Subgroups — #36525366

Order 22784.

602 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030289	C₂	1	1	yes	maximal, characteristic
2	#26029204	C₂	1	1	yes	maximal, characteristic
3	#26029200	C₂	1	1	yes	maximal, characteristic
4	#26019146	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019100	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019100	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019025	C₂	1	1	yes	maximal, characteristic
12	#26018705	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
14	C₈×#13083557	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1591	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	#19151935	C₄	1	1	yes	characteristic
19	#19151932	C₄	1	1	yes	characteristic
20	#19151892	C₄	1	1	yes	characteristic
21	#19151891	C₄	1	1	yes	characteristic
22	#19151807	C₄	1	1	yes	characteristic
23	#19151806	C₄	1	1	yes	characteristic
24	#19151755	C₄	1	1	yes	characteristic
25	#19151752	C₄	1	1	yes	characteristic
26	#19151729	C₂²	1	1	yes	characteristic
27	#19151727	—	2	1	no	—
28	#19151726	—	2	1	no	—
29	#19151726	—	2	1	no	—
30	#19151725	—	2	1	no	—
31	#19151725	C₂²	1	1	yes	characteristic
32	Q₈×#10623494	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
35	#19151722	C₂²	1	1	yes	characteristic
36	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
37	C₄×#13083564	C₂²	1	1	yes	characteristic
38	C₄×#13083564	C₂²	1	1	yes	characteristic
39	#19151649	C₂²	1	1	yes	characteristic
40	#19151623	—	2	1	no	—
41	#19151620	—	2	1	no	—
42	#19151620	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
44	#19151555	—	2	1	no	—
45	#19151550	—	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
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151350	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	#19151319	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	#446×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	C₈²×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083557	—	2	1	no	—
72	C₂×#13083557	D₄	1	1	yes	characteristic
73	C₂×#13083557	D₄	1	1	yes	characteristic
74	C₂×C₈×D₈₉	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	#15668011	C₂×C₄	1	1	yes	characteristic
77	#15668010	C₂×C₄	1	1	yes	characteristic
78	#15668002	—	2	1	no	—
79	#15667992	C₂×C₄	1	1	yes	characteristic
80	#15667990	—	2	1	no	—
81	#15667988	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₇₈	—	2	1	no	—
84	C₄×Dic₁₇₈	—	2	1	no	—
85	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
87	#15667977	—	2	1	no	—
88	#15667977	C₂×C₄	1	1	yes	characteristic
89	#15667969	—	2	1	no	—
90	C₄⋊C₄×D₈₉	—	2	1	no	—
91	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄²×D₈₉	—	2	1	no	—
93	C₄²×D₈₉	C₂³	1	1	yes	characteristic
94	#15667946	C₂×C₄	1	1	yes	characteristic
95	#15667945	C₂×C₄	1	1	yes	characteristic
96	#15667945	C₂×C₄	1	1	yes	characteristic
97	C₄⋊#10623494	—	2	1	no	—
98	C₄⋊#10623494	—	2	1	no	—
99	C₄⋊#10623494	C₂³	1	1	yes	characteristic
100	C₄⋊#10623494	C₂³	1	1	yes	characteristic
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	C₂×C₄	1	1	yes	characteristic
108	#15667941	C₂×C₄	1	1	yes	characteristic
109	#15667937	C₂×C₄	1	1	yes	characteristic
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667936	C₂×C₄	1	1	yes	characteristic
112	#15667936	C₂×C₄	1	1	yes	characteristic
113	#15667935	C₂×C₄	1	1	yes	characteristic
114	#15667935	C₂×C₄	1	1	yes	characteristic
115	#15667924	C₂×C₄	1	1	yes	characteristic
116	#15667924	C₂×C₄	1	1	yes	characteristic
117	#15667923	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	D₄	1	1	yes	characteristic
120	#15667922	D₄	1	1	yes	characteristic
121	C₄×#10623494	—	2	1	no	—
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	—	2	1	no	—
129	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₈₉	—	2	1	no	—
140	#97×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₈	—	2	1	no	—
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	Q₈×D₈₉	—	2	2	no	—
149	Q₈×D₈₉	—	4	1	no	—
150	C₂×C₄×D₈₉	—	2	1	no	—
151	C₂×C₄×D₈₉	—	2	1	no	—
152	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
155	Dic₃₅₆	—	2	2	no	—
156	#13083564	—	2	2	no	—
157	#13083564	—	4	1	no	—
158	#13083557	—	2	2	no	—
159	#13083557	—	4	2	no	—
160	#13083557	Q₁₆	1	4	yes	complemented
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	—	2	1	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
165	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
166	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
167	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
168	C₈×D₈₉	—	4	2	no	—
169	C₈×D₈₉	—	4	2	no	—
170	C₄⋊Dic₈₉	—	2	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	#13083553	—	2	1	no	—
175	#13083553	—	2	1	no	—
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	#13083551	—	2	1	no	—
183	#13083551	—	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	—	4	1	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	—	2	1	no	—
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	1	no	—
228	C₄×D₈₉	—	2	1	no	—
229	C₄×D₈₉	—	4	1	no	—
230	C₄×D₈₉	—	4	2	no	—
231	C₄×D₈₉	—	8	1	no	—
232	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
233	C₄×D₈₉	#135	1	2	yes	—
234	Dic₁₇₈	—	2	1	no	—
235	Dic₁₇₈	—	2	1	no	—
236	Dic₁₇₈	—	2	1	no	—
237	Dic₁₇₈	—	4	2	no	—
238	Dic₁₇₈	—	8	1	no	—
239	Dic₁₇₈	#131	1	2	yes	—
240	C₈×C₈₉	—	2	2	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	2	1	no	—
244	C₈×C₈₉	—	4	1	no	—
245	C₈×C₈₉	—	4	1	no	—
246	C₈×C₈₉	C₂×Q₁₆	1	2	yes	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	2	1	no	—
250	#10623494	—	4	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	C₂×Q₁₆	1	2	yes	—
254	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂×D₈₉	—	2	1	no	—
256	C₂×D₈₉	—	2	1	no	—
257	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
258	C₄×C₈₉	—	2	1	no	—
259	C₄×C₈₉	—	4	1	no	—
260	C₄×C₈₉	—	4	1	no	—
261	C₄×C₈₉	—	4	1	no	—
262	C₄×C₈₉	—	4	1	no	—
263	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
264	C₄×C₈₉	#568	1	1	yes	characteristic
265	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
266	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
267	Dic₈₉	—	2	2	no	—
268	Dic₈₉	—	2	1	no	—
269	Dic₈₉	—	2	1	no	—
270	Dic₈₉	—	4	1	no	—
271	Dic₈₉	—	4	1	no	—
272	Dic₈₉	—	4	1	no	—
273	Dic₈₉	C₄×Q₁₆	1	2	yes	—
274	#17998	—	89	1	no	maximal, Sylow
275	C₂×C₈₉	#2933	1	1	yes	characteristic
276	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
277	C₂×C₈₉	#2956	1	1	yes	characteristic
278	D₈₉	—	2	2	no	—
279	#3104	—	89	1	no	—
280	Q₈×M₁₆	—	89	1	no	—
281	#2962	—	89	1	no	—
282	#1591	—	89	1	no	—
283	#1591	D₈₉	1	1	yes	characteristic, complemented
284	#1584	—	89	1	no	—
285	#1584	—	89	1	no	—
286	#1584	—	89	1	no	—
287	#1584	—	89	1	no	—
288	C₈×Q₁₆	—	89	1	no	—
289	C₈×Q₁₆	—	89	1	no	—
290	#1571	—	89	1	no	—
291	#1493	—	89	1	no	—
292	C₂×Q₈⋊C₈	—	89	1	no	—
293	C₈×M₁₆	—	89	1	no	—
294	C₈₉	#17998	1	1	yes	characteristic, complemented, Sylow
295	#533	—	89	1	no	—
296	C₂×C₄×Q₈	—	89	1	no	—
297	#484	—	89	1	no	—
298	#484	—	89	1	no	—
299	#477	—	89	1	no	—
300	#477	—	89	1	no	—
301	#462	—	89	1	no	—
302	#462	—	89	1	no	—
303	#451	—	89	1	no	—
304	#451	—	89	1	no	—
305	#446	—	89	1	no	—
306	#446	—	89	1	no	—
307	#446	—	178	1	no	—
308	#446	—	178	1	no	—
309	#446	—	178	1	no	—
310	#446	—	178	1	no	—
311	#446	C₂×D₈₉	1	1	yes	characteristic
312	#446	C₂×D₈₉	1	1	yes	characteristic
313	C₈×Q₈	—	89	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	C₈×Q₈	—	89	1	no	—
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×Q₁₆	—	89	1	no	—
320	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
321	#431	—	89	1	no	—
322	#424	—	178	1	no	—
323	#423	—	89	1	no	—
324	#423	—	178	1	no	—
325	C₂×C₄⋊C₈	—	89	1	no	—
326	#405	—	178	1	no	—
327	C₄×M₁₆	—	89	1	no	—
328	C₄×M₁₆	—	178	1	no	—
329	C₂×C₄×C₈	—	89	1	no	—
330	#335	—	89	1	no	—
331	#335	—	89	1	no	—
332	#335	—	89	1	no	—
333	#335	C₂×D₈₉	1	1	yes	characteristic
334	Q₈⋊C₈	—	89	1	no	—
335	Q₈⋊C₈	—	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	C₂×D₈₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
342	#322	—	89	1	no	—
343	#322	—	89	1	no	—
344	C₈²	—	89	1	no	—
345	C₈²	C₂×D₈₉	1	1	yes	characteristic
346	C₂²×Q₈	—	89	1	no	—
347	C₂×Q₁₆	—	89	1	no	—
348	C₂×Q₁₆	—	89	1	no	—
349	C₂×Q₁₆	—	89	1	no	—
350	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
351	C₂×M₁₆	—	89	1	no	—
352	C₂×M₁₆	—	89	1	no	—
353	C₂×M₁₆	—	178	1	no	—
354	C₂²×C₈	—	178	1	no	—
355	C₂²×C₈	—	178	1	no	—
356	C₄⋊Q₈	—	89	1	no	—
357	C₄⋊Q₈	—	89	1	no	—
358	#125	—	178	1	no	—
359	C₂²⋊Q₈	—	89	1	no	—
360	C₂²⋊Q₈	—	89	1	no	—
361	C₂²⋊Q₈	—	178	1	no	—
362	C₄×Q₈	—	89	1	no	—
363	C₄×Q₈	—	89	1	no	—
364	C₄×Q₈	—	89	1	no	—
365	C₄×Q₈	—	89	1	no	—
366	C₄×Q₈	—	178	1	no	—
367	C₄×Q₈	—	178	1	no	—
368	C₄×Q₈	—	178	1	no	—
369	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
370	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
371	#117	—	178	1	no	—
372	C₂×C₄⋊C₄	—	89	1	no	—
373	C₂×C₄⋊C₄	—	178	1	no	—
374	C₂×C₄²	—	89	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	—	178	1	no	—
394	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
402	#103	C₄×D₈₉	1	1	yes	characteristic
403	#103	C₄×D₈₉	1	1	yes	characteristic
404	C₂²⋊C₈	—	89	1	no	—
405	C₂²⋊C₈	—	89	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	#97	—	89	1	no	—
409	#97	—	89	1	no	—
410	#97	—	178	1	no	—
411	#97	—	178	1	no	—
412	C₄×C₈	—	89	1	no	—
413	C₄×C₈	—	89	1	no	—
414	C₄×C₈	—	89	1	no	—
415	C₄×C₈	—	178	1	no	—
416	C₄×C₈	—	178	1	no	—
417	C₄×C₈	—	178	1	no	—
418	C₄×C₈	—	178	1	no	—
419	C₄×C₈	—	178	1	no	—
420	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
423	C₂×Q₈	—	89	1	no	—
424	C₂×Q₈	—	89	1	no	—
425	C₂×Q₈	—	356	1	no	—
426	C₂×Q₈	—	178	1	no	—
427	C₂×Q₈	—	178	1	no	—
428	C₂×Q₈	—	178	2	no	—
429	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
430	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₂²×C₄	—	89	1	no	—
432	C₂²×C₄	—	89	1	no	—
433	C₂²×C₄	—	89	1	no	—
434	C₂²×C₄	—	178	1	no	—
435	C₂²×C₄	—	178	1	no	—
436	Q₁₆	—	4	1	no	—
437	Q₁₆	—	356	1	no	—
438	Q₁₆	—	178	2	no	—
439	Q₁₆	—	178	2	no	—
440	M₁₆	—	89	4	no	—
441	M₁₆	—	356	2	no	—
442	M₁₆	—	178	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	89	1	no	—
447	C₂×C₈	—	89	1	no	—
448	C₂×C₈	—	89	1	no	—
449	C₂×C₈	—	89	1	no	—
450	C₂×C₈	—	356	2	no	—
451	C₂×C₈	—	356	2	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	178	1	no	—
455	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
458	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	89	1	no	—
462	C₄⋊C₄	—	89	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₄⋊C₄	—	178	1	no	—
466	C₄⋊C₄	—	178	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	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
475	C₂²⋊C₄	—	178	1	no	—
476	C₂²⋊C₄	—	178	1	no	—
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	C₂³×D₈₉	1	1	yes	characteristic
487	C₂³	—	89	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	89	2	no	—
493	Q₈	—	356	2	no	—
494	Q₈	—	178	1	no	—
495	Q₈	—	178	1	no	—
496	Q₈	—	178	1	no	—
497	Q₈	—	712	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	89	1	no	—
503	C₂×C₄	—	89	2	no	—
504	C₂×C₄	—	89	2	no	—
505	C₂×C₄	—	89	1	no	—
506	C₂×C₄	—	89	1	no	—
507	C₂×C₄	—	356	1	no	—
508	C₂×C₄	—	356	2	no	—
509	C₂×C₄	—	178	1	no	—
510	C₂×C₄	—	178	1	no	—
511	C₂×C₄	—	178	1	no	—
512	C₂×C₄	—	178	1	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	712	1	no	—
516	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
518	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
519	C₈	—	2	2	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	89	2	no	—
526	C₈	—	356	1	no	—
527	C₈	—	356	1	no	—
528	C₈	—	356	1	no	—
529	C₈	—	178	1	no	—
530	C₈	—	178	1	no	—
531	C₈	—	178	1	no	—
532	C₈	Q₁₆×D₈₉	1	2	yes	—
533	C₂²	—	89	2	no	—
534	C₂²	—	178	1	no	—
535	C₂²	—	178	1	no	—
536	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	89	2	no	—
543	C₄	—	356	1	no	—
544	C₄	—	356	1	no	—
545	C₄	—	356	1	no	—
546	C₄	—	178	1	no	—
547	C₄	—	178	1	no	—
548	C₄	—	178	2	no	—
549	C₄	#131×D₈₉	1	1	yes	characteristic
550	C₄	#19152364	1	1	yes	characteristic
551	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
552	C₄	#135×D₈₉	1	1	yes	characteristic
553	C₂	—	178	2	no	—
554	C₂	#26028981	1	1	yes	characteristic
555	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
556	C₂	#26029157	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×#1591	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1591	D₈₉
hypocenter	C₈₉	#17998
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
4. #26019146	C₂	semidirect
5. #26019103	C₂	semidirect
6. #26019101	C₂	semidirect
7. #26019100	C₂	semidirect
8. #26019100	C₂	semidirect
9. C₈×Dic₃₅₆	C₂	semidirect
10. #26019056	C₂	semidirect
15. C₈₉×#1591	C₂	semidirect
160. #13083557	Q₁₆	semidirect
283. #1591	D₈₉	semidirect
294. C₈₉	#17998	semidirect

Maximal subgroups

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

subgroup	index
#26030289	2
#26029204	2
#26029200	2
#26019146	2
#26019103	2
#26019101	2
#26019100	2
C₈×Dic₃₅₆	2
#26019056	2
#26019025	2
#26018705	2
Q₈⋊C₈×D₈₉	2
C₈×#13083557	2
C₈₉×#1591	2
#17998	89