Subgroups — C₈₉×#60698 #36438546

Order 22784.

1970 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3460	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3184	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3183	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3180	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3179	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3176	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3173	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3062	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
23	#544×C₈₉	C₂²	1	2	yes	—
24	#542×C₈₉	—	2	2	no	—
25	#542×C₈₉	C₂²	1	4	yes	complemented
26	#540×C₈₉	—	2	2	no	—
27	#540×C₈₉	C₂²	1	4	yes	complemented
28	#538×C₈₉	—	2	4	no	—
29	#537×C₈₉	C₂²	1	2	yes	—
30	#535×C₈₉	C₂²	1	2	yes	—
31	#535×C₈₉	C₂²	1	2	yes	—
32	#532×C₈₉	—	2	2	no	—
33	#532×C₈₉	C₂²	1	4	yes	complemented
34	#529×C₈₉	—	2	2	no	—
35	#529×C₈₉	C₂²	1	4	yes	complemented
36	#525×C₈₉	—	2	4	no	—
37	C₄×#41×C₈₉	C₂²	1	2	yes	—
38	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
40	#501×C₈₉	C₂²	1	4	yes	complemented
41	#499×C₈₉	C₂²	1	2	yes	complemented
42	#498×C₈₉	C₂²	1	2	yes	complemented
43	#496×C₈₉	C₂²	1	4	yes	—
44	#495×C₈₉	C₂²	1	2	yes	—
45	#493×C₈₉	C₂²	1	2	yes	—
46	#490×C₈₉	C₂²	1	4	yes	complemented
47	#489×C₈₉	C₂²	1	4	yes	complemented
48	#488×C₈₉	C₂²	1	4	yes	complemented
49	#486×C₈₉	C₂²	1	4	yes	complemented
50	#470×C₈₉	C₂²	1	2	yes	complemented
51	#469×C₈₉	C₂²	1	2	yes	—
52	#469×C₈₉	C₂²	1	2	yes	—
53	#469×C₈₉	C₂²	1	4	yes	complemented
54	#469×C₈₉	C₂²	1	2	yes	complemented
55	#468×C₈₉	C₂²	1	4	yes	complemented
56	#466×C₈₉	C₂²	1	4	yes	—
57	#466×C₈₉	C₂²	1	4	yes	complemented
58	#465×C₈₉	C₂²	1	4	yes	complemented
59	#465×C₈₉	C₂²	1	4	yes	complemented
60	#442×C₈₉	C₂²	1	2	yes	—
61	#442×C₈₉	C₂²	1	2	yes	—
62	#442×C₈₉	C₂²	1	2	yes	—
63	#442×C₈₉	C₂²	1	2	yes	—
64	#442×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#442×C₈₉	C₂²	1	4	yes	complemented
66	#442×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#441×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#441×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#440×C₈₉	C₂²	1	2	yes	complemented
70	#440×C₈₉	C₂²	1	2	yes	complemented
71	#440×C₈₉	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
73	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
74	#428×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
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	#405×C₈₉	C₂²	1	1	yes	characteristic
82	#405×C₈₉	C₂²	1	1	yes	characteristic
83	#405×C₈₉	C₂²	1	2	yes	complemented
84	#405×C₈₉	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
87	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
88	C₂×#97×C₈₉	C₂²	1	2	yes	complemented
89	C₂×#41×C₈₉	—	2	4	no	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₈₉	—	2	2	no	—
94	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
95	#135×C₈₉	—	2	4	no	—
96	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂×D₈×C₈₉	—	2	4	no	—
100	C₂×D₈×C₈₉	C₂³	1	4	yes	—
101	C₂×D₈×C₈₉	C₂³	1	2	yes	—
102	C₂×D₈×C₈₉	C₂³	1	2	yes	—
103	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
104	#131×C₈₉	—	2	4	no	—
105	#131×C₈₉	—	2	4	no	—
106	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
112	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₈₉	—	2	2	no	—
115	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
116	#127×C₈₉	—	2	2	no	—
117	#127×C₈₉	C₂³	1	4	yes	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	4	no	—
120	#125×C₈₉	—	2	2	no	—
121	#125×C₈₉	C₂³	1	4	yes	—
122	#124×C₈₉	—	2	2	no	—
123	#124×C₈₉	—	2	4	no	—
124	#124×C₈₉	—	2	4	no	—
125	#124×C₈₉	C₂³	1	4	yes	—
126	#123×C₈₉	—	2	4	no	—
127	#123×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	4	no	—
130	C₂²⋊Q₈×C₈₉	—	2	2	no	—
131	C₂²⋊Q₈×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
134	#121×C₈₉	—	2	4	no	—
135	#121×C₈₉	—	2	2	no	—
136	#121×C₈₉	—	2	4	no	—
137	#121×C₈₉	—	2	2	no	—
138	#121×C₈₉	—	2	2	no	—
139	#121×C₈₉	—	2	4	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	C₂³	1	4	yes	—
142	#121×C₈₉	C₂³	1	4	yes	—
143	#121×C₈₉	C₂³	1	4	yes	—
144	#120×C₈₉	—	2	4	no	—
145	#120×C₈₉	—	2	4	no	—
146	C₄×Q₈×C₈₉	D₄	1	2	yes	—
147	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
148	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	4	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	4	no	—
155	C₄×D₄×C₈₉	D₄	1	4	yes	—
156	C₄×D₄×C₈₉	D₄	1	2	yes	—
157	C₄×D₄×C₈₉	C₂³	1	2	yes	—
158	C₄×D₄×C₈₉	C₂³	1	4	yes	—
159	C₄×D₄×C₈₉	C₂³	1	4	yes	—
160	C₄×D₄×C₈₉	C₂³	1	2	yes	—
161	#117×C₈₉	—	2	2	no	—
162	#117×C₈₉	—	2	4	no	—
163	#117×C₈₉	C₂³	1	2	yes	—
164	#117×C₈₉	C₂³	1	1	yes	characteristic
165	#117×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
168	C₂×C₄²×C₈₉	—	2	2	no	—
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
171	#107×C₈₉	C₂³	1	2	yes	—
172	#107×C₈₉	C₂³	1	4	yes	—
173	#106×C₈₉	C₂³	1	2	yes	—
174	#106×C₈₉	C₂³	1	2	yes	—
175	#106×C₈₉	C₂³	1	1	yes	characteristic
176	#106×C₈₉	C₂³	1	1	yes	characteristic
177	#106×C₈₉	C₂³	1	4	yes	—
178	#103×C₈₉	C₂³	1	2	yes	—
179	#103×C₈₉	C₂³	1	2	yes	—
180	#103×C₈₉	C₂³	1	4	yes	—
181	#102×C₈₉	C₂³	1	4	yes	—
182	#102×C₈₉	C₂³	1	4	yes	—
183	#102×C₈₉	C₂³	1	2	yes	—
184	#102×C₈₉	C₂³	1	2	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	#102×C₈₉	C₂³	1	4	yes	—
187	#102×C₈₉	C₂³	1	4	yes	—
188	#97×C₈₉	C₂³	1	1	yes	characteristic
189	#97×C₈₉	C₂³	1	1	yes	characteristic
190	#97×C₈₉	C₂³	1	1	yes	characteristic
191	#97×C₈₉	C₂³	1	1	yes	characteristic
192	#97×C₈₉	C₂³	1	2	yes	—
193	#97×C₈₉	C₂³	1	2	yes	—
194	#97×C₈₉	C₂³	1	2	yes	—
195	C₄×C₈×C₈₉	C₂³	1	2	yes	—
196	C₄×C₈×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	C₂⁴×C₈₉	—	2	2	no	—
199	#41×C₈₉	—	2	2	no	—
200	#41×C₈₉	—	2	2	no	—
201	#41×C₈₉	—	2	4	no	—
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	8	8	no	—
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	2	4	no	—
209	C₂×D₄×C₈₉	—	2	4	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	4	no	—
216	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
219	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	2	2	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	8	4	no	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₈₉	—	2	2	no	—
232	SD₁₆×C₈₉	—	2	4	no	—
233	SD₁₆×C₈₉	—	2	8	no	—
234	D₈×C₈₉	—	2	4	no	—
235	D₈×C₈₉	—	2	4	no	—
236	D₈×C₈₉	—	2	2	no	—
237	D₈×C₈₉	—	2	8	no	—
238	M₁₆×C₈₉	—	2	2	no	—
239	M₁₆×C₈₉	—	2	4	no	—
240	M₁₆×C₈₉	—	2	4	no	—
241	M₁₆×C₈₉	#41	1	4	yes	complemented
242	C₂×C₈×C₈₉	—	2	2	no	—
243	C₂×C₈×C₈₉	—	2	4	no	—
244	C₂×C₈×C₈₉	—	2	4	no	—
245	C₂×C₈×C₈₉	#41	1	4	yes	complemented
246	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
251	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₄⋊C₄×C₈₉	—	2	2	no	—
253	C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
262	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	2	no	—
269	C₂²⋊C₄×C₈₉	—	2	2	no	—
270	C₂²⋊C₄×C₈₉	—	2	4	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
277	C₄²×C₈₉	—	2	2	no	—
278	C₄²×C₈₉	—	2	2	no	—
279	C₄²×C₈₉	—	2	2	no	—
280	C₄²×C₈₉	C₂×D₄	1	2	yes	—
281	C₄²×C₈₉	C₂×D₄	1	4	yes	—
282	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
283	C₄²×C₈₉	C₂⁴	1	2	yes	—
284	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
285	C₂³×C₈₉	—	2	4	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	4	4	no	—
288	C₂³×C₈₉	—	8	2	no	—
289	C₂³×C₈₉	—	8	2	no	—
290	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
291	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₈₉	—	2	2	no	—
293	Q₈×C₈₉	—	2	2	no	—
294	Q₈×C₈₉	—	2	2	no	—
295	Q₈×C₈₉	—	8	4	no	—
296	D₄×C₈₉	—	2	4	no	—
297	D₄×C₈₉	—	2	2	no	—
298	D₄×C₈₉	—	2	4	no	—
299	D₄×C₈₉	—	2	2	no	—
300	D₄×C₈₉	—	2	4	no	—
301	D₄×C₈₉	—	2	2	no	—
302	D₄×C₈₉	—	4	4	no	—
303	D₄×C₈₉	—	4	4	no	—
304	D₄×C₈₉	—	8	4	no	—
305	D₄×C₈₉	—	8	4	no	—
306	D₄×C₈₉	—	8	4	no	—
307	D₄×C₈₉	—	8	4	no	—
308	D₄×C₈₉	—	8	4	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	4	2	no	—
316	C₂×C₄×C₈₉	—	4	4	no	—
317	C₂×C₄×C₈₉	—	4	8	no	—
318	C₂×C₄×C₈₉	—	4	4	no	—
319	C₂×C₄×C₈₉	—	4	4	no	—
320	C₂×C₄×C₈₉	—	8	2	no	—
321	C₂×C₄×C₈₉	—	8	4	no	—
322	C₂×C₄×C₈₉	—	8	2	no	—
323	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
331	C₈×C₈₉	—	2	1	no	—
332	C₈×C₈₉	—	2	1	no	—
333	C₈×C₈₉	—	2	2	no	—
334	C₈×C₈₉	C₂×#41	1	2	yes	—
335	C₈×C₈₉	C₂×#41	1	4	yes	—
336	C₈×C₈₉	C₂×#41	1	2	yes	—
337	C₂²×C₈₉	—	2	2	no	—
338	C₂²×C₈₉	—	2	4	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	4	4	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	4	no	—
344	C₂²×C₈₉	—	4	2	no	—
345	C₂²×C₈₉	—	4	4	no	—
346	C₂²×C₈₉	—	8	8	no	—
347	C₂²×C₈₉	#532	1	2	yes	—
348	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	2	2	no	—
351	C₄×C₈₉	—	2	4	no	—
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	4	4	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	2	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	#532	1	2	yes	—
358	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
360	#60698	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₈₉	—	2	2	no	—
362	C₂×C₈₉	—	4	2	no	—
363	C₂×C₈₉	—	8	2	no	—
364	C₂×C₈₉	—	8	4	no	—
365	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
366	C₂×C₈₉	#3585	1	2	yes	—
367	#3460	C₂×C₈₉	1	2	yes	complemented
368	#3184	C₂×C₈₉	1	2	yes	complemented
369	#3183	C₂×C₈₉	1	2	yes	complemented
370	#3180	C₂×C₈₉	1	4	yes	complemented
371	#3179	C₂×C₈₉	1	4	yes	complemented
372	#3176	C₂×C₈₉	1	2	yes	complemented
373	#3173	C₂×C₈₉	1	2	yes	complemented
374	#3163	C₂×C₈₉	1	1	yes	characteristic, complemented
375	#3155	C₂×C₈₉	1	1	yes	characteristic, complemented
376	#3136	C₂×C₈₉	1	2	yes	complemented
377	#3062	C₂×C₈₉	1	2	yes	complemented
378	#3060	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#3058	C₂×C₈₉	1	1	yes	characteristic, complemented
380	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	2	yes	complemented
381	#2943	C₂×C₈₉	1	1	yes	characteristic, complemented
382	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
383	#2875	C₂×C₈₉	1	1	yes	characteristic, complemented
384	C₈₉	#60698	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	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
389	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
390	#544	C₂²×C₈₉	1	2	yes	—
391	#542	—	2	2	no	—
392	#542	C₂²×C₈₉	1	4	yes	complemented
393	#540	—	2	2	no	—
394	#540	C₂²×C₈₉	1	4	yes	complemented
395	#538	—	2	4	no	—
396	#537	C₂²×C₈₉	1	2	yes	—
397	#535	C₂²×C₈₉	1	2	yes	—
398	#535	C₂²×C₈₉	1	2	yes	—
399	#532	—	2	2	no	—
400	#532	C₂²×C₈₉	1	4	yes	complemented
401	#529	—	2	2	no	—
402	#529	C₂²×C₈₉	1	4	yes	complemented
403	#525	—	2	4	no	—
404	C₄×#41	C₂²×C₈₉	1	2	yes	—
405	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
407	#501	C₂²×C₈₉	1	4	yes	complemented
408	#499	C₂²×C₈₉	1	2	yes	complemented
409	#498	C₂²×C₈₉	1	2	yes	complemented
410	#496	C₂²×C₈₉	1	4	yes	—
411	#495	C₂²×C₈₉	1	2	yes	—
412	#493	C₂²×C₈₉	1	2	yes	—
413	#490	C₂²×C₈₉	1	4	yes	complemented
414	#489	C₂²×C₈₉	1	4	yes	complemented
415	#488	C₂²×C₈₉	1	4	yes	complemented
416	#486	C₂²×C₈₉	1	4	yes	complemented
417	#470	C₂²×C₈₉	1	2	yes	complemented
418	#469	C₂²×C₈₉	1	2	yes	—
419	#469	C₂²×C₈₉	1	2	yes	—
420	#469	C₂²×C₈₉	1	2	yes	complemented
421	#469	C₂²×C₈₉	1	4	yes	complemented
422	#468	C₂²×C₈₉	1	4	yes	complemented
423	#466	C₂²×C₈₉	1	4	yes	—
424	#466	C₂²×C₈₉	1	4	yes	complemented
425	#465	C₂²×C₈₉	1	4	yes	complemented
426	#465	C₂²×C₈₉	1	4	yes	complemented
427	#442	C₂²×C₈₉	1	2	yes	—
428	#442	C₂²×C₈₉	1	2	yes	—
429	#442	C₂²×C₈₉	1	2	yes	—
430	#442	C₂²×C₈₉	1	2	yes	—
431	#442	C₂²×C₈₉	1	1	yes	characteristic, complemented
432	#442	C₂²×C₈₉	1	4	yes	complemented
433	#442	C₂²×C₈₉	1	1	yes	characteristic, complemented
434	#441	C₂²×C₈₉	1	1	yes	characteristic, complemented
435	#441	C₂²×C₈₉	1	1	yes	characteristic, complemented
436	#440	C₂²×C₈₉	1	2	yes	complemented
437	#440	C₂²×C₈₉	1	2	yes	complemented
438	#440	C₂²×C₈₉	1	4	yes	complemented
439	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
440	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
441	#428	C₂²×C₈₉	1	2	yes	—
442	#427	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
444	#418	C₂²×C₈₉	1	2	yes	—
445	#417	C₂²×C₈₉	1	2	yes	—
446	#416	C₂²×C₈₉	1	2	yes	—
447	C₂×#102	C₂²×C₈₉	1	2	yes	—
448	#405	C₂²×C₈₉	1	1	yes	characteristic
449	#405	C₂²×C₈₉	1	1	yes	characteristic
450	#405	C₂²×C₈₉	1	2	yes	complemented
451	#405	C₂²×C₈₉	1	2	yes	complemented
452	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
453	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
454	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#97	C₂²×C₈₉	1	2	yes	complemented
456	C₂×#41	—	2	4	no	—
457	C₂×#41	C₂³×C₈₉	1	2	yes	—
458	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
460	C₂³×C₄	—	2	2	no	—
461	AGL(1,ℤ/8)	—	2	8	no	—
462	#135	—	2	4	no	—
463	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
464	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
466	C₂×D₈	—	2	4	no	—
467	C₂×D₈	C₂³×C₈₉	1	2	yes	—
468	C₂×D₈	C₂³×C₈₉	1	2	yes	—
469	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
470	C₂×D₈	C₂³×C₈₉	1	4	yes	—
471	#131	—	2	4	no	—
472	#131	—	2	4	no	—
473	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
475	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
476	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
479	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
480	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
483	#127	—	2	2	no	—
484	#127	C₂³×C₈₉	1	4	yes	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#125	—	2	2	no	—
488	#125	C₂³×C₈₉	1	4	yes	—
489	#124	—	2	2	no	—
490	#124	—	2	4	no	—
491	#124	—	2	4	no	—
492	#124	C₂³×C₈₉	1	4	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
501	#121	—	2	4	no	—
502	#121	—	2	2	no	—
503	#121	—	2	4	no	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	C₂³×C₈₉	1	4	yes	—
509	#121	C₂³×C₈₉	1	4	yes	—
510	#121	C₂³×C₈₉	1	4	yes	—
511	#120	—	2	4	no	—
512	#120	—	2	4	no	—
513	C₄×Q₈	D₄×C₈₉	1	2	yes	—
514	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
515	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	D₄×C₈₉	1	4	yes	—
523	C₄×D₄	D₄×C₈₉	1	2	yes	—
524	C₄×D₄	C₂³×C₈₉	1	4	yes	—
525	C₄×D₄	C₂³×C₈₉	1	4	yes	—
526	C₄×D₄	C₂³×C₈₉	1	2	yes	—
527	C₄×D₄	C₂³×C₈₉	1	2	yes	—
528	#117	—	2	2	no	—
529	#117	—	2	4	no	—
530	#117	C₂³×C₈₉	1	2	yes	—
531	#117	C₂³×C₈₉	1	1	yes	characteristic
532	#117	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
538	#107	C₂³×C₈₉	1	2	yes	—
539	#107	C₂³×C₈₉	1	4	yes	—
540	#106	C₂³×C₈₉	1	2	yes	—
541	#106	C₂³×C₈₉	1	2	yes	—
542	#106	C₂³×C₈₉	1	1	yes	characteristic
543	#106	C₂³×C₈₉	1	1	yes	characteristic
544	#106	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	#97	C₂³×C₈₉	1	1	yes	characteristic
556	#97	C₂³×C₈₉	1	1	yes	characteristic
557	#97	C₂³×C₈₉	1	1	yes	characteristic
558	#97	C₂³×C₈₉	1	1	yes	characteristic
559	#97	C₂³×C₈₉	1	2	yes	—
560	#97	C₂³×C₈₉	1	2	yes	—
561	#97	C₂³×C₈₉	1	2	yes	—
562	C₄×C₈	C₂³×C₈₉	1	2	yes	—
563	C₄×C₈	C₂³×C₈₉	1	2	yes	—
564	C₄×C₈	C₂³×C₈₉	1	2	yes	—
565	C₂⁴	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	4	no	—
569	#41	—	2	4	no	—
570	#41	—	8	8	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
585	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
586	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	8	4	no	—
594	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
598	Q₁₆	—	2	2	no	—
599	SD₁₆	—	2	4	no	—
600	SD₁₆	—	2	8	no	—
601	D₈	—	2	4	no	—
602	D₈	—	2	4	no	—
603	D₈	—	2	2	no	—
604	D₈	—	2	8	no	—
605	M₁₆	—	2	2	no	—
606	M₁₆	—	2	4	no	—
607	M₁₆	—	2	4	no	—
608	M₁₆	#41×C₈₉	1	4	yes	complemented
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#41×C₈₉	1	4	yes	complemented
613	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
614	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
618	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
628	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₄²	C₂×D₄×C₈₉	1	2	yes	—
648	C₄²	C₂×D₄×C₈₉	1	4	yes	—
649	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
650	C₄²	C₂⁴×C₈₉	1	2	yes	—
651	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	2	no	—
656	C₂³	—	8	2	no	—
657	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
658	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	8	4	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	4	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	2	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	8	4	no	—
672	D₄	—	8	4	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	D₄	—	8	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	8	2	no	—
688	C₂×C₄	—	8	4	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
694	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
695	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
696	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
697	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
698	C₈	—	2	1	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	2	no	—
701	C₈	C₂×#41×C₈₉	1	2	yes	—
702	C₈	C₂×#41×C₈₉	1	4	yes	—
703	C₈	C₂×#41×C₈₉	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	8	8	no	—
714	C₂²	#532×C₈₉	1	2	yes	—
715	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	#532×C₈₉	1	2	yes	—
725	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
726	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
727	C₂	—	2	2	no	—
728	C₂	—	4	2	no	—
729	C₂	—	8	2	no	—
730	C₂	—	8	4	no	—
731	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
732	C₂	C₈₉×#3585	1	2	yes	—

	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3460	C₂	semidirect
2. C₈₉×#3184	C₂	semidirect
3. C₈₉×#3183	C₂	semidirect
4. C₈₉×#3180	C₂	semidirect
5. C₈₉×#3179	C₂	semidirect
6. C₈₉×#3176	C₂	semidirect
7. C₈₉×#3173	C₂	semidirect
8. C₈₉×#3163	C₂	semidirect
9. C₈₉×#3155	C₂	semidirect
10. C₈₉×#3136	C₂	semidirect
11. C₈₉×#3062	C₂	semidirect
12. C₈₉×#3060	C₂	semidirect
13. C₈₉×#3058	C₂	semidirect
14. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
15. C₈₉×#2943	C₂	semidirect
16. C₂×#442×C₈₉	C₂	semidirect
17. C₈₉×#2875	C₂	semidirect
25. #542×C₈₉	C₂²	semidirect
27. #540×C₈₉	C₂²	semidirect
33. #532×C₈₉	C₂²	semidirect
35. #529×C₈₉	C₂²	semidirect
40. #501×C₈₉	C₂²	semidirect
41. #499×C₈₉	C₂²	semidirect
42. #498×C₈₉	C₂²	semidirect
46. #490×C₈₉	C₂²	semidirect
47. #489×C₈₉	C₂²	semidirect
48. #488×C₈₉	C₂²	semidirect
49. #486×C₈₉	C₂²	semidirect
50. #470×C₈₉	C₂²	semidirect
53. #469×C₈₉	C₂²	semidirect
54. #469×C₈₉	C₂²	semidirect
55. #468×C₈₉	C₂²	semidirect
57. #466×C₈₉	C₂²	semidirect
58. #465×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
64. #442×C₈₉	C₂²	semidirect
65. #442×C₈₉	C₂²	semidirect
66. #442×C₈₉	C₂²	semidirect
67. #441×C₈₉	C₂²	semidirect
68. #441×C₈₉	C₂²	semidirect
69. #440×C₈₉	C₂²	semidirect
70. #440×C₈₉	C₂²	semidirect
71. #440×C₈₉	C₂²	semidirect
72. C₄×SD₁₆×C₈₉	C₂²	semidirect
73. C₄×D₈×C₈₉	C₂²	semidirect
83. #405×C₈₉	C₂²	semidirect
84. #405×C₈₉	C₂²	semidirect
86. C₄×M₁₆×C₈₉	C₂²	semidirect
88. C₂×#97×C₈₉	C₂²	semidirect
241. M₁₆×C₈₉	#41	semidirect
245. C₂×C₈×C₈₉	#41	semidirect
360. #60698	C₈₉	direct (N × H)
367. #3460	C₂×C₈₉	semidirect
368. #3184	C₂×C₈₉	semidirect
369. #3183	C₂×C₈₉	semidirect
370. #3180	C₂×C₈₉	semidirect
371. #3179	C₂×C₈₉	semidirect
372. #3176	C₂×C₈₉	semidirect
373. #3173	C₂×C₈₉	semidirect
374. #3163	C₂×C₈₉	semidirect
375. #3155	C₂×C₈₉	semidirect
376. #3136	C₂×C₈₉	semidirect
377. #3062	C₂×C₈₉	semidirect
378. #3060	C₂×C₈₉	semidirect
379. #3058	C₂×C₈₉	semidirect
380. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
381. #2943	C₂×C₈₉	semidirect
382. C₂×#442	C₂×C₈₉	semidirect
383. #2875	C₂×C₈₉	semidirect
384. C₈₉	#60698	direct (N × H)
392. #542	C₂²×C₈₉	semidirect
394. #540	C₂²×C₈₉	semidirect
400. #532	C₂²×C₈₉	semidirect
402. #529	C₂²×C₈₉	semidirect
407. #501	C₂²×C₈₉	semidirect
408. #499	C₂²×C₈₉	semidirect
409. #498	C₂²×C₈₉	semidirect
413. #490	C₂²×C₈₉	semidirect
414. #489	C₂²×C₈₉	semidirect
415. #488	C₂²×C₈₉	semidirect
416. #486	C₂²×C₈₉	semidirect
417. #470	C₂²×C₈₉	semidirect
420. #469	C₂²×C₈₉	semidirect
421. #469	C₂²×C₈₉	semidirect
422. #468	C₂²×C₈₉	semidirect
424. #466	C₂²×C₈₉	semidirect
425. #465	C₂²×C₈₉	semidirect
426. #465	C₂²×C₈₉	semidirect
431. #442	C₂²×C₈₉	semidirect
432. #442	C₂²×C₈₉	semidirect
433. #442	C₂²×C₈₉	semidirect
434. #441	C₂²×C₈₉	semidirect
435. #441	C₂²×C₈₉	semidirect
436. #440	C₂²×C₈₉	semidirect
437. #440	C₂²×C₈₉	semidirect
438. #440	C₂²×C₈₉	semidirect
439. C₄×SD₁₆	C₂²×C₈₉	semidirect
440. C₄×D₈	C₂²×C₈₉	semidirect
450. #405	C₂²×C₈₉	semidirect
451. #405	C₂²×C₈₉	semidirect
453. C₄×M₁₆	C₂²×C₈₉	semidirect
455. C₂×#97	C₂²×C₈₉	semidirect
608. M₁₆	#41×C₈₉	semidirect
612. C₂×C₈	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3460	2
C₈₉×#3184	2
C₈₉×#3183	2
C₈₉×#3180	2
C₈₉×#3179	2
C₈₉×#3176	2
C₈₉×#3173	2
C₈₉×#3163	2
C₈₉×#3155	2
C₈₉×#3136	2
C₈₉×#3062	2
C₈₉×#3060	2
C₈₉×#3058	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₈₉×#2943	2
C₂×#442×C₈₉	2
C₈₉×#2875	2
#60698	89

Subgroups — C89×#60698 #36438546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60698 #36438546