Subgroups — C₈₉×#62887 #36440735

Order 22784.

6910 conjugacy classes of subgroups.

The subgroup lattice has 966 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×#3561	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3554	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3552	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3535	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3533	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3510	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3509	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3500	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3499	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3486	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3485	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
17	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#563×C₈₉	C₂²	1	8	yes	complemented
22	#563×C₈₉	C₂²	1	16	yes	complemented
23	#562×C₈₉	C₂²	1	16	yes	complemented
24	#562×C₈₉	C₂²	1	16	yes	complemented
25	#560×C₈₉	C₂²	1	8	yes	complemented
26	#559×C₈₉	C₂²	1	8	yes	complemented
27	#559×C₈₉	C₂²	1	8	yes	complemented
28	#557×C₈₉	C₂²	1	8	yes	complemented
29	#556×C₈₉	C₂²	1	8	yes	complemented
30	#556×C₈₉	C₂²	1	8	yes	complemented
31	#554×C₈₉	C₂²	1	16	yes	complemented
32	#553×C₈₉	C₂²	1	16	yes	complemented
33	#552×C₈₉	C₂²	1	16	yes	complemented
34	#551×C₈₉	C₂²	1	16	yes	complemented
35	#551×C₈₉	C₂²	1	8	yes	complemented
36	#551×C₈₉	C₂²	1	16	yes	complemented
37	#550×C₈₉	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
39	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
40	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
41	#548×C₈₉	C₂²	1	8	yes	complemented
42	#548×C₈₉	C₂²	1	8	yes	complemented
43	#548×C₈₉	C₂²	1	8	yes	complemented
44	#548×C₈₉	C₂²	1	8	yes	complemented
45	#547×C₈₉	C₂²	1	8	yes	—
46	#547×C₈₉	C₂²	1	16	yes	complemented
47	#547×C₈₉	C₂²	1	8	yes	complemented
48	#546×C₈₉	C₂²	1	8	yes	—
49	#546×C₈₉	C₂²	1	16	yes	—
50	#546×C₈₉	C₂²	1	8	yes	complemented
51	#544×C₈₉	C₂²	1	8	yes	complemented
52	#543×C₈₉	C₂²	1	8	yes	complemented
53	#542×C₈₉	C₂²	1	4	yes	complemented
54	#542×C₈₉	C₂²	1	4	yes	complemented
55	#542×C₈₉	C₂²	1	8	yes	complemented
56	#542×C₈₉	C₂²	1	16	yes	complemented
57	#542×C₈₉	C₂²	1	16	yes	complemented
58	#541×C₈₉	C₂²	1	4	yes	complemented
59	#541×C₈₉	C₂²	1	8	yes	complemented
60	#540×C₈₉	C₂²	1	4	yes	complemented
61	#540×C₈₉	C₂²	1	16	yes	complemented
62	#539×C₈₉	C₂²	1	8	yes	complemented
63	#539×C₈₉	C₂²	1	16	yes	complemented
64	#539×C₈₉	C₂²	1	16	yes	complemented
65	#539×C₈₉	C₂²	1	8	yes	complemented
66	#538×C₈₉	C₂²	1	8	yes	complemented
67	#538×C₈₉	C₂²	1	16	yes	complemented
68	#538×C₈₉	C₂²	1	8	yes	complemented
69	#536×C₈₉	C₂²	1	2	yes	—
70	#536×C₈₉	C₂²	1	2	yes	—
71	#536×C₈₉	C₂²	1	8	yes	complemented
72	#536×C₈₉	C₂²	1	8	yes	complemented
73	#536×C₈₉	C₂²	1	2	yes	complemented
74	#536×C₈₉	C₂²	1	8	yes	complemented
75	#536×C₈₉	C₂²	1	4	yes	complemented
76	#536×C₈₉	C₂²	1	4	yes	complemented
77	#536×C₈₉	C₂²	1	4	yes	complemented
78	#535×C₈₉	C₂²	1	2	yes	—
79	#535×C₈₉	C₂²	1	4	yes	complemented
80	#535×C₈₉	C₂²	1	4	yes	complemented
81	#534×C₈₉	C₂²	1	4	yes	—
82	#533×C₈₉	C₂²	1	2	yes	complemented
83	#533×C₈₉	C₂²	1	8	yes	complemented
84	#532×C₈₉	C₂²	1	2	yes	—
85	#532×C₈₉	C₂²	1	4	yes	complemented
86	#532×C₈₉	C₂²	1	4	yes	complemented
87	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
88	C₂×C₄⋊Q₈×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	—
93	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
94	#525×C₈₉	C₂²	1	2	yes	—
95	#525×C₈₉	C₂²	1	2	yes	complemented
96	#525×C₈₉	C₂²	1	8	yes	complemented
97	#525×C₈₉	C₂²	1	4	yes	complemented
98	C₂×#123×C₈₉	C₂²	1	4	yes	—
99	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
100	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
101	#519×C₈₉	C₂²	1	2	yes	complemented
102	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#518×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×#41×C₈₉	C₂²	1	2	yes	—
105	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
106	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	2₋¹⁺⁴×C₈₉	—	4	8	no	—
108	2₋¹⁺⁴×C₈₉	—	4	4	no	—
109	H(5,𝔽₂)×C₈₉	—	4	4	no	—
110	C₂×#41×C₈₉	—	4	4	no	—
111	C₂×#41×C₈₉	C₂³	1	2	yes	—
112	C₂×#41×C₈₉	C₂³	1	2	yes	—
113	C₂×#41×C₈₉	C₂³	1	4	yes	—
114	C₂×#41×C₈₉	C₂³	1	8	yes	—
115	C₂×#41×C₈₉	C₂³	1	4	yes	—
116	C₂×#41×C₈₉	C₂³	1	4	yes	—
117	C₂×#41×C₈₉	C₂³	1	4	yes	—
118	C₂×#41×C₈₉	C₂³	1	4	yes	—
119	C₂×#41×C₈₉	C₂³	1	8	yes	—
120	C₂²×Q₈×C₈₉	—	4	4	no	—
121	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
122	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
126	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
127	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
130	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
142	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
145	#127×C₈₉	C₂³	1	2	yes	—
146	#127×C₈₉	C₂³	1	4	yes	—
147	#127×C₈₉	C₂³	1	8	yes	—
148	#126×C₈₉	C₂³	1	8	yes	—
149	#126×C₈₉	C₂³	1	16	yes	—
150	#126×C₈₉	C₂³	1	8	yes	—
151	#126×C₈₉	C₂³	1	8	yes	—
152	#126×C₈₉	C₂³	1	8	yes	—
153	#126×C₈₉	C₂³	1	16	yes	—
154	#126×C₈₉	C₂³	1	16	yes	—
155	#126×C₈₉	C₂³	1	16	yes	—
156	#125×C₈₉	C₂³	1	4	yes	—
157	#125×C₈₉	C₂³	1	8	yes	—
158	#125×C₈₉	C₂³	1	8	yes	—
159	#125×C₈₉	C₂³	1	16	yes	—
160	#125×C₈₉	C₂³	1	16	yes	—
161	#125×C₈₉	C₂³	1	16	yes	—
162	#124×C₈₉	C₂³	1	4	yes	—
163	#124×C₈₉	C₂³	1	4	yes	—
164	#124×C₈₉	C₂³	1	8	yes	—
165	#124×C₈₉	C₂³	1	2	yes	—
166	#124×C₈₉	C₂³	1	4	yes	—
167	#124×C₈₉	C₂³	1	4	yes	—
168	#124×C₈₉	C₂³	1	16	yes	—
169	#124×C₈₉	C₂³	1	8	yes	—
170	#124×C₈₉	C₂³	1	8	yes	—
171	#124×C₈₉	C₂³	1	2	yes	—
172	#124×C₈₉	C₂³	1	4	yes	—
173	#124×C₈₉	C₂³	1	4	yes	—
174	#124×C₈₉	C₂³	1	8	yes	—
175	#124×C₈₉	C₂³	1	16	yes	—
176	#124×C₈₉	C₂³	1	16	yes	—
177	#123×C₈₉	C₂³	1	4	yes	—
178	#123×C₈₉	C₂³	1	8	yes	—
179	#123×C₈₉	C₂³	1	16	yes	—
180	#123×C₈₉	C₂³	1	16	yes	—
181	#123×C₈₉	C₂³	1	8	yes	—
182	#123×C₈₉	C₂³	1	8	yes	—
183	#123×C₈₉	C₂³	1	4	yes	—
184	#123×C₈₉	C₂³	1	8	yes	—
185	#123×C₈₉	C₂³	1	8	yes	—
186	#123×C₈₉	C₂³	1	8	yes	—
187	#123×C₈₉	C₂³	1	8	yes	—
188	#123×C₈₉	C₂³	1	8	yes	—
189	#123×C₈₉	C₂³	1	16	yes	—
190	#123×C₈₉	C₂³	1	8	yes	—
191	#123×C₈₉	C₂³	1	8	yes	—
192	#123×C₈₉	C₂³	1	16	yes	—
193	#123×C₈₉	C₂³	1	16	yes	—
194	#123×C₈₉	C₂³	1	16	yes	—
195	#123×C₈₉	C₂³	1	16	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
207	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
208	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
212	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
213	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
214	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
215	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
216	#121×C₈₉	C₂³	1	4	yes	—
217	#121×C₈₉	C₂³	1	8	yes	—
218	#121×C₈₉	C₂³	1	16	yes	—
219	#121×C₈₉	C₂³	1	4	yes	—
220	#121×C₈₉	C₂³	1	8	yes	—
221	#121×C₈₉	C₂³	1	8	yes	—
222	#121×C₈₉	C₂³	1	8	yes	—
223	#121×C₈₉	C₂³	1	8	yes	—
224	#121×C₈₉	C₂³	1	16	yes	—
225	#121×C₈₉	C₂³	1	16	yes	—
226	#121×C₈₉	C₂³	1	16	yes	—
227	#121×C₈₉	C₂³	1	16	yes	—
228	#121×C₈₉	C₂³	1	16	yes	—
229	#120×C₈₉	C₂³	1	4	yes	—
230	#120×C₈₉	C₂³	1	4	yes	—
231	#120×C₈₉	C₂³	1	8	yes	—
232	#120×C₈₉	C₂³	1	8	yes	—
233	#120×C₈₉	C₂³	1	16	yes	—
234	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
235	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
237	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
241	C₄×D₄×C₈₉	C₂³	1	8	yes	—
242	C₄×D₄×C₈₉	C₂³	1	4	yes	—
243	C₄×D₄×C₈₉	C₂³	1	8	yes	—
244	C₄×D₄×C₈₉	C₂³	1	4	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	16	yes	—
249	C₄×D₄×C₈₉	C₂³	1	16	yes	—
250	C₄×D₄×C₈₉	C₂³	1	16	yes	—
251	C₄×D₄×C₈₉	C₂³	1	8	yes	—
252	C₄×D₄×C₈₉	C₂³	1	16	yes	—
253	C₄×D₄×C₈₉	C₂³	1	16	yes	—
254	C₄×D₄×C₈₉	C₂³	1	16	yes	—
255	#117×C₈₉	C₂³	1	4	yes	—
256	#117×C₈₉	C₂³	1	4	yes	—
257	#117×C₈₉	C₂³	1	2	yes	—
258	#117×C₈₉	C₂³	1	4	yes	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	4	yes	—
261	#117×C₈₉	C₂³	1	4	yes	—
262	#117×C₈₉	C₂³	1	8	yes	—
263	#117×C₈₉	C₂³	1	16	yes	—
264	#117×C₈₉	C₂³	1	16	yes	—
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
267	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
269	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
274	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
275	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
276	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
277	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
278	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
280	#41×C₈₉	—	2	8	no	—
281	#41×C₈₉	—	2	8	no	—
282	#41×C₈₉	—	4	8	no	—
283	#41×C₈₉	—	4	16	no	—
284	#41×C₈₉	—	4	16	no	—
285	#41×C₈₉	—	4	8	no	—
286	#41×C₈₉	—	4	8	no	—
287	#41×C₈₉	—	4	8	no	—
288	#41×C₈₉	—	4	8	no	—
289	C₂×Q₈×C₈₉	—	2	8	no	—
290	C₂×Q₈×C₈₉	—	2	4	no	—
291	C₂×Q₈×C₈₉	—	4	4	no	—
292	C₂×Q₈×C₈₉	—	4	16	no	—
293	C₂×Q₈×C₈₉	—	4	8	no	—
294	C₂×Q₈×C₈₉	—	4	8	no	—
295	C₂×Q₈×C₈₉	—	4	8	no	—
296	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
297	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
302	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
303	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
304	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
305	C₂×D₄×C₈₉	—	2	4	no	—
306	C₂×D₄×C₈₉	—	4	8	no	—
307	C₂×D₄×C₈₉	—	4	4	no	—
308	C₂×D₄×C₈₉	—	4	8	no	—
309	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
310	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
322	C₂²×C₄×C₈₉	—	2	4	no	—
323	C₂²×C₄×C₈₉	—	4	4	no	—
324	C₂²×C₄×C₈₉	—	4	4	no	—
325	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
331	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
343	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
344	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
346	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
362	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
363	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
364	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
365	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
366	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
367	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
370	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	8	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	C₄²×C₈₉	C₂⁴	1	2	yes	—
383	C₄²×C₈₉	C₂⁴	1	2	yes	—
384	C₄²×C₈₉	C₂⁴	1	4	yes	—
385	C₄²×C₈₉	C₂⁴	1	4	yes	—
386	C₄²×C₈₉	C₂⁴	1	8	yes	—
387	C₄²×C₈₉	C₂⁴	1	4	yes	—
388	C₄²×C₈₉	C₂⁴	1	8	yes	—
389	C₄²×C₈₉	C₂⁴	1	16	yes	—
390	C₄²×C₈₉	C₂⁴	1	8	yes	—
391	C₂³×C₈₉	—	2	2	no	—
392	C₂³×C₈₉	—	2	4	no	—
393	C₂³×C₈₉	—	4	2	no	—
394	C₂³×C₈₉	—	4	4	no	—
395	C₂³×C₈₉	—	4	4	no	—
396	C₂³×C₈₉	—	4	8	no	—
397	C₂³×C₈₉	C₂⁵	1	4	yes	—
398	C₂³×C₈₉	C₂⁵	1	4	yes	—
399	C₂³×C₈₉	C₂⁵	1	2	yes	—
400	C₂³×C₈₉	C₂⁵	1	4	yes	—
401	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
402	Q₈×C₈₉	—	2	8	no	—
403	Q₈×C₈₉	—	2	8	no	—
404	Q₈×C₈₉	—	2	8	no	—
405	Q₈×C₈₉	—	2	4	no	—
406	Q₈×C₈₉	—	2	4	no	—
407	Q₈×C₈₉	—	4	8	no	—
408	Q₈×C₈₉	—	4	8	no	—
409	Q₈×C₈₉	—	4	4	no	—
410	Q₈×C₈₉	—	4	8	no	—
411	D₄×C₈₉	—	2	8	no	—
412	D₄×C₈₉	—	2	8	no	—
413	D₄×C₈₉	—	2	8	no	—
414	D₄×C₈₉	—	2	4	no	—
415	D₄×C₈₉	—	2	4	no	—
416	D₄×C₈₉	—	4	8	no	—
417	D₄×C₈₉	—	4	8	no	—
418	D₄×C₈₉	—	4	8	no	—
419	D₄×C₈₉	—	4	8	no	—
420	D₄×C₈₉	—	4	16	no	—
421	D₄×C₈₉	—	4	8	no	—
422	D₄×C₈₉	—	4	4	no	—
423	D₄×C₈₉	—	4	8	no	—
424	C₂×C₄×C₈₉	—	2	2	no	—
425	C₂×C₄×C₈₉	—	2	4	no	—
426	C₂×C₄×C₈₉	—	2	8	no	—
427	C₂×C₄×C₈₉	—	2	8	no	—
428	C₂×C₄×C₈₉	—	2	8	no	—
429	C₂×C₄×C₈₉	—	2	8	no	—
430	C₂×C₄×C₈₉	—	4	8	no	—
431	C₂×C₄×C₈₉	—	4	8	no	—
432	C₂×C₄×C₈₉	—	4	8	no	—
433	C₂×C₄×C₈₉	—	4	4	no	—
434	C₂×C₄×C₈₉	—	4	8	no	—
435	C₂×C₄×C₈₉	—	4	8	no	—
436	C₂×C₄×C₈₉	—	4	4	no	—
437	C₂×C₄×C₈₉	—	4	8	no	—
438	C₂×C₄×C₈₉	—	4	8	no	—
439	C₂×C₄×C₈₉	—	4	8	no	—
440	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
441	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
442	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
443	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
444	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
445	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
446	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
447	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
448	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
449	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
450	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
451	C₂²×C₈₉	—	2	2	no	—
452	C₂²×C₈₉	—	2	2	no	—
453	C₂²×C₈₉	—	2	4	no	—
454	C₂²×C₈₉	—	2	4	no	—
455	C₂²×C₈₉	—	2	4	no	—
456	C₂²×C₈₉	—	2	8	no	—
457	C₂²×C₈₉	—	2	8	no	—
458	C₂²×C₈₉	—	2	8	no	—
459	C₂²×C₈₉	—	2	4	no	—
460	C₂²×C₈₉	—	4	4	no	—
461	C₂²×C₈₉	—	8	4	no	—
462	C₂²×C₈₉	—	16	4	no	—
463	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
464	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
465	C₄×C₈₉	—	2	2	no	—
466	C₄×C₈₉	—	2	4	no	—
467	C₄×C₈₉	—	2	4	no	—
468	C₄×C₈₉	—	2	4	no	—
469	C₄×C₈₉	—	2	8	no	—
470	C₄×C₈₉	—	2	4	no	—
471	C₄×C₈₉	—	2	8	no	—
472	C₄×C₈₉	—	2	4	no	—
473	C₄×C₈₉	—	2	8	no	—
474	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
475	#62887	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂×C₈₉	—	2	2	no	—
477	C₂×C₈₉	—	4	4	no	—
478	C₂×C₈₉	—	4	2	no	—
479	C₂×C₈₉	—	4	4	no	—
480	C₂×C₈₉	—	4	4	no	—
481	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
483	#3562	C₂×C₈₉	1	8	yes	complemented
484	#3561	C₂×C₈₉	1	8	yes	complemented
485	#3554	C₂×C₈₉	1	8	yes	complemented
486	#3552	C₂×C₈₉	1	8	yes	complemented
487	#3535	C₂×C₈₉	1	8	yes	complemented
488	#3533	C₂×C₈₉	1	8	yes	complemented
489	#3510	C₂×C₈₉	1	2	yes	complemented
490	#3509	C₂×C₈₉	1	2	yes	complemented
491	#3500	C₂×C₈₉	1	2	yes	complemented
492	#3499	C₂×C₈₉	1	2	yes	complemented
493	#3487	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#3486	C₂×C₈₉	1	2	yes	complemented
495	#3485	C₂×C₈₉	1	1	yes	characteristic, complemented
496	#3455	C₂×C₈₉	1	2	yes	complemented
497	C₂×#536	C₂×C₈₉	1	1	yes	characteristic, complemented
498	C₈₉	#62887	1	1	yes	characteristic, direct product factor, Sylow
499	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
500	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
502	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
503	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
504	#563	C₂²×C₈₉	1	8	yes	complemented
505	#563	C₂²×C₈₉	1	16	yes	complemented
506	#562	C₂²×C₈₉	1	16	yes	complemented
507	#562	C₂²×C₈₉	1	16	yes	complemented
508	#560	C₂²×C₈₉	1	8	yes	complemented
509	#559	C₂²×C₈₉	1	8	yes	complemented
510	#559	C₂²×C₈₉	1	8	yes	complemented
511	#557	C₂²×C₈₉	1	8	yes	complemented
512	#556	C₂²×C₈₉	1	8	yes	complemented
513	#556	C₂²×C₈₉	1	8	yes	complemented
514	#554	C₂²×C₈₉	1	16	yes	complemented
515	#553	C₂²×C₈₉	1	16	yes	complemented
516	#552	C₂²×C₈₉	1	16	yes	complemented
517	#551	C₂²×C₈₉	1	16	yes	complemented
518	#551	C₂²×C₈₉	1	8	yes	complemented
519	#551	C₂²×C₈₉	1	16	yes	complemented
520	#550	C₂²×C₈₉	1	8	yes	complemented
521	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
522	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
523	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
524	#548	C₂²×C₈₉	1	8	yes	complemented
525	#548	C₂²×C₈₉	1	8	yes	complemented
526	#548	C₂²×C₈₉	1	8	yes	complemented
527	#548	C₂²×C₈₉	1	8	yes	complemented
528	#547	C₂²×C₈₉	1	8	yes	—
529	#547	C₂²×C₈₉	1	16	yes	complemented
530	#547	C₂²×C₈₉	1	8	yes	complemented
531	#546	C₂²×C₈₉	1	8	yes	—
532	#546	C₂²×C₈₉	1	16	yes	—
533	#546	C₂²×C₈₉	1	8	yes	complemented
534	#544	C₂²×C₈₉	1	8	yes	complemented
535	#543	C₂²×C₈₉	1	8	yes	complemented
536	#542	C₂²×C₈₉	1	4	yes	complemented
537	#542	C₂²×C₈₉	1	4	yes	complemented
538	#542	C₂²×C₈₉	1	8	yes	complemented
539	#542	C₂²×C₈₉	1	16	yes	complemented
540	#542	C₂²×C₈₉	1	16	yes	complemented
541	#541	C₂²×C₈₉	1	4	yes	complemented
542	#541	C₂²×C₈₉	1	8	yes	complemented
543	#540	C₂²×C₈₉	1	4	yes	complemented
544	#540	C₂²×C₈₉	1	16	yes	complemented
545	#539	C₂²×C₈₉	1	8	yes	complemented
546	#539	C₂²×C₈₉	1	16	yes	complemented
547	#539	C₂²×C₈₉	1	16	yes	complemented
548	#539	C₂²×C₈₉	1	8	yes	complemented
549	#538	C₂²×C₈₉	1	8	yes	complemented
550	#538	C₂²×C₈₉	1	16	yes	complemented
551	#538	C₂²×C₈₉	1	8	yes	complemented
552	#536	C₂²×C₈₉	1	2	yes	—
553	#536	C₂²×C₈₉	1	2	yes	—
554	#536	C₂²×C₈₉	1	8	yes	complemented
555	#536	C₂²×C₈₉	1	8	yes	complemented
556	#536	C₂²×C₈₉	1	2	yes	complemented
557	#536	C₂²×C₈₉	1	8	yes	complemented
558	#536	C₂²×C₈₉	1	4	yes	complemented
559	#536	C₂²×C₈₉	1	4	yes	complemented
560	#536	C₂²×C₈₉	1	4	yes	complemented
561	#535	C₂²×C₈₉	1	2	yes	—
562	#535	C₂²×C₈₉	1	4	yes	complemented
563	#535	C₂²×C₈₉	1	4	yes	complemented
564	#534	C₂²×C₈₉	1	4	yes	—
565	#533	C₂²×C₈₉	1	2	yes	complemented
566	#533	C₂²×C₈₉	1	8	yes	complemented
567	#532	C₂²×C₈₉	1	2	yes	—
568	#532	C₂²×C₈₉	1	4	yes	complemented
569	#532	C₂²×C₈₉	1	4	yes	complemented
570	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
571	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
572	#529	C₂²×C₈₉	1	8	yes	complemented
573	#529	C₂²×C₈₉	1	8	yes	complemented
574	#529	C₂²×C₈₉	1	8	yes	complemented
575	C₂×#124	C₂²×C₈₉	1	2	yes	—
576	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
577	#525	C₂²×C₈₉	1	2	yes	—
578	#525	C₂²×C₈₉	1	2	yes	complemented
579	#525	C₂²×C₈₉	1	8	yes	complemented
580	#525	C₂²×C₈₉	1	4	yes	complemented
581	C₂×#123	C₂²×C₈₉	1	4	yes	—
582	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
583	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
584	#519	C₂²×C₈₉	1	2	yes	complemented
585	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
586	#518	C₂²×C₈₉	1	1	yes	characteristic
587	C₄×#41	C₂²×C₈₉	1	2	yes	—
588	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
589	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
590	2₋¹⁺⁴	—	4	8	no	—
591	2₋¹⁺⁴	—	4	4	no	—
592	H(5,𝔽₂)	—	4	4	no	—
593	C₂×#41	—	4	4	no	—
594	C₂×#41	C₂³×C₈₉	1	2	yes	—
595	C₂×#41	C₂³×C₈₉	1	2	yes	—
596	C₂×#41	C₂³×C₈₉	1	4	yes	—
597	C₂×#41	C₂³×C₈₉	1	8	yes	—
598	C₂×#41	C₂³×C₈₉	1	4	yes	—
599	C₂×#41	C₂³×C₈₉	1	4	yes	—
600	C₂×#41	C₂³×C₈₉	1	4	yes	—
601	C₂×#41	C₂³×C₈₉	1	4	yes	—
602	C₂×#41	C₂³×C₈₉	1	8	yes	—
603	C₂²×Q₈	—	4	4	no	—
604	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
605	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
606	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
607	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
608	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
609	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
610	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
611	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
613	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
614	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
615	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
617	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
618	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
619	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
620	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
621	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
622	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
623	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
624	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
625	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
626	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
627	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
628	#127	C₂³×C₈₉	1	2	yes	—
629	#127	C₂³×C₈₉	1	4	yes	—
630	#127	C₂³×C₈₉	1	8	yes	—
631	#126	C₂³×C₈₉	1	8	yes	—
632	#126	C₂³×C₈₉	1	16	yes	—
633	#126	C₂³×C₈₉	1	8	yes	—
634	#126	C₂³×C₈₉	1	8	yes	—
635	#126	C₂³×C₈₉	1	8	yes	—
636	#126	C₂³×C₈₉	1	16	yes	—
637	#126	C₂³×C₈₉	1	16	yes	—
638	#126	C₂³×C₈₉	1	16	yes	—
639	#125	C₂³×C₈₉	1	4	yes	—
640	#125	C₂³×C₈₉	1	8	yes	—
641	#125	C₂³×C₈₉	1	8	yes	—
642	#125	C₂³×C₈₉	1	16	yes	—
643	#125	C₂³×C₈₉	1	16	yes	—
644	#125	C₂³×C₈₉	1	16	yes	—
645	#124	C₂³×C₈₉	1	4	yes	—
646	#124	C₂³×C₈₉	1	4	yes	—
647	#124	C₂³×C₈₉	1	8	yes	—
648	#124	C₂³×C₈₉	1	2	yes	—
649	#124	C₂³×C₈₉	1	4	yes	—
650	#124	C₂³×C₈₉	1	4	yes	—
651	#124	C₂³×C₈₉	1	16	yes	—
652	#124	C₂³×C₈₉	1	8	yes	—
653	#124	C₂³×C₈₉	1	8	yes	—
654	#124	C₂³×C₈₉	1	2	yes	—
655	#124	C₂³×C₈₉	1	4	yes	—
656	#124	C₂³×C₈₉	1	4	yes	—
657	#124	C₂³×C₈₉	1	8	yes	—
658	#124	C₂³×C₈₉	1	16	yes	—
659	#124	C₂³×C₈₉	1	16	yes	—
660	#123	C₂³×C₈₉	1	4	yes	—
661	#123	C₂³×C₈₉	1	8	yes	—
662	#123	C₂³×C₈₉	1	16	yes	—
663	#123	C₂³×C₈₉	1	16	yes	—
664	#123	C₂³×C₈₉	1	8	yes	—
665	#123	C₂³×C₈₉	1	8	yes	—
666	#123	C₂³×C₈₉	1	4	yes	—
667	#123	C₂³×C₈₉	1	8	yes	—
668	#123	C₂³×C₈₉	1	8	yes	—
669	#123	C₂³×C₈₉	1	8	yes	—
670	#123	C₂³×C₈₉	1	8	yes	—
671	#123	C₂³×C₈₉	1	8	yes	—
672	#123	C₂³×C₈₉	1	16	yes	—
673	#123	C₂³×C₈₉	1	8	yes	—
674	#123	C₂³×C₈₉	1	8	yes	—
675	#123	C₂³×C₈₉	1	16	yes	—
676	#123	C₂³×C₈₉	1	16	yes	—
677	#123	C₂³×C₈₉	1	16	yes	—
678	#123	C₂³×C₈₉	1	16	yes	—
679	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
680	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
681	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
682	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
683	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
684	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
685	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
686	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
687	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
688	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
689	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
697	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
698	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
699	#121	C₂³×C₈₉	1	4	yes	—
700	#121	C₂³×C₈₉	1	8	yes	—
701	#121	C₂³×C₈₉	1	16	yes	—
702	#121	C₂³×C₈₉	1	4	yes	—
703	#121	C₂³×C₈₉	1	8	yes	—
704	#121	C₂³×C₈₉	1	8	yes	—
705	#121	C₂³×C₈₉	1	8	yes	—
706	#121	C₂³×C₈₉	1	8	yes	—
707	#121	C₂³×C₈₉	1	16	yes	—
708	#121	C₂³×C₈₉	1	16	yes	—
709	#121	C₂³×C₈₉	1	16	yes	—
710	#121	C₂³×C₈₉	1	16	yes	—
711	#121	C₂³×C₈₉	1	16	yes	—
712	#120	C₂³×C₈₉	1	4	yes	—
713	#120	C₂³×C₈₉	1	4	yes	—
714	#120	C₂³×C₈₉	1	8	yes	—
715	#120	C₂³×C₈₉	1	8	yes	—
716	#120	C₂³×C₈₉	1	16	yes	—
717	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
718	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
719	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
720	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
721	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
722	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
723	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
724	C₄×D₄	C₂³×C₈₉	1	8	yes	—
725	C₄×D₄	C₂³×C₈₉	1	4	yes	—
726	C₄×D₄	C₂³×C₈₉	1	8	yes	—
727	C₄×D₄	C₂³×C₈₉	1	4	yes	—
728	C₄×D₄	C₂³×C₈₉	1	8	yes	—
729	C₄×D₄	C₂³×C₈₉	1	8	yes	—
730	C₄×D₄	C₂³×C₈₉	1	8	yes	—
731	C₄×D₄	C₂³×C₈₉	1	16	yes	—
732	C₄×D₄	C₂³×C₈₉	1	16	yes	—
733	C₄×D₄	C₂³×C₈₉	1	16	yes	—
734	C₄×D₄	C₂³×C₈₉	1	8	yes	—
735	C₄×D₄	C₂³×C₈₉	1	16	yes	—
736	C₄×D₄	C₂³×C₈₉	1	16	yes	—
737	C₄×D₄	C₂³×C₈₉	1	16	yes	—
738	#117	C₂³×C₈₉	1	4	yes	—
739	#117	C₂³×C₈₉	1	4	yes	—
740	#117	C₂³×C₈₉	1	2	yes	—
741	#117	C₂³×C₈₉	1	4	yes	—
742	#117	C₂³×C₈₉	1	2	yes	—
743	#117	C₂³×C₈₉	1	4	yes	—
744	#117	C₂³×C₈₉	1	4	yes	—
745	#117	C₂³×C₈₉	1	8	yes	—
746	#117	C₂³×C₈₉	1	16	yes	—
747	#117	C₂³×C₈₉	1	16	yes	—
748	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
750	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
751	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
757	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
758	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
759	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
760	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
761	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
763	#41	—	2	8	no	—
764	#41	—	2	8	no	—
765	#41	—	4	8	no	—
766	#41	—	4	16	no	—
767	#41	—	4	16	no	—
768	#41	—	4	8	no	—
769	#41	—	4	8	no	—
770	#41	—	4	8	no	—
771	#41	—	4	8	no	—
772	C₂×Q₈	—	2	8	no	—
773	C₂×Q₈	—	2	4	no	—
774	C₂×Q₈	—	4	4	no	—
775	C₂×Q₈	—	4	16	no	—
776	C₂×Q₈	—	4	8	no	—
777	C₂×Q₈	—	4	8	no	—
778	C₂×Q₈	—	4	8	no	—
779	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
780	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
781	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
782	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
783	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
784	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
785	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
786	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
787	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	4	8	no	—
790	C₂×D₄	—	4	4	no	—
791	C₂×D₄	—	4	8	no	—
792	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
793	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
794	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
795	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
796	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
797	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
798	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
799	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
800	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
801	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
802	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
803	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
804	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	4	4	no	—
807	C₂²×C₄	—	4	4	no	—
808	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
809	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
810	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
811	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
814	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
815	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
816	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
817	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
818	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
819	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
820	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
821	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
822	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
823	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
824	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
825	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
826	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
827	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
828	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
829	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
830	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
831	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
833	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
834	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
835	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
836	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
837	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
838	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
839	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
840	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
841	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
842	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
843	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
844	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
845	C₂²⋊C₄	C₂⁴×C₈₉	1	4	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	2	yes	—
850	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
851	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
852	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
853	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
854	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
855	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
856	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
857	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
858	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
859	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
860	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
861	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
862	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
864	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
865	C₄²	C₂⁴×C₈₉	1	2	yes	—
866	C₄²	C₂⁴×C₈₉	1	2	yes	—
867	C₄²	C₂⁴×C₈₉	1	4	yes	—
868	C₄²	C₂⁴×C₈₉	1	4	yes	—
869	C₄²	C₂⁴×C₈₉	1	8	yes	—
870	C₄²	C₂⁴×C₈₉	1	4	yes	—
871	C₄²	C₂⁴×C₈₉	1	8	yes	—
872	C₄²	C₂⁴×C₈₉	1	16	yes	—
873	C₄²	C₂⁴×C₈₉	1	8	yes	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	4	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	4	4	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	8	no	—
880	C₂³	C₂⁵×C₈₉	1	4	yes	—
881	C₂³	C₂⁵×C₈₉	1	4	yes	—
882	C₂³	C₂⁵×C₈₉	1	2	yes	—
883	C₂³	C₂⁵×C₈₉	1	4	yes	—
884	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
885	Q₈	—	2	8	no	—
886	Q₈	—	2	8	no	—
887	Q₈	—	2	8	no	—
888	Q₈	—	2	4	no	—
889	Q₈	—	2	4	no	—
890	Q₈	—	4	8	no	—
891	Q₈	—	4	8	no	—
892	Q₈	—	4	4	no	—
893	Q₈	—	4	8	no	—
894	D₄	—	2	8	no	—
895	D₄	—	2	8	no	—
896	D₄	—	2	8	no	—
897	D₄	—	2	4	no	—
898	D₄	—	2	4	no	—
899	D₄	—	4	8	no	—
900	D₄	—	4	8	no	—
901	D₄	—	4	8	no	—
902	D₄	—	4	8	no	—
903	D₄	—	4	16	no	—
904	D₄	—	4	8	no	—
905	D₄	—	4	4	no	—
906	D₄	—	4	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	8	no	—
911	C₂×C₄	—	2	8	no	—
912	C₂×C₄	—	2	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	8	no	—
918	C₂×C₄	—	4	8	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	4	8	no	—
921	C₂×C₄	—	4	8	no	—
922	C₂×C₄	—	4	8	no	—
923	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
924	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
925	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
926	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
927	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
928	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
929	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
930	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
931	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
932	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
933	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	8	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	8	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	4	4	no	—
944	C₂²	—	8	4	no	—
945	C₂²	—	16	4	no	—
946	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
947	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	2	4	no	—
951	C₄	—	2	4	no	—
952	C₄	—	2	8	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	8	no	—
955	C₄	—	2	4	no	—
956	C₄	—	2	8	no	—
957	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
958	C₂	—	2	2	no	—
959	C₂	—	4	4	no	—
960	C₂	—	4	2	no	—
961	C₂	—	4	4	no	—
962	C₂	—	4	4	no	—
963	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
964	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×#3562	C₂	semidirect
2. C₈₉×#3561	C₂	semidirect
3. C₈₉×#3554	C₂	semidirect
4. C₈₉×#3552	C₂	semidirect
5. C₈₉×#3535	C₂	semidirect
6. C₈₉×#3533	C₂	semidirect
7. C₈₉×#3510	C₂	semidirect
8. C₈₉×#3509	C₂	semidirect
9. C₈₉×#3500	C₂	semidirect
10. C₈₉×#3499	C₂	semidirect
11. C₈₉×#3487	C₂	semidirect
12. C₈₉×#3486	C₂	semidirect
13. C₈₉×#3485	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₂×#536×C₈₉	C₂	semidirect
17. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
20. C₂³×Q₈×C₈₉	C₂²	semidirect
21. #563×C₈₉	C₂²	semidirect
22. #563×C₈₉	C₂²	semidirect
23. #562×C₈₉	C₂²	semidirect
24. #562×C₈₉	C₂²	semidirect
25. #560×C₈₉	C₂²	semidirect
26. #559×C₈₉	C₂²	semidirect
27. #559×C₈₉	C₂²	semidirect
28. #557×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
30. #556×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
32. #553×C₈₉	C₂²	semidirect
33. #552×C₈₉	C₂²	semidirect
34. #551×C₈₉	C₂²	semidirect
35. #551×C₈₉	C₂²	semidirect
36. #551×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. D₄×Q₈×C₈₉	C₂²	semidirect
40. D₄×Q₈×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
43. #548×C₈₉	C₂²	semidirect
44. #548×C₈₉	C₂²	semidirect
46. #547×C₈₉	C₂²	semidirect
47. #547×C₈₉	C₂²	semidirect
50. #546×C₈₉	C₂²	semidirect
51. #544×C₈₉	C₂²	semidirect
52. #543×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #542×C₈₉	C₂²	semidirect
55. #542×C₈₉	C₂²	semidirect
56. #542×C₈₉	C₂²	semidirect
57. #542×C₈₉	C₂²	semidirect
58. #541×C₈₉	C₂²	semidirect
59. #541×C₈₉	C₂²	semidirect
60. #540×C₈₉	C₂²	semidirect
61. #540×C₈₉	C₂²	semidirect
62. #539×C₈₉	C₂²	semidirect
63. #539×C₈₉	C₂²	semidirect
64. #539×C₈₉	C₂²	semidirect
65. #539×C₈₉	C₂²	semidirect
66. #538×C₈₉	C₂²	semidirect
67. #538×C₈₉	C₂²	semidirect
68. #538×C₈₉	C₂²	semidirect
71. #536×C₈₉	C₂²	semidirect
72. #536×C₈₉	C₂²	semidirect
73. #536×C₈₉	C₂²	semidirect
74. #536×C₈₉	C₂²	semidirect
75. #536×C₈₉	C₂²	semidirect
76. #536×C₈₉	C₂²	semidirect
77. #536×C₈₉	C₂²	semidirect
79. #535×C₈₉	C₂²	semidirect
80. #535×C₈₉	C₂²	semidirect
82. #533×C₈₉	C₂²	semidirect
83. #533×C₈₉	C₂²	semidirect
85. #532×C₈₉	C₂²	semidirect
86. #532×C₈₉	C₂²	semidirect
87. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
88. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
89. #529×C₈₉	C₂²	semidirect
90. #529×C₈₉	C₂²	semidirect
91. #529×C₈₉	C₂²	semidirect
93. C₂×#124×C₈₉	C₂²	semidirect
95. #525×C₈₉	C₂²	semidirect
96. #525×C₈₉	C₂²	semidirect
97. #525×C₈₉	C₂²	semidirect
99. C₂×#123×C₈₉	C₂²	semidirect
100. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
101. #519×C₈₉	C₂²	semidirect
102. #519×C₈₉	C₂²	semidirect
105. C₄×#41×C₈₉	C₂²	semidirect
106. C₂×#117×C₈₉	C₂²	semidirect
475. #62887	C₈₉	direct (N × H)
483. #3562	C₂×C₈₉	semidirect
484. #3561	C₂×C₈₉	semidirect
485. #3554	C₂×C₈₉	semidirect
486. #3552	C₂×C₈₉	semidirect
487. #3535	C₂×C₈₉	semidirect
488. #3533	C₂×C₈₉	semidirect
489. #3510	C₂×C₈₉	semidirect
490. #3509	C₂×C₈₉	semidirect
491. #3500	C₂×C₈₉	semidirect
492. #3499	C₂×C₈₉	semidirect
493. #3487	C₂×C₈₉	semidirect
494. #3486	C₂×C₈₉	semidirect
495. #3485	C₂×C₈₉	semidirect
496. #3455	C₂×C₈₉	semidirect
497. C₂×#536	C₂×C₈₉	semidirect
498. C₈₉	#62887	direct (N × H)
500. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
503. C₂³×Q₈	C₂²×C₈₉	semidirect
504. #563	C₂²×C₈₉	semidirect
505. #563	C₂²×C₈₉	semidirect
506. #562	C₂²×C₈₉	semidirect
507. #562	C₂²×C₈₉	semidirect
508. #560	C₂²×C₈₉	semidirect
509. #559	C₂²×C₈₉	semidirect
510. #559	C₂²×C₈₉	semidirect
511. #557	C₂²×C₈₉	semidirect
512. #556	C₂²×C₈₉	semidirect
513. #556	C₂²×C₈₉	semidirect
514. #554	C₂²×C₈₉	semidirect
515. #553	C₂²×C₈₉	semidirect
516. #552	C₂²×C₈₉	semidirect
517. #551	C₂²×C₈₉	semidirect
518. #551	C₂²×C₈₉	semidirect
519. #551	C₂²×C₈₉	semidirect
520. #550	C₂²×C₈₉	semidirect
521. D₄×Q₈	C₂²×C₈₉	semidirect
522. D₄×Q₈	C₂²×C₈₉	semidirect
523. D₄×Q₈	C₂²×C₈₉	semidirect
524. #548	C₂²×C₈₉	semidirect
525. #548	C₂²×C₈₉	semidirect
526. #548	C₂²×C₈₉	semidirect
527. #548	C₂²×C₈₉	semidirect
529. #547	C₂²×C₈₉	semidirect
530. #547	C₂²×C₈₉	semidirect
533. #546	C₂²×C₈₉	semidirect
534. #544	C₂²×C₈₉	semidirect
535. #543	C₂²×C₈₉	semidirect
536. #542	C₂²×C₈₉	semidirect
537. #542	C₂²×C₈₉	semidirect
538. #542	C₂²×C₈₉	semidirect
539. #542	C₂²×C₈₉	semidirect
540. #542	C₂²×C₈₉	semidirect
541. #541	C₂²×C₈₉	semidirect
542. #541	C₂²×C₈₉	semidirect
543. #540	C₂²×C₈₉	semidirect
544. #540	C₂²×C₈₉	semidirect
545. #539	C₂²×C₈₉	semidirect
546. #539	C₂²×C₈₉	semidirect
547. #539	C₂²×C₈₉	semidirect
548. #539	C₂²×C₈₉	semidirect
549. #538	C₂²×C₈₉	semidirect
550. #538	C₂²×C₈₉	semidirect
551. #538	C₂²×C₈₉	semidirect
554. #536	C₂²×C₈₉	semidirect
555. #536	C₂²×C₈₉	semidirect
556. #536	C₂²×C₈₉	semidirect
557. #536	C₂²×C₈₉	semidirect
558. #536	C₂²×C₈₉	semidirect
559. #536	C₂²×C₈₉	semidirect
560. #536	C₂²×C₈₉	semidirect
562. #535	C₂²×C₈₉	semidirect
563. #535	C₂²×C₈₉	semidirect
565. #533	C₂²×C₈₉	semidirect
566. #533	C₂²×C₈₉	semidirect
568. #532	C₂²×C₈₉	semidirect
569. #532	C₂²×C₈₉	semidirect
570. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
571. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
572. #529	C₂²×C₈₉	semidirect
573. #529	C₂²×C₈₉	semidirect
574. #529	C₂²×C₈₉	semidirect
576. C₂×#124	C₂²×C₈₉	semidirect
578. #525	C₂²×C₈₉	semidirect
579. #525	C₂²×C₈₉	semidirect
580. #525	C₂²×C₈₉	semidirect
582. C₂×#123	C₂²×C₈₉	semidirect
583. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
584. #519	C₂²×C₈₉	semidirect
585. #519	C₂²×C₈₉	semidirect
588. C₄×#41	C₂²×C₈₉	semidirect
589. C₂×#117	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×#3562	2
C₈₉×#3561	2
C₈₉×#3554	2
C₈₉×#3552	2
C₈₉×#3535	2
C₈₉×#3533	2
C₈₉×#3510	2
C₈₉×#3509	2
C₈₉×#3500	2
C₈₉×#3499	2
C₈₉×#3487	2
C₈₉×#3486	2
C₈₉×#3485	2
C₈₉×#3455	2
C₂×#536×C₈₉	2
#62887	89

Subgroups — C89×#62887 #36440735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62887 #36440735