Subgroups — #36525475

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030306	C₂	1	1	yes	maximal, characteristic
2	#26029267	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019154	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019140	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019114	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019109	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019088	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019079	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019074	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019035	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018721	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018637	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018549	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13083574	C₂²	1	1	yes	characteristic
17	#19151919	C₄	1	1	yes	characteristic
18	#19151919	C₄	1	1	yes	characteristic
19	#19151890	C₄	1	1	yes	characteristic
20	#19151885	C₄	1	1	yes	characteristic
21	#19151795	C₄	1	1	yes	characteristic
22	#19151790	C₄	1	1	yes	characteristic
23	#19151741	C₄	1	1	yes	characteristic
24	#19151741	C₄	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	C₄×#13083562	C₂²	1	1	yes	characteristic
28	C₄×#13083562	C₂²	1	1	yes	characteristic
29	C₄×#13083559	C₂²	1	1	yes	characteristic
30	C₄×#13083559	C₂²	1	1	yes	characteristic
31	#19151667	—	2	1	no	—
32	#19151667	—	2	1	no	—
33	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
34	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
35	#19151655	C₂²	1	1	yes	characteristic
36	#19151653	—	2	1	no	—
37	#19151651	C₂²	1	1	yes	characteristic
38	#19151651	C₂²	1	1	yes	characteristic
39	#97×D₈₉	—	2	1	no	—
40	#19151350	C₂²	1	1	yes	characteristic
41	#19151350	C₂²	1	1	yes	characteristic
42	#19151348	C₂²	1	1	yes	characteristic
43	#19151348	C₂²	1	1	yes	characteristic
44	#19151328	C₂²	1	1	yes	characteristic
45	#19151328	C₂²	1	1	yes	characteristic
46	D₄⋊#10623494	C₂²	1	1	yes	characteristic
47	D₄⋊#10623494	C₂²	1	1	yes	characteristic
48	D₄⋊#10623494	C₂²	1	1	yes	characteristic
49	D₄⋊#10623494	C₂²	1	1	yes	characteristic
50	#19151325	C₂²	1	1	yes	characteristic
51	#19151325	C₂²	1	1	yes	characteristic
52	#19151320	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic
54	#19151319	C₂²	1	1	yes	characteristic
55	C₈×#10623494	C₂²	1	1	yes	characteristic
56	C₂×#131×C₈₉	—	2	1	no	—
57	#532×C₈₉	C₂²	1	1	yes	characteristic
58	#436×C₈₉	C₂²	1	1	yes	characteristic
59	#436×C₈₉	C₂²	1	1	yes	characteristic
60	#435×C₈₉	—	2	1	no	—
61	#435×C₈₉	—	2	1	no	—
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	#408×C₈₉	—	2	1	no	—
66	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₈₉	—	2	1	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
76	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
77	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
78	C₄×C₂²⋊D₈₉	—	2	1	no	—
79	C₄×C₂²⋊D₈₉	—	2	1	no	—
80	#15667971	C₂×C₄	1	1	yes	characteristic
81	#15667969	—	2	1	no	—
82	C₄²×D₈₉	—	2	1	no	—
83	#15667945	C₂×C₄	1	1	yes	characteristic
84	#15667945	C₂×C₄	1	1	yes	characteristic
85	#15667943	C₂×C₄	1	1	yes	characteristic
86	#15667943	C₂×C₄	1	1	yes	characteristic
87	C₄⋊#10623494	—	2	1	no	—
88	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
89	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
90	C₄⋊#10623494	C₂³	1	1	yes	characteristic
91	C₄⋊#10623494	C₂³	1	1	yes	characteristic
92	#15667941	—	2	1	no	—
93	#15667941	—	2	1	no	—
94	#15667935	C₂×C₄	1	1	yes	characteristic
95	#15667935	C₂×C₄	1	1	yes	characteristic
96	#15667933	C₂×C₄	1	1	yes	characteristic
97	#15667933	C₂×C₄	1	1	yes	characteristic
98	#15667933	C₂×C₄	1	1	yes	characteristic
99	#15667933	C₂×C₄	1	1	yes	characteristic
100	#15667932	C₂×C₄	1	1	yes	characteristic
101	#15667932	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊#10623494	—	2	1	no	—
103	C₂²⋊#10623494	—	2	1	no	—
104	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
106	#15667924	—	2	1	no	—
107	#15667924	—	2	1	no	—
108	#15667923	—	2	1	no	—
109	#15667922	—	2	1	no	—
110	#15667922	—	2	1	no	—
111	C₄×#10623494	C₂³	1	1	yes	characteristic
112	C₄×#10623494	C₂³	1	1	yes	characteristic
113	C₄×#10623494	C₂³	1	1	yes	characteristic
114	C₄×#10623494	C₂³	1	1	yes	characteristic
115	C₂×#41×C₈₉	—	2	1	no	—
116	#131×C₈₉	—	4	4	no	—
117	C₂×M₁₆×C₈₉	—	2	1	no	—
118	C₂×M₁₆×C₈₉	—	2	1	no	—
119	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
120	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
121	C₂²×C₈×C₈₉	—	2	1	no	—
122	C₂²×C₈×C₈₉	—	2	1	no	—
123	C₂²×C₈×C₈₉	—	2	1	no	—
124	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
125	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
126	#124×C₈₉	—	2	1	no	—
127	#121×C₈₉	—	2	1	no	—
128	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
129	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄×D₄×C₈₉	—	2	1	no	—
131	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₈₉	—	2	1	no	—
138	C₂²⋊C₈×C₈₉	—	2	1	no	—
139	C₂²⋊C₈×C₈₉	—	2	1	no	—
140	C₂²⋊C₈×C₈₉	—	2	1	no	—
141	#97×C₈₉	D₄	1	1	yes	characteristic
142	#97×C₈₉	D₄	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	#13083574	—	2	2	no	—
146	#13083574	—	4	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	C₂×C₄×D₈₉	—	2	1	no	—
151	C₂×C₄×D₈₉	—	2	1	no	—
152	C₂×C₄×D₈₉	—	2	1	no	—
153	#13083562	—	4	1	no	—
154	#13083562	—	4	1	no	—
155	#13083559	—	2	2	no	—
156	#13083559	—	2	2	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
164	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
165	C₈×D₈₉	—	4	2	no	—
166	C₈×D₈₉	—	4	2	no	—
167	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
169	#13083553	—	2	1	no	—
170	#13083553	—	2	1	no	—
171	C₂²⋊Dic₈₉	—	2	1	no	—
172	#13083551	—	2	1	no	—
173	#13083551	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₄×Dic₈₉	—	2	1	no	—
176	C₄×Dic₈₉	—	2	1	no	—
177	#41×C₈₉	—	4	2	no	—
178	#41×C₈₉	—	4	2	no	—
179	C₂×Q₈×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
191	M₁₆×C₈₉	—	2	2	no	—
192	M₁₆×C₈₉	—	4	1	no	—
193	M₁₆×C₈₉	—	4	2	no	—
194	M₁₆×C₈₉	—	4	2	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	—	4	2	no	—
198	C₂×C₈×C₈₉	—	4	2	no	—
199	C₂×C₈×C₈₉	—	4	2	no	—
200	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₈₉	—	2	1	no	—
205	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₈₉	—	2	1	no	—
208	C₂²⋊C₄×C₈₉	—	2	1	no	—
209	C₂²⋊C₄×C₈₉	—	2	1	no	—
210	C₂²⋊C₄×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₈₉	#41	1	1	yes	characteristic
214	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂³×C₈₉	—	2	1	no	—
216	C₂³×C₈₉	—	2	1	no	—
217	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
218	C₂²×D₈₉	—	2	1	no	—
219	Q₈×C₈₉	—	4	2	no	—
220	D₄×C₈₉	—	2	1	no	—
221	D₄×C₈₉	—	2	1	no	—
222	D₄×C₈₉	—	2	1	no	—
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	4	2	no	—
225	D₄×C₈₉	—	4	2	no	—
226	D₄×C₈₉	—	4	2	no	—
227	D₄×C₈₉	—	8	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	—	4	1	no	—
236	C₂×C₄×C₈₉	—	4	1	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
245	C₂²⋊D₈₉	—	4	2	no	—
246	C₂×Dic₈₉	—	2	1	no	—
247	C₂×Dic₈₉	—	2	1	no	—
248	C₂×Dic₈₉	—	2	1	no	—
249	D₃₅₆	—	2	1	no	—
250	D₃₅₆	#131	1	2	yes	complemented
251	C₄×D₈₉	—	4	2	no	—
252	C₄×D₈₉	—	4	1	no	—
253	C₄×D₈₉	—	4	1	no	—
254	C₄×D₈₉	—	8	1	no	—
255	Dic₁₇₈	—	2	1	no	—
256	Dic₁₇₈	—	2	1	no	—
257	C₈×C₈₉	—	2	1	no	—
258	C₈×C₈₉	—	2	1	no	—
259	C₈×C₈₉	—	2	1	no	—
260	C₈×C₈₉	—	4	1	no	—
261	C₈×C₈₉	—	4	1	no	—
262	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
263	#10623494	—	2	1	no	—
264	#10623494	—	2	1	no	—
265	#10623494	—	2	1	no	—
266	#10623494	—	2	1	no	—
267	#10623494	—	4	1	no	—
268	#10623494	—	4	1	no	—
269	#10623494	—	4	1	no	—
270	#10623494	—	4	1	no	—
271	C₂²×C₈₉	—	2	1	no	—
272	C₂²×C₈₉	—	2	1	no	—
273	C₂²×C₈₉	—	2	1	no	—
274	C₂²×C₈₉	—	4	1	no	—
275	C₂²×C₈₉	—	4	1	no	—
276	C₂²×C₈₉	—	4	1	no	—
277	C₂²×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	—	4	1	no	—
279	C₂²×C₈₉	—	4	1	no	—
280	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂×D₈₉	—	2	2	no	—
282	C₂×D₈₉	—	4	1	no	—
283	C₂×D₈₉	—	4	1	no	—
284	C₄×C₈₉	—	2	1	no	—
285	C₄×C₈₉	—	2	1	no	—
286	C₄×C₈₉	—	2	1	no	—
287	C₄×C₈₉	—	2	1	no	—
288	C₄×C₈₉	—	4	1	no	—
289	C₄×C₈₉	—	4	1	no	—
290	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
291	C₄×C₈₉	#568	1	1	yes	characteristic
292	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₄×C₈₉	#575	1	1	yes	characteristic
294	Dic₈₉	—	4	1	no	—
295	Dic₈₉	—	4	1	no	—
296	Dic₈₉	—	4	1	no	—
297	#18007	—	89	1	no	maximal, Sylow
298	C₂×C₈₉	—	4	1	no	—
299	C₂×C₈₉	—	8	1	no	—
300	C₂×C₈₉	—	8	1	no	—
301	C₂×C₈₉	#2933	1	1	yes	characteristic
302	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₂×C₈₉	#2957	1	1	yes	characteristic
304	D₈₉	—	4	2	no	—
305	#3106	—	89	1	no	—
306	#2970	—	89	1	no	—
307	#2935	D₈₉	1	1	yes	characteristic, complemented
308	#1592	—	89	1	no	—
309	#1590	—	89	1	no	—
310	#1586	—	89	1	no	—
311	#1585	—	89	1	no	—
312	#1582	—	89	1	no	—
313	#1581	—	89	1	no	—
314	#1580	—	89	1	no	—
315	C₈×D₈	—	89	1	no	—
316	#1573	—	89	1	no	—
317	#1496	—	89	1	no	—
318	#1477	—	89	1	no	—
319	#1453	—	89	1	no	—
320	C₈₉	#18007	1	1	yes	characteristic, complemented, Sylow
321	C₂×#131	—	2	1	no	—
322	#532	C₂×D₈₉	1	1	yes	characteristic
323	C₄×#41	—	89	1	no	—
324	#482	—	89	1	no	—
325	#482	—	89	1	no	—
326	#477	—	89	1	no	—
327	#476	—	89	1	no	—
328	#460	—	89	1	no	—
329	#459	—	89	1	no	—
330	#449	—	89	1	no	—
331	#449	—	89	1	no	—
332	#446	—	89	1	no	—
333	#446	—	89	1	no	—
334	C₄×SD₁₆	—	89	1	no	—
335	C₄×SD₁₆	—	89	1	no	—
336	C₄×D₈	—	89	1	no	—
337	C₄×D₈	—	89	1	no	—
338	#436	C₂×D₈₉	1	1	yes	characteristic
339	#436	C₂×D₈₉	1	1	yes	characteristic
340	#435	—	2	1	no	—
341	#435	—	2	1	no	—
342	#435	—	178	1	no	—
343	#435	—	178	1	no	—
344	C₈×D₄	—	89	1	no	—
345	C₈×D₄	—	89	1	no	—
346	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
347	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
348	#432	—	89	1	no	—
349	#432	—	178	1	no	—
350	#431	—	89	1	no	—
351	#431	—	89	1	no	—
352	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
353	#408	—	2	1	no	—
354	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
355	C₂×#97	—	178	1	no	—
356	#335	—	89	1	no	—
357	#335	—	89	1	no	—
358	#334	—	89	1	no	—
359	#334	—	89	1	no	—
360	Q₈⋊C₈	—	89	1	no	—
361	Q₈⋊C₈	—	89	1	no	—
362	D₄⋊C₈	—	89	1	no	—
363	D₄⋊C₈	—	89	1	no	—
364	D₄⋊C₈	—	89	1	no	—
365	D₄⋊C₈	—	89	1	no	—
366	D₄⋊C₈	—	89	1	no	—
367	D₄⋊C₈	—	89	1	no	—
368	#322	—	89	1	no	—
369	#322	—	89	1	no	—
370	#322	—	89	1	no	—
371	C₈²	—	89	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	89	1	no	—
374	C₂×SD₁₆	—	89	1	no	—
375	C₂×SD₁₆	—	89	1	no	—
376	C₂×D₈	—	89	1	no	—
377	C₂×D₈	—	89	1	no	—
378	#131	—	4	4	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
382	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	178	1	no	—
387	C₂²×C₈	—	178	1	no	—
388	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
389	#127	C₄×D₈₉	1	1	yes	characteristic
390	#124	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	C₄×D₈₉	1	1	yes	characteristic
393	#121	C₄×D₈₉	1	1	yes	characteristic
394	C₄×Q₈	—	89	1	no	—
395	C₄×Q₈	—	89	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	89	1	no	—
398	C₄×D₄	—	89	1	no	—
399	C₄×D₄	—	178	1	no	—
400	C₄×D₄	—	178	1	no	—
401	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
402	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
403	#117	—	89	1	no	—
404	#117	—	178	1	no	—
405	C₂×C₄²	—	178	1	no	—
406	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
407	#107	—	89	1	no	—
408	#107	—	89	1	no	—
409	#106	—	89	1	no	—
410	#106	—	89	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	89	1	no	—
413	C₄⋊C₈	—	89	1	no	—
414	C₄⋊C₈	—	89	1	no	—
415	C₄⋊C₈	—	89	1	no	—
416	C₄⋊C₈	—	178	1	no	—
417	C₄⋊C₈	—	178	1	no	—
418	C₄⋊C₈	—	178	1	no	—
419	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
421	#103	—	89	1	no	—
422	#103	—	89	1	no	—
423	#102	—	89	1	no	—
424	#102	—	89	1	no	—
425	#102	—	89	1	no	—
426	#102	—	89	1	no	—
427	#102	—	89	1	no	—
428	#102	—	89	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	89	1	no	—
434	C₂²⋊C₈	—	89	1	no	—
435	C₂²⋊C₈	—	178	1	no	—
436	C₂²⋊C₈	—	178	1	no	—
437	C₂²⋊C₈	—	178	1	no	—
438	C₂²⋊C₈	—	178	1	no	—
439	#97	—	178	1	no	—
440	#97	—	178	1	no	—
441	#97	—	178	1	no	—
442	#97	C₂²⋊D₈₉	1	1	yes	characteristic
443	#97	C₂²⋊D₈₉	1	1	yes	characteristic
444	C₄×C₈	—	89	1	no	—
445	C₄×C₈	—	89	1	no	—
446	C₄×C₈	—	89	1	no	—
447	C₄×C₈	—	89	1	no	—
448	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
449	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
450	#41	—	4	2	no	—
451	#41	—	4	2	no	—
452	#41	—	356	1	no	—
453	#41	—	178	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	89	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	89	1	no	—
461	C₂×D₄	—	178	1	no	—
462	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
463	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	178	1	no	—
467	C₂²×C₄	—	178	1	no	—
468	C₂²×C₄	—	178	1	no	—
469	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
471	C₂²×C₄	#13083574	1	1	yes	characteristic
472	SD₁₆	—	356	1	no	—
473	SD₁₆	—	356	1	no	—
474	D₈	—	178	2	no	—
475	D₈	—	178	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	—	4	2	no	—
479	M₁₆	—	4	2	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	4	2	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	89	1	no	—
486	C₂×C₈	—	89	1	no	—
487	C₂×C₈	—	89	1	no	—
488	C₂×C₈	—	89	1	no	—
489	C₂×C₈	—	356	2	no	—
490	C₂×C₈	—	356	2	no	—
491	C₂×C₈	—	178	1	no	—
492	C₂×C₈	—	178	1	no	—
493	C₂×C₈	—	178	1	no	—
494	C₂×C₈	—	178	1	no	—
495	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
496	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
497	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
498	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	89	1	no	—
501	C₄⋊C₄	—	89	1	no	—
502	C₄⋊C₄	—	178	1	no	—
503	C₄⋊C₄	—	178	1	no	—
504	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	178	1	no	—
511	C₂²⋊C₄	—	178	1	no	—
512	C₂²⋊C₄	—	178	1	no	—
513	C₄²	—	178	1	no	—
514	C₄²	—	178	1	no	—
515	C₄²	—	178	1	no	—
516	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
517	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
518	C₄²	#13083574	1	1	yes	characteristic
519	C₄²	C₂³×D₈₉	1	1	yes	characteristic
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	178	1	no	—
523	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
524	Q₈	—	4	2	no	—
525	Q₈	—	178	1	no	—
526	Q₈	—	178	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	1	no	—
535	D₄	—	89	2	no	—
536	D₄	—	356	2	no	—
537	D₄	—	178	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	356	2	no	—
550	C₂×C₄	—	356	1	no	—
551	C₂×C₄	—	356	1	no	—
552	C₂×C₄	—	178	1	no	—
553	C₂×C₄	—	178	1	no	—
554	C₂×C₄	—	178	1	no	—
555	C₂×C₄	—	712	1	no	—
556	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
557	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
558	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
560	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
561	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	356	1	no	—
568	C₈	—	356	1	no	—
569	C₈	—	356	1	no	—
570	C₈	—	356	1	no	—
571	C₈	—	178	1	no	—
572	C₈	—	178	1	no	—
573	C₈	—	178	1	no	—
574	C₈	—	178	1	no	—
575	C₈	#15668038	1	2	yes	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	356	1	no	—
586	C₂²	—	356	1	no	—
587	C₂²	—	178	2	no	—
588	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	356	1	no	—
596	C₄	—	356	1	no	—
597	C₄	—	356	1	no	—
598	C₄	#131×D₈₉	1	1	yes	characteristic
599	C₄	#19152363	1	1	yes	characteristic
600	C₄	C₂×#15668038	1	1	yes	characteristic
601	C₄	#19152396	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	8	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	356	2	no	—
606	C₂	#26028974	1	1	yes	characteristic
607	C₂	C₄×#15668038	1	1	yes	characteristic
608	C₂	#26029167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2935	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030306	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2935	D₈₉
hypocenter	C₈₉	#18007
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #26029267	C₂	semidirect
3. #26019154	C₂	semidirect
4. #26019140	C₂	semidirect
5. #26019114	C₂	semidirect
6. #26019109	C₂	semidirect
7. #26019088	C₂	semidirect
8. #26019079	C₂	semidirect
9. #26019074	C₂	semidirect
10. C₈×#13083559	C₂	semidirect
11. #26019035	C₂	semidirect
12. #26018721	C₂	semidirect
13. #26018637	C₂	semidirect
14. #26018549	C₂	semidirect
15. C₈₉×#2935	C₂	semidirect
250. D₃₅₆	#131	semidirect
307. #2935	D₈₉	semidirect
320. C₈₉	#18007	semidirect

Maximal subgroups

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

subgroup	index
#26030306	2
#26029267	2
#26019154	2
#26019140	2
#26019114	2
#26019109	2
#26019088	2
#26019079	2
#26019074	2
C₈×#13083559	2
#26019035	2
#26018721	2
#26018637	2
#26018549	2
C₈₉×#2935	2
#18007	89