Subgroups — C₈₉×#63092 #36440940

Order 22784.

10796 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3586	C₂	1	15	yes	maximal, complemented
4	C₈₉×#3585	C₂	1	15	yes	maximal, complemented
5	C₈₉×#3584	C₂	1	15	yes	maximal, complemented
6	C₂×#577×C₈₉	C₂	1	15	yes	maximal, complemented
7	C₈₉×#3573	C₂	1	1	yes	maximal, characteristic, complemented
8	#585×C₈₉	—	2	6	no	—
9	#585×C₈₉	—	2	10	no	—
10	#585×C₈₉	C₂²	1	1	yes	characteristic
11	#585×C₈₉	C₂²	1	15	yes	complemented
12	#585×C₈₉	C₂²	1	15	yes	complemented
13	C₂×2₋¹⁺⁴×C₈₉	—	2	6	no	—
14	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	15	yes	complemented
15	C₂×H(5,𝔽₂)×C₈₉	—	2	10	no	—
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	15	yes	complemented
17	#578×C₈₉	C₂²	1	60	yes	complemented
18	#577×C₈₉	C₂²	1	60	yes	complemented
19	#577×C₈₉	C₂²	1	120	yes	complemented
20	#577×C₈₉	C₂²	1	20	yes	complemented
21	#576×C₈₉	C₂²	1	60	yes	complemented
22	#575×C₈₉	C₂²	1	90	yes	complemented
23	C₂×#137×C₈₉	C₂²	1	45	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	45	yes	complemented
25	C₂×#135×C₈₉	C₂²	1	45	yes	complemented
26	C₂²×SD₁₆×C₈₉	C₂²	1	15	yes	complemented
27	#568×C₈₉	C₂²	1	15	yes	complemented
28	C₂×#131×C₈₉	C₂²	1	15	yes	complemented
29	2₋¹⁺⁴×C₈₉	—	2	60	no	—
30	2₋¹⁺⁴×C₈₉	—	2	15	no	—
31	2₋¹⁺⁴×C₈₉	—	2	15	no	—
32	2₋¹⁺⁴×C₈₉	D₄	1	6	yes	—
33	2₋¹⁺⁴×C₈₉	C₂³	1	20	yes	—
34	2₋¹⁺⁴×C₈₉	C₂³	1	60	yes	complemented
35	H(5,𝔽₂)×C₈₉	—	2	60	no	—
36	H(5,𝔽₂)×C₈₉	—	2	45	no	—
37	H(5,𝔽₂)×C₈₉	—	2	45	no	—
38	H(5,𝔽₂)×C₈₉	D₄	1	10	yes	—
39	H(5,𝔽₂)×C₈₉	C₂³	1	60	yes	—
40	H(5,𝔽₂)×C₈₉	C₂³	1	20	yes	complemented
41	C₂×#41×C₈₉	—	2	60	no	—
42	C₂×#41×C₈₉	—	2	60	no	—
43	C₂×#41×C₈₉	—	2	15	no	—
44	C₂×#41×C₈₉	—	2	45	no	—
45	C₂×#41×C₈₉	C₂³	1	45	yes	—
46	C₂×#41×C₈₉	C₂³	1	15	yes	—
47	C₂×#41×C₈₉	C₂³	1	45	yes	complemented
48	C₂²×Q₈×C₈₉	—	2	15	no	—
49	C₂²×Q₈×C₈₉	C₂³	1	15	yes	complemented
50	C₂²×D₄×C₈₉	—	2	45	no	—
51	C₂²×D₄×C₈₉	C₂³	1	15	yes	—
52	#137×C₈₉	C₂³	1	180	yes	complemented
53	#137×C₈₉	C₂³	1	60	yes	complemented
54	AGL(1,ℤ/8)×C₈₉	C₂³	1	180	yes	complemented
55	AGL(1,ℤ/8)×C₈₉	C₂³	1	60	yes	complemented
56	#135×C₈₉	C₂³	1	60	yes	complemented
57	#135×C₈₉	C₂³	1	180	yes	complemented
58	C₂×Q₁₆×C₈₉	C₂³	1	45	yes	complemented
59	C₂×SD₁₆×C₈₉	C₂³	1	45	yes	complemented
60	C₂×SD₁₆×C₈₉	C₂³	1	90	yes	complemented
61	C₂×SD₁₆×C₈₉	C₂³	1	15	yes	complemented
62	C₂×D₈×C₈₉	C₂³	1	45	yes	complemented
63	#131×C₈₉	C₂³	1	20	yes	complemented
64	#131×C₈₉	C₂³	1	60	yes	complemented
65	C₂×M₁₆×C₈₉	C₂³	1	45	yes	complemented
66	C₂²×C₈×C₈₉	C₂³	1	15	yes	complemented
67	C₂⁴×C₈₉	—	2	15	no	—
68	#41×C₈₉	—	2	60	no	—
69	#41×C₈₉	—	2	20	no	—
70	#41×C₈₉	—	2	60	no	—
71	#41×C₈₉	—	2	180	no	—
72	#41×C₈₉	—	2	90	no	—
73	#41×C₈₉	—	2	90	no	—
74	#41×C₈₉	C₂×D₄	1	60	yes	—
75	#41×C₈₉	C₂⁴	1	60	yes	—
76	#41×C₈₉	C₂⁴	1	60	yes	—
77	#41×C₈₉	C₂⁴	1	20	yes	—
78	C₂×Q₈×C₈₉	—	2	60	no	—
79	C₂×Q₈×C₈₉	—	2	20	no	—
80	C₂×Q₈×C₈₉	—	2	45	no	—
81	C₂×Q₈×C₈₉	C₂×D₄	1	15	yes	—
82	C₂×Q₈×C₈₉	C₂⁴	1	45	yes	—
83	C₂×Q₈×C₈₉	C₂⁴	1	15	yes	—
84	C₂×D₄×C₈₉	—	2	45	no	—
85	C₂×D₄×C₈₉	—	2	45	no	—
86	C₂×D₄×C₈₉	—	2	180	no	—
87	C₂×D₄×C₈₉	—	2	60	no	—
88	C₂×D₄×C₈₉	—	2	45	no	—
89	C₂×D₄×C₈₉	C₂×D₄	1	45	yes	—
90	C₂×D₄×C₈₉	C₂⁴	1	15	yes	—
91	C₂×D₄×C₈₉	C₂⁴	1	45	yes	—
92	C₂²×C₄×C₈₉	—	2	15	no	—
93	C₂²×C₄×C₈₉	—	2	45	no	—
94	C₂²×C₄×C₈₉	—	2	45	no	—
95	C₂²×C₄×C₈₉	C₂⁴	1	15	yes	—
96	Q₁₆×C₈₉	C₂⁴	1	60	yes	—
97	SD₁₆×C₈₉	C₂⁴	1	10	yes	—
98	SD₁₆×C₈₉	C₂⁴	1	6	yes	—
99	SD₁₆×C₈₉	C₂⁴	1	90	yes	—
100	SD₁₆×C₈₉	C₂⁴	1	30	yes	—
101	D₈×C₈₉	C₂⁴	1	60	yes	—
102	M₁₆×C₈₉	C₂⁴	1	60	yes	—
103	C₂×C₈×C₈₉	C₂⁴	1	15	yes	—
104	C₂×C₈×C₈₉	C₂⁴	1	45	yes	—
105	C₂³×C₈₉	—	2	15	no	—
106	C₂³×C₈₉	—	2	45	no	—
107	C₂³×C₈₉	—	16	15	no	—
108	C₂³×C₈₉	C₂²×D₄	1	15	yes	—
109	Q₈×C₈₉	—	2	45	no	—
110	Q₈×C₈₉	—	2	15	no	—
111	Q₈×C₈₉	C₂²×D₄	1	20	yes	—
112	Q₈×C₈₉	C₂⁵	1	10	yes	—
113	Q₈×C₈₉	C₂⁵	1	6	yes	—
114	D₄×C₈₉	—	2	60	no	—
115	D₄×C₈₉	—	2	60	no	—
116	D₄×C₈₉	—	2	45	no	—
117	D₄×C₈₉	—	2	15	no	—
118	D₄×C₈₉	C₂²×D₄	1	60	yes	—
119	D₄×C₈₉	C₂⁵	1	6	yes	—
120	D₄×C₈₉	C₂⁵	1	10	yes	—
121	C₂×C₄×C₈₉	—	2	15	no	—
122	C₂×C₄×C₈₉	—	2	45	no	—
123	C₂×C₄×C₈₉	—	2	60	no	—
124	C₂×C₄×C₈₉	—	2	60	no	—
125	C₂×C₄×C₈₉	C₂²×D₄	1	45	yes	—
126	C₂×C₄×C₈₉	C₂⁵	1	15	yes	—
127	C₈×C₈₉	C₂⁵	1	1	yes	characteristic
128	C₈×C₈₉	C₂⁵	1	15	yes	—
129	C₂²×C₈₉	—	2	6	no	—
130	C₂²×C₈₉	—	2	10	no	—
131	C₂²×C₈₉	—	4	15	no	—
132	C₂²×C₈₉	—	8	15	no	—
133	C₂²×C₈₉	—	8	45	no	—
134	C₂²×C₈₉	C₂³×D₄	1	15	yes	—
135	C₄×C₈₉	—	2	6	no	—
136	C₄×C₈₉	—	2	10	no	—
137	C₄×C₈₉	C₂³×D₄	1	15	yes	—
138	C₄×C₈₉	C₂⁶	1	1	yes	characteristic
139	#63092	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₈₉	—	2	15	no	—
141	C₂×C₈₉	—	4	6	no	—
142	C₂×C₈₉	—	4	10	no	—
143	C₂×C₈₉	C₂⁴×D₄	1	1	yes	characteristic
144	2₋¹⁺⁶	C₂×C₈₉	1	1	yes	characteristic, complemented
145	H(7,𝔽₂)	C₂×C₈₉	1	1	yes	characteristic, complemented
146	#3586	C₂×C₈₉	1	15	yes	complemented
147	#3585	C₂×C₈₉	1	15	yes	complemented
148	#3584	C₂×C₈₉	1	15	yes	complemented
149	C₂×#577	C₂×C₈₉	1	15	yes	complemented
150	#3573	C₂×C₈₉	1	1	yes	characteristic, complemented
151	C₈₉	#63092	1	1	yes	characteristic, direct product factor, Sylow
152	#585	—	2	6	no	—
153	#585	—	2	10	no	—
154	#585	C₂²×C₈₉	1	1	yes	characteristic
155	#585	C₂²×C₈₉	1	15	yes	complemented
156	#585	C₂²×C₈₉	1	15	yes	complemented
157	C₂×2₋¹⁺⁴	—	2	6	no	—
158	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	15	yes	complemented
159	C₂×H(5,𝔽₂)	—	2	10	no	—
160	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	15	yes	complemented
161	#578	C₂²×C₈₉	1	60	yes	complemented
162	#577	C₂²×C₈₉	1	60	yes	complemented
163	#577	C₂²×C₈₉	1	120	yes	complemented
164	#577	C₂²×C₈₉	1	20	yes	complemented
165	#576	C₂²×C₈₉	1	60	yes	complemented
166	#575	C₂²×C₈₉	1	90	yes	complemented
167	C₂×#137	C₂²×C₈₉	1	45	yes	complemented
168	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	45	yes	complemented
169	C₂×#135	C₂²×C₈₉	1	45	yes	complemented
170	C₂²×SD₁₆	C₂²×C₈₉	1	15	yes	complemented
171	#568	C₂²×C₈₉	1	15	yes	complemented
172	C₂×#131	C₂²×C₈₉	1	15	yes	complemented
173	2₋¹⁺⁴	—	2	60	no	—
174	2₋¹⁺⁴	—	2	15	no	—
175	2₋¹⁺⁴	—	2	15	no	—
176	2₋¹⁺⁴	D₄×C₈₉	1	6	yes	—
177	2₋¹⁺⁴	C₂³×C₈₉	1	20	yes	—
178	2₋¹⁺⁴	C₂³×C₈₉	1	60	yes	complemented
179	H(5,𝔽₂)	—	2	60	no	—
180	H(5,𝔽₂)	—	2	45	no	—
181	H(5,𝔽₂)	—	2	45	no	—
182	H(5,𝔽₂)	D₄×C₈₉	1	10	yes	—
183	H(5,𝔽₂)	C₂³×C₈₉	1	60	yes	—
184	H(5,𝔽₂)	C₂³×C₈₉	1	20	yes	complemented
185	C₂×#41	—	2	60	no	—
186	C₂×#41	—	2	60	no	—
187	C₂×#41	—	2	15	no	—
188	C₂×#41	—	2	45	no	—
189	C₂×#41	C₂³×C₈₉	1	45	yes	—
190	C₂×#41	C₂³×C₈₉	1	15	yes	—
191	C₂×#41	C₂³×C₈₉	1	45	yes	complemented
192	C₂²×Q₈	—	2	15	no	—
193	C₂²×Q₈	C₂³×C₈₉	1	15	yes	complemented
194	C₂²×D₄	—	2	45	no	—
195	C₂²×D₄	C₂³×C₈₉	1	15	yes	—
196	#137	C₂³×C₈₉	1	180	yes	complemented
197	#137	C₂³×C₈₉	1	60	yes	complemented
198	AGL(1,ℤ/8)	C₂³×C₈₉	1	180	yes	complemented
199	AGL(1,ℤ/8)	C₂³×C₈₉	1	60	yes	complemented
200	#135	C₂³×C₈₉	1	60	yes	complemented
201	#135	C₂³×C₈₉	1	180	yes	complemented
202	C₂×Q₁₆	C₂³×C₈₉	1	45	yes	complemented
203	C₂×SD₁₆	C₂³×C₈₉	1	45	yes	complemented
204	C₂×SD₁₆	C₂³×C₈₉	1	90	yes	complemented
205	C₂×SD₁₆	C₂³×C₈₉	1	15	yes	complemented
206	C₂×D₈	C₂³×C₈₉	1	45	yes	complemented
207	#131	C₂³×C₈₉	1	20	yes	complemented
208	#131	C₂³×C₈₉	1	60	yes	complemented
209	C₂×M₁₆	C₂³×C₈₉	1	45	yes	complemented
210	C₂²×C₈	C₂³×C₈₉	1	15	yes	complemented
211	C₂⁴	—	2	15	no	—
212	#41	—	2	60	no	—
213	#41	—	2	20	no	—
214	#41	—	2	60	no	—
215	#41	—	2	180	no	—
216	#41	—	2	90	no	—
217	#41	—	2	90	no	—
218	#41	C₂×D₄×C₈₉	1	60	yes	—
219	#41	C₂⁴×C₈₉	1	60	yes	—
220	#41	C₂⁴×C₈₉	1	60	yes	—
221	#41	C₂⁴×C₈₉	1	20	yes	—
222	C₂×Q₈	—	2	60	no	—
223	C₂×Q₈	—	2	20	no	—
224	C₂×Q₈	—	2	45	no	—
225	C₂×Q₈	C₂×D₄×C₈₉	1	15	yes	—
226	C₂×Q₈	C₂⁴×C₈₉	1	45	yes	—
227	C₂×Q₈	C₂⁴×C₈₉	1	15	yes	—
228	C₂×D₄	—	2	45	no	—
229	C₂×D₄	—	2	45	no	—
230	C₂×D₄	—	2	180	no	—
231	C₂×D₄	—	2	60	no	—
232	C₂×D₄	—	2	45	no	—
233	C₂×D₄	C₂×D₄×C₈₉	1	45	yes	—
234	C₂×D₄	C₂⁴×C₈₉	1	15	yes	—
235	C₂×D₄	C₂⁴×C₈₉	1	45	yes	—
236	C₂²×C₄	—	2	15	no	—
237	C₂²×C₄	—	2	45	no	—
238	C₂²×C₄	—	2	45	no	—
239	C₂²×C₄	C₂⁴×C₈₉	1	15	yes	—
240	Q₁₆	C₂⁴×C₈₉	1	60	yes	—
241	SD₁₆	C₂⁴×C₈₉	1	10	yes	—
242	SD₁₆	C₂⁴×C₈₉	1	6	yes	—
243	SD₁₆	C₂⁴×C₈₉	1	90	yes	—
244	SD₁₆	C₂⁴×C₈₉	1	30	yes	—
245	D₈	C₂⁴×C₈₉	1	60	yes	—
246	M₁₆	C₂⁴×C₈₉	1	60	yes	—
247	C₂×C₈	C₂⁴×C₈₉	1	15	yes	—
248	C₂×C₈	C₂⁴×C₈₉	1	45	yes	—
249	C₂³	—	2	15	no	—
250	C₂³	—	2	45	no	—
251	C₂³	—	16	15	no	—
252	C₂³	C₂²×D₄×C₈₉	1	15	yes	—
253	Q₈	—	2	45	no	—
254	Q₈	—	2	15	no	—
255	Q₈	C₂²×D₄×C₈₉	1	20	yes	—
256	Q₈	C₂⁵×C₈₉	1	10	yes	—
257	Q₈	C₂⁵×C₈₉	1	6	yes	—
258	D₄	—	2	60	no	—
259	D₄	—	2	60	no	—
260	D₄	—	2	45	no	—
261	D₄	—	2	15	no	—
262	D₄	C₂²×D₄×C₈₉	1	60	yes	—
263	D₄	C₂⁵×C₈₉	1	6	yes	—
264	D₄	C₂⁵×C₈₉	1	10	yes	—
265	C₂×C₄	—	2	15	no	—
266	C₂×C₄	—	2	45	no	—
267	C₂×C₄	—	2	60	no	—
268	C₂×C₄	—	2	60	no	—
269	C₂×C₄	C₂²×D₄×C₈₉	1	45	yes	—
270	C₂×C₄	C₂⁵×C₈₉	1	15	yes	—
271	C₈	C₂⁵×C₈₉	1	1	yes	characteristic
272	C₈	C₂⁵×C₈₉	1	15	yes	—
273	C₂²	—	2	6	no	—
274	C₂²	—	2	10	no	—
275	C₂²	—	4	15	no	—
276	C₂²	—	8	45	no	—
277	C₂²	—	8	15	no	—
278	C₂²	C₂³×D₄×C₈₉	1	15	yes	—
279	C₄	—	2	6	no	—
280	C₄	—	2	10	no	—
281	C₄	C₂³×D₄×C₈₉	1	15	yes	—
282	C₄	C₂⁶×C₈₉	1	1	yes	characteristic
283	C₂	—	2	15	no	—
284	C₂	—	4	6	no	—
285	C₂	—	4	10	no	—
286	C₂	C₂⁴×D₄×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	C₂⁴×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₈₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ #585×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×2₋¹⁺⁶	C₂	semidirect
2. C₈₉×H(7,𝔽₂)	C₂	semidirect
3. C₈₉×#3586	C₂	semidirect
4. C₈₉×#3585	C₂	semidirect
5. C₈₉×#3584	C₂	semidirect
6. C₂×#577×C₈₉	C₂	semidirect
7. C₈₉×#3573	C₂	semidirect
11. #585×C₈₉	C₂²	semidirect
12. #585×C₈₉	C₂²	semidirect
14. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
17. #578×C₈₉	C₂²	semidirect
18. #577×C₈₉	C₂²	semidirect
19. #577×C₈₉	C₂²	semidirect
20. #577×C₈₉	C₂²	semidirect
21. #576×C₈₉	C₂²	semidirect
22. #575×C₈₉	C₂²	semidirect
23. C₂×#137×C₈₉	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
25. C₂×#135×C₈₉	C₂²	semidirect
26. C₂²×SD₁₆×C₈₉	C₂²	semidirect
27. #568×C₈₉	C₂²	semidirect
28. C₂×#131×C₈₉	C₂²	semidirect
34. 2₋¹⁺⁴×C₈₉	C₂³	semidirect
40. H(5,𝔽₂)×C₈₉	C₂³	semidirect
47. C₂×#41×C₈₉	C₂³	semidirect
49. C₂²×Q₈×C₈₉	C₂³	semidirect
52. #137×C₈₉	C₂³	semidirect
53. #137×C₈₉	C₂³	semidirect
54. AGL(1,ℤ/8)×C₈₉	C₂³	semidirect
55. AGL(1,ℤ/8)×C₈₉	C₂³	semidirect
56. #135×C₈₉	C₂³	semidirect
57. #135×C₈₉	C₂³	semidirect
58. C₂×Q₁₆×C₈₉	C₂³	semidirect
59. C₂×SD₁₆×C₈₉	C₂³	semidirect
60. C₂×SD₁₆×C₈₉	C₂³	semidirect
61. C₂×SD₁₆×C₈₉	C₂³	semidirect
62. C₂×D₈×C₈₉	C₂³	semidirect
63. #131×C₈₉	C₂³	semidirect
64. #131×C₈₉	C₂³	semidirect
65. C₂×M₁₆×C₈₉	C₂³	semidirect
66. C₂²×C₈×C₈₉	C₂³	semidirect
139. #63092	C₈₉	direct (N × H)
144. 2₋¹⁺⁶	C₂×C₈₉	semidirect
145. H(7,𝔽₂)	C₂×C₈₉	semidirect
146. #3586	C₂×C₈₉	semidirect
147. #3585	C₂×C₈₉	semidirect
148. #3584	C₂×C₈₉	semidirect
149. C₂×#577	C₂×C₈₉	semidirect
150. #3573	C₂×C₈₉	semidirect
151. C₈₉	#63092	direct (N × H)
155. #585	C₂²×C₈₉	semidirect
156. #585	C₂²×C₈₉	semidirect
158. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
160. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
161. #578	C₂²×C₈₉	semidirect
162. #577	C₂²×C₈₉	semidirect
163. #577	C₂²×C₈₉	semidirect
164. #577	C₂²×C₈₉	semidirect
165. #576	C₂²×C₈₉	semidirect
166. #575	C₂²×C₈₉	semidirect
167. C₂×#137	C₂²×C₈₉	semidirect
168. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
169. C₂×#135	C₂²×C₈₉	semidirect
170. C₂²×SD₁₆	C₂²×C₈₉	semidirect
171. #568	C₂²×C₈₉	semidirect
172. C₂×#131	C₂²×C₈₉	semidirect
178. 2₋¹⁺⁴	C₂³×C₈₉	semidirect
184. H(5,𝔽₂)	C₂³×C₈₉	semidirect
191. C₂×#41	C₂³×C₈₉	semidirect
193. C₂²×Q₈	C₂³×C₈₉	semidirect
196. #137	C₂³×C₈₉	semidirect
197. #137	C₂³×C₈₉	semidirect
198. AGL(1,ℤ/8)	C₂³×C₈₉	semidirect
199. AGL(1,ℤ/8)	C₂³×C₈₉	semidirect
200. #135	C₂³×C₈₉	semidirect
201. #135	C₂³×C₈₉	semidirect
202. C₂×Q₁₆	C₂³×C₈₉	semidirect
203. C₂×SD₁₆	C₂³×C₈₉	semidirect
204. C₂×SD₁₆	C₂³×C₈₉	semidirect
205. C₂×SD₁₆	C₂³×C₈₉	semidirect
206. C₂×D₈	C₂³×C₈₉	semidirect
207. #131	C₂³×C₈₉	semidirect
208. #131	C₂³×C₈₉	semidirect
209. C₂×M₁₆	C₂³×C₈₉	semidirect
210. C₂²×C₈	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×2₋¹⁺⁶	2
C₈₉×H(7,𝔽₂)	2
C₈₉×#3586	2
C₈₉×#3585	2
C₈₉×#3584	2
C₂×#577×C₈₉	2
C₈₉×#3573	2
#63092	89

Subgroups — C89×#63092 #36440940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63092 #36440940