Subgroups — C₈₉×#62846 #36440694

Order 22784.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3521	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3519	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3514	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3513	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3506	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3505	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3493	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3490	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3484	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3460	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3459	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×#538×C₈₉	C₂	1	4	yes	maximal, complemented
16	C₄×H(5,𝔽₂)×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	—
19	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
20	#559×C₈₉	C₂²	1	8	yes	complemented
21	#556×C₈₉	C₂²	1	8	yes	complemented
22	#556×C₈₉	C₂²	1	4	yes	complemented
23	#555×C₈₉	C₂²	1	8	yes	complemented
24	#555×C₈₉	C₂²	1	4	yes	complemented
25	#554×C₈₉	C₂²	1	4	yes	complemented
26	#554×C₈₉	C₂²	1	8	yes	complemented
27	#553×C₈₉	C₂²	1	8	yes	complemented
28	#553×C₈₉	C₂²	1	8	yes	complemented
29	#553×C₈₉	C₂²	1	16	yes	complemented
30	#553×C₈₉	C₂²	1	8	yes	complemented
31	#552×C₈₉	C₂²	1	8	yes	complemented
32	#552×C₈₉	C₂²	1	8	yes	complemented
33	#551×C₈₉	C₂²	1	16	yes	complemented
34	#551×C₈₉	C₂²	1	16	yes	complemented
35	#551×C₈₉	C₂²	1	16	yes	complemented
36	#550×C₈₉	C₂²	1	4	yes	complemented
37	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
38	#548×C₈₉	C₂²	1	8	yes	complemented
39	#547×C₈₉	C₂²	1	4	yes	complemented
40	#547×C₈₉	C₂²	1	4	yes	complemented
41	#546×C₈₉	C₂²	1	8	yes	complemented
42	#546×C₈₉	C₂²	1	8	yes	complemented
43	#546×C₈₉	C₂²	1	16	yes	complemented
44	#546×C₈₉	C₂²	1	16	yes	complemented
45	#546×C₈₉	C₂²	1	8	yes	complemented
46	#546×C₈₉	C₂²	1	8	yes	complemented
47	D₄²×C₈₉	C₂²	1	8	yes	complemented
48	D₄²×C₈₉	C₂²	1	8	yes	complemented
49	D₄²×C₈₉	C₂²	1	4	yes	complemented
50	#544×C₈₉	C₂²	1	2	yes	complemented
51	#543×C₈₉	C₂²	1	4	yes	complemented
52	#542×C₈₉	C₂²	1	4	yes	complemented
53	#542×C₈₉	C₂²	1	4	yes	complemented
54	#542×C₈₉	C₂²	1	8	yes	complemented
55	#541×C₈₉	C₂²	1	4	yes	complemented
56	#540×C₈₉	C₂²	1	4	yes	complemented
57	#540×C₈₉	C₂²	1	8	yes	complemented
58	#539×C₈₉	C₂²	1	4	yes	complemented
59	#539×C₈₉	C₂²	1	4	yes	complemented
60	#539×C₈₉	C₂²	1	16	yes	complemented
61	#538×C₈₉	C₂²	1	4	yes	complemented
62	#538×C₈₉	C₂²	1	8	yes	complemented
63	#538×C₈₉	C₂²	1	4	yes	complemented
64	#538×C₈₉	C₂²	1	8	yes	complemented
65	#538×C₈₉	C₂²	1	8	yes	complemented
66	#538×C₈₉	C₂²	1	16	yes	complemented
67	#538×C₈₉	C₂²	1	16	yes	complemented
68	#538×C₈₉	C₂²	1	16	yes	complemented
69	#537×C₈₉	C₂²	1	2	yes	complemented
70	#535×C₈₉	C₂²	1	4	yes	complemented
71	#534×C₈₉	C₂²	1	8	yes	complemented
72	#534×C₈₉	C₂²	1	4	yes	complemented
73	#533×C₈₉	C₂²	1	2	yes	complemented
74	#532×C₈₉	C₂²	1	2	yes	complemented
75	#532×C₈₉	C₂²	1	8	yes	complemented
76	#529×C₈₉	C₂²	1	8	yes	complemented
77	#529×C₈₉	C₂²	1	8	yes	complemented
78	#529×C₈₉	C₂²	1	8	yes	complemented
79	#529×C₈₉	C₂²	1	16	yes	complemented
80	#529×C₈₉	C₂²	1	8	yes	complemented
81	C₂×#126×C₈₉	C₂²	1	8	yes	complemented
82	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
83	#525×C₈₉	C₂²	1	4	yes	complemented
84	#525×C₈₉	C₂²	1	8	yes	complemented
85	#525×C₈₉	C₂²	1	8	yes	complemented
86	#525×C₈₉	C₂²	1	16	yes	complemented
87	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
88	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
89	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
90	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
91	C₂×#120×C₈₉	C₂²	1	8	yes	complemented
92	#520×C₈₉	C₂²	1	4	yes	complemented
93	#520×C₈₉	C₂²	1	8	yes	complemented
94	#518×C₈₉	C₂²	1	2	yes	—
95	#518×C₈₉	C₂²	1	8	yes	complemented
96	#518×C₈₉	C₂²	1	8	yes	complemented
97	#518×C₈₉	C₂²	1	8	yes	complemented
98	#518×C₈₉	C₂²	1	8	yes	complemented
99	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
100	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
101	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
102	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
103	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
104	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
108	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
109	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
112	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
113	C₂⁵×C₈₉	C₂³	1	2	yes	—
114	H(5,𝔽₂)×C₈₉	—	2	16	no	—
115	C₂×#41×C₈₉	C₂³	1	4	yes	—
116	C₂×#41×C₈₉	C₂³	1	8	yes	—
117	C₂×#41×C₈₉	C₂³	1	8	yes	complemented
118	C₂×#41×C₈₉	C₂³	1	8	yes	complemented
119	C₂²×Q₈×C₈₉	C₂³	1	4	yes	complemented
120	C₂²×D₄×C₈₉	—	2	8	no	—
121	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
122	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
124	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
126	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
127	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₈₉	C₂³	1	4	yes	complemented
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	8	yes	complemented
136	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
137	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
138	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
139	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
140	#127×C₈₉	C₂³	1	8	yes	—
141	#127×C₈₉	C₂³	1	2	yes	complemented
142	#126×C₈₉	C₂³	1	8	yes	—
143	#126×C₈₉	C₂³	1	16	yes	—
144	#126×C₈₉	C₂³	1	8	yes	—
145	#126×C₈₉	C₂³	1	16	yes	complemented
146	#126×C₈₉	C₂³	1	16	yes	complemented
147	#126×C₈₉	C₂³	1	8	yes	complemented
148	#126×C₈₉	C₂³	1	16	yes	complemented
149	#126×C₈₉	C₂³	1	8	yes	complemented
150	#125×C₈₉	C₂³	1	8	yes	complemented
151	#125×C₈₉	C₂³	1	8	yes	complemented
152	#125×C₈₉	C₂³	1	8	yes	complemented
153	#125×C₈₉	C₂³	1	8	yes	complemented
154	#125×C₈₉	C₂³	1	4	yes	complemented
155	#124×C₈₉	C₂³	1	8	yes	—
156	#124×C₈₉	C₂³	1	16	yes	—
157	#124×C₈₉	C₂³	1	8	yes	—
158	#124×C₈₉	C₂³	1	8	yes	—
159	#124×C₈₉	C₂³	1	16	yes	complemented
160	#124×C₈₉	C₂³	1	16	yes	complemented
161	#124×C₈₉	C₂³	1	8	yes	complemented
162	#124×C₈₉	C₂³	1	4	yes	complemented
163	#123×C₈₉	C₂³	1	8	yes	—
164	#123×C₈₉	C₂³	1	16	yes	—
165	#123×C₈₉	C₂³	1	8	yes	—
166	#123×C₈₉	C₂³	1	16	yes	—
167	#123×C₈₉	C₂³	1	8	yes	—
168	#123×C₈₉	C₂³	1	16	yes	complemented
169	#123×C₈₉	C₂³	1	16	yes	complemented
170	#123×C₈₉	C₂³	1	8	yes	complemented
171	#123×C₈₉	C₂³	1	16	yes	complemented
172	#123×C₈₉	C₂³	1	16	yes	complemented
173	#123×C₈₉	C₂³	1	16	yes	complemented
174	#123×C₈₉	C₂³	1	8	yes	complemented
175	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
176	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
177	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
178	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
179	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
180	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
181	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
182	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
183	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
184	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
185	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
186	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
187	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
188	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
189	#121×C₈₉	C₂³	1	8	yes	—
190	#121×C₈₉	C₂³	1	4	yes	—
191	#121×C₈₉	C₂³	1	8	yes	—
192	#121×C₈₉	C₂³	1	16	yes	—
193	#121×C₈₉	C₂³	1	4	yes	—
194	#121×C₈₉	C₂³	1	16	yes	—
195	#121×C₈₉	C₂³	1	4	yes	—
196	#121×C₈₉	C₂³	1	4	yes	—
197	#121×C₈₉	C₂³	1	16	yes	—
198	#121×C₈₉	C₂³	1	8	yes	—
199	#121×C₈₉	C₂³	1	8	yes	—
200	#121×C₈₉	C₂³	1	8	yes	—
201	#121×C₈₉	C₂³	1	16	yes	complemented
202	#121×C₈₉	C₂³	1	8	yes	complemented
203	#121×C₈₉	C₂³	1	8	yes	complemented
204	#121×C₈₉	C₂³	1	16	yes	complemented
205	#121×C₈₉	C₂³	1	8	yes	complemented
206	#121×C₈₉	C₂³	1	8	yes	complemented
207	#121×C₈₉	C₂³	1	8	yes	complemented
208	#120×C₈₉	C₂³	1	8	yes	—
209	#120×C₈₉	C₂³	1	16	yes	—
210	#120×C₈₉	C₂³	1	16	yes	—
211	#120×C₈₉	C₂³	1	16	yes	—
212	#120×C₈₉	C₂³	1	16	yes	—
213	#120×C₈₉	C₂³	1	16	yes	complemented
214	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
215	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
216	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
217	C₄×Q₈×C₈₉	C₂³	1	8	yes	complemented
218	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
219	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
220	C₄×D₄×C₈₉	C₂³	1	8	yes	—
221	C₄×D₄×C₈₉	C₂³	1	4	yes	—
222	C₄×D₄×C₈₉	C₂³	1	4	yes	—
223	C₄×D₄×C₈₉	C₂³	1	8	yes	—
224	C₄×D₄×C₈₉	C₂³	1	8	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	8	yes	—
230	C₄×D₄×C₈₉	C₂³	1	4	yes	—
231	C₄×D₄×C₈₉	C₂³	1	16	yes	—
232	C₄×D₄×C₈₉	C₂³	1	8	yes	—
233	C₄×D₄×C₈₉	C₂³	1	8	yes	—
234	C₄×D₄×C₈₉	C₂³	1	8	yes	—
235	C₄×D₄×C₈₉	C₂³	1	8	yes	—
236	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
237	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
238	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
239	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
240	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
241	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
242	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
243	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
244	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
245	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
246	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
247	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
248	#117×C₈₉	C₂³	1	4	yes	—
249	#117×C₈₉	C₂³	1	4	yes	—
250	#117×C₈₉	C₂³	1	8	yes	—
251	#117×C₈₉	C₂³	1	4	yes	—
252	#117×C₈₉	C₂³	1	8	yes	complemented
253	#117×C₈₉	C₂³	1	16	yes	complemented
254	#117×C₈₉	C₂³	1	8	yes	complemented
255	#117×C₈₉	C₂³	1	8	yes	complemented
256	#117×C₈₉	C₂³	1	8	yes	complemented
257	#117×C₈₉	C₂³	1	16	yes	complemented
258	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
264	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
267	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
275	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
276	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
277	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
278	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
279	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
280	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
281	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	complemented
282	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
283	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
286	C₂×C₄²×C₈₉	C₂³	1	8	yes	complemented
287	C₂×C₄²×C₈₉	C₂³	1	8	yes	complemented
288	C₂⁴×C₈₉	—	2	8	no	—
289	C₂⁴×C₈₉	—	8	2	no	—
290	C₂⁴×C₈₉	—	8	2	no	—
291	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
292	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
294	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
295	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
296	#41×C₈₉	—	2	32	no	—
297	#41×C₈₉	—	2	16	no	—
298	#41×C₈₉	—	8	8	no	—
299	#41×C₈₉	—	8	8	no	—
300	C₂×Q₈×C₈₉	—	8	4	no	—
301	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
302	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
305	C₂×D₄×C₈₉	—	2	8	no	—
306	C₂×D₄×C₈₉	—	2	32	no	—
307	C₂×D₄×C₈₉	—	2	32	no	—
308	C₂×D₄×C₈₉	—	2	32	no	—
309	C₂×D₄×C₈₉	—	2	4	no	—
310	C₂×D₄×C₈₉	—	8	8	no	—
311	C₂×D₄×C₈₉	—	8	8	no	—
312	C₂×D₄×C₈₉	—	8	4	no	—
313	C₂×D₄×C₈₉	#41	1	8	yes	complemented
314	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
318	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
322	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
323	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
324	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
325	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
327	C₂²×C₄×C₈₉	—	2	4	no	—
328	C₂²×C₄×C₈₉	—	8	2	no	—
329	C₂²×C₄×C₈₉	—	8	2	no	—
330	C₂²×C₄×C₈₉	—	8	2	no	—
331	C₂²×C₄×C₈₉	—	8	2	no	—
332	C₂²×C₄×C₈₉	—	8	8	no	—
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
353	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
384	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
388	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
393	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
395	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
398	C₄²×C₈₉	C₂⁴	1	4	yes	—
399	C₄²×C₈₉	C₂⁴	1	8	yes	—
400	C₄²×C₈₉	C₂⁴	1	2	yes	—
401	C₄²×C₈₉	C₂⁴	1	2	yes	—
402	C₄²×C₈₉	C₂⁴	1	8	yes	—
403	C₄²×C₈₉	C₂⁴	1	8	yes	—
404	C₄²×C₈₉	C₂⁴	1	8	yes	—
405	C₄²×C₈₉	C₂⁴	1	16	yes	—
406	C₂³×C₈₉	—	2	2	no	—
407	C₂³×C₈₉	—	2	4	no	—
408	C₂³×C₈₉	—	2	16	no	—
409	C₂³×C₈₉	—	2	16	no	—
410	C₂³×C₈₉	—	4	2	no	—
411	C₂³×C₈₉	—	4	2	no	—
412	C₂³×C₈₉	—	4	2	no	—
413	C₂³×C₈₉	—	4	2	no	—
414	C₂³×C₈₉	—	4	1	no	—
415	C₂³×C₈₉	—	4	1	no	—
416	C₂³×C₈₉	—	4	8	no	—
417	C₂³×C₈₉	—	4	8	no	—
418	C₂³×C₈₉	—	4	8	no	—
419	C₂³×C₈₉	—	4	8	no	—
420	C₂³×C₈₉	—	8	16	no	—
421	C₂³×C₈₉	C₂×#41	1	8	yes	—
422	C₂³×C₈₉	C₂⁵	1	2	yes	—
423	C₂³×C₈₉	C₂⁵	1	4	yes	—
424	C₂³×C₈₉	C₂⁵	1	8	yes	—
425	C₂³×C₈₉	C₂⁵	1	4	yes	—
426	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
427	Q₈×C₈₉	—	2	8	no	—
428	Q₈×C₈₉	—	4	4	no	—
429	Q₈×C₈₉	—	4	8	no	—
430	Q₈×C₈₉	—	4	4	no	—
431	D₄×C₈₉	—	2	16	no	—
432	D₄×C₈₉	—	2	32	no	—
433	D₄×C₈₉	—	2	16	no	—
434	D₄×C₈₉	—	2	8	no	—
435	D₄×C₈₉	—	2	8	no	—
436	D₄×C₈₉	—	4	4	no	—
437	D₄×C₈₉	—	4	8	no	—
438	D₄×C₈₉	—	4	8	no	—
439	D₄×C₈₉	—	4	16	no	—
440	D₄×C₈₉	—	4	8	no	—
441	D₄×C₈₉	—	4	16	no	—
442	D₄×C₈₉	—	4	4	no	—
443	D₄×C₈₉	C₂×#41	1	16	yes	—
444	C₂×C₄×C₈₉	—	2	2	no	—
445	C₂×C₄×C₈₉	—	2	16	no	—
446	C₂×C₄×C₈₉	—	2	8	no	—
447	C₂×C₄×C₈₉	—	2	16	no	—
448	C₂×C₄×C₈₉	—	4	1	no	—
449	C₂×C₄×C₈₉	—	4	2	no	—
450	C₂×C₄×C₈₉	—	4	1	no	—
451	C₂×C₄×C₈₉	—	4	8	no	—
452	C₂×C₄×C₈₉	—	4	8	no	—
453	C₂×C₄×C₈₉	—	4	1	no	—
454	C₂×C₄×C₈₉	—	4	2	no	—
455	C₂×C₄×C₈₉	—	4	1	no	—
456	C₂×C₄×C₈₉	—	4	4	no	—
457	C₂×C₄×C₈₉	—	4	8	no	—
458	C₂×C₄×C₈₉	—	4	4	no	—
459	C₂×C₄×C₈₉	—	4	16	no	—
460	C₂×C₄×C₈₉	—	4	8	no	—
461	C₂×C₄×C₈₉	—	4	8	no	—
462	C₂×C₄×C₈₉	—	4	8	no	—
463	C₂×C₄×C₈₉	—	4	8	no	—
464	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
465	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
466	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
467	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
468	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
469	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
470	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
471	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
472	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
473	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
474	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
475	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
476	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
477	C₂²×C₈₉	—	2	1	no	—
478	C₂²×C₈₉	—	2	1	no	—
479	C₂²×C₈₉	—	2	4	no	—
480	C₂²×C₈₉	—	2	4	no	—
481	C₂²×C₈₉	—	2	2	no	—
482	C₂²×C₈₉	—	2	8	no	—
483	C₂²×C₈₉	—	2	4	no	—
484	C₂²×C₈₉	—	2	8	no	—
485	C₂²×C₈₉	—	2	4	no	—
486	C₂²×C₈₉	—	2	4	no	—
487	C₂²×C₈₉	—	2	8	no	—
488	C₂²×C₈₉	—	2	2	no	—
489	C₂²×C₈₉	—	2	2	no	—
490	C₂²×C₈₉	—	4	8	no	—
491	C₂²×C₈₉	—	4	8	no	—
492	C₂²×C₈₉	—	4	4	no	—
493	C₂²×C₈₉	—	8	16	no	—
494	C₂²×C₈₉	—	8	16	no	—
495	C₂²×C₈₉	C₂²×#41	1	8	yes	—
496	C₂²×C₈₉	C₂²×#41	1	2	yes	—
497	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
498	C₄×C₈₉	—	2	2	no	—
499	C₄×C₈₉	—	2	8	no	—
500	C₄×C₈₉	—	2	2	no	—
501	C₄×C₈₉	—	2	4	no	—
502	C₄×C₈₉	—	2	2	no	—
503	C₄×C₈₉	—	2	1	no	—
504	C₄×C₈₉	—	2	8	no	—
505	C₄×C₈₉	—	2	4	no	—
506	C₄×C₈₉	—	2	2	no	—
507	C₄×C₈₉	—	2	1	no	—
508	C₄×C₈₉	—	2	8	no	—
509	C₄×C₈₉	C₂²×#41	1	4	yes	—
510	#62846	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂×C₈₉	—	2	2	no	—
512	C₂×C₈₉	—	2	8	no	—
513	C₂×C₈₉	—	4	4	no	—
514	C₂×C₈₉	—	4	2	no	—
515	C₂×C₈₉	—	4	8	no	—
516	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
517	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
518	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
519	#3521	C₂×C₈₉	1	8	yes	complemented
520	#3519	C₂×C₈₉	1	8	yes	complemented
521	#3514	C₂×C₈₉	1	8	yes	complemented
522	#3513	C₂×C₈₉	1	8	yes	complemented
523	#3506	C₂×C₈₉	1	2	yes	complemented
524	#3505	C₂×C₈₉	1	4	yes	complemented
525	#3501	C₂×C₈₉	1	1	yes	characteristic, complemented
526	#3496	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#3493	C₂×C₈₉	1	2	yes	complemented
528	#3490	C₂×C₈₉	1	4	yes	complemented
529	#3484	C₂×C₈₉	1	2	yes	complemented
530	#3460	C₂×C₈₉	1	2	yes	complemented
531	#3459	C₂×C₈₉	1	4	yes	complemented
532	#3455	C₂×C₈₉	1	2	yes	complemented
533	C₂×#538	C₂×C₈₉	1	4	yes	complemented
534	C₄×H(5,𝔽₂)	C₂×C₈₉	1	2	yes	complemented
535	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
536	C₈₉	#62846	1	1	yes	characteristic, direct product factor, Sylow
537	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	—
538	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
539	#559	C₂²×C₈₉	1	8	yes	complemented
540	#556	C₂²×C₈₉	1	8	yes	complemented
541	#556	C₂²×C₈₉	1	4	yes	complemented
542	#555	C₂²×C₈₉	1	8	yes	complemented
543	#555	C₂²×C₈₉	1	4	yes	complemented
544	#554	C₂²×C₈₉	1	4	yes	complemented
545	#554	C₂²×C₈₉	1	8	yes	complemented
546	#553	C₂²×C₈₉	1	8	yes	complemented
547	#553	C₂²×C₈₉	1	8	yes	complemented
548	#553	C₂²×C₈₉	1	16	yes	complemented
549	#553	C₂²×C₈₉	1	8	yes	complemented
550	#552	C₂²×C₈₉	1	8	yes	complemented
551	#552	C₂²×C₈₉	1	8	yes	complemented
552	#551	C₂²×C₈₉	1	16	yes	complemented
553	#551	C₂²×C₈₉	1	16	yes	complemented
554	#551	C₂²×C₈₉	1	16	yes	complemented
555	#550	C₂²×C₈₉	1	4	yes	complemented
556	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
557	#548	C₂²×C₈₉	1	8	yes	complemented
558	#547	C₂²×C₈₉	1	4	yes	complemented
559	#547	C₂²×C₈₉	1	4	yes	complemented
560	#546	C₂²×C₈₉	1	8	yes	complemented
561	#546	C₂²×C₈₉	1	8	yes	complemented
562	#546	C₂²×C₈₉	1	16	yes	complemented
563	#546	C₂²×C₈₉	1	16	yes	complemented
564	#546	C₂²×C₈₉	1	8	yes	complemented
565	#546	C₂²×C₈₉	1	8	yes	complemented
566	D₄²	C₂²×C₈₉	1	8	yes	complemented
567	D₄²	C₂²×C₈₉	1	8	yes	complemented
568	D₄²	C₂²×C₈₉	1	4	yes	complemented
569	#544	C₂²×C₈₉	1	2	yes	complemented
570	#543	C₂²×C₈₉	1	4	yes	complemented
571	#542	C₂²×C₈₉	1	4	yes	complemented
572	#542	C₂²×C₈₉	1	4	yes	complemented
573	#542	C₂²×C₈₉	1	8	yes	complemented
574	#541	C₂²×C₈₉	1	4	yes	complemented
575	#540	C₂²×C₈₉	1	4	yes	complemented
576	#540	C₂²×C₈₉	1	8	yes	complemented
577	#539	C₂²×C₈₉	1	4	yes	complemented
578	#539	C₂²×C₈₉	1	4	yes	complemented
579	#539	C₂²×C₈₉	1	16	yes	complemented
580	#538	C₂²×C₈₉	1	4	yes	complemented
581	#538	C₂²×C₈₉	1	8	yes	complemented
582	#538	C₂²×C₈₉	1	4	yes	complemented
583	#538	C₂²×C₈₉	1	8	yes	complemented
584	#538	C₂²×C₈₉	1	8	yes	complemented
585	#538	C₂²×C₈₉	1	16	yes	complemented
586	#538	C₂²×C₈₉	1	16	yes	complemented
587	#538	C₂²×C₈₉	1	16	yes	complemented
588	#537	C₂²×C₈₉	1	2	yes	complemented
589	#535	C₂²×C₈₉	1	4	yes	complemented
590	#534	C₂²×C₈₉	1	8	yes	complemented
591	#534	C₂²×C₈₉	1	4	yes	complemented
592	#533	C₂²×C₈₉	1	2	yes	complemented
593	#532	C₂²×C₈₉	1	2	yes	complemented
594	#532	C₂²×C₈₉	1	8	yes	complemented
595	#529	C₂²×C₈₉	1	8	yes	complemented
596	#529	C₂²×C₈₉	1	8	yes	complemented
597	#529	C₂²×C₈₉	1	8	yes	complemented
598	#529	C₂²×C₈₉	1	16	yes	complemented
599	#529	C₂²×C₈₉	1	8	yes	complemented
600	C₂×#126	C₂²×C₈₉	1	8	yes	complemented
601	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
602	#525	C₂²×C₈₉	1	4	yes	complemented
603	#525	C₂²×C₈₉	1	8	yes	complemented
604	#525	C₂²×C₈₉	1	8	yes	complemented
605	#525	C₂²×C₈₉	1	16	yes	complemented
606	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
607	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
608	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
609	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
610	C₂×#120	C₂²×C₈₉	1	8	yes	complemented
611	#520	C₂²×C₈₉	1	4	yes	complemented
612	#520	C₂²×C₈₉	1	8	yes	complemented
613	#518	C₂²×C₈₉	1	2	yes	—
614	#518	C₂²×C₈₉	1	8	yes	complemented
615	#518	C₂²×C₈₉	1	8	yes	complemented
616	#518	C₂²×C₈₉	1	8	yes	complemented
617	#518	C₂²×C₈₉	1	8	yes	complemented
618	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
619	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
620	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
622	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
623	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
624	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
625	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
626	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
627	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
628	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
629	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
630	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
631	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
632	C₂⁵	C₂³×C₈₉	1	2	yes	—
633	H(5,𝔽₂)	—	2	16	no	—
634	C₂×#41	C₂³×C₈₉	1	4	yes	—
635	C₂×#41	C₂³×C₈₉	1	8	yes	—
636	C₂×#41	C₂³×C₈₉	1	8	yes	complemented
637	C₂×#41	C₂³×C₈₉	1	8	yes	complemented
638	C₂²×Q₈	C₂³×C₈₉	1	4	yes	complemented
639	C₂²×D₄	—	2	8	no	—
640	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
641	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
642	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
643	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
644	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
645	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
646	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
647	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
648	C₂²×D₄	C₂³×C₈₉	1	4	yes	complemented
649	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
651	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
652	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
653	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
654	C₂³×C₄	C₂³×C₈₉	1	8	yes	complemented
655	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
656	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
657	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
658	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
659	#127	C₂³×C₈₉	1	8	yes	—
660	#127	C₂³×C₈₉	1	2	yes	complemented
661	#126	C₂³×C₈₉	1	8	yes	—
662	#126	C₂³×C₈₉	1	16	yes	—
663	#126	C₂³×C₈₉	1	8	yes	—
664	#126	C₂³×C₈₉	1	16	yes	complemented
665	#126	C₂³×C₈₉	1	16	yes	complemented
666	#126	C₂³×C₈₉	1	8	yes	complemented
667	#126	C₂³×C₈₉	1	16	yes	complemented
668	#126	C₂³×C₈₉	1	8	yes	complemented
669	#125	C₂³×C₈₉	1	8	yes	complemented
670	#125	C₂³×C₈₉	1	8	yes	complemented
671	#125	C₂³×C₈₉	1	8	yes	complemented
672	#125	C₂³×C₈₉	1	8	yes	complemented
673	#125	C₂³×C₈₉	1	4	yes	complemented
674	#124	C₂³×C₈₉	1	8	yes	—
675	#124	C₂³×C₈₉	1	16	yes	—
676	#124	C₂³×C₈₉	1	8	yes	—
677	#124	C₂³×C₈₉	1	8	yes	—
678	#124	C₂³×C₈₉	1	16	yes	complemented
679	#124	C₂³×C₈₉	1	16	yes	complemented
680	#124	C₂³×C₈₉	1	8	yes	complemented
681	#124	C₂³×C₈₉	1	4	yes	complemented
682	#123	C₂³×C₈₉	1	8	yes	—
683	#123	C₂³×C₈₉	1	16	yes	—
684	#123	C₂³×C₈₉	1	8	yes	—
685	#123	C₂³×C₈₉	1	16	yes	—
686	#123	C₂³×C₈₉	1	8	yes	—
687	#123	C₂³×C₈₉	1	16	yes	complemented
688	#123	C₂³×C₈₉	1	16	yes	complemented
689	#123	C₂³×C₈₉	1	8	yes	complemented
690	#123	C₂³×C₈₉	1	16	yes	complemented
691	#123	C₂³×C₈₉	1	16	yes	complemented
692	#123	C₂³×C₈₉	1	16	yes	complemented
693	#123	C₂³×C₈₉	1	8	yes	complemented
694	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
698	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
699	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
700	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
701	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
702	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
703	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
704	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
705	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
706	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
707	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
708	#121	C₂³×C₈₉	1	8	yes	—
709	#121	C₂³×C₈₉	1	4	yes	—
710	#121	C₂³×C₈₉	1	8	yes	—
711	#121	C₂³×C₈₉	1	16	yes	—
712	#121	C₂³×C₈₉	1	4	yes	—
713	#121	C₂³×C₈₉	1	16	yes	—
714	#121	C₂³×C₈₉	1	4	yes	—
715	#121	C₂³×C₈₉	1	4	yes	—
716	#121	C₂³×C₈₉	1	16	yes	—
717	#121	C₂³×C₈₉	1	8	yes	—
718	#121	C₂³×C₈₉	1	8	yes	—
719	#121	C₂³×C₈₉	1	8	yes	—
720	#121	C₂³×C₈₉	1	16	yes	complemented
721	#121	C₂³×C₈₉	1	8	yes	complemented
722	#121	C₂³×C₈₉	1	8	yes	complemented
723	#121	C₂³×C₈₉	1	16	yes	complemented
724	#121	C₂³×C₈₉	1	8	yes	complemented
725	#121	C₂³×C₈₉	1	8	yes	complemented
726	#121	C₂³×C₈₉	1	8	yes	complemented
727	#120	C₂³×C₈₉	1	8	yes	—
728	#120	C₂³×C₈₉	1	16	yes	—
729	#120	C₂³×C₈₉	1	16	yes	—
730	#120	C₂³×C₈₉	1	16	yes	—
731	#120	C₂³×C₈₉	1	16	yes	—
732	#120	C₂³×C₈₉	1	16	yes	complemented
733	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
734	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
735	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
736	C₄×Q₈	C₂³×C₈₉	1	8	yes	complemented
737	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
738	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
739	C₄×D₄	C₂³×C₈₉	1	8	yes	—
740	C₄×D₄	C₂³×C₈₉	1	4	yes	—
741	C₄×D₄	C₂³×C₈₉	1	4	yes	—
742	C₄×D₄	C₂³×C₈₉	1	8	yes	—
743	C₄×D₄	C₂³×C₈₉	1	8	yes	—
744	C₄×D₄	C₂³×C₈₉	1	16	yes	—
745	C₄×D₄	C₂³×C₈₉	1	8	yes	—
746	C₄×D₄	C₂³×C₈₉	1	8	yes	—
747	C₄×D₄	C₂³×C₈₉	1	4	yes	—
748	C₄×D₄	C₂³×C₈₉	1	8	yes	—
749	C₄×D₄	C₂³×C₈₉	1	4	yes	—
750	C₄×D₄	C₂³×C₈₉	1	16	yes	—
751	C₄×D₄	C₂³×C₈₉	1	8	yes	—
752	C₄×D₄	C₂³×C₈₉	1	8	yes	—
753	C₄×D₄	C₂³×C₈₉	1	8	yes	—
754	C₄×D₄	C₂³×C₈₉	1	8	yes	—
755	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
756	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
757	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
758	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
759	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
760	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
761	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
762	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
763	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
764	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
765	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
766	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
767	#117	C₂³×C₈₉	1	4	yes	—
768	#117	C₂³×C₈₉	1	4	yes	—
769	#117	C₂³×C₈₉	1	8	yes	—
770	#117	C₂³×C₈₉	1	4	yes	—
771	#117	C₂³×C₈₉	1	8	yes	complemented
772	#117	C₂³×C₈₉	1	16	yes	complemented
773	#117	C₂³×C₈₉	1	8	yes	complemented
774	#117	C₂³×C₈₉	1	8	yes	complemented
775	#117	C₂³×C₈₉	1	8	yes	complemented
776	#117	C₂³×C₈₉	1	16	yes	complemented
777	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
781	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
782	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
783	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
784	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
785	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
786	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
800	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	complemented
801	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
802	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
805	C₂×C₄²	C₂³×C₈₉	1	8	yes	complemented
806	C₂×C₄²	C₂³×C₈₉	1	8	yes	complemented
807	C₂⁴	—	2	8	no	—
808	C₂⁴	—	8	2	no	—
809	C₂⁴	—	8	2	no	—
810	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
811	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
813	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
814	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
815	#41	—	2	32	no	—
816	#41	—	2	16	no	—
817	#41	—	8	8	no	—
818	#41	—	8	8	no	—
819	C₂×Q₈	—	8	4	no	—
820	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
821	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
822	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
823	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
824	C₂×D₄	—	2	8	no	—
825	C₂×D₄	—	2	32	no	—
826	C₂×D₄	—	2	32	no	—
827	C₂×D₄	—	2	32	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	8	8	no	—
830	C₂×D₄	—	8	8	no	—
831	C₂×D₄	—	8	4	no	—
832	C₂×D₄	#41×C₈₉	1	8	yes	complemented
833	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
834	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
835	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
836	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
837	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
838	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
839	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
840	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
841	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
842	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
843	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
844	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
845	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	8	2	no	—
848	C₂²×C₄	—	8	2	no	—
849	C₂²×C₄	—	8	2	no	—
850	C₂²×C₄	—	8	2	no	—
851	C₂²×C₄	—	8	8	no	—
852	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
854	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
855	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
856	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
864	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
865	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
866	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
868	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
869	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
870	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
871	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
872	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
873	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
874	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
875	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
877	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
879	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
881	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
882	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
883	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
884	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
885	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
886	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
887	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
888	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
892	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
893	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
894	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
895	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
897	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
898	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
900	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
901	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
903	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
907	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
908	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
909	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
910	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
911	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
912	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
914	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
916	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
917	C₄²	C₂⁴×C₈₉	1	4	yes	—
918	C₄²	C₂⁴×C₈₉	1	8	yes	—
919	C₄²	C₂⁴×C₈₉	1	2	yes	—
920	C₄²	C₂⁴×C₈₉	1	2	yes	—
921	C₄²	C₂⁴×C₈₉	1	8	yes	—
922	C₄²	C₂⁴×C₈₉	1	8	yes	—
923	C₄²	C₂⁴×C₈₉	1	8	yes	—
924	C₄²	C₂⁴×C₈₉	1	16	yes	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	16	no	—
928	C₂³	—	2	16	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	2	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	1	no	—
935	C₂³	—	4	8	no	—
936	C₂³	—	4	8	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	4	8	no	—
939	C₂³	—	8	16	no	—
940	C₂³	C₂×#41×C₈₉	1	8	yes	—
941	C₂³	C₂⁵×C₈₉	1	2	yes	—
942	C₂³	C₂⁵×C₈₉	1	4	yes	—
943	C₂³	C₂⁵×C₈₉	1	8	yes	—
944	C₂³	C₂⁵×C₈₉	1	4	yes	—
945	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
946	Q₈	—	2	8	no	—
947	Q₈	—	4	4	no	—
948	Q₈	—	4	8	no	—
949	Q₈	—	4	4	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	32	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	8	no	—
954	D₄	—	2	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	16	no	—
959	D₄	—	4	8	no	—
960	D₄	—	4	16	no	—
961	D₄	—	4	4	no	—
962	D₄	C₂×#41×C₈₉	1	16	yes	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	16	no	—
965	C₂×C₄	—	2	8	no	—
966	C₂×C₄	—	2	16	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	8	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	16	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
984	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
985	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
986	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
987	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
988	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
989	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
990	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
991	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
992	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
993	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
994	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	8	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	8	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	8	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	4	8	no	—
1010	C₂²	—	4	4	no	—
1011	C₂²	—	4	8	no	—
1012	C₂²	—	8	16	no	—
1013	C₂²	—	8	16	no	—
1014	C₂²	C₂²×#41×C₈₉	1	8	yes	—
1015	C₂²	C₂²×#41×C₈₉	1	2	yes	—
1016	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	8	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	4	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	8	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	8	no	—
1028	C₄	C₂²×#41×C₈₉	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	4	4	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	8	no	—
1034	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
1035	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic
1036	C₂	C₈₉×H(7,𝔽₂)	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×#3521	C₂	semidirect
2. C₈₉×#3519	C₂	semidirect
3. C₈₉×#3514	C₂	semidirect
4. C₈₉×#3513	C₂	semidirect
5. C₈₉×#3506	C₂	semidirect
6. C₈₉×#3505	C₂	semidirect
7. C₈₉×#3501	C₂	semidirect
8. C₈₉×#3496	C₂	semidirect
9. C₈₉×#3493	C₂	semidirect
10. C₈₉×#3490	C₂	semidirect
11. C₈₉×#3484	C₂	semidirect
12. C₈₉×#3460	C₂	semidirect
13. C₈₉×#3459	C₂	semidirect
14. C₈₉×#3455	C₂	semidirect
15. C₂×#538×C₈₉	C₂	semidirect
16. C₄×H(5,𝔽₂)×C₈₉	C₂	semidirect
17. C₂×#518×C₈₉	C₂	semidirect
20. #559×C₈₉	C₂²	semidirect
21. #556×C₈₉	C₂²	semidirect
22. #556×C₈₉	C₂²	semidirect
23. #555×C₈₉	C₂²	semidirect
24. #555×C₈₉	C₂²	semidirect
25. #554×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
29. #553×C₈₉	C₂²	semidirect
30. #553×C₈₉	C₂²	semidirect
31. #552×C₈₉	C₂²	semidirect
32. #552×C₈₉	C₂²	semidirect
33. #551×C₈₉	C₂²	semidirect
34. #551×C₈₉	C₂²	semidirect
35. #551×C₈₉	C₂²	semidirect
36. #550×C₈₉	C₂²	semidirect
37. D₄×Q₈×C₈₉	C₂²	semidirect
38. #548×C₈₉	C₂²	semidirect
39. #547×C₈₉	C₂²	semidirect
40. #547×C₈₉	C₂²	semidirect
41. #546×C₈₉	C₂²	semidirect
42. #546×C₈₉	C₂²	semidirect
43. #546×C₈₉	C₂²	semidirect
44. #546×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #546×C₈₉	C₂²	semidirect
47. D₄²×C₈₉	C₂²	semidirect
48. D₄²×C₈₉	C₂²	semidirect
49. D₄²×C₈₉	C₂²	semidirect
50. #544×C₈₉	C₂²	semidirect
51. #543×C₈₉	C₂²	semidirect
52. #542×C₈₉	C₂²	semidirect
53. #542×C₈₉	C₂²	semidirect
54. #542×C₈₉	C₂²	semidirect
55. #541×C₈₉	C₂²	semidirect
56. #540×C₈₉	C₂²	semidirect
57. #540×C₈₉	C₂²	semidirect
58. #539×C₈₉	C₂²	semidirect
59. #539×C₈₉	C₂²	semidirect
60. #539×C₈₉	C₂²	semidirect
61. #538×C₈₉	C₂²	semidirect
62. #538×C₈₉	C₂²	semidirect
63. #538×C₈₉	C₂²	semidirect
64. #538×C₈₉	C₂²	semidirect
65. #538×C₈₉	C₂²	semidirect
66. #538×C₈₉	C₂²	semidirect
67. #538×C₈₉	C₂²	semidirect
68. #538×C₈₉	C₂²	semidirect
69. #537×C₈₉	C₂²	semidirect
70. #535×C₈₉	C₂²	semidirect
71. #534×C₈₉	C₂²	semidirect
72. #534×C₈₉	C₂²	semidirect
73. #533×C₈₉	C₂²	semidirect
74. #532×C₈₉	C₂²	semidirect
75. #532×C₈₉	C₂²	semidirect
76. #529×C₈₉	C₂²	semidirect
77. #529×C₈₉	C₂²	semidirect
78. #529×C₈₉	C₂²	semidirect
79. #529×C₈₉	C₂²	semidirect
80. #529×C₈₉	C₂²	semidirect
81. C₂×#126×C₈₉	C₂²	semidirect
82. C₂×#124×C₈₉	C₂²	semidirect
83. #525×C₈₉	C₂²	semidirect
84. #525×C₈₉	C₂²	semidirect
85. #525×C₈₉	C₂²	semidirect
86. #525×C₈₉	C₂²	semidirect
87. C₂×#123×C₈₉	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
89. C₂×#121×C₈₉	C₂²	semidirect
90. C₂×#121×C₈₉	C₂²	semidirect
91. C₂×#120×C₈₉	C₂²	semidirect
92. #520×C₈₉	C₂²	semidirect
93. #520×C₈₉	C₂²	semidirect
95. #518×C₈₉	C₂²	semidirect
96. #518×C₈₉	C₂²	semidirect
97. #518×C₈₉	C₂²	semidirect
98. #518×C₈₉	C₂²	semidirect
99. C₄×#41×C₈₉	C₂²	semidirect
100. C₄×#41×C₈₉	C₂²	semidirect
103. C₂×C₄×D₄×C₈₉	C₂²	semidirect
104. C₂×C₄×D₄×C₈₉	C₂²	semidirect
105. C₂×C₄×D₄×C₈₉	C₂²	semidirect
106. C₂×C₄×D₄×C₈₉	C₂²	semidirect
107. C₂×C₄×D₄×C₈₉	C₂²	semidirect
108. C₂×C₄×D₄×C₈₉	C₂²	semidirect
109. C₂×#117×C₈₉	C₂²	semidirect
110. C₂×#117×C₈₉	C₂²	semidirect
111. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
112. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
117. C₂×#41×C₈₉	C₂³	semidirect
118. C₂×#41×C₈₉	C₂³	semidirect
119. C₂²×Q₈×C₈₉	C₂³	semidirect
129. C₂²×D₄×C₈₉	C₂³	semidirect
135. C₂³×C₄×C₈₉	C₂³	semidirect
136. C₄⋊Q₈×C₈₉	C₂³	semidirect
137. C₄⋊Q₈×C₈₉	C₂³	semidirect
138. C₄⋊Q₈×C₈₉	C₂³	semidirect
139. C₄⋊Q₈×C₈₉	C₂³	semidirect
141. #127×C₈₉	C₂³	semidirect
145. #126×C₈₉	C₂³	semidirect
146. #126×C₈₉	C₂³	semidirect
147. #126×C₈₉	C₂³	semidirect
148. #126×C₈₉	C₂³	semidirect
149. #126×C₈₉	C₂³	semidirect
150. #125×C₈₉	C₂³	semidirect
151. #125×C₈₉	C₂³	semidirect
152. #125×C₈₉	C₂³	semidirect
153. #125×C₈₉	C₂³	semidirect
154. #125×C₈₉	C₂³	semidirect
159. #124×C₈₉	C₂³	semidirect
160. #124×C₈₉	C₂³	semidirect
161. #124×C₈₉	C₂³	semidirect
162. #124×C₈₉	C₂³	semidirect
168. #123×C₈₉	C₂³	semidirect
169. #123×C₈₉	C₂³	semidirect
170. #123×C₈₉	C₂³	semidirect
171. #123×C₈₉	C₂³	semidirect
172. #123×C₈₉	C₂³	semidirect
173. #123×C₈₉	C₂³	semidirect
174. #123×C₈₉	C₂³	semidirect
180. C₂²⋊Q₈×C₈₉	C₂³	semidirect
181. C₂²⋊Q₈×C₈₉	C₂³	semidirect
182. C₂²⋊Q₈×C₈₉	C₂³	semidirect
183. C₂²⋊Q₈×C₈₉	C₂³	semidirect
184. C₂²⋊Q₈×C₈₉	C₂³	semidirect
185. C₂²⋊Q₈×C₈₉	C₂³	semidirect
186. C₂²⋊Q₈×C₈₉	C₂³	semidirect
187. C₂²⋊Q₈×C₈₉	C₂³	semidirect
188. C₂²⋊Q₈×C₈₉	C₂³	semidirect
201. #121×C₈₉	C₂³	semidirect
202. #121×C₈₉	C₂³	semidirect
203. #121×C₈₉	C₂³	semidirect
204. #121×C₈₉	C₂³	semidirect
205. #121×C₈₉	C₂³	semidirect
206. #121×C₈₉	C₂³	semidirect
207. #121×C₈₉	C₂³	semidirect
213. #120×C₈₉	C₂³	semidirect
214. C₄×Q₈×C₈₉	C₂³	semidirect
215. C₄×Q₈×C₈₉	C₂³	semidirect
216. C₄×Q₈×C₈₉	C₂³	semidirect
217. C₄×Q₈×C₈₉	C₂³	semidirect
218. C₄×Q₈×C₈₉	C₂³	semidirect
219. C₄×Q₈×C₈₉	C₂³	semidirect
236. C₄×D₄×C₈₉	C₂³	semidirect
237. C₄×D₄×C₈₉	C₂³	semidirect
238. C₄×D₄×C₈₉	C₂³	semidirect
239. C₄×D₄×C₈₉	C₂³	semidirect
240. C₄×D₄×C₈₉	C₂³	semidirect
241. C₄×D₄×C₈₉	C₂³	semidirect
242. C₄×D₄×C₈₉	C₂³	semidirect
243. C₄×D₄×C₈₉	C₂³	semidirect
244. C₄×D₄×C₈₉	C₂³	semidirect
245. C₄×D₄×C₈₉	C₂³	semidirect
246. C₄×D₄×C₈₉	C₂³	semidirect
247. C₄×D₄×C₈₉	C₂³	semidirect
252. #117×C₈₉	C₂³	semidirect
253. #117×C₈₉	C₂³	semidirect
254. #117×C₈₉	C₂³	semidirect
255. #117×C₈₉	C₂³	semidirect
256. #117×C₈₉	C₂³	semidirect
257. #117×C₈₉	C₂³	semidirect
262. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
263. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
264. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
265. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
266. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
280. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
281. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
282. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
286. C₂×C₄²×C₈₉	C₂³	semidirect
287. C₂×C₄²×C₈₉	C₂³	semidirect
313. C₂×D₄×C₈₉	#41	semidirect
510. #62846	C₈₉	direct (N × H)
519. #3521	C₂×C₈₉	semidirect
520. #3519	C₂×C₈₉	semidirect
521. #3514	C₂×C₈₉	semidirect
522. #3513	C₂×C₈₉	semidirect
523. #3506	C₂×C₈₉	semidirect
524. #3505	C₂×C₈₉	semidirect
525. #3501	C₂×C₈₉	semidirect
526. #3496	C₂×C₈₉	semidirect
527. #3493	C₂×C₈₉	semidirect
528. #3490	C₂×C₈₉	semidirect
529. #3484	C₂×C₈₉	semidirect
530. #3460	C₂×C₈₉	semidirect
531. #3459	C₂×C₈₉	semidirect
532. #3455	C₂×C₈₉	semidirect
533. C₂×#538	C₂×C₈₉	semidirect
534. C₄×H(5,𝔽₂)	C₂×C₈₉	semidirect
535. C₂×#518	C₂×C₈₉	semidirect
536. C₈₉	#62846	direct (N × H)
539. #559	C₂²×C₈₉	semidirect
540. #556	C₂²×C₈₉	semidirect
541. #556	C₂²×C₈₉	semidirect
542. #555	C₂²×C₈₉	semidirect
543. #555	C₂²×C₈₉	semidirect
544. #554	C₂²×C₈₉	semidirect
545. #554	C₂²×C₈₉	semidirect
546. #553	C₂²×C₈₉	semidirect
547. #553	C₂²×C₈₉	semidirect
548. #553	C₂²×C₈₉	semidirect
549. #553	C₂²×C₈₉	semidirect
550. #552	C₂²×C₈₉	semidirect
551. #552	C₂²×C₈₉	semidirect
552. #551	C₂²×C₈₉	semidirect
553. #551	C₂²×C₈₉	semidirect
554. #551	C₂²×C₈₉	semidirect
555. #550	C₂²×C₈₉	semidirect
556. D₄×Q₈	C₂²×C₈₉	semidirect
557. #548	C₂²×C₈₉	semidirect
558. #547	C₂²×C₈₉	semidirect
559. #547	C₂²×C₈₉	semidirect
560. #546	C₂²×C₈₉	semidirect
561. #546	C₂²×C₈₉	semidirect
562. #546	C₂²×C₈₉	semidirect
563. #546	C₂²×C₈₉	semidirect
564. #546	C₂²×C₈₉	semidirect
565. #546	C₂²×C₈₉	semidirect
566. D₄²	C₂²×C₈₉	semidirect
567. D₄²	C₂²×C₈₉	semidirect
568. D₄²	C₂²×C₈₉	semidirect
569. #544	C₂²×C₈₉	semidirect
570. #543	C₂²×C₈₉	semidirect
571. #542	C₂²×C₈₉	semidirect
572. #542	C₂²×C₈₉	semidirect
573. #542	C₂²×C₈₉	semidirect
574. #541	C₂²×C₈₉	semidirect
575. #540	C₂²×C₈₉	semidirect
576. #540	C₂²×C₈₉	semidirect
577. #539	C₂²×C₈₉	semidirect
578. #539	C₂²×C₈₉	semidirect
579. #539	C₂²×C₈₉	semidirect
580. #538	C₂²×C₈₉	semidirect
581. #538	C₂²×C₈₉	semidirect
582. #538	C₂²×C₈₉	semidirect
583. #538	C₂²×C₈₉	semidirect
584. #538	C₂²×C₈₉	semidirect
585. #538	C₂²×C₈₉	semidirect
586. #538	C₂²×C₈₉	semidirect
587. #538	C₂²×C₈₉	semidirect
588. #537	C₂²×C₈₉	semidirect
589. #535	C₂²×C₈₉	semidirect
590. #534	C₂²×C₈₉	semidirect
591. #534	C₂²×C₈₉	semidirect
592. #533	C₂²×C₈₉	semidirect
593. #532	C₂²×C₈₉	semidirect
594. #532	C₂²×C₈₉	semidirect
595. #529	C₂²×C₈₉	semidirect
596. #529	C₂²×C₈₉	semidirect
597. #529	C₂²×C₈₉	semidirect
598. #529	C₂²×C₈₉	semidirect
599. #529	C₂²×C₈₉	semidirect
600. C₂×#126	C₂²×C₈₉	semidirect
601. C₂×#124	C₂²×C₈₉	semidirect
602. #525	C₂²×C₈₉	semidirect
603. #525	C₂²×C₈₉	semidirect
604. #525	C₂²×C₈₉	semidirect
605. #525	C₂²×C₈₉	semidirect
606. C₂×#123	C₂²×C₈₉	semidirect
607. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
608. C₂×#121	C₂²×C₈₉	semidirect
609. C₂×#121	C₂²×C₈₉	semidirect
610. C₂×#120	C₂²×C₈₉	semidirect
611. #520	C₂²×C₈₉	semidirect
612. #520	C₂²×C₈₉	semidirect
614. #518	C₂²×C₈₉	semidirect
615. #518	C₂²×C₈₉	semidirect
616. #518	C₂²×C₈₉	semidirect
617. #518	C₂²×C₈₉	semidirect
618. C₄×#41	C₂²×C₈₉	semidirect
619. C₄×#41	C₂²×C₈₉	semidirect
622. C₂×C₄×D₄	C₂²×C₈₉	semidirect
623. C₂×C₄×D₄	C₂²×C₈₉	semidirect
624. C₂×C₄×D₄	C₂²×C₈₉	semidirect
625. C₂×C₄×D₄	C₂²×C₈₉	semidirect
626. C₂×C₄×D₄	C₂²×C₈₉	semidirect
627. C₂×C₄×D₄	C₂²×C₈₉	semidirect
628. C₂×#117	C₂²×C₈₉	semidirect
629. C₂×#117	C₂²×C₈₉	semidirect
630. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
631. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
636. C₂×#41	C₂³×C₈₉	semidirect
637. C₂×#41	C₂³×C₈₉	semidirect
638. C₂²×Q₈	C₂³×C₈₉	semidirect
648. C₂²×D₄	C₂³×C₈₉	semidirect
654. C₂³×C₄	C₂³×C₈₉	semidirect
655. C₄⋊Q₈	C₂³×C₈₉	semidirect
656. C₄⋊Q₈	C₂³×C₈₉	semidirect
657. C₄⋊Q₈	C₂³×C₈₉	semidirect
658. C₄⋊Q₈	C₂³×C₈₉	semidirect
660. #127	C₂³×C₈₉	semidirect
664. #126	C₂³×C₈₉	semidirect
665. #126	C₂³×C₈₉	semidirect
666. #126	C₂³×C₈₉	semidirect
667. #126	C₂³×C₈₉	semidirect
668. #126	C₂³×C₈₉	semidirect
669. #125	C₂³×C₈₉	semidirect
670. #125	C₂³×C₈₉	semidirect
671. #125	C₂³×C₈₉	semidirect
672. #125	C₂³×C₈₉	semidirect
673. #125	C₂³×C₈₉	semidirect
678. #124	C₂³×C₈₉	semidirect
679. #124	C₂³×C₈₉	semidirect
680. #124	C₂³×C₈₉	semidirect
681. #124	C₂³×C₈₉	semidirect
687. #123	C₂³×C₈₉	semidirect
688. #123	C₂³×C₈₉	semidirect
689. #123	C₂³×C₈₉	semidirect
690. #123	C₂³×C₈₉	semidirect
691. #123	C₂³×C₈₉	semidirect
692. #123	C₂³×C₈₉	semidirect
693. #123	C₂³×C₈₉	semidirect
699. C₂²⋊Q₈	C₂³×C₈₉	semidirect
700. C₂²⋊Q₈	C₂³×C₈₉	semidirect
701. C₂²⋊Q₈	C₂³×C₈₉	semidirect
702. C₂²⋊Q₈	C₂³×C₈₉	semidirect
703. C₂²⋊Q₈	C₂³×C₈₉	semidirect
704. C₂²⋊Q₈	C₂³×C₈₉	semidirect
705. C₂²⋊Q₈	C₂³×C₈₉	semidirect
706. C₂²⋊Q₈	C₂³×C₈₉	semidirect
707. C₂²⋊Q₈	C₂³×C₈₉	semidirect
720. #121	C₂³×C₈₉	semidirect
721. #121	C₂³×C₈₉	semidirect
722. #121	C₂³×C₈₉	semidirect
723. #121	C₂³×C₈₉	semidirect
724. #121	C₂³×C₈₉	semidirect
725. #121	C₂³×C₈₉	semidirect
726. #121	C₂³×C₈₉	semidirect
732. #120	C₂³×C₈₉	semidirect
733. C₄×Q₈	C₂³×C₈₉	semidirect
734. C₄×Q₈	C₂³×C₈₉	semidirect
735. C₄×Q₈	C₂³×C₈₉	semidirect
736. C₄×Q₈	C₂³×C₈₉	semidirect
737. C₄×Q₈	C₂³×C₈₉	semidirect
738. C₄×Q₈	C₂³×C₈₉	semidirect
755. C₄×D₄	C₂³×C₈₉	semidirect
756. C₄×D₄	C₂³×C₈₉	semidirect
757. C₄×D₄	C₂³×C₈₉	semidirect
758. C₄×D₄	C₂³×C₈₉	semidirect
759. C₄×D₄	C₂³×C₈₉	semidirect
760. C₄×D₄	C₂³×C₈₉	semidirect
761. C₄×D₄	C₂³×C₈₉	semidirect
762. C₄×D₄	C₂³×C₈₉	semidirect
763. C₄×D₄	C₂³×C₈₉	semidirect
764. C₄×D₄	C₂³×C₈₉	semidirect
765. C₄×D₄	C₂³×C₈₉	semidirect
766. C₄×D₄	C₂³×C₈₉	semidirect
771. #117	C₂³×C₈₉	semidirect
772. #117	C₂³×C₈₉	semidirect
773. #117	C₂³×C₈₉	semidirect
774. #117	C₂³×C₈₉	semidirect
775. #117	C₂³×C₈₉	semidirect
776. #117	C₂³×C₈₉	semidirect
781. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
782. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
783. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
784. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
785. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
799. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
800. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
801. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
805. C₂×C₄²	C₂³×C₈₉	semidirect
806. C₂×C₄²	C₂³×C₈₉	semidirect
832. C₂×D₄	#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×#3521	2
C₈₉×#3519	2
C₈₉×#3514	2
C₈₉×#3513	2
C₈₉×#3506	2
C₈₉×#3505	2
C₈₉×#3501	2
C₈₉×#3496	2
C₈₉×#3493	2
C₈₉×#3490	2
C₈₉×#3484	2
C₈₉×#3460	2
C₈₉×#3459	2
C₈₉×#3455	2
C₂×#538×C₈₉	2
C₄×H(5,𝔽₂)×C₈₉	2
C₂×#518×C₈₉	2
#62846	89

Subgroups — C89×#62846 #36440694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62846 #36440694