Subgroups — C₈₉×#60934 #36438782

Order 22784.

1892 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3494	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3262	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3259	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3257	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3250	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3247	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3245	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3083	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3081	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#466×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3045	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3041	C₂	1	2	yes	maximal, complemented
15	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
17	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	#555×C₈₉	—	2	2	no	—
22	#553×C₈₉	—	2	2	no	—
23	#553×C₈₉	—	2	2	no	—
24	#551×C₈₉	—	2	4	no	—
25	#547×C₈₉	—	2	2	no	—
26	#546×C₈₉	—	2	4	no	—
27	#544×C₈₉	C₂²	1	2	yes	—
28	#542×C₈₉	C₂²	1	4	yes	complemented
29	#540×C₈₉	C₂²	1	4	yes	complemented
30	#535×C₈₉	C₂²	1	2	yes	—
31	#532×C₈₉	C₂²	1	4	yes	complemented
32	#529×C₈₉	C₂²	1	4	yes	complemented
33	#525×C₈₉	C₂²	1	2	yes	—
34	C₂×#121×C₈₉	C₂²	1	2	yes	—
35	#520×C₈₉	C₂²	1	2	yes	—
36	#518×C₈₉	C₂²	1	2	yes	—
37	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
38	#479×C₈₉	C₂²	1	4	yes	complemented
39	#478×C₈₉	C₂²	1	4	yes	complemented
40	#478×C₈₉	C₂²	1	4	yes	complemented
41	#478×C₈₉	C₂²	1	4	yes	complemented
42	#477×C₈₉	C₂²	1	4	yes	complemented
43	#476×C₈₉	C₂²	1	4	yes	complemented
44	#474×C₈₉	C₂²	1	4	yes	complemented
45	#474×C₈₉	C₂²	1	4	yes	complemented
46	#469×C₈₉	C₂²	1	4	yes	complemented
47	#468×C₈₉	C₂²	1	4	yes	complemented
48	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#466×C₈₉	C₂²	1	2	yes	—
51	#466×C₈₉	C₂²	1	2	yes	—
52	#466×C₈₉	C₂²	1	2	yes	—
53	#466×C₈₉	C₂²	1	2	yes	—
54	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#466×C₈₉	C₂²	1	4	yes	complemented
56	#466×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#465×C₈₉	C₂²	1	2	yes	complemented
58	#465×C₈₉	C₂²	1	4	yes	complemented
59	#465×C₈₉	C₂²	1	2	yes	complemented
60	#464×C₈₉	C₂²	1	4	yes	complemented
61	#463×C₈₉	C₂²	1	4	yes	complemented
62	#463×C₈₉	C₂²	1	4	yes	complemented
63	#463×C₈₉	C₂²	1	4	yes	complemented
64	#460×C₈₉	C₂²	1	4	yes	complemented
65	#459×C₈₉	C₂²	1	4	yes	complemented
66	#459×C₈₉	C₂²	1	4	yes	complemented
67	#459×C₈₉	C₂²	1	4	yes	complemented
68	#428×C₈₉	C₂²	1	2	yes	—
69	#427×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
71	#424×C₈₉	C₂²	1	2	yes	—
72	#424×C₈₉	C₂²	1	2	yes	—
73	#424×C₈₉	C₂²	1	2	yes	complemented
74	#424×C₈₉	C₂²	1	2	yes	complemented
75	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
76	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
77	#418×C₈₉	C₂²	1	2	yes	—
78	#417×C₈₉	C₂²	1	2	yes	—
79	#416×C₈₉	C₂²	1	2	yes	—
80	C₂×#102×C₈₉	C₂²	1	2	yes	—
81	C₂×#41×C₈₉	—	2	4	no	—
82	C₂×#41×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	—	2	2	no	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
86	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
87	#135×C₈₉	—	4	2	no	—
88	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
91	C₂×D₈×C₈₉	—	4	2	no	—
92	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×D₈×C₈₉	C₂³	1	4	yes	—
94	C₂×D₈×C₈₉	C₂³	1	2	yes	—
95	C₂×D₈×C₈₉	C₂³	1	2	yes	—
96	C₂×M₁₆×C₈₉	—	4	2	no	—
97	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂²×C₈×C₈₉	—	4	2	no	—
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₈₉	—	2	2	no	—
108	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
109	#127×C₈₉	C₂³	1	4	yes	—
110	#126×C₈₉	—	2	4	no	—
111	#126×C₈₉	—	2	4	no	—
112	#125×C₈₉	—	2	2	no	—
113	#125×C₈₉	C₂³	1	4	yes	—
114	#124×C₈₉	—	2	4	no	—
115	#124×C₈₉	—	2	4	no	—
116	#124×C₈₉	C₂³	1	4	yes	—
117	#123×C₈₉	—	2	2	no	—
118	#123×C₈₉	—	2	4	no	—
119	#123×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	4	no	—
121	#123×C₈₉	—	2	4	no	—
122	C₂²⋊Q₈×C₈₉	—	2	4	no	—
123	C₂²⋊Q₈×C₈₉	—	2	4	no	—
124	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
126	#121×C₈₉	—	2	2	no	—
127	#121×C₈₉	—	2	2	no	—
128	#121×C₈₉	—	2	4	no	—
129	#121×C₈₉	—	2	2	no	—
130	#121×C₈₉	—	2	2	no	—
131	#121×C₈₉	—	2	4	no	—
132	#121×C₈₉	—	2	4	no	—
133	#121×C₈₉	C₂³	1	4	yes	—
134	#121×C₈₉	C₂³	1	2	yes	—
135	#121×C₈₉	C₂³	1	2	yes	—
136	#121×C₈₉	C₂³	1	4	yes	—
137	#120×C₈₉	—	2	2	no	—
138	#120×C₈₉	—	2	4	no	—
139	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	—	2	2	no	—
142	C₄×D₄×C₈₉	—	2	4	no	—
143	C₄×D₄×C₈₉	—	2	2	no	—
144	C₄×D₄×C₈₉	—	2	2	no	—
145	C₄×D₄×C₈₉	—	2	4	no	—
146	C₄×D₄×C₈₉	—	2	4	no	—
147	C₄×D₄×C₈₉	C₂³	1	4	yes	—
148	C₄×D₄×C₈₉	C₂³	1	4	yes	—
149	C₄×D₄×C₈₉	C₂³	1	4	yes	—
150	#117×C₈₉	—	2	2	no	—
151	#117×C₈₉	—	2	4	no	—
152	#117×C₈₉	D₄	1	2	yes	—
153	#117×C₈₉	D₄	1	2	yes	—
154	#117×C₈₉	C₂³	1	2	yes	—
155	#117×C₈₉	C₂³	1	2	yes	—
156	#117×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
158	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	#107×C₈₉	C₂³	1	2	yes	—
166	#107×C₈₉	C₂³	1	2	yes	—
167	#107×C₈₉	C₂³	1	1	yes	characteristic
168	#107×C₈₉	C₂³	1	1	yes	characteristic
169	#107×C₈₉	C₂³	1	4	yes	—
170	#106×C₈₉	C₂³	1	2	yes	—
171	#106×C₈₉	C₂³	1	4	yes	—
172	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
173	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
174	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
175	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
176	#103×C₈₉	C₂³	1	2	yes	—
177	#103×C₈₉	C₂³	1	2	yes	—
178	#103×C₈₉	C₂³	1	4	yes	—
179	#102×C₈₉	C₂³	1	4	yes	—
180	#102×C₈₉	C₂³	1	4	yes	—
181	#102×C₈₉	C₂³	1	2	yes	—
182	#102×C₈₉	C₂³	1	2	yes	—
183	#102×C₈₉	C₂³	1	4	yes	—
184	#102×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	C₂⁴×C₈₉	—	2	2	no	—
187	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
188	#41×C₈₉	—	2	4	no	—
189	#41×C₈₉	—	2	4	no	—
190	#41×C₈₉	—	8	8	no	—
191	C₂×Q₈×C₈₉	—	2	4	no	—
192	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
193	C₂×D₄×C₈₉	—	2	2	no	—
194	C₂×D₄×C₈₉	—	2	2	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	2	no	—
197	C₂×D₄×C₈₉	—	2	4	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	4	no	—
201	C₂×D₄×C₈₉	—	2	4	no	—
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	8	4	no	—
204	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
205	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	Q₁₆×C₈₉	—	4	1	no	—
222	SD₁₆×C₈₉	—	4	2	no	—
223	SD₁₆×C₈₉	—	4	4	no	—
224	D₈×C₈₉	—	4	2	no	—
225	D₈×C₈₉	—	4	2	no	—
226	D₈×C₈₉	—	4	1	no	—
227	D₈×C₈₉	—	4	4	no	—
228	M₁₆×C₈₉	—	2	4	no	—
229	M₁₆×C₈₉	—	4	2	no	—
230	C₂×C₈×C₈₉	—	2	2	no	—
231	C₂×C₈×C₈₉	—	2	2	no	—
232	C₂×C₈×C₈₉	—	4	1	no	—
233	C₂×C₈×C₈₉	—	4	1	no	—
234	C₂×C₈×C₈₉	—	4	1	no	—
235	C₂×C₈×C₈₉	—	4	1	no	—
236	C₂×C₈×C₈₉	—	4	2	no	—
237	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
240	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	2	no	—
249	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₈₉	—	2	2	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	2	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	2	no	—
268	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
269	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
270	C₄²×C₈₉	—	2	4	no	—
271	C₄²×C₈₉	—	2	2	no	—
272	C₄²×C₈₉	C₂×D₄	1	4	yes	—
273	C₄²×C₈₉	C₂⁴	1	4	yes	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	4	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	4	1	no	—
279	C₂³×C₈₉	—	4	4	no	—
280	C₂³×C₈₉	—	8	2	no	—
281	C₂³×C₈₉	—	8	2	no	—
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₈₉	—	2	2	no	—
286	Q₈×C₈₉	—	2	2	no	—
287	Q₈×C₈₉	—	8	4	no	—
288	D₄×C₈₉	—	2	4	no	—
289	D₄×C₈₉	—	2	2	no	—
290	D₄×C₈₉	—	2	4	no	—
291	D₄×C₈₉	—	2	2	no	—
292	D₄×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	4	8	no	—
294	D₄×C₈₉	—	4	4	no	—
295	D₄×C₈₉	—	4	4	no	—
296	D₄×C₈₉	—	8	4	no	—
297	D₄×C₈₉	—	8	4	no	—
298	D₄×C₈₉	—	8	2	no	—
299	D₄×C₈₉	—	8	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	2	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	4	no	—
312	C₂×C₄×C₈₉	—	4	2	no	—
313	C₂×C₄×C₈₉	—	4	4	no	—
314	C₂×C₄×C₈₉	—	8	4	no	—
315	C₂×C₄×C₈₉	—	8	4	no	—
316	C₂×C₄×C₈₉	—	8	4	no	—
317	C₂×C₄×C₈₉	—	8	2	no	—
318	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
324	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
325	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
326	C₈×C₈₉	—	2	1	no	—
327	C₈×C₈₉	—	2	1	no	—
328	C₈×C₈₉	—	2	1	no	—
329	C₈×C₈₉	—	2	1	no	—
330	C₈×C₈₉	—	2	4	no	—
331	C₂²×C₈₉	—	2	1	no	—
332	C₂²×C₈₉	—	2	1	no	—
333	C₂²×C₈₉	—	2	1	no	—
334	C₂²×C₈₉	—	2	1	no	—
335	C₂²×C₈₉	—	2	1	no	—
336	C₂²×C₈₉	—	2	1	no	—
337	C₂²×C₈₉	—	2	1	no	—
338	C₂²×C₈₉	—	4	4	no	—
339	C₂²×C₈₉	—	4	4	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	4	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	4	4	no	—
345	C₂²×C₈₉	—	16	4	no	—
346	C₂²×C₈₉	#537	1	2	yes	—
347	C₂²×C₈₉	#576	1	2	yes	—
348	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₈₉	—	2	4	no	—
350	C₄×C₈₉	—	2	1	no	—
351	C₄×C₈₉	—	2	1	no	—
352	C₄×C₈₉	—	2	4	no	—
353	C₄×C₈₉	—	4	2	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	4	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	#537	1	2	yes	—
358	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	#60934	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₈₉	—	2	2	no	—
362	C₂×C₈₉	—	2	2	no	—
363	C₂×C₈₉	—	4	1	no	—
364	C₂×C₈₉	—	8	2	no	—
365	C₂×C₈₉	—	8	4	no	—
366	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
367	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
368	C₂×C₈₉	#3584	1	1	yes	characteristic
369	#3494	C₂×C₈₉	1	2	yes	complemented
370	#3262	C₂×C₈₉	1	2	yes	complemented
371	#3259	C₂×C₈₉	1	2	yes	complemented
372	#3257	C₂×C₈₉	1	4	yes	complemented
373	#3250	C₂×C₈₉	1	2	yes	complemented
374	#3247	C₂×C₈₉	1	4	yes	complemented
375	#3245	C₂×C₈₉	1	2	yes	complemented
376	#3083	C₂×C₈₉	1	2	yes	complemented
377	#3081	C₂×C₈₉	1	2	yes	complemented
378	#3055	C₂×C₈₉	1	2	yes	complemented
379	#3050	C₂×C₈₉	1	1	yes	characteristic, complemented
380	C₂×#466	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#3045	C₂×C₈₉	1	2	yes	complemented
382	#3041	C₂×C₈₉	1	2	yes	complemented
383	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
384	C₈₉	#60934	1	1	yes	characteristic, direct product factor, Sylow
385	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
386	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
388	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
389	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
390	#555	—	2	2	no	—
391	#553	—	2	2	no	—
392	#553	—	2	2	no	—
393	#551	—	2	4	no	—
394	#547	—	2	2	no	—
395	#546	—	2	4	no	—
396	#544	C₂²×C₈₉	1	2	yes	—
397	#542	C₂²×C₈₉	1	4	yes	complemented
398	#540	C₂²×C₈₉	1	4	yes	complemented
399	#535	C₂²×C₈₉	1	2	yes	—
400	#532	C₂²×C₈₉	1	4	yes	complemented
401	#529	C₂²×C₈₉	1	4	yes	complemented
402	#525	C₂²×C₈₉	1	2	yes	—
403	C₂×#121	C₂²×C₈₉	1	2	yes	—
404	#520	C₂²×C₈₉	1	2	yes	—
405	#518	C₂²×C₈₉	1	2	yes	—
406	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
407	#479	C₂²×C₈₉	1	4	yes	complemented
408	#478	C₂²×C₈₉	1	4	yes	complemented
409	#478	C₂²×C₈₉	1	4	yes	complemented
410	#478	C₂²×C₈₉	1	4	yes	complemented
411	#477	C₂²×C₈₉	1	4	yes	complemented
412	#476	C₂²×C₈₉	1	4	yes	complemented
413	#474	C₂²×C₈₉	1	4	yes	complemented
414	#474	C₂²×C₈₉	1	4	yes	complemented
415	#469	C₂²×C₈₉	1	4	yes	complemented
416	#468	C₂²×C₈₉	1	4	yes	complemented
417	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
418	#467	C₂²×C₈₉	1	1	yes	characteristic, complemented
419	#466	C₂²×C₈₉	1	2	yes	—
420	#466	C₂²×C₈₉	1	2	yes	—
421	#466	C₂²×C₈₉	1	2	yes	—
422	#466	C₂²×C₈₉	1	2	yes	—
423	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
424	#466	C₂²×C₈₉	1	4	yes	complemented
425	#466	C₂²×C₈₉	1	1	yes	characteristic, complemented
426	#465	C₂²×C₈₉	1	2	yes	complemented
427	#465	C₂²×C₈₉	1	4	yes	complemented
428	#465	C₂²×C₈₉	1	2	yes	complemented
429	#464	C₂²×C₈₉	1	4	yes	complemented
430	#463	C₂²×C₈₉	1	4	yes	complemented
431	#463	C₂²×C₈₉	1	4	yes	complemented
432	#463	C₂²×C₈₉	1	4	yes	complemented
433	#460	C₂²×C₈₉	1	4	yes	complemented
434	#459	C₂²×C₈₉	1	4	yes	complemented
435	#459	C₂²×C₈₉	1	4	yes	complemented
436	#459	C₂²×C₈₉	1	4	yes	complemented
437	#428	C₂²×C₈₉	1	2	yes	—
438	#427	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
440	#424	C₂²×C₈₉	1	2	yes	—
441	#424	C₂²×C₈₉	1	2	yes	—
442	#424	C₂²×C₈₉	1	2	yes	complemented
443	#424	C₂²×C₈₉	1	2	yes	complemented
444	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
445	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
446	#418	C₂²×C₈₉	1	2	yes	—
447	#417	C₂²×C₈₉	1	2	yes	—
448	#416	C₂²×C₈₉	1	2	yes	—
449	C₂×#102	C₂²×C₈₉	1	2	yes	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	C₂³×C₈₉	1	2	yes	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
455	AGL(1,ℤ/8)	—	4	4	no	—
456	#135	—	4	2	no	—
457	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
458	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
459	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
460	C₂×D₈	—	4	2	no	—
461	C₂×D₈	C₂³×C₈₉	1	2	yes	—
462	C₂×D₈	C₂³×C₈₉	1	2	yes	—
463	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
464	C₂×D₈	C₂³×C₈₉	1	4	yes	—
465	C₂×M₁₆	—	4	2	no	—
466	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
467	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
468	C₂²×C₈	—	4	2	no	—
469	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
478	#127	C₂³×C₈₉	1	4	yes	—
479	#126	—	2	4	no	—
480	#126	—	2	4	no	—
481	#125	—	2	2	no	—
482	#125	C₂³×C₈₉	1	4	yes	—
483	#124	—	2	4	no	—
484	#124	—	2	4	no	—
485	#124	C₂³×C₈₉	1	4	yes	—
486	#123	—	2	2	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
494	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	4	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	4	no	—
501	#121	—	2	4	no	—
502	#121	C₂³×C₈₉	1	4	yes	—
503	#121	C₂³×C₈₉	1	4	yes	—
504	#121	C₂³×C₈₉	1	2	yes	—
505	#121	C₂³×C₈₉	1	2	yes	—
506	#120	—	2	2	no	—
507	#120	—	2	4	no	—
508	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	C₂³×C₈₉	1	4	yes	—
517	C₄×D₄	C₂³×C₈₉	1	4	yes	—
518	C₄×D₄	C₂³×C₈₉	1	4	yes	—
519	#117	—	2	2	no	—
520	#117	—	2	4	no	—
521	#117	D₄×C₈₉	1	2	yes	—
522	#117	D₄×C₈₉	1	2	yes	—
523	#117	C₂³×C₈₉	1	2	yes	—
524	#117	C₂³×C₈₉	1	2	yes	—
525	#117	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₂²⋊C₄	—	2	2	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
534	#107	C₂³×C₈₉	1	2	yes	—
535	#107	C₂³×C₈₉	1	2	yes	—
536	#107	C₂³×C₈₉	1	1	yes	characteristic
537	#107	C₂³×C₈₉	1	1	yes	characteristic
538	#107	C₂³×C₈₉	1	4	yes	—
539	#106	C₂³×C₈₉	1	2	yes	—
540	#106	C₂³×C₈₉	1	4	yes	—
541	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
542	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
543	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
544	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
545	#103	C₂³×C₈₉	1	2	yes	—
546	#103	C₂³×C₈₉	1	2	yes	—
547	#103	C₂³×C₈₉	1	4	yes	—
548	#102	C₂³×C₈₉	1	4	yes	—
549	#102	C₂³×C₈₉	1	4	yes	—
550	#102	C₂³×C₈₉	1	2	yes	—
551	#102	C₂³×C₈₉	1	2	yes	—
552	#102	C₂³×C₈₉	1	4	yes	—
553	#102	C₂³×C₈₉	1	4	yes	—
554	#102	C₂³×C₈₉	1	4	yes	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
557	#41	—	2	4	no	—
558	#41	—	2	4	no	—
559	#41	—	8	8	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	8	4	no	—
573	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
574	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
590	Q₁₆	—	4	1	no	—
591	SD₁₆	—	4	2	no	—
592	SD₁₆	—	4	4	no	—
593	D₈	—	4	2	no	—
594	D₈	—	4	2	no	—
595	D₈	—	4	1	no	—
596	D₈	—	4	4	no	—
597	M₁₆	—	2	4	no	—
598	M₁₆	—	4	2	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	4	1	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	—	4	1	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	—	4	2	no	—
606	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
607	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
608	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
609	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
624	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
638	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	C₂×D₄×C₈₉	1	4	yes	—
642	C₄²	C₂⁴×C₈₉	1	4	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	8	2	no	—
650	C₂³	—	8	2	no	—
651	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
652	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
653	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	8	4	no	—
657	D₄	—	2	4	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	4	no	—
665	D₄	—	8	4	no	—
666	D₄	—	8	4	no	—
667	D₄	—	8	2	no	—
668	D₄	—	8	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
690	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
692	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
693	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
694	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	2	1	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	4	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	16	4	no	—
715	C₂²	#537×C₈₉	1	2	yes	—
716	C₂²	#576×C₈₉	1	2	yes	—
717	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	4	4	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	#537×C₈₉	1	2	yes	—
727	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
728	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
729	C₂	—	2	2	no	—
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	8	2	no	—
733	C₂	—	8	4	no	—
734	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
735	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
736	C₂	C₈₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3494	C₂	semidirect
2. C₈₉×#3262	C₂	semidirect
3. C₈₉×#3259	C₂	semidirect
4. C₈₉×#3257	C₂	semidirect
5. C₈₉×#3250	C₂	semidirect
6. C₈₉×#3247	C₂	semidirect
7. C₈₉×#3245	C₂	semidirect
8. C₈₉×#3083	C₂	semidirect
9. C₈₉×#3081	C₂	semidirect
10. C₈₉×#3055	C₂	semidirect
11. C₈₉×#3050	C₂	semidirect
12. C₂×#466×C₈₉	C₂	semidirect
13. C₈₉×#3045	C₂	semidirect
14. C₈₉×#3041	C₂	semidirect
15. C₂×#424×C₈₉	C₂	semidirect
28. #542×C₈₉	C₂²	semidirect
29. #540×C₈₉	C₂²	semidirect
31. #532×C₈₉	C₂²	semidirect
32. #529×C₈₉	C₂²	semidirect
38. #479×C₈₉	C₂²	semidirect
39. #478×C₈₉	C₂²	semidirect
40. #478×C₈₉	C₂²	semidirect
41. #478×C₈₉	C₂²	semidirect
42. #477×C₈₉	C₂²	semidirect
43. #476×C₈₉	C₂²	semidirect
44. #474×C₈₉	C₂²	semidirect
45. #474×C₈₉	C₂²	semidirect
46. #469×C₈₉	C₂²	semidirect
47. #468×C₈₉	C₂²	semidirect
48. #467×C₈₉	C₂²	semidirect
49. #467×C₈₉	C₂²	semidirect
54. #466×C₈₉	C₂²	semidirect
55. #466×C₈₉	C₂²	semidirect
56. #466×C₈₉	C₂²	semidirect
57. #465×C₈₉	C₂²	semidirect
58. #465×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #463×C₈₉	C₂²	semidirect
62. #463×C₈₉	C₂²	semidirect
63. #463×C₈₉	C₂²	semidirect
64. #460×C₈₉	C₂²	semidirect
65. #459×C₈₉	C₂²	semidirect
66. #459×C₈₉	C₂²	semidirect
67. #459×C₈₉	C₂²	semidirect
73. #424×C₈₉	C₂²	semidirect
74. #424×C₈₉	C₂²	semidirect
75. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
76. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
360. #60934	C₈₉	direct (N × H)
369. #3494	C₂×C₈₉	semidirect
370. #3262	C₂×C₈₉	semidirect
371. #3259	C₂×C₈₉	semidirect
372. #3257	C₂×C₈₉	semidirect
373. #3250	C₂×C₈₉	semidirect
374. #3247	C₂×C₈₉	semidirect
375. #3245	C₂×C₈₉	semidirect
376. #3083	C₂×C₈₉	semidirect
377. #3081	C₂×C₈₉	semidirect
378. #3055	C₂×C₈₉	semidirect
379. #3050	C₂×C₈₉	semidirect
380. C₂×#466	C₂×C₈₉	semidirect
381. #3045	C₂×C₈₉	semidirect
382. #3041	C₂×C₈₉	semidirect
383. C₂×#424	C₂×C₈₉	semidirect
384. C₈₉	#60934	direct (N × H)
397. #542	C₂²×C₈₉	semidirect
398. #540	C₂²×C₈₉	semidirect
400. #532	C₂²×C₈₉	semidirect
401. #529	C₂²×C₈₉	semidirect
407. #479	C₂²×C₈₉	semidirect
408. #478	C₂²×C₈₉	semidirect
409. #478	C₂²×C₈₉	semidirect
410. #478	C₂²×C₈₉	semidirect
411. #477	C₂²×C₈₉	semidirect
412. #476	C₂²×C₈₉	semidirect
413. #474	C₂²×C₈₉	semidirect
414. #474	C₂²×C₈₉	semidirect
415. #469	C₂²×C₈₉	semidirect
416. #468	C₂²×C₈₉	semidirect
417. #467	C₂²×C₈₉	semidirect
418. #467	C₂²×C₈₉	semidirect
423. #466	C₂²×C₈₉	semidirect
424. #466	C₂²×C₈₉	semidirect
425. #466	C₂²×C₈₉	semidirect
426. #465	C₂²×C₈₉	semidirect
427. #465	C₂²×C₈₉	semidirect
428. #465	C₂²×C₈₉	semidirect
429. #464	C₂²×C₈₉	semidirect
430. #463	C₂²×C₈₉	semidirect
431. #463	C₂²×C₈₉	semidirect
432. #463	C₂²×C₈₉	semidirect
433. #460	C₂²×C₈₉	semidirect
434. #459	C₂²×C₈₉	semidirect
435. #459	C₂²×C₈₉	semidirect
436. #459	C₂²×C₈₉	semidirect
442. #424	C₂²×C₈₉	semidirect
443. #424	C₂²×C₈₉	semidirect
444. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
445. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3494	2
C₈₉×#3262	2
C₈₉×#3259	2
C₈₉×#3257	2
C₈₉×#3250	2
C₈₉×#3247	2
C₈₉×#3245	2
C₈₉×#3083	2
C₈₉×#3081	2
C₈₉×#3055	2
C₈₉×#3050	2
C₂×#466×C₈₉	2
C₈₉×#3045	2
C₈₉×#3041	2
C₂×#424×C₈₉	2
#60934	89

Subgroups — C89×#60934 #36438782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60934 #36438782