Subgroups — C₈₉×#35348 #36413196

Order 22784.

4922 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#120×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2534	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2424	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2411	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2410	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2408	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2315	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#379×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₈₉	C₂²	1	2	yes	complemented
17	C₂³×D₄×C₈₉	C₂²	1	2	yes	complemented
18	#534×C₈₉	—	2	8	no	—
19	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
20	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
22	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
23	C₂×#120×C₈₉	—	2	8	no	—
24	C₂×#120×C₈₉	—	2	8	no	—
25	C₂×#120×C₈₉	C₂²	1	4	yes	—
26	C₂×#120×C₈₉	C₂²	1	4	yes	—
27	C₂×#120×C₈₉	C₂²	1	4	yes	complemented
28	C₂×#120×C₈₉	C₂²	1	4	yes	complemented
29	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
30	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
31	#518×C₈₉	—	2	8	no	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
33	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊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	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
42	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
43	#396×C₈₉	C₂²	1	8	yes	complemented
44	#394×C₈₉	C₂²	1	8	yes	complemented
45	#394×C₈₉	C₂²	1	8	yes	complemented
46	#392×C₈₉	C₂²	1	8	yes	complemented
47	#390×C₈₉	C₂²	1	8	yes	complemented
48	#388×C₈₉	C₂²	1	8	yes	complemented
49	#386×C₈₉	C₂²	1	8	yes	complemented
50	#386×C₈₉	C₂²	1	4	yes	complemented
51	#386×C₈₉	C₂²	1	4	yes	complemented
52	#385×C₈₉	C₂²	1	4	yes	complemented
53	#385×C₈₉	C₂²	1	4	yes	complemented
54	#381×C₈₉	C₂²	1	2	yes	complemented
55	#380×C₈₉	C₂²	1	4	yes	complemented
56	#379×C₈₉	C₂²	1	4	yes	complemented
57	#379×C₈₉	C₂²	1	4	yes	complemented
58	#379×C₈₉	C₂²	1	2	yes	complemented
59	C₂⁵×C₈₉	—	2	4	no	—
60	C₂⁵×C₈₉	—	2	4	no	—
61	C₂⁵×C₈₉	—	2	4	no	—
62	C₂⁵×C₈₉	—	4	8	no	—
63	C₂⁵×C₈₉	C₂³	1	2	yes	—
64	C₂⁵×C₈₉	C₂³	1	2	yes	—
65	C₂⁵×C₈₉	C₂³	1	2	yes	—
66	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
67	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
68	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	—	2	4	no	—
70	C₂²×D₄×C₈₉	—	2	4	no	—
71	C₂²×D₄×C₈₉	—	2	4	no	—
72	C₂²×D₄×C₈₉	—	2	4	no	—
73	C₂²×D₄×C₈₉	—	2	8	no	—
74	C₂²×D₄×C₈₉	—	2	4	no	—
75	C₂²×D₄×C₈₉	—	2	8	no	—
76	C₂²×D₄×C₈₉	—	4	8	no	—
77	C₂²×D₄×C₈₉	—	4	8	no	—
78	C₂²×D₄×C₈₉	D₄	1	8	yes	complemented
79	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
82	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	4	yes	complemented
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	4	yes	complemented
93	#123×C₈₉	—	2	8	no	—
94	#123×C₈₉	—	2	8	no	—
95	#121×C₈₉	—	2	16	no	—
96	#121×C₈₉	—	4	16	no	—
97	#120×C₈₉	—	2	8	no	—
98	#120×C₈₉	—	2	16	no	—
99	#120×C₈₉	—	2	8	no	—
100	#120×C₈₉	—	2	16	no	—
101	#120×C₈₉	—	2	16	no	—
102	#120×C₈₉	—	2	16	no	—
103	C₄×D₄×C₈₉	—	2	16	no	—
104	C₄×D₄×C₈₉	—	2	16	no	—
105	#117×C₈₉	—	2	8	no	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
109	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
113	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
116	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	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	complemented
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	complemented
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	complemented
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
133	C₂×C₄²×C₈₉	C₂³	1	4	yes	complemented
134	#95×C₈₉	C₂³	1	8	yes	complemented
135	#95×C₈₉	C₂³	1	8	yes	complemented
136	C₂⁴×C₈₉	—	2	4	no	—
137	C₂⁴×C₈₉	—	2	4	no	—
138	C₂⁴×C₈₉	—	2	4	no	—
139	C₂⁴×C₈₉	—	2	8	no	—
140	C₂⁴×C₈₉	—	2	8	no	—
141	C₂⁴×C₈₉	—	2	8	no	—
142	C₂⁴×C₈₉	—	2	2	no	—
143	C₂⁴×C₈₉	—	2	2	no	—
144	C₂⁴×C₈₉	—	2	4	no	—
145	C₂⁴×C₈₉	—	2	4	no	—
146	C₂⁴×C₈₉	—	2	4	no	—
147	C₂⁴×C₈₉	—	2	4	no	—
148	C₂⁴×C₈₉	—	2	2	no	—
149	C₂⁴×C₈₉	—	2	4	no	—
150	C₂⁴×C₈₉	—	2	4	no	—
151	C₂⁴×C₈₉	—	2	2	no	—
152	C₂⁴×C₈₉	—	2	2	no	—
153	C₂⁴×C₈₉	—	4	4	no	—
154	C₂⁴×C₈₉	—	4	4	no	—
155	C₂⁴×C₈₉	—	4	4	no	—
156	C₂⁴×C₈₉	—	4	4	no	—
157	C₂⁴×C₈₉	—	4	4	no	—
158	C₂⁴×C₈₉	—	4	4	no	—
159	C₂⁴×C₈₉	—	4	32	no	—
160	C₂⁴×C₈₉	—	4	32	no	—
161	C₂⁴×C₈₉	—	4	32	no	—
162	C₂⁴×C₈₉	—	4	16	no	—
163	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
164	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
165	C₂⁴×C₈₉	C₂×D₄	1	4	yes	complemented
166	C₂⁴×C₈₉	#41	1	4	yes	—
167	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
168	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
169	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
170	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂×D₄×C₈₉	—	2	32	no	—
174	C₂×D₄×C₈₉	—	2	4	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	16	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	4	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	16	no	—
186	C₂×D₄×C₈₉	—	2	16	no	—
187	C₂×D₄×C₈₉	—	2	8	no	—
188	C₂×D₄×C₈₉	—	2	16	no	—
189	C₂×D₄×C₈₉	—	4	8	no	—
190	C₂×D₄×C₈₉	—	4	8	no	—
191	C₂×D₄×C₈₉	—	4	8	no	—
192	C₂×D₄×C₈₉	—	4	32	no	—
193	C₂×D₄×C₈₉	—	4	32	no	—
194	C₂×D₄×C₈₉	—	4	16	no	—
195	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
196	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	complemented
197	C₂²×C₄×C₈₉	—	2	2	no	—
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	4	no	—
200	C₂²×C₄×C₈₉	—	2	2	no	—
201	C₂²×C₄×C₈₉	—	2	2	no	—
202	C₂²×C₄×C₈₉	—	2	2	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	4	no	—
205	C₂²×C₄×C₈₉	—	2	8	no	—
206	C₂²×C₄×C₈₉	—	4	4	no	—
207	C₂²×C₄×C₈₉	—	4	4	no	—
208	C₂²×C₄×C₈₉	—	4	4	no	—
209	C₂²×C₄×C₈₉	—	4	4	no	—
210	C₂²×C₄×C₈₉	—	4	8	no	—
211	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	complemented
212	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	complemented
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₄⋊C₄×C₈₉	—	2	8	no	—
220	C₄⋊C₄×C₈₉	—	2	8	no	—
221	C₄⋊C₄×C₈₉	—	4	8	no	—
222	C₂²⋊C₄×C₈₉	—	2	4	no	—
223	C₂²⋊C₄×C₈₉	—	2	4	no	—
224	C₂²⋊C₄×C₈₉	—	2	4	no	—
225	C₂²⋊C₄×C₈₉	—	2	4	no	—
226	C₂²⋊C₄×C₈₉	—	2	4	no	—
227	C₂²⋊C₄×C₈₉	—	2	4	no	—
228	C₂²⋊C₄×C₈₉	—	2	8	no	—
229	C₂²⋊C₄×C₈₉	—	2	16	no	—
230	C₂²⋊C₄×C₈₉	—	2	16	no	—
231	C₂²⋊C₄×C₈₉	—	2	16	no	—
232	C₂²⋊C₄×C₈₉	—	2	8	no	—
233	C₂²⋊C₄×C₈₉	—	2	8	no	—
234	C₂²⋊C₄×C₈₉	—	4	8	no	—
235	C₂²⋊C₄×C₈₉	—	4	8	no	—
236	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
237	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	complemented
238	C₄²×C₈₉	—	2	8	no	—
239	C₂³×C₈₉	—	2	4	no	—
240	C₂³×C₈₉	—	2	4	no	—
241	C₂³×C₈₉	—	2	4	no	—
242	C₂³×C₈₉	—	2	16	no	—
243	C₂³×C₈₉	—	2	16	no	—
244	C₂³×C₈₉	—	2	16	no	—
245	C₂³×C₈₉	—	2	2	no	—
246	C₂³×C₈₉	—	2	4	no	—
247	C₂³×C₈₉	—	2	4	no	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	2	4	no	—
250	C₂³×C₈₉	—	2	4	no	—
251	C₂³×C₈₉	—	2	8	no	—
252	C₂³×C₈₉	—	2	4	no	—
253	C₂³×C₈₉	—	2	4	no	—
254	C₂³×C₈₉	—	2	8	no	—
255	C₂³×C₈₉	—	2	2	no	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	8	no	—
259	C₂³×C₈₉	—	4	8	no	—
260	C₂³×C₈₉	—	4	8	no	—
261	C₂³×C₈₉	—	4	8	no	—
262	C₂³×C₈₉	—	4	8	no	—
263	C₂³×C₈₉	—	4	16	no	—
264	C₂³×C₈₉	—	4	16	no	—
265	C₂³×C₈₉	—	4	16	no	—
266	C₂³×C₈₉	—	4	16	no	—
267	C₂³×C₈₉	—	4	16	no	—
268	C₂³×C₈₉	—	4	16	no	—
269	C₂³×C₈₉	—	4	8	no	—
270	C₂³×C₈₉	—	4	8	no	—
271	C₂³×C₈₉	—	4	8	no	—
272	C₂³×C₈₉	—	4	8	no	—
273	C₂³×C₈₉	—	4	128	no	—
274	C₂³×C₈₉	—	4	8	no	—
275	C₂³×C₈₉	—	4	8	no	—
276	C₂³×C₈₉	—	4	8	no	—
277	C₂³×C₈₉	—	4	4	no	—
278	C₂³×C₈₉	—	8	4	no	—
279	C₂³×C₈₉	—	8	4	no	—
280	C₂³×C₈₉	—	8	4	no	—
281	C₂³×C₈₉	—	8	4	no	—
282	C₂³×C₈₉	#121	1	16	yes	complemented
283	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
284	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
285	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
286	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
287	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
288	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
289	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
290	C₂³×C₈₉	C₂×#41	1	2	yes	—
291	C₂³×C₈₉	C₂×#41	1	2	yes	—
292	C₂³×C₈₉	C₂×#41	1	2	yes	—
293	C₂³×C₈₉	H(5,𝔽₂)	1	8	yes	—
294	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
295	D₄×C₈₉	—	2	16	no	—
296	D₄×C₈₉	—	2	16	no	—
297	D₄×C₈₉	—	4	32	no	—
298	D₄×C₈₉	—	4	32	no	—
299	D₄×C₈₉	—	4	8	no	—
300	D₄×C₈₉	—	4	8	no	—
301	D₄×C₈₉	—	8	8	no	—
302	C₂×C₄×C₈₉	—	2	8	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	8	no	—
306	C₂×C₄×C₈₉	—	2	4	no	—
307	C₂×C₄×C₈₉	—	2	4	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	2	no	—
312	C₂×C₄×C₈₉	—	2	8	no	—
313	C₂×C₄×C₈₉	—	2	8	no	—
314	C₂×C₄×C₈₉	—	2	8	no	—
315	C₂×C₄×C₈₉	—	4	8	no	—
316	C₂×C₄×C₈₉	—	4	8	no	—
317	C₂×C₄×C₈₉	—	4	4	no	—
318	C₂×C₄×C₈₉	—	8	8	no	—
319	C₂×C₄×C₈₉	—	8	4	no	—
320	C₂×C₄×C₈₉	—	8	4	no	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
322	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
323	C₂²×C₈₉	—	2	4	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	4	no	—
329	C₂²×C₈₉	—	2	4	no	—
330	C₂²×C₈₉	—	2	4	no	—
331	C₂²×C₈₉	—	2	4	no	—
332	C₂²×C₈₉	—	2	4	no	—
333	C₂²×C₈₉	—	2	8	no	—
334	C₂²×C₈₉	—	2	8	no	—
335	C₂²×C₈₉	—	2	8	no	—
336	C₂²×C₈₉	—	2	8	no	—
337	C₂²×C₈₉	—	4	16	no	—
338	C₂²×C₈₉	—	4	32	no	—
339	C₂²×C₈₉	—	4	32	no	—
340	C₂²×C₈₉	—	4	32	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	—	4	4	no	—
346	C₂²×C₈₉	—	4	4	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	—	4	4	no	—
349	C₂²×C₈₉	—	4	4	no	—
350	C₂²×C₈₉	—	4	4	no	—
351	C₂²×C₈₉	—	8	8	no	—
352	C₂²×C₈₉	—	8	8	no	—
353	C₂²×C₈₉	C₂×#121	1	4	yes	—
354	C₂²×C₈₉	C₂×#121	1	4	yes	—
355	C₂²×C₈₉	C₂×#121	1	4	yes	—
356	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
357	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
360	C₄×C₈₉	—	2	4	no	—
361	C₄×C₈₉	—	2	8	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	4	no	—
364	C₄×C₈₉	—	4	4	no	—
365	C₄×C₈₉	—	4	4	no	—
366	#35348	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂×C₈₉	—	2	4	no	—
368	C₂×C₈₉	—	2	4	no	—
369	C₂×C₈₉	—	2	4	no	—
370	C₂×C₈₉	—	4	8	no	—
371	C₂×C₈₉	—	4	4	no	—
372	C₂×C₈₉	—	8	2	no	—
373	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
374	C₂×C₈₉	#3484	1	2	yes	—
375	C₂×C₈₉	#3484	1	2	yes	—
376	C₂×C₈₉	#3490	1	2	yes	—
377	C₂×#534	C₂×C₈₉	1	1	yes	characteristic, complemented
378	C₂²×#120	C₂×C₈₉	1	1	yes	characteristic, complemented
379	C₂²×#120	C₂×C₈₉	1	1	yes	characteristic, complemented
380	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#2534	C₂×C₈₉	1	4	yes	complemented
382	#2424	C₂×C₈₉	1	8	yes	complemented
383	#2411	C₂×C₈₉	1	4	yes	complemented
384	#2410	C₂×C₈₉	1	4	yes	complemented
385	#2408	C₂×C₈₉	1	4	yes	complemented
386	#2315	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2308	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₂×#379	C₂×C₈₉	1	1	yes	characteristic, complemented
389	C₈₉	#35348	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁶	C₂²×C₈₉	1	1	yes	characteristic
391	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
392	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
393	C₂³×D₄	C₂²×C₈₉	1	2	yes	complemented
394	C₂³×D₄	C₂²×C₈₉	1	2	yes	complemented
395	#534	—	2	8	no	—
396	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
397	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
398	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
399	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
400	C₂×#120	—	2	8	no	—
401	C₂×#120	—	2	8	no	—
402	C₂×#120	C₂²×C₈₉	1	4	yes	—
403	C₂×#120	C₂²×C₈₉	1	4	yes	—
404	C₂×#120	C₂²×C₈₉	1	4	yes	complemented
405	C₂×#120	C₂²×C₈₉	1	4	yes	complemented
406	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
407	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
408	#518	—	2	8	no	—
409	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
410	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
411	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
412	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
417	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
418	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
419	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
420	#396	C₂²×C₈₉	1	8	yes	complemented
421	#394	C₂²×C₈₉	1	8	yes	complemented
422	#394	C₂²×C₈₉	1	8	yes	complemented
423	#392	C₂²×C₈₉	1	8	yes	complemented
424	#390	C₂²×C₈₉	1	8	yes	complemented
425	#388	C₂²×C₈₉	1	8	yes	complemented
426	#386	C₂²×C₈₉	1	8	yes	complemented
427	#386	C₂²×C₈₉	1	4	yes	complemented
428	#386	C₂²×C₈₉	1	4	yes	complemented
429	#385	C₂²×C₈₉	1	4	yes	complemented
430	#385	C₂²×C₈₉	1	4	yes	complemented
431	#381	C₂²×C₈₉	1	2	yes	complemented
432	#380	C₂²×C₈₉	1	4	yes	complemented
433	#379	C₂²×C₈₉	1	4	yes	complemented
434	#379	C₂²×C₈₉	1	4	yes	complemented
435	#379	C₂²×C₈₉	1	2	yes	complemented
436	C₂⁵	—	2	4	no	—
437	C₂⁵	—	2	4	no	—
438	C₂⁵	—	2	4	no	—
439	C₂⁵	—	4	8	no	—
440	C₂⁵	C₂³×C₈₉	1	2	yes	—
441	C₂⁵	C₂³×C₈₉	1	2	yes	—
442	C₂⁵	C₂³×C₈₉	1	2	yes	—
443	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
444	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
445	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
446	C₂²×D₄	—	2	4	no	—
447	C₂²×D₄	—	2	4	no	—
448	C₂²×D₄	—	2	4	no	—
449	C₂²×D₄	—	2	4	no	—
450	C₂²×D₄	—	2	8	no	—
451	C₂²×D₄	—	2	4	no	—
452	C₂²×D₄	—	2	8	no	—
453	C₂²×D₄	—	4	8	no	—
454	C₂²×D₄	—	4	8	no	—
455	C₂²×D₄	D₄×C₈₉	1	8	yes	complemented
456	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
457	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
458	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
459	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
460	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
461	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
462	C₂²×D₄	C₂³×C₈₉	1	4	yes	complemented
463	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
467	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
468	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
469	C₂³×C₄	C₂³×C₈₉	1	4	yes	complemented
470	#123	—	2	8	no	—
471	#123	—	2	8	no	—
472	#121	—	2	16	no	—
473	#121	—	4	16	no	—
474	#120	—	2	8	no	—
475	#120	—	2	16	no	—
476	#120	—	2	8	no	—
477	#120	—	2	16	no	—
478	#120	—	2	16	no	—
479	#120	—	2	16	no	—
480	C₄×D₄	—	2	16	no	—
481	C₄×D₄	—	2	16	no	—
482	#117	—	2	8	no	—
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
486	C₂×C₂²⋊C₄	—	2	4	no	—
487	C₂×C₂²⋊C₄	—	2	4	no	—
488	C₂×C₂²⋊C₄	—	2	4	no	—
489	C₂×C₂²⋊C₄	—	2	8	no	—
490	C₂×C₂²⋊C₄	—	2	8	no	—
491	C₂×C₂²⋊C₄	—	2	8	no	—
492	C₂×C₂²⋊C₄	—	4	8	no	—
493	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	complemented
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	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	complemented
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	complemented
508	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	complemented
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
510	C₂×C₄²	C₂³×C₈₉	1	4	yes	complemented
511	#95	C₂³×C₈₉	1	8	yes	complemented
512	#95	C₂³×C₈₉	1	8	yes	complemented
513	C₂⁴	—	2	4	no	—
514	C₂⁴	—	2	4	no	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	2	8	no	—
517	C₂⁴	—	2	8	no	—
518	C₂⁴	—	2	8	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	2	4	no	—
524	C₂⁴	—	2	4	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	4	4	no	—
531	C₂⁴	—	4	4	no	—
532	C₂⁴	—	4	4	no	—
533	C₂⁴	—	4	4	no	—
534	C₂⁴	—	4	4	no	—
535	C₂⁴	—	4	4	no	—
536	C₂⁴	—	4	32	no	—
537	C₂⁴	—	4	32	no	—
538	C₂⁴	—	4	32	no	—
539	C₂⁴	—	4	16	no	—
540	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
541	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
542	C₂⁴	C₂×D₄×C₈₉	1	4	yes	complemented
543	C₂⁴	#41×C₈₉	1	4	yes	—
544	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
545	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
546	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
547	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
548	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
549	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
550	C₂×D₄	—	2	32	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	16	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	16	no	—
563	C₂×D₄	—	2	16	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	16	no	—
566	C₂×D₄	—	4	8	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	8	no	—
569	C₂×D₄	—	4	32	no	—
570	C₂×D₄	—	4	32	no	—
571	C₂×D₄	—	4	16	no	—
572	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
573	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	complemented
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	8	no	—
588	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	complemented
589	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	complemented
590	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	4	8	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	16	no	—
607	C₂²⋊C₄	—	2	16	no	—
608	C₂²⋊C₄	—	2	16	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	4	8	no	—
612	C₂²⋊C₄	—	4	8	no	—
613	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
614	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	complemented
615	C₄²	—	2	8	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	16	no	—
620	C₂³	—	2	16	no	—
621	C₂³	—	2	16	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	8	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	8	no	—
636	C₂³	—	4	8	no	—
637	C₂³	—	4	8	no	—
638	C₂³	—	4	8	no	—
639	C₂³	—	4	8	no	—
640	C₂³	—	4	16	no	—
641	C₂³	—	4	16	no	—
642	C₂³	—	4	16	no	—
643	C₂³	—	4	16	no	—
644	C₂³	—	4	16	no	—
645	C₂³	—	4	16	no	—
646	C₂³	—	4	8	no	—
647	C₂³	—	4	8	no	—
648	C₂³	—	4	8	no	—
649	C₂³	—	4	8	no	—
650	C₂³	—	4	128	no	—
651	C₂³	—	4	8	no	—
652	C₂³	—	4	8	no	—
653	C₂³	—	4	8	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	#121×C₈₉	1	16	yes	complemented
660	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
661	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
662	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
663	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
664	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
665	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
666	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
667	C₂³	C₂×#41×C₈₉	1	2	yes	—
668	C₂³	C₂×#41×C₈₉	1	2	yes	—
669	C₂³	C₂×#41×C₈₉	1	2	yes	—
670	C₂³	H(5,𝔽₂)×C₈₉	1	8	yes	—
671	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
672	D₄	—	2	16	no	—
673	D₄	—	2	16	no	—
674	D₄	—	4	32	no	—
675	D₄	—	4	32	no	—
676	D₄	—	4	8	no	—
677	D₄	—	4	8	no	—
678	D₄	—	8	8	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	8	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	8	8	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	4	no	—
698	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
699	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	8	no	—
711	C₂²	—	2	8	no	—
712	C₂²	—	2	8	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	4	16	no	—
715	C₂²	—	4	32	no	—
716	C₂²	—	4	32	no	—
717	C₂²	—	4	32	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	8	8	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₂×#121×C₈₉	1	4	yes	—
731	C₂²	C₂×#121×C₈₉	1	4	yes	—
732	C₂²	C₂×#121×C₈₉	1	4	yes	—
733	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
734	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
735	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
736	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
737	C₄	—	2	4	no	—
738	C₄	—	2	8	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₂	—	2	4	no	—
744	C₂	—	2	4	no	—
745	C₂	—	2	4	no	—
746	C₂	—	4	8	no	—
747	C₂	—	4	4	no	—
748	C₂	—	8	2	no	—
749	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
750	C₂	C₈₉×#3484	1	2	yes	—
751	C₂	C₈₉×#3484	1	2	yes	—
752	C₂	C₈₉×#3490	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×#534×C₈₉	C₂	semidirect
2. C₂²×#120×C₈₉	C₂	semidirect
3. C₂²×#120×C₈₉	C₂	semidirect
4. C₂×#518×C₈₉	C₂	semidirect
5. C₈₉×#2534	C₂	semidirect
6. C₈₉×#2424	C₂	semidirect
7. C₈₉×#2411	C₂	semidirect
8. C₈₉×#2410	C₂	semidirect
9. C₈₉×#2408	C₂	semidirect
10. C₈₉×#2315	C₂	semidirect
11. C₈₉×#2308	C₂	semidirect
12. C₂×#379×C₈₉	C₂	semidirect
16. C₂³×D₄×C₈₉	C₂²	semidirect
17. C₂³×D₄×C₈₉	C₂²	semidirect
19. C₂×#123×C₈₉	C₂²	semidirect
20. C₂×#123×C₈₉	C₂²	semidirect
21. C₂×#121×C₈₉	C₂²	semidirect
22. C₂×#121×C₈₉	C₂²	semidirect
27. C₂×#120×C₈₉	C₂²	semidirect
28. C₂×#120×C₈₉	C₂²	semidirect
29. C₂×#120×C₈₉	C₂²	semidirect
30. C₂×#120×C₈₉	C₂²	semidirect
32. C₂×C₄×D₄×C₈₉	C₂²	semidirect
33. C₂×C₄×D₄×C₈₉	C₂²	semidirect
34. C₂×#117×C₈₉	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
43. #396×C₈₉	C₂²	semidirect
44. #394×C₈₉	C₂²	semidirect
45. #394×C₈₉	C₂²	semidirect
46. #392×C₈₉	C₂²	semidirect
47. #390×C₈₉	C₂²	semidirect
48. #388×C₈₉	C₂²	semidirect
49. #386×C₈₉	C₂²	semidirect
50. #386×C₈₉	C₂²	semidirect
51. #386×C₈₉	C₂²	semidirect
52. #385×C₈₉	C₂²	semidirect
53. #385×C₈₉	C₂²	semidirect
54. #381×C₈₉	C₂²	semidirect
55. #380×C₈₉	C₂²	semidirect
56. #379×C₈₉	C₂²	semidirect
57. #379×C₈₉	C₂²	semidirect
58. #379×C₈₉	C₂²	semidirect
78. C₂²×D₄×C₈₉	D₄	semidirect
85. C₂²×D₄×C₈₉	C₂³	semidirect
92. C₂³×C₄×C₈₉	C₂³	semidirect
106. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
107. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
108. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
129. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
130. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
131. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
132. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
133. C₂×C₄²×C₈₉	C₂³	semidirect
134. #95×C₈₉	C₂³	semidirect
135. #95×C₈₉	C₂³	semidirect
165. C₂⁴×C₈₉	C₂×D₄	semidirect
196. C₂×D₄×C₈₉	C₂×D₄	semidirect
211. C₂²×C₄×C₈₉	C₂×D₄	semidirect
212. C₂²×C₄×C₈₉	C₂×D₄	semidirect
237. C₂²⋊C₄×C₈₉	C₂×D₄	semidirect
282. C₂³×C₈₉	#121	semidirect
366. #35348	C₈₉	direct (N × H)
377. C₂×#534	C₂×C₈₉	semidirect
378. C₂²×#120	C₂×C₈₉	semidirect
379. C₂²×#120	C₂×C₈₉	semidirect
380. C₂×#518	C₂×C₈₉	semidirect
381. #2534	C₂×C₈₉	semidirect
382. #2424	C₂×C₈₉	semidirect
383. #2411	C₂×C₈₉	semidirect
384. #2410	C₂×C₈₉	semidirect
385. #2408	C₂×C₈₉	semidirect
386. #2315	C₂×C₈₉	semidirect
387. #2308	C₂×C₈₉	semidirect
388. C₂×#379	C₂×C₈₉	semidirect
389. C₈₉	#35348	direct (N × H)
393. C₂³×D₄	C₂²×C₈₉	semidirect
394. C₂³×D₄	C₂²×C₈₉	semidirect
396. C₂×#123	C₂²×C₈₉	semidirect
397. C₂×#123	C₂²×C₈₉	semidirect
398. C₂×#121	C₂²×C₈₉	semidirect
399. C₂×#121	C₂²×C₈₉	semidirect
404. C₂×#120	C₂²×C₈₉	semidirect
405. C₂×#120	C₂²×C₈₉	semidirect
406. C₂×#120	C₂²×C₈₉	semidirect
407. C₂×#120	C₂²×C₈₉	semidirect
409. C₂×C₄×D₄	C₂²×C₈₉	semidirect
410. C₂×C₄×D₄	C₂²×C₈₉	semidirect
411. C₂×#117	C₂²×C₈₉	semidirect
416. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
417. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
418. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
419. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
420. #396	C₂²×C₈₉	semidirect
421. #394	C₂²×C₈₉	semidirect
422. #394	C₂²×C₈₉	semidirect
423. #392	C₂²×C₈₉	semidirect
424. #390	C₂²×C₈₉	semidirect
425. #388	C₂²×C₈₉	semidirect
426. #386	C₂²×C₈₉	semidirect
427. #386	C₂²×C₈₉	semidirect
428. #386	C₂²×C₈₉	semidirect
429. #385	C₂²×C₈₉	semidirect
430. #385	C₂²×C₈₉	semidirect
431. #381	C₂²×C₈₉	semidirect
432. #380	C₂²×C₈₉	semidirect
433. #379	C₂²×C₈₉	semidirect
434. #379	C₂²×C₈₉	semidirect
435. #379	C₂²×C₈₉	semidirect
455. C₂²×D₄	D₄×C₈₉	semidirect
462. C₂²×D₄	C₂³×C₈₉	semidirect
469. C₂³×C₄	C₂³×C₈₉	semidirect
483. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
484. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
485. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
493. C₂×C₂²⋊C₄	D₄×C₈₉	semidirect
506. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
507. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
508. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
509. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
510. C₂×C₄²	C₂³×C₈₉	semidirect
511. #95	C₂³×C₈₉	semidirect
512. #95	C₂³×C₈₉	semidirect
542. C₂⁴	C₂×D₄×C₈₉	semidirect
573. C₂×D₄	C₂×D₄×C₈₉	semidirect
588. C₂²×C₄	C₂×D₄×C₈₉	semidirect
589. C₂²×C₄	C₂×D₄×C₈₉	semidirect
614. C₂²⋊C₄	C₂×D₄×C₈₉	semidirect
659. C₂³	#121×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₈₉	2
C₂²×#120×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2534	2
C₈₉×#2424	2
C₈₉×#2411	2
C₈₉×#2410	2
C₈₉×#2408	2
C₈₉×#2315	2
C₈₉×#2308	2
C₂×#379×C₈₉	2
#35348	89

Subgroups — C89×#35348 #36413196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35348 #36413196