Subgroups — C₈₉×#25180 #36403028

Order 22784.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#472×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3041	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#453×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3008	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1887	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
23	#535×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
25	#520×C₈₉	C₂²	1	1	yes	characteristic
26	#518×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#472×C₈₉	—	2	4	no	—
28	#463×C₈₉	—	2	1	no	—
29	#463×C₈₉	—	2	1	no	—
30	#459×C₈₉	—	2	1	no	—
31	#459×C₈₉	—	2	1	no	—
32	#453×C₈₉	—	2	4	no	—
33	#449×C₈₉	—	2	1	no	—
34	#449×C₈₉	—	2	1	no	—
35	#447×C₈₉	—	2	1	no	—
36	#447×C₈₉	—	2	1	no	—
37	#442×C₈₉	—	2	1	no	—
38	#440×C₈₉	—	2	1	no	—
39	C₄×SD₁₆×C₈₉	—	2	1	no	—
40	C₄×D₈×C₈₉	—	2	1	no	—
41	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#428×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#424×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
47	#418×C₈₉	—	2	1	no	—
48	#418×C₈₉	C₂²	1	1	yes	characteristic
49	#418×C₈₉	C₂²	1	1	yes	characteristic
50	#418×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#417×C₈₉	—	2	1	no	—
52	#417×C₈₉	C₂²	1	1	yes	characteristic
53	#416×C₈₉	—	2	1	no	—
54	#416×C₈₉	C₂²	1	1	yes	characteristic
55	#416×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#102×C₈₉	—	2	1	no	—
57	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#408×C₈₉	C₂²	1	1	yes	characteristic
63	#405×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#339×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#339×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#336×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	H(5,𝔽₂)×C₈₉	—	2	2	no	—
70	H(5,𝔽₂)×C₈₉	—	2	2	no	—
71	H(5,𝔽₂)×C₈₉	—	2	2	no	—
72	H(5,𝔽₂)×C₈₉	—	4	1	no	—
73	C₂×#41×C₈₉	—	2	1	no	—
74	C₂×#41×C₈₉	—	2	1	no	—
75	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	—	2	1	no	—
79	C₂²×D₄×C₈₉	—	4	1	no	—
80	C₂²×D₄×C₈₉	—	4	1	no	—
81	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
85	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
86	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
87	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
88	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
89	AGL(1,ℤ/8)×C₈₉	D₄	1	4	yes	complemented
90	C₂×SD₁₆×C₈₉	—	2	1	no	—
91	C₂×SD₁₆×C₈₉	—	2	1	no	—
92	C₂×SD₁₆×C₈₉	—	2	1	no	—
93	C₂×D₈×C₈₉	—	2	1	no	—
94	C₂×D₈×C₈₉	—	2	1	no	—
95	C₂×D₈×C₈₉	—	2	1	no	—
96	C₂×D₈×C₈₉	—	2	2	no	—
97	C₂×D₈×C₈₉	—	2	2	no	—
98	C₂×D₈×C₈₉	—	2	1	no	—
99	C₂×D₈×C₈₉	—	2	1	no	—
100	C₂×D₈×C₈₉	—	2	1	no	—
101	C₂×D₈×C₈₉	—	2	1	no	—
102	C₂×D₈×C₈₉	—	4	1	no	—
103	C₂×D₈×C₈₉	—	4	1	no	—
104	#131×C₈₉	—	2	2	no	—
105	#131×C₈₉	—	4	1	no	—
106	C₂×M₁₆×C₈₉	—	2	1	no	—
107	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₉	—	2	1	no	—
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	#127×C₈₉	—	2	2	no	—
115	#127×C₈₉	—	2	1	no	—
116	#127×C₈₉	—	2	2	no	—
117	#124×C₈₉	—	2	1	no	—
118	#121×C₈₉	—	2	1	no	—
119	#121×C₈₉	—	2	1	no	—
120	#120×C₈₉	—	4	1	no	—
121	C₄×Q₈×C₈₉	—	2	1	no	—
122	C₄×D₄×C₈₉	—	2	1	no	—
123	C₄×D₄×C₈₉	—	2	1	no	—
124	C₄×D₄×C₈₉	—	2	1	no	—
125	C₄×D₄×C₈₉	—	2	1	no	—
126	C₄×D₄×C₈₉	—	2	1	no	—
127	C₄×D₄×C₈₉	—	4	1	no	—
128	#117×C₈₉	—	2	1	no	—
129	#117×C₈₉	C₂³	1	1	yes	characteristic
130	#117×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	#108×C₈₉	—	2	2	no	—
137	#108×C₈₉	—	4	1	no	—
138	#107×C₈₉	—	2	1	no	—
139	#106×C₈₉	—	2	1	no	—
140	C₄⋊C₈×C₈₉	—	2	1	no	—
141	C₄⋊C₈×C₈₉	—	2	1	no	—
142	#104×C₈₉	—	2	2	no	—
143	#104×C₈₉	—	2	2	no	—
144	#103×C₈₉	—	2	1	no	—
145	#103×C₈₉	D₄	1	1	yes	characteristic, complemented
146	#103×C₈₉	D₄	1	1	yes	characteristic, complemented
147	#103×C₈₉	D₄	1	1	yes	characteristic, complemented
148	#103×C₈₉	D₄	1	1	yes	characteristic, complemented
149	#102×C₈₉	—	2	1	no	—
150	#102×C₈₉	—	2	1	no	—
151	#102×C₈₉	—	2	1	no	—
152	#102×C₈₉	—	2	1	no	—
153	#102×C₈₉	—	2	1	no	—
154	#102×C₈₉	—	2	1	no	—
155	#102×C₈₉	—	2	1	no	—
156	#102×C₈₉	—	2	1	no	—
157	#102×C₈₉	—	2	1	no	—
158	#102×C₈₉	—	2	1	no	—
159	#102×C₈₉	—	2	1	no	—
160	#102×C₈₉	D₄	1	1	yes	characteristic, complemented
161	#102×C₈₉	D₄	1	1	yes	characteristic, complemented
162	#102×C₈₉	D₄	1	1	yes	characteristic, complemented
163	#102×C₈₉	D₄	1	1	yes	characteristic, complemented
164	#100×C₈₉	—	2	2	no	—
165	#100×C₈₉	—	2	2	no	—
166	#100×C₈₉	—	2	2	no	—
167	C₂²⋊C₈×C₈₉	—	2	1	no	—
168	C₂²⋊C₈×C₈₉	—	2	1	no	—
169	#97×C₈₉	—	2	1	no	—
170	C₄×C₈×C₈₉	—	2	1	no	—
171	C₂⁴×C₈₉	—	2	1	no	—
172	C₂⁴×C₈₉	—	2	1	no	—
173	C₂⁴×C₈₉	—	2	1	no	—
174	C₂⁴×C₈₉	—	4	1	no	—
175	#41×C₈₉	—	2	1	no	—
176	#41×C₈₉	—	2	1	no	—
177	#41×C₈₉	—	2	4	no	—
178	#41×C₈₉	—	2	1	no	—
179	#41×C₈₉	—	2	1	no	—
180	#41×C₈₉	—	2	1	no	—
181	#41×C₈₉	—	2	1	no	—
182	#41×C₈₉	—	4	2	no	—
183	#41×C₈₉	—	4	2	no	—
184	#41×C₈₉	—	4	2	no	—
185	#41×C₈₉	C₂×D₄	1	2	yes	—
186	#41×C₈₉	#41	1	2	yes	—
187	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	2	1	no	—
205	C₂×D₄×C₈₉	—	2	1	no	—
206	C₂×D₄×C₈₉	—	2	1	no	—
207	C₂×D₄×C₈₉	—	2	1	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	1	no	—
210	C₂×D₄×C₈₉	—	4	1	no	—
211	C₂×D₄×C₈₉	—	4	1	no	—
212	C₂×D₄×C₈₉	—	4	1	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	4	4	no	—
215	C₂×D₄×C₈₉	—	4	4	no	—
216	C₂×D₄×C₈₉	—	4	2	no	—
217	C₂×D₄×C₈₉	—	4	4	no	—
218	C₂×D₄×C₈₉	—	8	2	no	—
219	C₂×D₄×C₈₉	—	8	2	no	—
220	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₈₉	#41	1	2	yes	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	1	no	—
227	C₂²×C₄×C₈₉	—	2	1	no	—
228	C₂²×C₄×C₈₉	—	4	1	no	—
229	C₂²×C₄×C₈₉	—	4	1	no	—
230	C₂²×C₄×C₈₉	—	4	1	no	—
231	C₂²×C₄×C₈₉	—	4	1	no	—
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	SD₁₆×C₈₉	—	2	4	no	—
234	SD₁₆×C₈₉	—	4	2	no	—
235	SD₁₆×C₈₉	—	4	2	no	—
236	D₈×C₈₉	—	2	4	no	—
237	D₈×C₈₉	—	4	2	no	—
238	D₈×C₈₉	—	4	2	no	—
239	D₈×C₈₉	—	4	2	no	—
240	D₈×C₈₉	—	4	2	no	—
241	D₈×C₈₉	—	4	2	no	—
242	D₈×C₈₉	—	4	2	no	—
243	M₁₆×C₈₉	—	2	1	no	—
244	M₁₆×C₈₉	—	2	1	no	—
245	M₁₆×C₈₉	—	2	1	no	—
246	M₁₆×C₈₉	—	2	1	no	—
247	M₁₆×C₈₉	—	2	1	no	—
248	M₁₆×C₈₉	—	2	1	no	—
249	M₁₆×C₈₉	—	2	1	no	—
250	M₁₆×C₈₉	—	4	2	no	—
251	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
252	C₂×C₈×C₈₉	—	2	1	no	—
253	C₂×C₈×C₈₉	—	2	1	no	—
254	C₂×C₈×C₈₉	—	2	1	no	—
255	C₂×C₈×C₈₉	—	2	1	no	—
256	C₂×C₈×C₈₉	—	2	1	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	—	4	2	no	—
261	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	4	1	no	—
268	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
271	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₂²⋊C₄×C₈₉	—	2	1	no	—
273	C₂²⋊C₄×C₈₉	—	2	1	no	—
274	C₂²⋊C₄×C₈₉	—	4	1	no	—
275	C₂²⋊C₄×C₈₉	—	4	1	no	—
276	C₂²⋊C₄×C₈₉	—	4	1	no	—
277	C₂²⋊C₄×C₈₉	—	4	1	no	—
278	C₂²⋊C₄×C₈₉	—	4	1	no	—
279	C₂²⋊C₄×C₈₉	—	8	2	no	—
280	C₄²×C₈₉	—	2	1	no	—
281	C₄²×C₈₉	—	2	1	no	—
282	C₄²×C₈₉	—	2	1	no	—
283	C₄²×C₈₉	—	2	1	no	—
284	C₄²×C₈₉	—	4	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	2	2	no	—
289	C₂³×C₈₉	—	4	4	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	4	1	no	—
293	C₂³×C₈₉	—	4	1	no	—
294	C₂³×C₈₉	—	4	1	no	—
295	C₂³×C₈₉	—	4	1	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	8	1	no	—
298	C₂³×C₈₉	—	8	1	no	—
299	C₂³×C₈₉	—	8	1	no	—
300	C₂³×C₈₉	—	8	1	no	—
301	C₂³×C₈₉	—	8	1	no	—
302	C₂³×C₈₉	—	8	1	no	—
303	C₂³×C₈₉	—	16	1	no	—
304	C₂³×C₈₉	—	16	1	no	—
305	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
306	Q₈×C₈₉	—	2	1	no	—
307	Q₈×C₈₉	—	2	1	no	—
308	Q₈×C₈₉	—	2	1	no	—
309	Q₈×C₈₉	#121	1	2	yes	—
310	D₄×C₈₉	—	2	2	no	—
311	D₄×C₈₉	—	2	2	no	—
312	D₄×C₈₉	—	2	2	no	—
313	D₄×C₈₉	—	2	1	no	—
314	D₄×C₈₉	—	2	2	no	—
315	D₄×C₈₉	—	2	2	no	—
316	D₄×C₈₉	—	2	1	no	—
317	D₄×C₈₉	—	2	1	no	—
318	D₄×C₈₉	—	2	2	no	—
319	D₄×C₈₉	—	4	4	no	—
320	D₄×C₈₉	—	4	4	no	—
321	D₄×C₈₉	—	4	1	no	—
322	D₄×C₈₉	—	4	1	no	—
323	D₄×C₈₉	—	4	1	no	—
324	D₄×C₈₉	—	4	1	no	—
325	D₄×C₈₉	—	4	1	no	—
326	D₄×C₈₉	—	4	1	no	—
327	D₄×C₈₉	—	4	1	no	—
328	D₄×C₈₉	—	4	1	no	—
329	D₄×C₈₉	—	4	1	no	—
330	D₄×C₈₉	—	4	1	no	—
331	D₄×C₈₉	—	8	8	no	—
332	D₄×C₈₉	—	16	1	no	—
333	D₄×C₈₉	—	16	1	no	—
334	D₄×C₈₉	#121	1	2	yes	—
335	C₂×C₄×C₈₉	—	2	1	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	1	no	—
342	C₂×C₄×C₈₉	—	2	1	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	4	1	no	—
349	C₂×C₄×C₈₉	—	4	1	no	—
350	C₂×C₄×C₈₉	—	8	1	no	—
351	C₂×C₄×C₈₉	—	16	1	no	—
352	C₂×C₄×C₈₉	—	16	1	no	—
353	C₂×C₄×C₈₉	—	16	1	no	—
354	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
360	C₈×C₈₉	—	2	2	no	—
361	C₈×C₈₉	—	2	1	no	—
362	C₈×C₈₉	—	2	1	no	—
363	C₈×C₈₉	—	2	1	no	—
364	C₈×C₈₉	—	2	1	no	—
365	C₈×C₈₉	—	4	1	no	—
366	C₈×C₈₉	—	4	1	no	—
367	C₈×C₈₉	—	4	1	no	—
368	C₂²×C₈₉	—	2	1	no	—
369	C₂²×C₈₉	—	2	1	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	4	1	no	—
372	C₂²×C₈₉	—	4	1	no	—
373	C₂²×C₈₉	—	4	1	no	—
374	C₂²×C₈₉	—	4	2	no	—
375	C₂²×C₈₉	—	4	2	no	—
376	C₂²×C₈₉	—	4	1	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	8	2	no	—
379	C₂²×C₈₉	—	8	2	no	—
380	C₂²×C₈₉	—	8	2	no	—
381	C₂²×C₈₉	—	8	1	no	—
382	C₂²×C₈₉	—	8	1	no	—
383	C₂²×C₈₉	—	8	1	no	—
384	C₂²×C₈₉	—	8	1	no	—
385	C₂²×C₈₉	—	8	1	no	—
386	C₂²×C₈₉	—	8	1	no	—
387	C₂²×C₈₉	—	8	1	no	—
388	C₂²×C₈₉	—	16	1	no	—
389	C₂²×C₈₉	—	16	1	no	—
390	C₂²×C₈₉	—	16	1	no	—
391	C₂²×C₈₉	—	16	4	no	—
392	C₂²×C₈₉	#538	1	1	yes	characteristic
393	C₂²×C₈₉	D₄²	1	1	yes	characteristic
394	C₂²×C₈₉	#546	1	1	yes	characteristic
395	C₄×C₈₉	—	2	2	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	1	no	—
398	C₄×C₈₉	—	4	1	no	—
399	C₄×C₈₉	—	4	1	no	—
400	C₄×C₈₉	—	4	1	no	—
401	C₄×C₈₉	—	4	1	no	—
402	C₄×C₈₉	—	8	1	no	—
403	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
404	C₄×C₈₉	#525	1	1	yes	characteristic
405	C₄×C₈₉	D₄²	1	1	yes	characteristic
406	C₄×C₈₉	#546	1	1	yes	characteristic
407	#25180	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂×C₈₉	—	2	1	no	—
409	C₂×C₈₉	—	2	1	no	—
410	C₂×C₈₉	—	4	2	no	—
411	C₂×C₈₉	—	8	1	no	—
412	C₂×C₈₉	—	8	2	no	—
413	C₂×C₈₉	—	8	2	no	—
414	C₂×C₈₉	—	16	1	no	—
415	C₂×C₈₉	#2424	1	1	yes	characteristic
416	C₂×C₈₉	#3288	1	1	yes	characteristic
417	C₂×C₈₉	#3292	1	1	yes	characteristic
418	C₂×#472	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#3041	C₂×C₈₉	1	1	yes	characteristic, complemented
420	C₂×#453	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#3008	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#2946	C₂×C₈₉	1	1	yes	characteristic, complemented
423	#2897	C₂×C₈₉	1	1	yes	characteristic, complemented
424	#2063	C₂×C₈₉	1	1	yes	characteristic, complemented
425	#2051	C₂×C₈₉	1	1	yes	characteristic, complemented
426	#2037	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#2011	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#1978	C₂×C₈₉	1	1	yes	characteristic, complemented
429	#1929	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#1887	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#1883	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#1866	C₂×C₈₉	1	1	yes	characteristic, complemented
433	C₈₉	#25180	1	1	yes	characteristic, direct product factor, Sylow
434	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
440	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
441	#535	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
443	#520	C₂²×C₈₉	1	1	yes	characteristic
444	#518	C₂²×C₈₉	1	1	yes	characteristic, complemented
445	#472	—	2	4	no	—
446	#463	—	2	1	no	—
447	#463	—	2	1	no	—
448	#459	—	2	1	no	—
449	#459	—	2	1	no	—
450	#453	—	2	4	no	—
451	#449	—	2	1	no	—
452	#449	—	2	1	no	—
453	#447	—	2	1	no	—
454	#447	—	2	1	no	—
455	#442	—	2	1	no	—
456	#440	—	2	1	no	—
457	C₄×SD₁₆	—	2	1	no	—
458	C₄×D₈	—	2	1	no	—
459	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
460	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	#428	C₂²×C₈₉	1	1	yes	characteristic, complemented
462	#424	C₂²×C₈₉	1	1	yes	characteristic, complemented
463	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
465	#418	—	2	1	no	—
466	#418	C₂²×C₈₉	1	1	yes	characteristic
467	#418	C₂²×C₈₉	1	1	yes	characteristic
468	#418	C₂²×C₈₉	1	1	yes	characteristic, complemented
469	#417	—	2	1	no	—
470	#417	C₂²×C₈₉	1	1	yes	characteristic
471	#416	—	2	1	no	—
472	#416	C₂²×C₈₉	1	1	yes	characteristic
473	#416	C₂²×C₈₉	1	1	yes	characteristic
474	C₂×#102	—	2	1	no	—
475	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
477	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#408	C₂²×C₈₉	1	1	yes	characteristic
481	#405	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
484	#339	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	#339	C₂²×C₈₉	1	1	yes	characteristic, complemented
486	#336	C₂²×C₈₉	1	1	yes	characteristic, complemented
487	H(5,𝔽₂)	—	2	2	no	—
488	H(5,𝔽₂)	—	2	2	no	—
489	H(5,𝔽₂)	—	2	2	no	—
490	H(5,𝔽₂)	—	4	1	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
494	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
502	AGL(1,ℤ/8)	—	2	2	no	—
503	AGL(1,ℤ/8)	—	2	2	no	—
504	AGL(1,ℤ/8)	—	2	2	no	—
505	AGL(1,ℤ/8)	—	2	2	no	—
506	AGL(1,ℤ/8)	—	4	1	no	—
507	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	complemented
508	C₂×SD₁₆	—	2	1	no	—
509	C₂×SD₁₆	—	2	1	no	—
510	C₂×SD₁₆	—	2	1	no	—
511	C₂×D₈	—	2	1	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	1	no	—
514	C₂×D₈	—	2	1	no	—
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	—	2	1	no	—
517	C₂×D₈	—	2	1	no	—
518	C₂×D₈	—	2	1	no	—
519	C₂×D₈	—	2	1	no	—
520	C₂×D₈	—	4	1	no	—
521	C₂×D₈	—	4	1	no	—
522	#131	—	2	2	no	—
523	#131	—	4	1	no	—
524	C₂×M₁₆	—	2	1	no	—
525	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
529	C₂²×C₈	—	2	1	no	—
530	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
532	#127	—	2	2	no	—
533	#127	—	2	1	no	—
534	#127	—	2	2	no	—
535	#124	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	—	2	1	no	—
538	#120	—	4	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	4	1	no	—
546	#117	—	2	1	no	—
547	#117	C₂³×C₈₉	1	1	yes	characteristic
548	#117	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	4	1	no	—
552	C₂×C₂²⋊C₄	—	4	1	no	—
553	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
554	#108	—	2	2	no	—
555	#108	—	4	1	no	—
556	#107	—	2	1	no	—
557	#106	—	2	1	no	—
558	C₄⋊C₈	—	2	1	no	—
559	C₄⋊C₈	—	2	1	no	—
560	#104	—	2	2	no	—
561	#104	—	2	2	no	—
562	#103	—	2	1	no	—
563	#103	D₄×C₈₉	1	1	yes	characteristic, complemented
564	#103	D₄×C₈₉	1	1	yes	characteristic, complemented
565	#103	D₄×C₈₉	1	1	yes	characteristic, complemented
566	#103	D₄×C₈₉	1	1	yes	characteristic, complemented
567	#102	—	2	1	no	—
568	#102	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#102	—	2	1	no	—
577	#102	—	2	1	no	—
578	#102	D₄×C₈₉	1	1	yes	characteristic, complemented
579	#102	D₄×C₈₉	1	1	yes	characteristic, complemented
580	#102	D₄×C₈₉	1	1	yes	characteristic, complemented
581	#102	D₄×C₈₉	1	1	yes	characteristic, complemented
582	#100	—	2	2	no	—
583	#100	—	2	2	no	—
584	#100	—	2	2	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	—	2	1	no	—
587	#97	—	2	1	no	—
588	C₄×C₈	—	2	1	no	—
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	2	1	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	4	1	no	—
593	#41	—	2	1	no	—
594	#41	—	2	1	no	—
595	#41	—	2	4	no	—
596	#41	—	2	1	no	—
597	#41	—	2	1	no	—
598	#41	—	2	1	no	—
599	#41	—	2	1	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	#41	—	4	2	no	—
603	#41	C₂×D₄×C₈₉	1	2	yes	—
604	#41	#41×C₈₉	1	2	yes	—
605	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
606	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	8	2	no	—
637	C₂×D₄	—	8	2	no	—
638	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
639	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂×D₄	#41×C₈₉	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
651	SD₁₆	—	2	4	no	—
652	SD₁₆	—	4	2	no	—
653	SD₁₆	—	4	2	no	—
654	D₈	—	2	4	no	—
655	D₈	—	4	2	no	—
656	D₈	—	4	2	no	—
657	D₈	—	4	2	no	—
658	D₈	—	4	2	no	—
659	D₈	—	4	2	no	—
660	D₈	—	4	2	no	—
661	M₁₆	—	2	1	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	4	2	no	—
669	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	4	2	no	—
679	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
680	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
681	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
687	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
688	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
689	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	4	1	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	8	2	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	4	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	4	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	—	8	1	no	—
718	C₂³	—	8	1	no	—
719	C₂³	—	8	1	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	16	1	no	—
722	C₂³	—	16	1	no	—
723	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	#121×C₈₉	1	2	yes	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	8	8	no	—
750	D₄	—	16	1	no	—
751	D₄	—	16	1	no	—
752	D₄	#121×C₈₉	1	2	yes	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	—	16	1	no	—
770	C₂×C₄	—	16	1	no	—
771	C₂×C₄	—	16	1	no	—
772	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
775	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
776	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
777	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
778	C₈	—	2	2	no	—
779	C₈	—	2	1	no	—
780	C₈	—	2	1	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	8	2	no	—
797	C₂²	—	8	2	no	—
798	C₂²	—	8	2	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	16	1	no	—
807	C₂²	—	16	1	no	—
808	C₂²	—	16	1	no	—
809	C₂²	—	16	4	no	—
810	C₂²	#538×C₈₉	1	1	yes	characteristic
811	C₂²	D₄²×C₈₉	1	1	yes	characteristic
812	C₂²	#546×C₈₉	1	1	yes	characteristic
813	C₄	—	2	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	8	1	no	—
821	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
822	C₄	#525×C₈₉	1	1	yes	characteristic
823	C₄	D₄²×C₈₉	1	1	yes	characteristic
824	C₄	#546×C₈₉	1	1	yes	characteristic
825	C₂	—	2	1	no	—
826	C₂	—	2	1	no	—
827	C₂	—	4	2	no	—
828	C₂	—	8	1	no	—
829	C₂	—	8	2	no	—
830	C₂	—	8	2	no	—
831	C₂	—	16	1	no	—
832	C₂	C₈₉×#2424	1	1	yes	characteristic
833	C₂	C₈₉×#3288	1	1	yes	characteristic
834	C₂	C₈₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#472×C₈₉	C₂	semidirect
2. C₈₉×#3041	C₂	semidirect
3. C₂×#453×C₈₉	C₂	semidirect
4. C₈₉×#3008	C₂	semidirect
5. C₈₉×#2946	C₂	semidirect
6. C₈₉×#2897	C₂	semidirect
7. C₈₉×#2063	C₂	semidirect
8. C₈₉×#2051	C₂	semidirect
9. C₈₉×#2037	C₂	semidirect
10. C₈₉×#2011	C₂	semidirect
11. C₈₉×#1978	C₂	semidirect
12. C₈₉×#1929	C₂	semidirect
13. C₈₉×#1887	C₂	semidirect
14. C₈₉×#1883	C₂	semidirect
15. C₈₉×#1866	C₂	semidirect
21. C₂²×D₈×C₈₉	C₂²	semidirect
26. #518×C₈₉	C₂²	semidirect
41. C₂×#108×C₈₉	C₂²	semidirect
42. C₂×#108×C₈₉	C₂²	semidirect
43. #428×C₈₉	C₂²	semidirect
44. #424×C₈₉	C₂²	semidirect
50. #418×C₈₉	C₂²	semidirect
58. C₂×#102×C₈₉	C₂²	semidirect
60. C₂×#100×C₈₉	C₂²	semidirect
61. C₂×#100×C₈₉	C₂²	semidirect
63. #405×C₈₉	C₂²	semidirect
64. #390×C₈₉	C₂²	semidirect
65. #343×C₈₉	C₂²	semidirect
66. #339×C₈₉	C₂²	semidirect
67. #339×C₈₉	C₂²	semidirect
68. #336×C₈₉	C₂²	semidirect
89. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
145. #103×C₈₉	D₄	semidirect
146. #103×C₈₉	D₄	semidirect
147. #103×C₈₉	D₄	semidirect
148. #103×C₈₉	D₄	semidirect
160. #102×C₈₉	D₄	semidirect
161. #102×C₈₉	D₄	semidirect
162. #102×C₈₉	D₄	semidirect
163. #102×C₈₉	D₄	semidirect
407. #25180	C₈₉	direct (N × H)
418. C₂×#472	C₂×C₈₉	semidirect
419. #3041	C₂×C₈₉	semidirect
420. C₂×#453	C₂×C₈₉	semidirect
421. #3008	C₂×C₈₉	semidirect
422. #2946	C₂×C₈₉	semidirect
423. #2897	C₂×C₈₉	semidirect
424. #2063	C₂×C₈₉	semidirect
425. #2051	C₂×C₈₉	semidirect
426. #2037	C₂×C₈₉	semidirect
427. #2011	C₂×C₈₉	semidirect
428. #1978	C₂×C₈₉	semidirect
429. #1929	C₂×C₈₉	semidirect
430. #1887	C₂×C₈₉	semidirect
431. #1883	C₂×C₈₉	semidirect
432. #1866	C₂×C₈₉	semidirect
433. C₈₉	#25180	direct (N × H)
439. C₂²×D₈	C₂²×C₈₉	semidirect
444. #518	C₂²×C₈₉	semidirect
459. C₂×#108	C₂²×C₈₉	semidirect
460. C₂×#108	C₂²×C₈₉	semidirect
461. #428	C₂²×C₈₉	semidirect
462. #424	C₂²×C₈₉	semidirect
468. #418	C₂²×C₈₉	semidirect
476. C₂×#102	C₂²×C₈₉	semidirect
478. C₂×#100	C₂²×C₈₉	semidirect
479. C₂×#100	C₂²×C₈₉	semidirect
481. #405	C₂²×C₈₉	semidirect
482. #390	C₂²×C₈₉	semidirect
483. #343	C₂²×C₈₉	semidirect
484. #339	C₂²×C₈₉	semidirect
485. #339	C₂²×C₈₉	semidirect
486. #336	C₂²×C₈₉	semidirect
507. AGL(1,ℤ/8)	D₄×C₈₉	semidirect
563. #103	D₄×C₈₉	semidirect
564. #103	D₄×C₈₉	semidirect
565. #103	D₄×C₈₉	semidirect
566. #103	D₄×C₈₉	semidirect
578. #102	D₄×C₈₉	semidirect
579. #102	D₄×C₈₉	semidirect
580. #102	D₄×C₈₉	semidirect
581. #102	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#472×C₈₉	2
C₈₉×#3041	2
C₂×#453×C₈₉	2
C₈₉×#3008	2
C₈₉×#2946	2
C₈₉×#2897	2
C₈₉×#2063	2
C₈₉×#2051	2
C₈₉×#2037	2
C₈₉×#2011	2
C₈₉×#1978	2
C₈₉×#1929	2
C₈₉×#1887	2
C₈₉×#1883	2
C₈₉×#1866	2
#25180	89

Subgroups — C89×#25180 #36403028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25180 #36403028