Subgroups — #36524014

Order 22784.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029215	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668036	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019114	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019111	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019109	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019087	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019085	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019084	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019082	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019001	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018641	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018636	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668036	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₈₉	—	2	1	no	—
18	C₄×#13083573	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	#19151728	C₂²	1	1	yes	characteristic, complemented
21	#19151725	C₂²	1	1	yes	characteristic, complemented
22	#19151710	C₄	1	1	yes	characteristic
23	#19151707	C₄	1	1	yes	characteristic
24	#19151697	C₄	1	1	yes	characteristic
25	#19151695	C₄	1	1	yes	characteristic
26	C₄×#13083563	C₂²	1	1	yes	characteristic
27	C₄×#13083562	C₂²	1	1	yes	characteristic
28	C₄×#13083559	C₂²	1	1	yes	characteristic
29	#19151676	C₂²	1	1	yes	characteristic, complemented
30	#19151672	—	2	1	no	—
31	#19151667	—	2	1	no	—
32	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
33	D₄×#10623494	C₂²	1	1	yes	characteristic
34	#19151663	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₈₉	—	2	1	no	—
36	#19151661	—	2	1	no	—
37	#19151650	C₂²	1	1	yes	characteristic
38	#19151649	C₂²	1	1	yes	characteristic
39	#19151648	—	2	1	no	—
40	#19151639	C₄	1	1	yes	characteristic
41	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
42	#19151601	C₄	1	1	yes	characteristic
43	#19151596	C₄	1	1	yes	characteristic
44	C₂²⋊C₈×D₈₉	—	2	1	no	—
45	M₁₆×Dic₈₉	—	2	1	no	—
46	C₄×#13083557	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic, complemented
49	#19151350	C₂²	1	1	yes	characteristic, complemented
50	#19151348	C₂²	1	1	yes	characteristic, complemented
51	#19151330	C₂²	1	1	yes	characteristic, complemented
52	#19151328	C₂²	1	1	yes	characteristic, complemented
53	#19151327	C₂²	1	1	yes	characteristic
54	D₄⋊#10623494	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
56	#19151325	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic, complemented
58	#19151320	C₂²	1	1	yes	characteristic, complemented
59	#19151320	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
61	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13083573	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₈₉	—	2	1	no	—
70	#15668036	—	2	4	no	—
71	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083558	—	2	1	no	—
75	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
76	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
77	C₂²×#10623494	—	2	1	no	—
78	C₂×C₈×D₈₉	—	2	1	no	—
79	C₂×C₈×D₈₉	—	2	1	no	—
80	C₂×C₈×D₈₉	—	2	1	no	—
81	C₂×C₈×D₈₉	—	4	4	no	—
82	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
83	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
84	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	#15667977	C₂×C₄	1	1	yes	characteristic
86	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
87	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	#15667974	C₂×C₄	1	1	yes	characteristic
90	C₄×C₂²⋊D₈₉	—	2	1	no	—
91	C₄×C₂²⋊D₈₉	—	2	1	no	—
92	#15667972	—	2	1	no	—
93	#15667972	—	2	1	no	—
94	#15667970	C₂×C₄	1	1	yes	characteristic
95	#15667968	—	2	1	no	—
96	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊C₄×D₈₉	—	2	1	no	—
98	C₂×C₄×Dic₈₉	—	2	1	no	—
99	C₄²×D₈₉	C₂³	1	1	yes	characteristic
100	#15667945	C₂×C₄	1	1	yes	characteristic
101	#15667944	C₂×C₄	1	1	yes	characteristic
102	#15667943	C₂×C₄	1	1	yes	characteristic
103	C₄⋊#10623494	C₂³	1	1	yes	characteristic
104	C₄⋊#10623494	C₂³	1	1	yes	characteristic
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667937	C₂×C₄	1	1	yes	characteristic
110	#15667935	C₂×C₄	1	1	yes	characteristic
111	#15667934	C₂×C₄	1	1	yes	characteristic
112	#15667933	C₂×C₄	1	1	yes	characteristic
113	#15667933	C₂×C₄	1	1	yes	characteristic
114	#15667932	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#10623494	—	2	1	no	—
116	C₂²⋊#10623494	—	2	1	no	—
117	#15667924	—	2	1	no	—
118	#15667924	—	2	1	no	—
119	#15667924	—	2	1	no	—
120	#15667924	—	2	1	no	—
121	#15667922	—	2	1	no	—
122	#15667922	—	2	1	no	—
123	#15667922	C₂×C₄	1	1	yes	characteristic
124	#15667922	C₂×C₄	1	1	yes	characteristic
125	C₄×#10623494	C₂³	1	1	yes	characteristic
126	C₄×#10623494	C₂³	1	1	yes	characteristic
127	C₄×#10623494	C₂³	1	1	yes	characteristic
128	C₈×Dic₈₉	—	2	1	no	—
129	C₈×Dic₈₉	D₄	1	1	yes	characteristic
130	C₈×Dic₈₉	D₄	1	1	yes	characteristic
131	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
132	C₂×M₁₆×C₈₉	—	2	1	no	—
133	C₂²×C₈×C₈₉	—	2	1	no	—
134	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
136	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₉	—	2	1	no	—
142	C₂²⋊C₈×C₈₉	—	2	1	no	—
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂³×D₈₉	—	2	1	no	—
147	#13083573	—	2	2	no	—
148	#13083573	—	2	2	no	—
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₈₉	—	2	1	no	—
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	D₄×D₈₉	—	2	2	no	—
154	D₄×D₈₉	M₁₆	1	4	yes	complemented
155	C₂²×Dic₈₉	—	2	1	no	—
156	C₂²×Dic₈₉	—	2	1	no	—
157	C₂²×Dic₈₉	—	2	1	no	—
158	C₂×C₄×D₈₉	—	2	1	no	—
159	C₂×C₄×D₈₉	—	2	1	no	—
160	C₂×C₄×D₈₉	—	2	1	no	—
161	C₂×C₄×D₈₉	—	4	2	no	—
162	C₂×C₄×D₈₉	—	4	2	no	—
163	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
166	#13083563	—	2	2	no	—
167	#13083562	—	2	2	no	—
168	#13083559	—	2	2	no	—
169	#13083558	—	4	2	no	—
170	#13083557	—	2	2	no	—
171	#13083557	—	2	2	no	—
172	C₂×#10623494	—	2	1	no	—
173	C₂×#10623494	—	2	1	no	—
174	C₂×#10623494	—	2	1	no	—
175	C₂×#10623494	—	4	2	no	—
176	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
177	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
178	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
179	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
180	C₈×D₈₉	—	2	2	no	—
181	C₈×D₈₉	—	4	1	no	—
182	C₈×D₈₉	—	4	2	no	—
183	C₈×D₈₉	—	4	2	no	—
184	C₈×D₈₉	—	4	2	no	—
185	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
187	#13083553	—	2	1	no	—
188	#13083553	—	2	1	no	—
189	#13083553	—	2	1	no	—
190	C₂²⋊Dic₈₉	—	2	1	no	—
191	C₂²⋊Dic₈₉	—	2	1	no	—
192	#13083551	—	2	1	no	—
193	#13083551	—	2	1	no	—
194	#13083551	—	2	1	no	—
195	C₄×Dic₈₉	—	2	1	no	—
196	C₄×Dic₈₉	—	2	1	no	—
197	C₄×Dic₈₉	—	2	1	no	—
198	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
200	C₄×Dic₈₉	#41	1	1	yes	characteristic
201	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
202	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	D₈×C₈₉	—	2	2	no	—
206	M₁₆×C₈₉	—	4	2	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	2	1	no	—
210	C₂×C₈×C₈₉	—	4	2	no	—
211	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
217	C₂²⋊C₄×C₈₉	—	2	1	no	—
218	C₂²⋊C₄×C₈₉	—	2	1	no	—
219	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂³×C₈₉	—	2	1	no	—
221	C₂³×C₈₉	—	2	1	no	—
222	C₂²×D₈₉	—	2	1	no	—
223	C₂²×D₈₉	—	2	4	no	—
224	C₂²×D₈₉	—	4	2	no	—
225	C₂²×D₈₉	—	4	2	no	—
226	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
227	D₄×C₈₉	—	2	1	no	—
228	D₄×C₈₉	—	2	1	no	—
229	D₄×C₈₉	—	2	1	no	—
230	D₄×C₈₉	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	—	4	1	no	—
236	C₂×C₄×C₈₉	—	4	1	no	—
237	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
240	C₂²⋊D₈₉	—	2	4	no	—
241	C₂²⋊D₈₉	—	4	2	no	—
242	C₂×Dic₈₉	—	2	1	no	—
243	C₂×Dic₈₉	—	2	1	no	—
244	C₂×Dic₈₉	—	2	1	no	—
245	C₂×Dic₈₉	—	4	2	no	—
246	C₂×Dic₈₉	—	4	2	no	—
247	C₂×Dic₈₉	—	4	2	no	—
248	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
249	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
250	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
251	D₃₅₆	—	2	1	no	—
252	D₃₅₆	C₂×M₁₆	1	2	yes	—
253	C₄×D₈₉	—	2	1	no	—
254	C₄×D₈₉	—	2	1	no	—
255	C₄×D₈₉	—	4	1	no	—
256	C₄×D₈₉	—	4	2	no	—
257	C₄×D₈₉	—	4	2	no	—
258	C₄×D₈₉	—	4	1	no	—
259	C₄×D₈₉	—	4	1	no	—
260	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
261	C₄×D₈₉	#131	1	2	yes	—
262	Dic₁₇₈	—	2	1	no	—
263	Dic₁₇₈	—	2	1	no	—
264	C₈×C₈₉	—	2	1	no	—
265	C₈×C₈₉	—	2	1	no	—
266	C₈×C₈₉	—	2	1	no	—
267	C₈×C₈₉	—	2	1	no	—
268	C₈×C₈₉	—	4	1	no	—
269	C₈×C₈₉	—	4	1	no	—
270	C₈×C₈₉	—	4	1	no	—
271	#10623494	—	2	1	no	—
272	#10623494	—	2	1	no	—
273	#10623494	—	2	1	no	—
274	#10623494	—	4	1	no	—
275	#10623494	—	4	1	no	—
276	#10623494	—	4	1	no	—
277	#10623494	AGL(1,ℤ/8)	1	2	yes	complemented
278	C₂²×C₈₉	—	2	2	no	—
279	C₂²×C₈₉	—	4	1	no	—
280	C₂²×C₈₉	—	4	1	no	—
281	C₂²×C₈₉	—	4	1	no	—
282	C₂²×C₈₉	—	4	1	no	—
283	C₂²×C₈₉	—	4	1	no	—
284	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂×D₈₉	—	2	1	no	—
286	C₂×D₈₉	—	2	1	no	—
287	C₂×D₈₉	—	2	2	no	—
288	C₂×D₈₉	—	4	8	no	—
289	C₂×D₈₉	—	4	1	no	—
290	C₂×D₈₉	—	4	1	no	—
291	C₂×D₈₉	#435	1	2	yes	—
292	C₄×C₈₉	—	2	1	no	—
293	C₄×C₈₉	—	4	1	no	—
294	C₄×C₈₉	—	4	1	no	—
295	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
296	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
297	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₄×C₈₉	#575	1	1	yes	characteristic
299	Dic₈₉	—	2	1	no	—
300	Dic₈₉	—	2	1	no	—
301	Dic₈₉	—	4	1	no	—
302	Dic₈₉	—	4	1	no	—
303	Dic₈₉	—	4	1	no	—
304	Dic₈₉	#435	1	2	yes	—
305	#17869	—	89	1	no	maximal, Sylow
306	C₂×C₈₉	—	4	2	no	—
307	C₂×C₈₉	—	8	1	no	—
308	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
309	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₂×C₈₉	#2955	1	1	yes	characteristic
311	D₈₉	—	2	2	no	—
312	D₈₉	—	4	2	no	—
313	#2965	—	89	1	no	—
314	C₄×AGL(1,ℤ/8)	—	89	1	no	—
315	C₂×C₈×D₄	—	89	1	no	—
316	#1586	—	89	1	no	—
317	#1586	D₈₉	1	1	yes	characteristic, complemented
318	#1585	—	89	1	no	—
319	#1585	—	89	1	no	—
320	#1582	—	89	1	no	—
321	#1582	—	89	1	no	—
322	#1581	—	89	1	no	—
323	#1581	—	89	1	no	—
324	#1565	—	89	1	no	—
325	#1478	—	89	1	no	—
326	#1477	—	89	1	no	—
327	#1451	—	89	1	no	—
328	C₈₉	#17869	1	1	yes	characteristic, complemented, Sylow
329	C₂×AGL(1,ℤ/8)	—	89	1	no	—
330	C₂³×C₈	—	178	1	no	—
331	C₄×#41	—	89	1	no	—
332	C₂×C₄×D₄	—	89	1	no	—
333	#446	—	89	1	no	—
334	#446	—	89	1	no	—
335	#442	—	89	1	no	—
336	#442	—	89	1	no	—
337	#440	—	89	1	no	—
338	#440	—	89	1	no	—
339	C₄×SD₁₆	—	89	1	no	—
340	C₄×SD₁₆	—	89	1	no	—
341	C₄×D₈	—	89	1	no	—
342	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
343	#436	—	89	1	no	—
344	#436	C₂×D₈₉	1	1	yes	characteristic, complemented
345	#435	—	178	1	no	—
346	#435	—	178	1	no	—
347	C₈×D₄	—	89	1	no	—
348	C₈×D₄	—	89	1	no	—
349	C₈×D₄	—	89	1	no	—
350	C₈×D₄	—	178	1	no	—
351	C₈×D₄	—	178	1	no	—
352	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
353	#431	—	89	1	no	—
354	#431	—	89	1	no	—
355	#431	—	178	1	no	—
356	#428	—	89	1	no	—
357	C₂×C₄⋊C₈	—	89	1	no	—
358	#418	—	89	1	no	—
359	#417	—	89	1	no	—
360	C₂×C₂²⋊C₈	—	178	1	no	—
361	C₄×M₁₆	—	89	1	no	—
362	C₄×M₁₆	—	178	1	no	—
363	C₂×C₄×C₈	—	89	1	no	—
364	#335	—	89	1	no	—
365	#335	—	89	1	no	—
366	#334	—	89	1	no	—
367	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
368	Q₈⋊C₈	—	89	1	no	—
369	Q₈⋊C₈	—	89	1	no	—
370	D₄⋊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	C₂×D₈₉	1	1	yes	characteristic
375	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
376	#322	—	89	1	no	—
377	#322	—	89	1	no	—
378	#322	—	89	1	no	—
379	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
380	C₂×#41	—	89	1	no	—
381	C₂²×D₄	—	89	1	no	—
382	C₂³×C₄	—	178	1	no	—
383	AGL(1,ℤ/8)	—	178	4	no	—
384	C₂×SD₁₆	—	89	1	no	—
385	C₂×SD₁₆	—	89	1	no	—
386	C₂×D₈	—	89	1	no	—
387	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	89	1	no	—
390	C₂×M₁₆	—	89	1	no	—
391	C₂×M₁₆	—	178	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	89	1	no	—
394	C₂²×C₈	—	89	1	no	—
395	C₂²×C₈	—	356	4	no	—
396	C₂²×C₈	—	178	1	no	—
397	C₂²×C₈	—	178	1	no	—
398	C₂²×C₈	—	178	1	no	—
399	C₂²×C₈	—	178	1	no	—
400	C₄×Q₈	—	89	1	no	—
401	C₄×Q₈	—	89	1	no	—
402	C₄×D₄	—	89	1	no	—
403	C₄×D₄	—	89	1	no	—
404	C₄×D₄	—	89	1	no	—
405	C₄×D₄	—	89	1	no	—
406	C₄×D₄	—	178	1	no	—
407	C₄×D₄	—	178	1	no	—
408	C₄×D₄	—	178	1	no	—
409	C₄×D₄	—	178	1	no	—
410	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
411	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
412	#117	—	89	1	no	—
413	#117	—	178	1	no	—
414	C₂×C₄⋊C₄	—	89	1	no	—
415	C₂×C₂²⋊C₄	—	178	1	no	—
416	C₂×C₄²	—	89	1	no	—
417	C₂×C₄²	—	178	1	no	—
418	#107	—	89	1	no	—
419	#107	C₄×D₈₉	1	1	yes	characteristic
420	#106	—	89	1	no	—
421	#106	—	89	1	no	—
422	C₄⋊C₈	—	89	1	no	—
423	C₄⋊C₈	—	89	1	no	—
424	C₄⋊C₈	—	178	1	no	—
425	C₄⋊C₈	—	178	1	no	—
426	C₄⋊C₈	—	178	1	no	—
427	C₄⋊C₈	—	178	1	no	—
428	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
429	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
430	#103	—	89	1	no	—
431	#103	—	89	1	no	—
432	#102	—	89	1	no	—
433	#102	—	89	1	no	—
434	#102	—	89	1	no	—
435	#102	—	89	1	no	—
436	#102	C₄×D₈₉	1	1	yes	characteristic
437	#102	C₄×D₈₉	1	1	yes	characteristic
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	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	C₄×C₈	—	89	1	no	—
451	C₄×C₈	—	89	1	no	—
452	C₄×C₈	—	89	1	no	—
453	C₄×C₈	—	89	1	no	—
454	C₄×C₈	—	89	1	no	—
455	C₄×C₈	—	178	1	no	—
456	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
457	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
458	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
459	C₂⁴	—	178	1	no	—
460	#41	—	178	2	no	—
461	#41	—	178	2	no	—
462	C₂×Q₈	—	89	1	no	—
463	C₂×D₄	—	89	4	no	—
464	C₂×D₄	—	89	1	no	—
465	C₂×D₄	—	178	2	no	—
466	C₂×D₄	—	178	1	no	—
467	C₂×D₄	—	178	1	no	—
468	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	89	1	no	—
473	C₂²×C₄	—	89	1	no	—
474	C₂²×C₄	—	89	1	no	—
475	C₂²×C₄	—	356	2	no	—
476	C₂²×C₄	—	356	2	no	—
477	C₂²×C₄	—	178	1	no	—
478	C₂²×C₄	—	178	1	no	—
479	C₂²×C₄	—	178	1	no	—
480	C₂²×C₄	—	178	1	no	—
481	C₂²×C₄	—	178	1	no	—
482	C₂²×C₄	—	178	1	no	—
483	SD₁₆	—	178	2	no	—
484	SD₁₆	—	178	2	no	—
485	D₈	—	2	2	no	—
486	D₈	—	178	2	no	—
487	M₁₆	—	4	2	no	—
488	M₁₆	—	356	2	no	—
489	M₁₆	—	178	2	no	—
490	M₁₆	—	178	2	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	4	2	no	—
495	C₂×C₈	—	89	1	no	—
496	C₂×C₈	—	89	1	no	—
497	C₂×C₈	—	89	1	no	—
498	C₂×C₈	—	89	1	no	—
499	C₂×C₈	—	356	2	no	—
500	C₂×C₈	—	356	1	no	—
501	C₂×C₈	—	356	2	no	—
502	C₂×C₈	—	356	2	no	—
503	C₂×C₈	—	356	2	no	—
504	C₂×C₈	—	178	2	no	—
505	C₂×C₈	—	178	1	no	—
506	C₂×C₈	—	178	1	no	—
507	C₂×C₈	—	178	1	no	—
508	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
509	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
510	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
511	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
512	C₄⋊C₄	—	89	1	no	—
513	C₄⋊C₄	—	89	1	no	—
514	C₄⋊C₄	—	178	1	no	—
515	C₄⋊C₄	—	178	1	no	—
516	C₄⋊C₄	—	178	1	no	—
517	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	178	1	no	—
522	C₂²⋊C₄	—	178	1	no	—
523	C₂²⋊C₄	—	178	1	no	—
524	C₂²⋊C₄	—	178	1	no	—
525	C₂²⋊C₄	—	178	1	no	—
526	C₄²	—	89	1	no	—
527	C₄²	—	89	1	no	—
528	C₄²	—	89	1	no	—
529	C₄²	—	178	1	no	—
530	C₄²	—	178	1	no	—
531	C₄²	—	178	1	no	—
532	C₄²	C₂³×D₈₉	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	89	1	no	—
536	C₂³	—	356	2	no	—
537	C₂³	—	356	2	no	—
538	C₂³	—	178	4	no	—
539	C₂³	—	178	1	no	—
540	Q₈	—	178	1	no	—
541	Q₈	—	178	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	89	2	no	—
546	D₄	—	356	2	no	—
547	D₄	—	178	4	no	—
548	D₄	—	178	1	no	—
549	D₄	M₁₆×D₈₉	1	2	yes	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	89	1	no	—
557	C₂×C₄	—	89	2	no	—
558	C₂×C₄	—	89	2	no	—
559	C₂×C₄	—	89	1	no	—
560	C₂×C₄	—	89	1	no	—
561	C₂×C₄	—	356	1	no	—
562	C₂×C₄	—	356	2	no	—
563	C₂×C₄	—	356	2	no	—
564	C₂×C₄	—	356	2	no	—
565	C₂×C₄	—	356	2	no	—
566	C₂×C₄	—	356	2	no	—
567	C₂×C₄	—	356	1	no	—
568	C₂×C₄	—	356	1	no	—
569	C₂×C₄	—	178	1	no	—
570	C₂×C₄	—	178	1	no	—
571	C₂×C₄	—	178	1	no	—
572	C₂×C₄	—	178	1	no	—
573	C₂×C₄	—	178	1	no	—
574	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
575	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
576	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	89	2	no	—
585	C₈	—	356	1	no	—
586	C₈	—	356	1	no	—
587	C₈	—	356	1	no	—
588	C₈	—	178	1	no	—
589	C₈	—	178	1	no	—
590	C₈	—	178	1	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	89	2	no	—
598	C₂²	—	356	8	no	—
599	C₂²	—	356	1	no	—
600	C₂²	—	356	1	no	—
601	C₂²	—	178	2	no	—
602	C₂²	—	178	1	no	—
603	C₂²	—	178	1	no	—
604	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	89	2	no	—
609	C₄	—	356	1	no	—
610	C₄	—	356	1	no	—
611	C₄	—	356	1	no	—
612	C₄	—	178	1	no	—
613	C₄	—	178	1	no	—
614	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
615	C₄	#131×D₈₉	1	1	yes	characteristic
616	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
617	C₄	#19152394	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	8	1	no	—
620	C₂	—	356	2	no	—
621	C₂	—	178	2	no	—
622	C₂	#435×D₈₉	1	1	yes	characteristic
623	C₂	#26029063	1	1	yes	characteristic
624	C₂	#26029150	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1586	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668036	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1586	D₈₉
hypocenter	C₈₉	#17869
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1586

Complements

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

N	H ≅ G/N	type
1. #26029215	C₂	semidirect
3. C₈×D₄×D₈₉	C₂	semidirect
4. #26019114	C₂	semidirect
5. #26019111	C₂	semidirect
6. #26019109	C₂	semidirect
7. #26019087	C₂	semidirect
8. #26019085	C₂	semidirect
9. #26019084	C₂	semidirect
10. #26019082	C₂	semidirect
11. #26019001	C₂	semidirect
12. #26018641	C₂	semidirect
13. #26018636	C₂	semidirect
14. #26018540	C₂	semidirect
15. C₈₉×#1586	C₂	semidirect
20. #19151728	C₂²	semidirect
21. #19151725	C₂²	semidirect
29. #19151676	C₂²	semidirect
48. #19151351	C₂²	semidirect
49. #19151350	C₂²	semidirect
50. #19151348	C₂²	semidirect
51. #19151330	C₂²	semidirect
52. #19151328	C₂²	semidirect
55. D₄⋊#10623494	C₂²	semidirect
57. #19151320	C₂²	semidirect
58. #19151320	C₂²	semidirect
59. #19151320	C₂²	semidirect
61. #436×C₈₉	C₂²	semidirect
63. #334×C₈₉	C₂²	semidirect
65. D₄⋊C₈×C₈₉	C₂²	semidirect
66. #322×C₈₉	C₂²	semidirect
154. D₄×D₈₉	M₁₆	semidirect
277. #10623494	AGL(1,ℤ/8)	semidirect
317. #1586	D₈₉	semidirect
328. C₈₉	#17869	semidirect
344. #436	C₂×D₈₉	semidirect
367. #334	C₂×D₈₉	semidirect
375. D₄⋊C₈	C₂×D₈₉	semidirect
379. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029215	2
C₄×#15668036	2
C₈×D₄×D₈₉	2
#26019114	2
#26019111	2
#26019109	2
#26019087	2
#26019085	2
#26019084	2
#26019082	2
#26019001	2
#26018641	2
#26018636	2
#26018540	2
C₈₉×#1586	2
#17869	89