Subgroups — C₈₉×#25144 #36402992

Order 22784.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#471×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3003	C₂	1	1	yes	maximal, characteristic
4	C₂×#450×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#100×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
25	#525×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	#471×C₈₉	—	2	4	no	—
28	#470×C₈₉	—	2	1	no	—
29	#468×C₈₉	—	2	1	no	—
30	#467×C₈₉	—	2	1	no	—
31	#465×C₈₉	—	2	1	no	—
32	#450×C₈₉	—	2	1	no	—
33	#450×C₈₉	—	2	1	no	—
34	#450×C₈₉	—	2	1	no	—
35	#450×C₈₉	—	2	1	no	—
36	#450×C₈₉	—	2	1	no	—
37	#450×C₈₉	—	2	1	no	—
38	#447×C₈₉	—	2	1	no	—
39	#447×C₈₉	—	2	1	no	—
40	#436×C₈₉	—	2	1	no	—
41	#435×C₈₉	—	2	1	no	—
42	#435×C₈₉	—	2	1	no	—
43	C₈×D₄×C₈₉	—	2	1	no	—
44	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#428×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#418×C₈₉	C₂²	1	1	yes	characteristic
50	#418×C₈₉	C₂²	1	1	yes	characteristic
51	#417×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×#100×C₈₉	—	2	4	no	—
57	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
61	#408×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#407×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
64	#405×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₈₉	—	2	1	no	—
70	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	—	2	2	no	—
73	C₂²×D₄×C₈₉	—	2	2	no	—
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	4	1	no	—
80	C₂²×D₄×C₈₉	—	4	1	no	—
81	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	#137×C₈₉	—	2	2	no	—
85	#137×C₈₉	—	4	1	no	—
86	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
87	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
88	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
89	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
90	C₂×Q₁₆×C₈₉	—	2	1	no	—
91	C₂×SD₁₆×C₈₉	—	2	1	no	—
92	C₂×SD₁₆×C₈₉	—	2	1	no	—
93	C₂×SD₁₆×C₈₉	—	2	1	no	—
94	C₂×SD₁₆×C₈₉	—	2	2	no	—
95	C₂×SD₁₆×C₈₉	—	2	2	no	—
96	C₂×SD₁₆×C₈₉	—	2	1	no	—
97	C₂×SD₁₆×C₈₉	—	2	1	no	—
98	C₂×SD₁₆×C₈₉	—	2	1	no	—
99	C₂×SD₁₆×C₈₉	—	2	1	no	—
100	C₂×SD₁₆×C₈₉	—	4	1	no	—
101	C₂×SD₁₆×C₈₉	—	4	1	no	—
102	C₂×D₈×C₈₉	—	2	1	no	—
103	C₂×D₈×C₈₉	—	2	1	no	—
104	#131×C₈₉	—	2	2	no	—
105	#131×C₈₉	—	4	1	no	—
106	C₂×M₁₆×C₈₉	—	2	1	no	—
107	C₂×M₁₆×C₈₉	—	2	1	no	—
108	C₂×M₁₆×C₈₉	—	2	1	no	—
109	C₂×M₁₆×C₈₉	—	2	2	no	—
110	C₂×M₁₆×C₈₉	—	2	2	no	—
111	C₂×M₁₆×C₈₉	—	4	1	no	—
112	C₂×M₁₆×C₈₉	—	4	1	no	—
113	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₈₉	—	2	1	no	—
120	C₂²×C₈×C₈₉	—	2	1	no	—
121	C₂²×C₈×C₈₉	—	2	1	no	—
122	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	#123×C₈₉	—	2	1	no	—
125	C₂²⋊Q₈×C₈₉	—	2	1	no	—
126	C₂²⋊Q₈×C₈₉	—	2	1	no	—
127	C₂²⋊Q₈×C₈₉	—	2	1	no	—
128	C₂²⋊Q₈×C₈₉	—	2	1	no	—
129	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
130	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
131	#121×C₈₉	D₄	1	1	yes	characteristic
132	#121×C₈₉	D₄	1	1	yes	characteristic
133	#120×C₈₉	—	2	1	no	—
134	C₄×D₄×C₈₉	—	2	1	no	—
135	C₄×D₄×C₈₉	—	2	1	no	—
136	#117×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
140	#108×C₈₉	—	2	2	no	—
141	#108×C₈₉	—	4	1	no	—
142	#107×C₈₉	—	2	1	no	—
143	#106×C₈₉	—	2	1	no	—
144	C₄⋊C₈×C₈₉	—	2	1	no	—
145	C₄⋊C₈×C₈₉	—	2	1	no	—
146	#103×C₈₉	—	2	1	no	—
147	#103×C₈₉	—	2	1	no	—
148	#103×C₈₉	—	2	1	no	—
149	#102×C₈₉	—	2	1	no	—
150	#102×C₈₉	—	2	1	no	—
151	#102×C₈₉	—	2	1	no	—
152	#102×C₈₉	—	2	1	no	—
153	#102×C₈₉	—	2	1	no	—
154	#102×C₈₉	—	2	1	no	—
155	#102×C₈₉	—	2	1	no	—
156	#102×C₈₉	—	2	1	no	—
157	#102×C₈₉	—	2	1	no	—
158	#101×C₈₉	—	2	2	no	—
159	#101×C₈₉	—	4	1	no	—
160	#100×C₈₉	—	2	2	no	—
161	#100×C₈₉	—	2	2	no	—
162	#100×C₈₉	—	2	2	no	—
163	#100×C₈₉	D₄	1	4	yes	complemented
164	C₂²⋊C₈×C₈₉	—	2	1	no	—
165	C₂²⋊C₈×C₈₉	—	2	1	no	—
166	C₂²⋊C₈×C₈₉	—	2	1	no	—
167	C₂²⋊C₈×C₈₉	—	2	1	no	—
168	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
169	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
170	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
171	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
172	#97×C₈₉	—	2	1	no	—
173	C₄×C₈×C₈₉	—	2	1	no	—
174	C₂⁴×C₈₉	—	2	4	no	—
175	C₂⁴×C₈₉	—	2	1	no	—
176	C₂⁴×C₈₉	—	2	1	no	—
177	C₂⁴×C₈₉	—	4	2	no	—
178	C₂⁴×C₈₉	—	4	1	no	—
179	C₂⁴×C₈₉	—	4	1	no	—
180	C₂⁴×C₈₉	—	8	2	no	—
181	C₂⁴×C₈₉	—	8	2	no	—
182	C₂⁴×C₈₉	#41	1	1	yes	characteristic
183	#41×C₈₉	—	2	1	no	—
184	#41×C₈₉	—	2	1	no	—
185	#41×C₈₉	—	2	1	no	—
186	#41×C₈₉	—	2	1	no	—
187	C₂×Q₈×C₈₉	—	2	1	no	—
188	C₂×Q₈×C₈₉	—	2	1	no	—
189	C₂×Q₈×C₈₉	—	2	1	no	—
190	C₂×Q₈×C₈₉	—	2	1	no	—
191	C₂×Q₈×C₈₉	—	2	1	no	—
192	C₂×Q₈×C₈₉	—	2	1	no	—
193	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	2	1	no	—
205	C₂×D₄×C₈₉	—	2	1	no	—
206	C₂×D₄×C₈₉	—	2	1	no	—
207	C₂×D₄×C₈₉	—	2	1	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	4	2	no	—
215	C₂×D₄×C₈₉	—	4	2	no	—
216	C₂×D₄×C₈₉	—	4	2	no	—
217	C₂×D₄×C₈₉	—	4	1	no	—
218	C₂×D₄×C₈₉	—	4	1	no	—
219	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₈₉	#41	1	2	yes	—
222	C₂²×C₄×C₈₉	—	2	1	no	—
223	C₂²×C₄×C₈₉	—	2	1	no	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	1	no	—
228	C₂²×C₄×C₈₉	—	2	1	no	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	Q₁₆×C₈₉	—	4	2	no	—
236	SD₁₆×C₈₉	—	4	2	no	—
237	SD₁₆×C₈₉	—	4	2	no	—
238	SD₁₆×C₈₉	—	4	2	no	—
239	SD₁₆×C₈₉	—	4	2	no	—
240	SD₁₆×C₈₉	—	4	2	no	—
241	SD₁₆×C₈₉	—	4	2	no	—
242	SD₁₆×C₈₉	—	4	2	no	—
243	D₈×C₈₉	—	4	2	no	—
244	D₈×C₈₉	—	4	2	no	—
245	M₁₆×C₈₉	—	2	1	no	—
246	M₁₆×C₈₉	—	2	1	no	—
247	M₁₆×C₈₉	—	2	1	no	—
248	M₁₆×C₈₉	—	2	1	no	—
249	M₁₆×C₈₉	—	2	1	no	—
250	M₁₆×C₈₉	—	2	1	no	—
251	M₁₆×C₈₉	—	2	1	no	—
252	M₁₆×C₈₉	—	2	1	no	—
253	M₁₆×C₈₉	—	2	1	no	—
254	M₁₆×C₈₉	—	2	1	no	—
255	M₁₆×C₈₉	—	4	2	no	—
256	M₁₆×C₈₉	—	4	2	no	—
257	M₁₆×C₈₉	—	4	2	no	—
258	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
259	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₈₉	—	2	1	no	—
261	C₂×C₈×C₈₉	—	2	1	no	—
262	C₂×C₈×C₈₉	—	2	1	no	—
263	C₂×C₈×C₈₉	—	2	1	no	—
264	C₂×C₈×C₈₉	—	2	1	no	—
265	C₂×C₈×C₈₉	—	2	1	no	—
266	C₂×C₈×C₈₉	—	2	1	no	—
267	C₂×C₈×C₈₉	—	2	1	no	—
268	C₂×C₈×C₈₉	—	2	1	no	—
269	C₂×C₈×C₈₉	—	2	1	no	—
270	C₂×C₈×C₈₉	—	4	2	no	—
271	C₂×C₈×C₈₉	—	4	2	no	—
272	C₂×C₈×C₈₉	—	4	2	no	—
273	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
276	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₄⋊C₄×C₈₉	—	2	1	no	—
278	C₄⋊C₄×C₈₉	—	2	1	no	—
279	C₄⋊C₄×C₈₉	—	2	1	no	—
280	C₄⋊C₄×C₈₉	—	2	1	no	—
281	C₄⋊C₄×C₈₉	—	4	1	no	—
282	C₄⋊C₄×C₈₉	—	4	1	no	—
283	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
284	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
285	C₂²⋊C₄×C₈₉	—	2	1	no	—
286	C₂²⋊C₄×C₈₉	—	2	1	no	—
287	C₂²⋊C₄×C₈₉	—	2	1	no	—
288	C₂²⋊C₄×C₈₉	—	2	1	no	—
289	C₂²⋊C₄×C₈₉	—	2	1	no	—
290	C₂²⋊C₄×C₈₉	—	4	1	no	—
291	C₂²⋊C₄×C₈₉	—	4	1	no	—
292	C₄²×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	1	no	—
294	C₂³×C₈₉	—	2	1	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	2	no	—
298	C₂³×C₈₉	—	2	2	no	—
299	C₂³×C₈₉	—	4	1	no	—
300	C₂³×C₈₉	—	4	4	no	—
301	C₂³×C₈₉	—	4	4	no	—
302	C₂³×C₈₉	—	4	1	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	1	no	—
305	C₂³×C₈₉	—	4	1	no	—
306	C₂³×C₈₉	—	8	1	no	—
307	C₂³×C₈₉	—	8	1	no	—
308	C₂³×C₈₉	—	8	1	no	—
309	C₂³×C₈₉	—	8	1	no	—
310	C₂³×C₈₉	—	8	2	no	—
311	C₂³×C₈₉	—	8	2	no	—
312	C₂³×C₈₉	—	8	2	no	—
313	C₂³×C₈₉	—	8	8	no	—
314	C₂³×C₈₉	—	8	8	no	—
315	C₂³×C₈₉	—	8	2	no	—
316	C₂³×C₈₉	#121	1	1	yes	characteristic
317	C₂³×C₈₉	#121	1	1	yes	characteristic
318	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
319	Q₈×C₈₉	—	2	1	no	—
320	Q₈×C₈₉	—	2	1	no	—
321	Q₈×C₈₉	—	4	1	no	—
322	Q₈×C₈₉	—	4	1	no	—
323	Q₈×C₈₉	—	4	1	no	—
324	Q₈×C₈₉	—	4	1	no	—
325	D₄×C₈₉	—	2	1	no	—
326	D₄×C₈₉	—	2	2	no	—
327	D₄×C₈₉	—	2	2	no	—
328	D₄×C₈₉	—	2	1	no	—
329	D₄×C₈₉	—	2	2	no	—
330	D₄×C₈₉	—	2	2	no	—
331	D₄×C₈₉	—	4	4	no	—
332	D₄×C₈₉	—	4	4	no	—
333	D₄×C₈₉	—	4	1	no	—
334	D₄×C₈₉	—	4	1	no	—
335	D₄×C₈₉	—	4	2	no	—
336	D₄×C₈₉	—	4	1	no	—
337	D₄×C₈₉	—	4	1	no	—
338	D₄×C₈₉	—	4	1	no	—
339	D₄×C₈₉	—	4	1	no	—
340	D₄×C₈₉	—	8	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	1	no	—
345	C₂×C₄×C₈₉	—	2	1	no	—
346	C₂×C₄×C₈₉	—	2	1	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	1	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	1	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	4	1	no	—
355	C₂×C₄×C₈₉	—	4	1	no	—
356	C₂×C₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	—	4	1	no	—
360	C₂×C₄×C₈₉	—	8	1	no	—
361	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
362	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
369	C₈×C₈₉	—	2	1	no	—
370	C₈×C₈₉	—	2	1	no	—
371	C₈×C₈₉	—	2	2	no	—
372	C₈×C₈₉	—	2	2	no	—
373	C₈×C₈₉	—	2	1	no	—
374	C₈×C₈₉	—	2	1	no	—
375	C₈×C₈₉	—	4	1	no	—
376	C₈×C₈₉	—	4	1	no	—
377	C₈×C₈₉	—	4	1	no	—
378	C₈×C₈₉	—	4	1	no	—
379	C₂²×C₈₉	—	2	1	no	—
380	C₂²×C₈₉	—	2	1	no	—
381	C₂²×C₈₉	—	2	1	no	—
382	C₂²×C₈₉	—	2	1	no	—
383	C₂²×C₈₉	—	2	1	no	—
384	C₂²×C₈₉	—	2	1	no	—
385	C₂²×C₈₉	—	2	1	no	—
386	C₂²×C₈₉	—	4	2	no	—
387	C₂²×C₈₉	—	4	2	no	—
388	C₂²×C₈₉	—	4	1	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	8	8	no	—
394	C₂²×C₈₉	—	8	2	no	—
395	C₂²×C₈₉	—	8	2	no	—
396	C₂²×C₈₉	—	8	2	no	—
397	C₂²×C₈₉	—	8	2	no	—
398	C₂²×C₈₉	—	8	8	no	—
399	C₂²×C₈₉	—	8	1	no	—
400	C₂²×C₈₉	—	8	1	no	—
401	C₂²×C₈₉	—	8	1	no	—
402	C₂²×C₈₉	—	8	1	no	—
403	C₂²×C₈₉	#471	1	2	yes	complemented
404	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
405	C₂²×C₈₉	#525	1	1	yes	characteristic
406	C₂²×C₈₉	#538	1	1	yes	characteristic
407	C₄×C₈₉	—	2	1	no	—
408	C₄×C₈₉	—	2	1	no	—
409	C₄×C₈₉	—	4	1	no	—
410	C₄×C₈₉	—	4	1	no	—
411	C₄×C₈₉	—	4	1	no	—
412	C₄×C₈₉	—	8	1	no	—
413	C₄×C₈₉	—	8	1	no	—
414	C₄×C₈₉	D₄²	1	1	yes	characteristic
415	C₄×C₈₉	D₄²	1	1	yes	characteristic
416	C₄×C₈₉	#546	1	1	yes	characteristic
417	C₄×C₈₉	#546	1	1	yes	characteristic
418	#25144	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₈₉	—	2	1	no	—
420	C₂×C₈₉	—	2	1	no	—
421	C₂×C₈₉	—	2	2	no	—
422	C₂×C₈₉	—	4	1	no	—
423	C₂×C₈₉	—	8	1	no	—
424	C₂×C₈₉	—	8	2	no	—
425	C₂×C₈₉	—	8	2	no	—
426	C₂×C₈₉	#2424	1	1	yes	characteristic
427	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
428	C₂×C₈₉	#3068	1	1	yes	characteristic
429	C₂×#471	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#3056	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#3003	C₂×C₈₉	1	1	yes	characteristic
432	C₂×#450	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#2933	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₂²×#100	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#2063	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#2051	C₂×C₈₉	1	1	yes	characteristic, complemented
437	#2046	C₂×C₈₉	1	1	yes	characteristic, complemented
438	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
439	#1977	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#1931	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
442	#1901	C₂×C₈₉	1	1	yes	characteristic, complemented
443	#1855	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₈₉	#25144	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
447	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
448	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
449	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
450	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic, complemented
452	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
453	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
454	#525	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
456	#471	—	2	4	no	—
457	#470	—	2	1	no	—
458	#468	—	2	1	no	—
459	#467	—	2	1	no	—
460	#465	—	2	1	no	—
461	#450	—	2	1	no	—
462	#450	—	2	1	no	—
463	#450	—	2	1	no	—
464	#450	—	2	1	no	—
465	#450	—	2	1	no	—
466	#450	—	2	1	no	—
467	#447	—	2	1	no	—
468	#447	—	2	1	no	—
469	#436	—	2	1	no	—
470	#435	—	2	1	no	—
471	#435	—	2	1	no	—
472	C₈×D₄	—	2	1	no	—
473	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
474	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	#428	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	#418	C₂²×C₈₉	1	1	yes	characteristic
479	#418	C₂²×C₈₉	1	1	yes	characteristic
480	#417	C₂²×C₈₉	1	1	yes	characteristic, complemented
481	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
482	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
483	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
484	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	C₂×#100	—	2	4	no	—
486	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
488	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
489	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
490	#408	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#407	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
493	#405	C₂²×C₈₉	1	1	yes	characteristic, complemented
494	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
495	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
496	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
497	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	C₂⁵	—	2	1	no	—
499	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	—	4	1	no	—
510	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
513	#137	—	2	2	no	—
514	#137	—	4	1	no	—
515	AGL(1,ℤ/8)	—	2	2	no	—
516	AGL(1,ℤ/8)	—	2	2	no	—
517	AGL(1,ℤ/8)	—	4	1	no	—
518	AGL(1,ℤ/8)	—	4	1	no	—
519	C₂×Q₁₆	—	2	1	no	—
520	C₂×SD₁₆	—	2	1	no	—
521	C₂×SD₁₆	—	2	1	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	1	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	1	no	—
526	C₂×SD₁₆	—	2	1	no	—
527	C₂×SD₁₆	—	2	1	no	—
528	C₂×SD₁₆	—	2	1	no	—
529	C₂×SD₁₆	—	4	1	no	—
530	C₂×SD₁₆	—	4	1	no	—
531	C₂×D₈	—	2	1	no	—
532	C₂×D₈	—	2	1	no	—
533	#131	—	2	2	no	—
534	#131	—	4	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	1	no	—
538	C₂×M₁₆	—	2	2	no	—
539	C₂×M₁₆	—	2	2	no	—
540	C₂×M₁₆	—	4	1	no	—
541	C₂×M₁₆	—	4	1	no	—
542	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
543	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
544	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
548	C₂²×C₈	—	2	1	no	—
549	C₂²×C₈	—	2	1	no	—
550	C₂²×C₈	—	2	1	no	—
551	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
552	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
553	#123	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
559	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
560	#121	D₄×C₈₉	1	1	yes	characteristic
561	#121	D₄×C₈₉	1	1	yes	characteristic
562	#120	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	#117	C₂³×C₈₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	#108	—	2	2	no	—
570	#108	—	4	1	no	—
571	#107	—	2	1	no	—
572	#106	—	2	1	no	—
573	C₄⋊C₈	—	2	1	no	—
574	C₄⋊C₈	—	2	1	no	—
575	#103	—	2	1	no	—
576	#103	—	2	1	no	—
577	#103	—	2	1	no	—
578	#102	—	2	1	no	—
579	#102	—	2	1	no	—
580	#102	—	2	1	no	—
581	#102	—	2	1	no	—
582	#102	—	2	1	no	—
583	#102	—	2	1	no	—
584	#102	—	2	1	no	—
585	#102	—	2	1	no	—
586	#102	—	2	1	no	—
587	#101	—	2	2	no	—
588	#101	—	4	1	no	—
589	#100	—	2	2	no	—
590	#100	—	2	2	no	—
591	#100	—	2	2	no	—
592	#100	D₄×C₈₉	1	4	yes	complemented
593	C₂²⋊C₈	—	2	1	no	—
594	C₂²⋊C₈	—	2	1	no	—
595	C₂²⋊C₈	—	2	1	no	—
596	C₂²⋊C₈	—	2	1	no	—
597	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
598	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
599	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
600	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
601	#97	—	2	1	no	—
602	C₄×C₈	—	2	1	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	—	4	1	no	—
608	C₂⁴	—	4	1	no	—
609	C₂⁴	—	8	2	no	—
610	C₂⁴	—	8	2	no	—
611	C₂⁴	#41×C₈₉	1	1	yes	characteristic
612	#41	—	2	1	no	—
613	#41	—	2	1	no	—
614	#41	—	2	1	no	—
615	#41	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
649	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
650	C₂×D₄	#41×C₈₉	1	2	yes	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
662	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
664	Q₁₆	—	4	2	no	—
665	SD₁₆	—	4	2	no	—
666	SD₁₆	—	4	2	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	2	no	—
670	SD₁₆	—	4	2	no	—
671	SD₁₆	—	4	2	no	—
672	D₈	—	4	2	no	—
673	D₈	—	4	2	no	—
674	M₁₆	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	2	1	no	—
679	M₁₆	—	2	1	no	—
680	M₁₆	—	2	1	no	—
681	M₁₆	—	2	1	no	—
682	M₁₆	—	2	1	no	—
683	M₁₆	—	2	1	no	—
684	M₁₆	—	4	2	no	—
685	M₁₆	—	4	2	no	—
686	M₁₆	—	4	2	no	—
687	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
688	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	4	2	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	—	4	2	no	—
702	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
703	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
704	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
705	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₄²	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	1	no	—
738	C₂³	—	8	1	no	—
739	C₂³	—	8	2	no	—
740	C₂³	—	8	2	no	—
741	C₂³	—	8	2	no	—
742	C₂³	—	8	8	no	—
743	C₂³	—	8	8	no	—
744	C₂³	—	8	2	no	—
745	C₂³	#121×C₈₉	1	1	yes	characteristic
746	C₂³	#121×C₈₉	1	1	yes	characteristic
747	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	4	1	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	4	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	8	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
791	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
796	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
797	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
798	C₈	—	2	1	no	—
799	C₈	—	2	1	no	—
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	4	1	no	—
805	C₈	—	4	1	no	—
806	C₈	—	4	1	no	—
807	C₈	—	4	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	2	no	—
823	C₂²	—	8	2	no	—
824	C₂²	—	8	2	no	—
825	C₂²	—	8	2	no	—
826	C₂²	—	8	8	no	—
827	C₂²	—	8	8	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	1	no	—
832	C₂²	#471×C₈₉	1	2	yes	complemented
833	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
834	C₂²	#525×C₈₉	1	1	yes	characteristic
835	C₂²	#538×C₈₉	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	8	1	no	—
842	C₄	—	8	1	no	—
843	C₄	D₄²×C₈₉	1	1	yes	characteristic
844	C₄	D₄²×C₈₉	1	1	yes	characteristic
845	C₄	#546×C₈₉	1	1	yes	characteristic
846	C₄	#546×C₈₉	1	1	yes	characteristic
847	C₂	—	2	2	no	—
848	C₂	—	2	1	no	—
849	C₂	—	2	1	no	—
850	C₂	—	4	1	no	—
851	C₂	—	8	1	no	—
852	C₂	—	8	2	no	—
853	C₂	—	8	2	no	—
854	C₂	C₈₉×#2424	1	1	yes	characteristic
855	C₂	C₂×#471×C₈₉	1	1	yes	characteristic
856	C₂	C₈₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#3003	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#471×C₈₉	C₂	semidirect
2. C₈₉×#3056	C₂	semidirect
4. C₂×#450×C₈₉	C₂	semidirect
5. C₈₉×#2933	C₂	semidirect
6. C₂²×#100×C₈₉	C₂	semidirect
7. C₈₉×#2063	C₂	semidirect
8. C₈₉×#2051	C₂	semidirect
9. C₈₉×#2046	C₂	semidirect
10. C₈₉×#2019	C₂	semidirect
11. C₈₉×#1977	C₂	semidirect
12. C₈₉×#1931	C₂	semidirect
13. C₈₉×#1907	C₂	semidirect
14. C₈₉×#1901	C₂	semidirect
15. C₈₉×#1855	C₂	semidirect
17. C₂×#137×C₈₉	C₂²	semidirect
22. C₂×#131×C₈₉	C₂²	semidirect
44. C₂×#108×C₈₉	C₂²	semidirect
45. C₂×#108×C₈₉	C₂²	semidirect
46. #428×C₈₉	C₂²	semidirect
47. #424×C₈₉	C₂²	semidirect
48. #419×C₈₉	C₂²	semidirect
51. #417×C₈₉	C₂²	semidirect
54. C₂×#101×C₈₉	C₂²	semidirect
55. C₂×#101×C₈₉	C₂²	semidirect
61. #408×C₈₉	C₂²	semidirect
64. #405×C₈₉	C₂²	semidirect
65. #343×C₈₉	C₂²	semidirect
66. #343×C₈₉	C₂²	semidirect
67. #341×C₈₉	C₂²	semidirect
68. #341×C₈₉	C₂²	semidirect
163. #100×C₈₉	D₄	semidirect
403. C₂²×C₈₉	#471	semidirect
418. #25144	C₈₉	direct (N × H)
429. C₂×#471	C₂×C₈₉	semidirect
430. #3056	C₂×C₈₉	semidirect
432. C₂×#450	C₂×C₈₉	semidirect
433. #2933	C₂×C₈₉	semidirect
434. C₂²×#100	C₂×C₈₉	semidirect
435. #2063	C₂×C₈₉	semidirect
436. #2051	C₂×C₈₉	semidirect
437. #2046	C₂×C₈₉	semidirect
438. #2019	C₂×C₈₉	semidirect
439. #1977	C₂×C₈₉	semidirect
440. #1931	C₂×C₈₉	semidirect
441. #1907	C₂×C₈₉	semidirect
442. #1901	C₂×C₈₉	semidirect
443. #1855	C₂×C₈₉	semidirect
444. C₈₉	#25144	direct (N × H)
446. C₂×#137	C₂²×C₈₉	semidirect
451. C₂×#131	C₂²×C₈₉	semidirect
473. C₂×#108	C₂²×C₈₉	semidirect
474. C₂×#108	C₂²×C₈₉	semidirect
475. #428	C₂²×C₈₉	semidirect
476. #424	C₂²×C₈₉	semidirect
477. #419	C₂²×C₈₉	semidirect
480. #417	C₂²×C₈₉	semidirect
483. C₂×#101	C₂²×C₈₉	semidirect
484. C₂×#101	C₂²×C₈₉	semidirect
490. #408	C₂²×C₈₉	semidirect
493. #405	C₂²×C₈₉	semidirect
494. #343	C₂²×C₈₉	semidirect
495. #343	C₂²×C₈₉	semidirect
496. #341	C₂²×C₈₉	semidirect
497. #341	C₂²×C₈₉	semidirect
592. #100	D₄×C₈₉	semidirect
832. C₂²	#471×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#471×C₈₉	2
C₈₉×#3056	2
C₈₉×#3003	2
C₂×#450×C₈₉	2
C₈₉×#2933	2
C₂²×#100×C₈₉	2
C₈₉×#2063	2
C₈₉×#2051	2
C₈₉×#2046	2
C₈₉×#2019	2
C₈₉×#1977	2
C₈₉×#1931	2
C₈₉×#1907	2
C₈₉×#1901	2
C₈₉×#1855	2
#25144	89

Subgroups — C89×#25144 #36402992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25144 #36402992