Subgroups — C₈₉×#62915 #36440763

Order 22784.

6986 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3559	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3552	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3547	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3544	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3538	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3535	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3515	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3503	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3499	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3494	C₂	1	4	yes	maximal, complemented
12	C₈₉×#3492	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3489	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3475	C₂	1	2	yes	maximal, complemented
15	C₂×#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#544×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	4	yes	complemented
19	C₂²×#41×C₈₉	C₂²	1	2	yes	—
20	#563×C₈₉	C₂²	1	16	yes	complemented
21	#563×C₈₉	C₂²	1	16	yes	complemented
22	#562×C₈₉	C₂²	1	16	yes	complemented
23	Q₈²×C₈₉	C₂²	1	4	yes	complemented
24	#557×C₈₉	C₂²	1	4	yes	complemented
25	#556×C₈₉	C₂²	1	2	yes	complemented
26	#555×C₈₉	C₂²	1	2	yes	complemented
27	#555×C₈₉	C₂²	1	8	yes	complemented
28	#554×C₈₉	C₂²	1	8	yes	—
29	#554×C₈₉	C₂²	1	2	yes	complemented
30	#554×C₈₉	C₂²	1	8	yes	complemented
31	#554×C₈₉	C₂²	1	4	yes	complemented
32	#554×C₈₉	C₂²	1	8	yes	complemented
33	#554×C₈₉	C₂²	1	4	yes	complemented
34	#553×C₈₉	C₂²	1	4	yes	complemented
35	#553×C₈₉	C₂²	1	8	yes	complemented
36	#553×C₈₉	C₂²	1	8	yes	complemented
37	#553×C₈₉	C₂²	1	8	yes	complemented
38	#552×C₈₉	C₂²	1	4	yes	—
39	#552×C₈₉	C₂²	1	4	yes	complemented
40	#552×C₈₉	C₂²	1	8	yes	complemented
41	#552×C₈₉	C₂²	1	16	yes	complemented
42	#552×C₈₉	C₂²	1	8	yes	complemented
43	#551×C₈₉	C₂²	1	8	yes	—
44	#551×C₈₉	C₂²	1	16	yes	—
45	D₄×Q₈×C₈₉	C₂²	1	8	yes	—
46	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
47	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
48	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
49	#548×C₈₉	C₂²	1	8	yes	complemented
50	#547×C₈₉	C₂²	1	4	yes	—
51	#547×C₈₉	C₂²	1	8	yes	—
52	#547×C₈₉	C₂²	1	4	yes	—
53	#547×C₈₉	C₂²	1	2	yes	complemented
54	#547×C₈₉	C₂²	1	8	yes	complemented
55	#547×C₈₉	C₂²	1	16	yes	complemented
56	#547×C₈₉	C₂²	1	8	yes	complemented
57	#547×C₈₉	C₂²	1	8	yes	complemented
58	#547×C₈₉	C₂²	1	16	yes	complemented
59	#546×C₈₉	C₂²	1	4	yes	—
60	#546×C₈₉	C₂²	1	16	yes	—
61	#544×C₈₉	C₂²	1	1	yes	characteristic
62	#544×C₈₉	C₂²	1	2	yes	—
63	#544×C₈₉	C₂²	1	4	yes	—
64	#544×C₈₉	C₂²	1	8	yes	—
65	#544×C₈₉	C₂²	1	8	yes	complemented
66	#544×C₈₉	C₂²	1	8	yes	complemented
67	#544×C₈₉	C₂²	1	8	yes	complemented
68	#544×C₈₉	C₂²	1	8	yes	complemented
69	#543×C₈₉	C₂²	1	4	yes	—
70	#542×C₈₉	C₂²	1	4	yes	complemented
71	#542×C₈₉	C₂²	1	8	yes	complemented
72	#542×C₈₉	C₂²	1	16	yes	complemented
73	#541×C₈₉	C₂²	1	8	yes	complemented
74	#540×C₈₉	C₂²	1	4	yes	complemented
75	#540×C₈₉	C₂²	1	8	yes	complemented
76	#539×C₈₉	C₂²	1	8	yes	—
77	#539×C₈₉	C₂²	1	16	yes	complemented
78	#539×C₈₉	C₂²	1	16	yes	complemented
79	#539×C₈₉	C₂²	1	8	yes	complemented
80	#538×C₈₉	C₂²	1	4	yes	—
81	#537×C₈₉	C₂²	1	1	yes	characteristic
82	#537×C₈₉	C₂²	1	4	yes	complemented
83	#537×C₈₉	C₂²	1	8	yes	complemented
84	#536×C₈₉	C₂²	1	8	yes	complemented
85	#536×C₈₉	C₂²	1	4	yes	complemented
86	#536×C₈₉	C₂²	1	16	yes	complemented
87	#536×C₈₉	C₂²	1	8	yes	complemented
88	#535×C₈₉	C₂²	1	2	yes	—
89	#533×C₈₉	C₂²	1	2	yes	—
90	#533×C₈₉	C₂²	1	4	yes	complemented
91	#532×C₈₉	C₂²	1	4	yes	complemented
92	#532×C₈₉	C₂²	1	8	yes	complemented
93	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
94	C₂×C₄⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
95	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
96	#529×C₈₉	C₂²	1	4	yes	complemented
97	#529×C₈₉	C₂²	1	8	yes	complemented
98	#529×C₈₉	C₂²	1	4	yes	complemented
99	#529×C₈₉	C₂²	1	8	yes	complemented
100	C₂×#125×C₈₉	C₂²	1	8	yes	complemented
101	#525×C₈₉	C₂²	1	4	yes	—
102	#525×C₈₉	C₂²	1	4	yes	—
103	#525×C₈₉	C₂²	1	8	yes	—
104	C₂×#123×C₈₉	C₂²	1	4	yes	—
105	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	—
106	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
107	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
108	C₂×#121×C₈₉	C₂²	1	2	yes	—
109	#520×C₈₉	C₂²	1	4	yes	—
110	#520×C₈₉	C₂²	1	4	yes	complemented
111	#518×C₈₉	C₂²	1	2	yes	—
112	C₄×#41×C₈₉	C₂²	1	2	yes	—
113	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
114	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₂×#117×C₈₉	C₂²	1	4	yes	—
117	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	2₋¹⁺⁴×C₈₉	—	4	16	no	—
119	C₂×#41×C₈₉	—	4	8	no	—
120	C₂×#41×C₈₉	C₂³	1	2	yes	—
121	C₂×#41×C₈₉	C₂³	1	4	yes	—
122	C₂×#41×C₈₉	C₂³	1	4	yes	—
123	C₂×#41×C₈₉	C₂³	1	4	yes	—
124	C₂×#41×C₈₉	C₂³	1	8	yes	—
125	C₂×#41×C₈₉	C₂³	1	16	yes	—
126	C₂×#41×C₈₉	C₂³	1	8	yes	—
127	C₂×#41×C₈₉	C₂³	1	4	yes	—
128	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
129	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
130	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
131	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
137	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
142	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
145	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
146	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
147	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
148	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
149	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
151	#127×C₈₉	C₂³	1	4	yes	—
152	#126×C₈₉	C₂³	1	8	yes	—
153	#126×C₈₉	C₂³	1	8	yes	—
154	#126×C₈₉	C₂³	1	8	yes	—
155	#126×C₈₉	C₂³	1	16	yes	—
156	#126×C₈₉	C₂³	1	8	yes	—
157	#126×C₈₉	C₂³	1	16	yes	—
158	#126×C₈₉	C₂³	1	16	yes	—
159	#125×C₈₉	C₂³	1	4	yes	—
160	#125×C₈₉	C₂³	1	8	yes	—
161	#125×C₈₉	C₂³	1	16	yes	—
162	#125×C₈₉	C₂³	1	16	yes	—
163	#125×C₈₉	C₂³	1	8	yes	—
164	#125×C₈₉	C₂³	1	8	yes	—
165	#125×C₈₉	C₂³	1	4	yes	—
166	#125×C₈₉	C₂³	1	8	yes	—
167	#125×C₈₉	C₂³	1	4	yes	—
168	#125×C₈₉	C₂³	1	16	yes	—
169	#125×C₈₉	C₂³	1	16	yes	—
170	#124×C₈₉	C₂³	1	4	yes	—
171	#124×C₈₉	C₂³	1	4	yes	—
172	#124×C₈₉	C₂³	1	8	yes	—
173	#124×C₈₉	C₂³	1	8	yes	—
174	#124×C₈₉	C₂³	1	16	yes	—
175	#124×C₈₉	C₂³	1	16	yes	—
176	#123×C₈₉	C₂³	1	16	yes	—
177	#123×C₈₉	C₂³	1	16	yes	—
178	#123×C₈₉	C₂³	1	16	yes	—
179	#123×C₈₉	C₂³	1	8	yes	—
180	#123×C₈₉	C₂³	1	8	yes	—
181	#123×C₈₉	C₂³	1	8	yes	—
182	#123×C₈₉	C₂³	1	16	yes	—
183	#123×C₈₉	C₂³	1	8	yes	—
184	#123×C₈₉	C₂³	1	8	yes	—
185	#123×C₈₉	C₂³	1	8	yes	—
186	#123×C₈₉	C₂³	1	16	yes	—
187	#123×C₈₉	C₂³	1	16	yes	—
188	#123×C₈₉	C₂³	1	16	yes	—
189	#123×C₈₉	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
207	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
208	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	8	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	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
217	#121×C₈₉	C₂³	1	8	yes	—
218	#121×C₈₉	C₂³	1	8	yes	—
219	#121×C₈₉	C₂³	1	4	yes	—
220	#121×C₈₉	C₂³	1	4	yes	—
221	#121×C₈₉	C₂³	1	4	yes	—
222	#121×C₈₉	C₂³	1	8	yes	—
223	#121×C₈₉	C₂³	1	4	yes	—
224	#121×C₈₉	C₂³	1	4	yes	—
225	#121×C₈₉	C₂³	1	8	yes	—
226	#121×C₈₉	C₂³	1	4	yes	—
227	#121×C₈₉	C₂³	1	4	yes	—
228	#121×C₈₉	C₂³	1	4	yes	—
229	#121×C₈₉	C₂³	1	16	yes	—
230	#121×C₈₉	C₂³	1	8	yes	—
231	#121×C₈₉	C₂³	1	16	yes	—
232	#121×C₈₉	C₂³	1	16	yes	—
233	#120×C₈₉	C₂³	1	8	yes	—
234	#120×C₈₉	C₂³	1	8	yes	—
235	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
241	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
242	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	C₄×D₄×C₈₉	C₂³	1	4	yes	—
245	C₄×D₄×C₈₉	C₂³	1	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	4	yes	—
247	C₄×D₄×C₈₉	C₂³	1	4	yes	—
248	C₄×D₄×C₈₉	C₂³	1	4	yes	—
249	C₄×D₄×C₈₉	C₂³	1	2	yes	—
250	C₄×D₄×C₈₉	C₂³	1	4	yes	—
251	C₄×D₄×C₈₉	C₂³	1	2	yes	—
252	C₄×D₄×C₈₉	C₂³	1	4	yes	—
253	C₄×D₄×C₈₉	C₂³	1	8	yes	—
254	C₄×D₄×C₈₉	C₂³	1	8	yes	—
255	C₄×D₄×C₈₉	C₂³	1	8	yes	—
256	C₄×D₄×C₈₉	C₂³	1	8	yes	—
257	C₄×D₄×C₈₉	C₂³	1	16	yes	—
258	C₄×D₄×C₈₉	C₂³	1	8	yes	—
259	C₄×D₄×C₈₉	C₂³	1	16	yes	—
260	C₄×D₄×C₈₉	C₂³	1	8	yes	—
261	C₄×D₄×C₈₉	C₂³	1	8	yes	—
262	C₄×D₄×C₈₉	C₂³	1	16	yes	—
263	C₄×D₄×C₈₉	C₂³	1	16	yes	—
264	#117×C₈₉	C₂³	1	2	yes	—
265	#117×C₈₉	C₂³	1	4	yes	—
266	#117×C₈₉	C₂³	1	8	yes	—
267	#117×C₈₉	C₂³	1	8	yes	—
268	#117×C₈₉	C₂³	1	4	yes	—
269	#117×C₈₉	C₂³	1	4	yes	—
270	#117×C₈₉	C₂³	1	4	yes	—
271	#117×C₈₉	C₂³	1	8	yes	—
272	#117×C₈₉	C₂³	1	4	yes	—
273	#117×C₈₉	C₂³	1	8	yes	—
274	#117×C₈₉	C₂³	1	4	yes	—
275	#117×C₈₉	C₂³	1	8	yes	—
276	#117×C₈₉	C₂³	1	16	yes	—
277	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
280	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
281	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
282	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
283	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
284	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
286	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
289	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
290	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
296	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
297	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
298	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
300	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
301	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
302	#41×C₈₉	—	2	16	no	—
303	#41×C₈₉	—	2	16	no	—
304	#41×C₈₉	—	2	8	no	—
305	#41×C₈₉	—	4	8	no	—
306	#41×C₈₉	—	4	16	no	—
307	#41×C₈₉	—	4	16	no	—
308	#41×C₈₉	—	4	32	no	—
309	#41×C₈₉	—	4	8	no	—
310	C₂×Q₈×C₈₉	—	4	16	no	—
311	C₂×Q₈×C₈₉	—	4	4	no	—
312	C₂×Q₈×C₈₉	—	4	8	no	—
313	C₂×Q₈×C₈₉	—	4	16	no	—
314	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
315	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
316	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
320	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
321	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
322	C₂×D₄×C₈₉	—	2	4	no	—
323	C₂×D₄×C₈₉	—	2	4	no	—
324	C₂×D₄×C₈₉	—	4	8	no	—
325	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
327	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
328	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
329	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
330	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
331	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
333	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
334	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
335	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
336	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
337	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₉	—	2	8	no	—
339	C₂²×C₄×C₈₉	—	4	4	no	—
340	C₂²×C₄×C₈₉	—	4	8	no	—
341	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
358	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
359	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
375	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
377	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
381	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
383	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
384	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
392	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
393	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
396	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
397	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
399	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
403	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
404	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
405	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
409	C₄²×C₈₉	C₂⁴	1	4	yes	—
410	C₄²×C₈₉	C₂⁴	1	2	yes	—
411	C₄²×C₈₉	C₂⁴	1	8	yes	—
412	C₄²×C₈₉	C₂⁴	1	2	yes	—
413	C₄²×C₈₉	C₂⁴	1	8	yes	—
414	C₄²×C₈₉	C₂⁴	1	4	yes	—
415	C₄²×C₈₉	C₂⁴	1	8	yes	—
416	C₄²×C₈₉	C₂⁴	1	4	yes	—
417	C₄²×C₈₉	C₂⁴	1	16	yes	—
418	C₂³×C₈₉	—	2	4	no	—
419	C₂³×C₈₉	—	2	4	no	—
420	C₂³×C₈₉	—	2	4	no	—
421	C₂³×C₈₉	—	4	2	no	—
422	C₂³×C₈₉	—	4	2	no	—
423	C₂³×C₈₉	—	4	2	no	—
424	C₂³×C₈₉	C₂⁵	1	4	yes	—
425	C₂³×C₈₉	C₂⁵	1	2	yes	—
426	C₂³×C₈₉	C₂⁵	1	4	yes	—
427	C₂³×C₈₉	C₂⁵	1	2	yes	—
428	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
429	Q₈×C₈₉	—	2	8	no	—
430	Q₈×C₈₉	—	2	8	no	—
431	Q₈×C₈₉	—	2	4	no	—
432	Q₈×C₈₉	—	4	4	no	—
433	Q₈×C₈₉	—	4	8	no	—
434	Q₈×C₈₉	—	4	16	no	—
435	Q₈×C₈₉	—	4	4	no	—
436	Q₈×C₈₉	—	4	4	no	—
437	D₄×C₈₉	—	2	4	no	—
438	D₄×C₈₉	—	2	16	no	—
439	D₄×C₈₉	—	2	16	no	—
440	D₄×C₈₉	—	2	8	no	—
441	D₄×C₈₉	—	2	2	no	—
442	D₄×C₈₉	—	2	8	no	—
443	D₄×C₈₉	—	2	4	no	—
444	D₄×C₈₉	—	4	8	no	—
445	D₄×C₈₉	—	4	8	no	—
446	D₄×C₈₉	—	4	8	no	—
447	D₄×C₈₉	—	4	4	no	—
448	D₄×C₈₉	—	4	8	no	—
449	D₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
450	C₂×C₄×C₈₉	—	2	16	no	—
451	C₂×C₄×C₈₉	—	2	16	no	—
452	C₂×C₄×C₈₉	—	2	4	no	—
453	C₂×C₄×C₈₉	—	2	2	no	—
454	C₂×C₄×C₈₉	—	2	8	no	—
455	C₂×C₄×C₈₉	—	2	8	no	—
456	C₂×C₄×C₈₉	—	2	8	no	—
457	C₂×C₄×C₈₉	—	2	8	no	—
458	C₂×C₄×C₈₉	—	2	8	no	—
459	C₂×C₄×C₈₉	—	4	2	no	—
460	C₂×C₄×C₈₉	—	4	4	no	—
461	C₂×C₄×C₈₉	—	4	4	no	—
462	C₂×C₄×C₈₉	—	4	8	no	—
463	C₂×C₄×C₈₉	—	4	8	no	—
464	C₂×C₄×C₈₉	—	4	4	no	—
465	C₂×C₄×C₈₉	—	4	8	no	—
466	C₂×C₄×C₈₉	—	4	1	no	—
467	C₂×C₄×C₈₉	—	4	16	no	—
468	C₂×C₄×C₈₉	—	4	8	no	—
469	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	complemented
470	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
471	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
472	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
473	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
474	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
475	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
476	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
477	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
478	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
479	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
480	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
481	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
482	C₂²×C₈₉	—	2	1	no	—
483	C₂²×C₈₉	—	2	2	no	—
484	C₂²×C₈₉	—	2	2	no	—
485	C₂²×C₈₉	—	2	1	no	—
486	C₂²×C₈₉	—	2	4	no	—
487	C₂²×C₈₉	—	2	4	no	—
488	C₂²×C₈₉	—	2	2	no	—
489	C₂²×C₈₉	—	2	2	no	—
490	C₂²×C₈₉	—	2	4	no	—
491	C₂²×C₈₉	—	2	4	no	—
492	C₂²×C₈₉	—	2	4	no	—
493	C₂²×C₈₉	—	2	4	no	—
494	C₂²×C₈₉	—	2	2	no	—
495	C₂²×C₈₉	—	4	8	no	—
496	C₂²×C₈₉	—	8	4	no	—
497	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
498	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
499	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
500	C₄×C₈₉	—	2	4	no	—
501	C₄×C₈₉	—	2	4	no	—
502	C₄×C₈₉	—	2	1	no	—
503	C₄×C₈₉	—	2	8	no	—
504	C₄×C₈₉	—	2	8	no	—
505	C₄×C₈₉	—	2	4	no	—
506	C₄×C₈₉	—	2	4	no	—
507	C₄×C₈₉	—	2	4	no	—
508	C₄×C₈₉	—	2	8	no	—
509	C₄×C₈₉	—	2	2	no	—
510	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
511	C₄×C₈₉	C₂×2₋¹⁺⁴	1	4	yes	—
512	#62915	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
513	C₂×C₈₉	—	2	2	no	—
514	C₂×C₈₉	—	2	4	no	—
515	C₂×C₈₉	—	4	4	no	—
516	C₂×C₈₉	—	4	2	no	—
517	C₂×C₈₉	—	4	4	no	—
518	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
521	#3559	C₂×C₈₉	1	8	yes	complemented
522	#3552	C₂×C₈₉	1	4	yes	complemented
523	#3547	C₂×C₈₉	1	4	yes	complemented
524	#3544	C₂×C₈₉	1	8	yes	complemented
525	#3538	C₂×C₈₉	1	4	yes	complemented
526	#3535	C₂×C₈₉	1	8	yes	complemented
527	#3515	C₂×C₈₉	1	4	yes	complemented
528	#3503	C₂×C₈₉	1	2	yes	complemented
529	#3501	C₂×C₈₉	1	1	yes	characteristic, complemented
530	#3499	C₂×C₈₉	1	4	yes	complemented
531	#3494	C₂×C₈₉	1	4	yes	complemented
532	#3492	C₂×C₈₉	1	2	yes	complemented
533	#3489	C₂×C₈₉	1	4	yes	complemented
534	#3475	C₂×C₈₉	1	2	yes	complemented
535	C₂×#547	C₂×C₈₉	1	1	yes	characteristic, complemented
536	#3460	C₂×C₈₉	1	1	yes	characteristic, complemented
537	C₂×#544	C₂×C₈₉	1	2	yes	complemented
538	C₈₉	#62915	1	1	yes	characteristic, direct product factor, Sylow
539	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	4	yes	complemented
540	C₂²×#41	C₂²×C₈₉	1	2	yes	—
541	#563	C₂²×C₈₉	1	16	yes	complemented
542	#563	C₂²×C₈₉	1	16	yes	complemented
543	#562	C₂²×C₈₉	1	16	yes	complemented
544	Q₈²	C₂²×C₈₉	1	4	yes	complemented
545	#557	C₂²×C₈₉	1	4	yes	complemented
546	#556	C₂²×C₈₉	1	2	yes	complemented
547	#555	C₂²×C₈₉	1	2	yes	complemented
548	#555	C₂²×C₈₉	1	8	yes	complemented
549	#554	C₂²×C₈₉	1	8	yes	—
550	#554	C₂²×C₈₉	1	2	yes	complemented
551	#554	C₂²×C₈₉	1	8	yes	complemented
552	#554	C₂²×C₈₉	1	4	yes	complemented
553	#554	C₂²×C₈₉	1	8	yes	complemented
554	#554	C₂²×C₈₉	1	4	yes	complemented
555	#553	C₂²×C₈₉	1	4	yes	complemented
556	#553	C₂²×C₈₉	1	8	yes	complemented
557	#553	C₂²×C₈₉	1	8	yes	complemented
558	#553	C₂²×C₈₉	1	8	yes	complemented
559	#552	C₂²×C₈₉	1	4	yes	—
560	#552	C₂²×C₈₉	1	4	yes	complemented
561	#552	C₂²×C₈₉	1	8	yes	complemented
562	#552	C₂²×C₈₉	1	16	yes	complemented
563	#552	C₂²×C₈₉	1	8	yes	complemented
564	#551	C₂²×C₈₉	1	8	yes	—
565	#551	C₂²×C₈₉	1	16	yes	—
566	D₄×Q₈	C₂²×C₈₉	1	8	yes	—
567	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
568	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
569	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
570	#548	C₂²×C₈₉	1	8	yes	complemented
571	#547	C₂²×C₈₉	1	4	yes	—
572	#547	C₂²×C₈₉	1	8	yes	—
573	#547	C₂²×C₈₉	1	4	yes	—
574	#547	C₂²×C₈₉	1	2	yes	complemented
575	#547	C₂²×C₈₉	1	8	yes	complemented
576	#547	C₂²×C₈₉	1	16	yes	complemented
577	#547	C₂²×C₈₉	1	8	yes	complemented
578	#547	C₂²×C₈₉	1	8	yes	complemented
579	#547	C₂²×C₈₉	1	16	yes	complemented
580	#546	C₂²×C₈₉	1	4	yes	—
581	#546	C₂²×C₈₉	1	16	yes	—
582	#544	C₂²×C₈₉	1	1	yes	characteristic
583	#544	C₂²×C₈₉	1	2	yes	—
584	#544	C₂²×C₈₉	1	4	yes	—
585	#544	C₂²×C₈₉	1	8	yes	—
586	#544	C₂²×C₈₉	1	8	yes	complemented
587	#544	C₂²×C₈₉	1	8	yes	complemented
588	#544	C₂²×C₈₉	1	8	yes	complemented
589	#544	C₂²×C₈₉	1	8	yes	complemented
590	#543	C₂²×C₈₉	1	4	yes	—
591	#542	C₂²×C₈₉	1	4	yes	complemented
592	#542	C₂²×C₈₉	1	8	yes	complemented
593	#542	C₂²×C₈₉	1	16	yes	complemented
594	#541	C₂²×C₈₉	1	8	yes	complemented
595	#540	C₂²×C₈₉	1	4	yes	complemented
596	#540	C₂²×C₈₉	1	8	yes	complemented
597	#539	C₂²×C₈₉	1	8	yes	—
598	#539	C₂²×C₈₉	1	16	yes	complemented
599	#539	C₂²×C₈₉	1	16	yes	complemented
600	#539	C₂²×C₈₉	1	8	yes	complemented
601	#538	C₂²×C₈₉	1	4	yes	—
602	#537	C₂²×C₈₉	1	1	yes	characteristic
603	#537	C₂²×C₈₉	1	4	yes	complemented
604	#537	C₂²×C₈₉	1	8	yes	complemented
605	#536	C₂²×C₈₉	1	8	yes	complemented
606	#536	C₂²×C₈₉	1	4	yes	complemented
607	#536	C₂²×C₈₉	1	16	yes	complemented
608	#536	C₂²×C₈₉	1	8	yes	complemented
609	#535	C₂²×C₈₉	1	2	yes	—
610	#533	C₂²×C₈₉	1	2	yes	—
611	#533	C₂²×C₈₉	1	4	yes	complemented
612	#532	C₂²×C₈₉	1	4	yes	complemented
613	#532	C₂²×C₈₉	1	8	yes	complemented
614	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
615	C₂×C₄⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
616	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
617	#529	C₂²×C₈₉	1	4	yes	complemented
618	#529	C₂²×C₈₉	1	8	yes	complemented
619	#529	C₂²×C₈₉	1	4	yes	complemented
620	#529	C₂²×C₈₉	1	8	yes	complemented
621	C₂×#125	C₂²×C₈₉	1	8	yes	complemented
622	#525	C₂²×C₈₉	1	4	yes	—
623	#525	C₂²×C₈₉	1	4	yes	—
624	#525	C₂²×C₈₉	1	8	yes	—
625	C₂×#123	C₂²×C₈₉	1	4	yes	—
626	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	—
627	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
628	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
629	C₂×#121	C₂²×C₈₉	1	2	yes	—
630	#520	C₂²×C₈₉	1	4	yes	—
631	#520	C₂²×C₈₉	1	4	yes	complemented
632	#518	C₂²×C₈₉	1	2	yes	—
633	C₄×#41	C₂²×C₈₉	1	2	yes	—
634	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
635	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
637	C₂×#117	C₂²×C₈₉	1	4	yes	—
638	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
639	2₋¹⁺⁴	—	4	16	no	—
640	C₂×#41	—	4	8	no	—
641	C₂×#41	C₂³×C₈₉	1	2	yes	—
642	C₂×#41	C₂³×C₈₉	1	4	yes	—
643	C₂×#41	C₂³×C₈₉	1	4	yes	—
644	C₂×#41	C₂³×C₈₉	1	4	yes	—
645	C₂×#41	C₂³×C₈₉	1	8	yes	—
646	C₂×#41	C₂³×C₈₉	1	16	yes	—
647	C₂×#41	C₂³×C₈₉	1	8	yes	—
648	C₂×#41	C₂³×C₈₉	1	4	yes	—
649	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
650	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
651	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
652	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
653	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
656	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
657	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
658	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
659	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
660	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
661	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
662	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
663	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
665	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
666	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
667	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
668	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
669	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
670	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
671	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
672	#127	C₂³×C₈₉	1	4	yes	—
673	#126	C₂³×C₈₉	1	8	yes	—
674	#126	C₂³×C₈₉	1	8	yes	—
675	#126	C₂³×C₈₉	1	8	yes	—
676	#126	C₂³×C₈₉	1	16	yes	—
677	#126	C₂³×C₈₉	1	8	yes	—
678	#126	C₂³×C₈₉	1	16	yes	—
679	#126	C₂³×C₈₉	1	16	yes	—
680	#125	C₂³×C₈₉	1	4	yes	—
681	#125	C₂³×C₈₉	1	8	yes	—
682	#125	C₂³×C₈₉	1	16	yes	—
683	#125	C₂³×C₈₉	1	16	yes	—
684	#125	C₂³×C₈₉	1	8	yes	—
685	#125	C₂³×C₈₉	1	8	yes	—
686	#125	C₂³×C₈₉	1	4	yes	—
687	#125	C₂³×C₈₉	1	8	yes	—
688	#125	C₂³×C₈₉	1	4	yes	—
689	#125	C₂³×C₈₉	1	16	yes	—
690	#125	C₂³×C₈₉	1	16	yes	—
691	#124	C₂³×C₈₉	1	4	yes	—
692	#124	C₂³×C₈₉	1	4	yes	—
693	#124	C₂³×C₈₉	1	8	yes	—
694	#124	C₂³×C₈₉	1	8	yes	—
695	#124	C₂³×C₈₉	1	16	yes	—
696	#124	C₂³×C₈₉	1	16	yes	—
697	#123	C₂³×C₈₉	1	16	yes	—
698	#123	C₂³×C₈₉	1	16	yes	—
699	#123	C₂³×C₈₉	1	16	yes	—
700	#123	C₂³×C₈₉	1	8	yes	—
701	#123	C₂³×C₈₉	1	8	yes	—
702	#123	C₂³×C₈₉	1	8	yes	—
703	#123	C₂³×C₈₉	1	16	yes	—
704	#123	C₂³×C₈₉	1	8	yes	—
705	#123	C₂³×C₈₉	1	8	yes	—
706	#123	C₂³×C₈₉	1	8	yes	—
707	#123	C₂³×C₈₉	1	16	yes	—
708	#123	C₂³×C₈₉	1	16	yes	—
709	#123	C₂³×C₈₉	1	16	yes	—
710	#123	C₂³×C₈₉	1	16	yes	—
711	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
712	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
713	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
714	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
715	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
716	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
717	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
718	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
719	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
720	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
721	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
722	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
723	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
724	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
725	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
726	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
727	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
728	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
729	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
730	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
731	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
732	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
733	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
734	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
735	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
736	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
737	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
738	#121	C₂³×C₈₉	1	8	yes	—
739	#121	C₂³×C₈₉	1	8	yes	—
740	#121	C₂³×C₈₉	1	4	yes	—
741	#121	C₂³×C₈₉	1	4	yes	—
742	#121	C₂³×C₈₉	1	4	yes	—
743	#121	C₂³×C₈₉	1	8	yes	—
744	#121	C₂³×C₈₉	1	4	yes	—
745	#121	C₂³×C₈₉	1	4	yes	—
746	#121	C₂³×C₈₉	1	8	yes	—
747	#121	C₂³×C₈₉	1	4	yes	—
748	#121	C₂³×C₈₉	1	4	yes	—
749	#121	C₂³×C₈₉	1	4	yes	—
750	#121	C₂³×C₈₉	1	16	yes	—
751	#121	C₂³×C₈₉	1	8	yes	—
752	#121	C₂³×C₈₉	1	16	yes	—
753	#121	C₂³×C₈₉	1	16	yes	—
754	#120	C₂³×C₈₉	1	8	yes	—
755	#120	C₂³×C₈₉	1	8	yes	—
756	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
757	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
758	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
759	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
760	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
761	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
762	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
763	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
764	C₄×D₄	C₂³×C₈₉	1	2	yes	—
765	C₄×D₄	C₂³×C₈₉	1	4	yes	—
766	C₄×D₄	C₂³×C₈₉	1	2	yes	—
767	C₄×D₄	C₂³×C₈₉	1	4	yes	—
768	C₄×D₄	C₂³×C₈₉	1	4	yes	—
769	C₄×D₄	C₂³×C₈₉	1	4	yes	—
770	C₄×D₄	C₂³×C₈₉	1	2	yes	—
771	C₄×D₄	C₂³×C₈₉	1	4	yes	—
772	C₄×D₄	C₂³×C₈₉	1	2	yes	—
773	C₄×D₄	C₂³×C₈₉	1	4	yes	—
774	C₄×D₄	C₂³×C₈₉	1	8	yes	—
775	C₄×D₄	C₂³×C₈₉	1	8	yes	—
776	C₄×D₄	C₂³×C₈₉	1	8	yes	—
777	C₄×D₄	C₂³×C₈₉	1	8	yes	—
778	C₄×D₄	C₂³×C₈₉	1	16	yes	—
779	C₄×D₄	C₂³×C₈₉	1	8	yes	—
780	C₄×D₄	C₂³×C₈₉	1	16	yes	—
781	C₄×D₄	C₂³×C₈₉	1	8	yes	—
782	C₄×D₄	C₂³×C₈₉	1	8	yes	—
783	C₄×D₄	C₂³×C₈₉	1	16	yes	—
784	C₄×D₄	C₂³×C₈₉	1	16	yes	—
785	#117	C₂³×C₈₉	1	2	yes	—
786	#117	C₂³×C₈₉	1	4	yes	—
787	#117	C₂³×C₈₉	1	8	yes	—
788	#117	C₂³×C₈₉	1	8	yes	—
789	#117	C₂³×C₈₉	1	4	yes	—
790	#117	C₂³×C₈₉	1	4	yes	—
791	#117	C₂³×C₈₉	1	4	yes	—
792	#117	C₂³×C₈₉	1	8	yes	—
793	#117	C₂³×C₈₉	1	4	yes	—
794	#117	C₂³×C₈₉	1	8	yes	—
795	#117	C₂³×C₈₉	1	4	yes	—
796	#117	C₂³×C₈₉	1	8	yes	—
797	#117	C₂³×C₈₉	1	16	yes	—
798	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
801	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
802	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
803	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
804	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
805	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
807	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
808	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
809	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
810	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
811	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
812	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
818	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
819	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
821	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
822	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
823	#41	—	2	16	no	—
824	#41	—	2	16	no	—
825	#41	—	2	8	no	—
826	#41	—	4	8	no	—
827	#41	—	4	16	no	—
828	#41	—	4	16	no	—
829	#41	—	4	32	no	—
830	#41	—	4	8	no	—
831	C₂×Q₈	—	4	16	no	—
832	C₂×Q₈	—	4	4	no	—
833	C₂×Q₈	—	4	8	no	—
834	C₂×Q₈	—	4	16	no	—
835	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
836	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
837	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
838	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
839	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
840	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
841	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
842	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	4	8	no	—
846	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
847	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
848	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
849	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
850	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
851	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
852	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
853	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
854	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
855	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
856	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
857	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
858	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
859	C₂²×C₄	—	2	8	no	—
860	C₂²×C₄	—	4	4	no	—
861	C₂²×C₄	—	4	8	no	—
862	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
864	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
868	C₂²×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	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
874	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
875	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
877	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
878	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
879	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
880	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
881	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
884	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
885	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
886	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
889	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
893	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
894	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
895	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
896	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
897	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
898	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
899	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
900	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
901	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
902	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
904	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
905	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
906	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
907	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
910	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
911	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
913	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
914	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
916	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
917	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
918	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
919	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
920	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
921	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
922	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
923	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
924	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
925	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
926	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
927	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
928	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
929	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
930	C₄²	C₂⁴×C₈₉	1	4	yes	—
931	C₄²	C₂⁴×C₈₉	1	2	yes	—
932	C₄²	C₂⁴×C₈₉	1	8	yes	—
933	C₄²	C₂⁴×C₈₉	1	2	yes	—
934	C₄²	C₂⁴×C₈₉	1	8	yes	—
935	C₄²	C₂⁴×C₈₉	1	4	yes	—
936	C₄²	C₂⁴×C₈₉	1	8	yes	—
937	C₄²	C₂⁴×C₈₉	1	4	yes	—
938	C₄²	C₂⁴×C₈₉	1	16	yes	—
939	C₂³	—	2	4	no	—
940	C₂³	—	2	4	no	—
941	C₂³	—	2	4	no	—
942	C₂³	—	4	2	no	—
943	C₂³	—	4	2	no	—
944	C₂³	—	4	2	no	—
945	C₂³	C₂⁵×C₈₉	1	4	yes	—
946	C₂³	C₂⁵×C₈₉	1	2	yes	—
947	C₂³	C₂⁵×C₈₉	1	4	yes	—
948	C₂³	C₂⁵×C₈₉	1	2	yes	—
949	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
950	Q₈	—	2	8	no	—
951	Q₈	—	2	8	no	—
952	Q₈	—	2	4	no	—
953	Q₈	—	4	4	no	—
954	Q₈	—	4	8	no	—
955	Q₈	—	4	16	no	—
956	Q₈	—	4	4	no	—
957	Q₈	—	4	4	no	—
958	D₄	—	2	4	no	—
959	D₄	—	2	16	no	—
960	D₄	—	2	16	no	—
961	D₄	—	2	8	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	8	no	—
964	D₄	—	2	4	no	—
965	D₄	—	4	8	no	—
966	D₄	—	4	8	no	—
967	D₄	—	4	8	no	—
968	D₄	—	4	4	no	—
969	D₄	—	4	8	no	—
970	D₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
971	C₂×C₄	—	2	16	no	—
972	C₂×C₄	—	2	16	no	—
973	C₂×C₄	—	2	4	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	8	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	16	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	complemented
991	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
992	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
993	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
994	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
995	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
996	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
997	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
998	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
999	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1000	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1001	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1002	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	8	no	—
1017	C₂²	—	8	4	no	—
1018	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
1019	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
1020	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1021	C₄	—	2	4	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	1	no	—
1024	C₄	—	2	8	no	—
1025	C₄	—	2	8	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	2	no	—
1031	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
1032	C₄	C₂×2₋¹⁺⁴×C₈₉	1	4	yes	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	4	no	—
1035	C₂	—	4	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	4	no	—
1038	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1039	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1040	C₂	C₈₉×2₋¹⁺⁶	1	1	yes	characteristic

	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×#3559	C₂	semidirect
2. C₈₉×#3552	C₂	semidirect
3. C₈₉×#3547	C₂	semidirect
4. C₈₉×#3544	C₂	semidirect
5. C₈₉×#3538	C₂	semidirect
6. C₈₉×#3535	C₂	semidirect
7. C₈₉×#3515	C₂	semidirect
8. C₈₉×#3503	C₂	semidirect
9. C₈₉×#3501	C₂	semidirect
10. C₈₉×#3499	C₂	semidirect
11. C₈₉×#3494	C₂	semidirect
12. C₈₉×#3492	C₂	semidirect
13. C₈₉×#3489	C₂	semidirect
14. C₈₉×#3475	C₂	semidirect
15. C₂×#547×C₈₉	C₂	semidirect
16. C₈₉×#3460	C₂	semidirect
17. C₂×#544×C₈₉	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #563×C₈₉	C₂²	semidirect
22. #562×C₈₉	C₂²	semidirect
23. Q₈²×C₈₉	C₂²	semidirect
24. #557×C₈₉	C₂²	semidirect
25. #556×C₈₉	C₂²	semidirect
26. #555×C₈₉	C₂²	semidirect
27. #555×C₈₉	C₂²	semidirect
29. #554×C₈₉	C₂²	semidirect
30. #554×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
32. #554×C₈₉	C₂²	semidirect
33. #554×C₈₉	C₂²	semidirect
34. #553×C₈₉	C₂²	semidirect
35. #553×C₈₉	C₂²	semidirect
36. #553×C₈₉	C₂²	semidirect
37. #553×C₈₉	C₂²	semidirect
39. #552×C₈₉	C₂²	semidirect
40. #552×C₈₉	C₂²	semidirect
41. #552×C₈₉	C₂²	semidirect
42. #552×C₈₉	C₂²	semidirect
46. D₄×Q₈×C₈₉	C₂²	semidirect
47. D₄×Q₈×C₈₉	C₂²	semidirect
48. D₄×Q₈×C₈₉	C₂²	semidirect
49. #548×C₈₉	C₂²	semidirect
53. #547×C₈₉	C₂²	semidirect
54. #547×C₈₉	C₂²	semidirect
55. #547×C₈₉	C₂²	semidirect
56. #547×C₈₉	C₂²	semidirect
57. #547×C₈₉	C₂²	semidirect
58. #547×C₈₉	C₂²	semidirect
65. #544×C₈₉	C₂²	semidirect
66. #544×C₈₉	C₂²	semidirect
67. #544×C₈₉	C₂²	semidirect
68. #544×C₈₉	C₂²	semidirect
70. #542×C₈₉	C₂²	semidirect
71. #542×C₈₉	C₂²	semidirect
72. #542×C₈₉	C₂²	semidirect
73. #541×C₈₉	C₂²	semidirect
74. #540×C₈₉	C₂²	semidirect
75. #540×C₈₉	C₂²	semidirect
77. #539×C₈₉	C₂²	semidirect
78. #539×C₈₉	C₂²	semidirect
79. #539×C₈₉	C₂²	semidirect
82. #537×C₈₉	C₂²	semidirect
83. #537×C₈₉	C₂²	semidirect
84. #536×C₈₉	C₂²	semidirect
85. #536×C₈₉	C₂²	semidirect
86. #536×C₈₉	C₂²	semidirect
87. #536×C₈₉	C₂²	semidirect
90. #533×C₈₉	C₂²	semidirect
91. #532×C₈₉	C₂²	semidirect
92. #532×C₈₉	C₂²	semidirect
94. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
95. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
96. #529×C₈₉	C₂²	semidirect
97. #529×C₈₉	C₂²	semidirect
98. #529×C₈₉	C₂²	semidirect
99. #529×C₈₉	C₂²	semidirect
100. C₂×#125×C₈₉	C₂²	semidirect
110. #520×C₈₉	C₂²	semidirect
113. C₄×#41×C₈₉	C₂²	semidirect
469. C₂×C₄×C₈₉	2₋¹⁺⁴	semidirect
512. #62915	C₈₉	direct (N × H)
521. #3559	C₂×C₈₉	semidirect
522. #3552	C₂×C₈₉	semidirect
523. #3547	C₂×C₈₉	semidirect
524. #3544	C₂×C₈₉	semidirect
525. #3538	C₂×C₈₉	semidirect
526. #3535	C₂×C₈₉	semidirect
527. #3515	C₂×C₈₉	semidirect
528. #3503	C₂×C₈₉	semidirect
529. #3501	C₂×C₈₉	semidirect
530. #3499	C₂×C₈₉	semidirect
531. #3494	C₂×C₈₉	semidirect
532. #3492	C₂×C₈₉	semidirect
533. #3489	C₂×C₈₉	semidirect
534. #3475	C₂×C₈₉	semidirect
535. C₂×#547	C₂×C₈₉	semidirect
536. #3460	C₂×C₈₉	semidirect
537. C₂×#544	C₂×C₈₉	semidirect
538. C₈₉	#62915	direct (N × H)
539. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
541. #563	C₂²×C₈₉	semidirect
542. #563	C₂²×C₈₉	semidirect
543. #562	C₂²×C₈₉	semidirect
544. Q₈²	C₂²×C₈₉	semidirect
545. #557	C₂²×C₈₉	semidirect
546. #556	C₂²×C₈₉	semidirect
547. #555	C₂²×C₈₉	semidirect
548. #555	C₂²×C₈₉	semidirect
550. #554	C₂²×C₈₉	semidirect
551. #554	C₂²×C₈₉	semidirect
552. #554	C₂²×C₈₉	semidirect
553. #554	C₂²×C₈₉	semidirect
554. #554	C₂²×C₈₉	semidirect
555. #553	C₂²×C₈₉	semidirect
556. #553	C₂²×C₈₉	semidirect
557. #553	C₂²×C₈₉	semidirect
558. #553	C₂²×C₈₉	semidirect
560. #552	C₂²×C₈₉	semidirect
561. #552	C₂²×C₈₉	semidirect
562. #552	C₂²×C₈₉	semidirect
563. #552	C₂²×C₈₉	semidirect
567. D₄×Q₈	C₂²×C₈₉	semidirect
568. D₄×Q₈	C₂²×C₈₉	semidirect
569. D₄×Q₈	C₂²×C₈₉	semidirect
570. #548	C₂²×C₈₉	semidirect
574. #547	C₂²×C₈₉	semidirect
575. #547	C₂²×C₈₉	semidirect
576. #547	C₂²×C₈₉	semidirect
577. #547	C₂²×C₈₉	semidirect
578. #547	C₂²×C₈₉	semidirect
579. #547	C₂²×C₈₉	semidirect
586. #544	C₂²×C₈₉	semidirect
587. #544	C₂²×C₈₉	semidirect
588. #544	C₂²×C₈₉	semidirect
589. #544	C₂²×C₈₉	semidirect
591. #542	C₂²×C₈₉	semidirect
592. #542	C₂²×C₈₉	semidirect
593. #542	C₂²×C₈₉	semidirect
594. #541	C₂²×C₈₉	semidirect
595. #540	C₂²×C₈₉	semidirect
596. #540	C₂²×C₈₉	semidirect
598. #539	C₂²×C₈₉	semidirect
599. #539	C₂²×C₈₉	semidirect
600. #539	C₂²×C₈₉	semidirect
603. #537	C₂²×C₈₉	semidirect
604. #537	C₂²×C₈₉	semidirect
605. #536	C₂²×C₈₉	semidirect
606. #536	C₂²×C₈₉	semidirect
607. #536	C₂²×C₈₉	semidirect
608. #536	C₂²×C₈₉	semidirect
611. #533	C₂²×C₈₉	semidirect
612. #532	C₂²×C₈₉	semidirect
613. #532	C₂²×C₈₉	semidirect
615. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
616. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
617. #529	C₂²×C₈₉	semidirect
618. #529	C₂²×C₈₉	semidirect
619. #529	C₂²×C₈₉	semidirect
620. #529	C₂²×C₈₉	semidirect
621. C₂×#125	C₂²×C₈₉	semidirect
631. #520	C₂²×C₈₉	semidirect
634. C₄×#41	C₂²×C₈₉	semidirect
990. C₂×C₄	2₋¹⁺⁴×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3559	2
C₈₉×#3552	2
C₈₉×#3547	2
C₈₉×#3544	2
C₈₉×#3538	2
C₈₉×#3535	2
C₈₉×#3515	2
C₈₉×#3503	2
C₈₉×#3501	2
C₈₉×#3499	2
C₈₉×#3494	2
C₈₉×#3492	2
C₈₉×#3489	2
C₈₉×#3475	2
C₂×#547×C₈₉	2
C₈₉×#3460	2
C₂×#544×C₈₉	2
#62915	89

Subgroups — C89×#62915 #36440763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62915 #36440763