Subgroups — C₈₉×#60806 #36438654

Order 22784.

2222 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3224	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3222	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3220	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3040	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3038	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3005	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3003	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
21	#542×C₈₉	C₂²	1	4	yes	complemented
22	#541×C₈₉	C₂²	1	2	yes	complemented
23	#540×C₈₉	C₂²	1	2	yes	complemented
24	#539×C₈₉	—	2	2	no	—
25	#538×C₈₉	—	2	2	no	—
26	#535×C₈₉	—	2	4	no	—
27	#535×C₈₉	C₂²	1	4	yes	—
28	#535×C₈₉	C₂²	1	4	yes	—
29	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
33	#529×C₈₉	—	2	4	no	—
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
36	#525×C₈₉	C₂²	1	2	yes	—
37	C₂×#121×C₈₉	—	2	2	no	—
38	C₂×#120×C₈₉	—	2	2	no	—
39	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
41	#497×C₈₉	C₂²	1	2	yes	complemented
42	#496×C₈₉	C₂²	1	2	yes	complemented
43	#496×C₈₉	C₂²	1	4	yes	complemented
44	#495×C₈₉	C₂²	1	4	yes	complemented
45	#493×C₈₉	C₂²	1	2	yes	complemented
46	#492×C₈₉	C₂²	1	2	yes	complemented
47	#490×C₈₉	C₂²	1	4	yes	complemented
48	#489×C₈₉	C₂²	1	4	yes	complemented
49	#488×C₈₉	C₂²	1	4	yes	complemented
50	#486×C₈₉	C₂²	1	4	yes	complemented
51	#464×C₈₉	C₂²	1	8	yes	complemented
52	#463×C₈₉	C₂²	1	8	yes	complemented
53	#460×C₈₉	C₂²	1	8	yes	complemented
54	#459×C₈₉	C₂²	1	8	yes	complemented
55	#452×C₈₉	C₂²	1	8	yes	complemented
56	#450×C₈₉	C₂²	1	8	yes	complemented
57	#449×C₈₉	C₂²	1	8	yes	complemented
58	#447×C₈₉	C₂²	1	8	yes	complemented
59	#433×C₈₉	C₂²	1	4	yes	complemented
60	#433×C₈₉	C₂²	1	4	yes	complemented
61	#423×C₈₉	C₂²	1	2	yes	complemented
62	#419×C₈₉	C₂²	1	2	yes	complemented
63	#418×C₈₉	C₂²	1	2	yes	—
64	#418×C₈₉	C₂²	1	2	yes	—
65	#418×C₈₉	C₂²	1	2	yes	complemented
66	#407×C₈₉	C₂²	1	2	yes	—
67	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₈₉	—	2	1	no	—
70	C₂×#41×C₈₉	—	2	2	no	—
71	C₂×#41×C₈₉	—	4	4	no	—
72	C₂×#41×C₈₉	C₂³	1	2	yes	—
73	C₂×#41×C₈₉	C₂³	1	4	yes	—
74	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₈₉	—	2	1	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	2	no	—
78	C₂²×D₄×C₈₉	—	2	2	no	—
79	C₂²×D₄×C₈₉	—	2	2	no	—
80	C₂²×D₄×C₈₉	—	4	4	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	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
85	C₂³×C₄×C₈₉	—	2	1	no	—
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	#137×C₈₉	—	4	4	no	—
88	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
89	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
90	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
91	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
92	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	complemented
95	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	complemented
96	C₂×D₈×C₈₉	C₂³	1	4	yes	—
97	C₂×D₈×C₈₉	C₂³	1	4	yes	—
98	C₂×D₈×C₈₉	C₂³	1	4	yes	complemented
99	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
102	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	complemented
103	#127×C₈₉	—	2	2	no	—
104	#127×C₈₉	—	2	2	no	—
105	#127×C₈₉	C₂³	1	4	yes	—
106	#127×C₈₉	C₂³	1	2	yes	—
107	#127×C₈₉	C₂³	1	2	yes	—
108	#127×C₈₉	C₂³	1	1	yes	characteristic, complemented
109	#126×C₈₉	—	2	4	no	—
110	#126×C₈₉	—	2	4	no	—
111	#125×C₈₉	—	2	4	no	—
112	#125×C₈₉	C₂³	1	2	yes	complemented
113	#124×C₈₉	—	2	4	no	—
114	#124×C₈₉	—	2	2	no	—
115	#124×C₈₉	—	2	2	no	—
116	#124×C₈₉	C₂³	1	4	yes	—
117	#124×C₈₉	C₂³	1	2	yes	—
118	#124×C₈₉	C₂³	1	2	yes	—
119	#124×C₈₉	C₂³	1	2	yes	complemented
120	#123×C₈₉	—	2	2	no	—
121	#123×C₈₉	—	2	4	no	—
122	#123×C₈₉	—	2	4	no	—
123	C₂²⋊Q₈×C₈₉	—	2	2	no	—
124	C₂²⋊Q₈×C₈₉	—	2	4	no	—
125	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
126	#121×C₈₉	—	2	2	no	—
127	#121×C₈₉	—	2	8	no	—
128	#121×C₈₉	—	2	8	no	—
129	#121×C₈₉	—	2	4	no	—
130	#121×C₈₉	C₂³	1	4	yes	—
131	#120×C₈₉	—	2	2	no	—
132	#120×C₈₉	—	2	8	no	—
133	#120×C₈₉	—	2	8	no	—
134	C₄×Q₈×C₈₉	—	2	2	no	—
135	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
136	C₄×D₄×C₈₉	—	2	4	no	—
137	C₄×D₄×C₈₉	—	2	4	no	—
138	C₄×D₄×C₈₉	—	2	2	no	—
139	C₄×D₄×C₈₉	C₂³	1	4	yes	complemented
140	#117×C₈₉	—	2	2	no	—
141	#117×C₈₉	D₄	1	4	yes	—
142	#117×C₈₉	C₂³	1	2	yes	—
143	#117×C₈₉	C₂³	1	2	yes	—
144	#117×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
149	C₂×C₄²×C₈₉	—	2	2	no	—
150	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	C₄⋊C₈×C₈₉	C₂³	1	8	yes	complemented
153	#103×C₈₉	C₂³	1	8	yes	complemented
154	#102×C₈₉	C₂³	1	8	yes	—
155	#102×C₈₉	C₂³	1	8	yes	—
156	#102×C₈₉	C₂³	1	8	yes	complemented
157	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
158	#97×C₈₉	C₂³	1	2	yes	complemented
159	#97×C₈₉	C₂³	1	2	yes	complemented
160	C₄×C₈×C₈₉	C₂³	1	2	yes	complemented
161	C₄×C₈×C₈₉	C₂³	1	2	yes	complemented
162	C₂⁴×C₈₉	—	2	1	no	—
163	C₂⁴×C₈₉	—	2	1	no	—
164	C₂⁴×C₈₉	—	2	1	no	—
165	C₂⁴×C₈₉	—	2	4	no	—
166	C₂⁴×C₈₉	—	4	4	no	—
167	C₂⁴×C₈₉	—	8	4	no	—
168	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
169	#41×C₈₉	—	2	4	no	—
170	#41×C₈₉	—	2	4	no	—
171	#41×C₈₉	—	4	8	no	—
172	#41×C₈₉	—	4	8	no	—
173	C₂×Q₈×C₈₉	—	2	1	no	—
174	C₂×Q₈×C₈₉	—	2	2	no	—
175	C₂×Q₈×C₈₉	—	2	4	no	—
176	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
177	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
178	C₂×D₄×C₈₉	—	2	2	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	2	no	—
186	C₂×D₄×C₈₉	—	2	8	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	4	8	no	—
193	C₂×D₄×C₈₉	—	4	4	no	—
194	C₂×D₄×C₈₉	—	4	8	no	—
195	C₂×D₄×C₈₉	—	4	4	no	—
196	C₂×D₄×C₈₉	—	8	4	no	—
197	C₂×D₄×C₈₉	—	8	4	no	—
198	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
199	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
200	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
201	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₈₉	—	2	4	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	2	no	—
205	C₂²×C₄×C₈₉	—	2	4	no	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	4	4	no	—
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	Q₁₆×C₈₉	—	4	4	no	—
215	SD₁₆×C₈₉	—	4	4	no	—
216	SD₁₆×C₈₉	—	4	4	no	—
217	SD₁₆×C₈₉	—	4	4	no	—
218	SD₁₆×C₈₉	—	4	4	no	—
219	D₈×C₈₉	—	4	4	no	—
220	D₈×C₈₉	—	4	4	no	—
221	D₈×C₈₉	—	4	4	no	—
222	M₁₆×C₈₉	—	2	4	no	—
223	M₁₆×C₈₉	—	2	4	no	—
224	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
225	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	2	no	—
228	C₄⋊C₄×C₈₉	—	2	4	no	—
229	C₄⋊C₄×C₈₉	—	2	4	no	—
230	C₄⋊C₄×C₈₉	—	2	2	no	—
231	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
234	C₂²⋊C₄×C₈₉	—	2	2	no	—
235	C₂²⋊C₄×C₈₉	—	2	4	no	—
236	C₂²⋊C₄×C₈₉	—	2	8	no	—
237	C₂²⋊C₄×C₈₉	—	2	4	no	—
238	C₂²⋊C₄×C₈₉	—	2	4	no	—
239	C₂²⋊C₄×C₈₉	—	2	4	no	—
240	C₂²⋊C₄×C₈₉	—	2	4	no	—
241	C₂²⋊C₄×C₈₉	—	2	4	no	—
242	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
244	C₄²×C₈₉	—	2	2	no	—
245	C₄²×C₈₉	—	2	4	no	—
246	C₄²×C₈₉	C₂×D₄	1	2	yes	—
247	C₄²×C₈₉	C₂×D₄	1	2	yes	—
248	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₄²×C₈₉	C₂⁴	1	2	yes	—
251	C₂³×C₈₉	—	2	2	no	—
252	C₂³×C₈₉	—	2	2	no	—
253	C₂³×C₈₉	—	2	2	no	—
254	C₂³×C₈₉	—	2	2	no	—
255	C₂³×C₈₉	—	2	2	no	—
256	C₂³×C₈₉	—	4	2	no	—
257	C₂³×C₈₉	—	4	8	no	—
258	C₂³×C₈₉	—	4	4	no	—
259	C₂³×C₈₉	—	4	4	no	—
260	C₂³×C₈₉	—	4	4	no	—
261	C₂³×C₈₉	—	4	2	no	—
262	C₂³×C₈₉	—	4	2	no	—
263	C₂³×C₈₉	—	4	2	no	—
264	C₂³×C₈₉	—	8	8	no	—
265	C₂³×C₈₉	—	8	16	no	—
266	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
267	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₈₉	—	2	2	no	—
269	Q₈×C₈₉	—	2	2	no	—
270	Q₈×C₈₉	—	2	4	no	—
271	Q₈×C₈₉	—	4	2	no	—
272	Q₈×C₈₉	—	8	2	no	—
273	D₄×C₈₉	—	2	2	no	—
274	D₄×C₈₉	—	2	2	no	—
275	D₄×C₈₉	—	2	4	no	—
276	D₄×C₈₉	—	2	4	no	—
277	D₄×C₈₉	—	2	4	no	—
278	D₄×C₈₉	—	4	8	no	—
279	D₄×C₈₉	—	4	8	no	—
280	D₄×C₈₉	—	4	4	no	—
281	D₄×C₈₉	—	4	2	no	—
282	D₄×C₈₉	—	4	2	no	—
283	D₄×C₈₉	—	4	2	no	—
284	D₄×C₈₉	—	8	2	no	—
285	D₄×C₈₉	—	8	8	no	—
286	D₄×C₈₉	—	8	4	no	—
287	D₄×C₈₉	—	8	4	no	—
288	D₄×C₈₉	—	8	4	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	4	no	—
291	C₂×C₄×C₈₉	—	2	4	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	4	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	4	2	no	—
296	C₂×C₄×C₈₉	—	4	2	no	—
297	C₂×C₄×C₈₉	—	4	8	no	—
298	C₂×C₄×C₈₉	—	4	2	no	—
299	C₂×C₄×C₈₉	—	4	4	no	—
300	C₂×C₄×C₈₉	—	8	4	no	—
301	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
307	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
308	C₈×C₈₉	—	2	4	no	—
309	C₈×C₈₉	—	2	4	no	—
310	C₂²×C₈₉	—	2	2	no	—
311	C₂²×C₈₉	—	2	4	no	—
312	C₂²×C₈₉	—	2	2	no	—
313	C₂²×C₈₉	—	4	4	no	—
314	C₂²×C₈₉	—	4	4	no	—
315	C₂²×C₈₉	—	4	4	no	—
316	C₂²×C₈₉	—	4	4	no	—
317	C₂²×C₈₉	—	4	4	no	—
318	C₂²×C₈₉	—	4	2	no	—
319	C₂²×C₈₉	—	4	2	no	—
320	C₂²×C₈₉	—	4	2	no	—
321	C₂²×C₈₉	—	4	2	no	—
322	C₂²×C₈₉	—	8	4	no	—
323	C₂²×C₈₉	—	8	4	no	—
324	C₂²×C₈₉	—	8	4	no	—
325	C₂²×C₈₉	—	8	16	no	—
326	C₂²×C₈₉	#535	1	2	yes	—
327	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₈₉	—	2	4	no	—
329	C₄×C₈₉	—	2	2	no	—
330	C₄×C₈₉	—	2	2	no	—
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	4	4	no	—
333	C₄×C₈₉	—	4	2	no	—
334	C₄×C₈₉	—	4	2	no	—
335	C₄×C₈₉	#535	1	2	yes	—
336	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
337	#60806	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂×C₈₉	—	2	2	no	—
339	C₂×C₈₉	—	4	2	no	—
340	C₂×C₈₉	—	8	2	no	—
341	C₂×C₈₉	—	8	2	no	—
342	C₂×C₈₉	—	8	2	no	—
343	C₂×C₈₉	—	8	2	no	—
344	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
345	C₂×C₈₉	#3585	1	2	yes	—
346	#3455	C₂×C₈₉	1	1	yes	characteristic, complemented
347	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
348	#3224	C₂×C₈₉	1	8	yes	complemented
349	#3222	C₂×C₈₉	1	4	yes	complemented
350	#3220	C₂×C₈₉	1	4	yes	complemented
351	#3153	C₂×C₈₉	1	1	yes	characteristic, complemented
352	#3151	C₂×C₈₉	1	1	yes	characteristic, complemented
353	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
354	#3138	C₂×C₈₉	1	1	yes	characteristic, complemented
355	#3040	C₂×C₈₉	1	2	yes	complemented
356	#3038	C₂×C₈₉	1	2	yes	complemented
357	#3005	C₂×C₈₉	1	2	yes	complemented
358	#3003	C₂×C₈₉	1	2	yes	complemented
359	#2921	C₂×C₈₉	1	1	yes	characteristic, complemented
360	C₈₉	#60806	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
362	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
363	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
364	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
365	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
366	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
367	#542	C₂²×C₈₉	1	4	yes	complemented
368	#541	C₂²×C₈₉	1	2	yes	complemented
369	#540	C₂²×C₈₉	1	2	yes	complemented
370	#539	—	2	2	no	—
371	#538	—	2	2	no	—
372	#535	—	2	4	no	—
373	#535	C₂²×C₈₉	1	4	yes	—
374	#535	C₂²×C₈₉	1	4	yes	—
375	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
376	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
377	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
378	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
379	#529	—	2	4	no	—
380	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
381	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
382	#525	C₂²×C₈₉	1	2	yes	—
383	C₂×#121	—	2	2	no	—
384	C₂×#120	—	2	2	no	—
385	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
386	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
387	#497	C₂²×C₈₉	1	2	yes	complemented
388	#496	C₂²×C₈₉	1	2	yes	complemented
389	#496	C₂²×C₈₉	1	4	yes	complemented
390	#495	C₂²×C₈₉	1	4	yes	complemented
391	#493	C₂²×C₈₉	1	2	yes	complemented
392	#492	C₂²×C₈₉	1	2	yes	complemented
393	#490	C₂²×C₈₉	1	4	yes	complemented
394	#489	C₂²×C₈₉	1	4	yes	complemented
395	#488	C₂²×C₈₉	1	4	yes	complemented
396	#486	C₂²×C₈₉	1	4	yes	complemented
397	#464	C₂²×C₈₉	1	8	yes	complemented
398	#463	C₂²×C₈₉	1	8	yes	complemented
399	#460	C₂²×C₈₉	1	8	yes	complemented
400	#459	C₂²×C₈₉	1	8	yes	complemented
401	#452	C₂²×C₈₉	1	8	yes	complemented
402	#450	C₂²×C₈₉	1	8	yes	complemented
403	#449	C₂²×C₈₉	1	8	yes	complemented
404	#447	C₂²×C₈₉	1	8	yes	complemented
405	#433	C₂²×C₈₉	1	4	yes	complemented
406	#433	C₂²×C₈₉	1	4	yes	complemented
407	#423	C₂²×C₈₉	1	2	yes	complemented
408	#419	C₂²×C₈₉	1	2	yes	complemented
409	#418	C₂²×C₈₉	1	2	yes	—
410	#418	C₂²×C₈₉	1	2	yes	—
411	#418	C₂²×C₈₉	1	2	yes	complemented
412	#407	C₂²×C₈₉	1	2	yes	—
413	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
414	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
415	C₂⁵	—	2	1	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	4	4	no	—
418	C₂×#41	C₂³×C₈₉	1	2	yes	—
419	C₂×#41	C₂³×C₈₉	1	4	yes	—
420	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	—	2	2	no	—
426	C₂²×D₄	—	4	4	no	—
427	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
430	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
433	#137	—	4	4	no	—
434	AGL(1,ℤ/8)	—	4	4	no	—
435	AGL(1,ℤ/8)	—	4	4	no	—
436	AGL(1,ℤ/8)	—	4	4	no	—
437	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
438	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
440	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	complemented
441	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	complemented
442	C₂×D₈	C₂³×C₈₉	1	4	yes	—
443	C₂×D₈	C₂³×C₈₉	1	4	yes	—
444	C₂×D₈	C₂³×C₈₉	1	4	yes	complemented
445	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
446	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
447	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
448	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	complemented
449	#127	—	2	2	no	—
450	#127	—	2	2	no	—
451	#127	C₂³×C₈₉	1	4	yes	—
452	#127	C₂³×C₈₉	1	2	yes	—
453	#127	C₂³×C₈₉	1	2	yes	—
454	#127	C₂³×C₈₉	1	1	yes	characteristic, complemented
455	#126	—	2	4	no	—
456	#126	—	2	4	no	—
457	#125	—	2	4	no	—
458	#125	C₂³×C₈₉	1	2	yes	complemented
459	#124	—	2	4	no	—
460	#124	—	2	2	no	—
461	#124	—	2	2	no	—
462	#124	C₂³×C₈₉	1	4	yes	—
463	#124	C₂³×C₈₉	1	2	yes	—
464	#124	C₂³×C₈₉	1	2	yes	—
465	#124	C₂³×C₈₉	1	2	yes	complemented
466	#123	—	2	2	no	—
467	#123	—	2	4	no	—
468	#123	—	2	4	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
472	#121	—	2	2	no	—
473	#121	—	2	8	no	—
474	#121	—	2	8	no	—
475	#121	—	2	4	no	—
476	#121	C₂³×C₈₉	1	4	yes	—
477	#120	—	2	2	no	—
478	#120	—	2	8	no	—
479	#120	—	2	8	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	C₂³×C₈₉	1	4	yes	complemented
486	#117	—	2	2	no	—
487	#117	D₄×C₈₉	1	4	yes	—
488	#117	C₂³×C₈₉	1	2	yes	—
489	#117	C₂³×C₈₉	1	2	yes	—
490	#117	C₂³×C₈₉	1	2	yes	—
491	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
495	C₂×C₄²	—	2	2	no	—
496	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
498	C₄⋊C₈	C₂³×C₈₉	1	8	yes	complemented
499	#103	C₂³×C₈₉	1	8	yes	complemented
500	#102	C₂³×C₈₉	1	8	yes	—
501	#102	C₂³×C₈₉	1	8	yes	—
502	#102	C₂³×C₈₉	1	8	yes	complemented
503	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
504	#97	C₂³×C₈₉	1	2	yes	complemented
505	#97	C₂³×C₈₉	1	2	yes	complemented
506	C₄×C₈	C₂³×C₈₉	1	2	yes	complemented
507	C₄×C₈	C₂³×C₈₉	1	2	yes	complemented
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	8	4	no	—
514	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
515	#41	—	2	4	no	—
516	#41	—	2	4	no	—
517	#41	—	4	8	no	—
518	#41	—	4	8	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
523	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	8	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	—	8	4	no	—
544	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
545	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
546	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
547	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
557	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
560	Q₁₆	—	4	4	no	—
561	SD₁₆	—	4	4	no	—
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	SD₁₆	—	4	4	no	—
565	D₈	—	4	4	no	—
566	D₈	—	4	4	no	—
567	D₈	—	4	4	no	—
568	M₁₆	—	2	4	no	—
569	M₁₆	—	2	4	no	—
570	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
571	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
578	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	C₂×D₄×C₈₉	1	2	yes	—
593	C₄²	C₂×D₄×C₈₉	1	2	yes	—
594	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
595	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₄²	C₂⁴×C₈₉	1	2	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	16	no	—
612	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
613	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	8	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	8	2	no	—
631	D₄	—	8	8	no	—
632	D₄	—	8	4	no	—
633	D₄	—	8	4	no	—
634	D₄	—	8	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
652	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
653	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
654	C₈	—	2	4	no	—
655	C₈	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	8	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	16	no	—
672	C₂²	#535×C₈₉	1	2	yes	—
673	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
674	C₄	—	2	4	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	#535×C₈₉	1	2	yes	—
682	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	2	no	—
688	C₂	—	8	2	no	—
689	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
690	C₂	C₈₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3455	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₈₉×#3224	C₂	semidirect
4. C₈₉×#3222	C₂	semidirect
5. C₈₉×#3220	C₂	semidirect
6. C₈₉×#3153	C₂	semidirect
7. C₈₉×#3151	C₂	semidirect
8. C₈₉×#3140	C₂	semidirect
9. C₈₉×#3138	C₂	semidirect
10. C₈₉×#3040	C₂	semidirect
11. C₈₉×#3038	C₂	semidirect
12. C₈₉×#3005	C₂	semidirect
13. C₈₉×#3003	C₂	semidirect
14. C₈₉×#2921	C₂	semidirect
17. C₂×#137×C₈₉	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
21. #542×C₈₉	C₂²	semidirect
22. #541×C₈₉	C₂²	semidirect
23. #540×C₈₉	C₂²	semidirect
29. #533×C₈₉	C₂²	semidirect
30. #532×C₈₉	C₂²	semidirect
39. C₄×#41×C₈₉	C₂²	semidirect
41. #497×C₈₉	C₂²	semidirect
42. #496×C₈₉	C₂²	semidirect
43. #496×C₈₉	C₂²	semidirect
44. #495×C₈₉	C₂²	semidirect
45. #493×C₈₉	C₂²	semidirect
46. #492×C₈₉	C₂²	semidirect
47. #490×C₈₉	C₂²	semidirect
48. #489×C₈₉	C₂²	semidirect
49. #488×C₈₉	C₂²	semidirect
50. #486×C₈₉	C₂²	semidirect
51. #464×C₈₉	C₂²	semidirect
52. #463×C₈₉	C₂²	semidirect
53. #460×C₈₉	C₂²	semidirect
54. #459×C₈₉	C₂²	semidirect
55. #452×C₈₉	C₂²	semidirect
56. #450×C₈₉	C₂²	semidirect
57. #449×C₈₉	C₂²	semidirect
58. #447×C₈₉	C₂²	semidirect
59. #433×C₈₉	C₂²	semidirect
60. #433×C₈₉	C₂²	semidirect
61. #423×C₈₉	C₂²	semidirect
62. #419×C₈₉	C₂²	semidirect
65. #418×C₈₉	C₂²	semidirect
67. C₄×M₁₆×C₈₉	C₂²	semidirect
68. C₄×M₁₆×C₈₉	C₂²	semidirect
91. C₂×Q₁₆×C₈₉	C₂³	semidirect
94. C₂×SD₁₆×C₈₉	C₂³	semidirect
95. C₂×SD₁₆×C₈₉	C₂³	semidirect
98. C₂×D₈×C₈₉	C₂³	semidirect
101. C₄⋊Q₈×C₈₉	C₂³	semidirect
102. C₄⋊Q₈×C₈₉	C₂³	semidirect
108. #127×C₈₉	C₂³	semidirect
112. #125×C₈₉	C₂³	semidirect
119. #124×C₈₉	C₂³	semidirect
135. C₄×Q₈×C₈₉	C₂³	semidirect
139. C₄×D₄×C₈₉	C₂³	semidirect
152. C₄⋊C₈×C₈₉	C₂³	semidirect
153. #103×C₈₉	C₂³	semidirect
156. #102×C₈₉	C₂³	semidirect
158. #97×C₈₉	C₂³	semidirect
159. #97×C₈₉	C₂³	semidirect
160. C₄×C₈×C₈₉	C₂³	semidirect
161. C₄×C₈×C₈₉	C₂³	semidirect
337. #60806	C₈₉	direct (N × H)
346. #3455	C₂×C₈₉	semidirect
347. C₂×#535	C₂×C₈₉	semidirect
348. #3224	C₂×C₈₉	semidirect
349. #3222	C₂×C₈₉	semidirect
350. #3220	C₂×C₈₉	semidirect
351. #3153	C₂×C₈₉	semidirect
352. #3151	C₂×C₈₉	semidirect
353. #3140	C₂×C₈₉	semidirect
354. #3138	C₂×C₈₉	semidirect
355. #3040	C₂×C₈₉	semidirect
356. #3038	C₂×C₈₉	semidirect
357. #3005	C₂×C₈₉	semidirect
358. #3003	C₂×C₈₉	semidirect
359. #2921	C₂×C₈₉	semidirect
360. C₈₉	#60806	direct (N × H)
363. C₂×#137	C₂²×C₈₉	semidirect
366. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
367. #542	C₂²×C₈₉	semidirect
368. #541	C₂²×C₈₉	semidirect
369. #540	C₂²×C₈₉	semidirect
375. #533	C₂²×C₈₉	semidirect
376. #532	C₂²×C₈₉	semidirect
385. C₄×#41	C₂²×C₈₉	semidirect
387. #497	C₂²×C₈₉	semidirect
388. #496	C₂²×C₈₉	semidirect
389. #496	C₂²×C₈₉	semidirect
390. #495	C₂²×C₈₉	semidirect
391. #493	C₂²×C₈₉	semidirect
392. #492	C₂²×C₈₉	semidirect
393. #490	C₂²×C₈₉	semidirect
394. #489	C₂²×C₈₉	semidirect
395. #488	C₂²×C₈₉	semidirect
396. #486	C₂²×C₈₉	semidirect
397. #464	C₂²×C₈₉	semidirect
398. #463	C₂²×C₈₉	semidirect
399. #460	C₂²×C₈₉	semidirect
400. #459	C₂²×C₈₉	semidirect
401. #452	C₂²×C₈₉	semidirect
402. #450	C₂²×C₈₉	semidirect
403. #449	C₂²×C₈₉	semidirect
404. #447	C₂²×C₈₉	semidirect
405. #433	C₂²×C₈₉	semidirect
406. #433	C₂²×C₈₉	semidirect
407. #423	C₂²×C₈₉	semidirect
408. #419	C₂²×C₈₉	semidirect
411. #418	C₂²×C₈₉	semidirect
413. C₄×M₁₆	C₂²×C₈₉	semidirect
414. C₄×M₁₆	C₂²×C₈₉	semidirect
437. C₂×Q₁₆	C₂³×C₈₉	semidirect
440. C₂×SD₁₆	C₂³×C₈₉	semidirect
441. C₂×SD₁₆	C₂³×C₈₉	semidirect
444. C₂×D₈	C₂³×C₈₉	semidirect
447. C₄⋊Q₈	C₂³×C₈₉	semidirect
448. C₄⋊Q₈	C₂³×C₈₉	semidirect
454. #127	C₂³×C₈₉	semidirect
458. #125	C₂³×C₈₉	semidirect
465. #124	C₂³×C₈₉	semidirect
481. C₄×Q₈	C₂³×C₈₉	semidirect
485. C₄×D₄	C₂³×C₈₉	semidirect
498. C₄⋊C₈	C₂³×C₈₉	semidirect
499. #103	C₂³×C₈₉	semidirect
502. #102	C₂³×C₈₉	semidirect
504. #97	C₂³×C₈₉	semidirect
505. #97	C₂³×C₈₉	semidirect
506. C₄×C₈	C₂³×C₈₉	semidirect
507. C₄×C₈	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3455	2
C₂×#535×C₈₉	2
C₈₉×#3224	2
C₈₉×#3222	2
C₈₉×#3220	2
C₈₉×#3153	2
C₈₉×#3151	2
C₈₉×#3140	2
C₈₉×#3138	2
C₈₉×#3040	2
C₈₉×#3038	2
C₈₉×#3005	2
C₈₉×#3003	2
C₈₉×#2921	2
#60806	89

Subgroups — C89×#60806 #36438654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60806 #36438654