Subgroups — C₈₉×#23878 #36401726

Order 22784.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#455×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#453×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3005	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2004	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	#575×C₈₉	—	2	4	no	—
20	#575×C₈₉	—	2	4	no	—
21	C₂×#137×C₈₉	—	2	1	no	—
22	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#135×C₈₉	—	2	1	no	—
30	C₂×#135×C₈₉	—	2	1	no	—
31	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	#550×C₈₉	—	2	1	no	—
33	#548×C₈₉	—	2	1	no	—
34	#546×C₈₉	—	2	1	no	—
35	#546×C₈₉	—	2	2	no	—
36	D₄²×C₈₉	—	2	2	no	—
37	D₄²×C₈₉	—	2	1	no	—
38	#537×C₈₉	—	2	1	no	—
39	#537×C₈₉	C₂²	1	1	yes	characteristic
40	#535×C₈₉	—	2	1	no	—
41	#535×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#525×C₈₉	—	2	1	no	—
45	#525×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	—	2	1	no	—
47	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
48	#520×C₈₉	C₂²	1	1	yes	characteristic
49	#455×C₈₉	—	2	4	no	—
50	#453×C₈₉	—	2	4	no	—
51	#452×C₈₉	—	2	1	no	—
52	#452×C₈₉	—	2	1	no	—
53	#449×C₈₉	—	2	1	no	—
54	#449×C₈₉	—	2	1	no	—
55	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#419×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#418×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#407×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#392×C₈₉	—	2	2	no	—
67	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#386×C₈₉	—	2	2	no	—
70	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#339×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#339×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	H(5,𝔽₂)×C₈₉	—	2	2	no	—
76	H(5,𝔽₂)×C₈₉	—	2	2	no	—
77	H(5,𝔽₂)×C₈₉	—	4	1	no	—
78	H(5,𝔽₂)×C₈₉	—	4	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	C₂×#41×C₈₉	—	2	1	no	—
83	C₂×#41×C₈₉	—	2	2	no	—
84	C₂×#41×C₈₉	—	2	2	no	—
85	C₂×#41×C₈₉	—	2	2	no	—
86	C₂×#41×C₈₉	—	2	2	no	—
87	C₂×#41×C₈₉	—	2	1	no	—
88	C₂×#41×C₈₉	—	2	1	no	—
89	C₂×#41×C₈₉	—	2	1	no	—
90	C₂×#41×C₈₉	—	2	1	no	—
91	C₂×#41×C₈₉	—	4	1	no	—
92	C₂×#41×C₈₉	—	4	1	no	—
93	C₂×#41×C₈₉	—	4	1	no	—
94	C₂×#41×C₈₉	—	4	1	no	—
95	C₂×#41×C₈₉	D₄	1	1	yes	characteristic, complemented
96	C₂×#41×C₈₉	D₄	1	1	yes	characteristic, complemented
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic, complemented
101	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₈₉	—	2	1	no	—
103	C₂²×D₄×C₈₉	—	2	2	no	—
104	C₂²×D₄×C₈₉	—	2	2	no	—
105	C₂²×D₄×C₈₉	—	2	1	no	—
106	C₂²×D₄×C₈₉	—	2	1	no	—
107	C₂²×D₄×C₈₉	—	2	1	no	—
108	C₂²×D₄×C₈₉	—	2	2	no	—
109	C₂²×D₄×C₈₉	D₄	1	2	yes	—
110	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic, complemented
111	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₈₉	—	2	1	no	—
114	C₂³×C₄×C₈₉	—	2	1	no	—
115	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	#137×C₈₉	—	2	8	no	—
117	#137×C₈₉	—	2	2	no	—
118	#137×C₈₉	—	2	2	no	—
119	#137×C₈₉	—	2	2	no	—
120	#137×C₈₉	—	2	2	no	—
121	#137×C₈₉	—	4	1	no	—
122	#137×C₈₉	D₄	1	4	yes	complemented
123	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
124	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
125	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
126	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
127	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
128	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
129	AGL(1,ℤ/8)×C₈₉	D₄	1	4	yes	complemented
130	#135×C₈₉	—	2	8	no	—
131	#135×C₈₉	—	2	8	no	—
132	C₂×Q₁₆×C₈₉	—	2	1	no	—
133	C₂×Q₁₆×C₈₉	—	2	1	no	—
134	C₂×Q₁₆×C₈₉	—	2	1	no	—
135	C₂×SD₁₆×C₈₉	—	2	1	no	—
136	C₂×SD₁₆×C₈₉	—	2	1	no	—
137	C₂×SD₁₆×C₈₉	—	2	1	no	—
138	C₂×SD₁₆×C₈₉	—	2	1	no	—
139	C₂×SD₁₆×C₈₉	—	2	1	no	—
140	C₂×SD₁₆×C₈₉	—	2	1	no	—
141	C₂×D₈×C₈₉	—	2	1	no	—
142	C₂×D₈×C₈₉	—	2	1	no	—
143	C₂×D₈×C₈₉	—	2	1	no	—
144	C₂×M₁₆×C₈₉	—	2	1	no	—
145	C₂×M₁₆×C₈₉	—	2	2	no	—
146	C₂×M₁₆×C₈₉	—	2	2	no	—
147	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₈₉	—	2	1	no	—
152	#127×C₈₉	—	2	2	no	—
153	#127×C₈₉	—	2	1	no	—
154	#127×C₈₉	—	2	2	no	—
155	#127×C₈₉	—	4	1	no	—
156	#124×C₈₉	—	2	2	no	—
157	#124×C₈₉	—	2	1	no	—
158	#124×C₈₉	—	2	2	no	—
159	#124×C₈₉	—	4	1	no	—
160	#123×C₈₉	—	2	2	no	—
161	#123×C₈₉	—	2	1	no	—
162	C₂²⋊Q₈×C₈₉	—	2	2	no	—
163	C₂²⋊Q₈×C₈₉	—	2	1	no	—
164	C₂²⋊Q₈×C₈₉	—	2	1	no	—
165	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic, complemented
166	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic, complemented
167	#121×C₈₉	—	2	2	no	—
168	#121×C₈₉	—	2	2	no	—
169	#121×C₈₉	—	2	2	no	—
170	#121×C₈₉	—	2	2	no	—
171	#121×C₈₉	—	2	2	no	—
172	#121×C₈₉	—	2	1	no	—
173	#121×C₈₉	—	2	1	no	—
174	#121×C₈₉	—	2	1	no	—
175	#121×C₈₉	—	2	1	no	—
176	#121×C₈₉	—	2	1	no	—
177	#121×C₈₉	—	2	1	no	—
178	#121×C₈₉	—	2	2	no	—
179	#121×C₈₉	—	2	1	no	—
180	#121×C₈₉	—	2	1	no	—
181	#121×C₈₉	D₄	1	1	yes	characteristic, complemented
182	#121×C₈₉	D₄	1	1	yes	characteristic, complemented
183	#120×C₈₉	—	2	2	no	—
184	#120×C₈₉	—	2	2	no	—
185	#120×C₈₉	—	2	2	no	—
186	#120×C₈₉	—	2	1	no	—
187	#120×C₈₉	—	2	2	no	—
188	C₄×Q₈×C₈₉	—	2	1	no	—
189	C₄×D₄×C₈₉	—	2	2	no	—
190	C₄×D₄×C₈₉	—	2	2	no	—
191	C₄×D₄×C₈₉	—	2	1	no	—
192	C₄×D₄×C₈₉	—	2	2	no	—
193	C₄×D₄×C₈₉	—	2	1	no	—
194	C₄×D₄×C₈₉	—	2	1	no	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
204	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
206	#104×C₈₉	—	2	2	no	—
207	#104×C₈₉	—	2	2	no	—
208	#104×C₈₉	—	2	2	no	—
209	#104×C₈₉	—	2	2	no	—
210	#104×C₈₉	—	4	1	no	—
211	#104×C₈₉	—	4	1	no	—
212	#103×C₈₉	—	2	1	no	—
213	#103×C₈₉	—	2	1	no	—
214	#102×C₈₉	—	2	1	no	—
215	#102×C₈₉	—	2	1	no	—
216	#100×C₈₉	—	2	2	no	—
217	#100×C₈₉	—	2	2	no	—
218	C₂²⋊C₈×C₈₉	—	2	1	no	—
219	C₂²⋊C₈×C₈₉	—	2	1	no	—
220	#95×C₈₉	—	2	1	no	—
221	#95×C₈₉	—	2	2	no	—
222	C₂⁴×C₈₉	—	2	2	no	—
223	C₂⁴×C₈₉	—	2	1	no	—
224	C₂⁴×C₈₉	—	2	1	no	—
225	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
226	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
227	#41×C₈₉	—	2	1	no	—
228	#41×C₈₉	—	2	1	no	—
229	#41×C₈₉	—	2	4	no	—
230	#41×C₈₉	—	2	4	no	—
231	#41×C₈₉	—	2	2	no	—
232	#41×C₈₉	—	2	2	no	—
233	#41×C₈₉	—	2	1	no	—
234	#41×C₈₉	—	2	1	no	—
235	#41×C₈₉	—	2	1	no	—
236	#41×C₈₉	—	2	1	no	—
237	#41×C₈₉	—	2	1	no	—
238	#41×C₈₉	—	2	1	no	—
239	#41×C₈₉	—	2	1	no	—
240	#41×C₈₉	—	2	1	no	—
241	#41×C₈₉	—	4	2	no	—
242	#41×C₈₉	—	4	2	no	—
243	#41×C₈₉	—	4	1	no	—
244	#41×C₈₉	—	4	1	no	—
245	#41×C₈₉	—	4	2	no	—
246	#41×C₈₉	—	4	2	no	—
247	#41×C₈₉	—	4	2	no	—
248	#41×C₈₉	—	4	2	no	—
249	#41×C₈₉	—	4	2	no	—
250	#41×C₈₉	—	4	2	no	—
251	#41×C₈₉	—	4	2	no	—
252	#41×C₈₉	—	4	2	no	—
253	#41×C₈₉	—	4	2	no	—
254	#41×C₈₉	—	4	2	no	—
255	#41×C₈₉	—	4	2	no	—
256	#41×C₈₉	—	4	2	no	—
257	#41×C₈₉	C₂×D₄	1	2	yes	—
258	#41×C₈₉	C₂×D₄	1	2	yes	—
259	C₂×Q₈×C₈₉	—	2	1	no	—
260	C₂×Q₈×C₈₉	—	2	1	no	—
261	C₂×Q₈×C₈₉	—	2	2	no	—
262	C₂×Q₈×C₈₉	—	2	1	no	—
263	C₂×Q₈×C₈₉	—	2	1	no	—
264	C₂×Q₈×C₈₉	—	2	1	no	—
265	C₂×Q₈×C₈₉	—	2	1	no	—
266	C₂×Q₈×C₈₉	—	4	1	no	—
267	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	complemented
271	C₂×D₄×C₈₉	—	2	1	no	—
272	C₂×D₄×C₈₉	—	2	2	no	—
273	C₂×D₄×C₈₉	—	2	2	no	—
274	C₂×D₄×C₈₉	—	2	2	no	—
275	C₂×D₄×C₈₉	—	2	2	no	—
276	C₂×D₄×C₈₉	—	2	1	no	—
277	C₂×D₄×C₈₉	—	2	1	no	—
278	C₂×D₄×C₈₉	—	2	1	no	—
279	C₂×D₄×C₈₉	—	2	1	no	—
280	C₂×D₄×C₈₉	—	2	1	no	—
281	C₂×D₄×C₈₉	—	2	2	no	—
282	C₂×D₄×C₈₉	—	2	2	no	—
283	C₂×D₄×C₈₉	—	2	2	no	—
284	C₂×D₄×C₈₉	—	2	1	no	—
285	C₂×D₄×C₈₉	—	2	2	no	—
286	C₂×D₄×C₈₉	—	2	1	no	—
287	C₂×D₄×C₈₉	—	2	1	no	—
288	C₂×D₄×C₈₉	—	2	1	no	—
289	C₂×D₄×C₈₉	—	2	1	no	—
290	C₂×D₄×C₈₉	—	2	1	no	—
291	C₂×D₄×C₈₉	—	2	1	no	—
292	C₂×D₄×C₈₉	—	2	1	no	—
293	C₂×D₄×C₈₉	—	2	1	no	—
294	C₂×D₄×C₈₉	—	2	1	no	—
295	C₂×D₄×C₈₉	—	2	1	no	—
296	C₂×D₄×C₈₉	—	2	1	no	—
297	C₂×D₄×C₈₉	—	2	1	no	—
298	C₂×D₄×C₈₉	—	4	1	no	—
299	C₂×D₄×C₈₉	—	4	2	no	—
300	C₂×D₄×C₈₉	—	4	2	no	—
301	C₂×D₄×C₈₉	—	4	2	no	—
302	C₂×D₄×C₈₉	—	4	4	no	—
303	C₂×D₄×C₈₉	—	4	2	no	—
304	C₂×D₄×C₈₉	—	4	2	no	—
305	C₂×D₄×C₈₉	—	4	4	no	—
306	C₂×D₄×C₈₉	—	4	4	no	—
307	C₂×D₄×C₈₉	—	4	2	no	—
308	C₂×D₄×C₈₉	—	4	2	no	—
309	C₂×D₄×C₈₉	—	4	1	no	—
310	C₂×D₄×C₈₉	—	4	1	no	—
311	C₂×D₄×C₈₉	—	4	2	no	—
312	C₂×D₄×C₈₉	—	4	4	no	—
313	C₂×D₄×C₈₉	—	8	2	no	—
314	C₂×D₄×C₈₉	—	8	2	no	—
315	C₂×D₄×C₈₉	—	8	4	no	—
316	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	complemented
320	C₂²×C₄×C₈₉	—	2	1	no	—
321	C₂²×C₄×C₈₉	—	2	1	no	—
322	C₂²×C₄×C₈₉	—	2	1	no	—
323	C₂²×C₄×C₈₉	—	2	1	no	—
324	C₂²×C₄×C₈₉	—	2	1	no	—
325	C₂²×C₄×C₈₉	—	2	2	no	—
326	C₂²×C₄×C₈₉	—	2	1	no	—
327	C₂²×C₄×C₈₉	—	2	1	no	—
328	C₂²×C₄×C₈₉	—	2	1	no	—
329	C₂²×C₄×C₈₉	—	2	2	no	—
330	C₂²×C₄×C₈₉	—	2	1	no	—
331	C₂²×C₄×C₈₉	—	2	1	no	—
332	C₂²×C₄×C₈₉	—	2	1	no	—
333	C₂²×C₄×C₈₉	—	2	1	no	—
334	C₂²×C₄×C₈₉	—	2	1	no	—
335	C₂²×C₄×C₈₉	—	4	2	no	—
336	C₂²×C₄×C₈₉	—	4	2	no	—
337	C₂²×C₄×C₈₉	—	4	2	no	—
338	C₂²×C₄×C₈₉	—	4	2	no	—
339	C₂²×C₄×C₈₉	—	4	1	no	—
340	C₂²×C₄×C₈₉	—	4	1	no	—
341	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₈₉	—	2	4	no	—
349	Q₁₆×C₈₉	—	2	4	no	—
350	Q₁₆×C₈₉	—	4	2	no	—
351	SD₁₆×C₈₉	—	2	4	no	—
352	SD₁₆×C₈₉	—	2	4	no	—
353	SD₁₆×C₈₉	—	2	4	no	—
354	SD₁₆×C₈₉	—	2	4	no	—
355	SD₁₆×C₈₉	—	4	2	no	—
356	SD₁₆×C₈₉	—	4	2	no	—
357	D₈×C₈₉	—	2	4	no	—
358	D₈×C₈₉	—	2	4	no	—
359	D₈×C₈₉	—	4	2	no	—
360	M₁₆×C₈₉	—	2	4	no	—
361	M₁₆×C₈₉	—	2	1	no	—
362	M₁₆×C₈₉	—	2	1	no	—
363	M₁₆×C₈₉	—	2	1	no	—
364	M₁₆×C₈₉	—	2	1	no	—
365	M₁₆×C₈₉	—	2	1	no	—
366	M₁₆×C₈₉	—	2	1	no	—
367	M₁₆×C₈₉	C₂×D₄	1	2	yes	complemented
368	M₁₆×C₈₉	C₂×D₄	1	2	yes	complemented
369	C₂×C₈×C₈₉	—	2	4	no	—
370	C₂×C₈×C₈₉	—	2	1	no	—
371	C₂×C₈×C₈₉	—	2	1	no	—
372	C₂×C₈×C₈₉	—	2	1	no	—
373	C₂×C₈×C₈₉	—	2	1	no	—
374	C₄⋊C₄×C₈₉	—	2	2	no	—
375	C₄⋊C₄×C₈₉	—	2	2	no	—
376	C₄⋊C₄×C₈₉	—	2	1	no	—
377	C₄⋊C₄×C₈₉	—	2	1	no	—
378	C₄⋊C₄×C₈₉	—	2	1	no	—
379	C₄⋊C₄×C₈₉	—	2	1	no	—
380	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
382	C₂²⋊C₄×C₈₉	—	2	2	no	—
383	C₂²⋊C₄×C₈₉	—	2	2	no	—
384	C₂²⋊C₄×C₈₉	—	2	2	no	—
385	C₂²⋊C₄×C₈₉	—	2	2	no	—
386	C₂²⋊C₄×C₈₉	—	2	2	no	—
387	C₂²⋊C₄×C₈₉	—	2	1	no	—
388	C₂²⋊C₄×C₈₉	—	2	1	no	—
389	C₂²⋊C₄×C₈₉	—	2	1	no	—
390	C₂²⋊C₄×C₈₉	—	2	1	no	—
391	C₂²⋊C₄×C₈₉	—	2	2	no	—
392	C₂²⋊C₄×C₈₉	—	2	2	no	—
393	C₂²⋊C₄×C₈₉	—	2	1	no	—
394	C₂²⋊C₄×C₈₉	—	4	4	no	—
395	C₂²⋊C₄×C₈₉	—	4	2	no	—
396	C₂²⋊C₄×C₈₉	—	8	2	no	—
397	C₄²×C₈₉	—	2	2	no	—
398	C₄²×C₈₉	—	2	1	no	—
399	C₄²×C₈₉	—	2	1	no	—
400	C₄²×C₈₉	—	2	1	no	—
401	C₄²×C₈₉	—	2	1	no	—
402	C₄²×C₈₉	—	2	1	no	—
403	C₂³×C₈₉	—	2	1	no	—
404	C₂³×C₈₉	—	2	1	no	—
405	C₂³×C₈₉	—	2	1	no	—
406	C₂³×C₈₉	—	2	2	no	—
407	C₂³×C₈₉	—	2	1	no	—
408	C₂³×C₈₉	—	2	1	no	—
409	C₂³×C₈₉	—	2	2	no	—
410	C₂³×C₈₉	—	2	2	no	—
411	C₂³×C₈₉	—	2	2	no	—
412	C₂³×C₈₉	—	4	1	no	—
413	C₂³×C₈₉	—	4	1	no	—
414	C₂³×C₈₉	—	4	2	no	—
415	C₂³×C₈₉	—	4	2	no	—
416	C₂³×C₈₉	—	4	2	no	—
417	C₂³×C₈₉	—	4	2	no	—
418	C₂³×C₈₉	—	4	4	no	—
419	C₂³×C₈₉	—	4	2	no	—
420	C₂³×C₈₉	—	4	2	no	—
421	C₂³×C₈₉	—	4	1	no	—
422	C₂³×C₈₉	—	4	1	no	—
423	C₂³×C₈₉	—	8	1	no	—
424	C₂³×C₈₉	—	8	2	no	—
425	C₂³×C₈₉	—	8	2	no	—
426	C₂³×C₈₉	#120	1	1	yes	characteristic
427	C₂³×C₈₉	#120	1	1	yes	characteristic
428	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
429	Q₈×C₈₉	—	2	1	no	—
430	Q₈×C₈₉	—	2	1	no	—
431	Q₈×C₈₉	—	2	2	no	—
432	Q₈×C₈₉	—	2	1	no	—
433	Q₈×C₈₉	—	2	1	no	—
434	Q₈×C₈₉	—	2	2	no	—
435	Q₈×C₈₉	—	2	1	no	—
436	Q₈×C₈₉	—	4	2	no	—
437	Q₈×C₈₉	—	4	1	no	—
438	Q₈×C₈₉	—	4	1	no	—
439	Q₈×C₈₉	#120	1	2	yes	—
440	D₄×C₈₉	—	2	2	no	—
441	D₄×C₈₉	—	2	2	no	—
442	D₄×C₈₉	—	2	1	no	—
443	D₄×C₈₉	—	2	2	no	—
444	D₄×C₈₉	—	2	1	no	—
445	D₄×C₈₉	—	2	1	no	—
446	D₄×C₈₉	—	2	1	no	—
447	D₄×C₈₉	—	2	2	no	—
448	D₄×C₈₉	—	2	1	no	—
449	D₄×C₈₉	—	4	2	no	—
450	D₄×C₈₉	—	4	2	no	—
451	D₄×C₈₉	—	4	4	no	—
452	D₄×C₈₉	—	4	2	no	—
453	D₄×C₈₉	—	4	4	no	—
454	D₄×C₈₉	—	4	4	no	—
455	D₄×C₈₉	—	4	2	no	—
456	D₄×C₈₉	—	4	4	no	—
457	D₄×C₈₉	—	4	4	no	—
458	D₄×C₈₉	—	4	1	no	—
459	D₄×C₈₉	—	4	1	no	—
460	D₄×C₈₉	—	4	1	no	—
461	D₄×C₈₉	—	4	1	no	—
462	D₄×C₈₉	—	4	1	no	—
463	D₄×C₈₉	—	4	1	no	—
464	D₄×C₈₉	—	4	1	no	—
465	D₄×C₈₉	—	4	1	no	—
466	D₄×C₈₉	—	4	1	no	—
467	D₄×C₈₉	—	4	1	no	—
468	D₄×C₈₉	—	8	1	no	—
469	D₄×C₈₉	—	8	2	no	—
470	D₄×C₈₉	—	8	2	no	—
471	D₄×C₈₉	—	8	2	no	—
472	D₄×C₈₉	—	8	2	no	—
473	D₄×C₈₉	—	8	8	no	—
474	D₄×C₈₉	#120	1	2	yes	—
475	C₂×C₄×C₈₉	—	2	1	no	—
476	C₂×C₄×C₈₉	—	2	1	no	—
477	C₂×C₄×C₈₉	—	2	1	no	—
478	C₂×C₄×C₈₉	—	2	1	no	—
479	C₂×C₄×C₈₉	—	2	1	no	—
480	C₂×C₄×C₈₉	—	2	1	no	—
481	C₂×C₄×C₈₉	—	2	1	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	1	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	2	no	—
487	C₂×C₄×C₈₉	—	2	2	no	—
488	C₂×C₄×C₈₉	—	2	2	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	4	2	no	—
496	C₂×C₄×C₈₉	—	4	2	no	—
497	C₂×C₄×C₈₉	—	4	2	no	—
498	C₂×C₄×C₈₉	—	4	4	no	—
499	C₂×C₄×C₈₉	—	4	4	no	—
500	C₂×C₄×C₈₉	—	4	4	no	—
501	C₂×C₄×C₈₉	—	4	1	no	—
502	C₂×C₄×C₈₉	—	4	1	no	—
503	C₂×C₄×C₈₉	—	4	1	no	—
504	C₂×C₄×C₈₉	—	4	1	no	—
505	C₂×C₄×C₈₉	—	4	1	no	—
506	C₂×C₄×C₈₉	—	4	1	no	—
507	C₂×C₄×C₈₉	—	4	1	no	—
508	C₂×C₄×C₈₉	—	4	1	no	—
509	C₂×C₄×C₈₉	—	4	2	no	—
510	C₂×C₄×C₈₉	—	4	1	no	—
511	C₂×C₄×C₈₉	—	4	1	no	—
512	C₂×C₄×C₈₉	—	4	1	no	—
513	C₂×C₄×C₈₉	—	8	2	no	—
514	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
515	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
516	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
521	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
522	C₈×C₈₉	—	2	2	no	—
523	C₈×C₈₉	—	2	2	no	—
524	C₈×C₈₉	—	4	1	no	—
525	C₈×C₈₉	—	4	1	no	—
526	C₂²×C₈₉	—	2	1	no	—
527	C₂²×C₈₉	—	2	1	no	—
528	C₂²×C₈₉	—	2	1	no	—
529	C₂²×C₈₉	—	2	1	no	—
530	C₂²×C₈₉	—	2	2	no	—
531	C₂²×C₈₉	—	2	1	no	—
532	C₂²×C₈₉	—	2	1	no	—
533	C₂²×C₈₉	—	2	1	no	—
534	C₂²×C₈₉	—	2	1	no	—
535	C₂²×C₈₉	—	4	4	no	—
536	C₂²×C₈₉	—	4	1	no	—
537	C₂²×C₈₉	—	4	1	no	—
538	C₂²×C₈₉	—	4	1	no	—
539	C₂²×C₈₉	—	4	2	no	—
540	C₂²×C₈₉	—	4	1	no	—
541	C₂²×C₈₉	—	4	2	no	—
542	C₂²×C₈₉	—	4	1	no	—
543	C₂²×C₈₉	—	4	2	no	—
544	C₂²×C₈₉	—	4	1	no	—
545	C₂²×C₈₉	—	4	2	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	1	no	—
548	C₂²×C₈₉	—	8	1	no	—
549	C₂²×C₈₉	—	8	1	no	—
550	C₂²×C₈₉	—	8	2	no	—
551	C₂²×C₈₉	—	8	2	no	—
552	C₂²×C₈₉	—	8	2	no	—
553	C₂²×C₈₉	—	8	4	no	—
554	C₂²×C₈₉	—	8	1	no	—
555	C₂²×C₈₉	—	8	1	no	—
556	C₂²×C₈₉	—	16	4	no	—
557	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
558	C₂²×C₈₉	D₄²	1	1	yes	characteristic
559	C₂²×C₈₉	D₄²	1	1	yes	characteristic
560	C₄×C₈₉	—	2	1	no	—
561	C₄×C₈₉	—	2	1	no	—
562	C₄×C₈₉	—	2	2	no	—
563	C₄×C₈₉	—	4	2	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	2	no	—
567	C₄×C₈₉	—	4	1	no	—
568	C₄×C₈₉	—	4	2	no	—
569	C₄×C₈₉	—	4	1	no	—
570	C₄×C₈₉	—	8	1	no	—
571	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
572	C₄×C₈₉	#534	1	1	yes	characteristic
573	C₄×C₈₉	D₄²	1	1	yes	characteristic
574	C₄×C₈₉	D₄²	1	1	yes	characteristic
575	#23878	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
576	C₂×C₈₉	—	2	1	no	—
577	C₂×C₈₉	—	2	1	no	—
578	C₂×C₈₉	—	4	1	no	—
579	C₂×C₈₉	—	4	1	no	—
580	C₂×C₈₉	—	4	2	no	—
581	C₂×C₈₉	—	8	2	no	—
582	C₂×C₈₉	—	8	1	no	—
583	C₂×C₈₉	—	8	2	no	—
584	C₂×C₈₉	—	8	1	no	—
585	C₂×C₈₉	#2403	1	1	yes	characteristic
586	C₂×C₈₉	#3018	1	1	yes	characteristic
587	C₂×C₈₉	#3019	1	1	yes	characteristic
588	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3488	C₂×C₈₉	1	1	yes	characteristic, complemented
590	C₂×#455	C₂×C₈₉	1	1	yes	characteristic, complemented
591	C₂×#453	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3005	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#2431	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#2007	C₂×C₈₉	1	1	yes	characteristic, complemented
595	#2006	C₂×C₈₉	1	1	yes	characteristic, complemented
596	#2004	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#2002	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#1900	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#1883	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#1882	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#1871	C₂×C₈₉	1	1	yes	characteristic, complemented
602	#1789	C₂×C₈₉	1	1	yes	characteristic, complemented
603	C₈₉	#23878	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
605	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
606	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
607	#575	—	2	4	no	—
608	#575	—	2	4	no	—
609	C₂×#137	—	2	1	no	—
610	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
611	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
612	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic, complemented
613	C₂×AGL(1,ℤ/8)	—	2	1	no	—
614	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
615	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
616	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic, complemented
617	C₂×#135	—	2	1	no	—
618	C₂×#135	—	2	1	no	—
619	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
620	#550	—	2	1	no	—
621	#548	—	2	1	no	—
622	#546	—	2	1	no	—
623	#546	—	2	2	no	—
624	D₄²	—	2	2	no	—
625	D₄²	—	2	1	no	—
626	#537	—	2	1	no	—
627	#537	C₂²×C₈₉	1	1	yes	characteristic
628	#535	—	2	1	no	—
629	#535	C₂²×C₈₉	1	1	yes	characteristic
630	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
631	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
632	#525	—	2	1	no	—
633	#525	C₂²×C₈₉	1	1	yes	characteristic
634	C₂×#121	—	2	1	no	—
635	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
636	#520	C₂²×C₈₉	1	1	yes	characteristic
637	#455	—	2	4	no	—
638	#453	—	2	4	no	—
639	#452	—	2	1	no	—
640	#452	—	2	1	no	—
641	#449	—	2	1	no	—
642	#449	—	2	1	no	—
643	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
644	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
645	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
646	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
647	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#419	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#418	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
652	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	#407	C₂²×C₈₉	1	1	yes	characteristic, complemented
654	#392	—	2	2	no	—
655	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
656	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#386	—	2	2	no	—
658	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
659	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
660	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#339	C₂²×C₈₉	1	1	yes	characteristic, complemented
662	#339	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	H(5,𝔽₂)	—	2	2	no	—
664	H(5,𝔽₂)	—	2	2	no	—
665	H(5,𝔽₂)	—	4	1	no	—
666	H(5,𝔽₂)	—	4	1	no	—
667	C₂×#41	—	2	1	no	—
668	C₂×#41	—	2	1	no	—
669	C₂×#41	—	2	1	no	—
670	C₂×#41	—	2	1	no	—
671	C₂×#41	—	2	2	no	—
672	C₂×#41	—	2	2	no	—
673	C₂×#41	—	2	2	no	—
674	C₂×#41	—	2	2	no	—
675	C₂×#41	—	2	1	no	—
676	C₂×#41	—	2	1	no	—
677	C₂×#41	—	2	1	no	—
678	C₂×#41	—	2	1	no	—
679	C₂×#41	—	4	1	no	—
680	C₂×#41	—	4	1	no	—
681	C₂×#41	—	4	1	no	—
682	C₂×#41	—	4	1	no	—
683	C₂×#41	D₄×C₈₉	1	1	yes	characteristic, complemented
684	C₂×#41	D₄×C₈₉	1	1	yes	characteristic, complemented
685	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
686	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
687	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
688	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic, complemented
689	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
690	C₂²×D₄	—	2	1	no	—
691	C₂²×D₄	—	2	2	no	—
692	C₂²×D₄	—	2	2	no	—
693	C₂²×D₄	—	2	1	no	—
694	C₂²×D₄	—	2	1	no	—
695	C₂²×D₄	—	2	1	no	—
696	C₂²×D₄	—	2	2	no	—
697	C₂²×D₄	D₄×C₈₉	1	2	yes	—
698	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic, complemented
699	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
701	C₂³×C₄	—	2	1	no	—
702	C₂³×C₄	—	2	1	no	—
703	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
704	#137	—	2	8	no	—
705	#137	—	2	2	no	—
706	#137	—	2	2	no	—
707	#137	—	2	2	no	—
708	#137	—	2	2	no	—
709	#137	—	4	1	no	—
710	#137	D₄×C₈₉	1	4	yes	complemented
711	AGL(1,ℤ/8)	—	2	8	no	—
712	AGL(1,ℤ/8)	—	2	2	no	—
713	AGL(1,ℤ/8)	—	2	2	no	—
714	AGL(1,ℤ/8)	—	2	2	no	—
715	AGL(1,ℤ/8)	—	2	2	no	—
716	AGL(1,ℤ/8)	—	4	1	no	—
717	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	complemented
718	#135	—	2	8	no	—
719	#135	—	2	8	no	—
720	C₂×Q₁₆	—	2	1	no	—
721	C₂×Q₁₆	—	2	1	no	—
722	C₂×Q₁₆	—	2	1	no	—
723	C₂×SD₁₆	—	2	1	no	—
724	C₂×SD₁₆	—	2	1	no	—
725	C₂×SD₁₆	—	2	1	no	—
726	C₂×SD₁₆	—	2	1	no	—
727	C₂×SD₁₆	—	2	1	no	—
728	C₂×SD₁₆	—	2	1	no	—
729	C₂×D₈	—	2	1	no	—
730	C₂×D₈	—	2	1	no	—
731	C₂×D₈	—	2	1	no	—
732	C₂×M₁₆	—	2	1	no	—
733	C₂×M₁₆	—	2	2	no	—
734	C₂×M₁₆	—	2	2	no	—
735	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
739	C₂²×C₈	—	2	1	no	—
740	#127	—	2	2	no	—
741	#127	—	2	1	no	—
742	#127	—	2	2	no	—
743	#127	—	4	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	4	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic, complemented
754	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic, complemented
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	D₄×C₈₉	1	1	yes	characteristic, complemented
770	#121	D₄×C₈₉	1	1	yes	characteristic, complemented
771	#120	—	2	2	no	—
772	#120	—	2	2	no	—
773	#120	—	2	2	no	—
774	#120	—	2	1	no	—
775	#120	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	C₂³×C₈₉	1	1	yes	characteristic
785	C₂×C₄⋊C₄	—	2	1	no	—
786	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	—	2	2	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₂²⋊C₄	—	2	1	no	—
790	C₂×C₂²⋊C₄	—	2	2	no	—
791	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
792	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
794	#104	—	2	2	no	—
795	#104	—	2	2	no	—
796	#104	—	2	2	no	—
797	#104	—	2	2	no	—
798	#104	—	4	1	no	—
799	#104	—	4	1	no	—
800	#103	—	2	1	no	—
801	#103	—	2	1	no	—
802	#102	—	2	1	no	—
803	#102	—	2	1	no	—
804	#100	—	2	2	no	—
805	#100	—	2	2	no	—
806	C₂²⋊C₈	—	2	1	no	—
807	C₂²⋊C₈	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	2	no	—
810	C₂⁴	—	2	2	no	—
811	C₂⁴	—	2	1	no	—
812	C₂⁴	—	2	1	no	—
813	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
814	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
815	#41	—	2	1	no	—
816	#41	—	2	1	no	—
817	#41	—	2	4	no	—
818	#41	—	2	4	no	—
819	#41	—	2	2	no	—
820	#41	—	2	2	no	—
821	#41	—	2	1	no	—
822	#41	—	2	1	no	—
823	#41	—	2	1	no	—
824	#41	—	2	1	no	—
825	#41	—	2	1	no	—
826	#41	—	2	1	no	—
827	#41	—	2	1	no	—
828	#41	—	2	1	no	—
829	#41	—	4	2	no	—
830	#41	—	4	2	no	—
831	#41	—	4	1	no	—
832	#41	—	4	1	no	—
833	#41	—	4	2	no	—
834	#41	—	4	2	no	—
835	#41	—	4	2	no	—
836	#41	—	4	2	no	—
837	#41	—	4	2	no	—
838	#41	—	4	2	no	—
839	#41	—	4	2	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	#41	—	4	2	no	—
843	#41	—	4	2	no	—
844	#41	—	4	2	no	—
845	#41	C₂×D₄×C₈₉	1	2	yes	—
846	#41	C₂×D₄×C₈₉	1	2	yes	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
856	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
857	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
858	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	complemented
859	C₂×D₄	—	2	1	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	4	1	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	4	no	—
891	C₂×D₄	—	4	2	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	4	4	no	—
894	C₂×D₄	—	4	4	no	—
895	C₂×D₄	—	4	2	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	1	no	—
898	C₂×D₄	—	4	1	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	4	no	—
901	C₂×D₄	—	8	2	no	—
902	C₂×D₄	—	8	2	no	—
903	C₂×D₄	—	8	4	no	—
904	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
906	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
907	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	complemented
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	2	no	—
927	C₂²×C₄	—	4	1	no	—
928	C₂²×C₄	—	4	1	no	—
929	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
936	Q₁₆	—	2	4	no	—
937	Q₁₆	—	2	4	no	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	2	4	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	D₈	—	2	4	no	—
946	D₈	—	2	4	no	—
947	D₈	—	4	2	no	—
948	M₁₆	—	2	4	no	—
949	M₁₆	—	2	1	no	—
950	M₁₆	—	2	1	no	—
951	M₁₆	—	2	1	no	—
952	M₁₆	—	2	1	no	—
953	M₁₆	—	2	1	no	—
954	M₁₆	—	2	1	no	—
955	M₁₆	C₂×D₄×C₈₉	1	2	yes	complemented
956	M₁₆	C₂×D₄×C₈₉	1	2	yes	complemented
957	C₂×C₈	—	2	4	no	—
958	C₂×C₈	—	2	1	no	—
959	C₂×C₈	—	2	1	no	—
960	C₂×C₈	—	2	1	no	—
961	C₂×C₈	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	4	4	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	8	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	2	no	—
1003	C₂³	—	4	2	no	—
1004	C₂³	—	4	2	no	—
1005	C₂³	—	4	2	no	—
1006	C₂³	—	4	4	no	—
1007	C₂³	—	4	2	no	—
1008	C₂³	—	4	2	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	8	1	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	8	2	no	—
1014	C₂³	#120×C₈₉	1	1	yes	characteristic
1015	C₂³	#120×C₈₉	1	1	yes	characteristic
1016	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	4	1	no	—
1026	Q₈	—	4	1	no	—
1027	Q₈	#120×C₈₉	1	2	yes	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	1	no	—
1047	D₄	—	4	1	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	4	1	no	—
1054	D₄	—	4	1	no	—
1055	D₄	—	4	1	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	8	no	—
1062	D₄	#120×C₈₉	1	2	yes	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
1103	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1108	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1109	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	4	1	no	—
1113	C₈	—	4	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	4	4	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	8	1	no	—
1137	C₂²	—	8	1	no	—
1138	C₂²	—	8	2	no	—
1139	C₂²	—	8	2	no	—
1140	C₂²	—	8	2	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	8	1	no	—
1143	C₂²	—	8	1	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
1146	C₂²	D₄²×C₈₉	1	1	yes	characteristic
1147	C₂²	D₄²×C₈₉	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	8	1	no	—
1159	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
1160	C₄	#534×C₈₉	1	1	yes	characteristic
1161	C₄	D₄²×C₈₉	1	1	yes	characteristic
1162	C₄	D₄²×C₈₉	1	1	yes	characteristic
1163	C₂	—	2	1	no	—
1164	C₂	—	2	1	no	—
1165	C₂	—	4	1	no	—
1166	C₂	—	4	1	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₈₉×#2403	1	1	yes	characteristic
1173	C₂	C₈₉×#3018	1	1	yes	characteristic
1174	C₂	C₈₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#575×C₈₉	C₂	semidirect
2. C₈₉×#3488	C₂	semidirect
3. C₂×#455×C₈₉	C₂	semidirect
4. C₂×#453×C₈₉	C₂	semidirect
5. C₈₉×#3005	C₂	semidirect
6. C₈₉×#2431	C₂	semidirect
7. C₈₉×#2007	C₂	semidirect
8. C₈₉×#2006	C₂	semidirect
9. C₈₉×#2004	C₂	semidirect
10. C₈₉×#2002	C₂	semidirect
11. C₈₉×#1900	C₂	semidirect
12. C₈₉×#1883	C₂	semidirect
13. C₈₉×#1882	C₂	semidirect
14. C₈₉×#1871	C₂	semidirect
15. C₈₉×#1789	C₂	semidirect
18. C₂²×#41×C₈₉	C₂²	semidirect
23. C₂×#137×C₈₉	C₂²	semidirect
24. C₂×#137×C₈₉	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
31. C₂²×M₁₆×C₈₉	C₂²	semidirect
42. C₂×#127×C₈₉	C₂²	semidirect
43. C₂×#124×C₈₉	C₂²	semidirect
57. C₂×#104×C₈₉	C₂²	semidirect
58. C₂×#104×C₈₉	C₂²	semidirect
59. C₂×#104×C₈₉	C₂²	semidirect
60. C₂×#104×C₈₉	C₂²	semidirect
61. #419×C₈₉	C₂²	semidirect
62. #418×C₈₉	C₂²	semidirect
63. C₂×#100×C₈₉	C₂²	semidirect
64. C₂×#100×C₈₉	C₂²	semidirect
65. #407×C₈₉	C₂²	semidirect
67. #391×C₈₉	C₂²	semidirect
68. #390×C₈₉	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
71. #343×C₈₉	C₂²	semidirect
72. #343×C₈₉	C₂²	semidirect
73. #339×C₈₉	C₂²	semidirect
74. #339×C₈₉	C₂²	semidirect
95. C₂×#41×C₈₉	D₄	semidirect
96. C₂×#41×C₈₉	D₄	semidirect
100. C₂²×Q₈×C₈₉	D₄	semidirect
110. C₂²×D₄×C₈₉	D₄	semidirect
122. #137×C₈₉	D₄	semidirect
129. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
165. C₂²⋊Q₈×C₈₉	D₄	semidirect
166. C₂²⋊Q₈×C₈₉	D₄	semidirect
181. #121×C₈₉	D₄	semidirect
182. #121×C₈₉	D₄	semidirect
270. C₂×Q₈×C₈₉	C₂×D₄	semidirect
319. C₂×D₄×C₈₉	C₂×D₄	semidirect
367. M₁₆×C₈₉	C₂×D₄	semidirect
368. M₁₆×C₈₉	C₂×D₄	semidirect
575. #23878	C₈₉	direct (N × H)
588. C₂×#575	C₂×C₈₉	semidirect
589. #3488	C₂×C₈₉	semidirect
590. C₂×#455	C₂×C₈₉	semidirect
591. C₂×#453	C₂×C₈₉	semidirect
592. #3005	C₂×C₈₉	semidirect
593. #2431	C₂×C₈₉	semidirect
594. #2007	C₂×C₈₉	semidirect
595. #2006	C₂×C₈₉	semidirect
596. #2004	C₂×C₈₉	semidirect
597. #2002	C₂×C₈₉	semidirect
598. #1900	C₂×C₈₉	semidirect
599. #1883	C₂×C₈₉	semidirect
600. #1882	C₂×C₈₉	semidirect
601. #1871	C₂×C₈₉	semidirect
602. #1789	C₂×C₈₉	semidirect
603. C₈₉	#23878	direct (N × H)
606. C₂²×#41	C₂²×C₈₉	semidirect
611. C₂×#137	C₂²×C₈₉	semidirect
612. C₂×#137	C₂²×C₈₉	semidirect
615. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
616. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
619. C₂²×M₁₆	C₂²×C₈₉	semidirect
630. C₂×#127	C₂²×C₈₉	semidirect
631. C₂×#124	C₂²×C₈₉	semidirect
645. C₂×#104	C₂²×C₈₉	semidirect
646. C₂×#104	C₂²×C₈₉	semidirect
647. C₂×#104	C₂²×C₈₉	semidirect
648. C₂×#104	C₂²×C₈₉	semidirect
649. #419	C₂²×C₈₉	semidirect
650. #418	C₂²×C₈₉	semidirect
651. C₂×#100	C₂²×C₈₉	semidirect
652. C₂×#100	C₂²×C₈₉	semidirect
653. #407	C₂²×C₈₉	semidirect
655. #391	C₂²×C₈₉	semidirect
656. #390	C₂²×C₈₉	semidirect
658. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
659. #343	C₂²×C₈₉	semidirect
660. #343	C₂²×C₈₉	semidirect
661. #339	C₂²×C₈₉	semidirect
662. #339	C₂²×C₈₉	semidirect
683. C₂×#41	D₄×C₈₉	semidirect
684. C₂×#41	D₄×C₈₉	semidirect
688. C₂²×Q₈	D₄×C₈₉	semidirect
698. C₂²×D₄	D₄×C₈₉	semidirect
710. #137	D₄×C₈₉	semidirect
717. AGL(1,ℤ/8)	D₄×C₈₉	semidirect
753. C₂²⋊Q₈	D₄×C₈₉	semidirect
754. C₂²⋊Q₈	D₄×C₈₉	semidirect
769. #121	D₄×C₈₉	semidirect
770. #121	D₄×C₈₉	semidirect
858. C₂×Q₈	C₂×D₄×C₈₉	semidirect
907. C₂×D₄	C₂×D₄×C₈₉	semidirect
955. M₁₆	C₂×D₄×C₈₉	semidirect
956. M₁₆	C₂×D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₈₉	2
C₈₉×#3488	2
C₂×#455×C₈₉	2
C₂×#453×C₈₉	2
C₈₉×#3005	2
C₈₉×#2431	2
C₈₉×#2007	2
C₈₉×#2006	2
C₈₉×#2004	2
C₈₉×#2002	2
C₈₉×#1900	2
C₈₉×#1883	2
C₈₉×#1882	2
C₈₉×#1871	2
C₈₉×#1789	2
#23878	89

Subgroups — C89×#23878 #36401726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23878 #36401726