Subgroups — C₂×C₈₉×#3055 #36438290

Order 22784.

3242 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
2. C₂³×M₁₆×C₈₉	C₂	semidirect
3. C₂×#525×C₈₉	C₂	semidirect
4. C₂²×#121×C₈₉	C₂	semidirect
5. C₈₉×#3055	C₂	direct (N × H)
6. C₂×#469×C₈₉	C₂	semidirect
7. C₂×#468×C₈₉	C₂	semidirect
8. C₂×#466×C₈₉	C₂	semidirect
9. C₂×#465×C₈₉	C₂	semidirect
10. C₂×#428×C₈₉	C₂	semidirect
11. C₂×#417×C₈₉	C₂	semidirect
12. C₂×#418×C₈₉	C₂	semidirect
18. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
19. C₂²×SD₁₆×C₈₉	C₂²	semidirect
20. C₂²×D₈×C₈₉	C₂²	semidirect
24. C₂²×M₁₆×C₈₉	C₂²	semidirect
25. C₂²×M₁₆×C₈₉	C₂²	semidirect
26. C₂³×C₈×C₈₉	C₂²	semidirect
28. #525×C₈₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
37. C₂×#121×C₈₉	C₂²	semidirect
38. C₂×#121×C₈₉	C₂²	semidirect
39. C₂×#121×C₈₉	C₂²	semidirect
46. #469×C₈₉	C₂²	semidirect
47. #468×C₈₉	C₂²	semidirect
48. #466×C₈₉	C₂²	semidirect
49. #465×C₈₉	C₂²	semidirect
50. #428×C₈₉	C₂²	semidirect
51. C₂×#107×C₈₉	C₂²	semidirect
52. C₂×#106×C₈₉	C₂²	semidirect
53. #418×C₈₉	C₂²	semidirect
54. #417×C₈₉	C₂²	semidirect
55. C₂×#103×C₈₉	C₂²	semidirect
56. C₂×#102×C₈₉	C₂²	semidirect
57. C₂×#102×C₈₉	C₂²	semidirect
58. C₂×#102×C₈₉	C₂²	semidirect
94. C₂×SD₁₆×C₈₉	C₂³	semidirect
96. C₂×D₈×C₈₉	C₂³	semidirect
100. C₂×M₁₆×C₈₉	D₄	semidirect
103. C₂×M₁₆×C₈₉	C₂³	semidirect
107. C₂²×C₈×C₈₉	C₂³	semidirect
111. C₂²⋊Q₈×C₈₉	C₂³	semidirect
112. C₂²⋊Q₈×C₈₉	C₂³	semidirect
121. #121×C₈₉	C₂³	semidirect
122. #121×C₈₉	C₂³	semidirect
145. #107×C₈₉	C₂³	semidirect
146. #106×C₈₉	C₂³	semidirect
147. #103×C₈₉	C₂³	semidirect
148. #102×C₈₉	C₂³	semidirect
149. #102×C₈₉	C₂³	semidirect
150. #102×C₈₉	C₂³	semidirect
232. M₁₆×C₈₉	C₂×D₄	semidirect
235. C₂×C₈×C₈₉	C₂×D₄	semidirect
279. C₂³×C₈₉	AGL(1,ℤ/8)	semidirect
332. C₈×C₈₉	C₂²×D₄	semidirect
356. C₂²×C₈₉	C₂×AGL(1,ℤ/8)	semidirect
369. C₂×#3055	C₈₉	direct (N × H)
375. C₂×C₈₉	#3055	direct (N × H)
379. C₂²×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
380. C₂³×M₁₆	C₂×C₈₉	semidirect
381. C₂×#525	C₂×C₈₉	semidirect
382. C₂²×#121	C₂×C₈₉	semidirect
383. #3055	C₂×C₈₉	direct (N × H)
384. C₂×#469	C₂×C₈₉	semidirect
385. C₂×#468	C₂×C₈₉	semidirect
386. C₂×#466	C₂×C₈₉	semidirect
387. C₂×#465	C₂×C₈₉	semidirect
388. C₂×#428	C₂×C₈₉	semidirect
389. C₂×#417	C₂×C₈₉	semidirect
390. C₂×#418	C₂×C₈₉	semidirect
391. C₈₉	C₂×#3055	direct (N × H)
397. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
398. C₂²×SD₁₆	C₂²×C₈₉	semidirect
399. C₂²×D₈	C₂²×C₈₉	semidirect
403. C₂²×M₁₆	C₂²×C₈₉	semidirect
404. C₂²×M₁₆	C₂²×C₈₉	semidirect
405. C₂³×C₈	C₂²×C₈₉	semidirect
407. #525	C₂²×C₈₉	semidirect
409. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
410. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
416. C₂×#121	C₂²×C₈₉	semidirect
417. C₂×#121	C₂²×C₈₉	semidirect
418. C₂×#121	C₂²×C₈₉	semidirect
425. #469	C₂²×C₈₉	semidirect
426. #468	C₂²×C₈₉	semidirect
427. #466	C₂²×C₈₉	semidirect
428. #465	C₂²×C₈₉	semidirect
429. #428	C₂²×C₈₉	semidirect
430. C₂×#107	C₂²×C₈₉	semidirect
431. C₂×#106	C₂²×C₈₉	semidirect
432. #418	C₂²×C₈₉	semidirect
433. #417	C₂²×C₈₉	semidirect
434. C₂×#103	C₂²×C₈₉	semidirect
435. C₂×#102	C₂²×C₈₉	semidirect
436. C₂×#102	C₂²×C₈₉	semidirect
437. C₂×#102	C₂²×C₈₉	semidirect
473. C₂×SD₁₆	C₂³×C₈₉	semidirect
475. C₂×D₈	C₂³×C₈₉	semidirect
479. C₂×M₁₆	D₄×C₈₉	semidirect
482. C₂×M₁₆	C₂³×C₈₉	semidirect
486. C₂²×C₈	C₂³×C₈₉	semidirect
490. C₂²⋊Q₈	C₂³×C₈₉	semidirect
491. C₂²⋊Q₈	C₂³×C₈₉	semidirect
500. #121	C₂³×C₈₉	semidirect
501. #121	C₂³×C₈₉	semidirect
524. #107	C₂³×C₈₉	semidirect
525. #106	C₂³×C₈₉	semidirect
526. #103	C₂³×C₈₉	semidirect
527. #102	C₂³×C₈₉	semidirect
528. #102	C₂³×C₈₉	semidirect
529. #102	C₂³×C₈₉	semidirect
611. M₁₆	C₂×D₄×C₈₉	semidirect
614. C₂×C₈	C₂×D₄×C₈₉	semidirect
658. C₂³	AGL(1,ℤ/8)×C₈₉	semidirect
711. C₈	C₂²×D₄×C₈₉	semidirect
735. C₂²	C₂×AGL(1,ℤ/8)×C₈₉	semidirect
753. C₂	C₈₉×#3055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₈₉	2
C₂³×M₁₆×C₈₉	2
C₂×#525×C₈₉	2
C₂²×#121×C₈₉	2
C₈₉×#3055	2
C₂×#469×C₈₉	2
C₂×#468×C₈₉	2
C₂×#466×C₈₉	2
C₂×#465×C₈₉	2
C₂×#428×C₈₉	2
C₂×#417×C₈₉	2
C₂×#418×C₈₉	2
C₂×#3055	89

Subgroups — C2×C89×#3055 #36438290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3055 #36438290