Subgroups — C₈₉×#62819 #36440667

Order 22784.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3541	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3538	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3536	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3535	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3520	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3505	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3501	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3495	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3492	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3492	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3490	C₂	1	4	yes	maximal, complemented
12	C₈₉×#3489	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3486	C₂	1	2	yes	maximal, complemented
14	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
17	C₂²×#41×C₈₉	C₂²	1	2	yes	complemented
18	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
20	#563×C₈₉	C₂²	1	16	yes	complemented
21	#562×C₈₉	C₂²	1	16	yes	complemented
22	#556×C₈₉	C₂²	1	8	yes	complemented
23	#554×C₈₉	C₂²	1	8	yes	complemented
24	#554×C₈₉	C₂²	1	16	yes	complemented
25	#554×C₈₉	C₂²	1	8	yes	complemented
26	#554×C₈₉	C₂²	1	16	yes	complemented
27	#553×C₈₉	C₂²	1	8	yes	complemented
28	#553×C₈₉	C₂²	1	16	yes	complemented
29	#552×C₈₉	C₂²	1	16	yes	complemented
30	#552×C₈₉	C₂²	1	8	yes	complemented
31	#552×C₈₉	C₂²	1	8	yes	complemented
32	#552×C₈₉	C₂²	1	8	yes	complemented
33	#551×C₈₉	C₂²	1	16	yes	complemented
34	#551×C₈₉	C₂²	1	16	yes	complemented
35	#551×C₈₉	C₂²	1	16	yes	complemented
36	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
37	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
39	#548×C₈₉	C₂²	1	8	yes	complemented
40	#548×C₈₉	C₂²	1	8	yes	complemented
41	#548×C₈₉	C₂²	1	8	yes	complemented
42	#547×C₈₉	C₂²	1	16	yes	complemented
43	#547×C₈₉	C₂²	1	8	yes	complemented
44	#547×C₈₉	C₂²	1	8	yes	complemented
45	#546×C₈₉	C₂²	1	16	yes	complemented
46	#546×C₈₉	C₂²	1	16	yes	complemented
47	#546×C₈₉	C₂²	1	8	yes	complemented
48	#544×C₈₉	C₂²	1	2	yes	complemented
49	#544×C₈₉	C₂²	1	4	yes	complemented
50	#544×C₈₉	C₂²	1	8	yes	complemented
51	#543×C₈₉	C₂²	1	4	yes	—
52	#543×C₈₉	C₂²	1	8	yes	complemented
53	#542×C₈₉	C₂²	1	8	yes	complemented
54	#542×C₈₉	C₂²	1	16	yes	complemented
55	#541×C₈₉	C₂²	1	8	yes	complemented
56	#539×C₈₉	C₂²	1	8	yes	complemented
57	#539×C₈₉	C₂²	1	8	yes	complemented
58	#539×C₈₉	C₂²	1	8	yes	complemented
59	#539×C₈₉	C₂²	1	8	yes	complemented
60	#539×C₈₉	C₂²	1	16	yes	complemented
61	#538×C₈₉	C₂²	1	8	yes	complemented
62	#538×C₈₉	C₂²	1	8	yes	complemented
63	#538×C₈₉	C₂²	1	8	yes	complemented
64	#537×C₈₉	C₂²	1	2	yes	complemented
65	#537×C₈₉	C₂²	1	4	yes	complemented
66	#537×C₈₉	C₂²	1	8	yes	complemented
67	#536×C₈₉	C₂²	1	4	yes	complemented
68	#536×C₈₉	C₂²	1	8	yes	complemented
69	#536×C₈₉	C₂²	1	8	yes	complemented
70	#534×C₈₉	C₂²	1	4	yes	—
71	#533×C₈₉	C₂²	1	8	yes	complemented
72	#529×C₈₉	C₂²	1	8	yes	complemented
73	#525×C₈₉	C₂²	1	4	yes	—
74	#525×C₈₉	C₂²	1	4	yes	—
75	#525×C₈₉	C₂²	1	4	yes	—
76	#525×C₈₉	C₂²	1	4	yes	—
77	#525×C₈₉	C₂²	1	4	yes	complemented
78	#525×C₈₉	C₂²	1	4	yes	complemented
79	#525×C₈₉	C₂²	1	4	yes	complemented
80	#525×C₈₉	C₂²	1	4	yes	complemented
81	#525×C₈₉	C₂²	1	8	yes	complemented
82	#525×C₈₉	C₂²	1	8	yes	complemented
83	#525×C₈₉	C₂²	1	8	yes	complemented
84	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
85	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
86	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
87	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
88	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
89	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
90	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
91	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
92	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
94	C₂×#121×C₈₉	C₂²	1	2	yes	—
95	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
96	C₂×#120×C₈₉	C₂²	1	4	yes	—
97	#520×C₈₉	C₂²	1	4	yes	complemented
98	#520×C₈₉	C₂²	1	8	yes	complemented
99	#519×C₈₉	C₂²	1	2	yes	complemented
100	#518×C₈₉	C₂²	1	8	yes	—
101	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
102	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
103	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
104	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
106	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
107	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
108	2₋¹⁺⁴×C₈₉	—	4	8	no	—
109	C₂×#41×C₈₉	—	4	8	no	—
110	C₂×#41×C₈₉	C₂³	1	4	yes	—
111	C₂×#41×C₈₉	C₂³	1	8	yes	—
112	C₂×#41×C₈₉	C₂³	1	4	yes	—
113	C₂×#41×C₈₉	C₂³	1	4	yes	—
114	C₂×#41×C₈₉	C₂³	1	4	yes	—
115	C₂×#41×C₈₉	C₂³	1	8	yes	—
116	C₂×#41×C₈₉	C₂³	1	8	yes	complemented
117	C₂²×Q₈×C₈₉	—	4	4	no	—
118	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
119	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
120	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
121	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
122	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	8	yes	complemented
124	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
126	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₈₉	—	4	4	no	—
129	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
141	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
142	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
143	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
144	#126×C₈₉	C₂³	1	16	yes	—
145	#126×C₈₉	C₂³	1	16	yes	—
146	#126×C₈₉	C₂³	1	16	yes	complemented
147	#126×C₈₉	C₂³	1	16	yes	complemented
148	#126×C₈₉	C₂³	1	16	yes	complemented
149	#125×C₈₉	C₂³	1	8	yes	complemented
150	#125×C₈₉	C₂³	1	16	yes	complemented
151	#125×C₈₉	C₂³	1	16	yes	complemented
152	#125×C₈₉	C₂³	1	16	yes	complemented
153	#125×C₈₉	C₂³	1	16	yes	complemented
154	#124×C₈₉	C₂³	1	16	yes	—
155	#124×C₈₉	C₂³	1	16	yes	—
156	#124×C₈₉	C₂³	1	8	yes	complemented
157	#124×C₈₉	C₂³	1	16	yes	complemented
158	#123×C₈₉	C₂³	1	8	yes	—
159	#123×C₈₉	C₂³	1	8	yes	—
160	#123×C₈₉	C₂³	1	8	yes	—
161	#123×C₈₉	C₂³	1	8	yes	—
162	#123×C₈₉	C₂³	1	16	yes	—
163	#123×C₈₉	C₂³	1	16	yes	—
164	#123×C₈₉	C₂³	1	16	yes	—
165	#123×C₈₉	C₂³	1	16	yes	—
166	#123×C₈₉	C₂³	1	16	yes	—
167	#123×C₈₉	C₂³	1	16	yes	complemented
168	#123×C₈₉	C₂³	1	16	yes	complemented
169	#123×C₈₉	C₂³	1	16	yes	complemented
170	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
171	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
172	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
173	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
174	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
175	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
188	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
189	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
193	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
194	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
195	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
196	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
197	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
198	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
199	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
200	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
201	#121×C₈₉	C₂³	1	4	yes	—
202	#121×C₈₉	C₂³	1	4	yes	—
203	#121×C₈₉	C₂³	1	4	yes	—
204	#121×C₈₉	C₂³	1	4	yes	—
205	#121×C₈₉	C₂³	1	4	yes	—
206	#121×C₈₉	C₂³	1	4	yes	—
207	#121×C₈₉	C₂³	1	4	yes	—
208	#121×C₈₉	C₂³	1	4	yes	—
209	#121×C₈₉	C₂³	1	8	yes	—
210	#121×C₈₉	C₂³	1	8	yes	—
211	#121×C₈₉	C₂³	1	8	yes	—
212	#121×C₈₉	C₂³	1	8	yes	—
213	#121×C₈₉	C₂³	1	16	yes	—
214	#121×C₈₉	C₂³	1	16	yes	—
215	#121×C₈₉	C₂³	1	8	yes	complemented
216	#121×C₈₉	C₂³	1	16	yes	complemented
217	#120×C₈₉	C₂³	1	8	yes	—
218	#120×C₈₉	C₂³	1	8	yes	—
219	#120×C₈₉	C₂³	1	8	yes	—
220	#120×C₈₉	C₂³	1	8	yes	—
221	#120×C₈₉	C₂³	1	16	yes	—
222	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
224	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
225	C₄×Q₈×C₈₉	C₂³	1	16	yes	complemented
226	C₄×D₄×C₈₉	C₂³	1	8	yes	—
227	C₄×D₄×C₈₉	C₂³	1	8	yes	—
228	C₄×D₄×C₈₉	C₂³	1	8	yes	—
229	C₄×D₄×C₈₉	C₂³	1	8	yes	—
230	C₄×D₄×C₈₉	C₂³	1	8	yes	—
231	C₄×D₄×C₈₉	C₂³	1	8	yes	—
232	C₄×D₄×C₈₉	C₂³	1	8	yes	—
233	C₄×D₄×C₈₉	C₂³	1	8	yes	—
234	C₄×D₄×C₈₉	C₂³	1	16	yes	—
235	C₄×D₄×C₈₉	C₂³	1	16	yes	—
236	C₄×D₄×C₈₉	C₂³	1	16	yes	—
237	C₄×D₄×C₈₉	C₂³	1	16	yes	—
238	C₄×D₄×C₈₉	C₂³	1	16	yes	—
239	C₄×D₄×C₈₉	C₂³	1	16	yes	—
240	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
241	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
242	#117×C₈₉	C₂³	1	4	yes	—
243	#117×C₈₉	C₂³	1	4	yes	—
244	#117×C₈₉	C₂³	1	4	yes	—
245	#117×C₈₉	C₂³	1	4	yes	—
246	#117×C₈₉	C₂³	1	16	yes	—
247	#117×C₈₉	C₂³	1	8	yes	—
248	#117×C₈₉	C₂³	1	8	yes	—
249	#117×C₈₉	C₂³	1	8	yes	complemented
250	#117×C₈₉	C₂³	1	16	yes	complemented
251	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
253	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
254	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
255	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
258	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
264	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	complemented
265	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
266	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
267	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
268	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
269	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
270	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
274	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
275	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
276	C₂⁴×C₈₉	—	2	4	no	—
277	C₂⁴×C₈₉	—	4	2	no	—
278	C₂⁴×C₈₉	—	4	2	no	—
279	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
281	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
282	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
283	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
285	#41×C₈₉	—	2	16	no	—
286	#41×C₈₉	—	4	8	no	—
287	#41×C₈₉	—	4	8	no	—
288	#41×C₈₉	—	4	16	no	—
289	#41×C₈₉	—	4	16	no	—
290	#41×C₈₉	—	4	8	no	—
291	#41×C₈₉	—	4	16	no	—
292	C₂×Q₈×C₈₉	—	2	8	no	—
293	C₂×Q₈×C₈₉	—	4	4	no	—
294	C₂×Q₈×C₈₉	—	4	8	no	—
295	C₂×Q₈×C₈₉	—	4	8	no	—
296	C₂×Q₈×C₈₉	—	4	4	no	—
297	C₂×Q₈×C₈₉	—	4	16	no	—
298	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
302	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
304	C₂×D₄×C₈₉	—	2	16	no	—
305	C₂×D₄×C₈₉	—	4	4	no	—
306	C₂×D₄×C₈₉	—	4	8	no	—
307	C₂×D₄×C₈₉	—	4	8	no	—
308	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
309	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
310	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₈₉	—	2	4	no	—
319	C₂²×C₄×C₈₉	—	2	8	no	—
320	C₂²×C₄×C₈₉	—	4	4	no	—
321	C₂²×C₄×C₈₉	—	4	4	no	—
322	C₂²×C₄×C₈₉	—	4	4	no	—
323	C₂²×C₄×C₈₉	—	4	4	no	—
324	C₂²×C₄×C₈₉	—	4	8	no	—
325	C₂²×C₄×C₈₉	—	4	4	no	—
326	C₂²×C₄×C₈₉	—	4	2	no	—
327	C₂²×C₄×C₈₉	—	4	4	no	—
328	C₂²×C₄×C₈₉	—	4	4	no	—
329	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
331	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
355	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
375	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
376	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
393	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
394	C₄²×C₈₉	C₂⁴	1	8	yes	—
395	C₄²×C₈₉	C₂⁴	1	8	yes	—
396	C₄²×C₈₉	C₂⁴	1	16	yes	—
397	C₄²×C₈₉	C₂⁴	1	16	yes	—
398	C₂³×C₈₉	—	2	2	no	—
399	C₂³×C₈₉	—	2	2	no	—
400	C₂³×C₈₉	—	2	2	no	—
401	C₂³×C₈₉	—	2	4	no	—
402	C₂³×C₈₉	—	2	4	no	—
403	C₂³×C₈₉	—	2	4	no	—
404	C₂³×C₈₉	—	2	2	no	—
405	C₂³×C₈₉	—	2	4	no	—
406	C₂³×C₈₉	—	2	8	no	—
407	C₂³×C₈₉	—	4	1	no	—
408	C₂³×C₈₉	—	4	2	no	—
409	C₂³×C₈₉	—	4	1	no	—
410	C₂³×C₈₉	—	4	1	no	—
411	C₂³×C₈₉	—	4	2	no	—
412	C₂³×C₈₉	—	4	1	no	—
413	C₂³×C₈₉	—	4	4	no	—
414	C₂³×C₈₉	—	4	4	no	—
415	C₂³×C₈₉	—	4	16	no	—
416	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	complemented
417	C₂³×C₈₉	C₂⁵	1	2	yes	—
418	C₂³×C₈₉	C₂⁵	1	8	yes	—
419	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
420	C₂³×C₈₉	C₂⁵	1	2	yes	—
421	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
422	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
423	Q₈×C₈₉	—	2	16	no	—
424	Q₈×C₈₉	—	2	8	no	—
425	Q₈×C₈₉	—	4	8	no	—
426	Q₈×C₈₉	—	4	8	no	—
427	Q₈×C₈₉	—	4	4	no	—
428	Q₈×C₈₉	—	4	8	no	—
429	D₄×C₈₉	—	2	16	no	—
430	D₄×C₈₉	—	2	16	no	—
431	D₄×C₈₉	—	2	16	no	—
432	D₄×C₈₉	—	2	16	no	—
433	D₄×C₈₉	—	2	8	no	—
434	D₄×C₈₉	—	4	8	no	—
435	D₄×C₈₉	—	4	4	no	—
436	D₄×C₈₉	—	4	8	no	—
437	D₄×C₈₉	—	4	8	no	—
438	D₄×C₈₉	—	4	8	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	4	no	—
441	C₂×C₄×C₈₉	—	2	8	no	—
442	C₂×C₄×C₈₉	—	2	8	no	—
443	C₂×C₄×C₈₉	—	2	8	no	—
444	C₂×C₄×C₈₉	—	2	4	no	—
445	C₂×C₄×C₈₉	—	2	4	no	—
446	C₂×C₄×C₈₉	—	2	4	no	—
447	C₂×C₄×C₈₉	—	2	4	no	—
448	C₂×C₄×C₈₉	—	2	4	no	—
449	C₂×C₄×C₈₉	—	2	4	no	—
450	C₂×C₄×C₈₉	—	2	16	no	—
451	C₂×C₄×C₈₉	—	4	1	no	—
452	C₂×C₄×C₈₉	—	4	2	no	—
453	C₂×C₄×C₈₉	—	4	2	no	—
454	C₂×C₄×C₈₉	—	4	2	no	—
455	C₂×C₄×C₈₉	—	4	1	no	—
456	C₂×C₄×C₈₉	—	4	2	no	—
457	C₂×C₄×C₈₉	—	4	2	no	—
458	C₂×C₄×C₈₉	—	4	4	no	—
459	C₂×C₄×C₈₉	—	4	4	no	—
460	C₂×C₄×C₈₉	—	4	4	no	—
461	C₂×C₄×C₈₉	—	4	4	no	—
462	C₂×C₄×C₈₉	—	4	4	no	—
463	C₂×C₄×C₈₉	—	4	8	no	—
464	C₂×C₄×C₈₉	—	4	4	no	—
465	C₂×C₄×C₈₉	—	4	16	no	—
466	C₂×C₄×C₈₉	—	4	16	no	—
467	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
468	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
469	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
470	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
471	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
472	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
473	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
474	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
475	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
476	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
477	C₂²×C₈₉	—	2	8	no	—
478	C₂²×C₈₉	—	2	1	no	—
479	C₂²×C₈₉	—	2	1	no	—
480	C₂²×C₈₉	—	2	2	no	—
481	C₂²×C₈₉	—	2	1	no	—
482	C₂²×C₈₉	—	2	1	no	—
483	C₂²×C₈₉	—	2	1	no	—
484	C₂²×C₈₉	—	2	1	no	—
485	C₂²×C₈₉	—	2	2	no	—
486	C₂²×C₈₉	—	2	2	no	—
487	C₂²×C₈₉	—	2	8	no	—
488	C₂²×C₈₉	—	2	8	no	—
489	C₂²×C₈₉	—	2	2	no	—
490	C₂²×C₈₉	—	2	8	no	—
491	C₂²×C₈₉	—	2	2	no	—
492	C₂²×C₈₉	—	4	4	no	—
493	C₂²×C₈₉	—	4	8	no	—
494	C₂²×C₈₉	—	4	8	no	—
495	C₂²×C₈₉	—	4	4	no	—
496	C₂²×C₈₉	—	8	8	no	—
497	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	4	yes	—
499	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
500	C₂²×C₈₉	#585	1	2	yes	—
501	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
502	C₄×C₈₉	—	2	2	no	—
503	C₄×C₈₉	—	2	2	no	—
504	C₄×C₈₉	—	2	2	no	—
505	C₄×C₈₉	—	2	8	no	—
506	C₄×C₈₉	—	2	8	no	—
507	C₄×C₈₉	—	2	8	no	—
508	C₄×C₈₉	—	2	8	no	—
509	C₄×C₈₉	—	2	8	no	—
510	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
511	#62819	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂×C₈₉	—	2	2	no	—
513	C₂×C₈₉	—	2	2	no	—
514	C₂×C₈₉	—	2	2	no	—
515	C₂×C₈₉	—	2	4	no	—
516	C₂×C₈₉	—	4	2	no	—
517	C₂×C₈₉	—	4	8	no	—
518	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×C₈₉	C₂×#585	1	1	yes	characteristic
521	#3541	C₂×C₈₉	1	8	yes	complemented
522	#3538	C₂×C₈₉	1	4	yes	complemented
523	#3536	C₂×C₈₉	1	4	yes	complemented
524	#3535	C₂×C₈₉	1	8	yes	complemented
525	#3520	C₂×C₈₉	1	8	yes	complemented
526	#3505	C₂×C₈₉	1	4	yes	complemented
527	#3501	C₂×C₈₉	1	4	yes	complemented
528	#3495	C₂×C₈₉	1	4	yes	complemented
529	#3492	C₂×C₈₉	1	2	yes	complemented
530	#3492	C₂×C₈₉	1	4	yes	complemented
531	#3490	C₂×C₈₉	1	4	yes	complemented
532	#3489	C₂×C₈₉	1	4	yes	complemented
533	#3486	C₂×C₈₉	1	2	yes	complemented
534	C₂×#525	C₂×C₈₉	1	2	yes	complemented
535	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
536	C₈₉	#62819	1	1	yes	characteristic, direct product factor, Sylow
537	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
538	C₂²×#41	C₂²×C₈₉	1	2	yes	complemented
539	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
540	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
541	#563	C₂²×C₈₉	1	16	yes	complemented
542	#562	C₂²×C₈₉	1	16	yes	complemented
543	#556	C₂²×C₈₉	1	8	yes	complemented
544	#554	C₂²×C₈₉	1	8	yes	complemented
545	#554	C₂²×C₈₉	1	16	yes	complemented
546	#554	C₂²×C₈₉	1	8	yes	complemented
547	#554	C₂²×C₈₉	1	16	yes	complemented
548	#553	C₂²×C₈₉	1	8	yes	complemented
549	#553	C₂²×C₈₉	1	16	yes	complemented
550	#552	C₂²×C₈₉	1	16	yes	complemented
551	#552	C₂²×C₈₉	1	8	yes	complemented
552	#552	C₂²×C₈₉	1	8	yes	complemented
553	#552	C₂²×C₈₉	1	8	yes	complemented
554	#551	C₂²×C₈₉	1	16	yes	complemented
555	#551	C₂²×C₈₉	1	16	yes	complemented
556	#551	C₂²×C₈₉	1	16	yes	complemented
557	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
558	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
559	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
560	#548	C₂²×C₈₉	1	8	yes	complemented
561	#548	C₂²×C₈₉	1	8	yes	complemented
562	#548	C₂²×C₈₉	1	8	yes	complemented
563	#547	C₂²×C₈₉	1	16	yes	complemented
564	#547	C₂²×C₈₉	1	8	yes	complemented
565	#547	C₂²×C₈₉	1	8	yes	complemented
566	#546	C₂²×C₈₉	1	16	yes	complemented
567	#546	C₂²×C₈₉	1	16	yes	complemented
568	#546	C₂²×C₈₉	1	8	yes	complemented
569	#544	C₂²×C₈₉	1	2	yes	complemented
570	#544	C₂²×C₈₉	1	4	yes	complemented
571	#544	C₂²×C₈₉	1	8	yes	complemented
572	#543	C₂²×C₈₉	1	4	yes	—
573	#543	C₂²×C₈₉	1	8	yes	complemented
574	#542	C₂²×C₈₉	1	8	yes	complemented
575	#542	C₂²×C₈₉	1	16	yes	complemented
576	#541	C₂²×C₈₉	1	8	yes	complemented
577	#539	C₂²×C₈₉	1	8	yes	complemented
578	#539	C₂²×C₈₉	1	8	yes	complemented
579	#539	C₂²×C₈₉	1	8	yes	complemented
580	#539	C₂²×C₈₉	1	8	yes	complemented
581	#539	C₂²×C₈₉	1	16	yes	complemented
582	#538	C₂²×C₈₉	1	8	yes	complemented
583	#538	C₂²×C₈₉	1	8	yes	complemented
584	#538	C₂²×C₈₉	1	8	yes	complemented
585	#537	C₂²×C₈₉	1	2	yes	complemented
586	#537	C₂²×C₈₉	1	4	yes	complemented
587	#537	C₂²×C₈₉	1	8	yes	complemented
588	#536	C₂²×C₈₉	1	4	yes	complemented
589	#536	C₂²×C₈₉	1	8	yes	complemented
590	#536	C₂²×C₈₉	1	8	yes	complemented
591	#534	C₂²×C₈₉	1	4	yes	—
592	#533	C₂²×C₈₉	1	8	yes	complemented
593	#529	C₂²×C₈₉	1	8	yes	complemented
594	#525	C₂²×C₈₉	1	4	yes	—
595	#525	C₂²×C₈₉	1	4	yes	—
596	#525	C₂²×C₈₉	1	4	yes	—
597	#525	C₂²×C₈₉	1	4	yes	—
598	#525	C₂²×C₈₉	1	4	yes	complemented
599	#525	C₂²×C₈₉	1	4	yes	complemented
600	#525	C₂²×C₈₉	1	4	yes	complemented
601	#525	C₂²×C₈₉	1	4	yes	complemented
602	#525	C₂²×C₈₉	1	8	yes	complemented
603	#525	C₂²×C₈₉	1	8	yes	complemented
604	#525	C₂²×C₈₉	1	8	yes	complemented
605	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
606	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
607	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
608	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
609	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
610	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
611	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
612	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
613	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
614	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
615	C₂×#121	C₂²×C₈₉	1	2	yes	—
616	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
617	C₂×#120	C₂²×C₈₉	1	4	yes	—
618	#520	C₂²×C₈₉	1	4	yes	complemented
619	#520	C₂²×C₈₉	1	8	yes	complemented
620	#519	C₂²×C₈₉	1	2	yes	complemented
621	#518	C₂²×C₈₉	1	8	yes	—
622	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
623	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
624	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
625	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
626	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
627	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
628	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
629	2₋¹⁺⁴	—	4	8	no	—
630	C₂×#41	—	4	8	no	—
631	C₂×#41	C₂³×C₈₉	1	4	yes	—
632	C₂×#41	C₂³×C₈₉	1	8	yes	—
633	C₂×#41	C₂³×C₈₉	1	4	yes	—
634	C₂×#41	C₂³×C₈₉	1	4	yes	—
635	C₂×#41	C₂³×C₈₉	1	4	yes	—
636	C₂×#41	C₂³×C₈₉	1	8	yes	—
637	C₂×#41	C₂³×C₈₉	1	8	yes	complemented
638	C₂²×Q₈	—	4	4	no	—
639	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
640	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
641	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
642	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
643	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
644	C₂²×Q₈	C₂³×C₈₉	1	8	yes	complemented
645	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
646	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
647	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
648	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
649	C₂³×C₄	—	4	4	no	—
650	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
652	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
653	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
654	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
656	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
657	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
658	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
659	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
660	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
661	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
662	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
663	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
664	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
665	#126	C₂³×C₈₉	1	16	yes	—
666	#126	C₂³×C₈₉	1	16	yes	—
667	#126	C₂³×C₈₉	1	16	yes	complemented
668	#126	C₂³×C₈₉	1	16	yes	complemented
669	#126	C₂³×C₈₉	1	16	yes	complemented
670	#125	C₂³×C₈₉	1	8	yes	complemented
671	#125	C₂³×C₈₉	1	16	yes	complemented
672	#125	C₂³×C₈₉	1	16	yes	complemented
673	#125	C₂³×C₈₉	1	16	yes	complemented
674	#125	C₂³×C₈₉	1	16	yes	complemented
675	#124	C₂³×C₈₉	1	16	yes	—
676	#124	C₂³×C₈₉	1	16	yes	—
677	#124	C₂³×C₈₉	1	8	yes	complemented
678	#124	C₂³×C₈₉	1	16	yes	complemented
679	#123	C₂³×C₈₉	1	8	yes	—
680	#123	C₂³×C₈₉	1	8	yes	—
681	#123	C₂³×C₈₉	1	8	yes	—
682	#123	C₂³×C₈₉	1	8	yes	—
683	#123	C₂³×C₈₉	1	16	yes	—
684	#123	C₂³×C₈₉	1	16	yes	—
685	#123	C₂³×C₈₉	1	16	yes	—
686	#123	C₂³×C₈₉	1	16	yes	—
687	#123	C₂³×C₈₉	1	16	yes	—
688	#123	C₂³×C₈₉	1	16	yes	complemented
689	#123	C₂³×C₈₉	1	16	yes	complemented
690	#123	C₂³×C₈₉	1	16	yes	complemented
691	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
698	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
699	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
700	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
701	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
703	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
704	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
705	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
706	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
707	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
708	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
709	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
710	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
711	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
712	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
713	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
714	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
715	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
716	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
717	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
718	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
719	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
720	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
721	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
722	#121	C₂³×C₈₉	1	4	yes	—
723	#121	C₂³×C₈₉	1	4	yes	—
724	#121	C₂³×C₈₉	1	4	yes	—
725	#121	C₂³×C₈₉	1	4	yes	—
726	#121	C₂³×C₈₉	1	4	yes	—
727	#121	C₂³×C₈₉	1	4	yes	—
728	#121	C₂³×C₈₉	1	4	yes	—
729	#121	C₂³×C₈₉	1	4	yes	—
730	#121	C₂³×C₈₉	1	8	yes	—
731	#121	C₂³×C₈₉	1	8	yes	—
732	#121	C₂³×C₈₉	1	8	yes	—
733	#121	C₂³×C₈₉	1	8	yes	—
734	#121	C₂³×C₈₉	1	16	yes	—
735	#121	C₂³×C₈₉	1	16	yes	—
736	#121	C₂³×C₈₉	1	8	yes	complemented
737	#121	C₂³×C₈₉	1	16	yes	complemented
738	#120	C₂³×C₈₉	1	8	yes	—
739	#120	C₂³×C₈₉	1	8	yes	—
740	#120	C₂³×C₈₉	1	8	yes	—
741	#120	C₂³×C₈₉	1	8	yes	—
742	#120	C₂³×C₈₉	1	16	yes	—
743	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
744	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
745	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
746	C₄×Q₈	C₂³×C₈₉	1	16	yes	complemented
747	C₄×D₄	C₂³×C₈₉	1	8	yes	—
748	C₄×D₄	C₂³×C₈₉	1	8	yes	—
749	C₄×D₄	C₂³×C₈₉	1	8	yes	—
750	C₄×D₄	C₂³×C₈₉	1	8	yes	—
751	C₄×D₄	C₂³×C₈₉	1	8	yes	—
752	C₄×D₄	C₂³×C₈₉	1	8	yes	—
753	C₄×D₄	C₂³×C₈₉	1	8	yes	—
754	C₄×D₄	C₂³×C₈₉	1	8	yes	—
755	C₄×D₄	C₂³×C₈₉	1	16	yes	—
756	C₄×D₄	C₂³×C₈₉	1	16	yes	—
757	C₄×D₄	C₂³×C₈₉	1	16	yes	—
758	C₄×D₄	C₂³×C₈₉	1	16	yes	—
759	C₄×D₄	C₂³×C₈₉	1	16	yes	—
760	C₄×D₄	C₂³×C₈₉	1	16	yes	—
761	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
762	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
763	#117	C₂³×C₈₉	1	4	yes	—
764	#117	C₂³×C₈₉	1	4	yes	—
765	#117	C₂³×C₈₉	1	4	yes	—
766	#117	C₂³×C₈₉	1	4	yes	—
767	#117	C₂³×C₈₉	1	16	yes	—
768	#117	C₂³×C₈₉	1	8	yes	—
769	#117	C₂³×C₈₉	1	8	yes	—
770	#117	C₂³×C₈₉	1	8	yes	complemented
771	#117	C₂³×C₈₉	1	16	yes	complemented
772	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
774	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
775	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
776	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
777	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
779	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
780	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
783	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
784	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
785	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	complemented
786	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
796	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
797	C₂⁴	—	2	4	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
801	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
802	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
803	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
804	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
805	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
806	#41	—	2	16	no	—
807	#41	—	4	8	no	—
808	#41	—	4	8	no	—
809	#41	—	4	16	no	—
810	#41	—	4	16	no	—
811	#41	—	4	8	no	—
812	#41	—	4	16	no	—
813	C₂×Q₈	—	2	8	no	—
814	C₂×Q₈	—	4	4	no	—
815	C₂×Q₈	—	4	8	no	—
816	C₂×Q₈	—	4	8	no	—
817	C₂×Q₈	—	4	4	no	—
818	C₂×Q₈	—	4	16	no	—
819	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
820	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
821	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
822	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
823	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
824	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
825	C₂×D₄	—	2	16	no	—
826	C₂×D₄	—	4	4	no	—
827	C₂×D₄	—	4	8	no	—
828	C₂×D₄	—	4	8	no	—
829	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
830	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
831	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
832	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
833	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
834	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
835	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
836	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
837	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
838	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	8	no	—
841	C₂²×C₄	—	4	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	—	4	4	no	—
845	C₂²×C₄	—	4	8	no	—
846	C₂²×C₄	—	4	4	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	4	no	—
849	C₂²×C₄	—	4	4	no	—
850	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
852	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
860	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
864	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
866	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
869	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
871	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
872	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
879	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
881	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
882	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
883	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
884	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
885	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
886	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
887	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
888	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
891	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
893	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
894	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
895	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
896	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
897	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
898	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
900	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
902	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
907	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
908	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
910	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
911	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
914	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
915	C₄²	C₂⁴×C₈₉	1	8	yes	—
916	C₄²	C₂⁴×C₈₉	1	8	yes	—
917	C₄²	C₂⁴×C₈₉	1	16	yes	—
918	C₄²	C₂⁴×C₈₉	1	16	yes	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	4	no	—
923	C₂³	—	2	4	no	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	4	1	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	1	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	4	no	—
935	C₂³	—	4	4	no	—
936	C₂³	—	4	16	no	—
937	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	complemented
938	C₂³	C₂⁵×C₈₉	1	2	yes	—
939	C₂³	C₂⁵×C₈₉	1	8	yes	—
940	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
941	C₂³	C₂⁵×C₈₉	1	2	yes	—
942	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
943	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
944	Q₈	—	2	16	no	—
945	Q₈	—	2	8	no	—
946	Q₈	—	4	8	no	—
947	Q₈	—	4	8	no	—
948	Q₈	—	4	4	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	16	no	—
954	D₄	—	2	8	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	8	no	—
959	D₄	—	4	8	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	8	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	16	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	16	no	—
987	C₂×C₄	—	4	16	no	—
988	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
989	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
990	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
991	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
992	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
993	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
994	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
995	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
996	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
997	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
998	C₂²	—	2	8	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	8	no	—
1015	C₂²	—	4	8	no	—
1016	C₂²	—	4	4	no	—
1017	C₂²	—	8	8	no	—
1018	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
1019	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	4	yes	—
1020	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
1021	C₂²	#585×C₈₉	1	2	yes	—
1022	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	8	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	8	no	—
1031	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
1032	C₂	—	2	2	no	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	2	no	—
1035	C₂	—	2	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	8	no	—
1038	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1039	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1040	C₂	C₂×#585×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3541	C₂	semidirect
2. C₈₉×#3538	C₂	semidirect
3. C₈₉×#3536	C₂	semidirect
4. C₈₉×#3535	C₂	semidirect
5. C₈₉×#3520	C₂	semidirect
6. C₈₉×#3505	C₂	semidirect
7. C₈₉×#3501	C₂	semidirect
8. C₈₉×#3495	C₂	semidirect
9. C₈₉×#3492	C₂	semidirect
10. C₈₉×#3492	C₂	semidirect
11. C₈₉×#3490	C₂	semidirect
12. C₈₉×#3489	C₂	semidirect
13. C₈₉×#3486	C₂	semidirect
14. C₂×#525×C₈₉	C₂	semidirect
15. C₂²×C₂²⋊Q₈×C₈₉	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
17. C₂²×#41×C₈₉	C₂²	semidirect
18. C₂³×Q₈×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. #556×C₈₉	C₂²	semidirect
23. #554×C₈₉	C₂²	semidirect
24. #554×C₈₉	C₂²	semidirect
25. #554×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
29. #552×C₈₉	C₂²	semidirect
30. #552×C₈₉	C₂²	semidirect
31. #552×C₈₉	C₂²	semidirect
32. #552×C₈₉	C₂²	semidirect
33. #551×C₈₉	C₂²	semidirect
34. #551×C₈₉	C₂²	semidirect
35. #551×C₈₉	C₂²	semidirect
36. D₄×Q₈×C₈₉	C₂²	semidirect
37. D₄×Q₈×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. #548×C₈₉	C₂²	semidirect
40. #548×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
42. #547×C₈₉	C₂²	semidirect
43. #547×C₈₉	C₂²	semidirect
44. #547×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #546×C₈₉	C₂²	semidirect
47. #546×C₈₉	C₂²	semidirect
48. #544×C₈₉	C₂²	semidirect
49. #544×C₈₉	C₂²	semidirect
50. #544×C₈₉	C₂²	semidirect
52. #543×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #542×C₈₉	C₂²	semidirect
55. #541×C₈₉	C₂²	semidirect
56. #539×C₈₉	C₂²	semidirect
57. #539×C₈₉	C₂²	semidirect
58. #539×C₈₉	C₂²	semidirect
59. #539×C₈₉	C₂²	semidirect
60. #539×C₈₉	C₂²	semidirect
61. #538×C₈₉	C₂²	semidirect
62. #538×C₈₉	C₂²	semidirect
63. #538×C₈₉	C₂²	semidirect
64. #537×C₈₉	C₂²	semidirect
65. #537×C₈₉	C₂²	semidirect
66. #537×C₈₉	C₂²	semidirect
67. #536×C₈₉	C₂²	semidirect
68. #536×C₈₉	C₂²	semidirect
69. #536×C₈₉	C₂²	semidirect
71. #533×C₈₉	C₂²	semidirect
72. #529×C₈₉	C₂²	semidirect
77. #525×C₈₉	C₂²	semidirect
78. #525×C₈₉	C₂²	semidirect
79. #525×C₈₉	C₂²	semidirect
80. #525×C₈₉	C₂²	semidirect
81. #525×C₈₉	C₂²	semidirect
82. #525×C₈₉	C₂²	semidirect
83. #525×C₈₉	C₂²	semidirect
84. C₂×#123×C₈₉	C₂²	semidirect
87. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
90. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
91. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
92. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
93. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
95. C₂×#121×C₈₉	C₂²	semidirect
97. #520×C₈₉	C₂²	semidirect
98. #520×C₈₉	C₂²	semidirect
99. #519×C₈₉	C₂²	semidirect
102. C₂×C₄×D₄×C₈₉	C₂²	semidirect
103. C₂×#117×C₈₉	C₂²	semidirect
104. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
105. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
116. C₂×#41×C₈₉	C₂³	semidirect
123. C₂²×Q₈×C₈₉	C₂³	semidirect
140. C₄⋊Q₈×C₈₉	C₂³	semidirect
141. C₄⋊Q₈×C₈₉	C₂³	semidirect
142. C₄⋊Q₈×C₈₉	C₂³	semidirect
143. C₄⋊Q₈×C₈₉	C₂³	semidirect
146. #126×C₈₉	C₂³	semidirect
147. #126×C₈₉	C₂³	semidirect
148. #126×C₈₉	C₂³	semidirect
149. #125×C₈₉	C₂³	semidirect
150. #125×C₈₉	C₂³	semidirect
151. #125×C₈₉	C₂³	semidirect
152. #125×C₈₉	C₂³	semidirect
153. #125×C₈₉	C₂³	semidirect
156. #124×C₈₉	C₂³	semidirect
157. #124×C₈₉	C₂³	semidirect
167. #123×C₈₉	C₂³	semidirect
168. #123×C₈₉	C₂³	semidirect
169. #123×C₈₉	C₂³	semidirect
192. C₂²⋊Q₈×C₈₉	C₂³	semidirect
193. C₂²⋊Q₈×C₈₉	C₂³	semidirect
194. C₂²⋊Q₈×C₈₉	C₂³	semidirect
195. C₂²⋊Q₈×C₈₉	C₂³	semidirect
196. C₂²⋊Q₈×C₈₉	C₂³	semidirect
197. C₂²⋊Q₈×C₈₉	C₂³	semidirect
198. C₂²⋊Q₈×C₈₉	C₂³	semidirect
199. C₂²⋊Q₈×C₈₉	C₂³	semidirect
200. C₂²⋊Q₈×C₈₉	C₂³	semidirect
215. #121×C₈₉	C₂³	semidirect
216. #121×C₈₉	C₂³	semidirect
222. C₄×Q₈×C₈₉	C₂³	semidirect
223. C₄×Q₈×C₈₉	C₂³	semidirect
224. C₄×Q₈×C₈₉	C₂³	semidirect
225. C₄×Q₈×C₈₉	C₂³	semidirect
240. C₄×D₄×C₈₉	C₂³	semidirect
241. C₄×D₄×C₈₉	C₂³	semidirect
249. #117×C₈₉	C₂³	semidirect
250. #117×C₈₉	C₂³	semidirect
263. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
264. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
416. C₂³×C₈₉	2₋¹⁺⁴	semidirect
511. #62819	C₈₉	direct (N × H)
521. #3541	C₂×C₈₉	semidirect
522. #3538	C₂×C₈₉	semidirect
523. #3536	C₂×C₈₉	semidirect
524. #3535	C₂×C₈₉	semidirect
525. #3520	C₂×C₈₉	semidirect
526. #3505	C₂×C₈₉	semidirect
527. #3501	C₂×C₈₉	semidirect
528. #3495	C₂×C₈₉	semidirect
529. #3492	C₂×C₈₉	semidirect
530. #3492	C₂×C₈₉	semidirect
531. #3490	C₂×C₈₉	semidirect
532. #3489	C₂×C₈₉	semidirect
533. #3486	C₂×C₈₉	semidirect
534. C₂×#525	C₂×C₈₉	semidirect
535. C₂²×C₂²⋊Q₈	C₂×C₈₉	semidirect
536. C₈₉	#62819	direct (N × H)
537. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
538. C₂²×#41	C₂²×C₈₉	semidirect
539. C₂³×Q₈	C₂²×C₈₉	semidirect
541. #563	C₂²×C₈₉	semidirect
542. #562	C₂²×C₈₉	semidirect
543. #556	C₂²×C₈₉	semidirect
544. #554	C₂²×C₈₉	semidirect
545. #554	C₂²×C₈₉	semidirect
546. #554	C₂²×C₈₉	semidirect
547. #554	C₂²×C₈₉	semidirect
548. #553	C₂²×C₈₉	semidirect
549. #553	C₂²×C₈₉	semidirect
550. #552	C₂²×C₈₉	semidirect
551. #552	C₂²×C₈₉	semidirect
552. #552	C₂²×C₈₉	semidirect
553. #552	C₂²×C₈₉	semidirect
554. #551	C₂²×C₈₉	semidirect
555. #551	C₂²×C₈₉	semidirect
556. #551	C₂²×C₈₉	semidirect
557. D₄×Q₈	C₂²×C₈₉	semidirect
558. D₄×Q₈	C₂²×C₈₉	semidirect
559. D₄×Q₈	C₂²×C₈₉	semidirect
560. #548	C₂²×C₈₉	semidirect
561. #548	C₂²×C₈₉	semidirect
562. #548	C₂²×C₈₉	semidirect
563. #547	C₂²×C₈₉	semidirect
564. #547	C₂²×C₈₉	semidirect
565. #547	C₂²×C₈₉	semidirect
566. #546	C₂²×C₈₉	semidirect
567. #546	C₂²×C₈₉	semidirect
568. #546	C₂²×C₈₉	semidirect
569. #544	C₂²×C₈₉	semidirect
570. #544	C₂²×C₈₉	semidirect
571. #544	C₂²×C₈₉	semidirect
573. #543	C₂²×C₈₉	semidirect
574. #542	C₂²×C₈₉	semidirect
575. #542	C₂²×C₈₉	semidirect
576. #541	C₂²×C₈₉	semidirect
577. #539	C₂²×C₈₉	semidirect
578. #539	C₂²×C₈₉	semidirect
579. #539	C₂²×C₈₉	semidirect
580. #539	C₂²×C₈₉	semidirect
581. #539	C₂²×C₈₉	semidirect
582. #538	C₂²×C₈₉	semidirect
583. #538	C₂²×C₈₉	semidirect
584. #538	C₂²×C₈₉	semidirect
585. #537	C₂²×C₈₉	semidirect
586. #537	C₂²×C₈₉	semidirect
587. #537	C₂²×C₈₉	semidirect
588. #536	C₂²×C₈₉	semidirect
589. #536	C₂²×C₈₉	semidirect
590. #536	C₂²×C₈₉	semidirect
592. #533	C₂²×C₈₉	semidirect
593. #529	C₂²×C₈₉	semidirect
598. #525	C₂²×C₈₉	semidirect
599. #525	C₂²×C₈₉	semidirect
600. #525	C₂²×C₈₉	semidirect
601. #525	C₂²×C₈₉	semidirect
602. #525	C₂²×C₈₉	semidirect
603. #525	C₂²×C₈₉	semidirect
604. #525	C₂²×C₈₉	semidirect
605. C₂×#123	C₂²×C₈₉	semidirect
608. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
609. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
610. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
611. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
612. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
613. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
614. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
616. C₂×#121	C₂²×C₈₉	semidirect
618. #520	C₂²×C₈₉	semidirect
619. #520	C₂²×C₈₉	semidirect
620. #519	C₂²×C₈₉	semidirect
623. C₂×C₄×D₄	C₂²×C₈₉	semidirect
624. C₂×#117	C₂²×C₈₉	semidirect
625. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
626. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
637. C₂×#41	C₂³×C₈₉	semidirect
644. C₂²×Q₈	C₂³×C₈₉	semidirect
661. C₄⋊Q₈	C₂³×C₈₉	semidirect
662. C₄⋊Q₈	C₂³×C₈₉	semidirect
663. C₄⋊Q₈	C₂³×C₈₉	semidirect
664. C₄⋊Q₈	C₂³×C₈₉	semidirect
667. #126	C₂³×C₈₉	semidirect
668. #126	C₂³×C₈₉	semidirect
669. #126	C₂³×C₈₉	semidirect
670. #125	C₂³×C₈₉	semidirect
671. #125	C₂³×C₈₉	semidirect
672. #125	C₂³×C₈₉	semidirect
673. #125	C₂³×C₈₉	semidirect
674. #125	C₂³×C₈₉	semidirect
677. #124	C₂³×C₈₉	semidirect
678. #124	C₂³×C₈₉	semidirect
688. #123	C₂³×C₈₉	semidirect
689. #123	C₂³×C₈₉	semidirect
690. #123	C₂³×C₈₉	semidirect
713. C₂²⋊Q₈	C₂³×C₈₉	semidirect
714. C₂²⋊Q₈	C₂³×C₈₉	semidirect
715. C₂²⋊Q₈	C₂³×C₈₉	semidirect
716. C₂²⋊Q₈	C₂³×C₈₉	semidirect
717. C₂²⋊Q₈	C₂³×C₈₉	semidirect
718. C₂²⋊Q₈	C₂³×C₈₉	semidirect
719. C₂²⋊Q₈	C₂³×C₈₉	semidirect
720. C₂²⋊Q₈	C₂³×C₈₉	semidirect
721. C₂²⋊Q₈	C₂³×C₈₉	semidirect
736. #121	C₂³×C₈₉	semidirect
737. #121	C₂³×C₈₉	semidirect
743. C₄×Q₈	C₂³×C₈₉	semidirect
744. C₄×Q₈	C₂³×C₈₉	semidirect
745. C₄×Q₈	C₂³×C₈₉	semidirect
746. C₄×Q₈	C₂³×C₈₉	semidirect
761. C₄×D₄	C₂³×C₈₉	semidirect
762. C₄×D₄	C₂³×C₈₉	semidirect
770. #117	C₂³×C₈₉	semidirect
771. #117	C₂³×C₈₉	semidirect
784. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
785. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
937. C₂³	2₋¹⁺⁴×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3541	2
C₈₉×#3538	2
C₈₉×#3536	2
C₈₉×#3535	2
C₈₉×#3520	2
C₈₉×#3505	2
C₈₉×#3501	2
C₈₉×#3495	2
C₈₉×#3492	2
C₈₉×#3490	2
C₈₉×#3489	2
C₈₉×#3486	2
C₂×#525×C₈₉	2
C₂²×C₂²⋊Q₈×C₈₉	2
#62819	89

Subgroups — C89×#62819 #36440667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62819 #36440667