Subgroups — C₈₉×#62805 #36440653

Order 22784.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1004 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	2	yes	maximal, complemented
2	C₈₉×#3520	C₂	1	6	yes	maximal, complemented
3	C₈₉×#3518	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3515	C₂	1	6	yes	maximal, complemented
5	C₈₉×#3511	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3509	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3503	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×#3482	C₂	1	6	yes	maximal, complemented
12	C₈₉×#3482	C₂	1	2	yes	maximal, complemented
13	Q₈×#41×C₈₉	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3475	C₂	1	6	yes	maximal, complemented
15	C₈₉×#3461	C₂	1	6	yes	maximal, complemented
16	C₈₉×#3444	C₂	1	3	yes	maximal, complemented
17	C₂×#533×C₈₉	C₂	1	3	yes	maximal, complemented
18	C₄×2₋¹⁺⁴×C₈₉	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
21	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
22	Q₈²×C₈₉	C₂²	1	2	yes	complemented
23	#557×C₈₉	C₂²	1	6	yes	complemented
24	#557×C₈₉	C₂²	1	2	yes	complemented
25	#557×C₈₉	C₂²	1	6	yes	complemented
26	#556×C₈₉	C₂²	1	6	yes	complemented
27	#556×C₈₉	C₂²	1	12	yes	complemented
28	#556×C₈₉	C₂²	1	6	yes	complemented
29	#556×C₈₉	C₂²	1	6	yes	complemented
30	#555×C₈₉	C₂²	1	6	yes	complemented
31	#554×C₈₉	C₂²	1	12	yes	—
32	#554×C₈₉	C₂²	1	6	yes	complemented
33	#554×C₈₉	C₂²	1	6	yes	complemented
34	#553×C₈₉	C₂²	1	12	yes	complemented
35	#552×C₈₉	C₂²	1	12	yes	—
36	#552×C₈₉	C₂²	1	12	yes	complemented
37	#552×C₈₉	C₂²	1	12	yes	complemented
38	#552×C₈₉	C₂²	1	24	yes	complemented
39	#552×C₈₉	C₂²	1	12	yes	complemented
40	#551×C₈₉	C₂²	1	24	yes	—
41	D₄×Q₈×C₈₉	C₂²	1	4	yes	—
42	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
43	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
44	D₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
45	#548×C₈₉	C₂²	1	4	yes	—
46	#548×C₈₉	C₂²	1	12	yes	complemented
47	#547×C₈₉	C₂²	1	12	yes	—
48	#547×C₈₉	C₂²	1	6	yes	complemented
49	#547×C₈₉	C₂²	1	6	yes	complemented
50	#547×C₈₉	C₂²	1	6	yes	complemented
51	#546×C₈₉	C₂²	1	12	yes	—
52	#544×C₈₉	C₂²	1	6	yes	complemented
53	#542×C₈₉	C₂²	1	12	yes	complemented
54	#542×C₈₉	C₂²	1	12	yes	complemented
55	#541×C₈₉	C₂²	1	12	yes	complemented
56	#541×C₈₉	C₂²	1	12	yes	complemented
57	#539×C₈₉	C₂²	1	24	yes	complemented
58	#537×C₈₉	C₂²	1	6	yes	—
59	#536×C₈₉	C₂²	1	6	yes	—
60	#536×C₈₉	C₂²	1	6	yes	complemented
61	#533×C₈₉	C₂²	1	3	yes	—
62	#533×C₈₉	C₂²	1	6	yes	—
63	#533×C₈₉	C₂²	1	6	yes	—
64	#533×C₈₉	C₂²	1	6	yes	—
65	#533×C₈₉	C₂²	1	6	yes	complemented
66	#533×C₈₉	C₂²	1	6	yes	complemented
67	#533×C₈₉	C₂²	1	6	yes	complemented
68	#533×C₈₉	C₂²	1	6	yes	complemented
69	#533×C₈₉	C₂²	1	3	yes	complemented
70	#533×C₈₉	C₂²	1	3	yes	complemented
71	#533×C₈₉	C₂²	1	12	yes	complemented
72	#532×C₈₉	C₂²	1	1	yes	characteristic
73	#532×C₈₉	C₂²	1	3	yes	complemented
74	#532×C₈₉	C₂²	1	3	yes	complemented
75	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
76	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
77	#529×C₈₉	C₂²	1	6	yes	—
78	#529×C₈₉	C₂²	1	6	yes	—
79	#529×C₈₉	C₂²	1	6	yes	complemented
80	#529×C₈₉	C₂²	1	6	yes	complemented
81	#529×C₈₉	C₂²	1	6	yes	complemented
82	#529×C₈₉	C₂²	1	6	yes	complemented
83	#529×C₈₉	C₂²	1	24	yes	complemented
84	#529×C₈₉	C₂²	1	12	yes	complemented
85	C₂×#125×C₈₉	C₂²	1	6	yes	complemented
86	#525×C₈₉	C₂²	1	6	yes	—
87	#525×C₈₉	C₂²	1	6	yes	—
88	#525×C₈₉	C₂²	1	6	yes	—
89	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
90	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
91	#520×C₈₉	C₂²	1	2	yes	—
92	#520×C₈₉	C₂²	1	6	yes	complemented
93	#520×C₈₉	C₂²	1	12	yes	complemented
94	#519×C₈₉	C₂²	1	6	yes	complemented
95	#519×C₈₉	C₂²	1	4	yes	complemented
96	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
97	C₄×#41×C₈₉	C₂²	1	3	yes	—
98	C₄×#41×C₈₉	C₂²	1	3	yes	—
99	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
100	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
101	C₄×#41×C₈₉	C₂²	1	3	yes	—
102	C₄×#41×C₈₉	C₂²	1	3	yes	—
103	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×#41×C₈₉	C₂²	1	6	yes	—
105	C₄×#41×C₈₉	C₂²	1	6	yes	complemented
106	C₄×#41×C₈₉	C₂²	1	12	yes	complemented
107	C₄×#41×C₈₉	C₂²	1	6	yes	complemented
108	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
109	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
110	C₂×C₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
111	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
112	C₂×C₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
113	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
114	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
115	C₂×#117×C₈₉	C₂²	1	3	yes	—
116	C₂×#117×C₈₉	C₂²	1	6	yes	—
117	C₂²×C₄²×C₈₉	C₂²	1	3	yes	—
118	2₋¹⁺⁴×C₈₉	—	2	16	no	—
119	C₂×#41×C₈₉	—	2	8	no	—
120	C₂×#41×C₈₉	C₂³	1	2	yes	—
121	C₂×#41×C₈₉	C₂³	1	3	yes	—
122	C₂×#41×C₈₉	C₂³	1	3	yes	—
123	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×#41×C₈₉	C₂³	1	6	yes	—
125	C₂×#41×C₈₉	C₂³	1	12	yes	—
126	C₂×#41×C₈₉	C₂³	1	6	yes	—
127	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
130	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
131	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
134	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
136	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
138	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
142	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
146	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
147	#127×C₈₉	C₂³	1	1	yes	characteristic
148	#126×C₈₉	C₂³	1	12	yes	—
149	#126×C₈₉	C₂³	1	12	yes	—
150	#126×C₈₉	C₂³	1	24	yes	—
151	#126×C₈₉	C₂³	1	24	yes	—
152	#126×C₈₉	C₂³	1	24	yes	—
153	#125×C₈₉	C₂³	1	6	yes	—
154	#125×C₈₉	C₂³	1	12	yes	—
155	#125×C₈₉	C₂³	1	12	yes	—
156	#125×C₈₉	C₂³	1	12	yes	—
157	#125×C₈₉	C₂³	1	6	yes	—
158	#125×C₈₉	C₂³	1	6	yes	—
159	#125×C₈₉	C₂³	1	24	yes	—
160	#125×C₈₉	C₂³	1	12	yes	—
161	#125×C₈₉	C₂³	1	24	yes	—
162	#124×C₈₉	C₂³	1	6	yes	—
163	#124×C₈₉	C₂³	1	6	yes	—
164	#124×C₈₉	C₂³	1	2	yes	—
165	#124×C₈₉	C₂³	1	12	yes	—
166	#124×C₈₉	C₂³	1	24	yes	—
167	#123×C₈₉	C₂³	1	12	yes	—
168	#123×C₈₉	C₂³	1	12	yes	—
169	#123×C₈₉	C₂³	1	12	yes	—
170	#123×C₈₉	C₂³	1	24	yes	—
171	#123×C₈₉	C₂³	1	24	yes	—
172	#123×C₈₉	C₂³	1	24	yes	—
173	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
174	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
175	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
188	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
189	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
190	#121×C₈₉	C₂³	1	2	yes	—
191	#121×C₈₉	C₂³	1	2	yes	—
192	#121×C₈₉	C₂³	1	6	yes	—
193	#121×C₈₉	C₂³	1	6	yes	—
194	#121×C₈₉	C₂³	1	6	yes	—
195	#121×C₈₉	C₂³	1	6	yes	—
196	#121×C₈₉	C₂³	1	24	yes	—
197	#121×C₈₉	C₂³	1	12	yes	—
198	#120×C₈₉	C₂³	1	12	yes	—
199	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
202	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
203	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
206	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
207	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
208	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
209	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
210	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
211	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
212	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
213	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
214	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
221	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
222	C₄×D₄×C₈₉	C₂³	1	3	yes	—
223	C₄×D₄×C₈₉	C₂³	1	3	yes	—
224	C₄×D₄×C₈₉	C₂³	1	3	yes	—
225	C₄×D₄×C₈₉	C₂³	1	6	yes	—
226	C₄×D₄×C₈₉	C₂³	1	6	yes	—
227	C₄×D₄×C₈₉	C₂³	1	3	yes	—
228	C₄×D₄×C₈₉	C₂³	1	3	yes	—
229	C₄×D₄×C₈₉	C₂³	1	3	yes	—
230	C₄×D₄×C₈₉	C₂³	1	3	yes	—
231	C₄×D₄×C₈₉	C₂³	1	6	yes	—
232	C₄×D₄×C₈₉	C₂³	1	6	yes	—
233	C₄×D₄×C₈₉	C₂³	1	3	yes	—
234	C₄×D₄×C₈₉	C₂³	1	12	yes	—
235	C₄×D₄×C₈₉	C₂³	1	12	yes	—
236	C₄×D₄×C₈₉	C₂³	1	6	yes	—
237	C₄×D₄×C₈₉	C₂³	1	6	yes	—
238	C₄×D₄×C₈₉	C₂³	1	12	yes	—
239	C₄×D₄×C₈₉	C₂³	1	2	yes	—
240	C₄×D₄×C₈₉	C₂³	1	2	yes	—
241	C₄×D₄×C₈₉	C₂³	1	12	yes	—
242	C₄×D₄×C₈₉	C₂³	1	12	yes	—
243	C₄×D₄×C₈₉	C₂³	1	6	yes	—
244	C₄×D₄×C₈₉	C₂³	1	24	yes	—
245	C₄×D₄×C₈₉	C₂³	1	12	yes	—
246	C₄×D₄×C₈₉	C₂³	1	12	yes	—
247	C₄×D₄×C₈₉	C₂³	1	6	yes	—
248	#117×C₈₉	C₂³	1	6	yes	—
249	#117×C₈₉	C₂³	1	3	yes	—
250	#117×C₈₉	C₂³	1	3	yes	—
251	#117×C₈₉	C₂³	1	6	yes	—
252	#117×C₈₉	C₂³	1	3	yes	—
253	#117×C₈₉	C₂³	1	6	yes	—
254	#117×C₈₉	C₂³	1	3	yes	—
255	#117×C₈₉	C₂³	1	12	yes	—
256	#117×C₈₉	C₂³	1	12	yes	—
257	#117×C₈₉	C₂³	1	12	yes	—
258	#117×C₈₉	C₂³	1	12	yes	—
259	#117×C₈₉	C₂³	1	6	yes	—
260	#117×C₈₉	C₂³	1	12	yes	—
261	#117×C₈₉	C₂³	1	24	yes	—
262	#117×C₈₉	C₂³	1	12	yes	—
263	#117×C₈₉	C₂³	1	6	yes	—
264	#117×C₈₉	C₂³	1	12	yes	—
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
267	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
269	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
270	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
271	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
272	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
273	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
274	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
275	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
276	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
278	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
279	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
280	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
281	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
282	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
283	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
284	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
285	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
286	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
287	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
288	C₂×C₄²×C₈₉	C₂³	1	12	yes	—
289	C₂×C₄²×C₈₉	C₂³	1	12	yes	—
290	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
291	#41×C₈₉	—	2	4	no	—
292	#41×C₈₉	—	2	12	no	—
293	#41×C₈₉	—	2	48	no	—
294	#41×C₈₉	—	2	12	no	—
295	#41×C₈₉	—	2	24	no	—
296	#41×C₈₉	—	2	8	no	—
297	#41×C₈₉	—	4	12	no	—
298	#41×C₈₉	#41	1	8	yes	complemented
299	C₂×Q₈×C₈₉	—	2	4	no	—
300	C₂×Q₈×C₈₉	—	2	16	no	—
301	C₂×Q₈×C₈₉	—	2	24	no	—
302	C₂×Q₈×C₈₉	—	4	12	no	—
303	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
305	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
306	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
307	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
308	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
309	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₂×D₄×C₈₉	—	2	12	no	—
311	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₈₉	—	2	12	no	—
321	C₂²×C₄×C₈₉	—	2	12	no	—
322	C₂²×C₄×C₈₉	—	4	6	no	—
323	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
328	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
330	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
331	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
347	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
348	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
349	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
370	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
384	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₄²×C₈₉	C₂⁴	1	3	yes	—
387	C₄²×C₈₉	C₂⁴	1	3	yes	—
388	C₄²×C₈₉	C₂⁴	1	3	yes	—
389	C₄²×C₈₉	C₂⁴	1	3	yes	—
390	C₄²×C₈₉	C₂⁴	1	3	yes	—
391	C₄²×C₈₉	C₂⁴	1	3	yes	—
392	C₄²×C₈₉	C₂⁴	1	3	yes	—
393	C₄²×C₈₉	C₂⁴	1	3	yes	—
394	C₄²×C₈₉	C₂⁴	1	3	yes	—
395	C₄²×C₈₉	C₂⁴	1	3	yes	—
396	C₄²×C₈₉	C₂⁴	1	12	yes	—
397	C₄²×C₈₉	C₂⁴	1	24	yes	—
398	C₄²×C₈₉	C₂⁴	1	12	yes	—
399	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄²×C₈₉	C₂⁴	1	3	yes	—
401	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₄²×C₈₉	C₂⁴	1	3	yes	—
403	C₄²×C₈₉	C₂⁴	1	12	yes	—
404	C₂³×C₈₉	—	2	6	no	—
405	C₂³×C₈₉	—	2	6	no	—
406	C₂³×C₈₉	—	4	3	no	—
407	C₂³×C₈₉	C₂⁵	1	3	yes	—
408	C₂³×C₈₉	C₂⁵	1	4	yes	—
409	C₂³×C₈₉	C₂⁵	1	3	yes	—
410	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
411	Q₈×C₈₉	—	2	24	no	—
412	Q₈×C₈₉	—	2	12	no	—
413	Q₈×C₈₉	—	2	6	no	—
414	Q₈×C₈₉	—	2	4	no	—
415	Q₈×C₈₉	—	2	12	no	—
416	Q₈×C₈₉	—	4	12	no	—
417	Q₈×C₈₉	C₂×#41	1	4	yes	—
418	D₄×C₈₉	—	2	12	no	—
419	D₄×C₈₉	—	2	24	no	—
420	D₄×C₈₉	—	2	8	no	—
421	D₄×C₈₉	—	2	6	no	—
422	D₄×C₈₉	—	2	4	no	—
423	D₄×C₈₉	—	2	4	no	—
424	D₄×C₈₉	—	2	4	no	—
425	D₄×C₈₉	—	4	12	no	—
426	D₄×C₈₉	C₂×#41	1	12	yes	—
427	C₂×C₄×C₈₉	—	2	6	no	—
428	C₂×C₄×C₈₉	—	2	24	no	—
429	C₂×C₄×C₈₉	—	2	6	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	6	no	—
432	C₂×C₄×C₈₉	—	2	6	no	—
433	C₂×C₄×C₈₉	—	2	6	no	—
434	C₂×C₄×C₈₉	—	2	24	no	—
435	C₂×C₄×C₈₉	—	2	6	no	—
436	C₂×C₄×C₈₉	—	2	6	no	—
437	C₂×C₄×C₈₉	—	2	6	no	—
438	C₂×C₄×C₈₉	—	2	6	no	—
439	C₂×C₄×C₈₉	—	2	8	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	6	no	—
442	C₂×C₄×C₈₉	—	2	6	no	—
443	C₂×C₄×C₈₉	—	4	3	no	—
444	C₂×C₄×C₈₉	—	4	3	no	—
445	C₂×C₄×C₈₉	—	4	3	no	—
446	C₂×C₄×C₈₉	—	4	12	no	—
447	C₂×C₄×C₈₉	—	4	12	no	—
448	C₂×C₄×C₈₉	C₂×#41	1	12	yes	—
449	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	complemented
450	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
451	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
452	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
453	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
454	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
455	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
456	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
457	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
458	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
459	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
460	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
461	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
462	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
463	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
464	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
465	C₂²×C₈₉	—	2	1	no	—
466	C₂²×C₈₉	—	2	3	no	—
467	C₂²×C₈₉	—	2	3	no	—
468	C₂²×C₈₉	—	2	1	no	—
469	C₂²×C₈₉	—	2	4	no	—
470	C₂²×C₈₉	—	2	3	no	—
471	C₂²×C₈₉	—	2	3	no	—
472	C₂²×C₈₉	—	2	4	no	—
473	C₂²×C₈₉	—	2	3	no	—
474	C₂²×C₈₉	—	2	4	no	—
475	C₂²×C₈₉	—	4	12	no	—
476	C₂²×C₈₉	C₂²×#41	1	6	yes	—
477	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
478	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
479	C₄×C₈₉	—	2	1	no	—
480	C₄×C₈₉	—	2	3	no	—
481	C₄×C₈₉	—	2	12	no	—
482	C₄×C₈₉	—	2	3	no	—
483	C₄×C₈₉	—	2	3	no	—
484	C₄×C₈₉	—	2	4	no	—
485	C₄×C₈₉	—	2	1	no	—
486	C₄×C₈₉	—	2	3	no	—
487	C₄×C₈₉	—	2	3	no	—
488	C₄×C₈₉	—	2	12	no	—
489	C₄×C₈₉	C₂²×#41	1	6	yes	—
490	C₄×C₈₉	C₂²×#41	1	2	yes	—
491	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
492	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
493	C₄×C₈₉	#585	1	2	yes	—
494	#62805	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
495	C₂×C₈₉	—	2	2	no	—
496	C₂×C₈₉	—	2	6	no	—
497	C₂×C₈₉	—	4	4	no	—
498	C₂×C₈₉	—	4	3	no	—
499	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
500	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂×C₈₉	C₂×#585	1	1	yes	characteristic
502	#3523	C₂×C₈₉	1	2	yes	complemented
503	#3520	C₂×C₈₉	1	6	yes	complemented
504	#3518	C₂×C₈₉	1	2	yes	complemented
505	#3515	C₂×C₈₉	1	6	yes	complemented
506	#3511	C₂×C₈₉	1	3	yes	complemented
507	#3509	C₂×C₈₉	1	3	yes	complemented
508	#3503	C₂×C₈₉	1	1	yes	characteristic, complemented
509	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
510	#3495	C₂×C₈₉	1	6	yes	complemented
511	#3489	C₂×C₈₉	1	2	yes	complemented
512	#3482	C₂×C₈₉	1	6	yes	complemented
513	#3482	C₂×C₈₉	1	2	yes	complemented
514	Q₈×#41	C₂×C₈₉	1	2	yes	complemented
515	#3475	C₂×C₈₉	1	6	yes	complemented
516	#3461	C₂×C₈₉	1	6	yes	complemented
517	#3444	C₂×C₈₉	1	3	yes	complemented
518	C₂×#533	C₂×C₈₉	1	3	yes	complemented
519	C₄×2₋¹⁺⁴	C₂×C₈₉	1	2	yes	complemented
520	C₂×C₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
521	C₈₉	#62805	1	1	yes	characteristic, direct product factor, Sylow
522	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
523	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
524	Q₈²	C₂²×C₈₉	1	2	yes	complemented
525	#557	C₂²×C₈₉	1	6	yes	complemented
526	#557	C₂²×C₈₉	1	2	yes	complemented
527	#557	C₂²×C₈₉	1	6	yes	complemented
528	#556	C₂²×C₈₉	1	6	yes	complemented
529	#556	C₂²×C₈₉	1	12	yes	complemented
530	#556	C₂²×C₈₉	1	6	yes	complemented
531	#556	C₂²×C₈₉	1	6	yes	complemented
532	#555	C₂²×C₈₉	1	6	yes	complemented
533	#554	C₂²×C₈₉	1	12	yes	—
534	#554	C₂²×C₈₉	1	6	yes	complemented
535	#554	C₂²×C₈₉	1	6	yes	complemented
536	#553	C₂²×C₈₉	1	12	yes	complemented
537	#552	C₂²×C₈₉	1	12	yes	—
538	#552	C₂²×C₈₉	1	12	yes	complemented
539	#552	C₂²×C₈₉	1	12	yes	complemented
540	#552	C₂²×C₈₉	1	24	yes	complemented
541	#552	C₂²×C₈₉	1	12	yes	complemented
542	#551	C₂²×C₈₉	1	24	yes	—
543	D₄×Q₈	C₂²×C₈₉	1	4	yes	—
544	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
545	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
546	D₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
547	#548	C₂²×C₈₉	1	4	yes	—
548	#548	C₂²×C₈₉	1	12	yes	complemented
549	#547	C₂²×C₈₉	1	12	yes	—
550	#547	C₂²×C₈₉	1	6	yes	complemented
551	#547	C₂²×C₈₉	1	6	yes	complemented
552	#547	C₂²×C₈₉	1	6	yes	complemented
553	#546	C₂²×C₈₉	1	12	yes	—
554	#544	C₂²×C₈₉	1	6	yes	complemented
555	#542	C₂²×C₈₉	1	12	yes	complemented
556	#542	C₂²×C₈₉	1	12	yes	complemented
557	#541	C₂²×C₈₉	1	12	yes	complemented
558	#541	C₂²×C₈₉	1	12	yes	complemented
559	#539	C₂²×C₈₉	1	24	yes	complemented
560	#537	C₂²×C₈₉	1	6	yes	—
561	#536	C₂²×C₈₉	1	6	yes	—
562	#536	C₂²×C₈₉	1	6	yes	complemented
563	#533	C₂²×C₈₉	1	3	yes	—
564	#533	C₂²×C₈₉	1	6	yes	—
565	#533	C₂²×C₈₉	1	6	yes	—
566	#533	C₂²×C₈₉	1	6	yes	—
567	#533	C₂²×C₈₉	1	6	yes	complemented
568	#533	C₂²×C₈₉	1	6	yes	complemented
569	#533	C₂²×C₈₉	1	6	yes	complemented
570	#533	C₂²×C₈₉	1	6	yes	complemented
571	#533	C₂²×C₈₉	1	3	yes	complemented
572	#533	C₂²×C₈₉	1	3	yes	complemented
573	#533	C₂²×C₈₉	1	12	yes	complemented
574	#532	C₂²×C₈₉	1	1	yes	characteristic
575	#532	C₂²×C₈₉	1	3	yes	complemented
576	#532	C₂²×C₈₉	1	3	yes	complemented
577	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
578	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
579	#529	C₂²×C₈₉	1	6	yes	—
580	#529	C₂²×C₈₉	1	6	yes	—
581	#529	C₂²×C₈₉	1	6	yes	complemented
582	#529	C₂²×C₈₉	1	6	yes	complemented
583	#529	C₂²×C₈₉	1	6	yes	complemented
584	#529	C₂²×C₈₉	1	6	yes	complemented
585	#529	C₂²×C₈₉	1	24	yes	complemented
586	#529	C₂²×C₈₉	1	12	yes	complemented
587	C₂×#125	C₂²×C₈₉	1	6	yes	complemented
588	#525	C₂²×C₈₉	1	6	yes	—
589	#525	C₂²×C₈₉	1	6	yes	—
590	#525	C₂²×C₈₉	1	6	yes	—
591	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
592	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
593	#520	C₂²×C₈₉	1	2	yes	—
594	#520	C₂²×C₈₉	1	6	yes	complemented
595	#520	C₂²×C₈₉	1	12	yes	complemented
596	#519	C₂²×C₈₉	1	6	yes	complemented
597	#519	C₂²×C₈₉	1	4	yes	complemented
598	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
599	C₄×#41	C₂²×C₈₉	1	3	yes	—
600	C₄×#41	C₂²×C₈₉	1	3	yes	—
601	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
602	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
603	C₄×#41	C₂²×C₈₉	1	3	yes	—
604	C₄×#41	C₂²×C₈₉	1	3	yes	—
605	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
606	C₄×#41	C₂²×C₈₉	1	6	yes	—
607	C₄×#41	C₂²×C₈₉	1	6	yes	complemented
608	C₄×#41	C₂²×C₈₉	1	12	yes	complemented
609	C₄×#41	C₂²×C₈₉	1	6	yes	complemented
610	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
611	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
612	C₂×C₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
613	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
614	C₂×C₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
615	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
616	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
617	C₂×#117	C₂²×C₈₉	1	3	yes	—
618	C₂×#117	C₂²×C₈₉	1	6	yes	—
619	C₂²×C₄²	C₂²×C₈₉	1	3	yes	—
620	2₋¹⁺⁴	—	2	16	no	—
621	C₂×#41	—	2	8	no	—
622	C₂×#41	C₂³×C₈₉	1	2	yes	—
623	C₂×#41	C₂³×C₈₉	1	3	yes	—
624	C₂×#41	C₂³×C₈₉	1	3	yes	—
625	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×#41	C₂³×C₈₉	1	6	yes	—
627	C₂×#41	C₂³×C₈₉	1	12	yes	—
628	C₂×#41	C₂³×C₈₉	1	6	yes	—
629	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
632	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
633	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
634	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
635	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
636	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
637	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
638	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
639	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
640	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
641	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
642	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
643	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
644	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
645	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
646	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
648	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
649	#127	C₂³×C₈₉	1	1	yes	characteristic
650	#126	C₂³×C₈₉	1	12	yes	—
651	#126	C₂³×C₈₉	1	12	yes	—
652	#126	C₂³×C₈₉	1	24	yes	—
653	#126	C₂³×C₈₉	1	24	yes	—
654	#126	C₂³×C₈₉	1	24	yes	—
655	#125	C₂³×C₈₉	1	6	yes	—
656	#125	C₂³×C₈₉	1	12	yes	—
657	#125	C₂³×C₈₉	1	12	yes	—
658	#125	C₂³×C₈₉	1	12	yes	—
659	#125	C₂³×C₈₉	1	6	yes	—
660	#125	C₂³×C₈₉	1	6	yes	—
661	#125	C₂³×C₈₉	1	24	yes	—
662	#125	C₂³×C₈₉	1	12	yes	—
663	#125	C₂³×C₈₉	1	24	yes	—
664	#124	C₂³×C₈₉	1	6	yes	—
665	#124	C₂³×C₈₉	1	6	yes	—
666	#124	C₂³×C₈₉	1	2	yes	—
667	#124	C₂³×C₈₉	1	12	yes	—
668	#124	C₂³×C₈₉	1	24	yes	—
669	#123	C₂³×C₈₉	1	12	yes	—
670	#123	C₂³×C₈₉	1	12	yes	—
671	#123	C₂³×C₈₉	1	12	yes	—
672	#123	C₂³×C₈₉	1	24	yes	—
673	#123	C₂³×C₈₉	1	24	yes	—
674	#123	C₂³×C₈₉	1	24	yes	—
675	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
676	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
677	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
678	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
679	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
680	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
681	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
682	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
683	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
684	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
685	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
686	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
687	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
688	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
689	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
690	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
691	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
692	#121	C₂³×C₈₉	1	2	yes	—
693	#121	C₂³×C₈₉	1	2	yes	—
694	#121	C₂³×C₈₉	1	6	yes	—
695	#121	C₂³×C₈₉	1	6	yes	—
696	#121	C₂³×C₈₉	1	6	yes	—
697	#121	C₂³×C₈₉	1	6	yes	—
698	#121	C₂³×C₈₉	1	24	yes	—
699	#121	C₂³×C₈₉	1	12	yes	—
700	#120	C₂³×C₈₉	1	12	yes	—
701	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
704	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
705	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
706	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
707	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
708	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
709	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
710	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
711	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
712	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
713	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
714	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
715	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
716	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
717	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
718	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
719	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
720	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
721	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
722	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
723	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
724	C₄×D₄	C₂³×C₈₉	1	3	yes	—
725	C₄×D₄	C₂³×C₈₉	1	3	yes	—
726	C₄×D₄	C₂³×C₈₉	1	3	yes	—
727	C₄×D₄	C₂³×C₈₉	1	6	yes	—
728	C₄×D₄	C₂³×C₈₉	1	6	yes	—
729	C₄×D₄	C₂³×C₈₉	1	3	yes	—
730	C₄×D₄	C₂³×C₈₉	1	3	yes	—
731	C₄×D₄	C₂³×C₈₉	1	3	yes	—
732	C₄×D₄	C₂³×C₈₉	1	3	yes	—
733	C₄×D₄	C₂³×C₈₉	1	6	yes	—
734	C₄×D₄	C₂³×C₈₉	1	6	yes	—
735	C₄×D₄	C₂³×C₈₉	1	3	yes	—
736	C₄×D₄	C₂³×C₈₉	1	12	yes	—
737	C₄×D₄	C₂³×C₈₉	1	12	yes	—
738	C₄×D₄	C₂³×C₈₉	1	6	yes	—
739	C₄×D₄	C₂³×C₈₉	1	6	yes	—
740	C₄×D₄	C₂³×C₈₉	1	12	yes	—
741	C₄×D₄	C₂³×C₈₉	1	2	yes	—
742	C₄×D₄	C₂³×C₈₉	1	2	yes	—
743	C₄×D₄	C₂³×C₈₉	1	12	yes	—
744	C₄×D₄	C₂³×C₈₉	1	12	yes	—
745	C₄×D₄	C₂³×C₈₉	1	6	yes	—
746	C₄×D₄	C₂³×C₈₉	1	24	yes	—
747	C₄×D₄	C₂³×C₈₉	1	12	yes	—
748	C₄×D₄	C₂³×C₈₉	1	12	yes	—
749	C₄×D₄	C₂³×C₈₉	1	6	yes	—
750	#117	C₂³×C₈₉	1	6	yes	—
751	#117	C₂³×C₈₉	1	3	yes	—
752	#117	C₂³×C₈₉	1	3	yes	—
753	#117	C₂³×C₈₉	1	6	yes	—
754	#117	C₂³×C₈₉	1	3	yes	—
755	#117	C₂³×C₈₉	1	6	yes	—
756	#117	C₂³×C₈₉	1	3	yes	—
757	#117	C₂³×C₈₉	1	12	yes	—
758	#117	C₂³×C₈₉	1	12	yes	—
759	#117	C₂³×C₈₉	1	12	yes	—
760	#117	C₂³×C₈₉	1	12	yes	—
761	#117	C₂³×C₈₉	1	6	yes	—
762	#117	C₂³×C₈₉	1	12	yes	—
763	#117	C₂³×C₈₉	1	24	yes	—
764	#117	C₂³×C₈₉	1	12	yes	—
765	#117	C₂³×C₈₉	1	6	yes	—
766	#117	C₂³×C₈₉	1	12	yes	—
767	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
768	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
769	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
770	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
771	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
772	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
773	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
774	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
775	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
778	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
779	C₂×C₄²	C₂³×C₈₉	1	12	yes	—
780	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
781	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
782	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
783	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
784	C₂×C₄²	C₂³×C₈₉	1	12	yes	—
785	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
786	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
787	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
788	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
789	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
790	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
791	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
792	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
793	#41	—	2	4	no	—
794	#41	—	2	12	no	—
795	#41	—	2	48	no	—
796	#41	—	2	12	no	—
797	#41	—	2	24	no	—
798	#41	—	2	8	no	—
799	#41	—	4	12	no	—
800	#41	#41×C₈₉	1	8	yes	complemented
801	C₂×Q₈	—	2	4	no	—
802	C₂×Q₈	—	2	16	no	—
803	C₂×Q₈	—	2	24	no	—
804	C₂×Q₈	—	4	12	no	—
805	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
807	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
808	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
809	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
810	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
811	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂×D₄	—	2	12	no	—
813	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
814	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
815	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
816	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
817	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
818	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
819	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
820	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
821	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
822	C₂²×C₄	—	2	12	no	—
823	C₂²×C₄	—	2	12	no	—
824	C₂²×C₄	—	4	6	no	—
825	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
826	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
830	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
831	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
832	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
833	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
834	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
835	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
836	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
837	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
838	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
839	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
840	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
842	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
843	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
844	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
845	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
846	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
847	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
849	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
850	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
851	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
852	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
853	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
854	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
855	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
856	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
857	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
858	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
859	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
860	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
861	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
862	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
863	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
864	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
865	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
866	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
869	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
870	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
871	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
872	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
873	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
874	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
875	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
876	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
877	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
878	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
879	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
880	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
881	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
882	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
883	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
884	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
885	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
886	C₄²	C₂⁴×C₈₉	1	3	yes	—
887	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
888	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
889	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
890	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
891	C₄²	C₂⁴×C₈₉	1	3	yes	—
892	C₄²	C₂⁴×C₈₉	1	3	yes	—
893	C₄²	C₂⁴×C₈₉	1	3	yes	—
894	C₄²	C₂⁴×C₈₉	1	3	yes	—
895	C₄²	C₂⁴×C₈₉	1	12	yes	—
896	C₄²	C₂⁴×C₈₉	1	3	yes	—
897	C₄²	C₂⁴×C₈₉	1	3	yes	—
898	C₄²	C₂⁴×C₈₉	1	3	yes	—
899	C₄²	C₂⁴×C₈₉	1	3	yes	—
900	C₄²	C₂⁴×C₈₉	1	3	yes	—
901	C₄²	C₂⁴×C₈₉	1	3	yes	—
902	C₄²	C₂⁴×C₈₉	1	3	yes	—
903	C₄²	C₂⁴×C₈₉	1	12	yes	—
904	C₄²	C₂⁴×C₈₉	1	24	yes	—
905	C₄²	C₂⁴×C₈₉	1	12	yes	—
906	C₂³	—	2	6	no	—
907	C₂³	—	2	6	no	—
908	C₂³	—	4	3	no	—
909	C₂³	C₂⁵×C₈₉	1	3	yes	—
910	C₂³	C₂⁵×C₈₉	1	4	yes	—
911	C₂³	C₂⁵×C₈₉	1	3	yes	—
912	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
913	Q₈	—	2	24	no	—
914	Q₈	—	2	12	no	—
915	Q₈	—	2	6	no	—
916	Q₈	—	2	4	no	—
917	Q₈	—	2	12	no	—
918	Q₈	—	4	12	no	—
919	Q₈	C₂×#41×C₈₉	1	4	yes	—
920	D₄	—	2	12	no	—
921	D₄	—	2	24	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	6	no	—
924	D₄	—	2	4	no	—
925	D₄	—	2	4	no	—
926	D₄	—	2	4	no	—
927	D₄	—	4	12	no	—
928	D₄	C₂×#41×C₈₉	1	12	yes	—
929	C₂×C₄	—	2	6	no	—
930	C₂×C₄	—	2	24	no	—
931	C₂×C₄	—	2	6	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	6	no	—
934	C₂×C₄	—	2	6	no	—
935	C₂×C₄	—	2	6	no	—
936	C₂×C₄	—	2	24	no	—
937	C₂×C₄	—	2	6	no	—
938	C₂×C₄	—	2	6	no	—
939	C₂×C₄	—	2	6	no	—
940	C₂×C₄	—	2	6	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	6	no	—
944	C₂×C₄	—	2	6	no	—
945	C₂×C₄	—	4	3	no	—
946	C₂×C₄	—	4	3	no	—
947	C₂×C₄	—	4	3	no	—
948	C₂×C₄	—	4	12	no	—
949	C₂×C₄	—	4	12	no	—
950	C₂×C₄	C₂×#41×C₈₉	1	12	yes	—
951	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	complemented
952	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
953	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
954	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
955	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
956	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
957	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
958	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
959	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
960	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
961	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
962	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
963	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
964	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
965	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
967	C₂²	—	2	1	no	—
968	C₂²	—	2	3	no	—
969	C₂²	—	2	3	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	3	no	—
973	C₂²	—	2	3	no	—
974	C₂²	—	2	4	no	—
975	C₂²	—	2	3	no	—
976	C₂²	—	2	4	no	—
977	C₂²	—	4	12	no	—
978	C₂²	C₂²×#41×C₈₉	1	6	yes	—
979	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
980	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	3	no	—
983	C₄	—	2	12	no	—
984	C₄	—	2	3	no	—
985	C₄	—	2	3	no	—
986	C₄	—	2	4	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	3	no	—
989	C₄	—	2	3	no	—
990	C₄	—	2	12	no	—
991	C₄	C₂²×#41×C₈₉	1	6	yes	—
992	C₄	C₂²×#41×C₈₉	1	2	yes	—
993	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
994	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
995	C₄	#585×C₈₉	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	2	6	no	—
998	C₂	—	4	4	no	—
999	C₂	—	4	3	no	—
1000	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
1001	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1002	C₂	C₂×#585×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
socle	C₂²×C₈₉	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#3520	C₂	semidirect
3. C₈₉×#3518	C₂	semidirect
4. C₈₉×#3515	C₂	semidirect
5. C₈₉×#3511	C₂	semidirect
6. C₈₉×#3509	C₂	semidirect
7. C₈₉×#3503	C₂	semidirect
8. C₈₉×#3499	C₂	semidirect
9. C₈₉×#3495	C₂	semidirect
10. C₈₉×#3489	C₂	semidirect
11. C₈₉×#3482	C₂	semidirect
12. C₈₉×#3482	C₂	semidirect
13. Q₈×#41×C₈₉	C₂	semidirect
14. C₈₉×#3475	C₂	semidirect
15. C₈₉×#3461	C₂	semidirect
16. C₈₉×#3444	C₂	semidirect
17. C₂×#533×C₈₉	C₂	semidirect
18. C₄×2₋¹⁺⁴×C₈₉	C₂	semidirect
19. C₂×C₄×#41×C₈₉	C₂	semidirect
22. Q₈²×C₈₉	C₂²	semidirect
23. #557×C₈₉	C₂²	semidirect
24. #557×C₈₉	C₂²	semidirect
25. #557×C₈₉	C₂²	semidirect
26. #556×C₈₉	C₂²	semidirect
27. #556×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #555×C₈₉	C₂²	semidirect
32. #554×C₈₉	C₂²	semidirect
33. #554×C₈₉	C₂²	semidirect
34. #553×C₈₉	C₂²	semidirect
36. #552×C₈₉	C₂²	semidirect
37. #552×C₈₉	C₂²	semidirect
38. #552×C₈₉	C₂²	semidirect
39. #552×C₈₉	C₂²	semidirect
42. D₄×Q₈×C₈₉	C₂²	semidirect
43. D₄×Q₈×C₈₉	C₂²	semidirect
44. D₄×Q₈×C₈₉	C₂²	semidirect
46. #548×C₈₉	C₂²	semidirect
48. #547×C₈₉	C₂²	semidirect
49. #547×C₈₉	C₂²	semidirect
50. #547×C₈₉	C₂²	semidirect
52. #544×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #542×C₈₉	C₂²	semidirect
55. #541×C₈₉	C₂²	semidirect
56. #541×C₈₉	C₂²	semidirect
57. #539×C₈₉	C₂²	semidirect
60. #536×C₈₉	C₂²	semidirect
65. #533×C₈₉	C₂²	semidirect
66. #533×C₈₉	C₂²	semidirect
67. #533×C₈₉	C₂²	semidirect
68. #533×C₈₉	C₂²	semidirect
69. #533×C₈₉	C₂²	semidirect
70. #533×C₈₉	C₂²	semidirect
71. #533×C₈₉	C₂²	semidirect
73. #532×C₈₉	C₂²	semidirect
74. #532×C₈₉	C₂²	semidirect
75. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
76. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
79. #529×C₈₉	C₂²	semidirect
80. #529×C₈₉	C₂²	semidirect
81. #529×C₈₉	C₂²	semidirect
82. #529×C₈₉	C₂²	semidirect
83. #529×C₈₉	C₂²	semidirect
84. #529×C₈₉	C₂²	semidirect
85. C₂×#125×C₈₉	C₂²	semidirect
92. #520×C₈₉	C₂²	semidirect
93. #520×C₈₉	C₂²	semidirect
94. #519×C₈₉	C₂²	semidirect
95. #519×C₈₉	C₂²	semidirect
105. C₄×#41×C₈₉	C₂²	semidirect
106. C₄×#41×C₈₉	C₂²	semidirect
107. C₄×#41×C₈₉	C₂²	semidirect
110. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
111. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
112. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
298. #41×C₈₉	#41	semidirect
449. C₂×C₄×C₈₉	2₋¹⁺⁴	semidirect
494. #62805	C₈₉	direct (N × H)
502. #3523	C₂×C₈₉	semidirect
503. #3520	C₂×C₈₉	semidirect
504. #3518	C₂×C₈₉	semidirect
505. #3515	C₂×C₈₉	semidirect
506. #3511	C₂×C₈₉	semidirect
507. #3509	C₂×C₈₉	semidirect
508. #3503	C₂×C₈₉	semidirect
509. #3499	C₂×C₈₉	semidirect
510. #3495	C₂×C₈₉	semidirect
511. #3489	C₂×C₈₉	semidirect
512. #3482	C₂×C₈₉	semidirect
513. #3482	C₂×C₈₉	semidirect
514. Q₈×#41	C₂×C₈₉	semidirect
515. #3475	C₂×C₈₉	semidirect
516. #3461	C₂×C₈₉	semidirect
517. #3444	C₂×C₈₉	semidirect
518. C₂×#533	C₂×C₈₉	semidirect
519. C₄×2₋¹⁺⁴	C₂×C₈₉	semidirect
520. C₂×C₄×#41	C₂×C₈₉	semidirect
521. C₈₉	#62805	direct (N × H)
524. Q₈²	C₂²×C₈₉	semidirect
525. #557	C₂²×C₈₉	semidirect
526. #557	C₂²×C₈₉	semidirect
527. #557	C₂²×C₈₉	semidirect
528. #556	C₂²×C₈₉	semidirect
529. #556	C₂²×C₈₉	semidirect
530. #556	C₂²×C₈₉	semidirect
531. #556	C₂²×C₈₉	semidirect
532. #555	C₂²×C₈₉	semidirect
534. #554	C₂²×C₈₉	semidirect
535. #554	C₂²×C₈₉	semidirect
536. #553	C₂²×C₈₉	semidirect
538. #552	C₂²×C₈₉	semidirect
539. #552	C₂²×C₈₉	semidirect
540. #552	C₂²×C₈₉	semidirect
541. #552	C₂²×C₈₉	semidirect
544. D₄×Q₈	C₂²×C₈₉	semidirect
545. D₄×Q₈	C₂²×C₈₉	semidirect
546. D₄×Q₈	C₂²×C₈₉	semidirect
548. #548	C₂²×C₈₉	semidirect
550. #547	C₂²×C₈₉	semidirect
551. #547	C₂²×C₈₉	semidirect
552. #547	C₂²×C₈₉	semidirect
554. #544	C₂²×C₈₉	semidirect
555. #542	C₂²×C₈₉	semidirect
556. #542	C₂²×C₈₉	semidirect
557. #541	C₂²×C₈₉	semidirect
558. #541	C₂²×C₈₉	semidirect
559. #539	C₂²×C₈₉	semidirect
562. #536	C₂²×C₈₉	semidirect
567. #533	C₂²×C₈₉	semidirect
568. #533	C₂²×C₈₉	semidirect
569. #533	C₂²×C₈₉	semidirect
570. #533	C₂²×C₈₉	semidirect
571. #533	C₂²×C₈₉	semidirect
572. #533	C₂²×C₈₉	semidirect
573. #533	C₂²×C₈₉	semidirect
575. #532	C₂²×C₈₉	semidirect
576. #532	C₂²×C₈₉	semidirect
577. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
578. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
581. #529	C₂²×C₈₉	semidirect
582. #529	C₂²×C₈₉	semidirect
583. #529	C₂²×C₈₉	semidirect
584. #529	C₂²×C₈₉	semidirect
585. #529	C₂²×C₈₉	semidirect
586. #529	C₂²×C₈₉	semidirect
587. C₂×#125	C₂²×C₈₉	semidirect
594. #520	C₂²×C₈₉	semidirect
595. #520	C₂²×C₈₉	semidirect
596. #519	C₂²×C₈₉	semidirect
597. #519	C₂²×C₈₉	semidirect
607. C₄×#41	C₂²×C₈₉	semidirect
608. C₄×#41	C₂²×C₈₉	semidirect
609. C₄×#41	C₂²×C₈₉	semidirect
612. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
613. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
614. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
800. #41	#41×C₈₉	semidirect
951. C₂×C₄	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×#3523	2
C₈₉×#3520	2
C₈₉×#3518	2
C₈₉×#3515	2
C₈₉×#3511	2
C₈₉×#3509	2
C₈₉×#3503	2
C₈₉×#3499	2
C₈₉×#3495	2
C₈₉×#3489	2
C₈₉×#3482	2
Q₈×#41×C₈₉	2
C₈₉×#3475	2
C₈₉×#3461	2
C₈₉×#3444	2
C₂×#533×C₈₉	2
C₄×2₋¹⁺⁴×C₈₉	2
C₂×C₄×#41×C₈₉	2
#62805	89

Subgroups — C89×#62805 #36440653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62805 #36440653