Subgroups — C₈₉×#60456 #36438304

Order 22784.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 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	C₂×#568×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#537×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3063	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3062	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3061	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3060	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3056	C₂	1	4	yes	maximal, complemented
10	C₈₉×#3055	C₂	1	4	yes	maximal, complemented
11	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	#575×C₈₉	—	2	8	no	—
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#135×C₈₉	C₂²	1	4	yes	complemented
23	#568×C₈₉	—	2	8	no	—
24	C₂×#131×C₈₉	C₂²	1	4	yes	complemented
25	C₂×#131×C₈₉	C₂²	1	4	yes	complemented
26	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₈₉	C₂²	1	4	yes	complemented
29	#537×C₈₉	—	2	2	no	—
30	#537×C₈₉	—	2	2	no	—
31	#537×C₈₉	C₂²	1	4	yes	—
32	#537×C₈₉	C₂²	1	4	yes	complemented
33	#537×C₈₉	C₂²	1	2	yes	complemented
34	#537×C₈₉	C₂²	1	2	yes	complemented
35	#536×C₈₉	—	2	1	no	—
36	#536×C₈₉	C₂²	1	2	yes	complemented
37	#535×C₈₉	—	2	1	no	—
38	#535×C₈₉	C₂²	1	2	yes	complemented
39	#534×C₈₉	—	2	2	no	—
40	#532×C₈₉	—	2	2	no	—
41	#525×C₈₉	—	2	2	no	—
42	#525×C₈₉	C₂²	1	4	yes	—
43	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
44	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
45	C₂×#121×C₈₉	—	2	1	no	—
46	C₂×#121×C₈₉	—	2	2	no	—
47	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
48	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
50	#470×C₈₉	C₂²	1	8	yes	complemented
51	#469×C₈₉	C₂²	1	8	yes	complemented
52	#468×C₈₉	C₂²	1	8	yes	complemented
53	#468×C₈₉	C₂²	1	8	yes	complemented
54	#467×C₈₉	C₂²	1	8	yes	complemented
55	#466×C₈₉	C₂²	1	8	yes	complemented
56	#465×C₈₉	C₂²	1	8	yes	complemented
57	#465×C₈₉	C₂²	1	8	yes	complemented
58	#428×C₈₉	C₂²	1	4	yes	complemented
59	#428×C₈₉	C₂²	1	4	yes	complemented
60	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
61	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
62	#419×C₈₉	C₂²	1	2	yes	complemented
63	#418×C₈₉	C₂²	1	2	yes	complemented
64	#417×C₈₉	C₂²	1	4	yes	—
65	#417×C₈₉	C₂²	1	4	yes	complemented
66	#417×C₈₉	C₂²	1	2	yes	complemented
67	#417×C₈₉	C₂²	1	2	yes	complemented
68	#416×C₈₉	C₂²	1	4	yes	complemented
69	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
70	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
71	C₂×#41×C₈₉	—	2	4	no	—
72	C₂×#41×C₈₉	—	2	1	no	—
73	C₂×#41×C₈₉	—	2	1	no	—
74	C₂×#41×C₈₉	—	2	1	no	—
75	C₂×#41×C₈₉	—	2	1	no	—
76	C₂×#41×C₈₉	—	2	4	no	—
77	C₂×#41×C₈₉	—	2	4	no	—
78	C₂×#41×C₈₉	—	2	4	no	—
79	C₂×#41×C₈₉	—	2	4	no	—
80	C₂×#41×C₈₉	—	2	4	no	—
81	C₂×#41×C₈₉	D₄	1	2	yes	—
82	C₂×#41×C₈₉	D₄	1	2	yes	—
83	C₂×#41×C₈₉	C₂³	1	2	yes	—
84	C₂×#41×C₈₉	C₂³	1	2	yes	—
85	C₂×#41×C₈₉	C₂³	1	2	yes	—
86	C₂×#41×C₈₉	C₂³	1	2	yes	—
87	C₂×#41×C₈₉	C₂³	1	2	yes	—
88	C₂×#41×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₈₉	—	2	1	no	—
93	C₂²×D₄×C₈₉	—	2	1	no	—
94	C₂²×D₄×C₈₉	—	2	2	no	—
95	C₂²×D₄×C₈₉	D₄	1	2	yes	—
96	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
97	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	—	2	1	no	—
100	C₂³×C₄×C₈₉	—	2	1	no	—
101	C₂³×C₄×C₈₉	—	2	1	no	—
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
104	#137×C₈₉	—	2	8	no	—
105	#137×C₈₉	—	2	8	no	—
106	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
107	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
108	#135×C₈₉	—	2	16	no	—
109	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×D₈×C₈₉	C₂³	1	4	yes	—
113	#131×C₈₉	—	2	16	no	—
114	#131×C₈₉	—	2	16	no	—
115	C₂×M₁₆×C₈₉	—	2	4	no	—
116	C₂×M₁₆×C₈₉	—	2	16	no	—
117	C₂×M₁₆×C₈₉	D₄	1	8	yes	complemented
118	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
119	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
120	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
121	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
122	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
123	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×C₈×C₈₉	C₂³	1	8	yes	—
125	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₈₉	—	2	2	no	—
127	#127×C₈₉	—	2	2	no	—
128	#124×C₈₉	—	2	2	no	—
129	#124×C₈₉	—	2	2	no	—
130	#123×C₈₉	—	2	4	no	—
131	#123×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	—	2	4	no	—
134	C₂²⋊Q₈×C₈₉	—	2	2	no	—
135	C₂²⋊Q₈×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
139	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	8	no	—
142	#121×C₈₉	—	2	4	no	—
143	#121×C₈₉	—	2	8	no	—
144	#121×C₈₉	—	2	2	no	—
145	#121×C₈₉	—	2	2	no	—
146	#121×C₈₉	—	2	4	no	—
147	#121×C₈₉	—	2	4	no	—
148	#121×C₈₉	—	2	4	no	—
149	#121×C₈₉	C₂³	1	4	yes	—
150	#121×C₈₉	C₂³	1	8	yes	—
151	#121×C₈₉	C₂³	1	4	yes	—
152	#120×C₈₉	—	2	4	no	—
153	#120×C₈₉	—	2	4	no	—
154	C₄×D₄×C₈₉	—	2	4	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	#117×C₈₉	—	2	1	no	—
157	#117×C₈₉	—	2	1	no	—
158	#117×C₈₉	C₂³	1	2	yes	—
159	#117×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
171	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
172	C₂×C₄²×C₈₉	—	2	1	no	—
173	#107×C₈₉	C₂³	1	8	yes	—
174	#106×C₈₉	C₂³	1	8	yes	—
175	#103×C₈₉	C₂³	1	8	yes	—
176	#103×C₈₉	C₂³	1	4	yes	—
177	#103×C₈₉	C₂³	1	4	yes	—
178	#102×C₈₉	C₂³	1	8	yes	—
179	#102×C₈₉	C₂³	1	4	yes	—
180	#102×C₈₉	C₂³	1	4	yes	—
181	C₂⁴×C₈₉	—	2	1	no	—
182	C₂⁴×C₈₉	—	2	1	no	—
183	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
184	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
185	#41×C₈₉	—	2	8	no	—
186	#41×C₈₉	—	2	8	no	—
187	#41×C₈₉	—	2	4	no	—
188	#41×C₈₉	—	2	4	no	—
189	#41×C₈₉	—	2	4	no	—
190	#41×C₈₉	—	2	4	no	—
191	#41×C₈₉	—	2	4	no	—
192	#41×C₈₉	—	2	4	no	—
193	#41×C₈₉	—	2	4	no	—
194	#41×C₈₉	—	2	4	no	—
195	#41×C₈₉	—	2	4	no	—
196	#41×C₈₉	—	2	4	no	—
197	#41×C₈₉	—	2	4	no	—
198	#41×C₈₉	—	2	4	no	—
199	#41×C₈₉	—	4	4	no	—
200	#41×C₈₉	—	4	4	no	—
201	#41×C₈₉	—	4	4	no	—
202	#41×C₈₉	—	4	4	no	—
203	C₂×Q₈×C₈₉	—	2	4	no	—
204	C₂×Q₈×C₈₉	—	2	1	no	—
205	C₂×Q₈×C₈₉	—	2	1	no	—
206	C₂×Q₈×C₈₉	—	2	2	no	—
207	C₂×Q₈×C₈₉	—	2	2	no	—
208	C₂×Q₈×C₈₉	—	2	2	no	—
209	C₂×Q₈×C₈₉	—	2	2	no	—
210	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
213	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
214	C₂×D₄×C₈₉	—	2	8	no	—
215	C₂×D₄×C₈₉	—	2	2	no	—
216	C₂×D₄×C₈₉	—	2	2	no	—
217	C₂×D₄×C₈₉	—	2	2	no	—
218	C₂×D₄×C₈₉	—	2	2	no	—
219	C₂×D₄×C₈₉	—	2	4	no	—
220	C₂×D₄×C₈₉	—	2	4	no	—
221	C₂×D₄×C₈₉	—	2	8	no	—
222	C₂×D₄×C₈₉	—	2	4	no	—
223	C₂×D₄×C₈₉	—	2	2	no	—
224	C₂×D₄×C₈₉	—	2	2	no	—
225	C₂×D₄×C₈₉	—	2	1	no	—
226	C₂×D₄×C₈₉	—	2	1	no	—
227	C₂×D₄×C₈₉	—	2	2	no	—
228	C₂×D₄×C₈₉	—	2	2	no	—
229	C₂×D₄×C₈₉	—	4	4	no	—
230	C₂×D₄×C₈₉	—	4	4	no	—
231	C₂×D₄×C₈₉	—	8	4	no	—
232	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₉	—	2	4	no	—
239	C₂²×C₄×C₈₉	—	2	4	no	—
240	C₂²×C₄×C₈₉	—	2	2	no	—
241	C₂²×C₄×C₈₉	—	2	1	no	—
242	C₂²×C₄×C₈₉	—	2	1	no	—
243	C₂²×C₄×C₈₉	—	2	1	no	—
244	C₂²×C₄×C₈₉	—	2	1	no	—
245	C₂²×C₄×C₈₉	—	2	2	no	—
246	C₂²×C₄×C₈₉	—	2	2	no	—
247	C₂²×C₄×C₈₉	—	2	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	2	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	4	4	no	—
252	C₂²×C₄×C₈₉	—	4	4	no	—
253	C₂²×C₄×C₈₉	—	8	2	no	—
254	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
256	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
260	C₂²×C₄×C₈₉	#41	1	4	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	4	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	1	yes	characteristic
265	Q₁₆×C₈₉	—	2	8	no	—
266	SD₁₆×C₈₉	—	2	8	no	—
267	SD₁₆×C₈₉	—	2	8	no	—
268	D₈×C₈₉	—	2	8	no	—
269	M₁₆×C₈₉	—	2	4	no	—
270	M₁₆×C₈₉	—	2	4	no	—
271	M₁₆×C₈₉	—	2	16	no	—
272	M₁₆×C₈₉	C₂×D₄	1	8	yes	—
273	M₁₆×C₈₉	C₂×D₄	1	8	yes	complemented
274	C₂×C₈×C₈₉	—	2	4	no	—
275	C₂×C₈×C₈₉	—	2	16	no	—
276	C₂×C₈×C₈₉	C₂×D₄	1	8	yes	complemented
277	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
278	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	2	no	—
282	C₄⋊C₄×C₈₉	—	2	8	no	—
283	C₄⋊C₄×C₈₉	—	2	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	4	no	—
286	C₄⋊C₄×C₈₉	—	2	4	no	—
287	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₈₉	—	2	2	no	—
291	C₂²⋊C₄×C₈₉	—	2	2	no	—
292	C₂²⋊C₄×C₈₉	—	2	8	no	—
293	C₂²⋊C₄×C₈₉	—	2	4	no	—
294	C₂²⋊C₄×C₈₉	—	2	4	no	—
295	C₂²⋊C₄×C₈₉	—	2	8	no	—
296	C₂²⋊C₄×C₈₉	—	2	4	no	—
297	C₂²⋊C₄×C₈₉	—	2	4	no	—
298	C₄²×C₈₉	—	2	2	no	—
299	C₄²×C₈₉	—	2	2	no	—
300	C₂³×C₈₉	—	2	4	no	—
301	C₂³×C₈₉	—	2	2	no	—
302	C₂³×C₈₉	—	2	2	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	1	no	—
305	C₂³×C₈₉	—	4	2	no	—
306	C₂³×C₈₉	—	4	2	no	—
307	C₂³×C₈₉	—	4	2	no	—
308	C₂³×C₈₉	—	4	2	no	—
309	C₂³×C₈₉	—	4	2	no	—
310	C₂³×C₈₉	—	4	2	no	—
311	C₂³×C₈₉	—	8	1	no	—
312	C₂³×C₈₉	—	8	1	no	—
313	C₂³×C₈₉	#121	1	4	yes	—
314	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
315	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₈₉	—	2	4	no	—
319	Q₈×C₈₉	—	2	4	no	—
320	Q₈×C₈₉	—	2	2	no	—
321	Q₈×C₈₉	—	2	2	no	—
322	Q₈×C₈₉	—	2	2	no	—
323	Q₈×C₈₉	—	2	2	no	—
324	Q₈×C₈₉	—	4	2	no	—
325	Q₈×C₈₉	—	4	2	no	—
326	D₄×C₈₉	—	2	8	no	—
327	D₄×C₈₉	—	2	8	no	—
328	D₄×C₈₉	—	2	4	no	—
329	D₄×C₈₉	—	2	4	no	—
330	D₄×C₈₉	—	2	2	no	—
331	D₄×C₈₉	—	2	2	no	—
332	D₄×C₈₉	—	2	2	no	—
333	D₄×C₈₉	—	2	2	no	—
334	D₄×C₈₉	—	4	4	no	—
335	D₄×C₈₉	—	4	4	no	—
336	D₄×C₈₉	—	4	4	no	—
337	D₄×C₈₉	—	4	4	no	—
338	D₄×C₈₉	—	4	2	no	—
339	D₄×C₈₉	—	4	2	no	—
340	D₄×C₈₉	—	8	4	no	—
341	D₄×C₈₉	—	8	4	no	—
342	D₄×C₈₉	—	8	8	no	—
343	C₂×C₄×C₈₉	—	2	4	no	—
344	C₂×C₄×C₈₉	—	2	8	no	—
345	C₂×C₄×C₈₉	—	2	4	no	—
346	C₂×C₄×C₈₉	—	2	4	no	—
347	C₂×C₄×C₈₉	—	2	2	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	4	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	4	4	no	—
353	C₂×C₄×C₈₉	—	4	2	no	—
354	C₂×C₄×C₈₉	—	4	2	no	—
355	C₂×C₄×C₈₉	—	4	4	no	—
356	C₂×C₄×C₈₉	—	4	4	no	—
357	C₂×C₄×C₈₉	—	4	4	no	—
358	C₂×C₄×C₈₉	—	4	4	no	—
359	C₂×C₄×C₈₉	—	8	1	no	—
360	C₂×C₄×C₈₉	—	8	1	no	—
361	C₂×C₄×C₈₉	—	8	2	no	—
362	C₂×C₄×C₈₉	—	8	2	no	—
363	C₂×C₄×C₈₉	#121	1	4	yes	—
364	C₂×C₄×C₈₉	#121	1	4	yes	—
365	C₂×C₄×C₈₉	#121	1	4	yes	—
366	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
374	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
376	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
377	C₈×C₈₉	—	2	4	no	—
378	C₈×C₈₉	C₂²×D₄	1	8	yes	—
379	C₂²×C₈₉	—	2	1	no	—
380	C₂²×C₈₉	—	2	1	no	—
381	C₂²×C₈₉	—	2	1	no	—
382	C₂²×C₈₉	—	2	1	no	—
383	C₂²×C₈₉	—	2	1	no	—
384	C₂²×C₈₉	—	2	1	no	—
385	C₂²×C₈₉	—	2	4	no	—
386	C₂²×C₈₉	—	2	4	no	—
387	C₂²×C₈₉	—	2	4	no	—
388	C₂²×C₈₉	—	4	4	no	—
389	C₂²×C₈₉	—	4	2	no	—
390	C₂²×C₈₉	—	4	2	no	—
391	C₂²×C₈₉	—	4	2	no	—
392	C₂²×C₈₉	—	4	2	no	—
393	C₂²×C₈₉	—	4	2	no	—
394	C₂²×C₈₉	—	4	2	no	—
395	C₂²×C₈₉	—	8	4	no	—
396	C₂²×C₈₉	—	8	4	no	—
397	C₂²×C₈₉	—	8	4	no	—
398	C₂²×C₈₉	C₂×#121	1	2	yes	—
399	C₂²×C₈₉	C₂×#121	1	2	yes	—
400	C₂²×C₈₉	C₂×#121	1	2	yes	—
401	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₈₉	—	2	4	no	—
403	C₄×C₈₉	—	4	4	no	—
404	C₄×C₈₉	—	4	2	no	—
405	C₄×C₈₉	—	4	2	no	—
406	C₄×C₈₉	—	4	2	no	—
407	C₄×C₈₉	—	4	2	no	—
408	C₄×C₈₉	C₂×#121	1	2	yes	—
409	C₄×C₈₉	C₂×#121	1	2	yes	—
410	C₄×C₈₉	C₂×#121	1	2	yes	—
411	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
413	#60456	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂×C₈₉	—	2	2	no	—
415	C₂×C₈₉	—	2	2	no	—
416	C₂×C₈₉	—	2	2	no	—
417	C₂×C₈₉	—	4	4	no	—
418	C₂×C₈₉	—	8	2	no	—
419	C₂×C₈₉	—	8	2	no	—
420	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
421	C₂×C₈₉	#3585	1	1	yes	characteristic
422	C₂×C₈₉	#3586	1	1	yes	characteristic
423	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
424	C₂×#568	C₂×C₈₉	1	1	yes	characteristic, complemented
425	#3449	C₂×C₈₉	1	1	yes	characteristic, complemented
426	C₂×#537	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#3063	C₂×C₈₉	1	4	yes	complemented
428	#3062	C₂×C₈₉	1	4	yes	complemented
429	#3061	C₂×C₈₉	1	4	yes	complemented
430	#3060	C₂×C₈₉	1	4	yes	complemented
431	#3056	C₂×C₈₉	1	4	yes	complemented
432	#3055	C₂×C₈₉	1	4	yes	complemented
433	C₂×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#2896	C₂×C₈₉	1	1	yes	characteristic, complemented
435	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
436	C₈₉	#60456	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
440	#575	—	2	8	no	—
441	C₂×#137	C₂²×C₈₉	1	2	yes	—
442	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
443	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
444	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
445	C₂×#135	C₂²×C₈₉	1	4	yes	complemented
446	#568	—	2	8	no	—
447	C₂×#131	C₂²×C₈₉	1	4	yes	complemented
448	C₂×#131	C₂²×C₈₉	1	4	yes	complemented
449	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
450	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
451	C₂²×M₁₆	C₂²×C₈₉	1	4	yes	complemented
452	#537	—	2	2	no	—
453	#537	—	2	2	no	—
454	#537	C₂²×C₈₉	1	4	yes	—
455	#537	C₂²×C₈₉	1	4	yes	complemented
456	#537	C₂²×C₈₉	1	2	yes	complemented
457	#537	C₂²×C₈₉	1	2	yes	complemented
458	#536	—	2	1	no	—
459	#536	C₂²×C₈₉	1	2	yes	complemented
460	#535	—	2	1	no	—
461	#535	C₂²×C₈₉	1	2	yes	complemented
462	#534	—	2	2	no	—
463	#532	—	2	2	no	—
464	#525	—	2	2	no	—
465	#525	C₂²×C₈₉	1	4	yes	—
466	C₂×C₂²⋊Q₈	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
468	C₂×#121	—	2	1	no	—
469	C₂×#121	—	2	2	no	—
470	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
471	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
472	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
473	#470	C₂²×C₈₉	1	8	yes	complemented
474	#469	C₂²×C₈₉	1	8	yes	complemented
475	#468	C₂²×C₈₉	1	8	yes	complemented
476	#468	C₂²×C₈₉	1	8	yes	complemented
477	#467	C₂²×C₈₉	1	8	yes	complemented
478	#466	C₂²×C₈₉	1	8	yes	complemented
479	#465	C₂²×C₈₉	1	8	yes	complemented
480	#465	C₂²×C₈₉	1	8	yes	complemented
481	#428	C₂²×C₈₉	1	4	yes	complemented
482	#428	C₂²×C₈₉	1	4	yes	complemented
483	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
484	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
485	#419	C₂²×C₈₉	1	2	yes	complemented
486	#418	C₂²×C₈₉	1	2	yes	complemented
487	#417	C₂²×C₈₉	1	4	yes	—
488	#417	C₂²×C₈₉	1	4	yes	complemented
489	#417	C₂²×C₈₉	1	2	yes	complemented
490	#417	C₂²×C₈₉	1	2	yes	complemented
491	#416	C₂²×C₈₉	1	4	yes	complemented
492	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
493	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
494	C₂×#41	—	2	4	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	2	4	no	—
501	C₂×#41	—	2	4	no	—
502	C₂×#41	—	2	4	no	—
503	C₂×#41	—	2	4	no	—
504	C₂×#41	D₄×C₈₉	1	2	yes	—
505	C₂×#41	D₄×C₈₉	1	2	yes	—
506	C₂×#41	C₂³×C₈₉	1	2	yes	—
507	C₂×#41	C₂³×C₈₉	1	2	yes	—
508	C₂×#41	C₂³×C₈₉	1	2	yes	—
509	C₂×#41	C₂³×C₈₉	1	2	yes	—
510	C₂×#41	C₂³×C₈₉	1	2	yes	—
511	C₂×#41	C₂³×C₈₉	1	2	yes	—
512	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	D₄×C₈₉	1	2	yes	—
519	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
526	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
527	#137	—	2	8	no	—
528	#137	—	2	8	no	—
529	AGL(1,ℤ/8)	—	2	8	no	—
530	AGL(1,ℤ/8)	—	2	8	no	—
531	#135	—	2	16	no	—
532	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
535	C₂×D₈	C₂³×C₈₉	1	4	yes	—
536	#131	—	2	16	no	—
537	#131	—	2	16	no	—
538	C₂×M₁₆	—	2	4	no	—
539	C₂×M₁₆	—	2	16	no	—
540	C₂×M₁₆	D₄×C₈₉	1	8	yes	complemented
541	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
542	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
543	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
544	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
545	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
546	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
547	C₂²×C₈	C₂³×C₈₉	1	8	yes	—
548	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
549	C₄⋊Q₈	—	2	2	no	—
550	#127	—	2	2	no	—
551	#124	—	2	2	no	—
552	#124	—	2	2	no	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
561	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
562	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
563	#121	—	2	4	no	—
564	#121	—	2	8	no	—
565	#121	—	2	4	no	—
566	#121	—	2	8	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	4	no	—
570	#121	—	2	4	no	—
571	#121	—	2	4	no	—
572	#121	C₂³×C₈₉	1	8	yes	—
573	#121	C₂³×C₈₉	1	4	yes	—
574	#121	C₂³×C₈₉	1	4	yes	—
575	#120	—	2	4	no	—
576	#120	—	2	4	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	#117	—	2	1	no	—
580	#117	—	2	1	no	—
581	#117	C₂³×C₈₉	1	2	yes	—
582	#117	C₂³×C₈₉	1	2	yes	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	2	no	—
594	C₂×C₂²⋊C₄	—	2	2	no	—
595	C₂×C₄²	—	2	1	no	—
596	#107	C₂³×C₈₉	1	8	yes	—
597	#106	C₂³×C₈₉	1	8	yes	—
598	#103	C₂³×C₈₉	1	8	yes	—
599	#103	C₂³×C₈₉	1	4	yes	—
600	#103	C₂³×C₈₉	1	4	yes	—
601	#102	C₂³×C₈₉	1	8	yes	—
602	#102	C₂³×C₈₉	1	4	yes	—
603	#102	C₂³×C₈₉	1	4	yes	—
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
607	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
608	#41	—	2	8	no	—
609	#41	—	2	8	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	2	4	no	—
615	#41	—	2	4	no	—
616	#41	—	2	4	no	—
617	#41	—	2	4	no	—
618	#41	—	2	4	no	—
619	#41	—	2	4	no	—
620	#41	—	2	4	no	—
621	#41	—	2	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	4	no	—
625	#41	—	4	4	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
634	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
635	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
636	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
637	C₂×D₄	—	2	8	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	8	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	8	4	no	—
655	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
656	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
657	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
659	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
660	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	8	2	no	—
677	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
678	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
679	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
683	C₂²×C₄	#41×C₈₉	1	4	yes	—
684	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
685	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
688	Q₁₆	—	2	8	no	—
689	SD₁₆	—	2	8	no	—
690	SD₁₆	—	2	8	no	—
691	D₈	—	2	8	no	—
692	M₁₆	—	2	4	no	—
693	M₁₆	—	2	4	no	—
694	M₁₆	—	2	16	no	—
695	M₁₆	C₂×D₄×C₈₉	1	8	yes	—
696	M₁₆	C₂×D₄×C₈₉	1	8	yes	complemented
697	C₂×C₈	—	2	4	no	—
698	C₂×C₈	—	2	16	no	—
699	C₂×C₈	C₂×D₄×C₈₉	1	8	yes	complemented
700	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
701	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	8	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
712	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	8	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	8	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	8	1	no	—
735	C₂³	—	8	1	no	—
736	C₂³	#121×C₈₉	1	4	yes	—
737	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
738	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
739	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
740	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
741	Q₈	—	2	4	no	—
742	Q₈	—	2	4	no	—
743	Q₈	—	2	2	no	—
744	Q₈	—	2	2	no	—
745	Q₈	—	2	2	no	—
746	Q₈	—	2	2	no	—
747	Q₈	—	4	2	no	—
748	Q₈	—	4	2	no	—
749	D₄	—	2	8	no	—
750	D₄	—	2	8	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	4	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	4	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	4	no	—
764	D₄	—	8	4	no	—
765	D₄	—	8	8	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	8	1	no	—
783	C₂×C₄	—	8	1	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	#121×C₈₉	1	4	yes	—
787	C₂×C₄	#121×C₈₉	1	4	yes	—
788	C₂×C₄	#121×C₈₉	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
796	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
797	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
798	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
799	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
800	C₈	—	2	4	no	—
801	C₈	C₂²×D₄×C₈₉	1	8	yes	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	8	4	no	—
819	C₂²	—	8	4	no	—
820	C₂²	—	8	4	no	—
821	C₂²	C₂×#121×C₈₉	1	2	yes	—
822	C₂²	C₂×#121×C₈₉	1	2	yes	—
823	C₂²	C₂×#121×C₈₉	1	2	yes	—
824	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
825	C₄	—	2	4	no	—
826	C₄	—	4	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	C₂×#121×C₈₉	1	2	yes	—
832	C₄	C₂×#121×C₈₉	1	2	yes	—
833	C₄	C₂×#121×C₈₉	1	2	yes	—
834	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
835	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
836	C₂	—	2	2	no	—
837	C₂	—	2	2	no	—
838	C₂	—	2	2	no	—
839	C₂	—	4	4	no	—
840	C₂	—	8	2	no	—
841	C₂	—	8	2	no	—
842	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
843	C₂	C₈₉×#3585	1	1	yes	characteristic
844	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×#41×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. C₂×#568×C₈₉	C₂	semidirect
3. C₈₉×#3449	C₂	semidirect
4. C₂×#537×C₈₉	C₂	semidirect
5. C₈₉×#3063	C₂	semidirect
6. C₈₉×#3062	C₂	semidirect
7. C₈₉×#3061	C₂	semidirect
8. C₈₉×#3060	C₂	semidirect
9. C₈₉×#3056	C₂	semidirect
10. C₈₉×#3055	C₂	semidirect
11. C₂×#428×C₈₉	C₂	semidirect
12. C₈₉×#2896	C₂	semidirect
13. C₂×#417×C₈₉	C₂	semidirect
19. C₂×#137×C₈₉	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
22. C₂×#135×C₈₉	C₂²	semidirect
24. C₂×#131×C₈₉	C₂²	semidirect
25. C₂×#131×C₈₉	C₂²	semidirect
28. C₂²×M₁₆×C₈₉	C₂²	semidirect
32. #537×C₈₉	C₂²	semidirect
33. #537×C₈₉	C₂²	semidirect
34. #537×C₈₉	C₂²	semidirect
36. #536×C₈₉	C₂²	semidirect
38. #535×C₈₉	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
47. C₂×#121×C₈₉	C₂²	semidirect
50. #470×C₈₉	C₂²	semidirect
51. #469×C₈₉	C₂²	semidirect
52. #468×C₈₉	C₂²	semidirect
53. #468×C₈₉	C₂²	semidirect
54. #467×C₈₉	C₂²	semidirect
55. #466×C₈₉	C₂²	semidirect
56. #465×C₈₉	C₂²	semidirect
57. #465×C₈₉	C₂²	semidirect
58. #428×C₈₉	C₂²	semidirect
59. #428×C₈₉	C₂²	semidirect
60. C₂×#107×C₈₉	C₂²	semidirect
61. C₂×#106×C₈₉	C₂²	semidirect
62. #419×C₈₉	C₂²	semidirect
63. #418×C₈₉	C₂²	semidirect
65. #417×C₈₉	C₂²	semidirect
66. #417×C₈₉	C₂²	semidirect
67. #417×C₈₉	C₂²	semidirect
68. #416×C₈₉	C₂²	semidirect
69. C₂×#103×C₈₉	C₂²	semidirect
70. C₂×#102×C₈₉	C₂²	semidirect
117. C₂×M₁₆×C₈₉	D₄	semidirect
273. M₁₆×C₈₉	C₂×D₄	semidirect
276. C₂×C₈×C₈₉	C₂×D₄	semidirect
413. #60456	C₈₉	direct (N × H)
423. C₂×#575	C₂×C₈₉	semidirect
424. C₂×#568	C₂×C₈₉	semidirect
425. #3449	C₂×C₈₉	semidirect
426. C₂×#537	C₂×C₈₉	semidirect
427. #3063	C₂×C₈₉	semidirect
428. #3062	C₂×C₈₉	semidirect
429. #3061	C₂×C₈₉	semidirect
430. #3060	C₂×C₈₉	semidirect
431. #3056	C₂×C₈₉	semidirect
432. #3055	C₂×C₈₉	semidirect
433. C₂×#428	C₂×C₈₉	semidirect
434. #2896	C₂×C₈₉	semidirect
435. C₂×#417	C₂×C₈₉	semidirect
436. C₈₉	#60456	direct (N × H)
442. C₂×#137	C₂²×C₈₉	semidirect
444. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
445. C₂×#135	C₂²×C₈₉	semidirect
447. C₂×#131	C₂²×C₈₉	semidirect
448. C₂×#131	C₂²×C₈₉	semidirect
451. C₂²×M₁₆	C₂²×C₈₉	semidirect
455. #537	C₂²×C₈₉	semidirect
456. #537	C₂²×C₈₉	semidirect
457. #537	C₂²×C₈₉	semidirect
459. #536	C₂²×C₈₉	semidirect
461. #535	C₂²×C₈₉	semidirect
467. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
470. C₂×#121	C₂²×C₈₉	semidirect
473. #470	C₂²×C₈₉	semidirect
474. #469	C₂²×C₈₉	semidirect
475. #468	C₂²×C₈₉	semidirect
476. #468	C₂²×C₈₉	semidirect
477. #467	C₂²×C₈₉	semidirect
478. #466	C₂²×C₈₉	semidirect
479. #465	C₂²×C₈₉	semidirect
480. #465	C₂²×C₈₉	semidirect
481. #428	C₂²×C₈₉	semidirect
482. #428	C₂²×C₈₉	semidirect
483. C₂×#107	C₂²×C₈₉	semidirect
484. C₂×#106	C₂²×C₈₉	semidirect
485. #419	C₂²×C₈₉	semidirect
486. #418	C₂²×C₈₉	semidirect
488. #417	C₂²×C₈₉	semidirect
489. #417	C₂²×C₈₉	semidirect
490. #417	C₂²×C₈₉	semidirect
491. #416	C₂²×C₈₉	semidirect
492. C₂×#103	C₂²×C₈₉	semidirect
493. C₂×#102	C₂²×C₈₉	semidirect
540. C₂×M₁₆	D₄×C₈₉	semidirect
696. M₁₆	C₂×D₄×C₈₉	semidirect
699. C₂×C₈	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
C₂×#568×C₈₉	2
C₈₉×#3449	2
C₂×#537×C₈₉	2
C₈₉×#3063	2
C₈₉×#3062	2
C₈₉×#3061	2
C₈₉×#3060	2
C₈₉×#3056	2
C₈₉×#3055	2
C₂×#428×C₈₉	2
C₈₉×#2896	2
C₂×#417×C₈₉	2
#60456	89

Subgroups — C89×#60456 #36438304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60456 #36438304