Subgroups — #36524121

Order 22784.

626 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029334	C₂	1	1	yes	maximal, characteristic
2	#26029331	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019126	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019123	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019121	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019120	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
11	#26018999	C₂	1	1	yes	maximal, characteristic
12	#26018645	C₂	1	1	yes	maximal, characteristic
13	#26018645	C₂	1	1	yes	maximal, characteristic
14	#26018543	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	#19151729	C₂²	1	1	yes	characteristic
20	#19151728	C₂²	1	1	yes	characteristic
21	#19151727	—	2	1	no	—
22	#19151726	—	2	1	no	—
23	#19151725	C₂²	1	1	yes	characteristic
24	Q₈×#10623494	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₇₈	—	2	1	no	—
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	#19151722	—	2	1	no	—
28	#19151722	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic
31	#19151692	C₄	1	1	yes	characteristic
32	C₄×#13083564	C₂²	1	1	yes	characteristic
33	C₄×#13083564	C₂²	1	1	yes	characteristic
34	#19151690	C₄	1	1	yes	characteristic
35	#19151690	C₄	1	1	yes	characteristic
36	#19151654	—	2	1	no	—
37	#19151653	—	2	1	no	—
38	#19151650	—	2	1	no	—
39	#19151650	C₂²	1	1	yes	characteristic
40	#19151650	C₂²	1	1	yes	characteristic
41	#19151649	—	2	1	no	—
42	#19151649	C₂²	1	1	yes	characteristic
43	#19151649	C₂²	1	1	yes	characteristic
44	#107×D₈₉	C₄	1	1	yes	characteristic
45	#103×D₈₉	C₄	1	1	yes	characteristic
46	#103×D₈₉	C₄	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151348	C₂²	1	1	yes	characteristic
50	#19151348	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
54	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	#19151328	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	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₈₉	—	2	4	no	—
73	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
75	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₇₈	—	2	1	no	—
78	C₄×Dic₁₇₈	—	2	1	no	—
79	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
81	#15667977	—	2	1	no	—
82	#15667977	—	2	1	no	—
83	#15667977	C₂×C₄	1	1	yes	characteristic
84	#15667977	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₄×D₈₉	—	2	1	no	—
86	C₄⋊C₄×D₈₉	—	2	1	no	—
87	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₈₉	—	2	1	no	—
90	C₄²×D₈₉	—	2	1	no	—
91	C₄²×D₈₉	C₂³	1	1	yes	characteristic
92	#15667946	C₂×C₄	1	1	yes	characteristic
93	#15667945	C₂×C₄	1	1	yes	characteristic
94	#15667945	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#10623494	—	2	1	no	—
96	C₄⋊#10623494	—	2	1	no	—
97	C₄⋊#10623494	C₂³	1	1	yes	characteristic
98	C₄⋊#10623494	C₂³	1	1	yes	characteristic
99	#15667941	—	2	1	no	—
100	#15667941	—	2	1	no	—
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	D₄	1	1	yes	characteristic
105	#15667941	D₄	1	1	yes	characteristic
106	#15667937	C₂×C₄	1	1	yes	characteristic
107	#15667937	C₂×C₄	1	1	yes	characteristic
108	#15667936	C₂×C₄	1	1	yes	characteristic
109	#15667936	C₂×C₄	1	1	yes	characteristic
110	#15667935	C₂×C₄	1	1	yes	characteristic
111	#15667935	C₂×C₄	1	1	yes	characteristic
112	#15667924	—	2	1	no	—
113	#15667924	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	D₄	1	1	yes	characteristic
116	#15667924	D₄	1	1	yes	characteristic
117	#15667923	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	C₄×#10623494	—	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	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
133	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	—	2	1	no	—
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	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#97×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	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₉	—	2	2	no	—
150	Q₈×D₈₉	—	2	2	no	—
151	Q₈×D₈₉	—	2	2	no	—
152	Q₈×D₈₉	M₁₆	1	4	yes	—
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	—	2	1	no	—
157	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
160	Dic₃₅₆	—	2	2	no	—
161	#13083564	—	2	2	no	—
162	#13083564	—	2	2	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
167	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
168	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
169	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
170	C₈×D₈₉	—	2	2	no	—
171	C₈×D₈₉	—	2	2	no	—
172	C₄⋊Dic₈₉	—	2	1	no	—
173	C₄⋊Dic₈₉	—	2	1	no	—
174	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
176	#13083553	—	2	1	no	—
177	#13083553	—	2	1	no	—
178	#13083553	—	2	1	no	—
179	#13083553	—	2	1	no	—
180	#13083553	—	2	1	no	—
181	#13083553	—	2	1	no	—
182	C₄×Dic₈₉	—	2	1	no	—
183	C₄×Dic₈₉	—	2	1	no	—
184	C₄×Dic₈₉	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₄×Dic₈₉	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₈₉	#41	1	1	yes	characteristic
191	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	Q₁₆×C₈₉	—	2	2	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₈₉	—	2	1	no	—
210	Q₈×C₈₉	—	2	1	no	—
211	Q₈×C₈₉	—	2	1	no	—
212	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₈₉	—	2	1	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	2	1	no	—
223	C₂×Dic₈₉	—	2	1	no	—
224	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
227	C₄×D₈₉	—	2	4	no	—
228	C₄×D₈₉	—	2	1	no	—
229	C₄×D₈₉	—	2	1	no	—
230	C₄×D₈₉	—	4	1	no	—
231	C₄×D₈₉	—	4	2	no	—
232	C₄×D₈₉	—	8	1	no	—
233	C₄×D₈₉	—	8	1	no	—
234	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
235	C₄×D₈₉	#131	1	2	yes	—
236	Dic₁₇₈	—	2	1	no	—
237	Dic₁₇₈	—	2	4	no	—
238	Dic₁₇₈	—	2	1	no	—
239	Dic₁₇₈	—	2	1	no	—
240	Dic₁₇₈	—	4	2	no	—
241	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	—	2	1	no	—
245	C₈×C₈₉	—	2	1	no	—
246	C₈×C₈₉	—	4	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	2	1	no	—
251	#10623494	—	2	1	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	#10623494	—	4	1	no	—
256	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₈₉	—	2	1	no	—
258	C₂×D₈₉	—	2	1	no	—
259	C₂×D₈₉	#435	1	2	yes	—
260	C₄×C₈₉	—	2	2	no	—
261	C₄×C₈₉	—	2	1	no	—
262	C₄×C₈₉	—	4	1	no	—
263	C₄×C₈₉	—	4	1	no	—
264	C₄×C₈₉	—	4	1	no	—
265	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
266	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
267	C₄×C₈₉	#578	1	1	yes	characteristic
268	C₄×C₈₉	#578	1	1	yes	characteristic
269	Dic₈₉	—	2	2	no	—
270	Dic₈₉	—	2	1	no	—
271	Dic₈₉	—	2	1	no	—
272	Dic₈₉	—	4	1	no	—
273	Dic₈₉	—	4	1	no	—
274	Dic₈₉	—	4	1	no	—
275	Dic₈₉	#435	1	2	yes	—
276	#17880	—	89	1	no	maximal, Sylow
277	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
278	C₂×C₈₉	#2950	1	1	yes	characteristic
279	C₂×C₈₉	#2957	1	1	yes	characteristic
280	D₈₉	—	2	2	no	—
281	#2983	—	89	1	no	—
282	#2982	—	89	1	no	—
283	C₂×C₄×Q₁₆	—	89	1	no	—
284	#1587	—	89	1	no	—
285	#1587	—	89	1	no	—
286	#1587	—	89	1	no	—
287	#1587	—	89	1	no	—
288	#1584	—	89	1	no	—
289	#1584	—	89	1	no	—
290	#1584	—	89	1	no	—
291	#1584	D₈₉	1	1	yes	characteristic, complemented
292	#1564	—	89	1	no	—
293	#1479	—	89	1	no	—
294	#1479	—	89	1	no	—
295	#1452	—	89	1	no	—
296	C₈₉	#17880	1	1	yes	characteristic, complemented, Sylow
297	C₂²×Q₁₆	—	89	1	no	—
298	C₂×C₄×Q₈	—	89	1	no	—
299	C₂×C₄×Q₈	—	89	1	no	—
300	#446	—	89	1	no	—
301	#446	—	89	1	no	—
302	#446	—	89	1	no	—
303	#446	—	178	1	no	—
304	#446	—	178	1	no	—
305	#446	C₂×D₈₉	1	1	yes	characteristic
306	C₈×Q₈	—	89	1	no	—
307	C₈×Q₈	—	89	1	no	—
308	C₈×Q₈	—	89	1	no	—
309	C₈×Q₈	—	178	1	no	—
310	C₈×Q₈	—	178	1	no	—
311	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
312	C₄×Q₁₆	—	89	1	no	—
313	C₄×Q₁₆	—	89	1	no	—
314	C₄×Q₁₆	—	89	1	no	—
315	C₄×Q₁₆	—	89	1	no	—
316	C₄×Q₁₆	—	89	1	no	—
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
320	#432	—	178	1	no	—
321	#432	—	178	1	no	—
322	#431	—	89	1	no	—
323	#431	—	89	1	no	—
324	#431	—	89	1	no	—
325	#431	—	89	1	no	—
326	#431	—	178	1	no	—
327	#431	—	178	1	no	—
328	C₂×#107	—	89	1	no	—
329	C₂×#103	—	89	1	no	—
330	C₂×#103	—	89	1	no	—
331	C₂×C₄×C₈	—	89	1	no	—
332	#335	—	89	1	no	—
333	#335	C₂×D₈₉	1	1	yes	characteristic
334	#334	—	89	1	no	—
335	#334	—	89	1	no	—
336	Q₈⋊C₈	—	89	1	no	—
337	Q₈⋊C₈	—	89	1	no	—
338	Q₈⋊C₈	—	89	1	no	—
339	Q₈⋊C₈	—	89	1	no	—
340	Q₈⋊C₈	—	89	1	no	—
341	Q₈⋊C₈	—	89	1	no	—
342	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
343	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
344	#322	—	89	1	no	—
345	#322	—	89	1	no	—
346	#322	—	89	1	no	—
347	#322	C₂×D₈₉	1	1	yes	characteristic
348	C₂²×Q₈	—	89	1	no	—
349	C₂²×Q₈	—	89	1	no	—
350	C₂×Q₁₆	—	89	1	no	—
351	C₂×Q₁₆	—	89	1	no	—
352	C₂×Q₁₆	—	89	1	no	—
353	C₂×Q₁₆	—	178	4	no	—
354	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
355	C₂²×C₈	—	89	1	no	—
356	C₂²×C₈	—	89	1	no	—
357	C₄×Q₈	—	89	1	no	—
358	C₄×Q₈	—	89	1	no	—
359	C₄×Q₈	—	89	1	no	—
360	C₄×Q₈	—	89	1	no	—
361	C₄×Q₈	—	89	1	no	—
362	C₄×Q₈	—	89	1	no	—
363	C₄×Q₈	—	178	1	no	—
364	C₄×Q₈	—	178	1	no	—
365	C₄×Q₈	—	178	1	no	—
366	C₄×Q₈	—	178	1	no	—
367	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
368	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	—	89	1	no	—
370	C₂×C₄⋊C₄	—	89	1	no	—
371	C₂×C₄⋊C₄	—	178	1	no	—
372	C₂×C₄⋊C₄	—	178	1	no	—
373	C₂×C₄²	—	89	1	no	—
374	C₂×C₄²	—	178	1	no	—
375	C₂×C₄²	—	178	1	no	—
376	#107	—	89	1	no	—
377	#107	—	89	1	no	—
378	#107	—	89	1	no	—
379	#107	C₄×D₈₉	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	89	1	no	—
383	C₄⋊C₈	—	89	1	no	—
384	C₄⋊C₈	—	89	1	no	—
385	C₄⋊C₈	—	89	1	no	—
386	C₄⋊C₈	—	178	1	no	—
387	C₄⋊C₈	—	178	1	no	—
388	C₄⋊C₈	—	178	1	no	—
389	C₄⋊C₈	—	178	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	—	178	1	no	—
393	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
395	#103	—	89	1	no	—
396	#103	—	89	1	no	—
397	#103	—	89	1	no	—
398	#103	—	89	1	no	—
399	#103	—	89	1	no	—
400	#103	—	89	1	no	—
401	#103	C₄×D₈₉	1	1	yes	characteristic
402	#103	C₄×D₈₉	1	1	yes	characteristic
403	C₂²⋊C₈	—	89	1	no	—
404	C₂²⋊C₈	—	89	1	no	—
405	C₂²⋊C₈	—	178	1	no	—
406	C₂²⋊C₈	—	178	1	no	—
407	C₂²⋊C₈	—	178	1	no	—
408	#97	—	2	1	no	—
409	#97	—	178	1	no	—
410	#97	—	178	1	no	—
411	#97	—	178	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	89	1	no	—
414	C₄×C₈	—	89	1	no	—
415	C₄×C₈	—	89	1	no	—
416	C₄×C₈	—	89	1	no	—
417	C₄×C₈	—	89	1	no	—
418	C₄×C₈	—	178	1	no	—
419	C₄×C₈	—	178	1	no	—
420	C₄×C₈	—	178	1	no	—
421	C₄×C₈	—	178	1	no	—
422	C₄×C₈	—	178	1	no	—
423	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
426	C₂×Q₈	—	89	4	no	—
427	C₂×Q₈	—	89	1	no	—
428	C₂×Q₈	—	89	1	no	—
429	C₂×Q₈	—	178	1	no	—
430	C₂×Q₈	—	178	1	no	—
431	C₂×Q₈	—	178	2	no	—
432	C₂×Q₈	—	178	2	no	—
433	C₂×Q₈	—	178	2	no	—
434	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
436	C₂²×C₄	—	89	1	no	—
437	C₂²×C₄	—	89	1	no	—
438	C₂²×C₄	—	89	1	no	—
439	C₂²×C₄	—	178	1	no	—
440	C₂²×C₄	—	178	1	no	—
441	C₂²×C₄	—	178	1	no	—
442	C₂²×C₄	—	178	1	no	—
443	Q₁₆	—	2	2	no	—
444	Q₁₆	—	178	2	no	—
445	Q₁₆	—	178	2	no	—
446	Q₁₆	—	178	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	89	1	no	—
451	C₂×C₈	—	89	1	no	—
452	C₂×C₈	—	89	1	no	—
453	C₂×C₈	—	89	1	no	—
454	C₂×C₈	—	178	2	no	—
455	C₂×C₈	—	178	2	no	—
456	C₂×C₈	—	178	1	no	—
457	C₂×C₈	—	178	1	no	—
458	C₂×C₈	—	178	1	no	—
459	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
461	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
462	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	89	1	no	—
466	C₄⋊C₄	—	89	1	no	—
467	C₄⋊C₄	—	178	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	1	no	—
472	C₄⋊C₄	—	178	1	no	—
473	C₄⋊C₄	—	178	1	no	—
474	C₄⋊C₄	—	178	1	no	—
475	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	89	1	no	—
480	C₄²	—	89	1	no	—
481	C₄²	—	89	1	no	—
482	C₄²	—	178	1	no	—
483	C₄²	—	178	1	no	—
484	C₄²	—	178	1	no	—
485	C₄²	—	178	1	no	—
486	C₄²	—	178	1	no	—
487	C₄²	—	178	1	no	—
488	C₄²	C₂³×D₈₉	1	1	yes	characteristic
489	C₂³	—	89	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	89	2	no	—
494	Q₈	—	356	2	no	—
495	Q₈	—	178	4	no	—
496	Q₈	—	178	1	no	—
497	Q₈	—	178	1	no	—
498	Q₈	—	178	1	no	—
499	Q₈	M₁₆×D₈₉	1	2	yes	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	89	1	no	—
505	C₂×C₄	—	89	2	no	—
506	C₂×C₄	—	89	2	no	—
507	C₂×C₄	—	89	1	no	—
508	C₂×C₄	—	89	1	no	—
509	C₂×C₄	—	356	1	no	—
510	C₂×C₄	—	356	2	no	—
511	C₂×C₄	—	178	4	no	—
512	C₂×C₄	—	178	1	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	—	178	1	no	—
518	C₂×C₄	—	712	1	no	—
519	C₂×C₄	—	712	1	no	—
520	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
521	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
522	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	356	1	no	—
531	C₈	—	356	1	no	—
532	C₈	—	356	1	no	—
533	C₈	—	178	1	no	—
534	C₈	—	178	1	no	—
535	C₈	—	178	1	no	—
536	C₈	—	178	1	no	—
537	C₂²	—	89	2	no	—
538	C₂²	—	178	1	no	—
539	C₂²	—	178	1	no	—
540	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	89	2	no	—
547	C₄	—	356	1	no	—
548	C₄	—	356	1	no	—
549	C₄	—	356	1	no	—
550	C₄	—	178	1	no	—
551	C₄	—	178	1	no	—
552	C₄	—	178	2	no	—
553	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
554	C₄	#131×D₈₉	1	1	yes	characteristic
555	C₄	#19152411	1	1	yes	characteristic
556	C₄	#19152412	1	1	yes	characteristic
557	C₂	—	178	2	no	—
558	C₂	#435×D₈₉	1	1	yes	characteristic
559	C₂	#26029115	1	1	yes	characteristic
560	C₂	#26029166	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×#1584	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1584	D₈₉
hypocenter	C₈₉	#17880
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #26019126	C₂	semidirect
5. #26019123	C₂	semidirect
6. #26019121	C₂	semidirect
7. #26019120	C₂	semidirect
8. #26019104	C₂	semidirect
9. #26019103	C₂	semidirect
10. #26019101	C₂	semidirect
15. C₈₉×#1584	C₂	semidirect
291. #1584	D₈₉	semidirect
296. C₈₉	#17880	semidirect

Maximal subgroups

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

subgroup	index
#26029334	2
#26029331	2
C₄×Q₁₆×D₈₉	2
#26019126	2
#26019123	2
#26019121	2
#26019120	2
#26019104	2
#26019103	2
#26019101	2
#26018999	2
#26018645	2
#26018543	2
C₈₉×#1584	2
#17880	89