Subgroups — C₈₉×#35394 #36413242

Order 22784.

2742 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2561	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2557	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2553	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2539	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2464	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2422	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2412	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2410	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2322	C₂	1	2	yes	maximal, complemented
14	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#538×C₈₉	—	2	8	no	—
19	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
20	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₈₉	—	2	8	no	—
22	C₂×#123×C₈₉	C₂²	1	4	yes	—
23	C₂×#123×C₈₉	C₂²	1	4	yes	—
24	C₂×#123×C₈₉	C₂²	1	2	yes	—
25	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₈₉	C₂²	1	4	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
30	C₂×#120×C₈₉	C₂²	1	2	yes	—
31	C₂×#120×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#399×C₈₉	C₂²	1	2	yes	complemented
41	#398×C₈₉	C₂²	1	4	yes	complemented
42	#397×C₈₉	C₂²	1	4	yes	complemented
43	#397×C₈₉	C₂²	1	4	yes	complemented
44	#397×C₈₉	C₂²	1	2	yes	complemented
45	#394×C₈₉	C₂²	1	4	yes	—
46	#394×C₈₉	C₂²	1	4	yes	complemented
47	#393×C₈₉	C₂²	1	2	yes	complemented
48	#392×C₈₉	C₂²	1	4	yes	—
49	#392×C₈₉	C₂²	1	2	yes	complemented
50	#391×C₈₉	C₂²	1	2	yes	complemented
51	#390×C₈₉	C₂²	1	4	yes	complemented
52	#390×C₈₉	C₂²	1	2	yes	complemented
53	#389×C₈₉	C₂²	1	4	yes	complemented
54	#388×C₈₉	C₂²	1	4	yes	complemented
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#387×C₈₉	C₂²	1	4	yes	complemented
57	#386×C₈₉	C₂²	1	4	yes	—
58	#386×C₈₉	C₂²	1	2	yes	—
59	#386×C₈₉	C₂²	1	2	yes	—
60	#386×C₈₉	C₂²	1	4	yes	complemented
61	#386×C₈₉	C₂²	1	4	yes	complemented
62	#385×C₈₉	C₂²	1	2	yes	—
63	#385×C₈₉	C₂²	1	2	yes	—
64	#385×C₈₉	C₂²	1	4	yes	complemented
65	#385×C₈₉	C₂²	1	4	yes	complemented
66	#384×C₈₉	C₂²	1	2	yes	complemented
67	#382×C₈₉	C₂²	1	2	yes	complemented
68	#381×C₈₉	C₂²	1	2	yes	—
69	#380×C₈₉	C₂²	1	4	yes	complemented
70	#379×C₈₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	—	2	4	no	—
81	C₂²×D₄×C₈₉	—	4	4	no	—
82	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₈₉	—	2	4	no	—
89	C₂³×C₄×C₈₉	—	4	4	no	—
90	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	#126×C₈₉	—	2	8	no	—
99	#124×C₈₉	—	2	8	no	—
100	#123×C₈₉	—	2	16	no	—
101	#123×C₈₉	—	2	16	no	—
102	#123×C₈₉	—	2	8	no	—
103	#123×C₈₉	—	2	8	no	—
104	C₂²⋊Q₈×C₈₉	—	2	4	no	—
105	#121×C₈₉	—	2	4	no	—
106	#121×C₈₉	—	2	8	no	—
107	#121×C₈₉	—	4	8	no	—
108	#120×C₈₉	—	2	8	no	—
109	#120×C₈₉	—	2	8	no	—
110	C₄×D₄×C₈₉	—	2	8	no	—
111	C₄×D₄×C₈₉	—	4	8	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
127	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	complemented
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	2	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	#95×C₈₉	C₂³	1	4	yes	—
152	#95×C₈₉	C₂³	1	2	yes	—
153	#95×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	#95×C₈₉	C₂³	1	4	yes	—
156	#95×C₈₉	C₂³	1	4	yes	—
157	#95×C₈₉	C₂³	1	4	yes	—
158	#95×C₈₉	C₂³	1	4	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	C₂⁴×C₈₉	—	2	2	no	—
161	C₂⁴×C₈₉	—	2	4	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	2	4	no	—
164	C₂⁴×C₈₉	—	4	2	no	—
165	C₂⁴×C₈₉	—	4	2	no	—
166	C₂⁴×C₈₉	—	4	2	no	—
167	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
168	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
169	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
171	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂×Q₈×C₈₉	—	2	2	no	—
173	C₂×Q₈×C₈₉	—	4	2	no	—
174	C₂×D₄×C₈₉	—	2	4	no	—
175	C₂×D₄×C₈₉	—	2	8	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	8	no	—
179	C₂×D₄×C₈₉	—	2	8	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	2	no	—
183	C₂×D₄×C₈₉	—	2	8	no	—
184	C₂×D₄×C₈₉	—	4	4	no	—
185	C₂×D₄×C₈₉	—	4	4	no	—
186	C₂×D₄×C₈₉	—	4	4	no	—
187	C₂×D₄×C₈₉	—	4	2	no	—
188	C₂×D₄×C₈₉	—	4	4	no	—
189	C₂×D₄×C₈₉	—	4	16	no	—
190	C₂²×C₄×C₈₉	—	2	2	no	—
191	C₂²×C₄×C₈₉	—	2	2	no	—
192	C₂²×C₄×C₈₉	—	2	2	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	8	no	—
195	C₂²×C₄×C₈₉	—	2	8	no	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	8	no	—
198	C₂²×C₄×C₈₉	—	4	2	no	—
199	C₂²×C₄×C₈₉	—	4	4	no	—
200	C₂²×C₄×C₈₉	—	4	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	2	no	—
203	C₂²×C₄×C₈₉	—	4	4	no	—
204	C₂²×C₄×C₈₉	—	4	4	no	—
205	C₂²×C₄×C₈₉	—	4	4	no	—
206	C₂²×C₄×C₈₉	—	4	16	no	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
220	C₄⋊C₄×C₈₉	—	2	8	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	4	no	—
224	C₄⋊C₄×C₈₉	—	2	4	no	—
225	C₄⋊C₄×C₈₉	—	2	2	no	—
226	C₄⋊C₄×C₈₉	—	2	2	no	—
227	C₄⋊C₄×C₈₉	—	2	8	no	—
228	C₄⋊C₄×C₈₉	—	4	4	no	—
229	C₄⋊C₄×C₈₉	—	4	4	no	—
230	C₂²⋊C₄×C₈₉	—	2	8	no	—
231	C₂²⋊C₄×C₈₉	—	2	4	no	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	8	no	—
236	C₂²⋊C₄×C₈₉	—	2	4	no	—
237	C₂²⋊C₄×C₈₉	—	2	4	no	—
238	C₂²⋊C₄×C₈₉	—	2	4	no	—
239	C₂²⋊C₄×C₈₉	—	2	4	no	—
240	C₂²⋊C₄×C₈₉	—	2	8	no	—
241	C₂²⋊C₄×C₈₉	—	2	8	no	—
242	C₂²⋊C₄×C₈₉	—	2	8	no	—
243	C₂²⋊C₄×C₈₉	—	4	4	no	—
244	C₂²⋊C₄×C₈₉	—	4	4	no	—
245	C₂²⋊C₄×C₈₉	—	4	4	no	—
246	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
247	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
248	C₂²⋊C₄×C₈₉	#41	1	8	yes	—
249	C₄²×C₈₉	—	2	4	no	—
250	C₄²×C₈₉	—	4	2	no	—
251	C₄²×C₈₉	—	4	2	no	—
252	C₄²×C₈₉	—	4	4	no	—
253	C₂³×C₈₉	—	2	2	no	—
254	C₂³×C₈₉	—	2	2	no	—
255	C₂³×C₈₉	—	2	8	no	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	4	no	—
259	C₂³×C₈₉	—	2	2	no	—
260	C₂³×C₈₉	—	2	2	no	—
261	C₂³×C₈₉	—	2	4	no	—
262	C₂³×C₈₉	—	2	4	no	—
263	C₂³×C₈₉	—	2	4	no	—
264	C₂³×C₈₉	—	2	8	no	—
265	C₂³×C₈₉	—	2	2	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	4	no	—
269	C₂³×C₈₉	—	2	4	no	—
270	C₂³×C₈₉	—	4	4	no	—
271	C₂³×C₈₉	—	4	4	no	—
272	C₂³×C₈₉	—	4	16	no	—
273	C₂³×C₈₉	—	4	4	no	—
274	C₂³×C₈₉	—	4	4	no	—
275	C₂³×C₈₉	—	8	8	no	—
276	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
277	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
278	C₂³×C₈₉	C₂×#41	1	4	yes	—
279	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
280	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₈₉	—	8	2	no	—
282	D₄×C₈₉	—	4	16	no	—
283	D₄×C₈₉	—	4	16	no	—
284	D₄×C₈₉	—	4	8	no	—
285	D₄×C₈₉	—	8	2	no	—
286	D₄×C₈₉	—	8	4	no	—
287	D₄×C₈₉	—	8	4	no	—
288	C₂×C₄×C₈₉	—	2	4	no	—
289	C₂×C₄×C₈₉	—	2	4	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	4	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	2	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	2	no	—
301	C₂×C₄×C₈₉	—	2	4	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	4	no	—
304	C₂×C₄×C₈₉	—	2	4	no	—
305	C₂×C₄×C₈₉	—	2	4	no	—
306	C₂×C₄×C₈₉	—	2	4	no	—
307	C₂×C₄×C₈₉	—	2	4	no	—
308	C₂×C₄×C₈₉	—	2	4	no	—
309	C₂×C₄×C₈₉	—	4	4	no	—
310	C₂×C₄×C₈₉	—	4	4	no	—
311	C₂×C₄×C₈₉	—	4	16	no	—
312	C₂×C₄×C₈₉	—	4	4	no	—
313	C₂×C₄×C₈₉	—	4	4	no	—
314	C₂×C₄×C₈₉	—	4	4	no	—
315	C₂×C₄×C₈₉	—	8	4	no	—
316	C₂×C₄×C₈₉	—	8	8	no	—
317	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
321	C₂²×C₈₉	—	2	2	no	—
322	C₂²×C₈₉	—	2	2	no	—
323	C₂²×C₈₉	—	2	8	no	—
324	C₂²×C₈₉	—	2	4	no	—
325	C₂²×C₈₉	—	2	4	no	—
326	C₂²×C₈₉	—	2	4	no	—
327	C₂²×C₈₉	—	2	4	no	—
328	C₂²×C₈₉	—	2	8	no	—
329	C₂²×C₈₉	—	4	16	no	—
330	C₂²×C₈₉	—	4	2	no	—
331	C₂²×C₈₉	—	4	2	no	—
332	C₂²×C₈₉	—	4	4	no	—
333	C₂²×C₈₉	—	4	4	no	—
334	C₂²×C₈₉	—	4	4	no	—
335	C₂²×C₈₉	—	4	2	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	—	8	8	no	—
341	C₂²×C₈₉	#532	1	4	yes	—
342	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₈₉	C₂²×#41	1	2	yes	—
344	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₈₉	#585	1	2	yes	—
346	C₄×C₈₉	—	2	4	no	—
347	C₄×C₈₉	—	2	2	no	—
348	C₄×C₈₉	—	2	2	no	—
349	C₄×C₈₉	—	2	8	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	2	no	—
352	C₄×C₈₉	—	4	2	no	—
353	C₄×C₈₉	—	4	2	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	2	no	—
356	C₄×C₈₉	—	4	4	no	—
357	#35394	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂×C₈₉	—	2	4	no	—
359	C₂×C₈₉	—	4	4	no	—
360	C₂×C₈₉	—	4	4	no	—
361	C₂×C₈₉	—	8	2	no	—
362	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
363	C₂×C₈₉	#3484	1	1	yes	characteristic
364	C₂×C₈₉	#3485	1	1	yes	characteristic
365	C₂×C₈₉	#3513	1	4	yes	—
366	C₂×#538	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₂²×#123	C₂×C₈₉	1	1	yes	characteristic, complemented
368	#2561	C₂×C₈₉	1	1	yes	characteristic, complemented
369	#2557	C₂×C₈₉	1	4	yes	complemented
370	#2553	C₂×C₈₉	1	4	yes	complemented
371	#2539	C₂×C₈₉	1	1	yes	characteristic, complemented
372	#2504	C₂×C₈₉	1	1	yes	characteristic, complemented
373	#2502	C₂×C₈₉	1	1	yes	characteristic, complemented
374	#2464	C₂×C₈₉	1	4	yes	complemented
375	#2422	C₂×C₈₉	1	4	yes	complemented
376	#2412	C₂×C₈₉	1	2	yes	complemented
377	#2410	C₂×C₈₉	1	2	yes	complemented
378	#2322	C₂×C₈₉	1	2	yes	complemented
379	C₄×#120	C₂×C₈₉	1	2	yes	complemented
380	#2273	C₂×C₈₉	1	1	yes	characteristic, complemented
381	C₈₉	#35394	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
383	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
384	#538	—	2	8	no	—
385	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
386	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
387	C₂×#123	—	2	8	no	—
388	C₂×#123	C₂²×C₈₉	1	2	yes	—
389	C₂×#123	C₂²×C₈₉	1	4	yes	—
390	C₂×#123	C₂²×C₈₉	1	4	yes	—
391	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
392	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
393	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
394	C₂×#121	C₂²×C₈₉	1	4	yes	—
395	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
396	C₂×#120	C₂²×C₈₉	1	2	yes	—
397	C₂×#120	C₂²×C₈₉	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
400	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
404	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
406	#399	C₂²×C₈₉	1	2	yes	complemented
407	#398	C₂²×C₈₉	1	4	yes	complemented
408	#397	C₂²×C₈₉	1	2	yes	complemented
409	#397	C₂²×C₈₉	1	4	yes	complemented
410	#397	C₂²×C₈₉	1	4	yes	complemented
411	#394	C₂²×C₈₉	1	4	yes	—
412	#394	C₂²×C₈₉	1	4	yes	complemented
413	#393	C₂²×C₈₉	1	2	yes	complemented
414	#392	C₂²×C₈₉	1	4	yes	—
415	#392	C₂²×C₈₉	1	2	yes	complemented
416	#391	C₂²×C₈₉	1	2	yes	complemented
417	#390	C₂²×C₈₉	1	4	yes	complemented
418	#390	C₂²×C₈₉	1	2	yes	complemented
419	#389	C₂²×C₈₉	1	4	yes	complemented
420	#388	C₂²×C₈₉	1	4	yes	complemented
421	#388	C₂²×C₈₉	1	4	yes	complemented
422	#387	C₂²×C₈₉	1	4	yes	complemented
423	#386	C₂²×C₈₉	1	2	yes	—
424	#386	C₂²×C₈₉	1	4	yes	—
425	#386	C₂²×C₈₉	1	2	yes	—
426	#386	C₂²×C₈₉	1	4	yes	complemented
427	#386	C₂²×C₈₉	1	4	yes	complemented
428	#385	C₂²×C₈₉	1	2	yes	—
429	#385	C₂²×C₈₉	1	2	yes	—
430	#385	C₂²×C₈₉	1	4	yes	complemented
431	#385	C₂²×C₈₉	1	4	yes	complemented
432	#384	C₂²×C₈₉	1	2	yes	complemented
433	#382	C₂²×C₈₉	1	2	yes	complemented
434	#381	C₂²×C₈₉	1	2	yes	—
435	#380	C₂²×C₈₉	1	4	yes	complemented
436	#379	C₂²×C₈₉	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
441	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
442	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
443	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
444	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
446	C₂²×D₄	—	2	4	no	—
447	C₂²×D₄	—	4	4	no	—
448	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
449	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
450	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
451	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
452	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
453	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
454	C₂³×C₄	—	2	4	no	—
455	C₂³×C₄	—	4	4	no	—
456	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
458	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
460	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
462	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
464	#126	—	2	8	no	—
465	#124	—	2	8	no	—
466	#123	—	2	16	no	—
467	#123	—	2	16	no	—
468	#123	—	2	8	no	—
469	#123	—	2	8	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	#121	—	2	4	no	—
472	#121	—	2	8	no	—
473	#121	—	4	8	no	—
474	#120	—	2	8	no	—
475	#120	—	2	8	no	—
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	4	8	no	—
478	C₂×C₄⋊C₄	—	2	4	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	8	no	—
493	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	complemented
494	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
514	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
515	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
517	#95	C₂³×C₈₉	1	4	yes	—
518	#95	C₂³×C₈₉	1	2	yes	—
519	#95	C₂³×C₈₉	1	2	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	#95	C₂³×C₈₉	1	4	yes	—
525	#95	C₂³×C₈₉	1	4	yes	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	2	4	no	—
530	C₂⁴	—	4	2	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
534	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
535	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
536	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
537	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	8	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	16	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	16	no	—
573	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
574	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
586	C₄⋊C₄	—	2	8	no	—
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	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	8	no	—
594	C₄⋊C₄	—	4	4	no	—
595	C₄⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	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	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
614	C₂²⋊C₄	#41×C₈₉	1	8	yes	—
615	C₄²	—	2	4	no	—
616	C₄²	—	4	4	no	—
617	C₄²	—	4	2	no	—
618	C₄²	—	4	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	8	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	8	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	4	4	no	—
637	C₂³	—	4	4	no	—
638	C₂³	—	4	16	no	—
639	C₂³	—	4	4	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	8	8	no	—
642	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
643	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
644	C₂³	C₂×#41×C₈₉	1	4	yes	—
645	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
646	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
647	Q₈	—	8	2	no	—
648	D₄	—	4	16	no	—
649	D₄	—	4	16	no	—
650	D₄	—	4	8	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	4	no	—
653	D₄	—	8	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	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	—	4	4	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	16	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	8	no	—
683	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
686	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	8	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	8	no	—
695	C₂²	—	4	16	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	8	8	no	—
707	C₂²	#532×C₈₉	1	4	yes	—
708	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
709	C₂²	C₂²×#41×C₈₉	1	2	yes	—
710	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
711	C₂²	#585×C₈₉	1	2	yes	—
712	C₄	—	2	4	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	8	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₂	—	2	4	no	—
724	C₂	—	4	4	no	—
725	C₂	—	4	4	no	—
726	C₂	—	8	2	no	—
727	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
728	C₂	C₈₉×#3484	1	1	yes	characteristic
729	C₂	C₈₉×#3485	1	1	yes	characteristic
730	C₂	C₈₉×#3513	1	4	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×#538×C₈₉	C₂	semidirect
2. C₂²×#123×C₈₉	C₂	semidirect
3. C₈₉×#2561	C₂	semidirect
4. C₈₉×#2557	C₂	semidirect
5. C₈₉×#2553	C₂	semidirect
6. C₈₉×#2539	C₂	semidirect
7. C₈₉×#2504	C₂	semidirect
8. C₈₉×#2502	C₂	semidirect
9. C₈₉×#2464	C₂	semidirect
10. C₈₉×#2422	C₂	semidirect
11. C₈₉×#2412	C₂	semidirect
12. C₈₉×#2410	C₂	semidirect
13. C₈₉×#2322	C₂	semidirect
14. C₄×#120×C₈₉	C₂	semidirect
15. C₈₉×#2273	C₂	semidirect
19. C₂×#126×C₈₉	C₂²	semidirect
20. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×#123×C₈₉	C₂²	semidirect
29. C₂×#121×C₈₉	C₂²	semidirect
33. C₂×C₄×D₄×C₈₉	C₂²	semidirect
40. #399×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
42. #397×C₈₉	C₂²	semidirect
43. #397×C₈₉	C₂²	semidirect
44. #397×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
47. #393×C₈₉	C₂²	semidirect
49. #392×C₈₉	C₂²	semidirect
50. #391×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #390×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
54. #388×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #387×C₈₉	C₂²	semidirect
60. #386×C₈₉	C₂²	semidirect
61. #386×C₈₉	C₂²	semidirect
64. #385×C₈₉	C₂²	semidirect
65. #385×C₈₉	C₂²	semidirect
66. #384×C₈₉	C₂²	semidirect
67. #382×C₈₉	C₂²	semidirect
69. #380×C₈₉	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
127. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
357. #35394	C₈₉	direct (N × H)
366. C₂×#538	C₂×C₈₉	semidirect
367. C₂²×#123	C₂×C₈₉	semidirect
368. #2561	C₂×C₈₉	semidirect
369. #2557	C₂×C₈₉	semidirect
370. #2553	C₂×C₈₉	semidirect
371. #2539	C₂×C₈₉	semidirect
372. #2504	C₂×C₈₉	semidirect
373. #2502	C₂×C₈₉	semidirect
374. #2464	C₂×C₈₉	semidirect
375. #2422	C₂×C₈₉	semidirect
376. #2412	C₂×C₈₉	semidirect
377. #2410	C₂×C₈₉	semidirect
378. #2322	C₂×C₈₉	semidirect
379. C₄×#120	C₂×C₈₉	semidirect
380. #2273	C₂×C₈₉	semidirect
381. C₈₉	#35394	direct (N × H)
385. C₂×#126	C₂²×C₈₉	semidirect
386. C₂×#124	C₂²×C₈₉	semidirect
391. C₂×#123	C₂²×C₈₉	semidirect
395. C₂×#121	C₂²×C₈₉	semidirect
399. C₂×C₄×D₄	C₂²×C₈₉	semidirect
406. #399	C₂²×C₈₉	semidirect
407. #398	C₂²×C₈₉	semidirect
408. #397	C₂²×C₈₉	semidirect
409. #397	C₂²×C₈₉	semidirect
410. #397	C₂²×C₈₉	semidirect
412. #394	C₂²×C₈₉	semidirect
413. #393	C₂²×C₈₉	semidirect
415. #392	C₂²×C₈₉	semidirect
416. #391	C₂²×C₈₉	semidirect
417. #390	C₂²×C₈₉	semidirect
418. #390	C₂²×C₈₉	semidirect
419. #389	C₂²×C₈₉	semidirect
420. #388	C₂²×C₈₉	semidirect
421. #388	C₂²×C₈₉	semidirect
422. #387	C₂²×C₈₉	semidirect
426. #386	C₂²×C₈₉	semidirect
427. #386	C₂²×C₈₉	semidirect
430. #385	C₂²×C₈₉	semidirect
431. #385	C₂²×C₈₉	semidirect
432. #384	C₂²×C₈₉	semidirect
433. #382	C₂²×C₈₉	semidirect
435. #380	C₂²×C₈₉	semidirect
440. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
441. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
442. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
493. C₂×C₂²⋊C₄	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×#538×C₈₉	2
C₂²×#123×C₈₉	2
C₈₉×#2561	2
C₈₉×#2557	2
C₈₉×#2553	2
C₈₉×#2539	2
C₈₉×#2504	2
C₈₉×#2502	2
C₈₉×#2464	2
C₈₉×#2422	2
C₈₉×#2412	2
C₈₉×#2410	2
C₈₉×#2322	2
C₄×#120×C₈₉	2
C₈₉×#2273	2
#35394	89

Subgroups — C89×#35394 #36413242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35394 #36413242