Subgroups — #36524973

Order 22784.

666 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030808	C₂	1	1	yes	maximal, characteristic
2	#26029181	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028959	C₂	1	1	yes	maximal, characteristic
4	#26019157	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019155	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019153	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019151	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	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018705	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018701	C₂	1	1	yes	maximal, characteristic
14	#322×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668018	—	2	1	no	—
17	#19152152	C₂²	1	1	yes	characteristic
18	#19152145	C₂²	1	1	yes	characteristic
19	#19151995	C₄	1	1	yes	characteristic
20	#19151969	C₄	1	1	yes	characteristic
21	#19151947	C₄	1	1	yes	characteristic
22	#19151943	C₄	1	1	yes	characteristic
23	#19151830	C₄	1	1	yes	characteristic
24	#19151828	C₄	1	1	yes	characteristic
25	#19151826	C₄	1	1	yes	characteristic
26	#19151824	C₄	1	1	yes	characteristic
27	#19151729	C₂²	1	1	yes	characteristic
28	#19151727	—	2	1	no	—
29	#19151725	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₇₈	—	2	1	no	—
31	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
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	#19151676	C₂²	1	1	yes	characteristic
36	#19151675	C₂²	1	1	yes	characteristic
37	#19151673	—	2	1	no	—
38	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
39	C₈×C₂²⋊D₈₉	—	2	1	no	—
40	#19151623	—	2	1	no	—
41	#19151620	C₂²	1	1	yes	characteristic
42	#19151620	C₂²	1	1	yes	characteristic
43	#19151563	—	2	1	no	—
44	#19151552	—	2	1	no	—
45	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151350	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
53	#19151328	C₂²	1	1	yes	characteristic
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
58	#19151320	C₂²	1	1	yes	characteristic
59	#19151319	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
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
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	—	2	1	no	—
68	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	#15668018	—	4	4	no	—
72	C₂×#13083558	—	2	1	no	—
73	C₂×#13083557	—	2	1	no	—
74	C₂×#13083557	—	2	1	no	—
75	C₂×#13083557	—	2	1	no	—
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	2	1	no	—
78	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
81	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
82	#15668011	C₂×C₄	1	1	yes	characteristic
83	#15668011	C₂×C₄	1	1	yes	characteristic
84	#15668010	C₂×C₄	1	1	yes	characteristic
85	#15668008	C₂×C₄	1	1	yes	characteristic
86	#15668002	—	2	1	no	—
87	#15667998	—	2	1	no	—
88	#15667992	C₂×C₄	1	1	yes	characteristic
89	#15667990	—	2	1	no	—
90	#15667988	C₂×C₄	1	1	yes	characteristic
91	#15667987	C₂×C₄	1	1	yes	characteristic
92	#15667985	—	2	1	no	—
93	#15667983	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₁₇₈	—	2	1	no	—
95	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
96	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
97	C₄×C₂²⋊D₈₉	—	2	1	no	—
98	#15667969	—	2	1	no	—
99	C₄²×D₈₉	C₂³	1	1	yes	characteristic
100	#15667944	C₂×C₄	1	1	yes	characteristic
101	#15667943	C₂×C₄	1	1	yes	characteristic
102	#15667943	C₂×C₄	1	1	yes	characteristic
103	C₄⋊#10623494	—	2	1	no	—
104	C₄⋊#10623494	C₂³	1	1	yes	characteristic
105	C₄⋊#10623494	C₂³	1	1	yes	characteristic
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667941	—	2	1	no	—
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	#15667923	—	2	1	no	—
120	#15667922	—	2	1	no	—
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
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	#13083574	—	4	2	no	—
146	#13083574	—	4	2	no	—
147	C₂×Dic₁₇₈	—	2	1	no	—
148	C₂×Dic₁₇₈	—	2	1	no	—
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₅₆	—	2	1	no	—
151	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	C₂×C₂²⋊D₈₉	—	2	1	no	—
154	C₂×C₂²⋊D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
159	#13083563	—	2	2	no	—
160	#13083562	—	2	2	no	—
161	#13083561	—	2	2	no	—
162	#13083558	—	4	2	no	—
163	#13083557	—	4	2	no	—
164	#13083557	—	4	2	no	—
165	#13083557	—	4	2	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	—	2	1	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	—	2	2	no	—
176	C₈×D₈₉	—	2	2	no	—
177	C₈×D₈₉	—	4	2	no	—
178	C₈×D₈₉	—	4	2	no	—
179	C₄⋊Dic₈₉	—	2	1	no	—
180	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
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	#13083553	—	2	1	no	—
188	C₂²⋊Dic₈₉	—	2	1	no	—
189	#13083551	—	2	1	no	—
190	#13083551	—	2	1	no	—
191	#13083551	—	2	1	no	—
192	#13083551	—	2	1	no	—
193	C₄×Dic₈₉	—	2	1	no	—
194	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
196	C₄×Dic₈₉	#41	1	1	yes	characteristic
197	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	SD₁₆×C₈₉	—	2	2	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	4	2	no	—
205	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₈₉	—	2	1	no	—
210	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	—	2	1	no	—
214	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂³×C₈₉	—	2	1	no	—
216	C₂²×D₈₉	—	2	1	no	—
217	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
218	Q₈×C₈₉	—	2	1	no	—
219	Q₈×C₈₉	—	2	1	no	—
220	D₄×C₈₉	—	2	1	no	—
221	D₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₈₉	—	4	2	no	—
231	C₂²⋊D₈₉	—	4	2	no	—
232	C₂²⋊D₈₉	—	4	2	no	—
233	C₂×Dic₈₉	—	2	1	no	—
234	C₂×Dic₈₉	—	2	1	no	—
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
239	D₃₅₆	—	2	1	no	—
240	D₃₅₆	—	2	1	no	—
241	D₃₅₆	—	4	2	no	—
242	C₄×D₈₉	—	2	1	no	—
243	C₄×D₈₉	—	2	1	no	—
244	C₄×D₈₉	—	2	2	no	—
245	C₄×D₈₉	—	4	1	no	—
246	C₄×D₈₉	—	4	1	no	—
247	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
248	C₄×D₈₉	#137	1	2	yes	—
249	Dic₁₇₈	—	2	1	no	—
250	Dic₁₇₈	—	2	1	no	—
251	Dic₁₇₈	—	4	2	no	—
252	Dic₁₇₈	—	4	2	no	—
253	C₈×C₈₉	—	2	1	no	—
254	C₈×C₈₉	—	2	1	no	—
255	C₈×C₈₉	—	2	1	no	—
256	C₈×C₈₉	—	4	1	no	—
257	C₈×C₈₉	—	4	1	no	—
258	C₈×C₈₉	—	4	1	no	—
259	C₈×C₈₉	#131	1	2	yes	complemented
260	#10623494	—	2	1	no	—
261	#10623494	—	2	1	no	—
262	#10623494	—	2	1	no	—
263	#10623494	—	4	1	no	—
264	#10623494	—	4	1	no	—
265	#10623494	—	4	1	no	—
266	#10623494	#131	1	2	yes	complemented
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	4	1	no	—
269	C₂²×C₈₉	—	4	1	no	—
270	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂×D₈₉	—	2	1	no	—
272	C₂×D₈₉	—	2	1	no	—
273	C₂×D₈₉	—	4	1	no	—
274	C₂×D₈₉	—	4	1	no	—
275	C₂×D₈₉	—	4	1	no	—
276	C₂×D₈₉	#440	1	2	yes	—
277	C₄×C₈₉	—	2	1	no	—
278	C₄×C₈₉	—	4	1	no	—
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	—	4	1	no	—
281	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
282	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
283	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
285	Dic₈₉	—	2	1	no	—
286	Dic₈₉	—	4	1	no	—
287	Dic₈₉	—	4	1	no	—
288	Dic₈₉	—	4	1	no	—
289	Dic₈₉	#440	1	2	yes	—
290	Dic₈₉	#444	1	2	yes	—
291	#17960	—	89	1	no	maximal, Sylow
292	C₂×C₈₉	—	8	1	no	—
293	C₂×C₈₉	#2931	1	1	yes	characteristic
294	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
295	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
296	D₈₉	—	2	2	no	—
297	D₈₉	—	8	1	no	—
298	#3167	—	89	1	no	—
299	#2960	—	89	1	no	—
300	#2931	—	89	1	no	—
301	#1592	—	89	1	no	—
302	#1592	—	89	1	no	—
303	#1592	—	89	1	no	—
304	#1592	—	89	1	no	—
305	SD₁₆⋊C₈	—	89	1	no	—
306	SD₁₆⋊C₈	—	89	1	no	—
307	SD₁₆⋊C₈	—	89	1	no	—
308	SD₁₆⋊C₈	D₈₉	1	1	yes	characteristic, complemented
309	#1567	—	89	1	no	—
310	#1493	—	89	1	no	—
311	#1492	—	89	1	no	—
312	C₂×#322	—	89	1	no	—
313	C₈₉	#17960	1	1	yes	characteristic, complemented, Sylow
314	C₂×#131	—	178	1	no	—
315	#533	—	89	1	no	—
316	#532	—	89	1	no	—
317	#498	—	89	1	no	—
318	#492	—	89	1	no	—
319	#487	—	89	1	no	—
320	#486	—	89	1	no	—
321	#465	—	89	1	no	—
322	#465	—	89	1	no	—
323	#465	—	89	1	no	—
324	#465	—	89	1	no	—
325	#446	—	89	1	no	—
326	#446	—	89	1	no	—
327	#446	—	178	1	no	—
328	C₈×Q₈	—	89	1	no	—
329	C₈×Q₈	—	178	1	no	—
330	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
331	C₄×SD₁₆	—	89	1	no	—
332	C₄×SD₁₆	—	89	1	no	—
333	C₄×SD₁₆	—	89	1	no	—
334	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
335	#436	—	89	1	no	—
336	#436	—	89	1	no	—
337	#436	—	178	1	no	—
338	C₈×D₄	—	89	1	no	—
339	C₈×D₄	—	178	1	no	—
340	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
341	#424	—	178	1	no	—
342	#423	—	89	1	no	—
343	#423	—	89	1	no	—
344	#408	—	178	1	no	—
345	#405	—	178	1	no	—
346	C₂×C₄×C₈	—	89	1	no	—
347	C₂×C₄×C₈	—	89	1	no	—
348	C₂×C₄×C₈	—	89	1	no	—
349	#335	—	89	1	no	—
350	#335	—	89	1	no	—
351	#335	—	89	1	no	—
352	#335	C₂×D₈₉	1	1	yes	characteristic
353	Q₈⋊C₈	—	89	1	no	—
354	Q₈⋊C₈	—	89	1	no	—
355	Q₈⋊C₈	—	89	1	no	—
356	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
357	D₄⋊C₈	—	89	1	no	—
358	D₄⋊C₈	—	89	1	no	—
359	D₄⋊C₈	—	89	1	no	—
360	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
361	#322	—	89	1	no	—
362	#322	—	89	1	no	—
363	#322	—	89	1	no	—
364	#322	C₂×D₈₉	1	1	yes	characteristic
365	C₂×#41	—	178	1	no	—
366	C₂×SD₁₆	—	89	1	no	—
367	C₂×SD₁₆	—	89	1	no	—
368	C₂×SD₁₆	—	89	1	no	—
369	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
370	#131	—	356	4	no	—
371	C₂×M₁₆	—	178	1	no	—
372	C₂×M₁₆	—	178	1	no	—
373	C₂×M₁₆	—	178	1	no	—
374	C₂×M₁₆	—	178	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	89	1	no	—
377	C₂²×C₈	—	89	1	no	—
378	C₂²×C₈	—	89	1	no	—
379	C₂²×C₈	—	89	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	C₄⋊Q₈	—	89	1	no	—
385	#127	—	89	1	no	—
386	#125	—	178	1	no	—
387	#124	—	178	1	no	—
388	C₂²⋊Q₈	—	89	1	no	—
389	C₂²⋊Q₈	—	89	1	no	—
390	C₂²⋊Q₈	—	178	1	no	—
391	#121	—	89	1	no	—
392	#121	—	89	1	no	—
393	#121	—	178	1	no	—
394	C₄×Q₈	—	89	1	no	—
395	C₄×Q₈	—	178	1	no	—
396	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
397	C₄×D₄	—	89	1	no	—
398	C₄×D₄	—	178	1	no	—
399	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
400	#117	—	178	1	no	—
401	C₂×C₄²	—	89	1	no	—
402	#106	—	89	1	no	—
403	#106	—	89	1	no	—
404	#106	—	89	1	no	—
405	#106	C₄×D₈₉	1	1	yes	characteristic
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	89	1	no	—
408	C₄⋊C₈	—	89	1	no	—
409	C₄⋊C₈	—	178	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	C₂²×D₈₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
416	#103	—	89	1	no	—
417	#103	—	89	1	no	—
418	#103	—	89	1	no	—
419	#103	C₄×D₈₉	1	1	yes	characteristic
420	#102	—	89	1	no	—
421	#102	—	89	1	no	—
422	#102	—	89	1	no	—
423	#102	C₄×D₈₉	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	178	1	no	—
426	C₂²⋊C₈	—	178	1	no	—
427	C₂²⋊C₈	—	178	1	no	—
428	#97	—	178	1	no	—
429	#97	—	178	1	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	—	89	1	no	—
432	C₄×C₈	—	89	1	no	—
433	C₄×C₈	—	89	1	no	—
434	C₄×C₈	—	89	1	no	—
435	C₄×C₈	—	89	1	no	—
436	C₄×C₈	—	89	1	no	—
437	C₄×C₈	—	89	1	no	—
438	C₄×C₈	—	178	1	no	—
439	C₄×C₈	—	178	1	no	—
440	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
443	#41	—	356	2	no	—
444	#41	—	356	2	no	—
445	C₂×Q₈	—	89	1	no	—
446	C₂×Q₈	—	178	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	1	no	—
452	C₂×D₄	—	178	1	no	—
453	C₂×D₄	—	178	1	no	—
454	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	89	1	no	—
457	C₂²×C₄	—	89	1	no	—
458	C₂²×C₄	—	89	1	no	—
459	C₂²×C₄	—	178	1	no	—
460	SD₁₆	—	2	2	no	—
461	SD₁₆	—	178	2	no	—
462	SD₁₆	—	178	2	no	—
463	SD₁₆	—	178	2	no	—
464	M₁₆	—	356	2	no	—
465	M₁₆	—	356	2	no	—
466	M₁₆	—	356	2	no	—
467	M₁₆	—	356	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	2	no	—
472	C₂×C₈	—	89	1	no	—
473	C₂×C₈	—	89	1	no	—
474	C₂×C₈	—	89	1	no	—
475	C₂×C₈	—	89	1	no	—
476	C₂×C₈	—	356	2	no	—
477	C₂×C₈	—	356	2	no	—
478	C₂×C₈	—	178	2	no	—
479	C₂×C₈	—	178	2	no	—
480	C₂×C₈	—	178	2	no	—
481	C₂×C₈	—	178	1	no	—
482	C₂×C₈	—	178	1	no	—
483	C₂×C₈	—	178	1	no	—
484	C₂×C₈	—	178	2	no	—
485	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
487	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
488	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	89	1	no	—
491	C₄⋊C₄	—	89	1	no	—
492	C₄⋊C₄	—	178	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	C₂×C₄×D₈₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	178	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	C₄²	—	2	1	no	—
508	C₄²	—	89	1	no	—
509	C₄²	—	89	1	no	—
510	C₄²	—	89	1	no	—
511	C₄²	—	178	1	no	—
512	C₄²	C₂³×D₈₉	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	89	1	no	—
515	C₂³	—	178	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	356	2	no	—
519	Q₈	—	356	2	no	—
520	Q₈	—	178	1	no	—
521	Q₈	—	178	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	356	2	no	—
525	D₄	—	356	2	no	—
526	D₄	—	356	2	no	—
527	D₄	—	356	2	no	—
528	D₄	—	178	1	no	—
529	D₄	—	178	1	no	—
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	1	no	—
537	C₂×C₄	—	89	2	no	—
538	C₂×C₄	—	89	2	no	—
539	C₂×C₄	—	89	1	no	—
540	C₂×C₄	—	356	1	no	—
541	C₂×C₄	—	356	1	no	—
542	C₂×C₄	—	178	2	no	—
543	C₂×C₄	—	178	1	no	—
544	C₂×C₄	—	178	1	no	—
545	C₂×C₄	—	178	1	no	—
546	C₂×C₄	—	178	1	no	—
547	C₂×C₄	—	178	1	no	—
548	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
550	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	89	2	no	—
558	C₈	—	356	1	no	—
559	C₈	—	356	1	no	—
560	C₈	—	356	1	no	—
561	C₈	—	178	1	no	—
562	C₈	—	178	1	no	—
563	C₈	—	178	1	no	—
564	C₈	#15668018	1	2	yes	complemented
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	89	2	no	—
569	C₂²	—	356	1	no	—
570	C₂²	—	356	1	no	—
571	C₂²	—	356	1	no	—
572	C₂²	—	178	1	no	—
573	C₂²	—	178	1	no	—
574	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	89	2	no	—
580	C₄	—	89	2	no	—
581	C₄	—	356	1	no	—
582	C₄	—	356	1	no	—
583	C₄	—	356	1	no	—
584	C₄	—	178	1	no	—
585	C₄	#131×D₈₉	1	1	yes	characteristic
586	C₄	C₂×#15668018	1	1	yes	characteristic
587	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
588	C₄	#137×D₈₉	1	1	yes	characteristic
589	C₂	—	8	1	no	—
590	C₂	—	178	2	no	—
591	C₂	—	712	1	no	—
592	C₂	#26028959	1	1	yes	characteristic
593	C₂	#440×D₈₉	1	1	yes	characteristic
594	C₂	#444×D₈₉	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	#19152145	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₈₉
hypocenter	C₈₉	#17960
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. #26019157	C₂	semidirect
5. #26019155	C₂	semidirect
6. #26019153	C₂	semidirect
7. #26019151	C₂	semidirect
8. #26019066	C₂	semidirect
9. #26019064	C₂	semidirect
10. #26019062	C₂	semidirect
11. #26019009	C₂	semidirect
12. #26018705	C₂	semidirect
14. #322×D₈₉	C₂	semidirect
15. C₈₉×SD₁₆⋊C₈	C₂	semidirect
259. C₈×C₈₉	#131	semidirect
266. #10623494	#131	semidirect
308. SD₁₆⋊C₈	D₈₉	semidirect
313. C₈₉	#17960	semidirect
564. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26030808	2
#26029181	2
#26028959	2
#26019157	2
#26019155	2
#26019153	2
#26019151	2
#26019066	2
#26019064	2
#26019062	2
#26019009	2
#26018705	2
#26018701	2
#322×D₈₉	2
C₈₉×SD₁₆⋊C₈	2
#17960	89