Subgroups — #36568374

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023524	C₂	1	1	yes	maximal, characteristic
2	#26021186	C₂	1	1	yes	maximal, characteristic, complemented
3	#26021186	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020970	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020968	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020811	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020810	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020808	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020436	C₂	1	1	yes	maximal, characteristic
10	#26020433	C₂	1	1	yes	maximal, characteristic
11	#26020235	C₂	1	1	yes	maximal, characteristic
12	C₈×#13083551	C₂	1	1	yes	maximal, characteristic
13	#26020022	C₂	1	1	yes	maximal, characteristic
14	#26019947	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#13083557	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
19	C₂×#15667969	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×#15667941	C₂²	1	1	yes	characteristic
22	C₂×#15667941	C₂²	1	1	yes	characteristic
23	C₂×#15667941	C₂²	1	1	yes	characteristic
24	C₂×#15667941	C₂²	1	1	yes	characteristic
25	C₂×#15667924	C₂²	1	1	yes	characteristic
26	C₂×#15667924	C₂²	1	1	yes	characteristic
27	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
30	#19151538	C₄	1	1	yes	characteristic
31	#19151535	C₄	1	1	yes	characteristic
32	#19151528	C₄	1	1	yes	characteristic
33	#19151528	C₄	1	1	yes	characteristic
34	#19151520	C₄	1	1	yes	characteristic
35	#19151520	C₄	1	1	yes	characteristic
36	#19151519	C₄	1	1	yes	characteristic
37	#19151511	C₄	1	1	yes	characteristic
38	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
40	C₄×#13083551	C₂²	1	1	yes	characteristic
41	C₄×#13083551	C₂²	1	1	yes	characteristic
42	#19151353	C₂²	1	1	yes	characteristic
43	#19151353	C₂²	1	1	yes	characteristic
44	#19151353	C₂²	1	1	yes	characteristic
45	#19151353	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	#19151352	C₂²	1	1	yes	characteristic
51	#19151352	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
61	C₂×#13083557	—	2	2	no	—
62	C₂×#13083557	—	4	1	no	—
63	C₂×#13083557	—	4	1	no	—
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	1	yes	characteristic
67	C₂²×#10623494	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₈₉	—	4	1	no	—
69	C₂×C₈×D₈₉	—	4	1	no	—
70	C₂×C₈×D₈₉	Q₈	1	4	yes	complemented
71	C₄×Dic₁₇₈	—	4	1	no	—
72	C₄×Dic₁₇₈	—	4	1	no	—
73	#15667969	—	4	1	no	—
74	#15667969	—	4	1	no	—
75	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
81	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
82	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
83	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
84	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
85	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
86	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
87	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
88	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
89	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊#10623494	—	4	1	no	—
94	#15667941	—	4	1	no	—
95	#15667941	—	4	1	no	—
96	#15667941	—	4	1	no	—
97	#15667941	—	4	1	no	—
98	#15667924	—	2	2	no	—
99	#15667924	—	2	2	no	—
100	C₄×#10623494	—	4	1	no	—
101	C₈×Dic₈₉	—	4	1	no	—
102	C₈×Dic₈₉	—	4	1	no	—
103	#15667919	C₂×C₄	1	1	yes	characteristic
104	#15667919	C₂×C₄	1	1	yes	characteristic
105	#15667919	C₂×C₄	1	1	yes	characteristic
106	#15667919	C₂×C₄	1	1	yes	characteristic
107	#15667919	C₂×C₄	1	1	yes	characteristic
108	#15667919	C₂×C₄	1	1	yes	characteristic
109	#15667919	C₂×C₄	1	1	yes	characteristic
110	#15667919	C₂×C₄	1	1	yes	characteristic
111	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₈₉	—	4	1	no	—
121	C₄×C₈×C₈₉	—	4	1	no	—
122	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
123	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
124	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₁₇₈	—	2	2	no	—
126	C₂×Dic₁₇₈	—	2	2	no	—
127	C₂×Dic₁₇₈	—	4	1	no	—
128	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₈₉	—	2	1	no	—
136	C₂×C₄×D₈₉	—	2	1	no	—
137	C₂×C₄×D₈₉	—	2	1	no	—
138	C₂×C₄×D₈₉	—	2	1	no	—
139	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
140	C₂×C₄×D₈₉	#41	1	2	yes	—
141	#13083557	—	4	4	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	—	2	1	no	—
146	C₂×#10623494	—	2	1	no	—
147	C₂×#10623494	—	2	1	no	—
148	C₂×#10623494	—	2	1	no	—
149	C₂×#10623494	—	2	1	no	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	C₂×Q₈	1	2	yes	—
154	C₈×D₈₉	—	4	4	no	—
155	C₄⋊Dic₈₉	—	2	2	no	—
156	C₄⋊Dic₈₉	—	2	2	no	—
157	C₄⋊Dic₈₉	—	2	2	no	—
158	C₄⋊Dic₈₉	—	2	2	no	—
159	C₄⋊Dic₈₉	—	4	1	no	—
160	#13083553	—	4	1	no	—
161	#13083553	—	4	1	no	—
162	#13083553	—	4	1	no	—
163	#13083553	—	4	1	no	—
164	#13083551	—	2	2	no	—
165	#13083551	—	2	2	no	—
166	#13083551	—	2	2	no	—
167	#13083551	—	2	2	no	—
168	#13083551	—	4	1	no	—
169	#13083551	—	4	1	no	—
170	C₄×Dic₈₉	—	2	1	no	—
171	C₄×Dic₈₉	—	2	1	no	—
172	C₄×Dic₈₉	—	2	1	no	—
173	C₄×Dic₈₉	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₄×Dic₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	—	2	1	no	—
188	C₂×C₈×C₈₉	—	2	1	no	—
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₂×C₈×C₈₉	—	2	1	no	—
194	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
195	C₄⋊C₄×C₈₉	—	2	2	no	—
196	C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₄²×C₈₉	—	2	1	no	—
198	C₄²×C₈₉	—	2	1	no	—
199	C₄²×C₈₉	—	2	1	no	—
200	C₄²×C₈₉	—	2	1	no	—
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	—	2	1	no	—
203	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
204	C₂²×D₈₉	—	2	1	no	—
205	C₂²×D₈₉	—	2	1	no	—
206	C₂²×D₈₉	—	2	1	no	—
207	C₂²×D₈₉	—	2	1	no	—
208	C₂²×D₈₉	—	2	1	no	—
209	C₂²×D₈₉	—	2	1	no	—
210	C₂²×D₈₉	C₄×Q₈	1	2	yes	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×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	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×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	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	#131	1	2	yes	—
228	C₂×C₄×C₈₉	#131	1	2	yes	—
229	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×Dic₈₉	—	2	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	2	1	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	2	1	no	—
242	C₂×Dic₈₉	—	2	1	no	—
243	C₂×Dic₈₉	—	2	1	no	—
244	C₂×Dic₈₉	—	2	1	no	—
245	C₂×Dic₈₉	—	2	1	no	—
246	C₂×Dic₈₉	—	2	1	no	—
247	C₂×Dic₈₉	—	2	1	no	—
248	C₂×Dic₈₉	—	2	1	no	—
249	C₂×Dic₈₉	—	2	1	no	—
250	C₂×Dic₈₉	—	2	1	no	—
251	C₂×Dic₈₉	—	2	1	no	—
252	C₂×Dic₈₉	—	2	1	no	—
253	C₂×Dic₈₉	C₄×Q₈	1	2	yes	—
254	C₂×Dic₈₉	#131	1	2	yes	—
255	C₂×Dic₈₉	#131	1	2	yes	—
256	C₄×D₈₉	—	2	2	no	—
257	C₄×D₈₉	—	2	2	no	—
258	C₄×D₈₉	—	2	2	no	—
259	C₄×D₈₉	—	2	2	no	—
260	Dic₁₇₈	—	4	4	no	—
261	C₈×C₈₉	—	2	2	no	—
262	C₈×C₈₉	—	4	1	no	—
263	C₈×C₈₉	—	4	1	no	—
264	C₈×C₈₉	—	4	1	no	—
265	#10623494	—	2	2	no	—
266	#10623494	—	4	1	no	—
267	#10623494	—	4	1	no	—
268	#10623494	—	4	1	no	—
269	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
270	C₂²×C₈₉	#518	1	1	yes	characteristic
271	C₂²×C₈₉	#520	1	1	yes	characteristic
272	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
273	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
274	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
275	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
276	C₂×D₈₉	—	2	2	no	—
277	C₂×D₈₉	—	2	2	no	—
278	C₂×D₈₉	—	2	2	no	—
279	C₂×D₈₉	—	4	1	no	—
280	C₂×D₈₉	—	4	1	no	—
281	C₂×D₈₉	—	4	1	no	—
282	C₂×D₈₉	—	4	1	no	—
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	2	2	no	—
285	C₄×C₈₉	—	4	1	no	—
286	C₄×C₈₉	—	4	1	no	—
287	C₄×C₈₉	—	4	1	no	—
288	C₄×C₈₉	—	4	1	no	—
289	C₄×C₈₉	#538	1	1	yes	characteristic
290	C₄×C₈₉	#539	1	1	yes	characteristic
291	C₄×C₈₉	#543	1	1	yes	characteristic
292	C₄×C₈₉	#544	1	1	yes	characteristic
293	Dic₈₉	—	2	2	no	—
294	Dic₈₉	—	2	2	no	—
295	Dic₈₉	—	2	2	no	—
296	Dic₈₉	—	4	1	no	—
297	Dic₈₉	—	4	1	no	—
298	Dic₈₉	—	4	1	no	—
299	Dic₈₉	—	4	1	no	—
300	#22288	—	89	1	no	maximal, Sylow
301	C₂×C₈₉	#2329	1	1	yes	characteristic
302	C₂×C₈₉	#2960	1	1	yes	characteristic
303	C₂×C₈₉	#2960	1	1	yes	characteristic
304	C₂×C₈₉	#2977	1	1	yes	characteristic
305	C₂×C₈₉	#2979	1	1	yes	characteristic
306	C₂×C₈₉	#2994	1	1	yes	characteristic
307	C₂×C₈₉	#2994	1	1	yes	characteristic
308	D₈₉	—	4	2	no	—
309	#2396	—	89	1	no	—
310	#1984	—	89	1	no	—
311	#1984	—	89	1	no	—
312	#1939	—	89	1	no	—
313	#1939	—	89	1	no	—
314	#1916	—	89	1	no	—
315	#1916	—	89	1	no	—
316	#1916	—	89	1	no	—
317	#1916	D₈₉	1	1	yes	characteristic, complemented
318	#1851	—	89	1	no	—
319	#1851	—	89	1	no	—
320	#1798	—	89	1	no	—
321	C₈×C₂²⋊C₄	—	89	1	no	—
322	C₈×C₂²⋊C₄	—	89	1	no	—
323	#1729	—	89	1	no	—
324	C₈₉	#22288	1	1	yes	characteristic, complemented, Sylow
325	C₂²×M₁₆	—	89	1	no	—
326	C₂³×C₈	—	89	1	no	—
327	C₂×C₄×Q₈	—	89	1	no	—
328	C₂×#117	—	89	1	no	—
329	C₂×C₄⋊C₈	—	89	1	no	—
330	C₂×C₄⋊C₈	—	89	1	no	—
331	C₂×C₄⋊C₈	—	89	1	no	—
332	C₂×C₄⋊C₈	—	89	1	no	—
333	C₂×C₄⋊C₈	—	89	1	no	—
334	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	—	89	1	no	—
336	C₂×C₂²⋊C₈	—	89	1	no	—
337	C₂×C₄×C₈	—	89	1	no	—
338	C₂×C₄×C₈	—	89	1	no	—
339	C₂×C₄×C₈	—	89	1	no	—
340	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
341	#400	—	89	1	no	—
342	#399	—	89	1	no	—
343	#398	—	89	1	no	—
344	#398	—	89	1	no	—
345	#396	—	89	1	no	—
346	#396	—	89	1	no	—
347	#395	—	89	1	no	—
348	#393	—	89	1	no	—
349	C₄×C₄⋊C₄	—	89	1	no	—
350	C₄×C₄⋊C₄	—	89	1	no	—
351	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	—	89	1	no	—
353	C₄×C₂²⋊C₄	—	89	1	no	—
354	#336	—	89	1	no	—
355	#336	—	89	1	no	—
356	#336	—	89	1	no	—
357	#336	—	89	1	no	—
358	#336	—	89	1	no	—
359	#336	—	89	1	no	—
360	#336	—	89	1	no	—
361	#336	—	89	1	no	—
362	#336	—	89	1	no	—
363	#336	—	89	1	no	—
364	#336	C₂×D₈₉	1	1	yes	characteristic
365	#336	C₂×D₈₉	1	1	yes	characteristic
366	#336	C₂×D₈₉	1	1	yes	characteristic
367	#336	C₂×D₈₉	1	1	yes	characteristic
368	C₂²×Q₈	—	89	1	no	—
369	C₂³×C₄	—	89	1	no	—
370	C₂×M₁₆	—	356	1	no	—
371	C₂×M₁₆	—	356	1	no	—
372	C₂×M₁₆	—	178	2	no	—
373	C₂²×C₈	—	89	1	no	—
374	C₂²×C₈	—	89	4	no	—
375	C₂²×C₈	—	89	1	no	—
376	C₂²×C₈	—	89	1	no	—
377	C₂²×C₈	—	89	1	no	—
378	C₂²×C₈	—	356	1	no	—
379	C₂²×C₈	—	356	1	no	—
380	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
381	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
382	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
383	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
384	C₄×Q₈	—	356	1	no	—
385	C₄×Q₈	—	356	1	no	—
386	#117	—	356	1	no	—
387	#117	—	356	1	no	—
388	C₂×C₄⋊C₄	—	89	1	no	—
389	C₂×C₄⋊C₄	—	89	1	no	—
390	C₂×C₄⋊C₄	—	89	1	no	—
391	C₂×C₄⋊C₄	—	89	1	no	—
392	C₂×C₄⋊C₄	—	89	1	no	—
393	C₂×C₄⋊C₄	—	89	1	no	—
394	C₂×C₄⋊C₄	—	89	1	no	—
395	C₂×C₄⋊C₄	—	89	1	no	—
396	C₂×C₄⋊C₄	—	89	1	no	—
397	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	—	89	1	no	—
400	C₂×C₂²⋊C₄	—	89	1	no	—
401	C₂×C₂²⋊C₄	—	89	1	no	—
402	C₂×C₂²⋊C₄	—	89	1	no	—
403	C₂×C₂²⋊C₄	—	89	1	no	—
404	C₂×C₂²⋊C₄	—	89	1	no	—
405	C₂×C₄²	—	89	1	no	—
406	C₂×C₄²	—	89	1	no	—
407	C₂×C₄²	—	89	1	no	—
408	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
410	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
411	C₄⋊C₈	—	4	1	no	—
412	C₄⋊C₈	—	356	1	no	—
413	C₄⋊C₈	—	356	1	no	—
414	C₄⋊C₈	—	356	1	no	—
415	C₄⋊C₈	—	356	1	no	—
416	C₄⋊C₈	—	356	1	no	—
417	C₂²⋊C₈	—	178	2	no	—
418	C₂²⋊C₈	—	178	2	no	—
419	C₄×C₈	—	4	1	no	—
420	C₄×C₈	—	356	1	no	—
421	C₄×C₈	—	356	1	no	—
422	C₄×C₈	—	356	1	no	—
423	#95	—	89	1	no	—
424	#95	—	89	1	no	—
425	#95	—	89	1	no	—
426	#95	—	89	1	no	—
427	#95	—	89	1	no	—
428	#95	—	89	1	no	—
429	#95	—	89	1	no	—
430	#95	—	89	1	no	—
431	#95	C₄×D₈₉	1	1	yes	characteristic
432	#95	C₄×D₈₉	1	1	yes	characteristic
433	C₂⁴	—	89	1	no	—
434	C₂×Q₈	—	356	1	no	—
435	C₂×Q₈	—	178	2	no	—
436	C₂×Q₈	—	178	2	no	—
437	C₂²×C₄	—	89	1	no	—
438	C₂²×C₄	—	89	1	no	—
439	C₂²×C₄	—	89	1	no	—
440	C₂²×C₄	—	89	2	no	—
441	C₂²×C₄	—	89	2	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	89	1	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	—	178	1	no	—
447	C₂²×C₄	—	178	1	no	—
448	C₂²×C₄	—	178	1	no	—
449	C₂²×C₄	—	178	1	no	—
450	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
456	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
457	M₁₆	—	356	4	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	89	2	no	—
470	C₂×C₈	—	356	4	no	—
471	C₂×C₈	—	178	1	no	—
472	C₂×C₈	—	178	1	no	—
473	C₂×C₈	—	178	1	no	—
474	C₂×C₈	—	178	1	no	—
475	C₂×C₈	—	178	1	no	—
476	C₂×C₈	—	178	1	no	—
477	C₂×C₈	—	178	1	no	—
478	C₂×C₈	—	178	1	no	—
479	C₂×C₈	—	178	1	no	—
480	C₂×C₈	—	178	1	no	—
481	C₂×C₈	—	178	1	no	—
482	C₂×C₈	Q₈×D₈₉	1	2	yes	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	356	1	no	—
486	C₄⋊C₄	—	356	1	no	—
487	C₄⋊C₄	—	356	1	no	—
488	C₄⋊C₄	—	356	1	no	—
489	C₄⋊C₄	—	356	1	no	—
490	C₄⋊C₄	—	178	2	no	—
491	C₄⋊C₄	—	178	2	no	—
492	C₄⋊C₄	—	178	2	no	—
493	C₄⋊C₄	—	178	2	no	—
494	C₂²⋊C₄	—	356	1	no	—
495	C₂²⋊C₄	—	356	1	no	—
496	C₂²⋊C₄	—	178	2	no	—
497	C₂²⋊C₄	—	178	2	no	—
498	C₂²⋊C₄	—	178	2	no	—
499	C₂²⋊C₄	—	178	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	178	1	no	—
507	C₄²	—	178	1	no	—
508	C₄²	—	178	1	no	—
509	C₄²	—	178	1	no	—
510	C₄²	—	178	1	no	—
511	C₄²	—	178	1	no	—
512	C₂³	—	89	2	no	—
513	C₂³	—	178	1	no	—
514	C₂³	—	178	1	no	—
515	C₂³	—	178	1	no	—
516	C₂³	—	178	1	no	—
517	C₂³	—	178	1	no	—
518	C₂³	—	178	1	no	—
519	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
520	Q₈	—	356	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	89	2	no	—
538	C₂×C₄	—	89	2	no	—
539	C₂×C₄	—	89	2	no	—
540	C₂×C₄	—	178	1	no	—
541	C₂×C₄	—	178	1	no	—
542	C₂×C₄	—	178	1	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	—	178	1	no	—
549	C₂×C₄	—	178	1	no	—
550	C₂×C₄	—	178	1	no	—
551	C₂×C₄	—	178	1	no	—
552	C₂×C₄	—	178	1	no	—
553	C₂×C₄	—	178	1	no	—
554	C₂×C₄	—	178	1	no	—
555	C₂×C₄	—	178	1	no	—
556	C₂×C₄	—	178	1	no	—
557	C₂×C₄	—	178	1	no	—
558	C₂×C₄	—	178	2	no	—
559	C₂×C₄	—	178	2	no	—
560	C₂×C₄	—	178	2	no	—
561	C₂×C₄	—	178	2	no	—
562	C₂×C₄	#15668018	1	2	yes	—
563	C₂×C₄	#15668020	1	2	yes	—
564	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
565	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
566	C₂×C₄	#15668057	1	1	yes	characteristic
567	C₂×C₄	#15668058	1	1	yes	characteristic
568	C₂×C₄	#15668058	1	1	yes	characteristic
569	C₂×C₄	#15668059	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	356	1	no	—
575	C₈	—	356	1	no	—
576	C₈	—	356	1	no	—
577	C₈	—	178	2	no	—
578	C₂²	—	356	1	no	—
579	C₂²	—	356	1	no	—
580	C₂²	—	356	1	no	—
581	C₂²	—	356	1	no	—
582	C₂²	—	178	2	no	—
583	C₂²	—	178	2	no	—
584	C₂²	—	178	2	no	—
585	C₂²	C₄×Q₈×D₈₉	1	1	yes	characteristic
586	C₂²	#19152072	1	1	yes	characteristic
587	C₂²	#19152077	1	1	yes	characteristic
588	C₂²	#131×D₈₉	1	1	yes	characteristic
589	C₂²	#131×D₈₉	1	1	yes	characteristic
590	C₂²	C₂×#15668018	1	1	yes	characteristic
591	C₂²	C₂×#15668020	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	356	1	no	—
599	C₄	—	356	1	no	—
600	C₄	—	356	1	no	—
601	C₄	—	356	1	no	—
602	C₄	—	178	2	no	—
603	C₄	—	178	2	no	—
604	C₄	—	178	2	no	—
605	C₄	#19152184	1	1	yes	characteristic
606	C₄	#19152189	1	1	yes	characteristic
607	C₄	#19152223	1	1	yes	characteristic
608	C₄	#19152228	1	1	yes	characteristic
609	C₂	—	356	2	no	—
610	C₂	#26022981	1	1	yes	characteristic
611	C₂	#26029181	1	1	yes	characteristic
612	C₂	#26029183	1	1	yes	characteristic
613	C₂	#26029307	1	1	yes	characteristic
614	C₂	#26029318	1	1	yes	characteristic
615	C₂	#26029405	1	1	yes	characteristic
616	C₂	#26029409	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1916	C₂
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1916	D₈₉
hypocenter	C₈₉	#22288
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
2. #26021186	C₂	semidirect
3. #26021186	C₂	semidirect
4. #26020970	C₂	semidirect
5. #26020968	C₂	semidirect
6. #26020811	C₂	semidirect
7. #26020810	C₂	semidirect
8. #26020808	C₂	semidirect
15. C₈₉×#1916	C₂	semidirect
70. C₂×C₈×D₈₉	Q₈	semidirect
317. #1916	D₈₉	semidirect
324. C₈₉	#22288	semidirect

Maximal subgroups

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

subgroup	index
#26023524	2
#26021186	2
#26020970	2
#26020968	2
#26020811	2
#26020810	2
#26020808	2
#26020436	2
#26020433	2
#26020235	2
C₈×#13083551	2
#26020022	2
#26019947	2
C₈₉×#1916	2
#22288	89