Subgroups — C₈₉×#62876 #36440724

Order 22784.

7414 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×#3562	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3558	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3546	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3543	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3534	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3532	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3510	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3508	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3500	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3498	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3484	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#562×C₈₉	C₂²	1	16	yes	complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	8	yes	complemented
23	#560×C₈₉	C₂²	1	16	yes	complemented
24	#560×C₈₉	C₂²	1	8	yes	complemented
25	#560×C₈₉	C₂²	1	16	yes	complemented
26	#559×C₈₉	C₂²	1	8	yes	complemented
27	#559×C₈₉	C₂²	1	8	yes	complemented
28	#556×C₈₉	C₂²	1	8	yes	complemented
29	#553×C₈₉	C₂²	1	16	yes	complemented
30	#551×C₈₉	C₂²	1	16	yes	complemented
31	#551×C₈₉	C₂²	1	8	yes	complemented
32	#550×C₈₉	C₂²	1	8	yes	complemented
33	#550×C₈₉	C₂²	1	8	yes	complemented
34	#550×C₈₉	C₂²	1	8	yes	complemented
35	#548×C₈₉	C₂²	1	8	yes	complemented
36	#548×C₈₉	C₂²	1	8	yes	complemented
37	#547×C₈₉	C₂²	1	8	yes	complemented
38	#546×C₈₉	C₂²	1	8	yes	complemented
39	#546×C₈₉	C₂²	1	8	yes	complemented
40	#546×C₈₉	C₂²	1	16	yes	complemented
41	#546×C₈₉	C₂²	1	16	yes	complemented
42	#546×C₈₉	C₂²	1	16	yes	complemented
43	#546×C₈₉	C₂²	1	8	yes	complemented
44	#546×C₈₉	C₂²	1	16	yes	complemented
45	#546×C₈₉	C₂²	1	8	yes	complemented
46	D₄²×C₈₉	C₂²	1	8	yes	complemented
47	D₄²×C₈₉	C₂²	1	8	yes	complemented
48	D₄²×C₈₉	C₂²	1	16	yes	complemented
49	D₄²×C₈₉	C₂²	1	8	yes	complemented
50	D₄²×C₈₉	C₂²	1	8	yes	complemented
51	#542×C₈₉	C₂²	1	4	yes	complemented
52	#542×C₈₉	C₂²	1	4	yes	complemented
53	#542×C₈₉	C₂²	1	8	yes	complemented
54	#541×C₈₉	C₂²	1	4	yes	complemented
55	#540×C₈₉	C₂²	1	4	yes	complemented
56	#540×C₈₉	C₂²	1	8	yes	complemented
57	#540×C₈₉	C₂²	1	16	yes	complemented
58	#539×C₈₉	C₂²	1	8	yes	complemented
59	#539×C₈₉	C₂²	1	8	yes	complemented
60	#538×C₈₉	C₂²	1	8	yes	complemented
61	#538×C₈₉	C₂²	1	16	yes	complemented
62	#538×C₈₉	C₂²	1	16	yes	complemented
63	#538×C₈₉	C₂²	1	16	yes	complemented
64	#538×C₈₉	C₂²	1	8	yes	complemented
65	#537×C₈₉	C₂²	1	8	yes	complemented
66	#536×C₈₉	C₂²	1	2	yes	complemented
67	#536×C₈₉	C₂²	1	4	yes	complemented
68	#535×C₈₉	C₂²	1	2	yes	—
69	#535×C₈₉	C₂²	1	8	yes	complemented
70	#535×C₈₉	C₂²	1	8	yes	complemented
71	#535×C₈₉	C₂²	1	2	yes	complemented
72	#535×C₈₉	C₂²	1	4	yes	complemented
73	#535×C₈₉	C₂²	1	2	yes	complemented
74	#535×C₈₉	C₂²	1	16	yes	complemented
75	#535×C₈₉	C₂²	1	4	yes	complemented
76	#535×C₈₉	C₂²	1	4	yes	complemented
77	#535×C₈₉	C₂²	1	4	yes	complemented
78	#534×C₈₉	C₂²	1	8	yes	complemented
79	#534×C₈₉	C₂²	1	4	yes	complemented
80	#534×C₈₉	C₂²	1	16	yes	complemented
81	#534×C₈₉	C₂²	1	8	yes	complemented
82	#533×C₈₉	C₂²	1	2	yes	complemented
83	#532×C₈₉	C₂²	1	2	yes	complemented
84	#532×C₈₉	C₂²	1	8	yes	complemented
85	#532×C₈₉	C₂²	1	4	yes	complemented
86	#532×C₈₉	C₂²	1	4	yes	complemented
87	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
88	C₂×#127×C₈₉	C₂²	1	4	yes	complemented
89	#529×C₈₉	C₂²	1	8	yes	complemented
90	#529×C₈₉	C₂²	1	8	yes	complemented
91	#529×C₈₉	C₂²	1	8	yes	complemented
92	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
93	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
94	#525×C₈₉	C₂²	1	2	yes	complemented
95	#525×C₈₉	C₂²	1	2	yes	complemented
96	#525×C₈₉	C₂²	1	4	yes	complemented
97	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
98	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
99	C₂×#120×C₈₉	C₂²	1	4	yes	complemented
100	C₂×#120×C₈₉	C₂²	1	8	yes	complemented
101	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#518×C₈₉	C₂²	1	2	yes	complemented
103	#518×C₈₉	C₂²	1	1	yes	characteristic, complemented
104	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
105	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
106	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₈₉	C₂³	1	2	yes	—
108	2₋¹⁺⁴×C₈₉	—	4	4	no	—
109	H(5,𝔽₂)×C₈₉	—	4	8	no	—
110	H(5,𝔽₂)×C₈₉	—	4	4	no	—
111	C₂×#41×C₈₉	—	4	4	no	—
112	C₂×#41×C₈₉	C₂³	1	2	yes	—
113	C₂×#41×C₈₉	C₂³	1	2	yes	—
114	C₂×#41×C₈₉	C₂³	1	4	yes	—
115	C₂×#41×C₈₉	C₂³	1	4	yes	—
116	C₂×#41×C₈₉	C₂³	1	4	yes	—
117	C₂×#41×C₈₉	C₂³	1	8	yes	—
118	C₂×#41×C₈₉	C₂³	1	4	yes	complemented
119	C₂×#41×C₈₉	C₂³	1	4	yes	complemented
120	C₂×#41×C₈₉	C₂³	1	16	yes	complemented
121	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₈₉	C₂³	1	4	yes	complemented
123	C₂²×D₄×C₈₉	—	4	4	no	—
124	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
130	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
133	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
135	C₂²×D₄×C₈₉	C₂³	1	4	yes	complemented
136	C₂²×D₄×C₈₉	C₂³	1	16	yes	complemented
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
140	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
141	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
142	#127×C₈₉	C₂³	1	4	yes	—
143	#127×C₈₉	C₂³	1	4	yes	—
144	#127×C₈₉	C₂³	1	4	yes	—
145	#127×C₈₉	C₂³	1	8	yes	—
146	#127×C₈₉	C₂³	1	4	yes	—
147	#127×C₈₉	C₂³	1	8	yes	—
148	#127×C₈₉	C₂³	1	2	yes	complemented
149	#127×C₈₉	C₂³	1	4	yes	complemented
150	#127×C₈₉	C₂³	1	16	yes	complemented
151	#126×C₈₉	C₂³	1	8	yes	—
152	#126×C₈₉	C₂³	1	8	yes	—
153	#126×C₈₉	C₂³	1	8	yes	complemented
154	#126×C₈₉	C₂³	1	16	yes	complemented
155	#126×C₈₉	C₂³	1	8	yes	complemented
156	#126×C₈₉	C₂³	1	16	yes	complemented
157	#125×C₈₉	C₂³	1	4	yes	complemented
158	#125×C₈₉	C₂³	1	8	yes	complemented
159	#125×C₈₉	C₂³	1	8	yes	complemented
160	#124×C₈₉	C₂³	1	4	yes	—
161	#124×C₈₉	C₂³	1	4	yes	—
162	#124×C₈₉	C₂³	1	8	yes	—
163	#124×C₈₉	C₂³	1	4	yes	—
164	#124×C₈₉	C₂³	1	8	yes	—
165	#124×C₈₉	C₂³	1	8	yes	—
166	#124×C₈₉	C₂³	1	4	yes	—
167	#124×C₈₉	C₂³	1	8	yes	—
168	#124×C₈₉	C₂³	1	2	yes	complemented
169	#124×C₈₉	C₂³	1	4	yes	complemented
170	#124×C₈₉	C₂³	1	16	yes	complemented
171	#124×C₈₉	C₂³	1	2	yes	complemented
172	#124×C₈₉	C₂³	1	4	yes	complemented
173	#124×C₈₉	C₂³	1	16	yes	complemented
174	#124×C₈₉	C₂³	1	16	yes	complemented
175	#123×C₈₉	C₂³	1	4	yes	—
176	#123×C₈₉	C₂³	1	8	yes	—
177	#123×C₈₉	C₂³	1	4	yes	—
178	#123×C₈₉	C₂³	1	8	yes	—
179	#123×C₈₉	C₂³	1	8	yes	—
180	#123×C₈₉	C₂³	1	8	yes	—
181	#123×C₈₉	C₂³	1	16	yes	—
182	#123×C₈₉	C₂³	1	16	yes	complemented
183	#123×C₈₉	C₂³	1	8	yes	complemented
184	#123×C₈₉	C₂³	1	16	yes	complemented
185	#123×C₈₉	C₂³	1	8	yes	complemented
186	#123×C₈₉	C₂³	1	16	yes	complemented
187	#123×C₈₉	C₂³	1	16	yes	complemented
188	#123×C₈₉	C₂³	1	16	yes	complemented
189	#123×C₈₉	C₂³	1	16	yes	complemented
190	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
194	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
195	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
196	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
197	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
198	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
199	#121×C₈₉	C₂³	1	8	yes	—
200	#121×C₈₉	C₂³	1	8	yes	—
201	#121×C₈₉	C₂³	1	16	yes	—
202	#121×C₈₉	C₂³	1	4	yes	—
203	#121×C₈₉	C₂³	1	4	yes	—
204	#121×C₈₉	C₂³	1	8	yes	—
205	#121×C₈₉	C₂³	1	8	yes	—
206	#121×C₈₉	C₂³	1	8	yes	—
207	#121×C₈₉	C₂³	1	8	yes	—
208	#121×C₈₉	C₂³	1	8	yes	—
209	#121×C₈₉	C₂³	1	16	yes	—
210	#121×C₈₉	C₂³	1	16	yes	—
211	#121×C₈₉	C₂³	1	16	yes	—
212	#121×C₈₉	C₂³	1	16	yes	—
213	#121×C₈₉	C₂³	1	8	yes	complemented
214	#121×C₈₉	C₂³	1	16	yes	complemented
215	#121×C₈₉	C₂³	1	16	yes	complemented
216	#121×C₈₉	C₂³	1	8	yes	complemented
217	#121×C₈₉	C₂³	1	16	yes	complemented
218	#121×C₈₉	C₂³	1	16	yes	complemented
219	#121×C₈₉	C₂³	1	16	yes	complemented
220	#121×C₈₉	C₂³	1	16	yes	complemented
221	#121×C₈₉	C₂³	1	16	yes	complemented
222	#121×C₈₉	C₂³	1	16	yes	complemented
223	#120×C₈₉	C₂³	1	4	yes	—
224	#120×C₈₉	C₂³	1	4	yes	—
225	#120×C₈₉	C₂³	1	8	yes	—
226	#120×C₈₉	C₂³	1	16	yes	—
227	#120×C₈₉	C₂³	1	8	yes	—
228	#120×C₈₉	C₂³	1	16	yes	—
229	#120×C₈₉	C₂³	1	8	yes	—
230	#120×C₈₉	C₂³	1	8	yes	—
231	#120×C₈₉	C₂³	1	16	yes	—
232	#120×C₈₉	C₂³	1	8	yes	—
233	#120×C₈₉	C₂³	1	8	yes	—
234	#120×C₈₉	C₂³	1	16	yes	—
235	#120×C₈₉	C₂³	1	16	yes	complemented
236	#120×C₈₉	C₂³	1	16	yes	complemented
237	#120×C₈₉	C₂³	1	16	yes	complemented
238	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
239	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
240	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
241	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
242	C₄×D₄×C₈₉	C₂³	1	8	yes	—
243	C₄×D₄×C₈₉	C₂³	1	8	yes	—
244	C₄×D₄×C₈₉	C₂³	1	8	yes	—
245	C₄×D₄×C₈₉	C₂³	1	8	yes	—
246	C₄×D₄×C₈₉	C₂³	1	8	yes	—
247	C₄×D₄×C₈₉	C₂³	1	8	yes	—
248	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
249	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
250	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
251	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
252	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
253	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
254	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
255	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
256	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
257	#117×C₈₉	C₂³	1	4	yes	—
258	#117×C₈₉	C₂³	1	4	yes	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	2	yes	—
261	#117×C₈₉	C₂³	1	4	yes	—
262	#117×C₈₉	C₂³	1	4	yes	complemented
263	#117×C₈₉	C₂³	1	4	yes	complemented
264	#117×C₈₉	C₂³	1	16	yes	complemented
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
267	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	8	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	complemented
274	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
275	C₂×C₄²×C₈₉	C₂³	1	4	yes	complemented
276	C₂×C₄²×C₈₉	C₂³	1	4	yes	complemented
277	C₂⁴×C₈₉	—	4	4	no	—
278	C₂⁴×C₈₉	—	8	4	no	—
279	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
280	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
282	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
283	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
284	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
285	#41×C₈₉	—	2	8	no	—
286	#41×C₈₉	—	2	8	no	—
287	#41×C₈₉	—	4	8	no	—
288	#41×C₈₉	—	4	16	no	—
289	#41×C₈₉	—	4	8	no	—
290	#41×C₈₉	—	4	8	no	—
291	#41×C₈₉	—	4	8	no	—
292	#41×C₈₉	—	4	8	no	—
293	#41×C₈₉	—	8	16	no	—
294	C₂×Q₈×C₈₉	—	2	4	no	—
295	C₂×Q₈×C₈₉	—	4	8	no	—
296	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
300	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
301	C₂×D₄×C₈₉	—	2	8	no	—
302	C₂×D₄×C₈₉	—	2	4	no	—
303	C₂×D₄×C₈₉	—	4	16	no	—
304	C₂×D₄×C₈₉	—	4	8	no	—
305	C₂×D₄×C₈₉	—	4	8	no	—
306	C₂×D₄×C₈₉	—	4	8	no	—
307	C₂×D₄×C₈₉	—	4	4	no	—
308	C₂×D₄×C₈₉	—	4	4	no	—
309	C₂×D₄×C₈₉	—	4	8	no	—
310	C₂×D₄×C₈₉	—	4	16	no	—
311	C₂×D₄×C₈₉	—	8	8	no	—
312	C₂×D₄×C₈₉	—	8	16	no	—
313	C₂×D₄×C₈₉	—	8	16	no	—
314	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
322	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
323	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
324	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
325	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
327	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
328	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
329	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
330	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
331	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
332	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
333	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
334	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
335	C₂²×C₄×C₈₉	—	2	4	no	—
336	C₂²×C₄×C₈₉	—	4	4	no	—
337	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
349	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
367	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
369	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	16	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	16	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
388	C₄²×C₈₉	C₂⁴	1	2	yes	—
389	C₄²×C₈₉	C₂⁴	1	2	yes	—
390	C₄²×C₈₉	C₂⁴	1	4	yes	—
391	C₄²×C₈₉	C₂⁴	1	4	yes	—
392	C₄²×C₈₉	C₂⁴	1	4	yes	—
393	C₄²×C₈₉	C₂⁴	1	8	yes	—
394	C₄²×C₈₉	C₂⁴	1	8	yes	—
395	C₄²×C₈₉	C₂⁴	1	8	yes	—
396	C₂³×C₈₉	—	2	2	no	—
397	C₂³×C₈₉	—	2	4	no	—
398	C₂³×C₈₉	—	2	8	no	—
399	C₂³×C₈₉	—	4	2	no	—
400	C₂³×C₈₉	—	4	8	no	—
401	C₂³×C₈₉	—	4	4	no	—
402	C₂³×C₈₉	—	4	8	no	—
403	C₂³×C₈₉	—	4	16	no	—
404	C₂³×C₈₉	—	4	8	no	—
405	C₂³×C₈₉	—	4	4	no	—
406	C₂³×C₈₉	—	4	16	no	—
407	C₂³×C₈₉	—	4	8	no	—
408	C₂³×C₈₉	—	8	16	no	—
409	C₂³×C₈₉	C₂⁵	1	2	yes	—
410	C₂³×C₈₉	C₂⁵	1	4	yes	—
411	C₂³×C₈₉	C₂⁵	1	8	yes	—
412	C₂³×C₈₉	C₂⁵	1	4	yes	—
413	C₂³×C₈₉	C₂⁵	1	4	yes	—
414	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
415	Q₈×C₈₉	—	2	8	no	—
416	Q₈×C₈₉	—	2	4	no	—
417	Q₈×C₈₉	—	2	4	no	—
418	Q₈×C₈₉	—	4	4	no	—
419	Q₈×C₈₉	—	4	8	no	—
420	D₄×C₈₉	—	2	8	no	—
421	D₄×C₈₉	—	2	8	no	—
422	D₄×C₈₉	—	2	8	no	—
423	D₄×C₈₉	—	2	8	no	—
424	D₄×C₈₉	—	2	8	no	—
425	D₄×C₈₉	—	2	4	no	—
426	D₄×C₈₉	—	2	4	no	—
427	D₄×C₈₉	—	4	8	no	—
428	D₄×C₈₉	—	4	8	no	—
429	D₄×C₈₉	—	4	8	no	—
430	D₄×C₈₉	—	4	8	no	—
431	D₄×C₈₉	—	4	8	no	—
432	D₄×C₈₉	—	4	8	no	—
433	D₄×C₈₉	—	4	16	no	—
434	D₄×C₈₉	—	4	8	no	—
435	D₄×C₈₉	—	4	8	no	—
436	D₄×C₈₉	—	4	16	no	—
437	D₄×C₈₉	—	4	16	no	—
438	D₄×C₈₉	—	4	16	no	—
439	D₄×C₈₉	—	4	16	no	—
440	D₄×C₈₉	—	4	4	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	4	no	—
443	C₂×C₄×C₈₉	—	2	8	no	—
444	C₂×C₄×C₈₉	—	2	8	no	—
445	C₂×C₄×C₈₉	—	2	8	no	—
446	C₂×C₄×C₈₉	—	4	8	no	—
447	C₂×C₄×C₈₉	—	4	4	no	—
448	C₂×C₄×C₈₉	—	4	8	no	—
449	C₂×C₄×C₈₉	—	4	8	no	—
450	C₂×C₄×C₈₉	—	4	4	no	—
451	C₂×C₄×C₈₉	—	4	16	no	—
452	C₂×C₄×C₈₉	—	4	8	no	—
453	C₂×C₄×C₈₉	—	4	8	no	—
454	C₂×C₄×C₈₉	—	4	8	no	—
455	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
456	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
457	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
458	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
459	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
460	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
461	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
462	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
463	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
464	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
465	C₂²×C₈₉	—	2	2	no	—
466	C₂²×C₈₉	—	2	2	no	—
467	C₂²×C₈₉	—	2	4	no	—
468	C₂²×C₈₉	—	2	4	no	—
469	C₂²×C₈₉	—	2	4	no	—
470	C₂²×C₈₉	—	2	8	no	—
471	C₂²×C₈₉	—	2	8	no	—
472	C₂²×C₈₉	—	2	8	no	—
473	C₂²×C₈₉	—	2	16	no	—
474	C₂²×C₈₉	—	2	8	no	—
475	C₂²×C₈₉	—	2	4	no	—
476	C₂²×C₈₉	—	4	4	no	—
477	C₂²×C₈₉	—	8	4	no	—
478	C₂²×C₈₉	—	8	8	no	—
479	C₂²×C₈₉	—	8	16	no	—
480	C₂²×C₈₉	—	16	8	no	—
481	C₂²×C₈₉	—	16	4	no	—
482	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
483	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
484	C₄×C₈₉	—	2	2	no	—
485	C₄×C₈₉	—	2	4	no	—
486	C₄×C₈₉	—	2	4	no	—
487	C₄×C₈₉	—	2	4	no	—
488	C₄×C₈₉	—	2	8	no	—
489	C₄×C₈₉	—	2	4	no	—
490	C₄×C₈₉	—	2	8	no	—
491	C₄×C₈₉	—	2	4	no	—
492	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
493	#62876	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₂×C₈₉	—	2	2	no	—
495	C₂×C₈₉	—	4	2	no	—
496	C₂×C₈₉	—	4	8	no	—
497	C₂×C₈₉	—	4	4	no	—
498	C₂×C₈₉	—	4	4	no	—
499	C₂×C₈₉	—	4	4	no	—
500	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₈₉	H(7,𝔽₂)	1	2	yes	—
502	#3562	C₂×C₈₉	1	8	yes	complemented
503	#3558	C₂×C₈₉	1	8	yes	complemented
504	#3546	C₂×C₈₉	1	8	yes	complemented
505	#3543	C₂×C₈₉	1	8	yes	complemented
506	#3534	C₂×C₈₉	1	8	yes	complemented
507	#3532	C₂×C₈₉	1	8	yes	complemented
508	#3510	C₂×C₈₉	1	2	yes	complemented
509	#3508	C₂×C₈₉	1	2	yes	complemented
510	#3500	C₂×C₈₉	1	2	yes	complemented
511	#3498	C₂×C₈₉	1	2	yes	complemented
512	#3487	C₂×C₈₉	1	1	yes	characteristic, complemented
513	#3485	C₂×C₈₉	1	1	yes	characteristic, complemented
514	#3484	C₂×C₈₉	1	2	yes	complemented
515	#3455	C₂×C₈₉	1	2	yes	complemented
516	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
517	C₈₉	#62876	1	1	yes	characteristic, direct product factor, Sylow
518	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
520	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic, complemented
521	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
523	#562	C₂²×C₈₉	1	16	yes	complemented
524	H(3,𝔽₄)	C₂²×C₈₉	1	8	yes	complemented
525	#560	C₂²×C₈₉	1	16	yes	complemented
526	#560	C₂²×C₈₉	1	8	yes	complemented
527	#560	C₂²×C₈₉	1	16	yes	complemented
528	#559	C₂²×C₈₉	1	8	yes	complemented
529	#559	C₂²×C₈₉	1	8	yes	complemented
530	#556	C₂²×C₈₉	1	8	yes	complemented
531	#553	C₂²×C₈₉	1	16	yes	complemented
532	#551	C₂²×C₈₉	1	16	yes	complemented
533	#551	C₂²×C₈₉	1	8	yes	complemented
534	#550	C₂²×C₈₉	1	8	yes	complemented
535	#550	C₂²×C₈₉	1	8	yes	complemented
536	#550	C₂²×C₈₉	1	8	yes	complemented
537	#548	C₂²×C₈₉	1	8	yes	complemented
538	#548	C₂²×C₈₉	1	8	yes	complemented
539	#547	C₂²×C₈₉	1	8	yes	complemented
540	#546	C₂²×C₈₉	1	8	yes	complemented
541	#546	C₂²×C₈₉	1	8	yes	complemented
542	#546	C₂²×C₈₉	1	16	yes	complemented
543	#546	C₂²×C₈₉	1	16	yes	complemented
544	#546	C₂²×C₈₉	1	16	yes	complemented
545	#546	C₂²×C₈₉	1	8	yes	complemented
546	#546	C₂²×C₈₉	1	16	yes	complemented
547	#546	C₂²×C₈₉	1	8	yes	complemented
548	D₄²	C₂²×C₈₉	1	8	yes	complemented
549	D₄²	C₂²×C₈₉	1	8	yes	complemented
550	D₄²	C₂²×C₈₉	1	16	yes	complemented
551	D₄²	C₂²×C₈₉	1	8	yes	complemented
552	D₄²	C₂²×C₈₉	1	8	yes	complemented
553	#542	C₂²×C₈₉	1	4	yes	complemented
554	#542	C₂²×C₈₉	1	4	yes	complemented
555	#542	C₂²×C₈₉	1	8	yes	complemented
556	#541	C₂²×C₈₉	1	4	yes	complemented
557	#540	C₂²×C₈₉	1	4	yes	complemented
558	#540	C₂²×C₈₉	1	8	yes	complemented
559	#540	C₂²×C₈₉	1	16	yes	complemented
560	#539	C₂²×C₈₉	1	8	yes	complemented
561	#539	C₂²×C₈₉	1	8	yes	complemented
562	#538	C₂²×C₈₉	1	8	yes	complemented
563	#538	C₂²×C₈₉	1	16	yes	complemented
564	#538	C₂²×C₈₉	1	16	yes	complemented
565	#538	C₂²×C₈₉	1	16	yes	complemented
566	#538	C₂²×C₈₉	1	8	yes	complemented
567	#537	C₂²×C₈₉	1	8	yes	complemented
568	#536	C₂²×C₈₉	1	2	yes	complemented
569	#536	C₂²×C₈₉	1	4	yes	complemented
570	#535	C₂²×C₈₉	1	2	yes	—
571	#535	C₂²×C₈₉	1	8	yes	complemented
572	#535	C₂²×C₈₉	1	8	yes	complemented
573	#535	C₂²×C₈₉	1	2	yes	complemented
574	#535	C₂²×C₈₉	1	4	yes	complemented
575	#535	C₂²×C₈₉	1	2	yes	complemented
576	#535	C₂²×C₈₉	1	16	yes	complemented
577	#535	C₂²×C₈₉	1	4	yes	complemented
578	#535	C₂²×C₈₉	1	4	yes	complemented
579	#535	C₂²×C₈₉	1	4	yes	complemented
580	#534	C₂²×C₈₉	1	8	yes	complemented
581	#534	C₂²×C₈₉	1	4	yes	complemented
582	#534	C₂²×C₈₉	1	16	yes	complemented
583	#534	C₂²×C₈₉	1	8	yes	complemented
584	#533	C₂²×C₈₉	1	2	yes	complemented
585	#532	C₂²×C₈₉	1	2	yes	complemented
586	#532	C₂²×C₈₉	1	8	yes	complemented
587	#532	C₂²×C₈₉	1	4	yes	complemented
588	#532	C₂²×C₈₉	1	4	yes	complemented
589	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
590	C₂×#127	C₂²×C₈₉	1	4	yes	complemented
591	#529	C₂²×C₈₉	1	8	yes	complemented
592	#529	C₂²×C₈₉	1	8	yes	complemented
593	#529	C₂²×C₈₉	1	8	yes	complemented
594	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
595	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
596	#525	C₂²×C₈₉	1	2	yes	complemented
597	#525	C₂²×C₈₉	1	2	yes	complemented
598	#525	C₂²×C₈₉	1	4	yes	complemented
599	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
600	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
601	C₂×#120	C₂²×C₈₉	1	4	yes	complemented
602	C₂×#120	C₂²×C₈₉	1	8	yes	complemented
603	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
604	#518	C₂²×C₈₉	1	2	yes	complemented
605	#518	C₂²×C₈₉	1	1	yes	characteristic, complemented
606	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
607	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
608	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
609	C₂⁵	C₂³×C₈₉	1	2	yes	—
610	2₋¹⁺⁴	—	4	4	no	—
611	H(5,𝔽₂)	—	4	8	no	—
612	H(5,𝔽₂)	—	4	4	no	—
613	C₂×#41	—	4	4	no	—
614	C₂×#41	C₂³×C₈₉	1	2	yes	—
615	C₂×#41	C₂³×C₈₉	1	2	yes	—
616	C₂×#41	C₂³×C₈₉	1	4	yes	—
617	C₂×#41	C₂³×C₈₉	1	4	yes	—
618	C₂×#41	C₂³×C₈₉	1	4	yes	—
619	C₂×#41	C₂³×C₈₉	1	8	yes	—
620	C₂×#41	C₂³×C₈₉	1	4	yes	complemented
621	C₂×#41	C₂³×C₈₉	1	4	yes	complemented
622	C₂×#41	C₂³×C₈₉	1	16	yes	complemented
623	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
624	C₂²×Q₈	C₂³×C₈₉	1	4	yes	complemented
625	C₂²×D₄	—	4	4	no	—
626	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
627	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
629	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
630	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
631	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
632	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
633	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
634	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
635	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
636	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
637	C₂²×D₄	C₂³×C₈₉	1	4	yes	complemented
638	C₂²×D₄	C₂³×C₈₉	1	16	yes	complemented
639	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
641	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
642	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
643	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
644	#127	C₂³×C₈₉	1	4	yes	—
645	#127	C₂³×C₈₉	1	4	yes	—
646	#127	C₂³×C₈₉	1	4	yes	—
647	#127	C₂³×C₈₉	1	8	yes	—
648	#127	C₂³×C₈₉	1	4	yes	—
649	#127	C₂³×C₈₉	1	8	yes	—
650	#127	C₂³×C₈₉	1	2	yes	complemented
651	#127	C₂³×C₈₉	1	4	yes	complemented
652	#127	C₂³×C₈₉	1	16	yes	complemented
653	#126	C₂³×C₈₉	1	8	yes	—
654	#126	C₂³×C₈₉	1	8	yes	—
655	#126	C₂³×C₈₉	1	8	yes	complemented
656	#126	C₂³×C₈₉	1	16	yes	complemented
657	#126	C₂³×C₈₉	1	8	yes	complemented
658	#126	C₂³×C₈₉	1	16	yes	complemented
659	#125	C₂³×C₈₉	1	4	yes	complemented
660	#125	C₂³×C₈₉	1	8	yes	complemented
661	#125	C₂³×C₈₉	1	8	yes	complemented
662	#124	C₂³×C₈₉	1	4	yes	—
663	#124	C₂³×C₈₉	1	4	yes	—
664	#124	C₂³×C₈₉	1	8	yes	—
665	#124	C₂³×C₈₉	1	4	yes	—
666	#124	C₂³×C₈₉	1	8	yes	—
667	#124	C₂³×C₈₉	1	8	yes	—
668	#124	C₂³×C₈₉	1	4	yes	—
669	#124	C₂³×C₈₉	1	8	yes	—
670	#124	C₂³×C₈₉	1	2	yes	complemented
671	#124	C₂³×C₈₉	1	4	yes	complemented
672	#124	C₂³×C₈₉	1	16	yes	complemented
673	#124	C₂³×C₈₉	1	2	yes	complemented
674	#124	C₂³×C₈₉	1	4	yes	complemented
675	#124	C₂³×C₈₉	1	16	yes	complemented
676	#124	C₂³×C₈₉	1	16	yes	complemented
677	#123	C₂³×C₈₉	1	4	yes	—
678	#123	C₂³×C₈₉	1	8	yes	—
679	#123	C₂³×C₈₉	1	4	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	complemented
685	#123	C₂³×C₈₉	1	8	yes	complemented
686	#123	C₂³×C₈₉	1	16	yes	complemented
687	#123	C₂³×C₈₉	1	8	yes	complemented
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	#123	C₂³×C₈₉	1	16	yes	complemented
692	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
696	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
697	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
698	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
699	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
700	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
701	#121	C₂³×C₈₉	1	8	yes	—
702	#121	C₂³×C₈₉	1	8	yes	—
703	#121	C₂³×C₈₉	1	16	yes	—
704	#121	C₂³×C₈₉	1	4	yes	—
705	#121	C₂³×C₈₉	1	4	yes	—
706	#121	C₂³×C₈₉	1	8	yes	—
707	#121	C₂³×C₈₉	1	8	yes	—
708	#121	C₂³×C₈₉	1	8	yes	—
709	#121	C₂³×C₈₉	1	8	yes	—
710	#121	C₂³×C₈₉	1	8	yes	—
711	#121	C₂³×C₈₉	1	16	yes	—
712	#121	C₂³×C₈₉	1	16	yes	—
713	#121	C₂³×C₈₉	1	16	yes	—
714	#121	C₂³×C₈₉	1	16	yes	—
715	#121	C₂³×C₈₉	1	8	yes	complemented
716	#121	C₂³×C₈₉	1	16	yes	complemented
717	#121	C₂³×C₈₉	1	16	yes	complemented
718	#121	C₂³×C₈₉	1	8	yes	complemented
719	#121	C₂³×C₈₉	1	16	yes	complemented
720	#121	C₂³×C₈₉	1	16	yes	complemented
721	#121	C₂³×C₈₉	1	16	yes	complemented
722	#121	C₂³×C₈₉	1	16	yes	complemented
723	#121	C₂³×C₈₉	1	16	yes	complemented
724	#121	C₂³×C₈₉	1	16	yes	complemented
725	#120	C₂³×C₈₉	1	4	yes	—
726	#120	C₂³×C₈₉	1	4	yes	—
727	#120	C₂³×C₈₉	1	8	yes	—
728	#120	C₂³×C₈₉	1	16	yes	—
729	#120	C₂³×C₈₉	1	8	yes	—
730	#120	C₂³×C₈₉	1	16	yes	—
731	#120	C₂³×C₈₉	1	8	yes	—
732	#120	C₂³×C₈₉	1	8	yes	—
733	#120	C₂³×C₈₉	1	16	yes	—
734	#120	C₂³×C₈₉	1	8	yes	—
735	#120	C₂³×C₈₉	1	8	yes	—
736	#120	C₂³×C₈₉	1	16	yes	—
737	#120	C₂³×C₈₉	1	16	yes	complemented
738	#120	C₂³×C₈₉	1	16	yes	complemented
739	#120	C₂³×C₈₉	1	16	yes	complemented
740	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
741	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
742	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
743	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
744	C₄×D₄	C₂³×C₈₉	1	8	yes	—
745	C₄×D₄	C₂³×C₈₉	1	8	yes	—
746	C₄×D₄	C₂³×C₈₉	1	8	yes	—
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	4	yes	complemented
751	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
752	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
753	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
754	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
755	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
756	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
757	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
758	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
759	#117	C₂³×C₈₉	1	4	yes	—
760	#117	C₂³×C₈₉	1	4	yes	—
761	#117	C₂³×C₈₉	1	2	yes	—
762	#117	C₂³×C₈₉	1	2	yes	—
763	#117	C₂³×C₈₉	1	4	yes	—
764	#117	C₂³×C₈₉	1	4	yes	complemented
765	#117	C₂³×C₈₉	1	4	yes	complemented
766	#117	C₂³×C₈₉	1	16	yes	complemented
767	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
769	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
775	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	complemented
776	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
777	C₂×C₄²	C₂³×C₈₉	1	4	yes	complemented
778	C₂×C₄²	C₂³×C₈₉	1	4	yes	complemented
779	C₂⁴	—	4	4	no	—
780	C₂⁴	—	8	4	no	—
781	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
782	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
783	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
784	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
785	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
786	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
787	#41	—	2	8	no	—
788	#41	—	2	8	no	—
789	#41	—	4	8	no	—
790	#41	—	4	16	no	—
791	#41	—	4	8	no	—
792	#41	—	4	8	no	—
793	#41	—	4	8	no	—
794	#41	—	4	8	no	—
795	#41	—	8	16	no	—
796	C₂×Q₈	—	2	4	no	—
797	C₂×Q₈	—	4	8	no	—
798	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
799	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
800	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
801	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
802	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
803	C₂×D₄	—	2	8	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	4	16	no	—
806	C₂×D₄	—	4	8	no	—
807	C₂×D₄	—	4	8	no	—
808	C₂×D₄	—	4	8	no	—
809	C₂×D₄	—	4	4	no	—
810	C₂×D₄	—	4	4	no	—
811	C₂×D₄	—	4	8	no	—
812	C₂×D₄	—	4	16	no	—
813	C₂×D₄	—	8	8	no	—
814	C₂×D₄	—	8	16	no	—
815	C₂×D₄	—	8	16	no	—
816	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
817	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
818	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
819	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
820	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
821	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
822	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
823	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
824	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
825	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
826	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
827	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
828	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
829	C₂×D₄	C₂⁴×C₈₉	1	16	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	8	yes	—
834	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
835	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
836	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	4	4	no	—
839	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
844	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
845	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
847	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
848	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
849	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
850	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
851	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
852	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
859	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
860	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
862	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
865	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
866	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
868	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
869	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
870	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
871	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
872	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
874	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
876	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
877	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
878	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
879	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
880	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
881	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
885	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
887	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
888	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
889	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₄²	C₂⁴×C₈₉	1	2	yes	—
891	C₄²	C₂⁴×C₈₉	1	2	yes	—
892	C₄²	C₂⁴×C₈₉	1	4	yes	—
893	C₄²	C₂⁴×C₈₉	1	4	yes	—
894	C₄²	C₂⁴×C₈₉	1	4	yes	—
895	C₄²	C₂⁴×C₈₉	1	8	yes	—
896	C₄²	C₂⁴×C₈₉	1	8	yes	—
897	C₄²	C₂⁴×C₈₉	1	8	yes	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	4	no	—
900	C₂³	—	2	8	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	8	no	—
903	C₂³	—	4	4	no	—
904	C₂³	—	4	8	no	—
905	C₂³	—	4	16	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	4	16	no	—
909	C₂³	—	4	8	no	—
910	C₂³	—	8	16	no	—
911	C₂³	C₂⁵×C₈₉	1	2	yes	—
912	C₂³	C₂⁵×C₈₉	1	4	yes	—
913	C₂³	C₂⁵×C₈₉	1	8	yes	—
914	C₂³	C₂⁵×C₈₉	1	4	yes	—
915	C₂³	C₂⁵×C₈₉	1	4	yes	—
916	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
917	Q₈	—	2	8	no	—
918	Q₈	—	2	4	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	4	4	no	—
921	Q₈	—	4	8	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	8	no	—
924	D₄	—	2	8	no	—
925	D₄	—	2	8	no	—
926	D₄	—	2	8	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	4	no	—
929	D₄	—	4	8	no	—
930	D₄	—	4	8	no	—
931	D₄	—	4	8	no	—
932	D₄	—	4	8	no	—
933	D₄	—	4	8	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	16	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	8	no	—
938	D₄	—	4	16	no	—
939	D₄	—	4	16	no	—
940	D₄	—	4	16	no	—
941	D₄	—	4	16	no	—
942	D₄	—	4	4	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	4	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	8	no	—
948	C₂×C₄	—	4	8	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	16	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
958	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
959	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
960	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
961	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
962	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
963	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
964	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
965	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
966	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	4	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	8	no	—
973	C₂²	—	2	8	no	—
974	C₂²	—	2	8	no	—
975	C₂²	—	2	16	no	—
976	C₂²	—	2	8	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	8	8	no	—
980	C₂²	—	8	4	no	—
981	C₂²	—	8	16	no	—
982	C₂²	—	16	8	no	—
983	C₂²	—	16	4	no	—
984	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
985	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	4	no	—
989	C₄	—	2	4	no	—
990	C₄	—	2	8	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	8	no	—
993	C₄	—	2	4	no	—
994	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	4	2	no	—
997	C₂	—	4	8	no	—
998	C₂	—	4	4	no	—
999	C₂	—	4	4	no	—
1000	C₂	—	4	4	no	—
1001	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1002	C₂	C₈₉×H(7,𝔽₂)	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×#3562	C₂	semidirect
2. C₈₉×#3558	C₂	semidirect
3. C₈₉×#3546	C₂	semidirect
4. C₈₉×#3543	C₂	semidirect
5. C₈₉×#3534	C₂	semidirect
6. C₈₉×#3532	C₂	semidirect
7. C₈₉×#3510	C₂	semidirect
8. C₈₉×#3508	C₂	semidirect
9. C₈₉×#3500	C₂	semidirect
10. C₈₉×#3498	C₂	semidirect
11. C₈₉×#3487	C₂	semidirect
12. C₈₉×#3485	C₂	semidirect
13. C₈₉×#3484	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₂×#535×C₈₉	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
17. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
18. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
19. C₂²×#41×C₈₉	C₂²	semidirect
20. C₂³×D₄×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. #560×C₈₉	C₂²	semidirect
24. #560×C₈₉	C₂²	semidirect
25. #560×C₈₉	C₂²	semidirect
26. #559×C₈₉	C₂²	semidirect
27. #559×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #553×C₈₉	C₂²	semidirect
30. #551×C₈₉	C₂²	semidirect
31. #551×C₈₉	C₂²	semidirect
32. #550×C₈₉	C₂²	semidirect
33. #550×C₈₉	C₂²	semidirect
34. #550×C₈₉	C₂²	semidirect
35. #548×C₈₉	C₂²	semidirect
36. #548×C₈₉	C₂²	semidirect
37. #547×C₈₉	C₂²	semidirect
38. #546×C₈₉	C₂²	semidirect
39. #546×C₈₉	C₂²	semidirect
40. #546×C₈₉	C₂²	semidirect
41. #546×C₈₉	C₂²	semidirect
42. #546×C₈₉	C₂²	semidirect
43. #546×C₈₉	C₂²	semidirect
44. #546×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. D₄²×C₈₉	C₂²	semidirect
47. D₄²×C₈₉	C₂²	semidirect
48. D₄²×C₈₉	C₂²	semidirect
49. D₄²×C₈₉	C₂²	semidirect
50. D₄²×C₈₉	C₂²	semidirect
51. #542×C₈₉	C₂²	semidirect
52. #542×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #541×C₈₉	C₂²	semidirect
55. #540×C₈₉	C₂²	semidirect
56. #540×C₈₉	C₂²	semidirect
57. #540×C₈₉	C₂²	semidirect
58. #539×C₈₉	C₂²	semidirect
59. #539×C₈₉	C₂²	semidirect
60. #538×C₈₉	C₂²	semidirect
61. #538×C₈₉	C₂²	semidirect
62. #538×C₈₉	C₂²	semidirect
63. #538×C₈₉	C₂²	semidirect
64. #538×C₈₉	C₂²	semidirect
65. #537×C₈₉	C₂²	semidirect
66. #536×C₈₉	C₂²	semidirect
67. #536×C₈₉	C₂²	semidirect
69. #535×C₈₉	C₂²	semidirect
70. #535×C₈₉	C₂²	semidirect
71. #535×C₈₉	C₂²	semidirect
72. #535×C₈₉	C₂²	semidirect
73. #535×C₈₉	C₂²	semidirect
74. #535×C₈₉	C₂²	semidirect
75. #535×C₈₉	C₂²	semidirect
76. #535×C₈₉	C₂²	semidirect
77. #535×C₈₉	C₂²	semidirect
78. #534×C₈₉	C₂²	semidirect
79. #534×C₈₉	C₂²	semidirect
80. #534×C₈₉	C₂²	semidirect
81. #534×C₈₉	C₂²	semidirect
82. #533×C₈₉	C₂²	semidirect
83. #532×C₈₉	C₂²	semidirect
84. #532×C₈₉	C₂²	semidirect
85. #532×C₈₉	C₂²	semidirect
86. #532×C₈₉	C₂²	semidirect
87. C₂×#127×C₈₉	C₂²	semidirect
88. C₂×#127×C₈₉	C₂²	semidirect
89. #529×C₈₉	C₂²	semidirect
90. #529×C₈₉	C₂²	semidirect
91. #529×C₈₉	C₂²	semidirect
92. C₂×#124×C₈₉	C₂²	semidirect
93. C₂×#124×C₈₉	C₂²	semidirect
94. #525×C₈₉	C₂²	semidirect
95. #525×C₈₉	C₂²	semidirect
96. #525×C₈₉	C₂²	semidirect
97. C₂×#123×C₈₉	C₂²	semidirect
98. C₂×#121×C₈₉	C₂²	semidirect
99. C₂×#120×C₈₉	C₂²	semidirect
100. C₂×#120×C₈₉	C₂²	semidirect
101. #519×C₈₉	C₂²	semidirect
102. #518×C₈₉	C₂²	semidirect
103. #518×C₈₉	C₂²	semidirect
104. C₄×#41×C₈₉	C₂²	semidirect
105. C₄×#41×C₈₉	C₂²	semidirect
106. C₂×#117×C₈₉	C₂²	semidirect
118. C₂×#41×C₈₉	C₂³	semidirect
119. C₂×#41×C₈₉	C₂³	semidirect
120. C₂×#41×C₈₉	C₂³	semidirect
122. C₂²×Q₈×C₈₉	C₂³	semidirect
135. C₂²×D₄×C₈₉	C₂³	semidirect
136. C₂²×D₄×C₈₉	C₂³	semidirect
139. C₄⋊Q₈×C₈₉	C₂³	semidirect
140. C₄⋊Q₈×C₈₉	C₂³	semidirect
141. C₄⋊Q₈×C₈₉	C₂³	semidirect
148. #127×C₈₉	C₂³	semidirect
149. #127×C₈₉	C₂³	semidirect
150. #127×C₈₉	C₂³	semidirect
153. #126×C₈₉	C₂³	semidirect
154. #126×C₈₉	C₂³	semidirect
155. #126×C₈₉	C₂³	semidirect
156. #126×C₈₉	C₂³	semidirect
157. #125×C₈₉	C₂³	semidirect
158. #125×C₈₉	C₂³	semidirect
159. #125×C₈₉	C₂³	semidirect
168. #124×C₈₉	C₂³	semidirect
169. #124×C₈₉	C₂³	semidirect
170. #124×C₈₉	C₂³	semidirect
171. #124×C₈₉	C₂³	semidirect
172. #124×C₈₉	C₂³	semidirect
173. #124×C₈₉	C₂³	semidirect
174. #124×C₈₉	C₂³	semidirect
182. #123×C₈₉	C₂³	semidirect
183. #123×C₈₉	C₂³	semidirect
184. #123×C₈₉	C₂³	semidirect
185. #123×C₈₉	C₂³	semidirect
186. #123×C₈₉	C₂³	semidirect
187. #123×C₈₉	C₂³	semidirect
188. #123×C₈₉	C₂³	semidirect
189. #123×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
213. #121×C₈₉	C₂³	semidirect
214. #121×C₈₉	C₂³	semidirect
215. #121×C₈₉	C₂³	semidirect
216. #121×C₈₉	C₂³	semidirect
217. #121×C₈₉	C₂³	semidirect
218. #121×C₈₉	C₂³	semidirect
219. #121×C₈₉	C₂³	semidirect
220. #121×C₈₉	C₂³	semidirect
221. #121×C₈₉	C₂³	semidirect
222. #121×C₈₉	C₂³	semidirect
235. #120×C₈₉	C₂³	semidirect
236. #120×C₈₉	C₂³	semidirect
237. #120×C₈₉	C₂³	semidirect
238. C₄×Q₈×C₈₉	C₂³	semidirect
239. C₄×Q₈×C₈₉	C₂³	semidirect
240. C₄×Q₈×C₈₉	C₂³	semidirect
241. C₄×Q₈×C₈₉	C₂³	semidirect
248. C₄×D₄×C₈₉	C₂³	semidirect
249. C₄×D₄×C₈₉	C₂³	semidirect
250. C₄×D₄×C₈₉	C₂³	semidirect
251. C₄×D₄×C₈₉	C₂³	semidirect
252. C₄×D₄×C₈₉	C₂³	semidirect
253. C₄×D₄×C₈₉	C₂³	semidirect
254. C₄×D₄×C₈₉	C₂³	semidirect
255. C₄×D₄×C₈₉	C₂³	semidirect
256. C₄×D₄×C₈₉	C₂³	semidirect
262. #117×C₈₉	C₂³	semidirect
263. #117×C₈₉	C₂³	semidirect
264. #117×C₈₉	C₂³	semidirect
266. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
272. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
273. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
275. C₂×C₄²×C₈₉	C₂³	semidirect
276. C₂×C₄²×C₈₉	C₂³	semidirect
493. #62876	C₈₉	direct (N × H)
502. #3562	C₂×C₈₉	semidirect
503. #3558	C₂×C₈₉	semidirect
504. #3546	C₂×C₈₉	semidirect
505. #3543	C₂×C₈₉	semidirect
506. #3534	C₂×C₈₉	semidirect
507. #3532	C₂×C₈₉	semidirect
508. #3510	C₂×C₈₉	semidirect
509. #3508	C₂×C₈₉	semidirect
510. #3500	C₂×C₈₉	semidirect
511. #3498	C₂×C₈₉	semidirect
512. #3487	C₂×C₈₉	semidirect
513. #3485	C₂×C₈₉	semidirect
514. #3484	C₂×C₈₉	semidirect
515. #3455	C₂×C₈₉	semidirect
516. C₂×#535	C₂×C₈₉	semidirect
517. C₈₉	#62876	direct (N × H)
518. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
519. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
520. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
521. C₂²×#41	C₂²×C₈₉	semidirect
522. C₂³×D₄	C₂²×C₈₉	semidirect
523. #562	C₂²×C₈₉	semidirect
524. H(3,𝔽₄)	C₂²×C₈₉	semidirect
525. #560	C₂²×C₈₉	semidirect
526. #560	C₂²×C₈₉	semidirect
527. #560	C₂²×C₈₉	semidirect
528. #559	C₂²×C₈₉	semidirect
529. #559	C₂²×C₈₉	semidirect
530. #556	C₂²×C₈₉	semidirect
531. #553	C₂²×C₈₉	semidirect
532. #551	C₂²×C₈₉	semidirect
533. #551	C₂²×C₈₉	semidirect
534. #550	C₂²×C₈₉	semidirect
535. #550	C₂²×C₈₉	semidirect
536. #550	C₂²×C₈₉	semidirect
537. #548	C₂²×C₈₉	semidirect
538. #548	C₂²×C₈₉	semidirect
539. #547	C₂²×C₈₉	semidirect
540. #546	C₂²×C₈₉	semidirect
541. #546	C₂²×C₈₉	semidirect
542. #546	C₂²×C₈₉	semidirect
543. #546	C₂²×C₈₉	semidirect
544. #546	C₂²×C₈₉	semidirect
545. #546	C₂²×C₈₉	semidirect
546. #546	C₂²×C₈₉	semidirect
547. #546	C₂²×C₈₉	semidirect
548. D₄²	C₂²×C₈₉	semidirect
549. D₄²	C₂²×C₈₉	semidirect
550. D₄²	C₂²×C₈₉	semidirect
551. D₄²	C₂²×C₈₉	semidirect
552. D₄²	C₂²×C₈₉	semidirect
553. #542	C₂²×C₈₉	semidirect
554. #542	C₂²×C₈₉	semidirect
555. #542	C₂²×C₈₉	semidirect
556. #541	C₂²×C₈₉	semidirect
557. #540	C₂²×C₈₉	semidirect
558. #540	C₂²×C₈₉	semidirect
559. #540	C₂²×C₈₉	semidirect
560. #539	C₂²×C₈₉	semidirect
561. #539	C₂²×C₈₉	semidirect
562. #538	C₂²×C₈₉	semidirect
563. #538	C₂²×C₈₉	semidirect
564. #538	C₂²×C₈₉	semidirect
565. #538	C₂²×C₈₉	semidirect
566. #538	C₂²×C₈₉	semidirect
567. #537	C₂²×C₈₉	semidirect
568. #536	C₂²×C₈₉	semidirect
569. #536	C₂²×C₈₉	semidirect
571. #535	C₂²×C₈₉	semidirect
572. #535	C₂²×C₈₉	semidirect
573. #535	C₂²×C₈₉	semidirect
574. #535	C₂²×C₈₉	semidirect
575. #535	C₂²×C₈₉	semidirect
576. #535	C₂²×C₈₉	semidirect
577. #535	C₂²×C₈₉	semidirect
578. #535	C₂²×C₈₉	semidirect
579. #535	C₂²×C₈₉	semidirect
580. #534	C₂²×C₈₉	semidirect
581. #534	C₂²×C₈₉	semidirect
582. #534	C₂²×C₈₉	semidirect
583. #534	C₂²×C₈₉	semidirect
584. #533	C₂²×C₈₉	semidirect
585. #532	C₂²×C₈₉	semidirect
586. #532	C₂²×C₈₉	semidirect
587. #532	C₂²×C₈₉	semidirect
588. #532	C₂²×C₈₉	semidirect
589. C₂×#127	C₂²×C₈₉	semidirect
590. C₂×#127	C₂²×C₈₉	semidirect
591. #529	C₂²×C₈₉	semidirect
592. #529	C₂²×C₈₉	semidirect
593. #529	C₂²×C₈₉	semidirect
594. C₂×#124	C₂²×C₈₉	semidirect
595. C₂×#124	C₂²×C₈₉	semidirect
596. #525	C₂²×C₈₉	semidirect
597. #525	C₂²×C₈₉	semidirect
598. #525	C₂²×C₈₉	semidirect
599. C₂×#123	C₂²×C₈₉	semidirect
600. C₂×#121	C₂²×C₈₉	semidirect
601. C₂×#120	C₂²×C₈₉	semidirect
602. C₂×#120	C₂²×C₈₉	semidirect
603. #519	C₂²×C₈₉	semidirect
604. #518	C₂²×C₈₉	semidirect
605. #518	C₂²×C₈₉	semidirect
606. C₄×#41	C₂²×C₈₉	semidirect
607. C₄×#41	C₂²×C₈₉	semidirect
608. C₂×#117	C₂²×C₈₉	semidirect
620. C₂×#41	C₂³×C₈₉	semidirect
621. C₂×#41	C₂³×C₈₉	semidirect
622. C₂×#41	C₂³×C₈₉	semidirect
624. C₂²×Q₈	C₂³×C₈₉	semidirect
637. C₂²×D₄	C₂³×C₈₉	semidirect
638. C₂²×D₄	C₂³×C₈₉	semidirect
641. C₄⋊Q₈	C₂³×C₈₉	semidirect
642. C₄⋊Q₈	C₂³×C₈₉	semidirect
643. C₄⋊Q₈	C₂³×C₈₉	semidirect
650. #127	C₂³×C₈₉	semidirect
651. #127	C₂³×C₈₉	semidirect
652. #127	C₂³×C₈₉	semidirect
655. #126	C₂³×C₈₉	semidirect
656. #126	C₂³×C₈₉	semidirect
657. #126	C₂³×C₈₉	semidirect
658. #126	C₂³×C₈₉	semidirect
659. #125	C₂³×C₈₉	semidirect
660. #125	C₂³×C₈₉	semidirect
661. #125	C₂³×C₈₉	semidirect
670. #124	C₂³×C₈₉	semidirect
671. #124	C₂³×C₈₉	semidirect
672. #124	C₂³×C₈₉	semidirect
673. #124	C₂³×C₈₉	semidirect
674. #124	C₂³×C₈₉	semidirect
675. #124	C₂³×C₈₉	semidirect
676. #124	C₂³×C₈₉	semidirect
684. #123	C₂³×C₈₉	semidirect
685. #123	C₂³×C₈₉	semidirect
686. #123	C₂³×C₈₉	semidirect
687. #123	C₂³×C₈₉	semidirect
688. #123	C₂³×C₈₉	semidirect
689. #123	C₂³×C₈₉	semidirect
690. #123	C₂³×C₈₉	semidirect
691. #123	C₂³×C₈₉	semidirect
695. C₂²⋊Q₈	C₂³×C₈₉	semidirect
696. C₂²⋊Q₈	C₂³×C₈₉	semidirect
697. C₂²⋊Q₈	C₂³×C₈₉	semidirect
698. C₂²⋊Q₈	C₂³×C₈₉	semidirect
699. C₂²⋊Q₈	C₂³×C₈₉	semidirect
700. C₂²⋊Q₈	C₂³×C₈₉	semidirect
715. #121	C₂³×C₈₉	semidirect
716. #121	C₂³×C₈₉	semidirect
717. #121	C₂³×C₈₉	semidirect
718. #121	C₂³×C₈₉	semidirect
719. #121	C₂³×C₈₉	semidirect
720. #121	C₂³×C₈₉	semidirect
721. #121	C₂³×C₈₉	semidirect
722. #121	C₂³×C₈₉	semidirect
723. #121	C₂³×C₈₉	semidirect
724. #121	C₂³×C₈₉	semidirect
737. #120	C₂³×C₈₉	semidirect
738. #120	C₂³×C₈₉	semidirect
739. #120	C₂³×C₈₉	semidirect
740. C₄×Q₈	C₂³×C₈₉	semidirect
741. C₄×Q₈	C₂³×C₈₉	semidirect
742. C₄×Q₈	C₂³×C₈₉	semidirect
743. C₄×Q₈	C₂³×C₈₉	semidirect
750. C₄×D₄	C₂³×C₈₉	semidirect
751. C₄×D₄	C₂³×C₈₉	semidirect
752. C₄×D₄	C₂³×C₈₉	semidirect
753. C₄×D₄	C₂³×C₈₉	semidirect
754. C₄×D₄	C₂³×C₈₉	semidirect
755. C₄×D₄	C₂³×C₈₉	semidirect
756. C₄×D₄	C₂³×C₈₉	semidirect
757. C₄×D₄	C₂³×C₈₉	semidirect
758. C₄×D₄	C₂³×C₈₉	semidirect
764. #117	C₂³×C₈₉	semidirect
765. #117	C₂³×C₈₉	semidirect
766. #117	C₂³×C₈₉	semidirect
768. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
774. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
775. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
777. C₂×C₄²	C₂³×C₈₉	semidirect
778. C₂×C₄²	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3562	2
C₈₉×#3558	2
C₈₉×#3546	2
C₈₉×#3543	2
C₈₉×#3534	2
C₈₉×#3532	2
C₈₉×#3510	2
C₈₉×#3508	2
C₈₉×#3500	2
C₈₉×#3498	2
C₈₉×#3487	2
C₈₉×#3485	2
C₈₉×#3484	2
C₈₉×#3455	2
C₂×#535×C₈₉	2
#62876	89

Subgroups — C89×#62876 #36440724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62876 #36440724