Subgroups — C₂×C₈₉×#3068 #36438315

Order 22784.

2746 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#568×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3068	C₂	1	16	yes	maximal, direct product factor
6	C₂×#472×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂×#471×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂×#430×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#413×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#100×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	#575×C₈₉	—	2	4	no	—
15	#575×C₈₉	C₂²	1	8	yes	complemented
16	C₂×#137×C₈₉	—	2	1	no	—
17	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
19	C₂×AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
21	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
22	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
23	C₂×AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	—
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	8	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	8	yes	complemented
28	C₂×#135×C₈₉	—	2	2	no	—
29	C₂²×SD₁₆×C₈₉	—	2	1	no	—
30	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
31	C₂²×D₈×C₈₉	—	2	1	no	—
32	C₂²×D₈×C₈₉	C₂²	1	2	yes	complemented
33	#568×C₈₉	—	2	4	no	—
34	#568×C₈₉	C₂²	1	8	yes	complemented
35	C₂×#131×C₈₉	—	2	2	no	—
36	C₂×#131×C₈₉	C₂²	1	4	yes	complemented
37	C₂²×M₁₆×C₈₉	—	2	2	no	—
38	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	#472×C₈₉	C₂²	1	32	yes	complemented
43	#471×C₈₉	C₂²	1	32	yes	complemented
44	#430×C₈₉	C₂²	1	8	yes	complemented
45	C₂×#108×C₈₉	C₂²	1	4	yes	complemented
46	#413×C₈₉	C₂²	1	8	yes	complemented
47	C₂×#101×C₈₉	C₂²	1	2	yes	complemented
48	C₂×#100×C₈₉	C₂²	1	4	yes	complemented
49	C₂×#100×C₈₉	C₂²	1	2	yes	complemented
50	C₂×#100×C₈₉	C₂²	1	8	yes	complemented
51	C₂⁵×C₈₉	—	2	1	no	—
52	C₂×#41×C₈₉	—	2	1	no	—
53	C₂×#41×C₈₉	—	2	2	no	—
54	C₂×#41×C₈₉	—	2	1	no	—
55	C₂×#41×C₈₉	—	2	2	no	—
56	C₂×#41×C₈₉	—	2	2	no	—
57	C₂×#41×C₈₉	—	2	1	no	—
58	C₂×#41×C₈₉	—	2	1	no	—
59	C₂×#41×C₈₉	—	2	1	no	—
60	C₂×#41×C₈₉	—	2	2	no	—
61	C₂×#41×C₈₉	—	2	1	no	—
62	C₂×#41×C₈₉	—	2	2	no	—
63	C₂×#41×C₈₉	D₄	1	2	yes	—
64	C₂×#41×C₈₉	D₄	1	4	yes	—
65	C₂×#41×C₈₉	C₂³	1	2	yes	—
66	C₂×#41×C₈₉	C₂³	1	4	yes	—
67	C₂×#41×C₈₉	C₂³	1	4	yes	—
68	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	2	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	2	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	2	2	no	—
80	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂³×C₄×C₈₉	—	2	1	no	—
85	C₂³×C₄×C₈₉	—	2	1	no	—
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	#137×C₈₉	—	2	4	no	—
88	#137×C₈₉	—	2	8	no	—
89	#137×C₈₉	C₂³	1	8	yes	complemented
90	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
91	AGL(1,ℤ/8)×C₈₉	—	2	16	no	—
92	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
93	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
94	AGL(1,ℤ/8)×C₈₉	—	2	16	no	—
95	AGL(1,ℤ/8)×C₈₉	—	2	16	no	—
96	AGL(1,ℤ/8)×C₈₉	C₂³	1	16	yes	—
97	AGL(1,ℤ/8)×C₈₉	C₂³	1	8	yes	complemented
98	#135×C₈₉	—	2	16	no	—
99	C₂×Q₁₆×C₈₉	—	2	2	no	—
100	C₂×SD₁₆×C₈₉	—	2	4	no	—
101	C₂×SD₁₆×C₈₉	—	2	8	no	—
102	C₂×SD₁₆×C₈₉	—	2	2	no	—
103	C₂×SD₁₆×C₈₉	—	2	2	no	—
104	C₂×SD₁₆×C₈₉	—	2	4	no	—
105	C₂×SD₁₆×C₈₉	—	2	4	no	—
106	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	complemented
107	C₂×D₈×C₈₉	—	2	4	no	—
108	C₂×D₈×C₈₉	—	2	8	no	—
109	C₂×D₈×C₈₉	—	2	2	no	—
110	C₂×D₈×C₈₉	—	2	4	no	—
111	C₂×D₈×C₈₉	—	2	4	no	—
112	C₂×D₈×C₈₉	C₂³	1	8	yes	complemented
113	#131×C₈₉	—	2	16	no	—
114	#131×C₈₉	—	2	8	no	—
115	#131×C₈₉	C₂³	1	16	yes	complemented
116	C₂×M₁₆×C₈₉	—	2	1	no	—
117	C₂×M₁₆×C₈₉	—	2	2	no	—
118	C₂×M₁₆×C₈₉	—	2	1	no	—
119	C₂×M₁₆×C₈₉	—	2	2	no	—
120	C₂×M₁₆×C₈₉	—	2	1	no	—
121	C₂×M₁₆×C₈₉	—	2	2	no	—
122	C₂×M₁₆×C₈₉	—	2	16	no	—
123	C₂×M₁₆×C₈₉	—	2	4	no	—
124	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
125	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
126	C₂×M₁₆×C₈₉	D₄	1	4	yes	—
127	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
128	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
129	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
130	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
131	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
132	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
133	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
134	C₂²×C₈×C₈₉	—	2	1	no	—
135	C₂²×C₈×C₈₉	—	2	1	no	—
136	C₂²×C₈×C₈₉	—	2	1	no	—
137	C₂²×C₈×C₈₉	—	2	4	no	—
138	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
139	#108×C₈₉	C₂³	1	16	yes	complemented
140	#101×C₈₉	C₂³	1	8	yes	complemented
141	#100×C₈₉	C₂³	1	16	yes	complemented
142	#100×C₈₉	C₂³	1	8	yes	complemented
143	C₂⁴×C₈₉	—	2	1	no	—
144	C₂⁴×C₈₉	—	2	1	no	—
145	C₂⁴×C₈₉	—	2	4	no	—
146	C₂⁴×C₈₉	—	2	2	no	—
147	C₂⁴×C₈₉	—	4	2	no	—
148	C₂⁴×C₈₉	—	4	1	no	—
149	C₂⁴×C₈₉	—	4	1	no	—
150	C₂⁴×C₈₉	—	8	4	no	—
151	C₂⁴×C₈₉	#41	1	1	yes	characteristic
152	#41×C₈₉	—	2	4	no	—
153	#41×C₈₉	—	2	4	no	—
154	#41×C₈₉	—	2	4	no	—
155	#41×C₈₉	—	2	4	no	—
156	#41×C₈₉	—	2	2	no	—
157	#41×C₈₉	—	2	4	no	—
158	#41×C₈₉	—	2	2	no	—
159	#41×C₈₉	—	2	4	no	—
160	#41×C₈₉	—	2	4	no	—
161	#41×C₈₉	—	2	4	no	—
162	#41×C₈₉	—	2	4	no	—
163	#41×C₈₉	—	4	2	no	—
164	#41×C₈₉	—	4	2	no	—
165	#41×C₈₉	—	4	2	no	—
166	#41×C₈₉	—	4	2	no	—
167	#41×C₈₉	C₂×D₄	1	8	yes	—
168	#41×C₈₉	C₂×D₄	1	4	yes	—
169	#41×C₈₉	C₂⁴	1	4	yes	—
170	C₂×Q₈×C₈₉	—	2	2	no	—
171	C₂×Q₈×C₈₉	—	2	1	no	—
172	C₂×Q₈×C₈₉	—	2	1	no	—
173	C₂×Q₈×C₈₉	—	2	1	no	—
174	C₂×Q₈×C₈₉	—	2	1	no	—
175	C₂×Q₈×C₈₉	—	2	1	no	—
176	C₂×Q₈×C₈₉	—	2	1	no	—
177	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
179	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	2	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	2	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	2	no	—
186	C₂×D₄×C₈₉	—	2	1	no	—
187	C₂×D₄×C₈₉	—	2	1	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	2	no	—
191	C₂×D₄×C₈₉	—	2	2	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	4	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	1	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	2	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	4	2	no	—
203	C₂×D₄×C₈₉	—	4	1	no	—
204	C₂×D₄×C₈₉	—	4	1	no	—
205	C₂×D₄×C₈₉	—	4	2	no	—
206	C₂×D₄×C₈₉	—	4	2	no	—
207	C₂×D₄×C₈₉	—	4	2	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	1	no	—
211	C₂×D₄×C₈₉	—	4	1	no	—
212	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₈₉	—	2	1	no	—
217	C₂²×C₄×C₈₉	—	2	4	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	2	1	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	—	4	2	no	—
224	C₂²×C₄×C₈₉	—	4	1	no	—
225	C₂²×C₄×C₈₉	—	4	1	no	—
226	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	#41	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	Q₁₆×C₈₉	—	2	8	no	—
237	SD₁₆×C₈₉	—	2	16	no	—
238	SD₁₆×C₈₉	—	2	8	no	—
239	SD₁₆×C₈₉	—	2	8	no	—
240	SD₁₆×C₈₉	—	2	16	no	—
241	D₈×C₈₉	—	2	16	no	—
242	D₈×C₈₉	—	2	8	no	—
243	D₈×C₈₉	—	2	16	no	—
244	M₁₆×C₈₉	—	2	4	no	—
245	M₁₆×C₈₉	—	2	2	no	—
246	M₁₆×C₈₉	—	2	4	no	—
247	M₁₆×C₈₉	—	2	2	no	—
248	M₁₆×C₈₉	—	2	4	no	—
249	M₁₆×C₈₉	—	2	2	no	—
250	M₁₆×C₈₉	—	2	16	no	—
251	M₁₆×C₈₉	C₂×D₄	1	8	yes	—
252	M₁₆×C₈₉	C₂×D₄	1	8	yes	—
253	M₁₆×C₈₉	C₂⁴	1	4	yes	—
254	M₁₆×C₈₉	C₂⁴	1	4	yes	—
255	M₁₆×C₈₉	C₂⁴	1	4	yes	—
256	C₂×C₈×C₈₉	—	2	2	no	—
257	C₂×C₈×C₈₉	—	2	4	no	—
258	C₂×C₈×C₈₉	—	2	4	no	—
259	C₂×C₈×C₈₉	—	2	2	no	—
260	C₂×C₈×C₈₉	—	2	2	no	—
261	C₂×C₈×C₈₉	—	2	4	no	—
262	C₂×C₈×C₈₉	—	2	16	no	—
263	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
264	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
265	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	4	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	4	no	—
270	C₂³×C₈₉	—	4	2	no	—
271	C₂³×C₈₉	—	4	1	no	—
272	C₂³×C₈₉	—	4	4	no	—
273	C₂³×C₈₉	—	4	4	no	—
274	C₂³×C₈₉	—	4	2	no	—
275	C₂³×C₈₉	—	4	1	no	—
276	C₂³×C₈₉	—	4	2	no	—
277	C₂³×C₈₉	—	8	2	no	—
278	C₂³×C₈₉	—	8	2	no	—
279	C₂³×C₈₉	—	8	4	no	—
280	C₂³×C₈₉	—	8	4	no	—
281	C₂³×C₈₉	—	8	4	no	—
282	C₂³×C₈₉	—	8	8	no	—
283	C₂³×C₈₉	—	8	8	no	—
284	C₂³×C₈₉	#121	1	1	yes	characteristic
285	C₂³×C₈₉	#121	1	1	yes	characteristic
286	C₂³×C₈₉	#121	1	2	yes	—
287	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
288	C₂³×C₈₉	C₂×#41	1	2	yes	—
289	Q₈×C₈₉	—	2	4	no	—
290	Q₈×C₈₉	—	2	2	no	—
291	Q₈×C₈₉	—	2	2	no	—
292	Q₈×C₈₉	—	2	2	no	—
293	Q₈×C₈₉	—	4	1	no	—
294	Q₈×C₈₉	—	4	1	no	—
295	Q₈×C₈₉	C₂²×D₄	1	4	yes	—
296	D₄×C₈₉	—	2	4	no	—
297	D₄×C₈₉	—	2	8	no	—
298	D₄×C₈₉	—	2	4	no	—
299	D₄×C₈₉	—	2	4	no	—
300	D₄×C₈₉	—	2	2	no	—
301	D₄×C₈₉	—	2	2	no	—
302	D₄×C₈₉	—	2	4	no	—
303	D₄×C₈₉	—	2	4	no	—
304	D₄×C₈₉	—	2	2	no	—
305	D₄×C₈₉	—	4	4	no	—
306	D₄×C₈₉	—	4	4	no	—
307	D₄×C₈₉	—	4	4	no	—
308	D₄×C₈₉	—	4	2	no	—
309	D₄×C₈₉	—	4	4	no	—
310	D₄×C₈₉	—	4	2	no	—
311	D₄×C₈₉	—	4	1	no	—
312	D₄×C₈₉	—	4	1	no	—
313	D₄×C₈₉	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	8	no	—
317	C₂×C₄×C₈₉	—	2	4	no	—
318	C₂×C₄×C₈₉	—	2	4	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	4	no	—
323	C₂×C₄×C₈₉	—	4	4	no	—
324	C₂×C₄×C₈₉	#121	1	2	yes	—
325	C₂×C₄×C₈₉	#121	1	2	yes	—
326	C₂×C₄×C₈₉	#121	1	2	yes	—
327	C₂×C₄×C₈₉	#121	1	2	yes	—
328	C₂×C₄×C₈₉	#121	1	2	yes	—
329	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
330	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
342	C₈×C₈₉	—	2	4	no	—
343	C₈×C₈₉	—	2	4	no	—
344	C₈×C₈₉	—	2	4	no	—
345	C₈×C₈₉	C₂²×D₄	1	8	yes	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	4	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	4	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	—	4	4	no	—
355	C₂²×C₈₉	—	8	4	no	—
356	C₂²×C₈₉	—	8	2	no	—
357	C₂²×C₈₉	—	8	8	no	—
358	C₂²×C₈₉	—	8	4	no	—
359	C₂²×C₈₉	—	8	8	no	—
360	C₂²×C₈₉	—	8	2	no	—
361	C₂²×C₈₉	—	8	4	no	—
362	C₂²×C₈₉	—	8	2	no	—
363	C₂²×C₈₉	—	8	4	no	—
364	C₂²×C₈₉	C₂×#121	1	2	yes	—
365	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
366	C₂²×C₈₉	C₂×#121	1	2	yes	—
367	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
368	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
369	C₄×C₈₉	—	2	4	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	C₂×#121	1	2	yes	—
372	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
373	C₄×C₈₉	C₂×#121	1	2	yes	—
374	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
375	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
377	C₂×#3068	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂×C₈₉	—	2	2	no	—
379	C₂×C₈₉	—	2	1	no	—
380	C₂×C₈₉	—	2	1	no	—
381	C₂×C₈₉	—	2	2	no	—
382	C₂×C₈₉	—	4	4	no	—
383	C₂×C₈₉	—	8	2	no	—
384	C₂×C₈₉	—	8	4	no	—
385	C₂×C₈₉	#3068	1	2	yes	direct product factor
386	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
387	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₂²×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
389	C₂²×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₂×#568	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#3068	C₂×C₈₉	1	16	yes	direct product factor
392	C₂×#472	C₂×C₈₉	1	4	yes	complemented
393	C₂×#471	C₂×C₈₉	1	4	yes	complemented
394	C₂×#430	C₂×C₈₉	1	1	yes	characteristic, complemented
395	C₂×#413	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₂²×#100	C₂×C₈₉	1	1	yes	characteristic, complemented
397	C₈₉	C₂×#3068	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
399	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
400	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
401	#575	—	2	4	no	—
402	#575	C₂²×C₈₉	1	8	yes	complemented
403	C₂×#137	—	2	1	no	—
404	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
405	C₂×AGL(1,ℤ/8)	—	2	2	no	—
406	C₂×AGL(1,ℤ/8)	—	2	4	no	—
407	C₂×AGL(1,ℤ/8)	—	2	1	no	—
408	C₂×AGL(1,ℤ/8)	—	2	2	no	—
409	C₂×AGL(1,ℤ/8)	—	2	2	no	—
410	C₂×AGL(1,ℤ/8)	—	2	4	no	—
411	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	—
412	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	8	yes	complemented
413	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
414	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	8	yes	complemented
415	C₂×#135	—	2	2	no	—
416	C₂²×SD₁₆	—	2	1	no	—
417	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
418	C₂²×D₈	—	2	1	no	—
419	C₂²×D₈	C₂²×C₈₉	1	2	yes	complemented
420	#568	—	2	4	no	—
421	#568	C₂²×C₈₉	1	8	yes	complemented
422	C₂×#131	—	2	2	no	—
423	C₂×#131	C₂²×C₈₉	1	4	yes	complemented
424	C₂²×M₁₆	—	2	2	no	—
425	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
426	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
427	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
428	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
429	#472	C₂²×C₈₉	1	32	yes	complemented
430	#471	C₂²×C₈₉	1	32	yes	complemented
431	#430	C₂²×C₈₉	1	8	yes	complemented
432	C₂×#108	C₂²×C₈₉	1	4	yes	complemented
433	#413	C₂²×C₈₉	1	8	yes	complemented
434	C₂×#101	C₂²×C₈₉	1	2	yes	complemented
435	C₂×#100	C₂²×C₈₉	1	4	yes	complemented
436	C₂×#100	C₂²×C₈₉	1	8	yes	complemented
437	C₂×#100	C₂²×C₈₉	1	2	yes	complemented
438	C₂⁵	—	2	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	2	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	D₄×C₈₉	1	2	yes	—
451	C₂×#41	D₄×C₈₉	1	4	yes	—
452	C₂×#41	C₂³×C₈₉	1	2	yes	—
453	C₂×#41	C₂³×C₈₉	1	4	yes	—
454	C₂×#41	C₂³×C₈₉	1	4	yes	—
455	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
470	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
474	#137	—	2	4	no	—
475	#137	—	2	8	no	—
476	#137	C₂³×C₈₉	1	8	yes	complemented
477	AGL(1,ℤ/8)	—	2	8	no	—
478	AGL(1,ℤ/8)	—	2	16	no	—
479	AGL(1,ℤ/8)	—	2	4	no	—
480	AGL(1,ℤ/8)	—	2	8	no	—
481	AGL(1,ℤ/8)	—	2	16	no	—
482	AGL(1,ℤ/8)	—	2	16	no	—
483	AGL(1,ℤ/8)	C₂³×C₈₉	1	16	yes	—
484	AGL(1,ℤ/8)	C₂³×C₈₉	1	8	yes	complemented
485	#135	—	2	16	no	—
486	C₂×Q₁₆	—	2	2	no	—
487	C₂×SD₁₆	—	2	4	no	—
488	C₂×SD₁₆	—	2	8	no	—
489	C₂×SD₁₆	—	2	2	no	—
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	4	no	—
492	C₂×SD₁₆	—	2	4	no	—
493	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	complemented
494	C₂×D₈	—	2	4	no	—
495	C₂×D₈	—	2	8	no	—
496	C₂×D₈	—	2	2	no	—
497	C₂×D₈	—	2	4	no	—
498	C₂×D₈	—	2	4	no	—
499	C₂×D₈	C₂³×C₈₉	1	8	yes	complemented
500	#131	—	2	16	no	—
501	#131	—	2	8	no	—
502	#131	C₂³×C₈₉	1	16	yes	complemented
503	C₂×M₁₆	—	2	1	no	—
504	C₂×M₁₆	—	2	2	no	—
505	C₂×M₁₆	—	2	1	no	—
506	C₂×M₁₆	—	2	2	no	—
507	C₂×M₁₆	—	2	1	no	—
508	C₂×M₁₆	—	2	2	no	—
509	C₂×M₁₆	—	2	16	no	—
510	C₂×M₁₆	—	2	4	no	—
511	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
512	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
513	C₂×M₁₆	D₄×C₈₉	1	4	yes	—
514	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
515	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
516	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
517	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
518	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
519	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
520	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
521	C₂²×C₈	—	2	1	no	—
522	C₂²×C₈	—	2	1	no	—
523	C₂²×C₈	—	2	1	no	—
524	C₂²×C₈	—	2	4	no	—
525	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
526	#108	C₂³×C₈₉	1	16	yes	complemented
527	#101	C₂³×C₈₉	1	8	yes	complemented
528	#100	C₂³×C₈₉	1	16	yes	complemented
529	#100	C₂³×C₈₉	1	8	yes	complemented
530	C₂⁴	—	2	1	no	—
531	C₂⁴	—	2	1	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	4	no	—
534	C₂⁴	—	4	1	no	—
535	C₂⁴	—	4	1	no	—
536	C₂⁴	—	4	2	no	—
537	C₂⁴	—	8	4	no	—
538	C₂⁴	#41×C₈₉	1	1	yes	characteristic
539	#41	—	2	4	no	—
540	#41	—	2	4	no	—
541	#41	—	2	4	no	—
542	#41	—	2	4	no	—
543	#41	—	2	2	no	—
544	#41	—	2	4	no	—
545	#41	—	2	2	no	—
546	#41	—	2	4	no	—
547	#41	—	2	4	no	—
548	#41	—	2	4	no	—
549	#41	—	2	4	no	—
550	#41	—	4	2	no	—
551	#41	—	4	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	2	no	—
554	#41	C₂×D₄×C₈₉	1	8	yes	—
555	#41	C₂×D₄×C₈₉	1	4	yes	—
556	#41	C₂⁴×C₈₉	1	4	yes	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
565	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
566	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
600	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
601	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
602	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
617	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
619	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	#41×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
623	Q₁₆	—	2	8	no	—
624	SD₁₆	—	2	16	no	—
625	SD₁₆	—	2	8	no	—
626	SD₁₆	—	2	8	no	—
627	SD₁₆	—	2	16	no	—
628	D₈	—	2	16	no	—
629	D₈	—	2	8	no	—
630	D₈	—	2	16	no	—
631	M₁₆	—	2	4	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	4	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	2	16	no	—
638	M₁₆	C₂×D₄×C₈₉	1	8	yes	—
639	M₁₆	C₂×D₄×C₈₉	1	8	yes	—
640	M₁₆	C₂⁴×C₈₉	1	4	yes	—
641	M₁₆	C₂⁴×C₈₉	1	4	yes	—
642	M₁₆	C₂⁴×C₈₉	1	4	yes	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	4	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	—	2	16	no	—
650	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
651	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
652	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	4	2	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	4	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	8	2	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	4	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	—	8	8	no	—
670	C₂³	—	8	8	no	—
671	C₂³	#121×C₈₉	1	1	yes	characteristic
672	C₂³	#121×C₈₉	1	1	yes	characteristic
673	C₂³	#121×C₈₉	1	2	yes	—
674	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
675	C₂³	C₂×#41×C₈₉	1	2	yes	—
676	Q₈	—	2	4	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	4	1	no	—
681	Q₈	—	4	1	no	—
682	Q₈	C₂²×D₄×C₈₉	1	4	yes	—
683	D₄	—	2	4	no	—
684	D₄	—	2	8	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	4	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	4	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	C₂²×D₄×C₈₉	1	4	yes	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
712	C₂×C₄	#121×C₈₉	1	2	yes	—
713	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
714	C₂×C₄	#121×C₈₉	1	2	yes	—
715	C₂×C₄	#121×C₈₉	1	2	yes	—
716	C₂×C₄	#121×C₈₉	1	2	yes	—
717	C₂×C₄	#121×C₈₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
726	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
727	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
728	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
729	C₈	—	2	4	no	—
730	C₈	—	2	4	no	—
731	C₈	—	2	4	no	—
732	C₈	C₂²×D₄×C₈₉	1	8	yes	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	8	4	no	—
743	C₂²	—	8	4	no	—
744	C₂²	—	8	2	no	—
745	C₂²	—	8	4	no	—
746	C₂²	—	8	8	no	—
747	C₂²	—	8	8	no	—
748	C₂²	—	8	2	no	—
749	C₂²	—	8	4	no	—
750	C₂²	—	8	2	no	—
751	C₂²	C₂×#121×C₈₉	1	2	yes	—
752	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
753	C₂²	C₂×#121×C₈₉	1	2	yes	—
754	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
755	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
756	C₄	—	2	4	no	—
757	C₄	—	4	2	no	—
758	C₄	C₂×#121×C₈₉	1	2	yes	—
759	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
760	C₄	C₂×#121×C₈₉	1	2	yes	—
761	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
762	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
763	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
764	C₂	—	2	2	no	—
765	C₂	—	2	1	no	—
766	C₂	—	2	1	no	—
767	C₂	—	2	2	no	—
768	C₂	—	4	4	no	—
769	C₂	—	8	2	no	—
770	C₂	—	8	4	no	—
771	C₂	C₈₉×#3068	1	2	yes	direct product factor
772	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₈₉	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
3. C₂²×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
4. C₂×#568×C₈₉	C₂	semidirect
5. C₈₉×#3068	C₂	direct (N × H)
6. C₂×#472×C₈₉	C₂	semidirect
7. C₂×#471×C₈₉	C₂	semidirect
8. C₂×#430×C₈₉	C₂	semidirect
9. C₂×#413×C₈₉	C₂	semidirect
10. C₂²×#100×C₈₉	C₂	semidirect
15. #575×C₈₉	C₂²	semidirect
17. C₂×#137×C₈₉	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
30. C₂²×SD₁₆×C₈₉	C₂²	semidirect
32. C₂²×D₈×C₈₉	C₂²	semidirect
34. #568×C₈₉	C₂²	semidirect
36. C₂×#131×C₈₉	C₂²	semidirect
42. #472×C₈₉	C₂²	semidirect
43. #471×C₈₉	C₂²	semidirect
44. #430×C₈₉	C₂²	semidirect
45. C₂×#108×C₈₉	C₂²	semidirect
46. #413×C₈₉	C₂²	semidirect
47. C₂×#101×C₈₉	C₂²	semidirect
48. C₂×#100×C₈₉	C₂²	semidirect
49. C₂×#100×C₈₉	C₂²	semidirect
50. C₂×#100×C₈₉	C₂²	semidirect
89. #137×C₈₉	C₂³	semidirect
97. AGL(1,ℤ/8)×C₈₉	C₂³	semidirect
106. C₂×SD₁₆×C₈₉	C₂³	semidirect
112. C₂×D₈×C₈₉	C₂³	semidirect
115. #131×C₈₉	C₂³	semidirect
139. #108×C₈₉	C₂³	semidirect
140. #101×C₈₉	C₂³	semidirect
141. #100×C₈₉	C₂³	semidirect
142. #100×C₈₉	C₂³	semidirect
377. C₂×#3068	C₈₉	direct (N × H)
385. C₂×C₈₉	#3068	direct (N × H)
387. C₂×#575	C₂×C₈₉	semidirect
388. C₂²×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
389. C₂²×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
390. C₂×#568	C₂×C₈₉	semidirect
391. #3068	C₂×C₈₉	direct (N × H)
392. C₂×#472	C₂×C₈₉	semidirect
393. C₂×#471	C₂×C₈₉	semidirect
394. C₂×#430	C₂×C₈₉	semidirect
395. C₂×#413	C₂×C₈₉	semidirect
396. C₂²×#100	C₂×C₈₉	semidirect
397. C₈₉	C₂×#3068	direct (N × H)
402. #575	C₂²×C₈₉	semidirect
404. C₂×#137	C₂²×C₈₉	semidirect
412. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
413. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
414. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
417. C₂²×SD₁₆	C₂²×C₈₉	semidirect
419. C₂²×D₈	C₂²×C₈₉	semidirect
421. #568	C₂²×C₈₉	semidirect
423. C₂×#131	C₂²×C₈₉	semidirect
429. #472	C₂²×C₈₉	semidirect
430. #471	C₂²×C₈₉	semidirect
431. #430	C₂²×C₈₉	semidirect
432. C₂×#108	C₂²×C₈₉	semidirect
433. #413	C₂²×C₈₉	semidirect
434. C₂×#101	C₂²×C₈₉	semidirect
435. C₂×#100	C₂²×C₈₉	semidirect
436. C₂×#100	C₂²×C₈₉	semidirect
437. C₂×#100	C₂²×C₈₉	semidirect
476. #137	C₂³×C₈₉	semidirect
484. AGL(1,ℤ/8)	C₂³×C₈₉	semidirect
493. C₂×SD₁₆	C₂³×C₈₉	semidirect
499. C₂×D₈	C₂³×C₈₉	semidirect
502. #131	C₂³×C₈₉	semidirect
526. #108	C₂³×C₈₉	semidirect
527. #101	C₂³×C₈₉	semidirect
528. #100	C₂³×C₈₉	semidirect
529. #100	C₂³×C₈₉	semidirect
771. C₂	C₈₉×#3068	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#575×C₈₉	2
C₂²×AGL(1,ℤ/8)×C₈₉	2
C₂×#568×C₈₉	2
C₈₉×#3068	2
C₂×#472×C₈₉	2
C₂×#471×C₈₉	2
C₂×#430×C₈₉	2
C₂×#413×C₈₉	2
C₂²×#100×C₈₉	2
C₂×#3068	89

Subgroups — C2×C89×#3068 #36438315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3068 #36438315