Subgroups — #36524342

Order 22784.

698 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030258	C₂	1	1	yes	maximal, characteristic
2	#26029181	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019112	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019110	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019108	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019106	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019066	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019064	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019062	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019025	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018675	C₂	1	1	yes	maximal, characteristic
13	#26018653	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₈₉	—	2	1	no	—
17	#19152152	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#19151930	C₄	1	1	yes	characteristic
20	#19151927	C₄	1	1	yes	characteristic
21	#19151887	C₄	1	1	yes	characteristic
22	#19151886	C₄	1	1	yes	characteristic
23	#19151802	C₄	1	1	yes	characteristic
24	#19151801	C₄	1	1	yes	characteristic
25	#19151750	C₄	1	1	yes	characteristic
26	#19151747	C₄	1	1	yes	characteristic
27	#19151729	C₂²	1	1	yes	characteristic, complemented
28	#19151727	—	2	1	no	—
29	#19151725	C₂²	1	1	yes	characteristic, complemented
30	C₈×Dic₁₇₈	—	2	1	no	—
31	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
32	C₄×#13083563	C₂²	1	1	yes	characteristic
33	C₄×#13083561	C₂²	1	1	yes	characteristic
34	C₄×#13083562	C₂²	1	1	yes	characteristic
35	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
36	D₄×#10623494	C₂²	1	1	yes	characteristic
37	#19151663	C₂²	1	1	yes	characteristic
38	C₈×C₂²⋊D₈₉	—	2	1	no	—
39	#19151661	—	2	1	no	—
40	#19151649	C₂²	1	1	yes	characteristic
41	#19151649	C₂²	1	1	yes	characteristic
42	#19151623	—	2	1	no	—
43	#19151620	C₂²	1	1	yes	characteristic
44	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
45	C₂²⋊C₈×D₈₉	—	2	1	no	—
46	#19151552	—	2	1	no	—
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	#19151350	C₂²	1	1	yes	characteristic, complemented
51	#19151330	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
53	#19151328	C₂²	1	1	yes	characteristic, complemented
54	#19151327	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic
56	#19151325	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic, complemented
58	#19151320	C₂²	1	1	yes	characteristic, complemented
59	#19151319	C₂²	1	1	yes	characteristic, complemented
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₈₉	—	2	1	no	—
69	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083557	—	2	1	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₂×C₈×D₈₉	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	4	4	no	—
78	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
79	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
80	#15668011	C₂×C₄	1	1	yes	characteristic
81	#15668010	C₂×C₄	1	1	yes	characteristic
82	#15668002	—	2	1	no	—
83	#15667992	C₂×C₄	1	1	yes	characteristic
84	#15667990	—	2	1	no	—
85	#15667988	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₇₈	—	2	1	no	—
87	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
89	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
90	#15667974	C₂×C₄	1	1	yes	characteristic
91	C₄×C₂²⋊D₈₉	—	2	1	no	—
92	#15667972	—	2	1	no	—
93	#15667969	—	2	1	no	—
94	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₄×D₈₉	—	2	1	no	—
96	C₄²×D₈₉	C₂³	1	1	yes	characteristic
97	#15667944	C₂×C₄	1	1	yes	characteristic
98	#15667943	C₂×C₄	1	1	yes	characteristic
99	#15667943	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#10623494	—	2	1	no	—
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	C₄⋊#10623494	C₂³	1	1	yes	characteristic
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	C₂×C₄	1	1	yes	characteristic
109	#15667941	C₂×C₄	1	1	yes	characteristic
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667936	C₂×C₄	1	1	yes	characteristic
112	#15667935	C₂×C₄	1	1	yes	characteristic
113	#15667934	C₂×C₄	1	1	yes	characteristic
114	#15667933	C₂×C₄	1	1	yes	characteristic
115	#15667932	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#10623494	—	2	1	no	—
117	#15667924	—	2	1	no	—
118	#15667924	—	2	1	no	—
119	#15667924	—	2	1	no	—
120	#15667924	C₂×C₄	1	1	yes	characteristic
121	#15667924	C₂×C₄	1	1	yes	characteristic
122	#15667923	—	2	1	no	—
123	#15667922	—	2	1	no	—
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₄×#10623494	C₂³	1	1	yes	characteristic
126	C₄×#10623494	C₂³	1	1	yes	characteristic
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	D₄	1	1	yes	characteristic
129	C₈×Dic₈₉	D₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₈₉	—	2	1	no	—
132	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₈₉	—	2	1	no	—
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₂³×D₈₉	—	2	1	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₂²⋊D₈₉	—	2	1	no	—
150	D₄×D₈₉	—	2	2	no	—
151	D₄×D₈₉	—	2	2	no	—
152	C₂²×Dic₈₉	—	2	1	no	—
153	C₂×C₄×D₈₉	—	2	1	no	—
154	C₂×C₄×D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	4	2	no	—
157	C₂×C₄×D₈₉	—	4	2	no	—
158	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
161	#13083563	—	2	2	no	—
162	#13083562	—	2	2	no	—
163	#13083561	—	2	2	no	—
164	#13083557	—	4	2	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	—	4	2	no	—
169	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
170	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
171	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
172	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
173	C₈×D₈₉	—	2	2	no	—
174	C₈×D₈₉	—	2	2	no	—
175	C₈×D₈₉	—	4	2	no	—
176	C₈×D₈₉	—	4	2	no	—
177	C₈×D₈₉	—	4	2	no	—
178	C₄⋊Dic₈₉	—	2	1	no	—
179	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
181	#13083553	—	2	1	no	—
182	#13083553	—	2	1	no	—
183	#13083553	—	2	1	no	—
184	#13083553	—	2	1	no	—
185	#13083553	—	2	1	no	—
186	#13083553	—	2	1	no	—
187	C₂²⋊Dic₈₉	—	2	1	no	—
188	#13083551	—	2	1	no	—
189	#13083551	—	2	1	no	—
190	#13083551	—	2	1	no	—
191	#13083551	—	2	1	no	—
192	C₄×Dic₈₉	—	2	1	no	—
193	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₈₉	#41	1	1	yes	characteristic
196	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	SD₁₆×C₈₉	—	2	2	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	4	2	no	—
204	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	—	2	1	no	—
209	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₈₉	—	2	1	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂³×C₈₉	—	2	1	no	—
215	C₂²×D₈₉	—	2	4	no	—
216	C₂²×D₈₉	—	2	1	no	—
217	C₂²×D₈₉	—	4	2	no	—
218	C₂²×D₈₉	—	4	2	no	—
219	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
220	Q₈×C₈₉	—	2	1	no	—
221	Q₈×C₈₉	—	2	1	no	—
222	D₄×C₈₉	—	2	1	no	—
223	D₄×C₈₉	#131	1	2	yes	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
232	C₂²⋊D₈₉	—	2	4	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	4	2	no	—
237	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
239	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
240	D₃₅₆	—	2	1	no	—
241	D₃₅₆	#131	1	2	yes	—
242	C₄×D₈₉	—	2	1	no	—
243	C₄×D₈₉	—	2	1	no	—
244	C₄×D₈₉	—	4	1	no	—
245	C₄×D₈₉	—	4	2	no	—
246	C₄×D₈₉	—	4	1	no	—
247	C₄×D₈₉	—	4	1	no	—
248	C₄×D₈₉	—	4	2	no	—
249	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
250	C₄×D₈₉	#137	1	2	yes	—
251	Dic₁₇₈	—	2	1	no	—
252	Dic₁₇₈	—	2	1	no	—
253	Dic₁₇₈	—	4	2	no	—
254	C₈×C₈₉	—	2	1	no	—
255	C₈×C₈₉	—	2	1	no	—
256	C₈×C₈₉	—	2	1	no	—
257	C₈×C₈₉	—	2	1	no	—
258	C₈×C₈₉	—	4	1	no	—
259	C₈×C₈₉	—	4	1	no	—
260	C₈×C₈₉	—	4	1	no	—
261	#10623494	—	2	1	no	—
262	#10623494	—	2	1	no	—
263	#10623494	—	2	1	no	—
264	#10623494	—	2	1	no	—
265	#10623494	—	4	1	no	—
266	#10623494	—	4	1	no	—
267	#10623494	—	4	1	no	—
268	C₂²×C₈₉	—	2	2	no	—
269	C₂²×C₈₉	—	4	1	no	—
270	C₂²×C₈₉	—	4	1	no	—
271	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂×D₈₉	—	2	1	no	—
273	C₂×D₈₉	—	2	1	no	—
274	C₂×D₈₉	—	2	2	no	—
275	C₂×D₈₉	—	4	8	no	—
276	C₂×D₈₉	—	4	1	no	—
277	C₂×D₈₉	—	4	1	no	—
278	C₂×D₈₉	#440	1	2	yes	—
279	C₄×C₈₉	—	2	1	no	—
280	C₄×C₈₉	—	4	1	no	—
281	C₄×C₈₉	—	4	1	no	—
282	C₄×C₈₉	—	4	1	no	—
283	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
284	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
285	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
287	Dic₈₉	—	2	1	no	—
288	Dic₈₉	—	2	1	no	—
289	Dic₈₉	—	4	1	no	—
290	Dic₈₉	—	4	1	no	—
291	Dic₈₉	—	4	1	no	—
292	Dic₈₉	#440	1	2	yes	—
293	#17905	—	89	1	no	maximal, Sylow
294	C₂×C₈₉	—	4	2	no	—
295	C₂×C₈₉	#2929	1	1	yes	characteristic
296	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
297	C₂×C₈₉	#2955	1	1	yes	characteristic
298	D₈₉	—	2	2	no	—
299	D₈₉	—	4	2	no	—
300	#3101	—	89	1	no	—
301	#2960	—	89	1	no	—
302	C₂×C₈×D₄	—	89	1	no	—
303	#1585	—	89	1	no	—
304	#1585	—	89	1	no	—
305	#1585	—	89	1	no	—
306	#1585	—	89	1	no	—
307	SD₁₆⋊C₈	—	89	1	no	—
308	SD₁₆⋊C₈	—	89	1	no	—
309	SD₁₆⋊C₈	—	89	1	no	—
310	SD₁₆⋊C₈	D₈₉	1	1	yes	characteristic, complemented
311	#1571	—	89	1	no	—
312	#1486	—	89	1	no	—
313	#1481	—	89	1	no	—
314	#1452	—	89	1	no	—
315	C₈₉	#17905	1	1	yes	characteristic, complemented, Sylow
316	C₂³×C₈	—	178	1	no	—
317	#533	—	89	1	no	—
318	C₂×C₄×D₄	—	89	1	no	—
319	#483	—	89	1	no	—
320	#483	—	89	1	no	—
321	#476	—	89	1	no	—
322	#476	—	89	1	no	—
323	#461	—	89	1	no	—
324	#461	—	89	1	no	—
325	#450	—	89	1	no	—
326	#450	—	89	1	no	—
327	#446	—	89	1	no	—
328	#446	—	89	1	no	—
329	#446	—	178	1	no	—
330	C₈×Q₈	—	89	1	no	—
331	C₈×Q₈	—	178	1	no	—
332	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
333	C₄×SD₁₆	—	89	1	no	—
334	C₄×SD₁₆	—	89	1	no	—
335	C₄×SD₁₆	—	89	1	no	—
336	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
337	C₈×D₄	—	89	1	no	—
338	C₈×D₄	—	89	1	no	—
339	C₈×D₄	—	89	1	no	—
340	C₈×D₄	—	178	1	no	—
341	C₈×D₄	—	178	1	no	—
342	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
343	#431	—	89	1	no	—
344	#431	—	89	1	no	—
345	#424	—	178	1	no	—
346	#423	—	89	1	no	—
347	C₂×C₄⋊C₈	—	89	1	no	—
348	C₂×C₂²⋊C₈	—	178	1	no	—
349	#405	—	178	1	no	—
350	C₂×C₄×C₈	—	89	1	no	—
351	#335	—	89	1	no	—
352	#335	—	89	1	no	—
353	#335	—	89	1	no	—
354	#335	C₂×D₈₉	1	1	yes	characteristic, complemented
355	Q₈⋊C₈	—	89	1	no	—
356	Q₈⋊C₈	—	89	1	no	—
357	Q₈⋊C₈	—	89	1	no	—
358	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
359	D₄⋊C₈	—	89	1	no	—
360	D₄⋊C₈	—	89	1	no	—
361	D₄⋊C₈	—	89	1	no	—
362	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
363	#322	—	89	1	no	—
364	#322	—	89	1	no	—
365	#322	—	89	1	no	—
366	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
367	C₂²×D₄	—	89	1	no	—
368	C₂³×C₄	—	178	1	no	—
369	C₂×SD₁₆	—	89	1	no	—
370	C₂×SD₁₆	—	89	1	no	—
371	C₂×SD₁₆	—	89	1	no	—
372	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
373	C₂×M₁₆	—	178	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	89	1	no	—
376	C₂²×C₈	—	89	1	no	—
377	C₂²×C₈	—	356	4	no	—
378	C₂²×C₈	—	178	1	no	—
379	C₂²×C₈	—	178	1	no	—
380	C₂²×C₈	—	178	1	no	—
381	C₂²×C₈	—	178	1	no	—
382	C₄⋊Q₈	—	89	1	no	—
383	C₄⋊Q₈	—	89	1	no	—
384	#125	—	178	1	no	—
385	C₂²⋊Q₈	—	89	1	no	—
386	C₂²⋊Q₈	—	89	1	no	—
387	C₂²⋊Q₈	—	178	1	no	—
388	C₄×Q₈	—	89	1	no	—
389	C₄×Q₈	—	178	1	no	—
390	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
391	C₄×D₄	—	89	1	no	—
392	C₄×D₄	—	89	1	no	—
393	C₄×D₄	—	89	1	no	—
394	C₄×D₄	—	178	1	no	—
395	C₄×D₄	—	178	1	no	—
396	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
397	#117	—	178	1	no	—
398	C₂×C₄⋊C₄	—	89	1	no	—
399	C₂×C₂²⋊C₄	—	178	1	no	—
400	C₂×C₄²	—	89	1	no	—
401	#106	—	89	1	no	—
402	#106	—	89	1	no	—
403	#106	—	89	1	no	—
404	#106	C₄×D₈₉	1	1	yes	characteristic
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	89	1	no	—
407	C₄⋊C₈	—	89	1	no	—
408	C₄⋊C₈	—	89	1	no	—
409	C₄⋊C₈	—	89	1	no	—
410	C₄⋊C₈	—	178	1	no	—
411	C₄⋊C₈	—	178	1	no	—
412	C₄⋊C₈	—	178	1	no	—
413	C₄⋊C₈	—	178	1	no	—
414	C₄⋊C₈	—	178	1	no	—
415	C₄⋊C₈	—	178	1	no	—
416	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
418	#103	—	89	1	no	—
419	#103	—	89	1	no	—
420	#103	—	89	1	no	—
421	#103	C₄×D₈₉	1	1	yes	characteristic
422	#102	—	89	1	no	—
423	#102	—	89	1	no	—
424	#102	—	89	1	no	—
425	#102	C₄×D₈₉	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	89	1	no	—
428	C₂²⋊C₈	—	89	1	no	—
429	C₂²⋊C₈	—	178	1	no	—
430	C₂²⋊C₈	—	178	1	no	—
431	C₂²⋊C₈	—	178	1	no	—
432	C₂²⋊C₈	—	178	1	no	—
433	#97	—	178	1	no	—
434	#97	—	178	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	89	1	no	—
437	C₄×C₈	—	89	1	no	—
438	C₄×C₈	—	89	1	no	—
439	C₄×C₈	—	89	1	no	—
440	C₄×C₈	—	89	1	no	—
441	C₄×C₈	—	178	1	no	—
442	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
444	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
445	C₂⁴	—	178	1	no	—
446	C₂×Q₈	—	89	1	no	—
447	C₂×Q₈	—	178	1	no	—
448	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
449	C₂×D₄	—	89	1	no	—
450	C₂×D₄	—	178	1	no	—
451	C₂×D₄	—	178	2	no	—
452	C₂×D₄	—	178	2	no	—
453	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	89	1	no	—
456	C₂²×C₄	—	89	1	no	—
457	C₂²×C₄	—	89	1	no	—
458	C₂²×C₄	—	356	2	no	—
459	C₂²×C₄	—	356	2	no	—
460	C₂²×C₄	—	178	1	no	—
461	C₂²×C₄	—	178	1	no	—
462	C₂²×C₄	—	178	1	no	—
463	C₂²×C₄	—	178	1	no	—
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	178	2	no	—
466	SD₁₆	—	178	2	no	—
467	SD₁₆	—	178	2	no	—
468	M₁₆	—	356	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	4	2	no	—
473	C₂×C₈	—	89	1	no	—
474	C₂×C₈	—	89	1	no	—
475	C₂×C₈	—	89	1	no	—
476	C₂×C₈	—	89	1	no	—
477	C₂×C₈	—	356	2	no	—
478	C₂×C₈	—	356	2	no	—
479	C₂×C₈	—	356	2	no	—
480	C₂×C₈	—	356	2	no	—
481	C₂×C₈	—	178	2	no	—
482	C₂×C₈	—	178	2	no	—
483	C₂×C₈	—	178	1	no	—
484	C₂×C₈	—	178	1	no	—
485	C₂×C₈	—	178	1	no	—
486	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
487	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
488	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
489	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	89	1	no	—
492	C₄⋊C₄	—	89	1	no	—
493	C₄⋊C₄	—	178	1	no	—
494	C₄⋊C₄	—	178	1	no	—
495	C₄⋊C₄	—	178	1	no	—
496	C₄⋊C₄	—	178	1	no	—
497	C₄⋊C₄	—	178	1	no	—
498	C₄⋊C₄	—	178	1	no	—
499	C₄⋊C₄	—	178	1	no	—
500	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	178	1	no	—
504	C₂²⋊C₄	—	178	1	no	—
505	C₂²⋊C₄	—	178	1	no	—
506	C₂²⋊C₄	—	178	1	no	—
507	C₂²⋊C₄	—	178	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	89	1	no	—
510	C₄²	—	89	1	no	—
511	C₄²	—	89	1	no	—
512	C₄²	—	178	1	no	—
513	C₄²	C₂³×D₈₉	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	89	1	no	—
516	C₂³	—	356	2	no	—
517	C₂³	—	356	2	no	—
518	C₂³	—	178	4	no	—
519	C₂³	—	178	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	356	2	no	—
523	Q₈	—	178	1	no	—
524	Q₈	—	178	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	89	2	no	—
527	D₄	—	178	4	no	—
528	D₄	—	178	1	no	—
529	D₄	#15668018	1	2	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	89	1	no	—
536	C₂×C₄	—	89	2	no	—
537	C₂×C₄	—	89	2	no	—
538	C₂×C₄	—	89	1	no	—
539	C₂×C₄	—	89	1	no	—
540	C₂×C₄	—	356	1	no	—
541	C₂×C₄	—	356	2	no	—
542	C₂×C₄	—	356	2	no	—
543	C₂×C₄	—	356	2	no	—
544	C₂×C₄	—	356	1	no	—
545	C₂×C₄	—	356	1	no	—
546	C₂×C₄	—	178	1	no	—
547	C₂×C₄	—	178	1	no	—
548	C₂×C₄	—	178	1	no	—
549	C₂×C₄	—	178	1	no	—
550	C₂×C₄	—	178	1	no	—
551	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
552	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
553	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	356	1	no	—
562	C₈	—	356	1	no	—
563	C₈	—	356	1	no	—
564	C₈	—	178	1	no	—
565	C₈	—	178	1	no	—
566	C₈	—	178	1	no	—
567	C₈	—	178	1	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	89	2	no	—
572	C₂²	—	356	8	no	—
573	C₂²	—	356	1	no	—
574	C₂²	—	356	1	no	—
575	C₂²	—	178	2	no	—
576	C₂²	—	178	1	no	—
577	C₂²	—	178	1	no	—
578	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	89	2	no	—
584	C₄	—	356	1	no	—
585	C₄	—	356	1	no	—
586	C₄	—	356	1	no	—
587	C₄	—	178	1	no	—
588	C₄	—	178	1	no	—
589	C₄	#131×D₈₉	1	1	yes	characteristic
590	C₄	C₂×#15668018	1	1	yes	characteristic
591	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
592	C₄	#137×D₈₉	1	1	yes	characteristic
593	C₂	—	4	2	no	—
594	C₂	—	356	2	no	—
595	C₂	—	178	2	no	—
596	C₂	#26028941	1	1	yes	characteristic
597	C₂	#440×D₈₉	1	1	yes	characteristic
598	C₂	#26029152	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×SD₁₆⋊C₈	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×D₄×D₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₈₉
hypocenter	C₈₉	#17905
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
2. #26029181	C₂	semidirect
4. #26019112	C₂	semidirect
5. #26019110	C₂	semidirect
6. #26019108	C₂	semidirect
7. #26019106	C₂	semidirect
8. #26019066	C₂	semidirect
9. #26019064	C₂	semidirect
10. #26019062	C₂	semidirect
11. #26019025	C₂	semidirect
13. #26018653	C₂	semidirect
14. #26018543	C₂	semidirect
15. C₈₉×SD₁₆⋊C₈	C₂	semidirect
27. #19151729	C₂²	semidirect
29. #19151725	C₂²	semidirect
31. C₈×Dic₁₇₈	C₂²	semidirect
48. #19151351	C₂²	semidirect
49. #19151350	C₂²	semidirect
50. #19151350	C₂²	semidirect
51. #19151330	C₂²	semidirect
52. Q₈⋊#10623494	C₂²	semidirect
53. #19151328	C₂²	semidirect
57. #19151320	C₂²	semidirect
58. #19151320	C₂²	semidirect
59. #19151319	C₂²	semidirect
60. C₈×Q₈×C₈₉	C₂²	semidirect
63. #335×C₈₉	C₂²	semidirect
64. Q₈⋊C₈×C₈₉	C₂²	semidirect
66. #322×C₈₉	C₂²	semidirect
310. SD₁₆⋊C₈	D₈₉	semidirect
315. C₈₉	#17905	semidirect
332. C₈×Q₈	C₂×D₈₉	semidirect
354. #335	C₂×D₈₉	semidirect
358. Q₈⋊C₈	C₂×D₈₉	semidirect
366. #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
#26030258	2
#26029181	2
C₈×D₄×D₈₉	2
#26019112	2
#26019110	2
#26019108	2
#26019106	2
#26019066	2
#26019064	2
#26019062	2
#26019025	2
#26018675	2
#26018653	2
#26018543	2
C₈₉×SD₁₆⋊C₈	2
#17905	89