Subgroups — C₈₉×#62888 #36440736

Order 22784.

6906 conjugacy classes of subgroups.

The subgroup lattice has 904 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×#3560	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3559	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3552	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3541	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3539	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3538	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3512	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3507	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3499	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3497	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3489	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	4	yes	complemented
17	C₂²×#41×C₈₉	C₂²	1	2	yes	—
18	#563×C₈₉	C₂²	1	16	yes	complemented
19	#563×C₈₉	C₂²	1	16	yes	complemented
20	#562×C₈₉	C₂²	1	16	yes	complemented
21	#560×C₈₉	C₂²	1	16	yes	complemented
22	#559×C₈₉	C₂²	1	4	yes	complemented
23	#557×C₈₉	C₂²	1	4	yes	complemented
24	#556×C₈₉	C₂²	1	4	yes	complemented
25	#556×C₈₉	C₂²	1	8	yes	complemented
26	#554×C₈₉	C₂²	1	4	yes	complemented
27	#554×C₈₉	C₂²	1	16	yes	complemented
28	#553×C₈₉	C₂²	1	8	yes	complemented
29	#553×C₈₉	C₂²	1	16	yes	complemented
30	#553×C₈₉	C₂²	1	16	yes	complemented
31	#553×C₈₉	C₂²	1	16	yes	complemented
32	#552×C₈₉	C₂²	1	8	yes	complemented
33	#552×C₈₉	C₂²	1	8	yes	complemented
34	#551×C₈₉	C₂²	1	16	yes	complemented
35	#550×C₈₉	C₂²	1	4	yes	complemented
36	#550×C₈₉	C₂²	1	4	yes	complemented
37	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
39	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
41	#548×C₈₉	C₂²	1	8	yes	—
42	#548×C₈₉	C₂²	1	8	yes	complemented
43	#548×C₈₉	C₂²	1	8	yes	complemented
44	#547×C₈₉	C₂²	1	8	yes	—
45	#547×C₈₉	C₂²	1	16	yes	complemented
46	#547×C₈₉	C₂²	1	8	yes	complemented
47	#547×C₈₉	C₂²	1	16	yes	complemented
48	#546×C₈₉	C₂²	1	16	yes	—
49	#546×C₈₉	C₂²	1	8	yes	complemented
50	#544×C₈₉	C₂²	1	16	yes	complemented
51	#542×C₈₉	C₂²	1	4	yes	complemented
52	#542×C₈₉	C₂²	1	16	yes	complemented
53	#541×C₈₉	C₂²	1	4	yes	complemented
54	#541×C₈₉	C₂²	1	4	yes	complemented
55	#541×C₈₉	C₂²	1	8	yes	complemented
56	#541×C₈₉	C₂²	1	2	yes	complemented
57	#541×C₈₉	C₂²	1	4	yes	complemented
58	#540×C₈₉	C₂²	1	2	yes	complemented
59	#540×C₈₉	C₂²	1	4	yes	complemented
60	#540×C₈₉	C₂²	1	16	yes	complemented
61	#539×C₈₉	C₂²	1	4	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	16	yes	complemented
66	#538×C₈₉	C₂²	1	4	yes	—
67	#538×C₈₉	C₂²	1	16	yes	complemented
68	#538×C₈₉	C₂²	1	16	yes	complemented
69	#537×C₈₉	C₂²	1	4	yes	—
70	#537×C₈₉	C₂²	1	8	yes	—
71	#537×C₈₉	C₂²	1	4	yes	complemented
72	#537×C₈₉	C₂²	1	8	yes	complemented
73	#536×C₈₉	C₂²	1	4	yes	—
74	#536×C₈₉	C₂²	1	8	yes	—
75	#536×C₈₉	C₂²	1	4	yes	complemented
76	#536×C₈₉	C₂²	1	8	yes	complemented
77	#535×C₈₉	C₂²	1	4	yes	—
78	#534×C₈₉	C₂²	1	4	yes	—
79	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	#532×C₈₉	C₂²	1	2	yes	—
81	#532×C₈₉	C₂²	1	2	yes	—
82	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#532×C₈₉	C₂²	1	8	yes	complemented
84	#532×C₈₉	C₂²	1	4	yes	complemented
85	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
87	#529×C₈₉	C₂²	1	8	yes	complemented
88	#529×C₈₉	C₂²	1	8	yes	complemented
89	#529×C₈₉	C₂²	1	8	yes	complemented
90	C₂×#126×C₈₉	C₂²	1	4	yes	—
91	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₂×#125×C₈₉	C₂²	1	4	yes	complemented
93	#525×C₈₉	C₂²	1	4	yes	—
94	#525×C₈₉	C₂²	1	4	yes	—
95	#525×C₈₉	C₂²	1	2	yes	—
96	#525×C₈₉	C₂²	1	8	yes	complemented
97	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
98	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
99	#520×C₈₉	C₂²	1	4	yes	complemented
100	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
101	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
102	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
103	2₋¹⁺⁴×C₈₉	—	4	16	no	—
104	C₂×#41×C₈₉	—	4	8	no	—
105	C₂×#41×C₈₉	C₂³	1	2	yes	—
106	C₂×#41×C₈₉	C₂³	1	4	yes	—
107	C₂×#41×C₈₉	C₂³	1	4	yes	—
108	C₂×#41×C₈₉	C₂³	1	8	yes	—
109	C₂×#41×C₈₉	C₂³	1	8	yes	—
110	C₂×#41×C₈₉	C₂³	1	16	yes	—
111	C₂×#41×C₈₉	C₂³	1	4	yes	—
112	C₂×#41×C₈₉	C₂³	1	4	yes	—
113	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
114	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
115	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
116	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
118	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
121	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
124	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
125	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
126	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
129	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
131	#127×C₈₉	C₂³	1	2	yes	—
132	#127×C₈₉	C₂³	1	2	yes	—
133	#127×C₈₉	C₂³	1	1	yes	characteristic
134	#127×C₈₉	C₂³	1	8	yes	—
135	#126×C₈₉	C₂³	1	16	yes	—
136	#126×C₈₉	C₂³	1	16	yes	—
137	#126×C₈₉	C₂³	1	8	yes	—
138	#126×C₈₉	C₂³	1	16	yes	—
139	#126×C₈₉	C₂³	1	16	yes	—
140	#126×C₈₉	C₂³	1	8	yes	—
141	#126×C₈₉	C₂³	1	16	yes	—
142	#126×C₈₉	C₂³	1	16	yes	—
143	#125×C₈₉	C₂³	1	4	yes	—
144	#125×C₈₉	C₂³	1	16	yes	—
145	#125×C₈₉	C₂³	1	4	yes	—
146	#125×C₈₉	C₂³	1	16	yes	—
147	#125×C₈₉	C₂³	1	8	yes	—
148	#125×C₈₉	C₂³	1	8	yes	—
149	#125×C₈₉	C₂³	1	2	yes	—
150	#125×C₈₉	C₂³	1	16	yes	—
151	#125×C₈₉	C₂³	1	16	yes	—
152	#124×C₈₉	C₂³	1	4	yes	—
153	#124×C₈₉	C₂³	1	8	yes	—
154	#124×C₈₉	C₂³	1	8	yes	—
155	#124×C₈₉	C₂³	1	4	yes	—
156	#124×C₈₉	C₂³	1	8	yes	—
157	#124×C₈₉	C₂³	1	16	yes	—
158	#124×C₈₉	C₂³	1	2	yes	—
159	#124×C₈₉	C₂³	1	16	yes	—
160	#123×C₈₉	C₂³	1	8	yes	—
161	#123×C₈₉	C₂³	1	8	yes	—
162	#123×C₈₉	C₂³	1	4	yes	—
163	#123×C₈₉	C₂³	1	16	yes	—
164	#123×C₈₉	C₂³	1	16	yes	—
165	#123×C₈₉	C₂³	1	8	yes	—
166	#123×C₈₉	C₂³	1	8	yes	—
167	#123×C₈₉	C₂³	1	16	yes	—
168	#123×C₈₉	C₂³	1	16	yes	—
169	#123×C₈₉	C₂³	1	16	yes	—
170	#123×C₈₉	C₂³	1	16	yes	—
171	#123×C₈₉	C₂³	1	16	yes	—
172	#123×C₈₉	C₂³	1	16	yes	—
173	#123×C₈₉	C₂³	1	16	yes	—
174	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
175	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
181	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
182	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
183	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
184	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
187	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
188	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
189	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
193	#121×C₈₉	C₂³	1	4	yes	—
194	#121×C₈₉	C₂³	1	8	yes	—
195	#121×C₈₉	C₂³	1	8	yes	—
196	#121×C₈₉	C₂³	1	8	yes	—
197	#121×C₈₉	C₂³	1	4	yes	—
198	#121×C₈₉	C₂³	1	8	yes	—
199	#121×C₈₉	C₂³	1	8	yes	—
200	#121×C₈₉	C₂³	1	4	yes	—
201	#121×C₈₉	C₂³	1	8	yes	—
202	#121×C₈₉	C₂³	1	4	yes	—
203	#121×C₈₉	C₂³	1	16	yes	—
204	#121×C₈₉	C₂³	1	16	yes	—
205	#121×C₈₉	C₂³	1	16	yes	—
206	#121×C₈₉	C₂³	1	16	yes	—
207	#121×C₈₉	C₂³	1	16	yes	—
208	#121×C₈₉	C₂³	1	16	yes	—
209	#121×C₈₉	C₂³	1	16	yes	—
210	#121×C₈₉	C₂³	1	16	yes	—
211	#120×C₈₉	C₂³	1	8	yes	—
212	#120×C₈₉	C₂³	1	8	yes	—
213	#120×C₈₉	C₂³	1	4	yes	—
214	#120×C₈₉	C₂³	1	16	yes	—
215	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
219	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
221	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
222	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
223	C₄×D₄×C₈₉	C₂³	1	8	yes	—
224	C₄×D₄×C₈₉	C₂³	1	4	yes	—
225	C₄×D₄×C₈₉	C₂³	1	16	yes	—
226	C₄×D₄×C₈₉	C₂³	1	8	yes	—
227	C₄×D₄×C₈₉	C₂³	1	8	yes	—
228	C₄×D₄×C₈₉	C₂³	1	4	yes	—
229	C₄×D₄×C₈₉	C₂³	1	4	yes	—
230	C₄×D₄×C₈₉	C₂³	1	8	yes	—
231	C₄×D₄×C₈₉	C₂³	1	16	yes	—
232	C₄×D₄×C₈₉	C₂³	1	16	yes	—
233	C₄×D₄×C₈₉	C₂³	1	4	yes	—
234	C₄×D₄×C₈₉	C₂³	1	8	yes	—
235	C₄×D₄×C₈₉	C₂³	1	16	yes	—
236	C₄×D₄×C₈₉	C₂³	1	16	yes	—
237	C₄×D₄×C₈₉	C₂³	1	16	yes	—
238	C₄×D₄×C₈₉	C₂³	1	8	yes	—
239	C₄×D₄×C₈₉	C₂³	1	8	yes	—
240	#117×C₈₉	C₂³	1	2	yes	—
241	#117×C₈₉	C₂³	1	2	yes	—
242	#117×C₈₉	C₂³	1	4	yes	—
243	#117×C₈₉	C₂³	1	2	yes	—
244	#117×C₈₉	C₂³	1	4	yes	—
245	#117×C₈₉	C₂³	1	8	yes	—
246	#117×C₈₉	C₂³	1	16	yes	—
247	#117×C₈₉	C₂³	1	16	yes	—
248	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
251	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
252	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
253	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
254	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
255	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
257	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
259	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
260	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
263	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
264	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
266	#41×C₈₉	—	2	16	no	—
267	#41×C₈₉	—	2	8	no	—
268	#41×C₈₉	—	4	8	no	—
269	#41×C₈₉	—	4	8	no	—
270	#41×C₈₉	—	4	32	no	—
271	#41×C₈₉	—	4	8	no	—
272	#41×C₈₉	—	4	16	no	—
273	#41×C₈₉	—	4	16	no	—
274	C₂×Q₈×C₈₉	—	2	8	no	—
275	C₂×Q₈×C₈₉	—	4	4	no	—
276	C₂×Q₈×C₈₉	—	4	16	no	—
277	C₂×Q₈×C₈₉	—	4	16	no	—
278	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
280	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
281	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
282	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
283	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
284	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
285	C₂×D₄×C₈₉	—	4	4	no	—
286	C₂×D₄×C₈₉	—	4	8	no	—
287	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
288	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
289	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
291	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
292	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
293	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
294	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
295	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
296	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
297	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
298	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
299	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₈₉	—	2	4	no	—
301	C₂²×C₄×C₈₉	—	4	8	no	—
302	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
312	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
313	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
314	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
315	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
321	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
325	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
328	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
329	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
330	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
331	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
332	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
333	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
338	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
339	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
340	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
342	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
343	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
344	C₂²⋊C₄×C₈₉	C₂⁴	1	16	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	4	yes	—
349	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
350	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
354	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
355	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
357	C₄²×C₈₉	C₂⁴	1	2	yes	—
358	C₄²×C₈₉	C₂⁴	1	2	yes	—
359	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₄²×C₈₉	C₂⁴	1	4	yes	—
361	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
362	C₄²×C₈₉	C₂⁴	1	8	yes	—
363	C₄²×C₈₉	C₂⁴	1	2	yes	—
364	C₄²×C₈₉	C₂⁴	1	8	yes	—
365	C₄²×C₈₉	C₂⁴	1	8	yes	—
366	C₄²×C₈₉	C₂⁴	1	16	yes	—
367	C₂³×C₈₉	—	2	2	no	—
368	C₂³×C₈₉	—	4	4	no	—
369	C₂³×C₈₉	—	4	2	no	—
370	C₂³×C₈₉	—	4	8	no	—
371	C₂³×C₈₉	C₂⁵	1	2	yes	—
372	C₂³×C₈₉	C₂⁵	1	8	yes	—
373	C₂³×C₈₉	C₂⁵	1	4	yes	—
374	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
375	Q₈×C₈₉	—	2	8	no	—
376	Q₈×C₈₉	—	2	8	no	—
377	Q₈×C₈₉	—	2	4	no	—
378	Q₈×C₈₉	—	2	8	no	—
379	Q₈×C₈₉	—	4	16	no	—
380	Q₈×C₈₉	—	4	4	no	—
381	Q₈×C₈₉	—	4	4	no	—
382	D₄×C₈₉	—	2	16	no	—
383	D₄×C₈₉	—	2	8	no	—
384	D₄×C₈₉	—	2	8	no	—
385	D₄×C₈₉	—	2	4	no	—
386	D₄×C₈₉	—	4	4	no	—
387	D₄×C₈₉	—	4	8	no	—
388	D₄×C₈₉	—	4	8	no	—
389	D₄×C₈₉	—	4	16	no	—
390	D₄×C₈₉	—	4	8	no	—
391	D₄×C₈₉	—	4	4	no	—
392	D₄×C₈₉	—	4	4	no	—
393	D₄×C₈₉	—	4	4	no	—
394	D₄×C₈₉	—	4	16	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	8	no	—
397	C₂×C₄×C₈₉	—	2	4	no	—
398	C₂×C₄×C₈₉	—	2	4	no	—
399	C₂×C₄×C₈₉	—	2	16	no	—
400	C₂×C₄×C₈₉	—	2	8	no	—
401	C₂×C₄×C₈₉	—	4	4	no	—
402	C₂×C₄×C₈₉	—	4	8	no	—
403	C₂×C₄×C₈₉	—	4	2	no	—
404	C₂×C₄×C₈₉	—	4	4	no	—
405	C₂×C₄×C₈₉	—	4	16	no	—
406	C₂×C₄×C₈₉	—	4	8	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	16	no	—
409	C₂×C₄×C₈₉	—	4	16	no	—
410	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
411	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
412	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
413	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
414	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
415	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
416	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
417	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
418	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
419	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
420	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
421	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
422	C₂²×C₈₉	—	2	2	no	—
423	C₂²×C₈₉	—	2	2	no	—
424	C₂²×C₈₉	—	2	4	no	—
425	C₂²×C₈₉	—	2	8	no	—
426	C₂²×C₈₉	—	2	8	no	—
427	C₂²×C₈₉	—	2	8	no	—
428	C₂²×C₈₉	—	2	8	no	—
429	C₂²×C₈₉	—	2	4	no	—
430	C₂²×C₈₉	—	8	2	no	—
431	C₂²×C₈₉	—	8	8	no	—
432	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
433	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
434	C₄×C₈₉	—	2	2	no	—
435	C₄×C₈₉	—	2	8	no	—
436	C₄×C₈₉	—	2	4	no	—
437	C₄×C₈₉	—	2	8	no	—
438	C₄×C₈₉	—	2	8	no	—
439	C₄×C₈₉	—	2	4	no	—
440	C₄×C₈₉	—	2	8	no	—
441	C₄×C₈₉	—	2	2	no	—
442	C₄×C₈₉	—	2	2	no	—
443	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
445	#62888	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂×C₈₉	—	2	2	no	—
447	C₂×C₈₉	—	4	4	no	—
448	C₂×C₈₉	—	4	8	no	—
449	C₂×C₈₉	—	4	2	no	—
450	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
452	#3562	C₂×C₈₉	1	8	yes	complemented
453	#3560	C₂×C₈₉	1	8	yes	complemented
454	#3559	C₂×C₈₉	1	8	yes	complemented
455	#3552	C₂×C₈₉	1	8	yes	complemented
456	#3541	C₂×C₈₉	1	8	yes	complemented
457	#3539	C₂×C₈₉	1	4	yes	complemented
458	#3538	C₂×C₈₉	1	4	yes	complemented
459	#3512	C₂×C₈₉	1	2	yes	complemented
460	#3507	C₂×C₈₉	1	2	yes	complemented
461	#3499	C₂×C₈₉	1	2	yes	complemented
462	#3497	C₂×C₈₉	1	2	yes	complemented
463	#3489	C₂×C₈₉	1	4	yes	complemented
464	#3455	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
466	#3449	C₂×C₈₉	1	1	yes	characteristic, complemented
467	C₈₉	#62888	1	1	yes	characteristic, direct product factor, Sylow
468	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	4	yes	complemented
469	C₂²×#41	C₂²×C₈₉	1	2	yes	—
470	#563	C₂²×C₈₉	1	16	yes	complemented
471	#563	C₂²×C₈₉	1	16	yes	complemented
472	#562	C₂²×C₈₉	1	16	yes	complemented
473	#560	C₂²×C₈₉	1	16	yes	complemented
474	#559	C₂²×C₈₉	1	4	yes	complemented
475	#557	C₂²×C₈₉	1	4	yes	complemented
476	#556	C₂²×C₈₉	1	4	yes	complemented
477	#556	C₂²×C₈₉	1	8	yes	complemented
478	#554	C₂²×C₈₉	1	4	yes	complemented
479	#554	C₂²×C₈₉	1	16	yes	complemented
480	#553	C₂²×C₈₉	1	8	yes	complemented
481	#553	C₂²×C₈₉	1	16	yes	complemented
482	#553	C₂²×C₈₉	1	16	yes	complemented
483	#553	C₂²×C₈₉	1	16	yes	complemented
484	#552	C₂²×C₈₉	1	8	yes	complemented
485	#552	C₂²×C₈₉	1	8	yes	complemented
486	#551	C₂²×C₈₉	1	16	yes	complemented
487	#550	C₂²×C₈₉	1	4	yes	complemented
488	#550	C₂²×C₈₉	1	4	yes	complemented
489	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
490	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
491	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
492	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
493	#548	C₂²×C₈₉	1	8	yes	—
494	#548	C₂²×C₈₉	1	8	yes	complemented
495	#548	C₂²×C₈₉	1	8	yes	complemented
496	#547	C₂²×C₈₉	1	8	yes	—
497	#547	C₂²×C₈₉	1	16	yes	complemented
498	#547	C₂²×C₈₉	1	8	yes	complemented
499	#547	C₂²×C₈₉	1	16	yes	complemented
500	#546	C₂²×C₈₉	1	16	yes	—
501	#546	C₂²×C₈₉	1	8	yes	complemented
502	#544	C₂²×C₈₉	1	16	yes	complemented
503	#542	C₂²×C₈₉	1	4	yes	complemented
504	#542	C₂²×C₈₉	1	16	yes	complemented
505	#541	C₂²×C₈₉	1	4	yes	complemented
506	#541	C₂²×C₈₉	1	4	yes	complemented
507	#541	C₂²×C₈₉	1	8	yes	complemented
508	#541	C₂²×C₈₉	1	2	yes	complemented
509	#541	C₂²×C₈₉	1	4	yes	complemented
510	#540	C₂²×C₈₉	1	2	yes	complemented
511	#540	C₂²×C₈₉	1	4	yes	complemented
512	#540	C₂²×C₈₉	1	16	yes	complemented
513	#539	C₂²×C₈₉	1	4	yes	complemented
514	#539	C₂²×C₈₉	1	8	yes	complemented
515	#539	C₂²×C₈₉	1	16	yes	complemented
516	#539	C₂²×C₈₉	1	16	yes	complemented
517	#539	C₂²×C₈₉	1	16	yes	complemented
518	#538	C₂²×C₈₉	1	4	yes	—
519	#538	C₂²×C₈₉	1	16	yes	complemented
520	#538	C₂²×C₈₉	1	16	yes	complemented
521	#537	C₂²×C₈₉	1	4	yes	—
522	#537	C₂²×C₈₉	1	8	yes	—
523	#537	C₂²×C₈₉	1	4	yes	complemented
524	#537	C₂²×C₈₉	1	8	yes	complemented
525	#536	C₂²×C₈₉	1	4	yes	—
526	#536	C₂²×C₈₉	1	8	yes	—
527	#536	C₂²×C₈₉	1	4	yes	complemented
528	#536	C₂²×C₈₉	1	8	yes	complemented
529	#535	C₂²×C₈₉	1	4	yes	—
530	#534	C₂²×C₈₉	1	4	yes	—
531	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#532	C₂²×C₈₉	1	2	yes	—
533	#532	C₂²×C₈₉	1	2	yes	—
534	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
535	#532	C₂²×C₈₉	1	8	yes	complemented
536	#532	C₂²×C₈₉	1	4	yes	complemented
537	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
539	#529	C₂²×C₈₉	1	8	yes	complemented
540	#529	C₂²×C₈₉	1	8	yes	complemented
541	#529	C₂²×C₈₉	1	8	yes	complemented
542	C₂×#126	C₂²×C₈₉	1	4	yes	—
543	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
544	C₂×#125	C₂²×C₈₉	1	4	yes	complemented
545	#525	C₂²×C₈₉	1	4	yes	—
546	#525	C₂²×C₈₉	1	4	yes	—
547	#525	C₂²×C₈₉	1	2	yes	—
548	#525	C₂²×C₈₉	1	8	yes	complemented
549	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
550	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
551	#520	C₂²×C₈₉	1	4	yes	complemented
552	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
553	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
554	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
555	2₋¹⁺⁴	—	4	16	no	—
556	C₂×#41	—	4	8	no	—
557	C₂×#41	C₂³×C₈₉	1	2	yes	—
558	C₂×#41	C₂³×C₈₉	1	4	yes	—
559	C₂×#41	C₂³×C₈₉	1	4	yes	—
560	C₂×#41	C₂³×C₈₉	1	8	yes	—
561	C₂×#41	C₂³×C₈₉	1	8	yes	—
562	C₂×#41	C₂³×C₈₉	1	16	yes	—
563	C₂×#41	C₂³×C₈₉	1	4	yes	—
564	C₂×#41	C₂³×C₈₉	1	4	yes	—
565	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
566	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
567	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
568	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
569	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
570	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
571	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
573	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
575	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
576	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
577	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
578	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
579	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
580	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
581	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
583	#127	C₂³×C₈₉	1	2	yes	—
584	#127	C₂³×C₈₉	1	2	yes	—
585	#127	C₂³×C₈₉	1	1	yes	characteristic
586	#127	C₂³×C₈₉	1	8	yes	—
587	#126	C₂³×C₈₉	1	16	yes	—
588	#126	C₂³×C₈₉	1	16	yes	—
589	#126	C₂³×C₈₉	1	8	yes	—
590	#126	C₂³×C₈₉	1	16	yes	—
591	#126	C₂³×C₈₉	1	16	yes	—
592	#126	C₂³×C₈₉	1	8	yes	—
593	#126	C₂³×C₈₉	1	16	yes	—
594	#126	C₂³×C₈₉	1	16	yes	—
595	#125	C₂³×C₈₉	1	4	yes	—
596	#125	C₂³×C₈₉	1	16	yes	—
597	#125	C₂³×C₈₉	1	4	yes	—
598	#125	C₂³×C₈₉	1	16	yes	—
599	#125	C₂³×C₈₉	1	8	yes	—
600	#125	C₂³×C₈₉	1	8	yes	—
601	#125	C₂³×C₈₉	1	2	yes	—
602	#125	C₂³×C₈₉	1	16	yes	—
603	#125	C₂³×C₈₉	1	16	yes	—
604	#124	C₂³×C₈₉	1	4	yes	—
605	#124	C₂³×C₈₉	1	8	yes	—
606	#124	C₂³×C₈₉	1	8	yes	—
607	#124	C₂³×C₈₉	1	4	yes	—
608	#124	C₂³×C₈₉	1	8	yes	—
609	#124	C₂³×C₈₉	1	16	yes	—
610	#124	C₂³×C₈₉	1	2	yes	—
611	#124	C₂³×C₈₉	1	16	yes	—
612	#123	C₂³×C₈₉	1	8	yes	—
613	#123	C₂³×C₈₉	1	8	yes	—
614	#123	C₂³×C₈₉	1	4	yes	—
615	#123	C₂³×C₈₉	1	16	yes	—
616	#123	C₂³×C₈₉	1	16	yes	—
617	#123	C₂³×C₈₉	1	8	yes	—
618	#123	C₂³×C₈₉	1	8	yes	—
619	#123	C₂³×C₈₉	1	16	yes	—
620	#123	C₂³×C₈₉	1	16	yes	—
621	#123	C₂³×C₈₉	1	16	yes	—
622	#123	C₂³×C₈₉	1	16	yes	—
623	#123	C₂³×C₈₉	1	16	yes	—
624	#123	C₂³×C₈₉	1	16	yes	—
625	#123	C₂³×C₈₉	1	16	yes	—
626	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
627	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
628	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
629	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
630	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
631	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
632	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
633	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
634	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
635	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
636	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
637	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
638	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
639	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
640	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
641	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
642	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
643	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
644	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
645	#121	C₂³×C₈₉	1	4	yes	—
646	#121	C₂³×C₈₉	1	8	yes	—
647	#121	C₂³×C₈₉	1	8	yes	—
648	#121	C₂³×C₈₉	1	8	yes	—
649	#121	C₂³×C₈₉	1	4	yes	—
650	#121	C₂³×C₈₉	1	8	yes	—
651	#121	C₂³×C₈₉	1	8	yes	—
652	#121	C₂³×C₈₉	1	4	yes	—
653	#121	C₂³×C₈₉	1	8	yes	—
654	#121	C₂³×C₈₉	1	4	yes	—
655	#121	C₂³×C₈₉	1	16	yes	—
656	#121	C₂³×C₈₉	1	16	yes	—
657	#121	C₂³×C₈₉	1	16	yes	—
658	#121	C₂³×C₈₉	1	16	yes	—
659	#121	C₂³×C₈₉	1	16	yes	—
660	#121	C₂³×C₈₉	1	16	yes	—
661	#121	C₂³×C₈₉	1	16	yes	—
662	#121	C₂³×C₈₉	1	16	yes	—
663	#120	C₂³×C₈₉	1	8	yes	—
664	#120	C₂³×C₈₉	1	8	yes	—
665	#120	C₂³×C₈₉	1	4	yes	—
666	#120	C₂³×C₈₉	1	16	yes	—
667	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
668	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
669	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
670	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
671	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
672	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
673	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
674	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
675	C₄×D₄	C₂³×C₈₉	1	8	yes	—
676	C₄×D₄	C₂³×C₈₉	1	4	yes	—
677	C₄×D₄	C₂³×C₈₉	1	16	yes	—
678	C₄×D₄	C₂³×C₈₉	1	8	yes	—
679	C₄×D₄	C₂³×C₈₉	1	8	yes	—
680	C₄×D₄	C₂³×C₈₉	1	4	yes	—
681	C₄×D₄	C₂³×C₈₉	1	4	yes	—
682	C₄×D₄	C₂³×C₈₉	1	8	yes	—
683	C₄×D₄	C₂³×C₈₉	1	16	yes	—
684	C₄×D₄	C₂³×C₈₉	1	16	yes	—
685	C₄×D₄	C₂³×C₈₉	1	4	yes	—
686	C₄×D₄	C₂³×C₈₉	1	8	yes	—
687	C₄×D₄	C₂³×C₈₉	1	16	yes	—
688	C₄×D₄	C₂³×C₈₉	1	16	yes	—
689	C₄×D₄	C₂³×C₈₉	1	16	yes	—
690	C₄×D₄	C₂³×C₈₉	1	8	yes	—
691	C₄×D₄	C₂³×C₈₉	1	8	yes	—
692	#117	C₂³×C₈₉	1	2	yes	—
693	#117	C₂³×C₈₉	1	2	yes	—
694	#117	C₂³×C₈₉	1	4	yes	—
695	#117	C₂³×C₈₉	1	2	yes	—
696	#117	C₂³×C₈₉	1	4	yes	—
697	#117	C₂³×C₈₉	1	8	yes	—
698	#117	C₂³×C₈₉	1	16	yes	—
699	#117	C₂³×C₈₉	1	16	yes	—
700	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
703	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
704	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
705	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
706	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
707	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
708	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
712	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
715	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
716	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
718	#41	—	2	16	no	—
719	#41	—	2	8	no	—
720	#41	—	4	8	no	—
721	#41	—	4	8	no	—
722	#41	—	4	32	no	—
723	#41	—	4	8	no	—
724	#41	—	4	16	no	—
725	#41	—	4	16	no	—
726	C₂×Q₈	—	2	8	no	—
727	C₂×Q₈	—	4	4	no	—
728	C₂×Q₈	—	4	16	no	—
729	C₂×Q₈	—	4	16	no	—
730	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
732	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
733	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
734	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
735	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
736	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
740	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
741	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
742	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
743	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
744	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
745	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
746	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
747	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
748	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
749	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
750	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
751	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	8	no	—
754	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
758	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
763	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
764	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
765	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
766	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
767	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
768	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
772	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
773	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
777	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
778	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
779	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
784	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
785	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
787	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
788	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
789	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
790	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
791	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
792	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
793	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
795	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
796	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
798	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
800	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
801	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
802	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
803	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
804	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
805	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
806	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
807	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
808	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
809	C₄²	C₂⁴×C₈₉	1	2	yes	—
810	C₄²	C₂⁴×C₈₉	1	2	yes	—
811	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₄²	C₂⁴×C₈₉	1	4	yes	—
813	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
814	C₄²	C₂⁴×C₈₉	1	8	yes	—
815	C₄²	C₂⁴×C₈₉	1	2	yes	—
816	C₄²	C₂⁴×C₈₉	1	8	yes	—
817	C₄²	C₂⁴×C₈₉	1	8	yes	—
818	C₄²	C₂⁴×C₈₉	1	16	yes	—
819	C₂³	—	2	2	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	4	8	no	—
823	C₂³	C₂⁵×C₈₉	1	2	yes	—
824	C₂³	C₂⁵×C₈₉	1	8	yes	—
825	C₂³	C₂⁵×C₈₉	1	4	yes	—
826	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	8	no	—
831	Q₈	—	4	16	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	4	no	—
834	D₄	—	2	16	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	16	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	16	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	16	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	16	no	—
861	C₂×C₄	—	4	16	no	—
862	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
863	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
864	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
865	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
866	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
867	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
868	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
869	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
870	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
871	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
872	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
873	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	8	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	8	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
885	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
886	C₄	—	2	2	no	—
887	C₄	—	2	8	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	8	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
896	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
897	C₂	—	2	2	no	—
898	C₂	—	4	4	no	—
899	C₂	—	4	8	no	—
900	C₂	—	4	2	no	—
901	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
902	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×#3560	C₂	semidirect
3. C₈₉×#3559	C₂	semidirect
4. C₈₉×#3552	C₂	semidirect
5. C₈₉×#3541	C₂	semidirect
6. C₈₉×#3539	C₂	semidirect
7. C₈₉×#3538	C₂	semidirect
8. C₈₉×#3512	C₂	semidirect
9. C₈₉×#3507	C₂	semidirect
10. C₈₉×#3499	C₂	semidirect
11. C₈₉×#3497	C₂	semidirect
12. C₈₉×#3489	C₂	semidirect
13. C₈₉×#3455	C₂	semidirect
14. C₂×#541×C₈₉	C₂	semidirect
15. C₈₉×#3449	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
19. #563×C₈₉	C₂²	semidirect
20. #562×C₈₉	C₂²	semidirect
21. #560×C₈₉	C₂²	semidirect
22. #559×C₈₉	C₂²	semidirect
23. #557×C₈₉	C₂²	semidirect
24. #556×C₈₉	C₂²	semidirect
25. #556×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #554×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
29. #553×C₈₉	C₂²	semidirect
30. #553×C₈₉	C₂²	semidirect
31. #553×C₈₉	C₂²	semidirect
32. #552×C₈₉	C₂²	semidirect
33. #552×C₈₉	C₂²	semidirect
34. #551×C₈₉	C₂²	semidirect
35. #550×C₈₉	C₂²	semidirect
36. #550×C₈₉	C₂²	semidirect
37. D₄×Q₈×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. D₄×Q₈×C₈₉	C₂²	semidirect
40. D₄×Q₈×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
43. #548×C₈₉	C₂²	semidirect
45. #547×C₈₉	C₂²	semidirect
46. #547×C₈₉	C₂²	semidirect
47. #547×C₈₉	C₂²	semidirect
49. #546×C₈₉	C₂²	semidirect
50. #544×C₈₉	C₂²	semidirect
51. #542×C₈₉	C₂²	semidirect
52. #542×C₈₉	C₂²	semidirect
53. #541×C₈₉	C₂²	semidirect
54. #541×C₈₉	C₂²	semidirect
55. #541×C₈₉	C₂²	semidirect
56. #541×C₈₉	C₂²	semidirect
57. #541×C₈₉	C₂²	semidirect
58. #540×C₈₉	C₂²	semidirect
59. #540×C₈₉	C₂²	semidirect
60. #540×C₈₉	C₂²	semidirect
61. #539×C₈₉	C₂²	semidirect
62. #539×C₈₉	C₂²	semidirect
63. #539×C₈₉	C₂²	semidirect
64. #539×C₈₉	C₂²	semidirect
65. #539×C₈₉	C₂²	semidirect
67. #538×C₈₉	C₂²	semidirect
68. #538×C₈₉	C₂²	semidirect
71. #537×C₈₉	C₂²	semidirect
72. #537×C₈₉	C₂²	semidirect
75. #536×C₈₉	C₂²	semidirect
76. #536×C₈₉	C₂²	semidirect
79. #533×C₈₉	C₂²	semidirect
82. #532×C₈₉	C₂²	semidirect
83. #532×C₈₉	C₂²	semidirect
84. #532×C₈₉	C₂²	semidirect
85. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
86. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
87. #529×C₈₉	C₂²	semidirect
88. #529×C₈₉	C₂²	semidirect
89. #529×C₈₉	C₂²	semidirect
91. C₂×#125×C₈₉	C₂²	semidirect
92. C₂×#125×C₈₉	C₂²	semidirect
96. #525×C₈₉	C₂²	semidirect
98. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
99. #520×C₈₉	C₂²	semidirect
100. C₄×#41×C₈₉	C₂²	semidirect
101. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
445. #62888	C₈₉	direct (N × H)
452. #3562	C₂×C₈₉	semidirect
453. #3560	C₂×C₈₉	semidirect
454. #3559	C₂×C₈₉	semidirect
455. #3552	C₂×C₈₉	semidirect
456. #3541	C₂×C₈₉	semidirect
457. #3539	C₂×C₈₉	semidirect
458. #3538	C₂×C₈₉	semidirect
459. #3512	C₂×C₈₉	semidirect
460. #3507	C₂×C₈₉	semidirect
461. #3499	C₂×C₈₉	semidirect
462. #3497	C₂×C₈₉	semidirect
463. #3489	C₂×C₈₉	semidirect
464. #3455	C₂×C₈₉	semidirect
465. C₂×#541	C₂×C₈₉	semidirect
466. #3449	C₂×C₈₉	semidirect
467. C₈₉	#62888	direct (N × H)
468. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
470. #563	C₂²×C₈₉	semidirect
471. #563	C₂²×C₈₉	semidirect
472. #562	C₂²×C₈₉	semidirect
473. #560	C₂²×C₈₉	semidirect
474. #559	C₂²×C₈₉	semidirect
475. #557	C₂²×C₈₉	semidirect
476. #556	C₂²×C₈₉	semidirect
477. #556	C₂²×C₈₉	semidirect
478. #554	C₂²×C₈₉	semidirect
479. #554	C₂²×C₈₉	semidirect
480. #553	C₂²×C₈₉	semidirect
481. #553	C₂²×C₈₉	semidirect
482. #553	C₂²×C₈₉	semidirect
483. #553	C₂²×C₈₉	semidirect
484. #552	C₂²×C₈₉	semidirect
485. #552	C₂²×C₈₉	semidirect
486. #551	C₂²×C₈₉	semidirect
487. #550	C₂²×C₈₉	semidirect
488. #550	C₂²×C₈₉	semidirect
489. D₄×Q₈	C₂²×C₈₉	semidirect
490. D₄×Q₈	C₂²×C₈₉	semidirect
491. D₄×Q₈	C₂²×C₈₉	semidirect
492. D₄×Q₈	C₂²×C₈₉	semidirect
494. #548	C₂²×C₈₉	semidirect
495. #548	C₂²×C₈₉	semidirect
497. #547	C₂²×C₈₉	semidirect
498. #547	C₂²×C₈₉	semidirect
499. #547	C₂²×C₈₉	semidirect
501. #546	C₂²×C₈₉	semidirect
502. #544	C₂²×C₈₉	semidirect
503. #542	C₂²×C₈₉	semidirect
504. #542	C₂²×C₈₉	semidirect
505. #541	C₂²×C₈₉	semidirect
506. #541	C₂²×C₈₉	semidirect
507. #541	C₂²×C₈₉	semidirect
508. #541	C₂²×C₈₉	semidirect
509. #541	C₂²×C₈₉	semidirect
510. #540	C₂²×C₈₉	semidirect
511. #540	C₂²×C₈₉	semidirect
512. #540	C₂²×C₈₉	semidirect
513. #539	C₂²×C₈₉	semidirect
514. #539	C₂²×C₈₉	semidirect
515. #539	C₂²×C₈₉	semidirect
516. #539	C₂²×C₈₉	semidirect
517. #539	C₂²×C₈₉	semidirect
519. #538	C₂²×C₈₉	semidirect
520. #538	C₂²×C₈₉	semidirect
523. #537	C₂²×C₈₉	semidirect
524. #537	C₂²×C₈₉	semidirect
527. #536	C₂²×C₈₉	semidirect
528. #536	C₂²×C₈₉	semidirect
531. #533	C₂²×C₈₉	semidirect
534. #532	C₂²×C₈₉	semidirect
535. #532	C₂²×C₈₉	semidirect
536. #532	C₂²×C₈₉	semidirect
537. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
538. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
539. #529	C₂²×C₈₉	semidirect
540. #529	C₂²×C₈₉	semidirect
541. #529	C₂²×C₈₉	semidirect
543. C₂×#125	C₂²×C₈₉	semidirect
544. C₂×#125	C₂²×C₈₉	semidirect
548. #525	C₂²×C₈₉	semidirect
550. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
551. #520	C₂²×C₈₉	semidirect
552. C₄×#41	C₂²×C₈₉	semidirect
553. C₂×C₄×Q₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3562	2
C₈₉×#3560	2
C₈₉×#3559	2
C₈₉×#3552	2
C₈₉×#3541	2
C₈₉×#3539	2
C₈₉×#3538	2
C₈₉×#3512	2
C₈₉×#3507	2
C₈₉×#3499	2
C₈₉×#3497	2
C₈₉×#3489	2
C₈₉×#3455	2
C₂×#541×C₈₉	2
C₈₉×#3449	2
#62888	89

Subgroups — C89×#62888 #36440736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62888 #36440736