Subgroups — C₈₉×#25138 #36402986

Order 22784.

1118 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#436×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#419×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2414	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2409	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
27	#468×C₈₉	—	2	4	no	—
28	#448×C₈₉	—	2	4	no	—
29	#436×C₈₉	—	2	4	no	—
30	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
33	#419×C₈₉	—	2	4	no	—
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#395×C₈₉	—	2	1	no	—
46	#394×C₈₉	—	2	1	no	—
47	#393×C₈₉	—	2	1	no	—
48	#392×C₈₉	—	2	1	no	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	—	2	1	no	—
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#388×C₈₉	—	2	1	no	—
55	#386×C₈₉	—	2	1	no	—
56	#385×C₈₉	—	2	1	no	—
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#340×C₈₉	C₂²	1	1	yes	characteristic
62	#340×C₈₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₈₉	—	2	1	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	2	no	—
66	C₂²×Q₈×C₈₉	—	2	2	no	—
67	C₂²×Q₈×C₈₉	—	2	2	no	—
68	C₂²×Q₈×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	—	4	1	no	—
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₈₉	—	2	1	no	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	—	2	2	no	—
80	C₂×SD₁₆×C₈₉	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	—	2	2	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	4	1	no	—
84	C₂×SD₁₆×C₈₉	—	4	1	no	—
85	C₂×M₁₆×C₈₉	—	2	2	no	—
86	C₂×M₁₆×C₈₉	—	2	2	no	—
87	C₂×M₁₆×C₈₉	—	2	2	no	—
88	C₂×M₁₆×C₈₉	—	2	2	no	—
89	C₂×M₁₆×C₈₉	—	4	1	no	—
90	C₂×M₁₆×C₈₉	—	4	1	no	—
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²⋊Q₈×C₈₉	—	2	2	no	—
96	C₂²⋊Q₈×C₈₉	—	2	2	no	—
97	C₂²⋊Q₈×C₈₉	—	4	1	no	—
98	C₂²⋊Q₈×C₈₉	—	4	1	no	—
99	#121×C₈₉	—	2	2	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	4	1	no	—
103	C₄×D₄×C₈₉	—	2	2	no	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	#117×C₈₉	—	2	2	no	—
106	#117×C₈₉	—	4	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	#107×C₈₉	—	2	2	no	—
130	#106×C₈₉	—	4	1	no	—
131	C₄⋊C₈×C₈₉	—	2	2	no	—
132	#103×C₈₉	—	2	2	no	—
133	#103×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	D₄	1	4	yes	complemented
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	4	1	no	—
140	C₂²⋊C₈×C₈₉	—	2	2	no	—
141	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
142	C₄×C₈×C₈₉	—	2	2	no	—
143	#95×C₈₉	—	2	1	no	—
144	#95×C₈₉	—	2	1	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	—	2	1	no	—
149	#95×C₈₉	—	2	1	no	—
150	C₂⁴×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	8	no	—
156	C₂×Q₈×C₈₉	—	2	1	no	—
157	C₂×Q₈×C₈₉	—	2	1	no	—
158	C₂×Q₈×C₈₉	—	2	1	no	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	4	2	no	—
165	C₂×Q₈×C₈₉	—	4	2	no	—
166	C₂×Q₈×C₈₉	—	4	4	no	—
167	C₂×Q₈×C₈₉	—	4	4	no	—
168	C₂×Q₈×C₈₉	—	4	4	no	—
169	C₂×Q₈×C₈₉	—	4	2	no	—
170	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
171	C₂×Q₈×C₈₉	#41	1	2	yes	—
172	C₂×D₄×C₈₉	—	2	2	no	—
173	C₂×D₄×C₈₉	—	2	2	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	—	2	1	no	—
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	4	1	no	—
181	C₂×D₄×C₈₉	—	4	2	no	—
182	C₂×D₄×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	8	1	no	—
185	C₂×D₄×C₈₉	—	8	1	no	—
186	C₂×D₄×C₈₉	—	8	1	no	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	4	2	no	—
205	C₂²×C₄×C₈₉	—	4	2	no	—
206	C₂²×C₄×C₈₉	—	4	2	no	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	#41	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	SD₁₆×C₈₉	—	4	4	no	—
215	SD₁₆×C₈₉	—	4	4	no	—
216	M₁₆×C₈₉	—	4	4	no	—
217	M₁₆×C₈₉	—	4	4	no	—
218	C₂×C₈×C₈₉	—	2	1	no	—
219	C₂×C₈×C₈₉	—	2	1	no	—
220	C₂×C₈×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	1	no	—
227	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
228	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
229	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₈₉	—	2	2	no	—
231	C₄⋊C₄×C₈₉	—	2	1	no	—
232	C₄⋊C₄×C₈₉	—	2	1	no	—
233	C₄⋊C₄×C₈₉	—	2	1	no	—
234	C₄⋊C₄×C₈₉	—	2	1	no	—
235	C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₄⋊C₄×C₈₉	—	2	1	no	—
237	C₄⋊C₄×C₈₉	—	2	1	no	—
238	C₄⋊C₄×C₈₉	—	2	1	no	—
239	C₄⋊C₄×C₈₉	—	2	1	no	—
240	C₄⋊C₄×C₈₉	—	4	2	no	—
241	C₄⋊C₄×C₈₉	—	4	2	no	—
242	C₄⋊C₄×C₈₉	—	8	1	no	—
243	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
244	C₂²⋊C₄×C₈₉	—	2	2	no	—
245	C₂²⋊C₄×C₈₉	—	2	2	no	—
246	C₂²⋊C₄×C₈₉	—	4	2	no	—
247	C₂²⋊C₄×C₈₉	—	4	2	no	—
248	C₂²⋊C₄×C₈₉	—	4	2	no	—
249	C₂²⋊C₄×C₈₉	—	4	2	no	—
250	C₂²⋊C₄×C₈₉	—	4	2	no	—
251	C₂²⋊C₄×C₈₉	—	4	2	no	—
252	C₂²⋊C₄×C₈₉	—	4	2	no	—
253	C₂²⋊C₄×C₈₉	—	8	1	no	—
254	C₂²⋊C₄×C₈₉	—	8	1	no	—
255	C₄²×C₈₉	—	2	1	no	—
256	C₄²×C₈₉	—	2	1	no	—
257	C₄²×C₈₉	—	4	2	no	—
258	C₂³×C₈₉	—	2	1	no	—
259	C₂³×C₈₉	—	2	1	no	—
260	C₂³×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	2	1	no	—
267	C₂³×C₈₉	—	2	1	no	—
268	C₂³×C₈₉	—	2	1	no	—
269	C₂³×C₈₉	—	2	1	no	—
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	4	1	no	—
272	C₂³×C₈₉	—	4	1	no	—
273	C₂³×C₈₉	—	4	1	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	—	4	1	no	—
276	C₂³×C₈₉	—	4	1	no	—
277	C₂³×C₈₉	—	4	1	no	—
278	C₂³×C₈₉	#121	1	2	yes	—
279	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₈₉	—	2	2	no	—
281	Q₈×C₈₉	—	2	2	no	—
282	Q₈×C₈₉	—	2	2	no	—
283	Q₈×C₈₉	—	2	2	no	—
284	Q₈×C₈₉	—	4	8	no	—
285	Q₈×C₈₉	—	4	1	no	—
286	Q₈×C₈₉	—	4	1	no	—
287	Q₈×C₈₉	—	4	1	no	—
288	Q₈×C₈₉	—	4	1	no	—
289	D₄×C₈₉	—	4	4	no	—
290	D₄×C₈₉	—	4	1	no	—
291	D₄×C₈₉	—	4	1	no	—
292	D₄×C₈₉	—	4	1	no	—
293	D₄×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	8	4	no	—
295	D₄×C₈₉	—	8	4	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	4	8	no	—
314	C₂×C₄×C₈₉	—	4	1	no	—
315	C₂×C₄×C₈₉	—	4	1	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	1	no	—
323	C₂×C₄×C₈₉	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	4	1	no	—
330	C₂×C₄×C₈₉	—	4	1	no	—
331	C₂×C₄×C₈₉	—	4	1	no	—
332	C₂×C₄×C₈₉	—	4	1	no	—
333	C₂×C₄×C₈₉	—	4	1	no	—
334	C₂×C₄×C₈₉	—	4	1	no	—
335	C₂×C₄×C₈₉	—	4	1	no	—
336	C₂×C₄×C₈₉	#121	1	2	yes	—
337	C₂×C₄×C₈₉	#137	1	2	yes	—
338	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₈₉	—	2	2	no	—
345	C₈×C₈₉	—	2	2	no	—
346	C₈×C₈₉	—	2	2	no	—
347	C₈×C₈₉	—	4	1	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	2	2	no	—
351	C₂²×C₈₉	—	4	1	no	—
352	C₂²×C₈₉	—	4	1	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	4	1	no	—
355	C₂²×C₈₉	—	4	1	no	—
356	C₂²×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	4	1	no	—
359	C₂²×C₈₉	—	4	1	no	—
360	C₂²×C₈₉	—	4	1	no	—
361	C₂²×C₈₉	—	4	1	no	—
362	C₂²×C₈₉	—	8	1	no	—
363	C₂²×C₈₉	—	8	1	no	—
364	C₂²×C₈₉	—	8	1	no	—
365	C₂²×C₈₉	—	8	1	no	—
366	C₂²×C₈₉	—	8	1	no	—
367	C₂²×C₈₉	—	8	1	no	—
368	C₂²×C₈₉	—	8	1	no	—
369	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
370	C₂²×C₈₉	D₄²	1	1	yes	characteristic
371	C₂²×C₈₉	#546	1	1	yes	characteristic
372	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
373	C₂²×C₈₉	#575	1	1	yes	characteristic
374	C₂²×C₈₉	#577	1	1	yes	characteristic
375	C₂²×C₈₉	#577	1	1	yes	characteristic
376	C₄×C₈₉	—	2	2	no	—
377	C₄×C₈₉	—	2	2	no	—
378	C₄×C₈₉	—	4	1	no	—
379	C₄×C₈₉	—	4	2	no	—
380	C₄×C₈₉	—	4	2	no	—
381	C₄×C₈₉	—	4	2	no	—
382	C₄×C₈₉	—	4	1	no	—
383	C₄×C₈₉	—	8	1	no	—
384	C₄×C₈₉	—	8	1	no	—
385	C₄×C₈₉	—	8	1	no	—
386	C₄×C₈₉	—	8	1	no	—
387	C₄×C₈₉	#525	1	1	yes	characteristic
388	C₄×C₈₉	#538	1	1	yes	characteristic
389	C₄×C₈₉	D₄²	1	1	yes	characteristic
390	C₄×C₈₉	#546	1	1	yes	characteristic
391	#25138	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂×C₈₉	—	4	2	no	—
393	C₂×C₈₉	—	8	1	no	—
394	C₂×C₈₉	—	16	1	no	—
395	C₂×C₈₉	#2424	1	1	yes	characteristic
396	C₂×C₈₉	#3056	1	1	yes	characteristic
397	C₂×C₈₉	#3057	1	1	yes	characteristic
398	C₂×C₈₉	#3275	1	1	yes	characteristic
399	C₂×C₈₉	#3278	1	1	yes	characteristic
400	C₂×C₈₉	#3326	1	1	yes	characteristic
401	C₂×C₈₉	#3329	1	1	yes	characteristic
402	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
403	C₂×#448	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₂×#436	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₂×#419	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2414	C₂×C₈₉	1	1	yes	characteristic
407	#2409	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#2068	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#1933	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
415	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
416	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
417	C₈₉	#25138	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
421	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
422	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
429	#468	—	2	4	no	—
430	#448	—	2	4	no	—
431	#436	—	2	4	no	—
432	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
435	#419	—	2	4	no	—
436	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
447	#395	—	2	1	no	—
448	#394	—	2	1	no	—
449	#393	—	2	1	no	—
450	#392	—	2	1	no	—
451	#391	C₂²×C₈₉	1	1	yes	characteristic
452	#391	C₂²×C₈₉	1	1	yes	characteristic
453	#390	—	2	1	no	—
454	#390	C₂²×C₈₉	1	1	yes	characteristic
455	#389	C₂²×C₈₉	1	1	yes	characteristic
456	#388	—	2	1	no	—
457	#386	—	2	1	no	—
458	#385	—	2	1	no	—
459	#380	C₂²×C₈₉	1	1	yes	characteristic
460	#380	C₂²×C₈₉	1	1	yes	characteristic
461	#340	C₂²×C₈₉	1	1	yes	characteristic
462	#340	C₂²×C₈₉	1	1	yes	characteristic
463	#340	C₂²×C₈₉	1	1	yes	characteristic
464	#340	C₂²×C₈₉	1	1	yes	characteristic
465	C₂²×Q₈	—	2	1	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	—	2	2	no	—
470	C₂²×Q₈	—	4	1	no	—
471	C₂²×Q₈	—	4	1	no	—
472	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×SD₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	4	1	no	—
486	C₂×SD₁₆	—	4	1	no	—
487	C₂×M₁₆	—	2	2	no	—
488	C₂×M₁₆	—	2	2	no	—
489	C₂×M₁₆	—	2	2	no	—
490	C₂×M₁₆	—	2	2	no	—
491	C₂×M₁₆	—	4	1	no	—
492	C₂×M₁₆	—	4	1	no	—
493	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	4	1	no	—
500	C₂²⋊Q₈	—	4	1	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	4	1	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	#117	—	2	2	no	—
508	#117	—	4	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
531	#107	—	2	2	no	—
532	#106	—	4	1	no	—
533	C₄⋊C₈	—	2	2	no	—
534	#103	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#103	—	2	2	no	—
538	#103	—	2	2	no	—
539	#103	D₄×C₈₉	1	4	yes	complemented
540	#102	—	2	2	no	—
541	#102	—	4	1	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
544	C₄×C₈	—	2	2	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	—	2	1	no	—
550	#95	—	2	1	no	—
551	#95	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
554	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	8	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
573	C₂×Q₈	#41×C₈₉	1	2	yes	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	1	no	—
588	C₂×D₄	—	8	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
613	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	#41×C₈₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
616	SD₁₆	—	4	4	no	—
617	SD₁₆	—	4	4	no	—
618	M₁₆	—	4	4	no	—
619	M₁₆	—	4	4	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
630	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
631	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	8	1	no	—
645	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	8	1	no	—
656	C₂²⋊C₄	—	8	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	4	2	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	#121×C₈₉	1	2	yes	—
681	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	4	no	—
697	D₄	—	8	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	4	8	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	#121×C₈₉	1	2	yes	—
739	C₂×C₄	#137×C₈₉	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
744	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
745	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	4	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
772	C₂²	D₄²×C₈₉	1	1	yes	characteristic
773	C₂²	#546×C₈₉	1	1	yes	characteristic
774	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
775	C₂²	#575×C₈₉	1	1	yes	characteristic
776	C₂²	#577×C₈₉	1	1	yes	characteristic
777	C₂²	#577×C₈₉	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	—	8	1	no	—
788	C₄	—	8	1	no	—
789	C₄	#525×C₈₉	1	1	yes	characteristic
790	C₄	#538×C₈₉	1	1	yes	characteristic
791	C₄	D₄²×C₈₉	1	1	yes	characteristic
792	C₄	#546×C₈₉	1	1	yes	characteristic
793	C₂	—	4	2	no	—
794	C₂	—	8	1	no	—
795	C₂	—	16	1	no	—
796	C₂	C₈₉×#2424	1	1	yes	characteristic
797	C₂	C₈₉×#3056	1	1	yes	characteristic
798	C₂	C₈₉×#3057	1	1	yes	characteristic
799	C₂	C₈₉×#3275	1	1	yes	characteristic
800	C₂	C₈₉×#3278	1	1	yes	characteristic
801	C₂	C₈₉×#3326	1	1	yes	characteristic
802	C₂	C₈₉×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#2414	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#468×C₈₉	C₂	semidirect
2. C₂×#448×C₈₉	C₂	semidirect
3. C₂×#436×C₈₉	C₂	semidirect
4. C₂×#419×C₈₉	C₂	semidirect
6. C₈₉×#2409	C₂	semidirect
7. C₈₉×#2068	C₂	semidirect
8. C₈₉×#2055	C₂	semidirect
9. C₈₉×#2035	C₂	semidirect
10. C₈₉×#2000	C₂	semidirect
11. C₈₉×#1968	C₂	semidirect
12. C₈₉×#1933	C₂	semidirect
13. C₈₉×#1895	C₂	semidirect
14. C₈₉×#1894	C₂	semidirect
15. C₈₉×#1854	C₂	semidirect
137. #103×C₈₉	D₄	semidirect
141. C₂²⋊C₈×C₈₉	D₄	semidirect
391. #25138	C₈₉	direct (N × H)
402. C₂×#468	C₂×C₈₉	semidirect
403. C₂×#448	C₂×C₈₉	semidirect
404. C₂×#436	C₂×C₈₉	semidirect
405. C₂×#419	C₂×C₈₉	semidirect
407. #2409	C₂×C₈₉	semidirect
408. #2068	C₂×C₈₉	semidirect
409. #2055	C₂×C₈₉	semidirect
410. #2035	C₂×C₈₉	semidirect
411. #2000	C₂×C₈₉	semidirect
412. #1968	C₂×C₈₉	semidirect
413. #1933	C₂×C₈₉	semidirect
414. #1895	C₂×C₈₉	semidirect
415. #1894	C₂×C₈₉	semidirect
416. #1854	C₂×C₈₉	semidirect
417. C₈₉	#25138	direct (N × H)
539. #103	D₄×C₈₉	semidirect
543. C₂²⋊C₈	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×#468×C₈₉	2
C₂×#448×C₈₉	2
C₂×#436×C₈₉	2
C₂×#419×C₈₉	2
C₈₉×#2414	2
C₈₉×#2409	2
C₈₉×#2068	2
C₈₉×#2055	2
C₈₉×#2035	2
C₈₉×#2000	2
C₈₉×#1968	2
C₈₉×#1933	2
C₈₉×#1895	2
C₈₉×#1894	2
C₈₉×#1854	2
#25138	89

Subgroups — C89×#25138 #36402986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25138 #36402986