Subgroups — C₈₉×#35261 #36413109

Order 22784.

2706 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2847	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2624	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2476	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2471	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2443	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2424	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2324	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#121×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
17	#540×C₈₉	—	2	8	no	—
18	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
21	C₂×#121×C₈₉	C₂²	1	2	yes	—
22	C₂×#121×C₈₉	C₂²	1	2	yes	—
23	C₂×#121×C₈₉	C₂²	1	2	yes	—
24	C₂×#121×C₈₉	C₂²	1	4	yes	—
25	C₂×#121×C₈₉	C₂²	1	4	yes	—
26	C₂×#120×C₈₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
29	C₂×#117×C₈₉	—	2	8	no	—
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	C₂²	1	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
40	#399×C₈₉	C₂²	1	4	yes	complemented
41	#398×C₈₉	C₂²	1	4	yes	complemented
42	#397×C₈₉	C₂²	1	4	yes	complemented
43	#396×C₈₉	C₂²	1	4	yes	—
44	#394×C₈₉	C₂²	1	4	yes	—
45	#394×C₈₉	C₂²	1	4	yes	—
46	#394×C₈₉	C₂²	1	4	yes	complemented
47	#392×C₈₉	C₂²	1	4	yes	—
48	#390×C₈₉	C₂²	1	4	yes	—
49	#390×C₈₉	C₂²	1	2	yes	complemented
50	#390×C₈₉	C₂²	1	2	yes	complemented
51	#390×C₈₉	C₂²	1	4	yes	complemented
52	#389×C₈₉	C₂²	1	2	yes	complemented
53	#389×C₈₉	C₂²	1	2	yes	complemented
54	#388×C₈₉	C₂²	1	4	yes	—
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#388×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#387×C₈₉	C₂²	1	4	yes	complemented
59	#386×C₈₉	C₂²	1	4	yes	—
60	#386×C₈₉	C₂²	1	4	yes	—
61	#386×C₈₉	C₂²	1	4	yes	—
62	#386×C₈₉	C₂²	1	4	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#385×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	4	yes	complemented
66	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#380×C₈₉	C₂²	1	2	yes	—
69	#380×C₈₉	C₂²	1	2	yes	—
70	#380×C₈₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
73	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
79	C₂³×C₄×C₈₉	—	2	4	no	—
80	C₂³×C₄×C₈₉	—	2	4	no	—
81	C₂³×C₄×C₈₉	—	2	4	no	—
82	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
91	#127×C₈₉	—	2	4	no	—
92	#125×C₈₉	—	2	4	no	—
93	#123×C₈₉	—	2	16	no	—
94	#121×C₈₉	—	2	8	no	—
95	#121×C₈₉	—	2	8	no	—
96	#121×C₈₉	—	2	8	no	—
97	#121×C₈₉	—	2	16	no	—
98	#121×C₈₉	—	4	8	no	—
99	#120×C₈₉	—	4	8	no	—
100	C₄×D₄×C₈₉	—	2	8	no	—
101	C₄×D₄×C₈₉	—	4	8	no	—
102	#117×C₈₉	—	2	4	no	—
103	#117×C₈₉	—	2	8	no	—
104	#117×C₈₉	—	2	8	no	—
105	#117×C₈₉	—	2	4	no	—
106	#117×C₈₉	—	2	4	no	—
107	#117×C₈₉	D₄	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₈₉	—	2	4	no	—
137	C₂×C₄²×C₈₉	—	2	4	no	—
138	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
143	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
145	#95×C₈₉	C₂³	1	4	yes	—
146	#95×C₈₉	C₂³	1	4	yes	—
147	#95×C₈₉	C₂³	1	4	yes	—
148	#95×C₈₉	C₂³	1	4	yes	—
149	#95×C₈₉	C₂³	1	4	yes	—
150	#95×C₈₉	C₂³	1	4	yes	—
151	#95×C₈₉	C₂³	1	4	yes	—
152	C₂⁴×C₈₉	—	2	2	no	—
153	C₂⁴×C₈₉	—	2	2	no	—
154	C₂⁴×C₈₉	—	2	2	no	—
155	C₂⁴×C₈₉	—	2	4	no	—
156	C₂⁴×C₈₉	—	4	2	no	—
157	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
158	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂×D₄×C₈₉	—	2	8	no	—
162	C₂×D₄×C₈₉	—	2	8	no	—
163	C₂×D₄×C₈₉	—	2	8	no	—
164	C₂×D₄×C₈₉	—	2	8	no	—
165	C₂×D₄×C₈₉	—	2	8	no	—
166	C₂×D₄×C₈₉	—	2	4	no	—
167	C₂×D₄×C₈₉	—	2	8	no	—
168	C₂×D₄×C₈₉	—	2	4	no	—
169	C₂×D₄×C₈₉	—	2	4	no	—
170	C₂×D₄×C₈₉	—	4	4	no	—
171	C₂×D₄×C₈₉	—	4	4	no	—
172	C₂×D₄×C₈₉	—	4	4	no	—
173	C₂×D₄×C₈₉	—	4	4	no	—
174	C₂×D₄×C₈₉	—	4	4	no	—
175	C₂×D₄×C₈₉	—	4	4	no	—
176	C₂²×C₄×C₈₉	—	2	32	no	—
177	C₂²×C₄×C₈₉	—	2	2	no	—
178	C₂²×C₄×C₈₉	—	2	2	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	2	no	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	2	no	—
187	C₂²×C₄×C₈₉	—	2	2	no	—
188	C₂²×C₄×C₈₉	—	2	2	no	—
189	C₂²×C₄×C₈₉	—	2	2	no	—
190	C₂²×C₄×C₈₉	—	2	2	no	—
191	C₂²×C₄×C₈₉	—	2	2	no	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	4	no	—
195	C₂²×C₄×C₈₉	—	2	4	no	—
196	C₂²×C₄×C₈₉	—	2	8	no	—
197	C₂²×C₄×C₈₉	—	4	2	no	—
198	C₂²×C₄×C₈₉	—	4	2	no	—
199	C₂²×C₄×C₈₉	—	4	4	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₈₉	#41	1	4	yes	—
203	C₂²×C₄×C₈₉	#41	1	4	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₈₉	—	2	4	no	—
216	C₄⋊C₄×C₈₉	—	2	4	no	—
217	C₄⋊C₄×C₈₉	—	2	4	no	—
218	C₄⋊C₄×C₈₉	—	2	4	no	—
219	C₄⋊C₄×C₈₉	—	2	8	no	—
220	C₄⋊C₄×C₈₉	—	2	4	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	4	4	no	—
223	C₄⋊C₄×C₈₉	—	4	4	no	—
224	C₄⋊C₄×C₈₉	—	4	4	no	—
225	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
226	C₂²⋊C₄×C₈₉	—	2	4	no	—
227	C₂²⋊C₄×C₈₉	—	2	8	no	—
228	C₂²⋊C₄×C₈₉	—	2	4	no	—
229	C₂²⋊C₄×C₈₉	—	2	4	no	—
230	C₂²⋊C₄×C₈₉	—	2	8	no	—
231	C₂²⋊C₄×C₈₉	—	2	8	no	—
232	C₂²⋊C₄×C₈₉	—	2	8	no	—
233	C₂²⋊C₄×C₈₉	—	2	8	no	—
234	C₂²⋊C₄×C₈₉	—	4	4	no	—
235	C₂²⋊C₄×C₈₉	—	4	4	no	—
236	C₂²⋊C₄×C₈₉	—	4	4	no	—
237	C₂²⋊C₄×C₈₉	—	4	4	no	—
238	C₂²⋊C₄×C₈₉	—	4	4	no	—
239	C₂²⋊C₄×C₈₉	—	4	4	no	—
240	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
241	C₄²×C₈₉	—	2	4	no	—
242	C₄²×C₈₉	—	2	4	no	—
243	C₄²×C₈₉	—	2	2	no	—
244	C₄²×C₈₉	—	2	2	no	—
245	C₄²×C₈₉	—	4	4	no	—
246	C₄²×C₈₉	C₂×D₄	1	4	yes	—
247	C₄²×C₈₉	C₂×D₄	1	4	yes	—
248	C₂³×C₈₉	—	2	1	no	—
249	C₂³×C₈₉	—	2	1	no	—
250	C₂³×C₈₉	—	2	2	no	—
251	C₂³×C₈₉	—	2	8	no	—
252	C₂³×C₈₉	—	2	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	1	no	—
255	C₂³×C₈₉	—	2	1	no	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	2	no	—
259	C₂³×C₈₉	—	2	2	no	—
260	C₂³×C₈₉	—	2	4	no	—
261	C₂³×C₈₉	—	2	4	no	—
262	C₂³×C₈₉	—	2	4	no	—
263	C₂³×C₈₉	—	2	4	no	—
264	C₂³×C₈₉	—	2	4	no	—
265	C₂³×C₈₉	—	2	4	no	—
266	C₂³×C₈₉	—	2	4	no	—
267	C₂³×C₈₉	—	4	8	no	—
268	C₂³×C₈₉	—	4	8	no	—
269	C₂³×C₈₉	—	4	4	no	—
270	C₂³×C₈₉	—	4	4	no	—
271	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
272	C₂³×C₈₉	C₂×#41	1	2	yes	—
273	C₂³×C₈₉	C₂×#41	1	2	yes	—
274	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
275	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
276	D₄×C₈₉	—	4	16	no	—
277	D₄×C₈₉	—	4	8	no	—
278	D₄×C₈₉	—	8	8	no	—
279	D₄×C₈₉	—	8	8	no	—
280	D₄×C₈₉	—	8	8	no	—
281	C₂×C₄×C₈₉	—	2	8	no	—
282	C₂×C₄×C₈₉	—	2	8	no	—
283	C₂×C₄×C₈₉	—	2	8	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	8	no	—
295	C₂×C₄×C₈₉	—	2	8	no	—
296	C₂×C₄×C₈₉	—	2	8	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	4	no	—
300	C₂×C₄×C₈₉	—	2	4	no	—
301	C₂×C₄×C₈₉	—	2	4	no	—
302	C₂×C₄×C₈₉	—	2	4	no	—
303	C₂×C₄×C₈₉	—	2	4	no	—
304	C₂×C₄×C₈₉	—	2	4	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	4	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	4	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	4	no	—
312	C₂×C₄×C₈₉	—	4	8	no	—
313	C₂×C₄×C₈₉	—	4	8	no	—
314	C₂×C₄×C₈₉	—	8	8	no	—
315	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
320	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
321	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
322	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
323	C₂²×C₈₉	—	2	2	no	—
324	C₂²×C₈₉	—	2	2	no	—
325	C₂²×C₈₉	—	2	4	no	—
326	C₂²×C₈₉	—	2	4	no	—
327	C₂²×C₈₉	—	2	2	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	4	no	—
330	C₂²×C₈₉	—	2	4	no	—
331	C₂²×C₈₉	—	4	16	no	—
332	C₂²×C₈₉	—	4	1	no	—
333	C₂²×C₈₉	—	4	1	no	—
334	C₂²×C₈₉	—	4	1	no	—
335	C₂²×C₈₉	—	4	1	no	—
336	C₂²×C₈₉	—	4	2	no	—
337	C₂²×C₈₉	—	4	2	no	—
338	C₂²×C₈₉	—	4	4	no	—
339	C₂²×C₈₉	—	4	4	no	—
340	C₂²×C₈₉	—	4	4	no	—
341	C₂²×C₈₉	—	4	4	no	—
342	C₂²×C₈₉	—	4	4	no	—
343	C₂²×C₈₉	—	4	4	no	—
344	C₂²×C₈₉	—	4	4	no	—
345	C₂²×C₈₉	#540	1	4	yes	complemented
346	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
350	C₂²×C₈₉	#585	1	2	yes	—
351	C₄×C₈₉	—	2	2	no	—
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	2	2	no	—
354	C₄×C₈₉	—	2	4	no	—
355	C₄×C₈₉	—	2	4	no	—
356	C₄×C₈₉	—	4	4	no	—
357	C₄×C₈₉	—	4	2	no	—
358	C₄×C₈₉	—	4	2	no	—
359	C₄×C₈₉	—	4	4	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	#525	1	4	yes	—
362	#35261	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
363	C₂×C₈₉	—	2	4	no	—
364	C₂×C₈₉	—	4	2	no	—
365	C₂×C₈₉	—	4	2	no	—
366	C₂×C₈₉	—	8	4	no	—
367	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
368	C₂×C₈₉	C₂×#540	1	1	yes	characteristic
369	C₂×C₈₉	#3455	1	1	yes	characteristic
370	C₂×C₈₉	#3488	1	2	yes	—
371	C₂×C₈₉	#3494	1	2	yes	—
372	C₂×#540	C₂×C₈₉	1	1	yes	characteristic, complemented
373	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
374	#2856	C₂×C₈₉	1	1	yes	characteristic, complemented
375	#2851	C₂×C₈₉	1	1	yes	characteristic, complemented
376	#2847	C₂×C₈₉	1	2	yes	complemented
377	#2629	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#2624	C₂×C₈₉	1	2	yes	complemented
379	#2619	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#2476	C₂×C₈₉	1	4	yes	complemented
381	#2471	C₂×C₈₉	1	4	yes	complemented
382	#2443	C₂×C₈₉	1	4	yes	complemented
383	#2424	C₂×C₈₉	1	4	yes	complemented
384	#2324	C₂×C₈₉	1	2	yes	complemented
385	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
386	C₄×#121	C₂×C₈₉	1	2	yes	complemented
387	C₈₉	#35261	1	1	yes	characteristic, direct product factor, Sylow
388	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
389	#540	—	2	8	no	—
390	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
391	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
392	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
393	C₂×#121	C₂²×C₈₉	1	2	yes	—
394	C₂×#121	C₂²×C₈₉	1	2	yes	—
395	C₂×#121	C₂²×C₈₉	1	2	yes	—
396	C₂×#121	C₂²×C₈₉	1	4	yes	—
397	C₂×#121	C₂²×C₈₉	1	4	yes	—
398	C₂×#120	C₂²×C₈₉	1	4	yes	—
399	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
400	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
401	C₂×#117	—	2	8	no	—
402	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#117	C₂²×C₈₉	1	2	yes	—
406	C₂×#117	C₂²×C₈₉	1	2	yes	—
407	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
409	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
410	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
412	#399	C₂²×C₈₉	1	4	yes	complemented
413	#398	C₂²×C₈₉	1	4	yes	complemented
414	#397	C₂²×C₈₉	1	4	yes	complemented
415	#396	C₂²×C₈₉	1	4	yes	—
416	#394	C₂²×C₈₉	1	4	yes	—
417	#394	C₂²×C₈₉	1	4	yes	—
418	#394	C₂²×C₈₉	1	4	yes	complemented
419	#392	C₂²×C₈₉	1	4	yes	—
420	#390	C₂²×C₈₉	1	4	yes	—
421	#390	C₂²×C₈₉	1	2	yes	complemented
422	#390	C₂²×C₈₉	1	4	yes	complemented
423	#390	C₂²×C₈₉	1	2	yes	complemented
424	#389	C₂²×C₈₉	1	2	yes	complemented
425	#389	C₂²×C₈₉	1	2	yes	complemented
426	#388	C₂²×C₈₉	1	4	yes	—
427	#388	C₂²×C₈₉	1	4	yes	complemented
428	#388	C₂²×C₈₉	1	4	yes	complemented
429	#387	C₂²×C₈₉	1	4	yes	complemented
430	#387	C₂²×C₈₉	1	4	yes	complemented
431	#386	C₂²×C₈₉	1	4	yes	—
432	#386	C₂²×C₈₉	1	4	yes	—
433	#386	C₂²×C₈₉	1	4	yes	—
434	#386	C₂²×C₈₉	1	4	yes	—
435	#386	C₂²×C₈₉	1	4	yes	—
436	#385	C₂²×C₈₉	1	4	yes	—
437	#385	C₂²×C₈₉	1	4	yes	complemented
438	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
439	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
440	#380	C₂²×C₈₉	1	2	yes	—
441	#380	C₂²×C₈₉	1	2	yes	—
442	#380	C₂²×C₈₉	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
445	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
447	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
448	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
449	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
450	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	—	2	4	no	—
453	C₂³×C₄	—	2	4	no	—
454	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
458	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
459	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
463	#127	—	2	4	no	—
464	#125	—	2	4	no	—
465	#123	—	2	16	no	—
466	#121	—	2	8	no	—
467	#121	—	2	8	no	—
468	#121	—	2	8	no	—
469	#121	—	2	16	no	—
470	#121	—	4	8	no	—
471	#120	—	4	8	no	—
472	C₄×D₄	—	2	8	no	—
473	C₄×D₄	—	4	8	no	—
474	#117	—	2	4	no	—
475	#117	—	2	8	no	—
476	#117	—	2	8	no	—
477	#117	—	2	4	no	—
478	#117	—	2	4	no	—
479	#117	D₄×C₈₉	1	8	yes	complemented
480	C₂×C₄⋊C₄	—	2	8	no	—
481	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
492	C₂×C₂²⋊C₄	—	2	8	no	—
493	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
508	C₂×C₄²	—	2	4	no	—
509	C₂×C₄²	—	2	4	no	—
510	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
511	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
515	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
517	#95	C₂³×C₈₉	1	4	yes	—
518	#95	C₂³×C₈₉	1	4	yes	—
519	#95	C₂³×C₈₉	1	4	yes	—
520	#95	C₂³×C₈₉	1	4	yes	—
521	#95	C₂³×C₈₉	1	4	yes	—
522	#95	C₂³×C₈₉	1	4	yes	—
523	#95	C₂³×C₈₉	1	4	yes	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	4	2	no	—
529	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
530	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
531	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
532	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	2	8	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂²×C₄	—	2	32	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	8	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
574	C₂²×C₄	#41×C₈₉	1	4	yes	—
575	C₂²×C₄	#41×C₈₉	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	4	4	no	—
595	C₄⋊C₄	—	4	4	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	4	4	no	—
610	C₂²⋊C₄	—	4	4	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	4	4	no	—
618	C₄²	C₂×D₄×C₈₉	1	4	yes	—
619	C₄²	C₂×D₄×C₈₉	1	4	yes	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	8	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	4	8	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	4	no	—
643	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
644	C₂³	C₂×#41×C₈₉	1	2	yes	—
645	C₂³	C₂×#41×C₈₉	1	2	yes	—
646	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
647	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
648	D₄	—	4	16	no	—
649	D₄	—	4	8	no	—
650	D₄	—	8	8	no	—
651	D₄	—	8	8	no	—
652	D₄	—	8	8	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	8	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	8	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	8	8	no	—
687	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
691	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
692	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
693	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
694	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	4	16	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	4	no	—
717	C₂²	#540×C₈₉	1	4	yes	complemented
718	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
719	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
720	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
721	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
722	C₂²	#585×C₈₉	1	2	yes	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	4	4	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	4	no	—
732	C₄	—	4	4	no	—
733	C₄	#525×C₈₉	1	4	yes	—
734	C₂	—	2	4	no	—
735	C₂	—	4	2	no	—
736	C₂	—	4	2	no	—
737	C₂	—	8	4	no	—
738	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
739	C₂	C₂×#540×C₈₉	1	1	yes	characteristic
740	C₂	C₈₉×#3455	1	1	yes	characteristic
741	C₂	C₈₉×#3488	1	2	yes	—
742	C₂	C₈₉×#3494	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#540×C₈₉	C₂	semidirect
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#2856	C₂	semidirect
4. C₈₉×#2851	C₂	semidirect
5. C₈₉×#2847	C₂	semidirect
6. C₈₉×#2629	C₂	semidirect
7. C₈₉×#2624	C₂	semidirect
8. C₈₉×#2619	C₂	semidirect
9. C₈₉×#2476	C₂	semidirect
10. C₈₉×#2471	C₂	semidirect
11. C₈₉×#2443	C₂	semidirect
12. C₈₉×#2424	C₂	semidirect
13. C₈₉×#2324	C₂	semidirect
14. C₈₉×#2314	C₂	semidirect
15. C₄×#121×C₈₉	C₂	semidirect
18. C₂×#127×C₈₉	C₂²	semidirect
19. C₂×#125×C₈₉	C₂²	semidirect
20. C₂×#123×C₈₉	C₂²	semidirect
28. C₂×C₄×D₄×C₈₉	C₂²	semidirect
40. #399×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
42. #397×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
49. #390×C₈₉	C₂²	semidirect
50. #390×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #388×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
58. #387×C₈₉	C₂²	semidirect
65. #385×C₈₉	C₂²	semidirect
66. #384×C₈₉	C₂²	semidirect
67. #382×C₈₉	C₂²	semidirect
71. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
107. #117×C₈₉	D₄	semidirect
345. C₂²×C₈₉	#540	semidirect
362. #35261	C₈₉	direct (N × H)
372. C₂×#540	C₂×C₈₉	semidirect
373. C₂²×#117	C₂×C₈₉	semidirect
374. #2856	C₂×C₈₉	semidirect
375. #2851	C₂×C₈₉	semidirect
376. #2847	C₂×C₈₉	semidirect
377. #2629	C₂×C₈₉	semidirect
378. #2624	C₂×C₈₉	semidirect
379. #2619	C₂×C₈₉	semidirect
380. #2476	C₂×C₈₉	semidirect
381. #2471	C₂×C₈₉	semidirect
382. #2443	C₂×C₈₉	semidirect
383. #2424	C₂×C₈₉	semidirect
384. #2324	C₂×C₈₉	semidirect
385. #2314	C₂×C₈₉	semidirect
386. C₄×#121	C₂×C₈₉	semidirect
387. C₈₉	#35261	direct (N × H)
390. C₂×#127	C₂²×C₈₉	semidirect
391. C₂×#125	C₂²×C₈₉	semidirect
392. C₂×#123	C₂²×C₈₉	semidirect
400. C₂×C₄×D₄	C₂²×C₈₉	semidirect
412. #399	C₂²×C₈₉	semidirect
413. #398	C₂²×C₈₉	semidirect
414. #397	C₂²×C₈₉	semidirect
418. #394	C₂²×C₈₉	semidirect
421. #390	C₂²×C₈₉	semidirect
422. #390	C₂²×C₈₉	semidirect
423. #390	C₂²×C₈₉	semidirect
424. #389	C₂²×C₈₉	semidirect
425. #389	C₂²×C₈₉	semidirect
427. #388	C₂²×C₈₉	semidirect
428. #388	C₂²×C₈₉	semidirect
429. #387	C₂²×C₈₉	semidirect
430. #387	C₂²×C₈₉	semidirect
437. #385	C₂²×C₈₉	semidirect
438. #384	C₂²×C₈₉	semidirect
439. #382	C₂²×C₈₉	semidirect
443. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
479. #117	D₄×C₈₉	semidirect
717. C₂²	#540×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2856	2
C₈₉×#2851	2
C₈₉×#2847	2
C₈₉×#2629	2
C₈₉×#2624	2
C₈₉×#2619	2
C₈₉×#2476	2
C₈₉×#2471	2
C₈₉×#2443	2
C₈₉×#2424	2
C₈₉×#2324	2
C₈₉×#2314	2
C₄×#121×C₈₉	2
#35261	89

Subgroups — C89×#35261 #36413109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35261 #36413109