Subgroups — C₂²×#575×C₈₉ #36440931

Order 22784.

11294 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₈₉	C₂	semidirect
2. C₂×#575×C₈₉	C₂	direct (N × H)
3. C₂²×#137×C₈₉	C₂	semidirect
4. C₂²×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
5. C₂²×#135×C₈₉	C₂	semidirect
6. C₂³×M₁₆×C₈₉	C₂	semidirect
11. C₂²×#41×C₈₉	C₂²	semidirect
12. C₂²×#41×C₈₉	C₂²	semidirect
13. C₂³×Q₈×C₈₉	C₂²	semidirect
15. C₂³×D₄×C₈₉	C₂²	semidirect
18. #575×C₈₉	C₂²	direct (N × H)
19. C₂×#137×C₈₉	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
21. C₂×#135×C₈₉	C₂²	semidirect
22. C₂²×Q₁₆×C₈₉	C₂²	semidirect
23. C₂²×SD₁₆×C₈₉	C₂²	semidirect
24. C₂²×D₈×C₈₉	C₂²	semidirect
25. C₂²×M₁₆×C₈₉	C₂²	semidirect
26. C₂²×M₁₆×C₈₉	C₂²	semidirect
27. C₂³×C₈×C₈₉	C₂²	semidirect
36. C₂×#41×C₈₉	C₂³	semidirect
37. C₂×#41×C₈₉	C₂³	semidirect
41. C₂²×Q₈×C₈₉	C₂³	semidirect
48. C₂²×D₄×C₈₉	C₂³	semidirect
59. #137×C₈₉	C₂³	semidirect
60. AGL(1,ℤ/8)×C₈₉	C₂³	semidirect
61. #135×C₈₉	C₂³	semidirect
62. C₂×Q₁₆×C₈₉	C₂³	semidirect
63. C₂×SD₁₆×C₈₉	C₂³	semidirect
64. C₂×D₈×C₈₉	C₂³	semidirect
65. C₂×M₁₆×C₈₉	C₂³	semidirect
66. C₂×M₁₆×C₈₉	C₂³	semidirect
68. C₂²×C₈×C₈₉	C₂³	semidirect
81. #41×C₈₉	C₂⁴	semidirect
86. C₂×Q₈×C₈₉	C₂⁴	semidirect
94. C₂×D₄×C₈₉	C₂⁴	semidirect
111. Q₁₆×C₈₉	C₂⁴	semidirect
112. SD₁₆×C₈₉	C₂⁴	semidirect
113. D₈×C₈₉	C₂⁴	semidirect
114. M₁₆×C₈₉	C₂⁴	semidirect
116. C₂×C₈×C₈₉	C₂⁴	semidirect
157. C₂²×C₈₉	#575	direct (N × H)
166. C₂²×#575	C₈₉	direct (N × H)
170. C₂×C₈₉	C₂×#575	direct (N × H)
172. C₂³×#41	C₂×C₈₉	semidirect
173. C₂×#575	C₂×C₈₉	direct (N × H)
174. C₂²×#137	C₂×C₈₉	semidirect
175. C₂²×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
176. C₂²×#135	C₂×C₈₉	semidirect
177. C₂³×M₁₆	C₂×C₈₉	semidirect
178. C₈₉	C₂²×#575	direct (N × H)
183. C₂²×#41	C₂²×C₈₉	semidirect
184. C₂²×#41	C₂²×C₈₉	semidirect
185. C₂³×Q₈	C₂²×C₈₉	semidirect
187. C₂³×D₄	C₂²×C₈₉	semidirect
190. #575	C₂²×C₈₉	direct (N × H)
191. C₂×#137	C₂²×C₈₉	semidirect
192. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
193. C₂×#135	C₂²×C₈₉	semidirect
194. C₂²×Q₁₆	C₂²×C₈₉	semidirect
195. C₂²×SD₁₆	C₂²×C₈₉	semidirect
196. C₂²×D₈	C₂²×C₈₉	semidirect
197. C₂²×M₁₆	C₂²×C₈₉	semidirect
198. C₂²×M₁₆	C₂²×C₈₉	semidirect
199. C₂³×C₈	C₂²×C₈₉	semidirect
208. C₂×#41	C₂³×C₈₉	semidirect
209. C₂×#41	C₂³×C₈₉	semidirect
213. C₂²×Q₈	C₂³×C₈₉	semidirect
220. C₂²×D₄	C₂³×C₈₉	semidirect
231. #137	C₂³×C₈₉	semidirect
232. AGL(1,ℤ/8)	C₂³×C₈₉	semidirect
233. #135	C₂³×C₈₉	semidirect
234. C₂×Q₁₆	C₂³×C₈₉	semidirect
235. C₂×SD₁₆	C₂³×C₈₉	semidirect
236. C₂×D₈	C₂³×C₈₉	semidirect
237. C₂×M₁₆	C₂³×C₈₉	semidirect
238. C₂×M₁₆	C₂³×C₈₉	semidirect
240. C₂²×C₈	C₂³×C₈₉	semidirect
253. #41	C₂⁴×C₈₉	semidirect
258. C₂×Q₈	C₂⁴×C₈₉	semidirect
266. C₂×D₄	C₂⁴×C₈₉	semidirect
283. Q₁₆	C₂⁴×C₈₉	semidirect
284. SD₁₆	C₂⁴×C₈₉	semidirect
285. D₈	C₂⁴×C₈₉	semidirect
286. M₁₆	C₂⁴×C₈₉	semidirect
288. C₂×C₈	C₂⁴×C₈₉	semidirect
329. C₂²	#575×C₈₉	direct (N × H)
341. C₂	C₂×#575×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₈₉	2
C₂×#575×C₈₉	2
C₂²×#137×C₈₉	2
C₂²×AGL(1,ℤ/8)×C₈₉	2
C₂²×#135×C₈₉	2
C₂³×M₁₆×C₈₉	2
C₂²×#575	89

Subgroups — C22×#575×C89 #36440931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#575×C₈₉ #36440931