Subgroups — C₈₉×#62861 #36440709

Order 22784.

6854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3523	C₂	1	4	yes	maximal, complemented
2	C₈₉×#3521	C₂	1	12	yes	maximal, complemented
3	C₈₉×#3516	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3515	C₂	1	12	yes	maximal, complemented
5	C₈₉×#3512	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3509	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3495	C₂	1	6	yes	maximal, complemented
10	C₈₉×#3489	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3461	C₂	1	6	yes	maximal, complemented
12	C₈₉×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×#541×C₈₉	C₂	1	3	yes	maximal, complemented
14	C₄×2₋¹⁺⁴×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	#557×C₈₉	C₂²	1	4	yes	complemented
19	#557×C₈₉	C₂²	1	12	yes	complemented
20	#556×C₈₉	C₂²	1	12	yes	—
21	#556×C₈₉	C₂²	1	12	yes	complemented
22	#554×C₈₉	C₂²	1	12	yes	complemented
23	#554×C₈₉	C₂²	1	12	yes	complemented
24	#553×C₈₉	C₂²	1	24	yes	complemented
25	#553×C₈₉	C₂²	1	12	yes	complemented
26	#552×C₈₉	C₂²	1	12	yes	—
27	#552×C₈₉	C₂²	1	24	yes	complemented
28	#552×C₈₉	C₂²	1	12	yes	complemented
29	#552×C₈₉	C₂²	1	24	yes	complemented
30	#552×C₈₉	C₂²	1	12	yes	complemented
31	#551×C₈₉	C₂²	1	24	yes	—
32	D₄×Q₈×C₈₉	C₂²	1	4	yes	—
33	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
34	#548×C₈₉	C₂²	1	4	yes	—
35	#547×C₈₉	C₂²	1	12	yes	—
36	#547×C₈₉	C₂²	1	12	yes	complemented
37	#546×C₈₉	C₂²	1	12	yes	—
38	#544×C₈₉	C₂²	1	6	yes	complemented
39	#542×C₈₉	C₂²	1	6	yes	—
40	#542×C₈₉	C₂²	1	6	yes	complemented
41	#542×C₈₉	C₂²	1	12	yes	complemented
42	#541×C₈₉	C₂²	1	3	yes	—
43	#541×C₈₉	C₂²	1	6	yes	—
44	#541×C₈₉	C₂²	1	12	yes	—
45	#541×C₈₉	C₂²	1	6	yes	complemented
46	#541×C₈₉	C₂²	1	6	yes	complemented
47	#541×C₈₉	C₂²	1	12	yes	complemented
48	#541×C₈₉	C₂²	1	3	yes	complemented
49	#541×C₈₉	C₂²	1	12	yes	complemented
50	#540×C₈₉	C₂²	1	1	yes	characteristic
51	#540×C₈₉	C₂²	1	3	yes	complemented
52	#539×C₈₉	C₂²	1	12	yes	complemented
53	#539×C₈₉	C₂²	1	24	yes	complemented
54	#538×C₈₉	C₂²	1	12	yes	—
55	#537×C₈₉	C₂²	1	6	yes	—
56	#536×C₈₉	C₂²	1	6	yes	—
57	#536×C₈₉	C₂²	1	6	yes	complemented
58	#533×C₈₉	C₂²	1	3	yes	complemented
59	#533×C₈₉	C₂²	1	12	yes	complemented
60	#533×C₈₉	C₂²	1	12	yes	complemented
61	#532×C₈₉	C₂²	1	3	yes	complemented
62	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
63	#529×C₈₉	C₂²	1	12	yes	—
64	#529×C₈₉	C₂²	1	12	yes	complemented
65	#529×C₈₉	C₂²	1	12	yes	complemented
66	#529×C₈₉	C₂²	1	24	yes	complemented
67	#529×C₈₉	C₂²	1	12	yes	complemented
68	C₂×#126×C₈₉	C₂²	1	12	yes	—
69	C₂×#125×C₈₉	C₂²	1	3	yes	complemented
70	C₂×#125×C₈₉	C₂²	1	12	yes	complemented
71	#525×C₈₉	C₂²	1	6	yes	—
72	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
73	#520×C₈₉	C₂²	1	6	yes	—
74	#520×C₈₉	C₂²	1	2	yes	—
75	#520×C₈₉	C₂²	1	2	yes	—
76	#520×C₈₉	C₂²	1	6	yes	complemented
77	#520×C₈₉	C₂²	1	12	yes	complemented
78	#519×C₈₉	C₂²	1	2	yes	—
79	#519×C₈₉	C₂²	1	6	yes	complemented
80	#519×C₈₉	C₂²	1	4	yes	complemented
81	#518×C₈₉	C₂²	1	6	yes	—
82	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
83	C₄×#41×C₈₉	C₂²	1	3	yes	—
84	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
85	C₄×#41×C₈₉	C₂²	1	3	yes	—
86	C₄×#41×C₈₉	C₂²	1	6	yes	complemented
87	C₄×#41×C₈₉	C₂²	1	12	yes	complemented
88	C₂×C₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
89	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
90	C₂×#117×C₈₉	C₂²	1	3	yes	—
91	C₂×#117×C₈₉	C₂²	1	3	yes	—
92	2₋¹⁺⁴×C₈₉	—	2	16	no	—
93	C₂×#41×C₈₉	—	2	8	no	—
94	C₂×#41×C₈₉	C₂³	1	3	yes	—
95	C₂×#41×C₈₉	C₂³	1	6	yes	—
96	C₂×#41×C₈₉	C₂³	1	12	yes	—
97	C₂×#41×C₈₉	C₂³	1	3	yes	—
98	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
101	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
105	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
106	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
107	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
108	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
109	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
110	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
111	#127×C₈₉	C₂³	1	1	yes	characteristic
112	#126×C₈₉	C₂³	1	12	yes	—
113	#126×C₈₉	C₂³	1	24	yes	—
114	#126×C₈₉	C₂³	1	24	yes	—
115	#126×C₈₉	C₂³	1	24	yes	—
116	#126×C₈₉	C₂³	1	12	yes	—
117	#126×C₈₉	C₂³	1	12	yes	—
118	#126×C₈₉	C₂³	1	24	yes	—
119	#126×C₈₉	C₂³	1	12	yes	—
120	#125×C₈₉	C₂³	1	12	yes	—
121	#125×C₈₉	C₂³	1	3	yes	—
122	#125×C₈₉	C₂³	1	6	yes	—
123	#125×C₈₉	C₂³	1	24	yes	—
124	#125×C₈₉	C₂³	1	24	yes	—
125	#125×C₈₉	C₂³	1	24	yes	—
126	#125×C₈₉	C₂³	1	12	yes	—
127	#125×C₈₉	C₂³	1	12	yes	—
128	#125×C₈₉	C₂³	1	12	yes	—
129	#125×C₈₉	C₂³	1	1	yes	characteristic
130	#125×C₈₉	C₂³	1	24	yes	—
131	#124×C₈₉	C₂³	1	12	yes	—
132	#124×C₈₉	C₂³	1	12	yes	—
133	#124×C₈₉	C₂³	1	6	yes	—
134	#124×C₈₉	C₂³	1	12	yes	—
135	#123×C₈₉	C₂³	1	12	yes	—
136	#123×C₈₉	C₂³	1	12	yes	—
137	#123×C₈₉	C₂³	1	12	yes	—
138	#123×C₈₉	C₂³	1	12	yes	—
139	#123×C₈₉	C₂³	1	4	yes	—
140	#123×C₈₉	C₂³	1	24	yes	—
141	#123×C₈₉	C₂³	1	24	yes	—
142	#123×C₈₉	C₂³	1	24	yes	—
143	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
146	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
147	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
148	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
149	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
156	#121×C₈₉	C₂³	1	2	yes	—
157	#121×C₈₉	C₂³	1	6	yes	—
158	#121×C₈₉	C₂³	1	4	yes	—
159	#121×C₈₉	C₂³	1	24	yes	—
160	#121×C₈₉	C₂³	1	12	yes	—
161	#121×C₈₉	C₂³	1	12	yes	—
162	#121×C₈₉	C₂³	1	12	yes	—
163	#120×C₈₉	C₂³	1	12	yes	—
164	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
167	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
173	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
174	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
175	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
176	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
177	C₄×Q₈×C₈₉	C₂³	1	24	yes	—
178	C₄×D₄×C₈₉	C₂³	1	6	yes	—
179	C₄×D₄×C₈₉	C₂³	1	12	yes	—
180	C₄×D₄×C₈₉	C₂³	1	6	yes	—
181	C₄×D₄×C₈₉	C₂³	1	6	yes	—
182	C₄×D₄×C₈₉	C₂³	1	12	yes	—
183	C₄×D₄×C₈₉	C₂³	1	6	yes	—
184	C₄×D₄×C₈₉	C₂³	1	12	yes	—
185	C₄×D₄×C₈₉	C₂³	1	2	yes	—
186	C₄×D₄×C₈₉	C₂³	1	12	yes	—
187	C₄×D₄×C₈₉	C₂³	1	12	yes	—
188	C₄×D₄×C₈₉	C₂³	1	6	yes	—
189	C₄×D₄×C₈₉	C₂³	1	24	yes	—
190	C₄×D₄×C₈₉	C₂³	1	12	yes	—
191	C₄×D₄×C₈₉	C₂³	1	12	yes	—
192	C₄×D₄×C₈₉	C₂³	1	12	yes	—
193	C₄×D₄×C₈₉	C₂³	1	24	yes	—
194	#117×C₈₉	C₂³	1	1	yes	characteristic
195	#117×C₈₉	C₂³	1	3	yes	—
196	#117×C₈₉	C₂³	1	3	yes	—
197	#117×C₈₉	C₂³	1	3	yes	—
198	#117×C₈₉	C₂³	1	3	yes	—
199	#117×C₈₉	C₂³	1	3	yes	—
200	#117×C₈₉	C₂³	1	6	yes	—
201	#117×C₈₉	C₂³	1	6	yes	—
202	#117×C₈₉	C₂³	1	6	yes	—
203	#117×C₈₉	C₂³	1	6	yes	—
204	#117×C₈₉	C₂³	1	6	yes	—
205	#117×C₈₉	C₂³	1	12	yes	—
206	#117×C₈₉	C₂³	1	24	yes	—
207	#117×C₈₉	C₂³	1	12	yes	—
208	#117×C₈₉	C₂³	1	24	yes	—
209	#117×C₈₉	C₂³	1	24	yes	—
210	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
211	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
212	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
213	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
214	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
215	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
216	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
217	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
218	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
219	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
220	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
221	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
222	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
223	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
224	C₂×C₄²×C₈₉	C₂³	1	12	yes	—
225	C₂×C₄²×C₈₉	C₂³	1	12	yes	—
226	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
227	#41×C₈₉	—	2	4	no	—
228	#41×C₈₉	—	2	12	no	—
229	#41×C₈₉	—	2	48	no	—
230	#41×C₈₉	—	2	12	no	—
231	#41×C₈₉	—	2	24	no	—
232	#41×C₈₉	#41	1	8	yes	—
233	C₂×Q₈×C₈₉	—	2	4	no	—
234	C₂×Q₈×C₈₉	—	2	16	no	—
235	C₂×Q₈×C₈₉	—	2	24	no	—
236	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
237	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
238	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
239	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
240	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₈₉	—	2	12	no	—
242	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
243	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
244	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
245	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
246	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
247	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
248	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
249	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
250	C₂²×C₄×C₈₉	—	2	12	no	—
251	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
252	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
262	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
265	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
266	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
267	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
269	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
270	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
271	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
273	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
281	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
283	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
284	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
285	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
286	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
288	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
289	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
290	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
291	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
292	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
294	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
296	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
297	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
298	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
299	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
300	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
301	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
302	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₄²×C₈₉	C₂⁴	1	3	yes	—
304	C₄²×C₈₉	C₂⁴	1	6	yes	—
305	C₄²×C₈₉	C₂⁴	1	3	yes	—
306	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
307	C₄²×C₈₉	C₂⁴	1	12	yes	—
308	C₄²×C₈₉	C₂⁴	1	12	yes	—
309	C₄²×C₈₉	C₂⁴	1	24	yes	—
310	C₄²×C₈₉	C₂⁴	1	12	yes	—
311	C₄²×C₈₉	C₂⁴	1	6	yes	—
312	C₄²×C₈₉	C₂⁴	1	12	yes	—
313	C₂³×C₈₉	—	2	6	no	—
314	C₂³×C₈₉	—	4	6	no	—
315	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
316	C₂³×C₈₉	C₂⁵	1	3	yes	—
317	C₂³×C₈₉	C₂⁵	1	4	yes	—
318	C₂³×C₈₉	C₂⁵	1	3	yes	—
319	Q₈×C₈₉	—	2	24	no	—
320	Q₈×C₈₉	—	2	12	no	—
321	Q₈×C₈₉	—	2	6	no	—
322	Q₈×C₈₉	—	4	12	no	—
323	Q₈×C₈₉	C₂×#41	1	4	yes	—
324	D₄×C₈₉	—	2	12	no	—
325	D₄×C₈₉	—	2	24	no	—
326	D₄×C₈₉	—	2	6	no	—
327	D₄×C₈₉	—	2	4	no	—
328	D₄×C₈₉	—	4	4	no	—
329	D₄×C₈₉	—	4	12	no	—
330	D₄×C₈₉	—	4	4	no	—
331	D₄×C₈₉	C₂×#41	1	12	yes	—
332	C₂×C₄×C₈₉	—	2	6	no	—
333	C₂×C₄×C₈₉	—	2	24	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	6	no	—
336	C₂×C₄×C₈₉	—	2	6	no	—
337	C₂×C₄×C₈₉	—	2	6	no	—
338	C₂×C₄×C₈₉	—	2	24	no	—
339	C₂×C₄×C₈₉	—	4	6	no	—
340	C₂×C₄×C₈₉	—	4	12	no	—
341	C₂×C₄×C₈₉	—	4	12	no	—
342	C₂×C₄×C₈₉	—	4	4	no	—
343	C₂×C₄×C₈₉	—	4	6	no	—
344	C₂×C₄×C₈₉	—	4	12	no	—
345	C₂×C₄×C₈₉	C₂×#41	1	12	yes	—
346	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
347	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
348	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
349	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
350	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
351	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
352	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
353	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
354	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
355	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
356	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
357	C₂²×C₈₉	—	2	6	no	—
358	C₂²×C₈₉	—	2	1	no	—
359	C₂²×C₈₉	—	2	4	no	—
360	C₂²×C₈₉	—	2	3	no	—
361	C₂²×C₈₉	—	2	4	no	—
362	C₂²×C₈₉	—	2	6	no	—
363	C₂²×C₈₉	—	2	4	no	—
364	C₂²×C₈₉	—	2	2	no	—
365	C₂²×C₈₉	—	8	6	no	—
366	C₂²×C₈₉	C₂²×#41	1	6	yes	—
367	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
368	C₄×C₈₉	—	2	1	no	—
369	C₄×C₈₉	—	2	3	no	—
370	C₄×C₈₉	—	2	12	no	—
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	2	6	no	—
373	C₄×C₈₉	—	2	2	no	—
374	C₄×C₈₉	—	2	12	no	—
375	C₄×C₈₉	—	2	6	no	—
376	C₄×C₈₉	—	2	4	no	—
377	C₄×C₈₉	C₂²×#41	1	6	yes	—
378	C₄×C₈₉	C₂²×#41	1	2	yes	—
379	#62861	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₈₉	—	2	6	no	—
381	C₂×C₈₉	—	4	4	no	—
382	C₂×C₈₉	—	4	3	no	—
383	C₂×C₈₉	—	4	1	no	—
384	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
385	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
386	#3523	C₂×C₈₉	1	4	yes	complemented
387	#3521	C₂×C₈₉	1	12	yes	complemented
388	#3516	C₂×C₈₉	1	4	yes	complemented
389	#3515	C₂×C₈₉	1	12	yes	complemented
390	#3512	C₂×C₈₉	1	3	yes	complemented
391	#3509	C₂×C₈₉	1	3	yes	complemented
392	#3504	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#3495	C₂×C₈₉	1	6	yes	complemented
395	#3489	C₂×C₈₉	1	2	yes	complemented
396	#3461	C₂×C₈₉	1	6	yes	complemented
397	#3455	C₂×C₈₉	1	3	yes	complemented
398	C₂×#541	C₂×C₈₉	1	3	yes	complemented
399	C₄×2₋¹⁺⁴	C₂×C₈₉	1	2	yes	complemented
400	#3428	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₈₉	#62861	1	1	yes	characteristic, direct product factor, Sylow
402	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
403	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
404	#557	C₂²×C₈₉	1	4	yes	complemented
405	#557	C₂²×C₈₉	1	12	yes	complemented
406	#556	C₂²×C₈₉	1	12	yes	—
407	#556	C₂²×C₈₉	1	12	yes	complemented
408	#554	C₂²×C₈₉	1	12	yes	complemented
409	#554	C₂²×C₈₉	1	12	yes	complemented
410	#553	C₂²×C₈₉	1	24	yes	complemented
411	#553	C₂²×C₈₉	1	12	yes	complemented
412	#552	C₂²×C₈₉	1	12	yes	—
413	#552	C₂²×C₈₉	1	24	yes	complemented
414	#552	C₂²×C₈₉	1	12	yes	complemented
415	#552	C₂²×C₈₉	1	24	yes	complemented
416	#552	C₂²×C₈₉	1	12	yes	complemented
417	#551	C₂²×C₈₉	1	24	yes	—
418	D₄×Q₈	C₂²×C₈₉	1	4	yes	—
419	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
420	#548	C₂²×C₈₉	1	4	yes	—
421	#547	C₂²×C₈₉	1	12	yes	—
422	#547	C₂²×C₈₉	1	12	yes	complemented
423	#546	C₂²×C₈₉	1	12	yes	—
424	#544	C₂²×C₈₉	1	6	yes	complemented
425	#542	C₂²×C₈₉	1	6	yes	—
426	#542	C₂²×C₈₉	1	6	yes	complemented
427	#542	C₂²×C₈₉	1	12	yes	complemented
428	#541	C₂²×C₈₉	1	3	yes	—
429	#541	C₂²×C₈₉	1	6	yes	—
430	#541	C₂²×C₈₉	1	12	yes	—
431	#541	C₂²×C₈₉	1	6	yes	complemented
432	#541	C₂²×C₈₉	1	6	yes	complemented
433	#541	C₂²×C₈₉	1	12	yes	complemented
434	#541	C₂²×C₈₉	1	3	yes	complemented
435	#541	C₂²×C₈₉	1	12	yes	complemented
436	#540	C₂²×C₈₉	1	1	yes	characteristic
437	#540	C₂²×C₈₉	1	3	yes	complemented
438	#539	C₂²×C₈₉	1	12	yes	complemented
439	#539	C₂²×C₈₉	1	24	yes	complemented
440	#538	C₂²×C₈₉	1	12	yes	—
441	#537	C₂²×C₈₉	1	6	yes	—
442	#536	C₂²×C₈₉	1	6	yes	—
443	#536	C₂²×C₈₉	1	6	yes	complemented
444	#533	C₂²×C₈₉	1	3	yes	complemented
445	#533	C₂²×C₈₉	1	12	yes	complemented
446	#533	C₂²×C₈₉	1	12	yes	complemented
447	#532	C₂²×C₈₉	1	3	yes	complemented
448	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
449	#529	C₂²×C₈₉	1	12	yes	—
450	#529	C₂²×C₈₉	1	12	yes	complemented
451	#529	C₂²×C₈₉	1	12	yes	complemented
452	#529	C₂²×C₈₉	1	24	yes	complemented
453	#529	C₂²×C₈₉	1	12	yes	complemented
454	C₂×#126	C₂²×C₈₉	1	12	yes	—
455	C₂×#125	C₂²×C₈₉	1	3	yes	complemented
456	C₂×#125	C₂²×C₈₉	1	12	yes	complemented
457	#525	C₂²×C₈₉	1	6	yes	—
458	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
459	#520	C₂²×C₈₉	1	6	yes	—
460	#520	C₂²×C₈₉	1	2	yes	—
461	#520	C₂²×C₈₉	1	2	yes	—
462	#520	C₂²×C₈₉	1	6	yes	complemented
463	#520	C₂²×C₈₉	1	12	yes	complemented
464	#519	C₂²×C₈₉	1	2	yes	—
465	#519	C₂²×C₈₉	1	6	yes	complemented
466	#519	C₂²×C₈₉	1	4	yes	complemented
467	#518	C₂²×C₈₉	1	6	yes	—
468	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
469	C₄×#41	C₂²×C₈₉	1	3	yes	—
470	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
471	C₄×#41	C₂²×C₈₉	1	3	yes	—
472	C₄×#41	C₂²×C₈₉	1	6	yes	complemented
473	C₄×#41	C₂²×C₈₉	1	12	yes	complemented
474	C₂×C₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
475	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
476	C₂×#117	C₂²×C₈₉	1	3	yes	—
477	C₂×#117	C₂²×C₈₉	1	3	yes	—
478	2₋¹⁺⁴	—	2	16	no	—
479	C₂×#41	—	2	8	no	—
480	C₂×#41	C₂³×C₈₉	1	3	yes	—
481	C₂×#41	C₂³×C₈₉	1	6	yes	—
482	C₂×#41	C₂³×C₈₉	1	12	yes	—
483	C₂×#41	C₂³×C₈₉	1	3	yes	—
484	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
487	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
488	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
490	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
491	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
492	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
493	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
494	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
495	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
496	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
497	#127	C₂³×C₈₉	1	1	yes	characteristic
498	#126	C₂³×C₈₉	1	12	yes	—
499	#126	C₂³×C₈₉	1	24	yes	—
500	#126	C₂³×C₈₉	1	24	yes	—
501	#126	C₂³×C₈₉	1	24	yes	—
502	#126	C₂³×C₈₉	1	12	yes	—
503	#126	C₂³×C₈₉	1	12	yes	—
504	#126	C₂³×C₈₉	1	24	yes	—
505	#126	C₂³×C₈₉	1	12	yes	—
506	#125	C₂³×C₈₉	1	12	yes	—
507	#125	C₂³×C₈₉	1	3	yes	—
508	#125	C₂³×C₈₉	1	6	yes	—
509	#125	C₂³×C₈₉	1	24	yes	—
510	#125	C₂³×C₈₉	1	24	yes	—
511	#125	C₂³×C₈₉	1	24	yes	—
512	#125	C₂³×C₈₉	1	12	yes	—
513	#125	C₂³×C₈₉	1	12	yes	—
514	#125	C₂³×C₈₉	1	12	yes	—
515	#125	C₂³×C₈₉	1	1	yes	characteristic
516	#125	C₂³×C₈₉	1	24	yes	—
517	#124	C₂³×C₈₉	1	12	yes	—
518	#124	C₂³×C₈₉	1	12	yes	—
519	#124	C₂³×C₈₉	1	6	yes	—
520	#124	C₂³×C₈₉	1	12	yes	—
521	#123	C₂³×C₈₉	1	12	yes	—
522	#123	C₂³×C₈₉	1	12	yes	—
523	#123	C₂³×C₈₉	1	12	yes	—
524	#123	C₂³×C₈₉	1	12	yes	—
525	#123	C₂³×C₈₉	1	4	yes	—
526	#123	C₂³×C₈₉	1	24	yes	—
527	#123	C₂³×C₈₉	1	24	yes	—
528	#123	C₂³×C₈₉	1	24	yes	—
529	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
530	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
531	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
532	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
533	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
534	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
535	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
536	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
537	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
538	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
539	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
540	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
541	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
542	#121	C₂³×C₈₉	1	2	yes	—
543	#121	C₂³×C₈₉	1	6	yes	—
544	#121	C₂³×C₈₉	1	4	yes	—
545	#121	C₂³×C₈₉	1	24	yes	—
546	#121	C₂³×C₈₉	1	12	yes	—
547	#121	C₂³×C₈₉	1	12	yes	—
548	#121	C₂³×C₈₉	1	12	yes	—
549	#120	C₂³×C₈₉	1	12	yes	—
550	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
551	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
552	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
553	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
554	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
555	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
556	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
557	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
558	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
559	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
560	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
561	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
562	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
563	C₄×Q₈	C₂³×C₈₉	1	24	yes	—
564	C₄×D₄	C₂³×C₈₉	1	6	yes	—
565	C₄×D₄	C₂³×C₈₉	1	12	yes	—
566	C₄×D₄	C₂³×C₈₉	1	6	yes	—
567	C₄×D₄	C₂³×C₈₉	1	6	yes	—
568	C₄×D₄	C₂³×C₈₉	1	12	yes	—
569	C₄×D₄	C₂³×C₈₉	1	6	yes	—
570	C₄×D₄	C₂³×C₈₉	1	12	yes	—
571	C₄×D₄	C₂³×C₈₉	1	2	yes	—
572	C₄×D₄	C₂³×C₈₉	1	12	yes	—
573	C₄×D₄	C₂³×C₈₉	1	12	yes	—
574	C₄×D₄	C₂³×C₈₉	1	6	yes	—
575	C₄×D₄	C₂³×C₈₉	1	24	yes	—
576	C₄×D₄	C₂³×C₈₉	1	12	yes	—
577	C₄×D₄	C₂³×C₈₉	1	12	yes	—
578	C₄×D₄	C₂³×C₈₉	1	12	yes	—
579	C₄×D₄	C₂³×C₈₉	1	24	yes	—
580	#117	C₂³×C₈₉	1	1	yes	characteristic
581	#117	C₂³×C₈₉	1	3	yes	—
582	#117	C₂³×C₈₉	1	3	yes	—
583	#117	C₂³×C₈₉	1	3	yes	—
584	#117	C₂³×C₈₉	1	3	yes	—
585	#117	C₂³×C₈₉	1	3	yes	—
586	#117	C₂³×C₈₉	1	6	yes	—
587	#117	C₂³×C₈₉	1	6	yes	—
588	#117	C₂³×C₈₉	1	6	yes	—
589	#117	C₂³×C₈₉	1	6	yes	—
590	#117	C₂³×C₈₉	1	6	yes	—
591	#117	C₂³×C₈₉	1	12	yes	—
592	#117	C₂³×C₈₉	1	24	yes	—
593	#117	C₂³×C₈₉	1	12	yes	—
594	#117	C₂³×C₈₉	1	24	yes	—
595	#117	C₂³×C₈₉	1	24	yes	—
596	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
597	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
598	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
599	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
607	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
608	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
609	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
610	C₂×C₄²	C₂³×C₈₉	1	12	yes	—
611	C₂×C₄²	C₂³×C₈₉	1	12	yes	—
612	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
613	#41	—	2	4	no	—
614	#41	—	2	12	no	—
615	#41	—	2	48	no	—
616	#41	—	2	12	no	—
617	#41	—	2	24	no	—
618	#41	#41×C₈₉	1	8	yes	—
619	C₂×Q₈	—	2	4	no	—
620	C₂×Q₈	—	2	16	no	—
621	C₂×Q₈	—	2	24	no	—
622	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
623	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
624	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
625	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
626	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
627	C₂×D₄	—	2	12	no	—
628	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
629	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
630	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
631	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
632	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
633	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
634	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
635	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
636	C₂²×C₄	—	2	12	no	—
637	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
641	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
643	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
645	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
647	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
648	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
649	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
650	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
651	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
652	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
653	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
655	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
656	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
657	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
658	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
659	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
660	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
661	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
662	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
663	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
664	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
665	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
666	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
667	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
670	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
672	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
673	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
674	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
675	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
676	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
677	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
678	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
679	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
680	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
681	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
682	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
683	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
684	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
685	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
686	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
687	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
688	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
689	C₄²	C₂⁴×C₈₉	1	3	yes	—
690	C₄²	C₂⁴×C₈₉	1	6	yes	—
691	C₄²	C₂⁴×C₈₉	1	3	yes	—
692	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
693	C₄²	C₂⁴×C₈₉	1	12	yes	—
694	C₄²	C₂⁴×C₈₉	1	12	yes	—
695	C₄²	C₂⁴×C₈₉	1	24	yes	—
696	C₄²	C₂⁴×C₈₉	1	12	yes	—
697	C₄²	C₂⁴×C₈₉	1	6	yes	—
698	C₄²	C₂⁴×C₈₉	1	12	yes	—
699	C₂³	—	2	6	no	—
700	C₂³	—	4	6	no	—
701	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
702	C₂³	C₂⁵×C₈₉	1	3	yes	—
703	C₂³	C₂⁵×C₈₉	1	4	yes	—
704	C₂³	C₂⁵×C₈₉	1	3	yes	—
705	Q₈	—	2	24	no	—
706	Q₈	—	2	12	no	—
707	Q₈	—	2	6	no	—
708	Q₈	—	4	12	no	—
709	Q₈	C₂×#41×C₈₉	1	4	yes	—
710	D₄	—	2	12	no	—
711	D₄	—	2	24	no	—
712	D₄	—	2	6	no	—
713	D₄	—	2	4	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	12	no	—
716	D₄	—	4	4	no	—
717	D₄	C₂×#41×C₈₉	1	12	yes	—
718	C₂×C₄	—	2	6	no	—
719	C₂×C₄	—	2	24	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	6	no	—
722	C₂×C₄	—	2	6	no	—
723	C₂×C₄	—	2	6	no	—
724	C₂×C₄	—	2	24	no	—
725	C₂×C₄	—	4	6	no	—
726	C₂×C₄	—	4	12	no	—
727	C₂×C₄	—	4	12	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	6	no	—
730	C₂×C₄	—	4	12	no	—
731	C₂×C₄	C₂×#41×C₈₉	1	12	yes	—
732	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
733	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
734	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
735	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
736	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
737	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
738	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
739	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
740	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
741	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
742	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
743	C₂²	—	2	6	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	3	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	6	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	8	6	no	—
752	C₂²	C₂²×#41×C₈₉	1	6	yes	—
753	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	3	no	—
756	C₄	—	2	12	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	6	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	12	no	—
761	C₄	—	2	6	no	—
762	C₄	—	2	4	no	—
763	C₄	C₂²×#41×C₈₉	1	6	yes	—
764	C₄	C₂²×#41×C₈₉	1	2	yes	—
765	C₂	—	2	6	no	—
766	C₂	—	4	4	no	—
767	C₂	—	4	3	no	—
768	C₂	—	4	1	no	—
769	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
770	C₂	C₈₉×2₋¹⁺⁶	1	2	yes	—

	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×#3523	C₂	semidirect
2. C₈₉×#3521	C₂	semidirect
3. C₈₉×#3516	C₂	semidirect
4. C₈₉×#3515	C₂	semidirect
5. C₈₉×#3512	C₂	semidirect
6. C₈₉×#3509	C₂	semidirect
7. C₈₉×#3504	C₂	semidirect
8. C₈₉×#3499	C₂	semidirect
9. C₈₉×#3495	C₂	semidirect
10. C₈₉×#3489	C₂	semidirect
11. C₈₉×#3461	C₂	semidirect
12. C₈₉×#3455	C₂	semidirect
13. C₂×#541×C₈₉	C₂	semidirect
14. C₄×2₋¹⁺⁴×C₈₉	C₂	semidirect
15. C₈₉×#3428	C₂	semidirect
18. #557×C₈₉	C₂²	semidirect
19. #557×C₈₉	C₂²	semidirect
21. #556×C₈₉	C₂²	semidirect
22. #554×C₈₉	C₂²	semidirect
23. #554×C₈₉	C₂²	semidirect
24. #553×C₈₉	C₂²	semidirect
25. #553×C₈₉	C₂²	semidirect
27. #552×C₈₉	C₂²	semidirect
28. #552×C₈₉	C₂²	semidirect
29. #552×C₈₉	C₂²	semidirect
30. #552×C₈₉	C₂²	semidirect
33. D₄×Q₈×C₈₉	C₂²	semidirect
36. #547×C₈₉	C₂²	semidirect
38. #544×C₈₉	C₂²	semidirect
40. #542×C₈₉	C₂²	semidirect
41. #542×C₈₉	C₂²	semidirect
45. #541×C₈₉	C₂²	semidirect
46. #541×C₈₉	C₂²	semidirect
47. #541×C₈₉	C₂²	semidirect
48. #541×C₈₉	C₂²	semidirect
49. #541×C₈₉	C₂²	semidirect
51. #540×C₈₉	C₂²	semidirect
52. #539×C₈₉	C₂²	semidirect
53. #539×C₈₉	C₂²	semidirect
57. #536×C₈₉	C₂²	semidirect
58. #533×C₈₉	C₂²	semidirect
59. #533×C₈₉	C₂²	semidirect
60. #533×C₈₉	C₂²	semidirect
61. #532×C₈₉	C₂²	semidirect
62. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
64. #529×C₈₉	C₂²	semidirect
65. #529×C₈₉	C₂²	semidirect
66. #529×C₈₉	C₂²	semidirect
67. #529×C₈₉	C₂²	semidirect
69. C₂×#125×C₈₉	C₂²	semidirect
70. C₂×#125×C₈₉	C₂²	semidirect
76. #520×C₈₉	C₂²	semidirect
77. #520×C₈₉	C₂²	semidirect
79. #519×C₈₉	C₂²	semidirect
80. #519×C₈₉	C₂²	semidirect
86. C₄×#41×C₈₉	C₂²	semidirect
87. C₄×#41×C₈₉	C₂²	semidirect
88. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
89. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
379. #62861	C₈₉	direct (N × H)
386. #3523	C₂×C₈₉	semidirect
387. #3521	C₂×C₈₉	semidirect
388. #3516	C₂×C₈₉	semidirect
389. #3515	C₂×C₈₉	semidirect
390. #3512	C₂×C₈₉	semidirect
391. #3509	C₂×C₈₉	semidirect
392. #3504	C₂×C₈₉	semidirect
393. #3499	C₂×C₈₉	semidirect
394. #3495	C₂×C₈₉	semidirect
395. #3489	C₂×C₈₉	semidirect
396. #3461	C₂×C₈₉	semidirect
397. #3455	C₂×C₈₉	semidirect
398. C₂×#541	C₂×C₈₉	semidirect
399. C₄×2₋¹⁺⁴	C₂×C₈₉	semidirect
400. #3428	C₂×C₈₉	semidirect
401. C₈₉	#62861	direct (N × H)
404. #557	C₂²×C₈₉	semidirect
405. #557	C₂²×C₈₉	semidirect
407. #556	C₂²×C₈₉	semidirect
408. #554	C₂²×C₈₉	semidirect
409. #554	C₂²×C₈₉	semidirect
410. #553	C₂²×C₈₉	semidirect
411. #553	C₂²×C₈₉	semidirect
413. #552	C₂²×C₈₉	semidirect
414. #552	C₂²×C₈₉	semidirect
415. #552	C₂²×C₈₉	semidirect
416. #552	C₂²×C₈₉	semidirect
419. D₄×Q₈	C₂²×C₈₉	semidirect
422. #547	C₂²×C₈₉	semidirect
424. #544	C₂²×C₈₉	semidirect
426. #542	C₂²×C₈₉	semidirect
427. #542	C₂²×C₈₉	semidirect
431. #541	C₂²×C₈₉	semidirect
432. #541	C₂²×C₈₉	semidirect
433. #541	C₂²×C₈₉	semidirect
434. #541	C₂²×C₈₉	semidirect
435. #541	C₂²×C₈₉	semidirect
437. #540	C₂²×C₈₉	semidirect
438. #539	C₂²×C₈₉	semidirect
439. #539	C₂²×C₈₉	semidirect
443. #536	C₂²×C₈₉	semidirect
444. #533	C₂²×C₈₉	semidirect
445. #533	C₂²×C₈₉	semidirect
446. #533	C₂²×C₈₉	semidirect
447. #532	C₂²×C₈₉	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
450. #529	C₂²×C₈₉	semidirect
451. #529	C₂²×C₈₉	semidirect
452. #529	C₂²×C₈₉	semidirect
453. #529	C₂²×C₈₉	semidirect
455. C₂×#125	C₂²×C₈₉	semidirect
456. C₂×#125	C₂²×C₈₉	semidirect
462. #520	C₂²×C₈₉	semidirect
463. #520	C₂²×C₈₉	semidirect
465. #519	C₂²×C₈₉	semidirect
466. #519	C₂²×C₈₉	semidirect
472. C₄×#41	C₂²×C₈₉	semidirect
473. C₄×#41	C₂²×C₈₉	semidirect
474. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
475. C₂×C₄×Q₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3523	2
C₈₉×#3521	2
C₈₉×#3516	2
C₈₉×#3515	2
C₈₉×#3512	2
C₈₉×#3509	2
C₈₉×#3504	2
C₈₉×#3499	2
C₈₉×#3495	2
C₈₉×#3489	2
C₈₉×#3461	2
C₈₉×#3455	2
C₂×#541×C₈₉	2
C₄×2₋¹⁺⁴×C₈₉	2
C₈₉×#3428	2
#62861	89

Subgroups — C89×#62861 #36440709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62861 #36440709