	characteristic
534	C₄²	C₂³×D₈₉	1	1	yes	characteristic
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	8	1	no	—
541	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	C₂×#13083558	1	2	yes	—
551	D₄	C₂×#13083558	1	2	yes	complemented
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
574	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
575	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
576	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
577	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
578	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	89	2	no	—
583	C₈	—	356	1	no	—
584	C₈	—	356	1	no	—
585	C₈	—	356	1	no	—
586	C₈	—	356	1	no	—
587	C₈	—	356	1	no	—
588	C₈	—	178	2	no	—
589	C₈	—	178	1	no	—
590	C₈	—	178	1	no	—
591	C₈	—	178	1	no	—
592	C₈	C₂×#13083558	1	2	yes	complemented
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	8	4	no	—
606	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	C₂²×#13083558	1	1	yes	characteristic
617	C₄	#19152365	1	1	yes	characteristic
618	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
619	C₄	#19152394	1	1	yes	characteristic
620	C₂	—	4	1	no	—
621	C₂	—	4	2	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	D₄×#13083558	1	1	yes	characteristic
625	C₂	AGL(1,ℤ/8)×Dic₈₉	1	1	yes	characteristic
626	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₄×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#18046
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #26029266	C₂	semidirect
2. D₄×#13083558	C₂	semidirect
3. #26019155	C₂	semidirect
4. #26019143	C₂	semidirect
5. #26019117	C₂	semidirect
6. #26019110	C₂	semidirect
7. #26019089	C₂	semidirect
8. #26019082	C₂	semidirect
9. #26019076	C₂	semidirect
10. D₈×#10623494	C₂	semidirect
11. #26019019	C₂	semidirect
12. #26018695	C₂	semidirect
13. #26018691	C₂	semidirect
14. #26018555	C₂	semidirect
17. #19151729	C₂²	semidirect
18. #19151729	C₂²	semidirect
27. D₄×#10623494	C₂²	semidirect
28. D₄×#10623494	C₂²	semidirect
36. #19151351	C₂²	semidirect
37. #19151351	C₂²	semidirect
38. #19151349	C₂²	semidirect
39. #19151349	C₂²	semidirect
40. Q₈⋊#10623494	C₂²	semidirect
41. Q₈⋊#10623494	C₂²	semidirect
46. D₄⋊#10623494	C₂²	semidirect
47. D₄⋊#10623494	C₂²	semidirect
48. #19151320	C₂²	semidirect
49. #19151320	C₂²	semidirect
50. #19151319	C₂²	semidirect
51. C₈×#10623494	C₂²	semidirect
193. D₈×C₈₉	M₁₆	semidirect
237. D₄×C₈₉	C₂×M₁₆	semidirect
268. C₈×C₈₉	C₂×M₁₆	semidirect
278. #10623494	AGL(1,ℤ/8)	semidirect
329. C₈₉	#18046	semidirect
487. D₈	#13083558	semidirect
551. D₄	C₂×#13083558	semidirect
592. 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
#26029266	2
D₄×#13083558	2
#26019155	2
#26019143	2
#26019117	2
#26019110	2
#26019089	2
#26019082	2
#26019076	2
D₈×#10623494	2
#26019019	2
#26018695	2
#26018691	2
#26018555	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#18046	89