Subgroups — #36526000

Order 22784.

640 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029268	C₂	1	1	yes	maximal, characteristic
2	Q₈×#13083557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668041	C₂	1	1	yes	maximal, characteristic
4	#26019154	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019145	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019125	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019096	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019069	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019018	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018697	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018688	C₂	1	1	yes	maximal, characteristic
14	#26018556	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1588	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668041	C₄	1	1	yes	characteristic
17	C₄×#13083573	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	#19151728	—	2	1	no	—
20	#19151728	C₂²	1	1	yes	characteristic
21	#19151725	—	2	1	no	—
22	#19151725	C₂²	1	1	yes	characteristic
23	Q₈×#10623494	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
25	#19151722	C₂²	1	1	yes	characteristic
26	#19151704	C₄	1	1	yes	characteristic
27	#19151702	C₄	1	1	yes	characteristic
28	#19151699	C₄	1	1	yes	characteristic
29	#19151695	C₄	1	1	yes	characteristic
30	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
31	C₄×#13083564	C₂²	1	1	yes	characteristic
32	C₄×#13083562	C₂²	1	1	yes	characteristic
33	#19151676	C₂²	1	1	yes	characteristic
34	#19151674	—	2	1	no	—
35	#19151673	—	2	1	no	—
36	#19151654	C₂²	1	1	yes	characteristic
37	#19151652	—	2	1	no	—
38	#19151637	C₄	1	1	yes	characteristic
39	#19151620	—	2	1	no	—
40	#19151620	C₂²	1	1	yes	characteristic
41	#19151605	C₄	1	1	yes	characteristic
42	#19151596	C₄	1	1	yes	characteristic
43	M₁₆×Dic₈₉	—	2	1	no	—
44	C₄×#13083557	—	2	1	no	—
45	C₄×#13083557	C₂²	1	1	yes	characteristic
46	C₄×#13083557	C₂²	1	1	yes	characteristic
47	C₄×#13083557	C₂²	1	1	yes	characteristic
48	#19151350	C₂²	1	1	yes	characteristic
49	#19151349	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	#19151328	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	D₄⋊#10623494	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	#19151320	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	#436×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×#13083573	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
69	#15668041	—	2	4	no	—
70	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
73	C₂×#13083558	—	2	1	no	—
74	C₂×#13083557	—	2	1	no	—
75	C₂×#13083557	—	2	1	no	—
76	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
77	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
78	C₂×#13083557	D₄	1	1	yes	characteristic
79	C₂×#13083557	D₄	1	1	yes	characteristic
80	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₇₈	—	2	1	no	—
82	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
83	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
84	#15667977	—	2	1	no	—
85	#15667977	C₂×C₄	1	1	yes	characteristic
86	#15667977	C₂×C₄	1	1	yes	characteristic
87	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₈₉	—	2	1	no	—
89	#15667972	—	2	1	no	—
90	#15667970	C₂×C₄	1	1	yes	characteristic
91	#15667968	—	2	1	no	—
92	C₄⋊C₄×D₈₉	—	2	1	no	—
93	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₈₉	—	2	1	no	—
95	C₄²×D₈₉	—	2	1	no	—
96	C₄²×D₈₉	C₂³	1	1	yes	characteristic
97	#15667946	C₂×C₄	1	1	yes	characteristic
98	#15667945	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	#15667937	C₂×C₄	1	1	yes	characteristic
109	#15667937	C₂×C₄	1	1	yes	characteristic
110	#15667936	C₂×C₄	1	1	yes	characteristic
111	#15667935	C₂×C₄	1	1	yes	characteristic
112	#15667935	C₂×C₄	1	1	yes	characteristic
113	#15667933	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#10623494	—	2	1	no	—
115	#15667924	—	2	1	no	—
116	#15667922	—	2	1	no	—
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	#15667922	C₂×C₄	1	1	yes	characteristic
121	#15667922	C₂×C₄	1	1	yes	characteristic
122	#15667922	D₄	1	1	yes	characteristic
123	#15667922	D₄	1	1	yes	characteristic
124	C₄×#10623494	—	2	1	no	—
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	—	2	1	no	—
130	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×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	#13083573	—	2	2	no	—
146	#13083573	—	4	1	no	—
147	C₂×Dic₁₇₈	—	2	1	no	—
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
150	Q₈×D₈₉	—	2	2	no	—
151	Q₈×D₈₉	—	4	1	no	—
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	C₂²×Dic₈₉	—	2	1	no	—
154	C₂²×Dic₈₉	—	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	M₁₆	1	4	yes	complemented
162	#13083562	—	2	2	no	—
163	#13083558	—	4	2	no	—
164	#13083557	—	2	2	no	—
165	#13083557	—	2	2	no	—
166	#13083557	—	4	1	no	—
167	#13083557	—	4	1	no	—
168	#13083557	—	4	2	no	—
169	#13083557	—	4	2	no	—
170	C₂×#10623494	—	2	1	no	—
171	C₂×#10623494	—	2	1	no	—
172	C₂×#10623494	—	2	1	no	—
173	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
174	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
175	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
176	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
177	C₄⋊Dic₈₉	—	2	1	no	—
178	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
180	#13083553	—	2	1	no	—
181	#13083553	—	2	1	no	—
182	#13083553	—	2	1	no	—
183	#13083553	—	2	1	no	—
184	#13083553	—	2	1	no	—
185	C₂²⋊Dic₈₉	—	2	1	no	—
186	#13083551	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	—	2	1	no	—
190	C₄×Dic₈₉	—	2	1	no	—
191	C₄×Dic₈₉	—	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	M₁₆×C₈₉	—	4	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	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	C₄×D₄	1	1	yes	characteristic
216	Q₈×C₈₉	—	2	1	no	—
217	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
218	D₄×C₈₉	—	2	1	no	—
219	D₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₈₉	—	4	2	no	—
229	C₂×Dic₈₉	—	2	1	no	—
230	C₂×Dic₈₉	—	2	1	no	—
231	C₂×Dic₈₉	—	2	1	no	—
232	C₂×Dic₈₉	—	2	1	no	—
233	C₂×Dic₈₉	—	4	2	no	—
234	C₂×Dic₈₉	—	8	1	no	—
235	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
238	C₄×D₈₉	—	2	1	no	—
239	C₄×D₈₉	—	2	1	no	—
240	C₄×D₈₉	—	2	1	no	—
241	C₄×D₈₉	—	2	1	no	—
242	C₄×D₈₉	—	4	1	no	—
243	C₄×D₈₉	—	4	2	no	—
244	C₄×D₈₉	—	8	1	no	—
245	Dic₁₇₈	—	2	1	no	—
246	Dic₁₇₈	—	2	1	no	—
247	Dic₁₇₈	—	2	1	no	—
248	Dic₁₇₈	—	4	2	no	—
249	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
250	C₈×C₈₉	—	2	2	no	—
251	C₈×C₈₉	—	2	1	no	—
252	C₈×C₈₉	—	2	1	no	—
253	C₈×C₈₉	—	2	1	no	—
254	C₈×C₈₉	—	2	1	no	—
255	C₈×C₈₉	—	4	1	no	—
256	C₈×C₈₉	—	4	1	no	—
257	#10623494	—	2	1	no	—
258	#10623494	—	2	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	—	4	1	no	—
261	#10623494	—	4	1	no	—
262	#10623494	C₂×M₁₆	1	2	yes	—
263	#10623494	#137	1	2	yes	complemented
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂×D₈₉	—	2	1	no	—
269	C₂×D₈₉	—	2	1	no	—
270	C₂×D₈₉	—	2	1	no	—
271	C₄×C₈₉	—	2	2	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
276	C₄×C₈₉	#568	1	1	yes	characteristic
277	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
278	C₄×C₈₉	#575	1	1	yes	characteristic
279	Dic₈₉	—	2	2	no	—
280	Dic₈₉	—	2	1	no	—
281	Dic₈₉	—	2	1	no	—
282	Dic₈₉	—	2	1	no	—
283	Dic₈₉	—	4	1	no	—
284	Dic₈₉	—	4	1	no	—
285	Dic₈₉	—	4	1	no	—
286	#18049	—	89	1	no	maximal, Sylow
287	C₂×C₈₉	—	8	1	no	—
288	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
289	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
290	C₂×C₈₉	#2956	1	1	yes	characteristic
291	D₈₉	—	4	1	no	—
292	#2971	—	89	1	no	—
293	Q₈×M₁₆	—	89	1	no	—
294	C₄×#137	—	89	1	no	—
295	#1592	—	89	1	no	—
296	#1590	—	89	1	no	—
297	#1588	D₈₉	1	1	yes	characteristic, complemented
298	#1587	—	89	1	no	—
299	#1584	—	89	1	no	—
300	#1583	—	89	1	no	—
301	#1579	—	89	1	no	—
302	C₈×Q₁₆	—	89	1	no	—
303	#1569	—	89	1	no	—
304	#1491	—	89	1	no	—
305	#1489	—	89	1	no	—
306	#1455	—	89	1	no	—
307	C₈₉	#18049	1	1	yes	characteristic, complemented, Sylow
308	C₂×#137	—	89	1	no	—
309	C₄×#41	—	89	1	no	—
310	C₂×C₄×Q₈	—	89	1	no	—
311	#446	—	89	1	no	—
312	#446	—	89	1	no	—
313	#446	—	178	1	no	—
314	#446	—	178	1	no	—
315	C₈×Q₈	—	89	1	no	—
316	C₈×Q₈	—	89	1	no	—
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
319	#441	—	89	1	no	—
320	#441	—	89	1	no	—
321	#440	—	89	1	no	—
322	#440	—	89	1	no	—
323	C₄×Q₁₆	—	89	1	no	—
324	C₄×Q₁₆	—	89	1	no	—
325	C₄×SD₁₆	—	89	1	no	—
326	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
327	#436	—	89	1	no	—
328	#436	—	178	1	no	—
329	#436	—	178	1	no	—
330	#436	C₂×D₈₉	1	1	yes	characteristic
331	#432	—	89	1	no	—
332	#432	—	178	1	no	—
333	#428	—	89	1	no	—
334	#423	—	89	1	no	—
335	#423	—	178	1	no	—
336	#419	—	89	1	no	—
337	#417	—	89	1	no	—
338	C₄×M₁₆	—	89	1	no	—
339	C₄×M₁₆	—	89	1	no	—
340	C₄×M₁₆	—	89	1	no	—
341	C₄×M₁₆	—	178	1	no	—
342	C₄×M₁₆	—	178	1	no	—
343	#335	—	89	1	no	—
344	#335	C₂×D₈₉	1	1	yes	characteristic
345	#334	—	89	1	no	—
346	#334	—	89	1	no	—
347	Q₈⋊C₈	—	89	1	no	—
348	Q₈⋊C₈	—	89	1	no	—
349	Q₈⋊C₈	—	89	1	no	—
350	Q₈⋊C₈	—	89	1	no	—
351	Q₈⋊C₈	—	89	1	no	—
352	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
353	D₄⋊C₈	—	89	1	no	—
354	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
355	#322	—	89	1	no	—
356	#322	—	89	1	no	—
357	#322	C₂×D₈₉	1	1	yes	characteristic
358	C₈²	—	89	1	no	—
359	C₂×#41	—	89	1	no	—
360	C₂²×Q₈	—	89	1	no	—
361	#137	—	178	4	no	—
362	C₂×Q₁₆	—	89	1	no	—
363	C₂×Q₁₆	—	89	1	no	—
364	C₂×SD₁₆	—	89	1	no	—
365	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	89	1	no	—
368	C₂×M₁₆	—	89	1	no	—
369	C₂×M₁₆	—	89	1	no	—
370	C₂×M₁₆	—	89	1	no	—
371	C₂×M₁₆	—	178	1	no	—
372	C₂×M₁₆	—	178	1	no	—
373	C₂×M₁₆	—	178	1	no	—
374	C₄×Q₈	—	89	1	no	—
375	C₄×Q₈	—	89	1	no	—
376	C₄×Q₈	—	89	1	no	—
377	C₄×Q₈	—	89	1	no	—
378	C₄×Q₈	—	89	1	no	—
379	C₄×Q₈	—	178	1	no	—
380	C₄×Q₈	—	178	1	no	—
381	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
382	C₄×D₄	—	89	1	no	—
383	C₄×D₄	—	178	1	no	—
384	C₄×D₄	—	178	1	no	—
385	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
386	#117	—	89	1	no	—
387	#117	—	178	1	no	—
388	C₂×C₄⋊C₄	—	89	1	no	—
389	C₂×C₄⋊C₄	—	178	1	no	—
390	C₂×C₄²	—	89	1	no	—
391	C₂×C₄²	—	178	1	no	—
392	C₂×C₄²	—	178	1	no	—
393	#107	—	89	1	no	—
394	#107	—	89	1	no	—
395	#106	—	89	1	no	—
396	#106	C₄×D₈₉	1	1	yes	characteristic
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	89	1	no	—
399	C₄⋊C₈	—	89	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	—	178	1	no	—
403	C₄⋊C₈	—	178	1	no	—
404	C₄⋊C₈	—	178	1	no	—
405	C₄⋊C₈	—	178	1	no	—
406	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
408	#103	—	89	1	no	—
409	#103	—	89	1	no	—
410	#103	—	89	1	no	—
411	#103	—	89	1	no	—
412	#103	—	89	1	no	—
413	#103	C₄×D₈₉	1	1	yes	characteristic
414	#102	—	89	1	no	—
415	#102	C₄×D₈₉	1	1	yes	characteristic
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	178	1	no	—
418	C₂²⋊C₈	—	178	1	no	—
419	#97	—	89	1	no	—
420	#97	—	89	1	no	—
421	#97	—	89	1	no	—
422	#97	—	89	1	no	—
423	#97	—	178	1	no	—
424	#97	—	178	1	no	—
425	#97	—	178	1	no	—
426	#97	—	178	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	89	1	no	—
429	C₄×C₈	—	89	1	no	—
430	C₄×C₈	—	89	1	no	—
431	C₄×C₈	—	178	1	no	—
432	C₄×C₈	—	178	1	no	—
433	C₄×C₈	—	178	1	no	—
434	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
436	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
437	#41	—	356	1	no	—
438	#41	—	178	2	no	—
439	C₂×Q₈	—	89	1	no	—
440	C₂×Q₈	—	89	1	no	—
441	C₂×Q₈	—	356	1	no	—
442	C₂×Q₈	—	178	1	no	—
443	C₂×Q₈	—	178	2	no	—
444	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
445	C₂×D₄	—	178	1	no	—
446	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	89	1	no	—
449	C₂²×C₄	—	89	1	no	—
450	C₂²×C₄	—	89	1	no	—
451	C₂²×C₄	—	178	1	no	—
452	C₂²×C₄	—	178	1	no	—
453	C₂²×C₄	—	178	1	no	—
454	C₂²×C₄	—	178	1	no	—
455	Q₁₆	—	89	4	no	—
456	Q₁₆	—	178	2	no	—
457	SD₁₆	—	2	2	no	—
458	SD₁₆	—	178	2	no	—
459	M₁₆	—	4	2	no	—
460	M₁₆	—	356	2	no	—
461	M₁₆	—	356	1	no	—
462	M₁₆	—	356	1	no	—
463	M₁₆	—	356	2	no	—
464	M₁₆	—	356	2	no	—
465	M₁₆	—	178	2	no	—
466	M₁₆	—	178	2	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	89	1	no	—
471	C₂×C₈	—	89	1	no	—
472	C₂×C₈	—	89	1	no	—
473	C₂×C₈	—	89	1	no	—
474	C₂×C₈	—	178	1	no	—
475	C₂×C₈	—	178	1	no	—
476	C₂×C₈	—	178	1	no	—
477	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
478	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
479	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
480	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	89	1	no	—
483	C₄⋊C₄	—	89	1	no	—
484	C₄⋊C₄	—	178	1	no	—
485	C₄⋊C₄	—	178	1	no	—
486	C₄⋊C₄	—	178	1	no	—
487	C₄⋊C₄	—	178	1	no	—
488	C₄⋊C₄	—	178	1	no	—
489	C₄⋊C₄	—	178	1	no	—
490	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	178	1	no	—
494	C₂²⋊C₄	—	178	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	89	1	no	—
497	C₄²	—	89	1	no	—
498	C₄²	—	89	1	no	—
499	C₄²	—	178	1	no	—
500	C₄²	—	178	1	no	—
501	C₄²	—	178	1	no	—
502	C₄²	—	178	1	no	—
503	C₄²	—	178	1	no	—
504	C₄²	—	178	1	no	—
505	C₄²	C₂³×D₈₉	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	—	89	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	89	2	no	—
510	Q₈	—	356	2	no	—
511	Q₈	—	178	1	no	—
512	Q₈	—	178	1	no	—
513	Q₈	—	178	1	no	—
514	Q₈	M₁₆×D₈₉	1	2	yes	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	356	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	89	1	no	—
524	C₂×C₄	—	89	1	no	—
525	C₂×C₄	—	89	1	no	—
526	C₂×C₄	—	356	2	no	—
527	C₂×C₄	—	356	1	no	—
528	C₂×C₄	—	356	2	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	—	178	1	no	—
531	C₂×C₄	—	178	1	no	—
532	C₂×C₄	—	178	1	no	—
533	C₂×C₄	—	178	1	no	—
534	C₂×C₄	—	178	1	no	—
535	C₂×C₄	—	178	1	no	—
536	C₂×C₄	—	178	1	no	—
537	C₂×C₄	—	712	1	no	—
538	C₂×C₄	—	712	1	no	—
539	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
540	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
541	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	89	2	no	—
550	C₈	—	89	2	no	—
551	C₈	—	356	1	no	—
552	C₈	—	356	1	no	—
553	C₈	—	356	1	no	—
554	C₈	—	178	1	no	—
555	C₈	—	178	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	178	1	no	—
560	C₂²	—	178	1	no	—
561	C₂²	—	178	1	no	—
562	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	356	1	no	—
568	C₄	—	356	1	no	—
569	C₄	—	356	1	no	—
570	C₄	—	178	1	no	—
571	C₄	—	178	1	no	—
572	C₄	—	178	1	no	—
573	C₄	—	178	2	no	—
574	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
575	C₄	#19152363	1	1	yes	characteristic
576	C₄	#137×D₈₉	1	1	yes	characteristic
577	C₄	#19152394	1	1	yes	characteristic
578	C₂	—	8	1	no	—
579	C₂	—	356	1	no	—
580	C₂	#26028985	1	1	yes	characteristic
581	C₂	#26029074	1	1	yes	characteristic
582	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×#1588	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083573	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1588	D₈₉
hypocenter	C₈₉	#18049
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
2. Q₈×#13083557	C₂	semidirect
4. #26019154	C₂	semidirect
5. #26019145	C₂	semidirect
6. #26019125	C₂	semidirect
7. #26019101	C₂	semidirect
8. #26019096	C₂	semidirect
9. #26019069	C₂	semidirect
10. #26019056	C₂	semidirect
11. #26019018	C₂	semidirect
12. #26018697	C₂	semidirect
14. #26018556	C₂	semidirect
15. C₈₉×#1588	C₂	semidirect
161. #13083564	M₁₆	semidirect
263. #10623494	#137	semidirect
297. #1588	D₈₉	semidirect
307. C₈₉	#18049	semidirect

Maximal subgroups

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

subgroup	index
#26029268	2
Q₈×#13083557	2
C₄×#15668041	2
#26019154	2
#26019145	2
#26019125	2
#26019101	2
#26019096	2
#26019069	2
#26019056	2
#26019018	2
#26018697	2
#26018688	2
#26018556	2
C₈₉×#1588	2
#18049	89