Subgroups — C₈₉×#35397 #36413245

Order 22784.

2602 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2561	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2560	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2556	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2539	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2461	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2452	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2413	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2411	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×#2274	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#539×C₈₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
20	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#123×C₈₉	C₂²	1	2	yes	—
24	C₂×#123×C₈₉	C₂²	1	2	yes	—
25	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₈₉	—	2	8	no	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#120×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	#399×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	4	yes	complemented
43	#397×C₈₉	C₂²	1	2	yes	—
44	#396×C₈₉	C₂²	1	4	yes	—
45	#396×C₈₉	C₂²	1	4	yes	complemented
46	#395×C₈₉	C₂²	1	4	yes	complemented
47	#394×C₈₉	C₂²	1	4	yes	—
48	#393×C₈₉	C₂²	1	2	yes	—
49	#393×C₈₉	C₂²	1	4	yes	complemented
50	#392×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	complemented
52	#391×C₈₉	C₂²	1	2	yes	complemented
53	#390×C₈₉	C₂²	1	4	yes	—
54	#390×C₈₉	C₂²	1	4	yes	—
55	#389×C₈₉	C₂²	1	4	yes	complemented
56	#389×C₈₉	C₂²	1	4	yes	complemented
57	#388×C₈₉	C₂²	1	4	yes	—
58	#388×C₈₉	C₂²	1	4	yes	—
59	#388×C₈₉	C₂²	1	4	yes	complemented
60	#388×C₈₉	C₂²	1	4	yes	complemented
61	#387×C₈₉	C₂²	1	4	yes	complemented
62	#386×C₈₉	C₂²	1	4	yes	—
63	#386×C₈₉	C₂²	1	2	yes	—
64	#386×C₈₉	C₂²	1	2	yes	—
65	#385×C₈₉	C₂²	1	4	yes	—
66	#385×C₈₉	C₂²	1	2	yes	—
67	#385×C₈₉	C₂²	1	2	yes	—
68	#385×C₈₉	C₂²	1	4	yes	complemented
69	#381×C₈₉	C₂²	1	2	yes	—
70	#379×C₈₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
72	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₈₉	—	2	4	no	—
79	C₂²×Q₈×C₈₉	—	4	4	no	—
80	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
81	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
82	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	—	2	4	no	—
87	C₂³×C₄×C₈₉	—	4	4	no	—
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	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₈₉	—	4	4	no	—
97	#126×C₈₉	—	2	8	no	—
98	#125×C₈₉	—	2	8	no	—
99	#124×C₈₉	—	4	4	no	—
100	#123×C₈₉	—	2	8	no	—
101	#123×C₈₉	—	2	8	no	—
102	#123×C₈₉	—	2	8	no	—
103	C₂²⋊Q₈×C₈₉	—	2	4	no	—
104	C₂²⋊Q₈×C₈₉	—	2	16	no	—
105	C₂²⋊Q₈×C₈₉	—	2	16	no	—
106	C₂²⋊Q₈×C₈₉	—	2	8	no	—
107	#121×C₈₉	—	2	4	no	—
108	#120×C₈₉	—	2	8	no	—
109	C₄×D₄×C₈₉	—	2	8	no	—
110	C₄×D₄×C₈₉	—	4	8	no	—
111	#117×C₈₉	—	2	8	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
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	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	4	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	4	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
152	#95×C₈₉	C₂³	1	4	yes	—
153	#95×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	2	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	#95×C₈₉	C₂³	1	4	yes	—
161	C₂⁴×C₈₉	—	2	2	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	2	4	no	—
164	C₂⁴×C₈₉	—	4	2	no	—
165	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
166	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
167	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₂×Q₈×C₈₉	—	2	4	no	—
169	C₂×Q₈×C₈₉	—	2	4	no	—
170	C₂×Q₈×C₈₉	—	2	2	no	—
171	C₂×Q₈×C₈₉	—	2	4	no	—
172	C₂×Q₈×C₈₉	—	2	4	no	—
173	C₂×Q₈×C₈₉	—	4	2	no	—
174	C₂×Q₈×C₈₉	—	4	2	no	—
175	C₂×Q₈×C₈₉	—	4	2	no	—
176	C₂×Q₈×C₈₉	—	4	16	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	8	no	—
181	C₂×D₄×C₈₉	—	2	2	no	—
182	C₂×D₄×C₈₉	—	2	8	no	—
183	C₂×D₄×C₈₉	—	4	4	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	4	no	—
187	C₂²×C₄×C₈₉	—	2	4	no	—
188	C₂²×C₄×C₈₉	—	2	2	no	—
189	C₂²×C₄×C₈₉	—	2	2	no	—
190	C₂²×C₄×C₈₉	—	2	4	no	—
191	C₂²×C₄×C₈₉	—	2	8	no	—
192	C₂²×C₄×C₈₉	—	2	8	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	4	2	no	—
195	C₂²×C₄×C₈₉	—	4	4	no	—
196	C₂²×C₄×C₈₉	—	4	2	no	—
197	C₂²×C₄×C₈₉	—	4	2	no	—
198	C₂²×C₄×C₈₉	—	4	4	no	—
199	C₂²×C₄×C₈₉	—	4	16	no	—
200	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₄⋊C₄×C₈₉	—	2	8	no	—
216	C₄⋊C₄×C₈₉	—	2	8	no	—
217	C₄⋊C₄×C₈₉	—	2	4	no	—
218	C₄⋊C₄×C₈₉	—	2	2	no	—
219	C₄⋊C₄×C₈₉	—	2	4	no	—
220	C₄⋊C₄×C₈₉	—	2	4	no	—
221	C₄⋊C₄×C₈₉	—	2	2	no	—
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	8	no	—
224	C₄⋊C₄×C₈₉	—	2	8	no	—
225	C₄⋊C₄×C₈₉	—	2	8	no	—
226	C₄⋊C₄×C₈₉	—	4	4	no	—
227	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
228	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
229	C₂²⋊C₄×C₈₉	—	2	4	no	—
230	C₂²⋊C₄×C₈₉	—	2	4	no	—
231	C₂²⋊C₄×C₈₉	—	2	8	no	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	8	no	—
235	C₂²⋊C₄×C₈₉	—	2	4	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	8	no	—
240	C₂²⋊C₄×C₈₉	—	2	8	no	—
241	C₂²⋊C₄×C₈₉	—	2	8	no	—
242	C₂²⋊C₄×C₈₉	—	4	4	no	—
243	C₂²⋊C₄×C₈₉	—	4	4	no	—
244	C₂²⋊C₄×C₈₉	#41	1	8	yes	—
245	C₄²×C₈₉	—	2	4	no	—
246	C₄²×C₈₉	—	2	8	no	—
247	C₄²×C₈₉	—	4	4	no	—
248	C₄²×C₈₉	—	4	2	no	—
249	C₄²×C₈₉	—	4	2	no	—
250	C₂³×C₈₉	—	2	2	no	—
251	C₂³×C₈₉	—	2	2	no	—
252	C₂³×C₈₉	—	2	8	no	—
253	C₂³×C₈₉	—	2	2	no	—
254	C₂³×C₈₉	—	2	4	no	—
255	C₂³×C₈₉	—	2	4	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	—	4	16	no	—
263	C₂³×C₈₉	—	4	4	no	—
264	C₂³×C₈₉	—	4	4	no	—
265	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
266	C₂³×C₈₉	C₂×#41	1	4	yes	—
267	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
268	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
269	Q₈×C₈₉	—	4	8	no	—
270	Q₈×C₈₉	—	4	8	no	—
271	Q₈×C₈₉	—	8	2	no	—
272	D₄×C₈₉	—	4	16	no	—
273	D₄×C₈₉	—	4	8	no	—
274	D₄×C₈₉	—	8	2	no	—
275	C₂×C₄×C₈₉	—	2	8	no	—
276	C₂×C₄×C₈₉	—	2	8	no	—
277	C₂×C₄×C₈₉	—	2	2	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	4	no	—
281	C₂×C₄×C₈₉	—	2	4	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	4	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	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	4	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	4	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	4	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	—	4	4	no	—
302	C₂×C₄×C₈₉	—	4	4	no	—
303	C₂×C₄×C₈₉	—	4	16	no	—
304	C₂×C₄×C₈₉	—	4	4	no	—
305	C₂×C₄×C₈₉	—	4	4	no	—
306	C₂×C₄×C₈₉	—	8	4	no	—
307	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
308	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
309	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
312	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
313	C₂²×C₈₉	—	2	2	no	—
314	C₂²×C₈₉	—	2	2	no	—
315	C₂²×C₈₉	—	2	8	no	—
316	C₂²×C₈₉	—	2	4	no	—
317	C₂²×C₈₉	—	2	8	no	—
318	C₂²×C₈₉	—	4	16	no	—
319	C₂²×C₈₉	—	4	2	no	—
320	C₂²×C₈₉	—	4	2	no	—
321	C₂²×C₈₉	—	4	4	no	—
322	C₂²×C₈₉	—	4	2	no	—
323	C₂²×C₈₉	—	4	2	no	—
324	C₂²×C₈₉	—	4	2	no	—
325	C₂²×C₈₉	—	4	4	no	—
326	C₂²×C₈₉	—	4	4	no	—
327	C₂²×C₈₉	#532	1	4	yes	—
328	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
329	C₂²×C₈₉	C₂²×#41	1	2	yes	—
330	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
332	C₄×C₈₉	—	2	4	no	—
333	C₄×C₈₉	—	2	4	no	—
334	C₄×C₈₉	—	2	4	no	—
335	C₄×C₈₉	—	2	2	no	—
336	C₄×C₈₉	—	2	2	no	—
337	C₄×C₈₉	—	2	8	no	—
338	C₄×C₈₉	—	4	2	no	—
339	C₄×C₈₉	—	4	2	no	—
340	C₄×C₈₉	—	4	2	no	—
341	C₄×C₈₉	—	4	2	no	—
342	C₄×C₈₉	—	4	2	no	—
343	C₄×C₈₉	—	4	4	no	—
344	#35397	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₈₉	—	2	4	no	—
346	C₂×C₈₉	—	4	4	no	—
347	C₂×C₈₉	—	8	2	no	—
348	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
349	C₂×C₈₉	#3484	1	1	yes	characteristic
350	C₂×C₈₉	#3486	1	1	yes	characteristic
351	C₂×C₈₉	#3520	1	4	yes	—
352	C₂×#539	C₂×C₈₉	1	1	yes	characteristic, complemented
353	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
354	#2561	C₂×C₈₉	1	1	yes	characteristic, complemented
355	#2560	C₂×C₈₉	1	4	yes	complemented
356	#2556	C₂×C₈₉	1	4	yes	complemented
357	#2539	C₂×C₈₉	1	1	yes	characteristic
358	#2461	C₂×C₈₉	1	4	yes	complemented
359	#2452	C₂×C₈₉	1	4	yes	complemented
360	#2436	C₂×C₈₉	1	1	yes	characteristic, complemented
361	#2434	C₂×C₈₉	1	1	yes	characteristic, complemented
362	#2413	C₂×C₈₉	1	2	yes	complemented
363	#2411	C₂×C₈₉	1	2	yes	complemented
364	#2322	C₂×C₈₉	1	2	yes	complemented
365	C₄×#120	C₂×C₈₉	1	2	yes	complemented
366	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₈₉	#35397	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
370	#539	—	2	8	no	—
371	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
372	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
373	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
374	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
375	C₂×#123	C₂²×C₈₉	1	2	yes	—
376	C₂×#123	C₂²×C₈₉	1	2	yes	—
377	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
378	C₂×C₂²⋊Q₈	—	2	8	no	—
379	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
380	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
383	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
384	C₂×#120	C₂²×C₈₉	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
387	C₂×#117	C₂²×C₈₉	1	2	yes	—
388	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
393	#399	C₂²×C₈₉	1	2	yes	—
394	#398	C₂²×C₈₉	1	4	yes	complemented
395	#397	C₂²×C₈₉	1	2	yes	—
396	#396	C₂²×C₈₉	1	4	yes	—
397	#396	C₂²×C₈₉	1	4	yes	complemented
398	#395	C₂²×C₈₉	1	4	yes	complemented
399	#394	C₂²×C₈₉	1	4	yes	—
400	#393	C₂²×C₈₉	1	2	yes	—
401	#393	C₂²×C₈₉	1	4	yes	complemented
402	#392	C₂²×C₈₉	1	2	yes	—
403	#391	C₂²×C₈₉	1	2	yes	complemented
404	#391	C₂²×C₈₉	1	2	yes	complemented
405	#390	C₂²×C₈₉	1	4	yes	—
406	#390	C₂²×C₈₉	1	4	yes	—
407	#389	C₂²×C₈₉	1	4	yes	complemented
408	#389	C₂²×C₈₉	1	4	yes	complemented
409	#388	C₂²×C₈₉	1	4	yes	—
410	#388	C₂²×C₈₉	1	4	yes	—
411	#388	C₂²×C₈₉	1	4	yes	complemented
412	#388	C₂²×C₈₉	1	4	yes	complemented
413	#387	C₂²×C₈₉	1	4	yes	complemented
414	#386	C₂²×C₈₉	1	4	yes	—
415	#386	C₂²×C₈₉	1	2	yes	—
416	#386	C₂²×C₈₉	1	2	yes	—
417	#385	C₂²×C₈₉	1	2	yes	—
418	#385	C₂²×C₈₉	1	2	yes	—
419	#385	C₂²×C₈₉	1	4	yes	—
420	#385	C₂²×C₈₉	1	4	yes	complemented
421	#381	C₂²×C₈₉	1	2	yes	—
422	#379	C₂²×C₈₉	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
424	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
425	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
427	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
429	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
430	C₂²×Q₈	—	2	4	no	—
431	C₂²×Q₈	—	4	4	no	—
432	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
433	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
434	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
435	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
436	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
437	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
438	C₂³×C₄	—	2	4	no	—
439	C₂³×C₄	—	4	4	no	—
440	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
443	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₄⋊Q₈	—	4	4	no	—
449	#126	—	2	8	no	—
450	#125	—	2	8	no	—
451	#124	—	4	4	no	—
452	#123	—	2	8	no	—
453	#123	—	2	8	no	—
454	#123	—	2	8	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	—	2	16	no	—
457	C₂²⋊Q₈	—	2	16	no	—
458	C₂²⋊Q₈	—	2	8	no	—
459	#121	—	2	4	no	—
460	#120	—	2	8	no	—
461	C₄×D₄	—	2	8	no	—
462	C₄×D₄	—	4	8	no	—
463	#117	—	2	8	no	—
464	C₂×C₄⋊C₄	—	2	4	no	—
465	C₂×C₄⋊C₄	—	2	4	no	—
466	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
467	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
481	C₂×C₂²⋊C₄	—	2	4	no	—
482	C₂×C₂²⋊C₄	—	2	4	no	—
483	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	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	2	yes	—
499	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
500	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
502	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
504	#95	C₂³×C₈₉	1	4	yes	—
505	#95	C₂³×C₈₉	1	2	yes	—
506	#95	C₂³×C₈₉	1	2	yes	—
507	#95	C₂³×C₈₉	1	4	yes	—
508	#95	C₂³×C₈₉	1	4	yes	—
509	#95	C₂³×C₈₉	1	4	yes	—
510	#95	C₂³×C₈₉	1	4	yes	—
511	#95	C₂³×C₈₉	1	4	yes	—
512	#95	C₂³×C₈₉	1	4	yes	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	4	no	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	4	2	no	—
517	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
518	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
519	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	—	4	2	no	—
528	C₂×Q₈	—	4	16	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	4	4	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	16	no	—
552	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
553	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
554	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
567	C₄⋊C₄	—	2	8	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	8	no	—
576	C₄⋊C₄	—	2	8	no	—
577	C₄⋊C₄	—	2	8	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
580	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	#41×C₈₉	1	8	yes	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	8	no	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	4	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	4	16	no	—
615	C₂³	—	4	4	no	—
616	C₂³	—	4	4	no	—
617	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
618	C₂³	C₂×#41×C₈₉	1	4	yes	—
619	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
620	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
621	Q₈	—	4	8	no	—
622	Q₈	—	4	8	no	—
623	Q₈	—	8	2	no	—
624	D₄	—	4	16	no	—
625	D₄	—	4	8	no	—
626	D₄	—	8	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	4	16	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	8	4	no	—
659	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
660	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
661	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
664	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	8	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	8	no	—
670	C₂²	—	4	16	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	4	no	—
678	C₂²	—	4	4	no	—
679	C₂²	#532×C₈₉	1	4	yes	—
680	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
681	C₂²	C₂²×#41×C₈₉	1	2	yes	—
682	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
683	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	8	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	4	no	—
696	C₂	—	2	4	no	—
697	C₂	—	4	4	no	—
698	C₂	—	8	2	no	—
699	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
700	C₂	C₈₉×#3484	1	1	yes	characteristic
701	C₂	C₈₉×#3486	1	1	yes	characteristic
702	C₂	C₈₉×#3520	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2539	C₂
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×#539×C₈₉	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₈₉	C₂	semidirect
3. C₈₉×#2561	C₂	semidirect
4. C₈₉×#2560	C₂	semidirect
5. C₈₉×#2556	C₂	semidirect
7. C₈₉×#2461	C₂	semidirect
8. C₈₉×#2452	C₂	semidirect
9. C₈₉×#2436	C₂	semidirect
10. C₈₉×#2434	C₂	semidirect
11. C₈₉×#2413	C₂	semidirect
12. C₈₉×#2411	C₂	semidirect
13. C₈₉×#2322	C₂	semidirect
14. C₄×#120×C₈₉	C₂	semidirect
15. C₈₉×#2274	C₂	semidirect
19. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
20. C₂×#126×C₈₉	C₂²	semidirect
21. C₂×#125×C₈₉	C₂²	semidirect
22. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×#123×C₈₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
42. #398×C₈₉	C₂²	semidirect
45. #396×C₈₉	C₂²	semidirect
46. #395×C₈₉	C₂²	semidirect
49. #393×C₈₉	C₂²	semidirect
51. #391×C₈₉	C₂²	semidirect
52. #391×C₈₉	C₂²	semidirect
55. #389×C₈₉	C₂²	semidirect
56. #389×C₈₉	C₂²	semidirect
59. #388×C₈₉	C₂²	semidirect
60. #388×C₈₉	C₂²	semidirect
61. #387×C₈₉	C₂²	semidirect
68. #385×C₈₉	C₂²	semidirect
71. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
72. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
114. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
344. #35397	C₈₉	direct (N × H)
352. C₂×#539	C₂×C₈₉	semidirect
353. C₂²×C₂²⋊Q₈	C₂×C₈₉	semidirect
354. #2561	C₂×C₈₉	semidirect
355. #2560	C₂×C₈₉	semidirect
356. #2556	C₂×C₈₉	semidirect
358. #2461	C₂×C₈₉	semidirect
359. #2452	C₂×C₈₉	semidirect
360. #2436	C₂×C₈₉	semidirect
361. #2434	C₂×C₈₉	semidirect
362. #2413	C₂×C₈₉	semidirect
363. #2411	C₂×C₈₉	semidirect
364. #2322	C₂×C₈₉	semidirect
365. C₄×#120	C₂×C₈₉	semidirect
366. #2274	C₂×C₈₉	semidirect
367. C₈₉	#35397	direct (N × H)
371. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
372. C₂×#126	C₂²×C₈₉	semidirect
373. C₂×#125	C₂²×C₈₉	semidirect
374. C₂×#124	C₂²×C₈₉	semidirect
377. C₂×#123	C₂²×C₈₉	semidirect
382. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
394. #398	C₂²×C₈₉	semidirect
397. #396	C₂²×C₈₉	semidirect
398. #395	C₂²×C₈₉	semidirect
401. #393	C₂²×C₈₉	semidirect
403. #391	C₂²×C₈₉	semidirect
404. #391	C₂²×C₈₉	semidirect
407. #389	C₂²×C₈₉	semidirect
408. #389	C₂²×C₈₉	semidirect
411. #388	C₂²×C₈₉	semidirect
412. #388	C₂²×C₈₉	semidirect
413. #387	C₂²×C₈₉	semidirect
420. #385	C₂²×C₈₉	semidirect
423. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
424. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
466. C₂×C₄⋊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×#539×C₈₉	2
C₂²×C₂²⋊Q₈×C₈₉	2
C₈₉×#2561	2
C₈₉×#2560	2
C₈₉×#2556	2
C₈₉×#2539	2
C₈₉×#2461	2
C₈₉×#2452	2
C₈₉×#2436	2
C₈₉×#2434	2
C₈₉×#2413	2
C₈₉×#2411	2
C₈₉×#2322	2
C₄×#120×C₈₉	2
C₈₉×#2274	2
#35397	89

Subgroups — C89×#35397 #36413245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35397 #36413245