Subgroups — #36568365

Order 22784.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15667992	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	#26020431	C₂	1	1	yes	maximal, characteristic
10	#26020428	C₂	1	1	yes	maximal, characteristic
11	#26020231	C₂	1	1	yes	maximal, characteristic
12	C₈×#13083551	C₂	1	1	yes	maximal, characteristic
13	#26020022	C₂	1	1	yes	maximal, characteristic
14	#336×D₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×#15667992	C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10623494	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×#15667941	C₂²	1	1	yes	characteristic
26	C₂×#15667924	C₂²	1	1	yes	characteristic
27	C₂×#15667924	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151503	C₄	1	1	yes	characteristic
32	#19151497	C₄	1	1	yes	characteristic
33	#19151483	C₄	1	1	yes	characteristic
34	#19151483	C₄	1	1	yes	characteristic
35	#19151472	C₄	1	1	yes	characteristic
36	#19151472	C₄	1	1	yes	characteristic
37	#19151455	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	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₈₉	—	2	2	no	—
68	C₂×C₈×D₈₉	—	4	1	no	—
69	C₂×C₈×D₈₉	—	4	1	no	—
70	C₂×C₈×D₈₉	—	4	1	no	—
71	C₂×C₈×D₈₉	—	4	1	no	—
72	C₂×C₈×D₈₉	Q₈	1	4	yes	complemented
73	#15667992	C₈	1	8	yes	complemented
74	C₄×Dic₁₇₈	—	4	1	no	—
75	C₄×Dic₁₇₈	—	4	1	no	—
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×C₄⋊Dic₈₉	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×#13083551	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×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
92	C₄²×D₈₉	—	4	1	no	—
93	C₄²×D₈₉	—	4	1	no	—
94	C₄⋊#10623494	—	4	1	no	—
95	#15667941	—	4	1	no	—
96	#15667941	—	4	1	no	—
97	#15667941	—	4	1	no	—
98	#15667941	—	4	1	no	—
99	#15667924	—	2	2	no	—
100	#15667924	—	2	2	no	—
101	C₄×#10623494	—	4	1	no	—
102	C₈×Dic₈₉	—	4	1	no	—
103	C₈×Dic₈₉	—	4	1	no	—
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	#15667919	C₂×C₄	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	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₈₉	—	4	1	no	—
122	C₄×C₈×C₈₉	—	4	1	no	—
123	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
124	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
125	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×Dic₁₇₈	—	4	1	no	—
127	C₂×Dic₁₇₈	—	4	1	no	—
128	C₂×Dic₁₇₈	C₂×C₈	1	4	yes	complemented
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	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
140	C₂×C₄×D₈₉	—	2	2	no	—
141	C₂×C₄×D₈₉	—	4	1	no	—
142	C₂×C₄×D₈₉	—	4	1	no	—
143	C₂×C₄×D₈₉	—	4	1	no	—
144	C₂×C₄×D₈₉	—	4	1	no	—
145	C₂×C₄×D₈₉	C₂×C₈	1	4	yes	—
146	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
147	C₂×C₄×D₈₉	#41	1	2	yes	—
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	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	C₂×Q₈	1	2	yes	—
160	C₈×D₈₉	—	4	4	no	—
161	C₈×D₈₉	—	4	4	no	—
162	C₄⋊Dic₈₉	—	4	1	no	—
163	C₄⋊Dic₈₉	—	4	1	no	—
164	C₄⋊Dic₈₉	—	4	1	no	—
165	C₄⋊Dic₈₉	C₂×C₈	1	4	yes	complemented
166	C₄⋊Dic₈₉	C₂×C₈	1	4	yes	complemented
167	#13083553	—	4	1	no	—
168	#13083553	—	4	1	no	—
169	#13083551	—	2	2	no	—
170	#13083551	—	2	2	no	—
171	#13083551	C₂×C₈	1	4	yes	—
172	#13083551	C₂×C₈	1	4	yes	—
173	C₄×Dic₈₉	—	2	1	no	—
174	C₄×Dic₈₉	—	2	1	no	—
175	C₄×Dic₈₉	—	2	1	no	—
176	C₄×Dic₈₉	—	2	1	no	—
177	C₄×Dic₈₉	—	2	1	no	—
178	C₄×Dic₈₉	—	2	1	no	—
179	C₄×Dic₈₉	—	4	1	no	—
180	C₄×Dic₈₉	—	4	1	no	—
181	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
200	C₄⋊C₄×C₈₉	—	4	1	no	—
201	C₄⋊C₄×C₈₉	C₂×C₈	1	4	yes	complemented
202	C₄²×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	—	2	1	no	—
208	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
209	C₂²×D₈₉	—	2	1	no	—
210	C₂²×D₈₉	—	2	1	no	—
211	C₂²×D₈₉	—	2	1	no	—
212	C₂²×D₈₉	—	2	1	no	—
213	C₂²×D₈₉	C₄×Q₈	1	2	yes	—
214	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
215	C₂²×D₈₉	#131	1	2	yes	—
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	—	2	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	C₂²×C₈	1	2	yes	—
232	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
233	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
234	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
254	C₂×Dic₈₉	—	2	1	no	—
255	C₂×Dic₈₉	—	2	1	no	—
256	C₂×Dic₈₉	—	2	1	no	—
257	C₂×Dic₈₉	C₄×Q₈	1	2	yes	—
258	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
259	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
260	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
261	C₄×D₈₉	—	2	2	no	—
262	C₄×D₈₉	—	2	2	no	—
263	C₄×D₈₉	—	2	2	no	—
264	C₄×D₈₉	—	2	2	no	—
265	C₄×D₈₉	—	4	4	no	—
266	C₄×D₈₉	—	4	4	no	—
267	Dic₁₇₈	—	4	4	no	—
268	C₈×C₈₉	—	2	2	no	—
269	C₈×C₈₉	—	4	1	no	—
270	C₈×C₈₉	—	4	1	no	—
271	C₈×C₈₉	—	4	1	no	—
272	#10623494	—	2	2	no	—
273	#10623494	—	4	1	no	—
274	#10623494	—	4	1	no	—
275	#10623494	—	4	1	no	—
276	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
277	C₂²×C₈₉	#518	1	1	yes	characteristic
278	C₂²×C₈₉	#520	1	1	yes	characteristic
279	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
280	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
281	C₂²×C₈₉	#568	1	1	yes	characteristic
282	C₂²×C₈₉	#568	1	1	yes	characteristic
283	C₂×D₈₉	—	2	2	no	—
284	C₂×D₈₉	—	2	2	no	—
285	C₂×D₈₉	—	2	2	no	—
286	C₂×D₈₉	—	2	2	no	—
287	C₂×D₈₉	—	2	2	no	—
288	C₂×D₈₉	—	2	2	no	—
289	C₂×D₈₉	C₈×Q₈	1	4	yes	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	2	2	no	—
292	C₄×C₈₉	—	2	2	no	—
293	C₄×C₈₉	—	4	1	no	—
294	C₄×C₈₉	—	4	1	no	—
295	C₄×C₈₉	—	4	1	no	—
296	C₄×C₈₉	#538	1	1	yes	characteristic
297	C₄×C₈₉	#539	1	1	yes	characteristic
298	C₄×C₈₉	#543	1	1	yes	characteristic
299	C₄×C₈₉	#544	1	1	yes	characteristic
300	Dic₈₉	—	2	2	no	—
301	Dic₈₉	—	2	2	no	—
302	Dic₈₉	—	2	2	no	—
303	Dic₈₉	—	2	2	no	—
304	Dic₈₉	—	4	1	no	—
305	Dic₈₉	—	4	1	no	—
306	Dic₈₉	—	4	1	no	—
307	#22287	—	89	1	no	maximal, Sylow
308	C₂×C₈₉	#2329	1	1	yes	characteristic
309	C₂×C₈₉	C₂×C₈×Q₈	1	1	yes	characteristic
310	C₂×C₈₉	#2961	1	1	yes	characteristic
311	C₂×C₈₉	#2972	1	1	yes	characteristic
312	C₂×C₈₉	#2976	1	1	yes	characteristic
313	C₂×C₈₉	#2988	1	1	yes	characteristic
314	C₂×C₈₉	#2992	1	1	yes	characteristic
315	D₈₉	—	2	4	no	—
316	C₄×C₂²⋊Q₈	—	89	1	no	—
317	#1984	—	89	1	no	—
318	#1984	—	89	1	no	—
319	#1939	—	89	1	no	—
320	#1939	—	89	1	no	—
321	#1916	—	89	1	no	—
322	#1916	—	89	1	no	—
323	#1916	—	89	1	no	—
324	#1916	D₈₉	1	1	yes	characteristic, complemented
325	#1850	—	89	1	no	—
326	#1850	—	89	1	no	—
327	#1797	—	89	1	no	—
328	C₈×C₂²⋊C₄	—	89	1	no	—
329	C₈×C₂²⋊C₄	—	89	1	no	—
330	C₂×#336	—	89	1	no	—
331	C₈₉	#22287	1	1	yes	characteristic, complemented, Sylow
332	C₂³×C₈	—	89	1	no	—
333	C₂³×C₈	—	89	1	no	—
334	C₂×C₂²⋊Q₈	—	89	1	no	—
335	C₂×C₄×Q₈	—	89	1	no	—
336	C₂²×C₄²	—	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	—	89	1	no	—
341	C₂×C₄⋊C₈	—	89	1	no	—
342	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
343	C₂×C₂²⋊C₈	—	89	1	no	—
344	C₂×C₂²⋊C₈	—	89	1	no	—
345	C₂×C₄×C₈	—	89	1	no	—
346	C₂×C₄×C₈	—	89	1	no	—
347	C₂×C₄×C₈	—	89	1	no	—
348	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
349	#391	—	89	1	no	—
350	#389	—	89	1	no	—
351	#387	—	89	1	no	—
352	#387	—	89	1	no	—
353	#385	—	89	1	no	—
354	#385	—	89	1	no	—
355	#380	—	89	1	no	—
356	C₄×C₄⋊C₄	—	89	1	no	—
357	C₄×C₄⋊C₄	—	89	1	no	—
358	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	—	89	1	no	—
360	C₄×C₂²⋊C₄	—	89	1	no	—
361	#336	—	89	1	no	—
362	#336	—	89	1	no	—
363	#336	—	89	1	no	—
364	#336	—	89	1	no	—
365	#336	—	89	1	no	—
366	#336	—	89	1	no	—
367	#336	—	89	1	no	—
368	#336	—	89	1	no	—
369	#336	—	89	1	no	—
370	#336	—	89	1	no	—
371	#336	C₂×D₈₉	1	1	yes	characteristic
372	#336	C₂×D₈₉	1	1	yes	characteristic
373	#336	C₂×D₈₉	1	1	yes	characteristic
374	#336	C₂×D₈₉	1	1	yes	characteristic
375	C₂²×Q₈	—	89	1	no	—
376	C₂³×C₄	—	89	1	no	—
377	C₂³×C₄	—	89	1	no	—
378	C₂³×C₄	—	89	1	no	—
379	C₂²×C₈	—	89	1	no	—
380	C₂²×C₈	—	89	4	no	—
381	C₂²×C₈	—	89	1	no	—
382	C₂²×C₈	—	89	1	no	—
383	C₂²×C₈	—	89	1	no	—
384	C₂²×C₈	—	356	1	no	—
385	C₂²×C₈	—	356	1	no	—
386	C₂²×C₈	—	356	1	no	—
387	C₂²×C₈	—	356	1	no	—
388	C₂²×C₈	—	178	2	no	—
389	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
390	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
391	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
392	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
393	C₂²⋊Q₈	—	89	8	no	—
394	C₄×Q₈	—	356	1	no	—
395	C₄×Q₈	—	356	1	no	—
396	C₂×C₄⋊C₄	—	89	1	no	—
397	C₂×C₄⋊C₄	—	89	1	no	—
398	C₂×C₄⋊C₄	—	89	1	no	—
399	C₂×C₄⋊C₄	—	89	1	no	—
400	C₂×C₄⋊C₄	—	89	1	no	—
401	C₂×C₄⋊C₄	—	89	1	no	—
402	C₂×C₄⋊C₄	—	89	1	no	—
403	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	89	1	no	—
406	C₂×C₂²⋊C₄	—	89	1	no	—
407	C₂×C₂²⋊C₄	—	89	1	no	—
408	C₂×C₂²⋊C₄	—	89	1	no	—
409	C₂×C₄²	—	89	1	no	—
410	C₂×C₄²	—	89	1	no	—
411	C₂×C₄²	—	89	1	no	—
412	C₂×C₄²	—	89	1	no	—
413	C₂×C₄²	—	89	1	no	—
414	C₂×C₄²	—	356	1	no	—
415	C₂×C₄²	—	356	1	no	—
416	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
417	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
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	C₄⋊C₈	—	356	1	no	—
424	C₄⋊C₈	—	356	1	no	—
425	C₂²⋊C₈	—	178	2	no	—
426	C₂²⋊C₈	—	178	2	no	—
427	C₄×C₈	—	4	1	no	—
428	C₄×C₈	—	356	1	no	—
429	C₄×C₈	—	356	1	no	—
430	C₄×C₈	—	356	1	no	—
431	#95	—	89	1	no	—
432	#95	—	89	1	no	—
433	#95	—	89	1	no	—
434	#95	—	89	1	no	—
435	#95	—	89	1	no	—
436	#95	—	89	1	no	—
437	#95	—	89	1	no	—
438	#95	—	89	1	no	—
439	#95	C₄×D₈₉	1	1	yes	characteristic
440	#95	C₄×D₈₉	1	1	yes	characteristic
441	C₂⁴	—	89	1	no	—
442	C₂×Q₈	—	89	4	no	—
443	C₂×Q₈	—	356	1	no	—
444	C₂×Q₈	—	356	1	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	—	89	1	no	—
447	C₂²×C₄	—	89	1	no	—
448	C₂²×C₄	—	89	1	no	—
449	C₂²×C₄	—	89	4	no	—
450	C₂²×C₄	—	89	2	no	—
451	C₂²×C₄	—	89	2	no	—
452	C₂²×C₄	—	89	1	no	—
453	C₂²×C₄	—	89	1	no	—
454	C₂²×C₄	—	89	1	no	—
455	C₂²×C₄	—	356	1	no	—
456	C₂²×C₄	—	356	1	no	—
457	C₂²×C₄	—	356	1	no	—
458	C₂²×C₄	—	356	1	no	—
459	C₂²×C₄	—	178	2	no	—
460	C₂²×C₄	—	178	1	no	—
461	C₂²×C₄	—	178	1	no	—
462	C₂²×C₄	—	178	1	no	—
463	C₂²×C₄	—	178	1	no	—
464	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	89	2	no	—
483	C₂×C₈	—	356	4	no	—
484	C₂×C₈	—	356	4	no	—
485	C₂×C₈	—	178	1	no	—
486	C₂×C₈	—	178	1	no	—
487	C₂×C₈	—	178	1	no	—
488	C₂×C₈	—	178	1	no	—
489	C₂×C₈	—	178	1	no	—
490	C₂×C₈	—	178	1	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	—	178	1	no	—
496	C₂×C₈	Q₈×D₈₉	1	2	yes	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	89	4	no	—
499	C₄⋊C₄	—	89	4	no	—
500	C₄⋊C₄	—	356	1	no	—
501	C₄⋊C₄	—	356	1	no	—
502	C₄⋊C₄	—	356	1	no	—
503	C₄⋊C₄	—	356	1	no	—
504	C₄⋊C₄	—	356	1	no	—
505	C₄⋊C₄	C₈×D₈₉	1	4	yes	complemented
506	C₂²⋊C₄	—	89	4	no	—
507	C₂²⋊C₄	—	89	4	no	—
508	C₂²⋊C₄	—	178	2	no	—
509	C₂²⋊C₄	—	178	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	356	1	no	—
517	C₄²	—	356	1	no	—
518	C₄²	—	178	1	no	—
519	C₄²	—	178	1	no	—
520	C₄²	—	178	1	no	—
521	C₄²	—	178	1	no	—
522	C₄²	—	178	1	no	—
523	C₄²	—	178	1	no	—
524	C₂³	—	89	2	no	—
525	C₂³	—	89	2	no	—
526	C₂³	—	89	2	no	—
527	C₂³	—	178	1	no	—
528	C₂³	—	178	1	no	—
529	C₂³	—	178	1	no	—
530	C₂³	—	178	1	no	—
531	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
532	Q₈	—	356	4	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	—	2	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	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	89	2	no	—
549	C₂×C₄	—	89	2	no	—
550	C₂×C₄	—	89	2	no	—
551	C₂×C₄	—	89	2	no	—
552	C₂×C₄	—	356	4	no	—
553	C₂×C₄	—	356	4	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	1	no	—
559	C₂×C₄	—	178	1	no	—
560	C₂×C₄	—	178	1	no	—
561	C₂×C₄	—	178	1	no	—
562	C₂×C₄	—	178	1	no	—
563	C₂×C₄	—	178	1	no	—
564	C₂×C₄	—	178	1	no	—
565	C₂×C₄	—	178	1	no	—
566	C₂×C₄	—	178	1	no	—
567	C₂×C₄	—	178	1	no	—
568	C₂×C₄	—	178	1	no	—
569	C₂×C₄	—	178	1	no	—
570	C₂×C₄	—	178	1	no	—
571	C₂×C₄	—	178	2	no	—
572	C₂×C₄	—	178	2	no	—
573	C₂×C₄	—	178	2	no	—
574	C₂×C₄	—	178	2	no	—
575	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
576	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
577	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
578	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
579	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
580	C₂×C₄	#15668057	1	1	yes	characteristic
581	C₂×C₄	#15668058	1	1	yes	characteristic
582	C₂×C₄	#15668058	1	1	yes	characteristic
583	C₂×C₄	#15668059	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	356	1	no	—
589	C₈	—	356	1	no	—
590	C₈	—	356	1	no	—
591	C₈	—	178	2	no	—
592	C₂²	—	89	4	no	—
593	C₂²	—	178	2	no	—
594	C₂²	—	178	2	no	—
595	C₂²	—	178	2	no	—
596	C₂²	—	178	2	no	—
597	C₂²	—	178	2	no	—
598	C₂²	—	178	2	no	—
599	C₂²	C₄×Q₈×D₈₉	1	1	yes	characteristic
600	C₂²	#19152072	1	1	yes	characteristic
601	C₂²	#19152077	1	1	yes	characteristic
602	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
603	C₂²	#131×D₈₉	1	1	yes	characteristic
604	C₂²	#19152363	1	1	yes	characteristic
605	C₂²	#19152364	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	356	1	no	—
613	C₄	—	356	1	no	—
614	C₄	—	356	1	no	—
615	C₄	—	178	2	no	—
616	C₄	—	178	2	no	—
617	C₄	—	178	2	no	—
618	C₄	—	178	2	no	—
619	C₄	#19152184	1	1	yes	characteristic
620	C₄	#19152189	1	1	yes	characteristic
621	C₄	#19152223	1	1	yes	characteristic
622	C₄	#19152228	1	1	yes	characteristic
623	C₂	—	178	4	no	—
624	C₂	#26022981	1	1	yes	characteristic
625	C₂	C₈×Q₈×D₈₉	1	1	yes	characteristic
626	C₂	#26029188	1	1	yes	characteristic
627	C₂	#26029275	1	1	yes	characteristic
628	C₂	#26029298	1	1	yes	characteristic
629	C₂	#26029359	1	1	yes	characteristic
630	C₂	#26029387	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#1916	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1916	D₈₉
hypocenter	C₈₉	#22287
LCS	G ▷ C₂²×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
72. C₂×C₈×D₈₉	Q₈	semidirect
73. #15667992	C₈	semidirect
128. C₂×Dic₁₇₈	C₂×C₈	semidirect
165. C₄⋊Dic₈₉	C₂×C₈	semidirect
166. C₄⋊Dic₈₉	C₂×C₈	semidirect
201. C₄⋊C₄×C₈₉	C₂×C₈	semidirect
324. #1916	D₈₉	semidirect
331. C₈₉	#22287	semidirect
505. C₄⋊C₄	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15667992	2
#26021186	2
#26020970	2
#26020968	2
#26020811	2
#26020810	2
#26020808	2
#26020431	2
#26020428	2
#26020231	2
C₈×#13083551	2
#26020022	2
#336×D₈₉	2
C₈₉×#1916	2
#22287	89