Subgroups — C₈₉×#62856 #36440704

Order 22784.

7086 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3512	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3511	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3505	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3495	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3494	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3493	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3492	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3461	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3460	C₂	1	4	yes	maximal, complemented
10	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3449	C₂	1	2	yes	maximal, complemented
12	C₂×#537×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3428	C₂	1	2	yes	maximal, complemented
14	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₈₉	C₂²	1	2	yes	—
17	#556×C₈₉	C₂²	1	16	yes	complemented
18	#555×C₈₉	C₂²	1	16	yes	complemented
19	#554×C₈₉	C₂²	1	16	yes	complemented
20	#553×C₈₉	C₂²	1	16	yes	complemented
21	#553×C₈₉	C₂²	1	16	yes	complemented
22	#553×C₈₉	C₂²	1	32	yes	complemented
23	#553×C₈₉	C₂²	1	16	yes	complemented
24	#552×C₈₉	C₂²	1	16	yes	complemented
25	#552×C₈₉	C₂²	1	16	yes	complemented
26	#552×C₈₉	C₂²	1	16	yes	complemented
27	#551×C₈₉	C₂²	1	32	yes	complemented
28	#548×C₈₉	C₂²	1	16	yes	complemented
29	#547×C₈₉	C₂²	1	16	yes	complemented
30	#546×C₈₉	C₂²	1	16	yes	complemented
31	#544×C₈₉	C₂²	1	4	yes	complemented
32	#544×C₈₉	C₂²	1	4	yes	complemented
33	#544×C₈₉	C₂²	1	8	yes	complemented
34	#542×C₈₉	C₂²	1	16	yes	complemented
35	#542×C₈₉	C₂²	1	16	yes	complemented
36	#541×C₈₉	C₂²	1	16	yes	complemented
37	#540×C₈₉	C₂²	1	16	yes	complemented
38	#539×C₈₉	C₂²	1	16	yes	complemented
39	#538×C₈₉	C₂²	1	16	yes	complemented
40	#537×C₈₉	C₂²	1	4	yes	—
41	#537×C₈₉	C₂²	1	4	yes	—
42	#537×C₈₉	C₂²	1	8	yes	complemented
43	#537×C₈₉	C₂²	1	4	yes	complemented
44	#537×C₈₉	C₂²	1	4	yes	complemented
45	#536×C₈₉	C₂²	1	4	yes	—
46	#536×C₈₉	C₂²	1	4	yes	complemented
47	#535×C₈₉	C₂²	1	4	yes	—
48	#535×C₈₉	C₂²	1	4	yes	complemented
49	#534×C₈₉	C₂²	1	8	yes	—
50	#533×C₈₉	C₂²	1	16	yes	complemented
51	#532×C₈₉	C₂²	1	8	yes	complemented
52	#532×C₈₉	C₂²	1	16	yes	complemented
53	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
54	#529×C₈₉	C₂²	1	16	yes	complemented
55	#529×C₈₉	C₂²	1	16	yes	complemented
56	#529×C₈₉	C₂²	1	16	yes	complemented
57	C₂×#125×C₈₉	C₂²	1	4	yes	complemented
58	#525×C₈₉	C₂²	1	8	yes	—
59	#525×C₈₉	C₂²	1	8	yes	complemented
60	#525×C₈₉	C₂²	1	16	yes	complemented
61	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
62	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
63	C₂×#121×C₈₉	C₂²	1	4	yes	—
64	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
65	#520×C₈₉	C₂²	1	8	yes	—
66	#520×C₈₉	C₂²	1	8	yes	complemented
67	#520×C₈₉	C₂²	1	4	yes	complemented
68	#520×C₈₉	C₂²	1	4	yes	complemented
69	#520×C₈₉	C₂²	1	4	yes	complemented
70	#520×C₈₉	C₂²	1	4	yes	complemented
71	#519×C₈₉	C₂²	1	4	yes	complemented
72	#518×C₈₉	C₂²	1	8	yes	—
73	#518×C₈₉	C₂²	1	4	yes	complemented
74	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
75	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
76	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
78	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
79	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
80	C₂×#117×C₈₉	C₂²	1	2	yes	—
81	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
82	C₂×#117×C₈₉	C₂²	1	8	yes	complemented
83	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
84	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
85	C₂×#41×C₈₉	—	2	8	no	—
86	C₂×#41×C₈₉	—	2	16	no	—
87	C₂×#41×C₈₉	C₂³	1	4	yes	—
88	C₂×#41×C₈₉	C₂³	1	4	yes	—
89	C₂×#41×C₈₉	C₂³	1	4	yes	—
90	C₂×#41×C₈₉	C₂³	1	4	yes	—
91	C₂×#41×C₈₉	C₂³	1	4	yes	—
92	C₂×#41×C₈₉	C₂³	1	4	yes	—
93	C₂×#41×C₈₉	C₂³	1	16	yes	—
94	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
96	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
108	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
109	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
110	#127×C₈₉	C₂³	1	8	yes	—
111	#126×C₈₉	C₂³	1	32	yes	—
112	#126×C₈₉	C₂³	1	32	yes	—
113	#126×C₈₉	C₂³	1	32	yes	—
114	#125×C₈₉	C₂³	1	16	yes	—
115	#125×C₈₉	C₂³	1	16	yes	—
116	#125×C₈₉	C₂³	1	16	yes	—
117	#125×C₈₉	C₂³	1	32	yes	—
118	#124×C₈₉	C₂³	1	8	yes	—
119	#124×C₈₉	C₂³	1	8	yes	—
120	#124×C₈₉	C₂³	1	16	yes	—
121	#124×C₈₉	C₂³	1	32	yes	—
122	#123×C₈₉	C₂³	1	16	yes	—
123	#123×C₈₉	C₂³	1	16	yes	—
124	#123×C₈₉	C₂³	1	32	yes	—
125	#123×C₈₉	C₂³	1	32	yes	—
126	#123×C₈₉	C₂³	1	32	yes	—
127	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
128	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
129	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
130	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
131	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
132	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
135	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
136	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	—
137	#121×C₈₉	C₂³	1	16	yes	—
138	#121×C₈₉	C₂³	1	16	yes	—
139	#121×C₈₉	C₂³	1	16	yes	—
140	#121×C₈₉	C₂³	1	16	yes	—
141	#121×C₈₉	C₂³	1	8	yes	—
142	#121×C₈₉	C₂³	1	8	yes	—
143	#121×C₈₉	C₂³	1	8	yes	—
144	#121×C₈₉	C₂³	1	8	yes	—
145	#121×C₈₉	C₂³	1	16	yes	—
146	#121×C₈₉	C₂³	1	16	yes	—
147	#121×C₈₉	C₂³	1	16	yes	—
148	#121×C₈₉	C₂³	1	32	yes	—
149	#120×C₈₉	C₂³	1	16	yes	—
150	#120×C₈₉	C₂³	1	16	yes	—
151	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
152	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
153	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
154	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
155	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
156	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
157	C₄×D₄×C₈₉	C₂³	1	16	yes	—
158	C₄×D₄×C₈₉	C₂³	1	16	yes	—
159	C₄×D₄×C₈₉	C₂³	1	16	yes	—
160	C₄×D₄×C₈₉	C₂³	1	16	yes	—
161	C₄×D₄×C₈₉	C₂³	1	16	yes	—
162	C₄×D₄×C₈₉	C₂³	1	16	yes	—
163	C₄×D₄×C₈₉	C₂³	1	16	yes	—
164	C₄×D₄×C₈₉	C₂³	1	8	yes	—
165	C₄×D₄×C₈₉	C₂³	1	8	yes	—
166	C₄×D₄×C₈₉	C₂³	1	8	yes	—
167	C₄×D₄×C₈₉	C₂³	1	8	yes	—
168	C₄×D₄×C₈₉	C₂³	1	16	yes	—
169	C₄×D₄×C₈₉	C₂³	1	16	yes	—
170	C₄×D₄×C₈₉	C₂³	1	32	yes	—
171	C₄×D₄×C₈₉	C₂³	1	16	yes	—
172	#117×C₈₉	C₂³	1	4	yes	—
173	#117×C₈₉	C₂³	1	4	yes	—
174	#117×C₈₉	C₂³	1	4	yes	—
175	#117×C₈₉	C₂³	1	4	yes	—
176	#117×C₈₉	C₂³	1	4	yes	—
177	#117×C₈₉	C₂³	1	4	yes	—
178	#117×C₈₉	C₂³	1	16	yes	—
179	#117×C₈₉	C₂³	1	16	yes	—
180	#117×C₈₉	C₂³	1	16	yes	—
181	#117×C₈₉	C₂³	1	8	yes	—
182	#117×C₈₉	C₂³	1	8	yes	—
183	#117×C₈₉	C₂³	1	16	yes	—
184	#117×C₈₉	C₂³	1	32	yes	—
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
192	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
199	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
205	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
208	C₂×C₄²×C₈₉	C₂³	1	16	yes	—
209	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
210	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
211	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
212	#41×C₈₉	—	2	16	no	—
213	#41×C₈₉	—	2	16	no	—
214	#41×C₈₉	—	2	16	no	—
215	#41×C₈₉	—	2	16	no	—
216	#41×C₈₉	—	2	16	no	—
217	#41×C₈₉	—	2	16	no	—
218	#41×C₈₉	—	8	16	no	—
219	C₂×Q₈×C₈₉	—	2	8	no	—
220	C₂×Q₈×C₈₉	—	2	4	no	—
221	C₂×Q₈×C₈₉	—	8	4	no	—
222	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
223	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
224	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
226	C₂×D₄×C₈₉	—	2	8	no	—
227	C₂×D₄×C₈₉	—	2	16	no	—
228	C₂×D₄×C₈₉	—	2	8	no	—
229	C₂×D₄×C₈₉	—	2	4	no	—
230	C₂×D₄×C₈₉	—	8	4	no	—
231	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
232	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
233	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
234	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
235	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
236	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
237	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
238	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
239	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
240	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
241	C₂²×C₄×C₈₉	—	2	16	no	—
242	C₂²×C₄×C₈₉	—	2	8	no	—
243	C₂²×C₄×C₈₉	—	8	2	no	—
244	C₂²×C₄×C₈₉	—	8	4	no	—
245	C₂²×C₄×C₈₉	#41	1	8	yes	complemented
246	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
250	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
267	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
270	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
273	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	32	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
281	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
282	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
283	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
284	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
285	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
286	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
287	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
288	C₂²⋊C₄×C₈₉	C₂⁴	1	32	yes	—
289	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
290	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
291	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
292	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
293	C₄²×C₈₉	C₂⁴	1	8	yes	—
294	C₄²×C₈₉	C₂⁴	1	8	yes	—
295	C₄²×C₈₉	C₂⁴	1	16	yes	—
296	C₄²×C₈₉	C₂⁴	1	16	yes	—
297	C₄²×C₈₉	C₂⁴	1	16	yes	—
298	C₄²×C₈₉	C₂⁴	1	8	yes	—
299	C₂³×C₈₉	—	2	4	no	—
300	C₂³×C₈₉	—	2	8	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	2	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	2	no	—
305	C₂³×C₈₉	—	4	4	no	—
306	C₂³×C₈₉	—	4	4	no	—
307	C₂³×C₈₉	C₂×#41	1	4	yes	—
308	C₂³×C₈₉	C₂⁵	1	4	yes	—
309	C₂³×C₈₉	C₂⁵	1	8	yes	—
310	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
311	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
312	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
313	Q₈×C₈₉	—	2	8	no	—
314	Q₈×C₈₉	—	2	8	no	—
315	Q₈×C₈₉	—	2	8	no	—
316	Q₈×C₈₉	—	4	16	no	—
317	D₄×C₈₉	—	2	8	no	—
318	D₄×C₈₉	—	2	16	no	—
319	D₄×C₈₉	—	2	8	no	—
320	D₄×C₈₉	—	2	16	no	—
321	D₄×C₈₉	—	2	8	no	—
322	D₄×C₈₉	—	2	8	no	—
323	D₄×C₈₉	—	2	8	no	—
324	D₄×C₈₉	—	4	16	no	—
325	D₄×C₈₉	—	4	16	no	—
326	D₄×C₈₉	—	4	16	no	—
327	C₂×C₄×C₈₉	—	2	8	no	—
328	C₂×C₄×C₈₉	—	2	4	no	—
329	C₂×C₄×C₈₉	—	2	16	no	—
330	C₂×C₄×C₈₉	—	2	16	no	—
331	C₂×C₄×C₈₉	—	2	16	no	—
332	C₂×C₄×C₈₉	—	4	2	no	—
333	C₂×C₄×C₈₉	—	4	4	no	—
334	C₂×C₄×C₈₉	—	4	4	no	—
335	C₂×C₄×C₈₉	—	4	4	no	—
336	C₂×C₄×C₈₉	—	4	16	no	—
337	C₂×C₄×C₈₉	—	4	2	no	—
338	C₂×C₄×C₈₉	—	4	16	no	—
339	C₂×C₄×C₈₉	—	4	4	no	—
340	C₂×C₄×C₈₉	—	4	4	no	—
341	C₂×C₄×C₈₉	—	4	16	no	—
342	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
343	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
344	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
345	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
346	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
347	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
348	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
349	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
350	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
351	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
352	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
353	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
354	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
355	C₂²×C₈₉	—	2	1	no	—
356	C₂²×C₈₉	—	2	1	no	—
357	C₂²×C₈₉	—	2	1	no	—
358	C₂²×C₈₉	—	2	1	no	—
359	C₂²×C₈₉	—	2	1	no	—
360	C₂²×C₈₉	—	2	1	no	—
361	C₂²×C₈₉	—	2	4	no	—
362	C₂²×C₈₉	—	2	8	no	—
363	C₂²×C₈₉	—	2	4	no	—
364	C₂²×C₈₉	—	2	8	no	—
365	C₂²×C₈₉	—	2	8	no	—
366	C₂²×C₈₉	—	2	4	no	—
367	C₂²×C₈₉	—	4	4	no	—
368	C₂²×C₈₉	—	4	8	no	—
369	C₂²×C₈₉	—	8	8	no	—
370	C₂²×C₈₉	C₂²×#41	1	2	yes	—
371	C₂²×C₈₉	C₂²×#41	1	2	yes	—
372	C₂²×C₈₉	C₂²×#41	1	2	yes	—
373	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
374	C₄×C₈₉	—	2	8	no	—
375	C₄×C₈₉	—	2	4	no	—
376	C₄×C₈₉	—	2	4	no	—
377	C₄×C₈₉	—	2	8	no	—
378	C₄×C₈₉	—	2	8	no	—
379	C₄×C₈₉	—	2	4	no	—
380	C₄×C₈₉	—	2	8	no	—
381	C₄×C₈₉	C₂²×#41	1	4	yes	—
382	C₄×C₈₉	C₂²×#41	1	4	yes	—
383	#62856	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂×C₈₉	—	2	2	no	—
385	C₂×C₈₉	—	2	2	no	—
386	C₂×C₈₉	—	2	2	no	—
387	C₂×C₈₉	—	4	4	no	—
388	C₂×C₈₉	—	4	8	no	—
389	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
390	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
391	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
392	#3512	C₂×C₈₉	1	8	yes	complemented
393	#3511	C₂×C₈₉	1	8	yes	complemented
394	#3505	C₂×C₈₉	1	8	yes	complemented
395	#3495	C₂×C₈₉	1	8	yes	complemented
396	#3494	C₂×C₈₉	1	8	yes	complemented
397	#3493	C₂×C₈₉	1	4	yes	complemented
398	#3492	C₂×C₈₉	1	4	yes	complemented
399	#3461	C₂×C₈₉	1	4	yes	complemented
400	#3460	C₂×C₈₉	1	4	yes	complemented
401	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#3449	C₂×C₈₉	1	2	yes	complemented
403	C₂×#537	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#3428	C₂×C₈₉	1	2	yes	complemented
405	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₈₉	#62856	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×#41	C₂²×C₈₉	1	2	yes	—
409	#556	C₂²×C₈₉	1	16	yes	complemented
410	#555	C₂²×C₈₉	1	16	yes	complemented
411	#554	C₂²×C₈₉	1	16	yes	complemented
412	#553	C₂²×C₈₉	1	16	yes	complemented
413	#553	C₂²×C₈₉	1	16	yes	complemented
414	#553	C₂²×C₈₉	1	32	yes	complemented
415	#553	C₂²×C₈₉	1	16	yes	complemented
416	#552	C₂²×C₈₉	1	16	yes	complemented
417	#552	C₂²×C₈₉	1	16	yes	complemented
418	#552	C₂²×C₈₉	1	16	yes	complemented
419	#551	C₂²×C₈₉	1	32	yes	complemented
420	#548	C₂²×C₈₉	1	16	yes	complemented
421	#547	C₂²×C₈₉	1	16	yes	complemented
422	#546	C₂²×C₈₉	1	16	yes	complemented
423	#544	C₂²×C₈₉	1	4	yes	complemented
424	#544	C₂²×C₈₉	1	4	yes	complemented
425	#544	C₂²×C₈₉	1	8	yes	complemented
426	#542	C₂²×C₈₉	1	16	yes	complemented
427	#542	C₂²×C₈₉	1	16	yes	complemented
428	#541	C₂²×C₈₉	1	16	yes	complemented
429	#540	C₂²×C₈₉	1	16	yes	complemented
430	#539	C₂²×C₈₉	1	16	yes	complemented
431	#538	C₂²×C₈₉	1	16	yes	complemented
432	#537	C₂²×C₈₉	1	4	yes	—
433	#537	C₂²×C₈₉	1	4	yes	—
434	#537	C₂²×C₈₉	1	8	yes	complemented
435	#537	C₂²×C₈₉	1	4	yes	complemented
436	#537	C₂²×C₈₉	1	4	yes	complemented
437	#536	C₂²×C₈₉	1	4	yes	—
438	#536	C₂²×C₈₉	1	4	yes	complemented
439	#535	C₂²×C₈₉	1	4	yes	—
440	#535	C₂²×C₈₉	1	4	yes	complemented
441	#534	C₂²×C₈₉	1	8	yes	—
442	#533	C₂²×C₈₉	1	16	yes	complemented
443	#532	C₂²×C₈₉	1	8	yes	complemented
444	#532	C₂²×C₈₉	1	16	yes	complemented
445	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
446	#529	C₂²×C₈₉	1	16	yes	complemented
447	#529	C₂²×C₈₉	1	16	yes	complemented
448	#529	C₂²×C₈₉	1	16	yes	complemented
449	C₂×#125	C₂²×C₈₉	1	4	yes	complemented
450	#525	C₂²×C₈₉	1	8	yes	—
451	#525	C₂²×C₈₉	1	8	yes	complemented
452	#525	C₂²×C₈₉	1	16	yes	complemented
453	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
454	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
455	C₂×#121	C₂²×C₈₉	1	4	yes	—
456	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
457	#520	C₂²×C₈₉	1	8	yes	—
458	#520	C₂²×C₈₉	1	8	yes	complemented
459	#520	C₂²×C₈₉	1	4	yes	complemented
460	#520	C₂²×C₈₉	1	4	yes	complemented
461	#520	C₂²×C₈₉	1	4	yes	complemented
462	#520	C₂²×C₈₉	1	4	yes	complemented
463	#519	C₂²×C₈₉	1	4	yes	complemented
464	#518	C₂²×C₈₉	1	8	yes	—
465	#518	C₂²×C₈₉	1	4	yes	complemented
466	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
467	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
468	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
469	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
470	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
471	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
472	C₂×#117	C₂²×C₈₉	1	2	yes	—
473	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
474	C₂×#117	C₂²×C₈₉	1	8	yes	complemented
475	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
476	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
477	C₂×#41	—	2	8	no	—
478	C₂×#41	—	2	16	no	—
479	C₂×#41	C₂³×C₈₉	1	4	yes	—
480	C₂×#41	C₂³×C₈₉	1	4	yes	—
481	C₂×#41	C₂³×C₈₉	1	4	yes	—
482	C₂×#41	C₂³×C₈₉	1	4	yes	—
483	C₂×#41	C₂³×C₈₉	1	4	yes	—
484	C₂×#41	C₂³×C₈₉	1	4	yes	—
485	C₂×#41	C₂³×C₈₉	1	16	yes	—
486	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
488	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
489	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
492	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
494	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
496	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
497	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
498	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
500	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
501	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
502	#127	C₂³×C₈₉	1	8	yes	—
503	#126	C₂³×C₈₉	1	32	yes	—
504	#126	C₂³×C₈₉	1	32	yes	—
505	#126	C₂³×C₈₉	1	32	yes	—
506	#125	C₂³×C₈₉	1	16	yes	—
507	#125	C₂³×C₈₉	1	16	yes	—
508	#125	C₂³×C₈₉	1	16	yes	—
509	#125	C₂³×C₈₉	1	32	yes	—
510	#124	C₂³×C₈₉	1	8	yes	—
511	#124	C₂³×C₈₉	1	8	yes	—
512	#124	C₂³×C₈₉	1	16	yes	—
513	#124	C₂³×C₈₉	1	32	yes	—
514	#123	C₂³×C₈₉	1	16	yes	—
515	#123	C₂³×C₈₉	1	16	yes	—
516	#123	C₂³×C₈₉	1	32	yes	—
517	#123	C₂³×C₈₉	1	32	yes	—
518	#123	C₂³×C₈₉	1	32	yes	—
519	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
520	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
521	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
522	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
523	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
524	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
525	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
526	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
527	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
528	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	—
529	#121	C₂³×C₈₉	1	16	yes	—
530	#121	C₂³×C₈₉	1	16	yes	—
531	#121	C₂³×C₈₉	1	16	yes	—
532	#121	C₂³×C₈₉	1	16	yes	—
533	#121	C₂³×C₈₉	1	8	yes	—
534	#121	C₂³×C₈₉	1	8	yes	—
535	#121	C₂³×C₈₉	1	8	yes	—
536	#121	C₂³×C₈₉	1	8	yes	—
537	#121	C₂³×C₈₉	1	16	yes	—
538	#121	C₂³×C₈₉	1	16	yes	—
539	#121	C₂³×C₈₉	1	16	yes	—
540	#121	C₂³×C₈₉	1	32	yes	—
541	#120	C₂³×C₈₉	1	16	yes	—
542	#120	C₂³×C₈₉	1	16	yes	—
543	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
544	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
545	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
546	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
547	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
548	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
549	C₄×D₄	C₂³×C₈₉	1	16	yes	—
550	C₄×D₄	C₂³×C₈₉	1	16	yes	—
551	C₄×D₄	C₂³×C₈₉	1	16	yes	—
552	C₄×D₄	C₂³×C₈₉	1	16	yes	—
553	C₄×D₄	C₂³×C₈₉	1	16	yes	—
554	C₄×D₄	C₂³×C₈₉	1	16	yes	—
555	C₄×D₄	C₂³×C₈₉	1	16	yes	—
556	C₄×D₄	C₂³×C₈₉	1	8	yes	—
557	C₄×D₄	C₂³×C₈₉	1	8	yes	—
558	C₄×D₄	C₂³×C₈₉	1	8	yes	—
559	C₄×D₄	C₂³×C₈₉	1	8	yes	—
560	C₄×D₄	C₂³×C₈₉	1	16	yes	—
561	C₄×D₄	C₂³×C₈₉	1	16	yes	—
562	C₄×D₄	C₂³×C₈₉	1	32	yes	—
563	C₄×D₄	C₂³×C₈₉	1	16	yes	—
564	#117	C₂³×C₈₉	1	4	yes	—
565	#117	C₂³×C₈₉	1	4	yes	—
566	#117	C₂³×C₈₉	1	4	yes	—
567	#117	C₂³×C₈₉	1	4	yes	—
568	#117	C₂³×C₈₉	1	4	yes	—
569	#117	C₂³×C₈₉	1	4	yes	—
570	#117	C₂³×C₈₉	1	16	yes	—
571	#117	C₂³×C₈₉	1	16	yes	—
572	#117	C₂³×C₈₉	1	16	yes	—
573	#117	C₂³×C₈₉	1	8	yes	—
574	#117	C₂³×C₈₉	1	8	yes	—
575	#117	C₂³×C₈₉	1	16	yes	—
576	#117	C₂³×C₈₉	1	32	yes	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
580	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
584	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
588	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
597	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
599	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
600	C₂×C₄²	C₂³×C₈₉	1	16	yes	—
601	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
602	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
603	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
604	#41	—	2	16	no	—
605	#41	—	2	16	no	—
606	#41	—	2	16	no	—
607	#41	—	2	16	no	—
608	#41	—	2	16	no	—
609	#41	—	2	16	no	—
610	#41	—	8	16	no	—
611	C₂×Q₈	—	2	8	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	8	4	no	—
614	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
615	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
616	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
617	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	16	no	—
620	C₂×D₄	—	2	8	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	8	4	no	—
623	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
624	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
625	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
626	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
627	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
628	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
629	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
630	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
631	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
632	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
633	C₂²×C₄	—	2	16	no	—
634	C₂²×C₄	—	2	8	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	—	8	4	no	—
637	C₂²×C₄	#41×C₈₉	1	8	yes	complemented
638	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
643	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
645	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
648	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
649	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
650	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
652	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
653	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
659	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
660	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
661	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
662	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
663	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
664	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
667	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
668	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	32	yes	—
670	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
671	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
672	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
673	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
674	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
675	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
676	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
677	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
678	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
679	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
680	C₂²⋊C₄	C₂⁴×C₈₉	1	32	yes	—
681	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
682	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
683	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
684	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
685	C₄²	C₂⁴×C₈₉	1	8	yes	—
686	C₄²	C₂⁴×C₈₉	1	8	yes	—
687	C₄²	C₂⁴×C₈₉	1	16	yes	—
688	C₄²	C₂⁴×C₈₉	1	16	yes	—
689	C₄²	C₂⁴×C₈₉	1	16	yes	—
690	C₄²	C₂⁴×C₈₉	1	8	yes	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	C₂×#41×C₈₉	1	4	yes	—
700	C₂³	C₂⁵×C₈₉	1	4	yes	—
701	C₂³	C₂⁵×C₈₉	1	8	yes	—
702	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
703	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
704	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
705	Q₈	—	2	8	no	—
706	Q₈	—	2	8	no	—
707	Q₈	—	2	8	no	—
708	Q₈	—	4	16	no	—
709	D₄	—	2	8	no	—
710	D₄	—	2	16	no	—
711	D₄	—	2	8	no	—
712	D₄	—	2	16	no	—
713	D₄	—	2	8	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	8	no	—
716	D₄	—	4	16	no	—
717	D₄	—	4	16	no	—
718	D₄	—	4	16	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	16	no	—
722	C₂×C₄	—	2	16	no	—
723	C₂×C₄	—	2	16	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	16	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	16	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	16	no	—
734	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
735	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
736	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
737	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
738	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
739	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
740	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
741	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
742	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
743	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
744	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
745	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
746	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	8	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	8	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	8	no	—
761	C₂²	—	8	8	no	—
762	C₂²	C₂²×#41×C₈₉	1	2	yes	—
763	C₂²	C₂²×#41×C₈₉	1	2	yes	—
764	C₂²	C₂²×#41×C₈₉	1	2	yes	—
765	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
766	C₄	—	2	8	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	8	no	—
770	C₄	—	2	8	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	8	no	—
773	C₄	C₂²×#41×C₈₉	1	4	yes	—
774	C₄	C₂²×#41×C₈₉	1	4	yes	—
775	C₂	—	2	2	no	—
776	C₂	—	2	2	no	—
777	C₂	—	2	2	no	—
778	C₂	—	4	4	no	—
779	C₂	—	4	8	no	—
780	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
781	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic
782	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×#3512	C₂	semidirect
2. C₈₉×#3511	C₂	semidirect
3. C₈₉×#3505	C₂	semidirect
4. C₈₉×#3495	C₂	semidirect
5. C₈₉×#3494	C₂	semidirect
6. C₈₉×#3493	C₂	semidirect
7. C₈₉×#3492	C₂	semidirect
8. C₈₉×#3461	C₂	semidirect
9. C₈₉×#3460	C₂	semidirect
10. C₂×#544×C₈₉	C₂	semidirect
11. C₈₉×#3449	C₂	semidirect
12. C₂×#537×C₈₉	C₂	semidirect
13. C₈₉×#3428	C₂	semidirect
14. C₂×#520×C₈₉	C₂	semidirect
17. #556×C₈₉	C₂²	semidirect
18. #555×C₈₉	C₂²	semidirect
19. #554×C₈₉	C₂²	semidirect
20. #553×C₈₉	C₂²	semidirect
21. #553×C₈₉	C₂²	semidirect
22. #553×C₈₉	C₂²	semidirect
23. #553×C₈₉	C₂²	semidirect
24. #552×C₈₉	C₂²	semidirect
25. #552×C₈₉	C₂²	semidirect
26. #552×C₈₉	C₂²	semidirect
27. #551×C₈₉	C₂²	semidirect
28. #548×C₈₉	C₂²	semidirect
29. #547×C₈₉	C₂²	semidirect
30. #546×C₈₉	C₂²	semidirect
31. #544×C₈₉	C₂²	semidirect
32. #544×C₈₉	C₂²	semidirect
33. #544×C₈₉	C₂²	semidirect
34. #542×C₈₉	C₂²	semidirect
35. #542×C₈₉	C₂²	semidirect
36. #541×C₈₉	C₂²	semidirect
37. #540×C₈₉	C₂²	semidirect
38. #539×C₈₉	C₂²	semidirect
39. #538×C₈₉	C₂²	semidirect
42. #537×C₈₉	C₂²	semidirect
43. #537×C₈₉	C₂²	semidirect
44. #537×C₈₉	C₂²	semidirect
46. #536×C₈₉	C₂²	semidirect
48. #535×C₈₉	C₂²	semidirect
50. #533×C₈₉	C₂²	semidirect
51. #532×C₈₉	C₂²	semidirect
52. #532×C₈₉	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
54. #529×C₈₉	C₂²	semidirect
55. #529×C₈₉	C₂²	semidirect
56. #529×C₈₉	C₂²	semidirect
57. C₂×#125×C₈₉	C₂²	semidirect
59. #525×C₈₉	C₂²	semidirect
60. #525×C₈₉	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
64. C₂×#121×C₈₉	C₂²	semidirect
66. #520×C₈₉	C₂²	semidirect
67. #520×C₈₉	C₂²	semidirect
68. #520×C₈₉	C₂²	semidirect
69. #520×C₈₉	C₂²	semidirect
70. #520×C₈₉	C₂²	semidirect
71. #519×C₈₉	C₂²	semidirect
73. #518×C₈₉	C₂²	semidirect
74. C₄×#41×C₈₉	C₂²	semidirect
75. C₄×#41×C₈₉	C₂²	semidirect
76. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
78. C₂×C₄×D₄×C₈₉	C₂²	semidirect
81. C₂×#117×C₈₉	C₂²	semidirect
82. C₂×#117×C₈₉	C₂²	semidirect
84. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
245. C₂²×C₄×C₈₉	#41	semidirect
383. #62856	C₈₉	direct (N × H)
392. #3512	C₂×C₈₉	semidirect
393. #3511	C₂×C₈₉	semidirect
394. #3505	C₂×C₈₉	semidirect
395. #3495	C₂×C₈₉	semidirect
396. #3494	C₂×C₈₉	semidirect
397. #3493	C₂×C₈₉	semidirect
398. #3492	C₂×C₈₉	semidirect
399. #3461	C₂×C₈₉	semidirect
400. #3460	C₂×C₈₉	semidirect
401. C₂×#544	C₂×C₈₉	semidirect
402. #3449	C₂×C₈₉	semidirect
403. C₂×#537	C₂×C₈₉	semidirect
404. #3428	C₂×C₈₉	semidirect
405. C₂×#520	C₂×C₈₉	semidirect
406. C₈₉	#62856	direct (N × H)
409. #556	C₂²×C₈₉	semidirect
410. #555	C₂²×C₈₉	semidirect
411. #554	C₂²×C₈₉	semidirect
412. #553	C₂²×C₈₉	semidirect
413. #553	C₂²×C₈₉	semidirect
414. #553	C₂²×C₈₉	semidirect
415. #553	C₂²×C₈₉	semidirect
416. #552	C₂²×C₈₉	semidirect
417. #552	C₂²×C₈₉	semidirect
418. #552	C₂²×C₈₉	semidirect
419. #551	C₂²×C₈₉	semidirect
420. #548	C₂²×C₈₉	semidirect
421. #547	C₂²×C₈₉	semidirect
422. #546	C₂²×C₈₉	semidirect
423. #544	C₂²×C₈₉	semidirect
424. #544	C₂²×C₈₉	semidirect
425. #544	C₂²×C₈₉	semidirect
426. #542	C₂²×C₈₉	semidirect
427. #542	C₂²×C₈₉	semidirect
428. #541	C₂²×C₈₉	semidirect
429. #540	C₂²×C₈₉	semidirect
430. #539	C₂²×C₈₉	semidirect
431. #538	C₂²×C₈₉	semidirect
434. #537	C₂²×C₈₉	semidirect
435. #537	C₂²×C₈₉	semidirect
436. #537	C₂²×C₈₉	semidirect
438. #536	C₂²×C₈₉	semidirect
440. #535	C₂²×C₈₉	semidirect
442. #533	C₂²×C₈₉	semidirect
443. #532	C₂²×C₈₉	semidirect
444. #532	C₂²×C₈₉	semidirect
445. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
446. #529	C₂²×C₈₉	semidirect
447. #529	C₂²×C₈₉	semidirect
448. #529	C₂²×C₈₉	semidirect
449. C₂×#125	C₂²×C₈₉	semidirect
451. #525	C₂²×C₈₉	semidirect
452. #525	C₂²×C₈₉	semidirect
454. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
456. C₂×#121	C₂²×C₈₉	semidirect
458. #520	C₂²×C₈₉	semidirect
459. #520	C₂²×C₈₉	semidirect
460. #520	C₂²×C₈₉	semidirect
461. #520	C₂²×C₈₉	semidirect
462. #520	C₂²×C₈₉	semidirect
463. #519	C₂²×C₈₉	semidirect
465. #518	C₂²×C₈₉	semidirect
466. C₄×#41	C₂²×C₈₉	semidirect
467. C₄×#41	C₂²×C₈₉	semidirect
468. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
470. C₂×C₄×D₄	C₂²×C₈₉	semidirect
473. C₂×#117	C₂²×C₈₉	semidirect
474. C₂×#117	C₂²×C₈₉	semidirect
476. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
637. C₂²×C₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3512	2
C₈₉×#3511	2
C₈₉×#3505	2
C₈₉×#3495	2
C₈₉×#3494	2
C₈₉×#3493	2
C₈₉×#3492	2
C₈₉×#3461	2
C₈₉×#3460	2
C₂×#544×C₈₉	2
C₈₉×#3449	2
C₂×#537×C₈₉	2
C₈₉×#3428	2
C₂×#520×C₈₉	2
#62856	89

Subgroups — C89×#62856 #36440704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62856 #36440704