Subgroups — C₈₉×#60864 #36438712

Order 22784.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3235	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3234	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3228	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3227	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3226	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3165	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3138	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3094	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3077	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	—	2	1	no	—
14	#533×C₈₉	—	2	1	no	—
15	#533×C₈₉	—	2	1	no	—
16	#533×C₈₉	—	2	1	no	—
17	#533×C₈₉	—	2	1	no	—
18	#533×C₈₉	C₂²	1	2	yes	—
19	#533×C₈₉	C₂²	1	2	yes	—
20	#533×C₈₉	C₂²	1	2	yes	complemented
21	#533×C₈₉	C₂²	1	2	yes	complemented
22	#532×C₈₉	—	2	1	no	—
23	#532×C₈₉	—	2	1	no	—
24	#532×C₈₉	—	2	1	no	—
25	#532×C₈₉	—	2	1	no	—
26	#532×C₈₉	C₂²	1	2	yes	—
27	#532×C₈₉	C₂²	1	2	yes	—
28	#532×C₈₉	C₂²	1	2	yes	—
29	#532×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
35	C₂×#124×C₈₉	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
37	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
38	C₂×#121×C₈₉	—	2	1	no	—
39	C₂×#121×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
41	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
42	C₂×C₄×D₄×C₈₉	—	2	1	no	—
43	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
44	C₂×#117×C₈₉	C₂²	1	2	yes	—
45	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
46	#501×C₈₉	C₂²	1	8	yes	complemented
47	#500×C₈₉	C₂²	1	4	yes	complemented
48	#498×C₈₉	C₂²	1	4	yes	complemented
49	#490×C₈₉	C₂²	1	8	yes	complemented
50	#486×C₈₉	C₂²	1	4	yes	complemented
51	#486×C₈₉	C₂²	1	4	yes	complemented
52	#482×C₈₉	C₂²	1	16	yes	complemented
53	#481×C₈₉	C₂²	1	8	yes	complemented
54	#480×C₈₉	C₂²	1	8	yes	complemented
55	#478×C₈₉	C₂²	1	16	yes	complemented
56	#476×C₈₉	C₂²	1	8	yes	complemented
57	#474×C₈₉	C₂²	1	8	yes	complemented
58	#432×C₈₉	C₂²	1	2	yes	complemented
59	#432×C₈₉	C₂²	1	2	yes	complemented
60	#431×C₈₉	C₂²	1	2	yes	complemented
61	#431×C₈₉	C₂²	1	2	yes	complemented
62	#428×C₈₉	C₂²	1	8	yes	—
63	#423×C₈₉	C₂²	1	2	yes	—
64	#418×C₈₉	C₂²	1	8	yes	—
65	#407×C₈₉	C₂²	1	2	yes	—
66	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	2	no	—
70	C₂×#41×C₈₉	—	2	2	no	—
71	C₂×#41×C₈₉	—	4	8	no	—
72	C₂²×Q₈×C₈₉	—	2	1	no	—
73	C₂²×Q₈×C₈₉	—	2	1	no	—
74	C₂²×Q₈×C₈₉	—	2	1	no	—
75	C₂²×D₄×C₈₉	—	2	2	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₈₉	—	2	2	no	—
80	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
84	C₄⋊Q₈×C₈₉	—	2	1	no	—
85	C₄⋊Q₈×C₈₉	—	2	1	no	—
86	C₄⋊Q₈×C₈₉	—	2	1	no	—
87	C₄⋊Q₈×C₈₉	—	2	1	no	—
88	C₄⋊Q₈×C₈₉	—	2	1	no	—
89	C₄⋊Q₈×C₈₉	—	2	1	no	—
90	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	#127×C₈₉	—	2	1	no	—
97	#127×C₈₉	—	2	1	no	—
98	#127×C₈₉	C₂³	1	2	yes	—
99	#127×C₈₉	C₂³	1	2	yes	—
100	#125×C₈₉	—	2	2	no	—
101	#125×C₈₉	—	2	2	no	—
102	#125×C₈₉	C₂³	1	4	yes	—
103	#125×C₈₉	C₂³	1	4	yes	—
104	#124×C₈₉	—	2	2	no	—
105	#124×C₈₉	—	2	2	no	—
106	#124×C₈₉	—	2	2	no	—
107	#124×C₈₉	—	2	2	no	—
108	C₂²⋊Q₈×C₈₉	—	2	2	no	—
109	C₂²⋊Q₈×C₈₉	—	2	2	no	—
110	C₂²⋊Q₈×C₈₉	—	2	2	no	—
111	C₂²⋊Q₈×C₈₉	—	2	2	no	—
112	C₂²⋊Q₈×C₈₉	—	2	2	no	—
113	C₂²⋊Q₈×C₈₉	—	2	2	no	—
114	C₂²⋊Q₈×C₈₉	—	2	2	no	—
115	C₂²⋊Q₈×C₈₉	—	2	2	no	—
116	#121×C₈₉	—	2	2	no	—
117	#121×C₈₉	—	2	2	no	—
118	#121×C₈₉	—	2	2	no	—
119	#121×C₈₉	—	2	2	no	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	—	2	2	no	—
122	#121×C₈₉	C₂³	1	4	yes	—
123	#121×C₈₉	C₂³	1	4	yes	—
124	C₄×Q₈×C₈₉	—	2	2	no	—
125	C₄×Q₈×C₈₉	—	2	2	no	—
126	C₄×Q₈×C₈₉	—	2	2	no	—
127	C₄×Q₈×C₈₉	—	2	2	no	—
128	C₄×Q₈×C₈₉	—	2	2	no	—
129	C₄×Q₈×C₈₉	—	2	2	no	—
130	C₄×Q₈×C₈₉	—	2	2	no	—
131	C₄×Q₈×C₈₉	—	2	2	no	—
132	C₄×D₄×C₈₉	—	2	2	no	—
133	C₄×D₄×C₈₉	—	2	2	no	—
134	C₄×D₄×C₈₉	—	2	2	no	—
135	C₄×D₄×C₈₉	—	2	2	no	—
136	C₄×D₄×C₈₉	—	2	2	no	—
137	C₄×D₄×C₈₉	—	2	2	no	—
138	C₄×D₄×C₈₉	C₂³	1	4	yes	—
139	C₄×D₄×C₈₉	C₂³	1	4	yes	—
140	#117×C₈₉	—	2	2	no	—
141	#117×C₈₉	—	2	2	no	—
142	#117×C₈₉	C₂³	1	4	yes	—
143	#117×C₈₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
147	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
153	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
155	C₂×C₄²×C₈₉	—	2	2	no	—
156	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	#107×C₈₉	C₂³	1	16	yes	—
169	#106×C₈₉	C₂³	1	16	yes	—
170	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
171	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
172	#102×C₈₉	C₂³	1	16	yes	—
173	#102×C₈₉	C₂³	1	16	yes	—
174	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
175	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
176	#97×C₈₉	C₂³	1	4	yes	—
177	C₄×C₈×C₈₉	C₂³	1	4	yes	—
178	C₂⁴×C₈₉	—	2	2	no	—
179	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
180	#41×C₈₉	—	4	8	no	—
181	#41×C₈₉	—	4	8	no	—
182	#41×C₈₉	—	4	8	no	—
183	#41×C₈₉	—	4	8	no	—
184	C₂×Q₈×C₈₉	—	2	2	no	—
185	C₂×Q₈×C₈₉	—	2	2	no	—
186	C₂×Q₈×C₈₉	—	2	2	no	—
187	C₂×Q₈×C₈₉	—	2	2	no	—
188	C₂×Q₈×C₈₉	—	2	2	no	—
189	C₂×Q₈×C₈₉	—	2	2	no	—
190	C₂×Q₈×C₈₉	—	4	4	no	—
191	C₂×Q₈×C₈₉	—	4	4	no	—
192	C₂×Q₈×C₈₉	—	4	4	no	—
193	C₂×D₄×C₈₉	—	2	4	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	2	no	—
196	C₂×D₄×C₈₉	—	2	2	no	—
197	C₂×D₄×C₈₉	—	2	2	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	2	2	no	—
200	C₂×D₄×C₈₉	—	2	8	no	—
201	C₂×D₄×C₈₉	—	4	4	no	—
202	C₂×D₄×C₈₉	—	4	4	no	—
203	C₂×D₄×C₈₉	—	4	8	no	—
204	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₈₉	—	2	4	no	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	4	2	no	—
213	C₂²×C₄×C₈₉	—	4	8	no	—
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	M₁₆×C₈₉	—	2	8	no	—
233	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
234	C₄⋊C₄×C₈₉	—	2	2	no	—
235	C₄⋊C₄×C₈₉	—	2	2	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	2	no	—
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	2	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
249	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
250	C₂²⋊C₄×C₈₉	—	2	4	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	—	2	4	no	—
258	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
272	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	4	no	—
277	C₂³×C₈₉	—	4	1	no	—
278	C₂³×C₈₉	—	4	4	no	—
279	C₂³×C₈₉	—	4	4	no	—
280	C₂³×C₈₉	—	4	4	no	—
281	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₈₉	—	4	4	no	—
285	Q₈×C₈₉	—	4	4	no	—
286	Q₈×C₈₉	—	4	4	no	—
287	Q₈×C₈₉	—	4	4	no	—
288	Q₈×C₈₉	—	4	4	no	—
289	Q₈×C₈₉	—	4	4	no	—
290	D₄×C₈₉	—	2	8	no	—
291	D₄×C₈₉	—	4	4	no	—
292	D₄×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	4	8	no	—
294	D₄×C₈₉	—	4	8	no	—
295	D₄×C₈₉	—	4	4	no	—
296	D₄×C₈₉	—	4	4	no	—
297	D₄×C₈₉	—	4	4	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	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	4	no	—
312	C₂×C₄×C₈₉	—	2	4	no	—
313	C₂×C₄×C₈₉	—	2	4	no	—
314	C₂×C₄×C₈₉	—	4	1	no	—
315	C₂×C₄×C₈₉	—	4	1	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	8	no	—
318	C₂×C₄×C₈₉	—	4	4	no	—
319	C₂×C₄×C₈₉	—	4	4	no	—
320	C₂×C₄×C₈₉	—	4	4	no	—
321	C₂×C₄×C₈₉	—	4	8	no	—
322	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
323	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
335	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
336	C₈×C₈₉	—	2	8	no	—
337	C₂²×C₈₉	—	2	1	no	—
338	C₂²×C₈₉	—	2	1	no	—
339	C₂²×C₈₉	—	2	1	no	—
340	C₂²×C₈₉	—	2	1	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	1	no	—
344	C₂²×C₈₉	—	4	4	no	—
345	C₂²×C₈₉	—	4	4	no	—
346	C₂²×C₈₉	—	4	4	no	—
347	C₂²×C₈₉	—	4	4	no	—
348	C₂²×C₈₉	—	8	8	no	—
349	C₂²×C₈₉	#536	1	2	yes	—
350	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
351	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₈₉	—	2	1	no	—
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	1	no	—
355	C₄×C₈₉	—	2	1	no	—
356	C₄×C₈₉	—	2	1	no	—
357	C₄×C₈₉	—	2	1	no	—
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	4	4	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	—	4	4	no	—
362	C₄×C₈₉	#536	1	2	yes	—
363	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
364	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
365	C₄×C₈₉	#575	1	2	yes	—
366	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
367	#60864	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂×C₈₉	—	2	2	no	—
369	C₂×C₈₉	—	2	2	no	—
370	C₂×C₈₉	—	4	1	no	—
371	C₂×C₈₉	—	8	4	no	—
372	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
373	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
375	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
376	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
377	#3235	C₂×C₈₉	1	4	yes	complemented
378	#3234	C₂×C₈₉	1	4	yes	complemented
379	#3228	C₂×C₈₉	1	4	yes	complemented
380	#3227	C₂×C₈₉	1	2	yes	complemented
381	#3226	C₂×C₈₉	1	2	yes	complemented
382	#3165	C₂×C₈₉	1	2	yes	complemented
383	#3138	C₂×C₈₉	1	2	yes	complemented
384	#3094	C₂×C₈₉	1	4	yes	complemented
385	#3077	C₂×C₈₉	1	4	yes	complemented
386	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
387	C₈₉	#60864	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²×#41	—	2	1	no	—
389	#533	—	2	1	no	—
390	#533	—	2	1	no	—
391	#533	—	2	1	no	—
392	#533	—	2	1	no	—
393	#533	C₂²×C₈₉	1	2	yes	—
394	#533	C₂²×C₈₉	1	2	yes	—
395	#533	C₂²×C₈₉	1	2	yes	complemented
396	#533	C₂²×C₈₉	1	2	yes	complemented
397	#532	—	2	1	no	—
398	#532	—	2	1	no	—
399	#532	—	2	1	no	—
400	#532	—	2	1	no	—
401	#532	C₂²×C₈₉	1	2	yes	—
402	#532	C₂²×C₈₉	1	2	yes	—
403	#532	C₂²×C₈₉	1	2	yes	—
404	#532	C₂²×C₈₉	1	2	yes	—
405	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
407	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
408	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
410	C₂×#124	—	2	1	no	—
411	C₂×C₂²⋊Q₈	—	2	1	no	—
412	C₂×C₂²⋊Q₈	—	2	1	no	—
413	C₂×#121	—	2	1	no	—
414	C₂×#121	C₂²×C₈₉	1	2	yes	—
415	C₂×C₄×Q₈	—	2	1	no	—
416	C₂×C₄×Q₈	—	2	1	no	—
417	C₂×C₄×D₄	—	2	1	no	—
418	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
419	C₂×#117	C₂²×C₈₉	1	2	yes	—
420	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
421	#501	C₂²×C₈₉	1	8	yes	complemented
422	#500	C₂²×C₈₉	1	4	yes	complemented
423	#498	C₂²×C₈₉	1	4	yes	complemented
424	#490	C₂²×C₈₉	1	8	yes	complemented
425	#486	C₂²×C₈₉	1	4	yes	complemented
426	#486	C₂²×C₈₉	1	4	yes	complemented
427	#482	C₂²×C₈₉	1	16	yes	complemented
428	#481	C₂²×C₈₉	1	8	yes	complemented
429	#480	C₂²×C₈₉	1	8	yes	complemented
430	#478	C₂²×C₈₉	1	16	yes	complemented
431	#476	C₂²×C₈₉	1	8	yes	complemented
432	#474	C₂²×C₈₉	1	8	yes	complemented
433	#432	C₂²×C₈₉	1	2	yes	complemented
434	#432	C₂²×C₈₉	1	2	yes	complemented
435	#431	C₂²×C₈₉	1	2	yes	complemented
436	#431	C₂²×C₈₉	1	2	yes	complemented
437	#428	C₂²×C₈₉	1	8	yes	—
438	#423	C₂²×C₈₉	1	2	yes	—
439	#418	C₂²×C₈₉	1	8	yes	—
440	#407	C₂²×C₈₉	1	2	yes	—
441	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	4	8	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
454	C₂³×C₄	—	2	2	no	—
455	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
456	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	—	2	1	no	—
464	C₄⋊Q₈	—	2	1	no	—
465	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
469	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
470	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
471	#127	—	2	1	no	—
472	#127	—	2	1	no	—
473	#127	C₂³×C₈₉	1	2	yes	—
474	#127	C₂³×C₈₉	1	2	yes	—
475	#125	—	2	2	no	—
476	#125	—	2	2	no	—
477	#125	C₂³×C₈₉	1	4	yes	—
478	#125	C₂³×C₈₉	1	4	yes	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#124	—	2	2	no	—
482	#124	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	C₂³×C₈₉	1	4	yes	—
498	#121	C₂³×C₈₉	1	4	yes	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	C₂³×C₈₉	1	4	yes	—
514	C₄×D₄	C₂³×C₈₉	1	4	yes	—
515	#117	—	2	2	no	—
516	#117	—	2	2	no	—
517	#117	C₂³×C₈₉	1	4	yes	—
518	#117	C₂³×C₈₉	1	4	yes	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
532	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
533	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
534	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
535	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
536	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
543	#107	C₂³×C₈₉	1	16	yes	—
544	#106	C₂³×C₈₉	1	16	yes	—
545	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
546	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
547	#102	C₂³×C₈₉	1	16	yes	—
548	#102	C₂³×C₈₉	1	16	yes	—
549	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
551	#97	C₂³×C₈₉	1	4	yes	—
552	C₄×C₈	C₂³×C₈₉	1	4	yes	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
555	#41	—	4	8	no	—
556	#41	—	4	8	no	—
557	#41	—	4	8	no	—
558	#41	—	4	8	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	4	4	no	—
566	C₂×Q₈	—	4	4	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	8	no	—
579	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	8	no	—
589	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
607	M₁₆	—	2	8	no	—
608	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
623	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
624	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
634	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
635	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
646	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
648	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
657	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
658	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
659	Q₈	—	4	4	no	—
660	Q₈	—	4	4	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	4	no	—
665	D₄	—	2	8	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	8	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
709	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
710	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
711	C₈	—	2	8	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	8	8	no	—
724	C₂²	#536×C₈₉	1	2	yes	—
725	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
726	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	4	no	—
737	C₄	#536×C₈₉	1	2	yes	—
738	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
739	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
740	C₄	#575×C₈₉	1	2	yes	—
741	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	8	4	no	—
746	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
747	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
748	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3235	C₂	semidirect
4. C₈₉×#3234	C₂	semidirect
5. C₈₉×#3228	C₂	semidirect
6. C₈₉×#3227	C₂	semidirect
7. C₈₉×#3226	C₂	semidirect
8. C₈₉×#3165	C₂	semidirect
9. C₈₉×#3138	C₂	semidirect
10. C₈₉×#3094	C₂	semidirect
11. C₈₉×#3077	C₂	semidirect
12. C₈₉×#2920	C₂	semidirect
20. #533×C₈₉	C₂²	semidirect
21. #533×C₈₉	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
32. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
34. C₂×#125×C₈₉	C₂²	semidirect
46. #501×C₈₉	C₂²	semidirect
47. #500×C₈₉	C₂²	semidirect
48. #498×C₈₉	C₂²	semidirect
49. #490×C₈₉	C₂²	semidirect
50. #486×C₈₉	C₂²	semidirect
51. #486×C₈₉	C₂²	semidirect
52. #482×C₈₉	C₂²	semidirect
53. #481×C₈₉	C₂²	semidirect
54. #480×C₈₉	C₂²	semidirect
55. #478×C₈₉	C₂²	semidirect
56. #476×C₈₉	C₂²	semidirect
57. #474×C₈₉	C₂²	semidirect
58. #432×C₈₉	C₂²	semidirect
59. #432×C₈₉	C₂²	semidirect
60. #431×C₈₉	C₂²	semidirect
61. #431×C₈₉	C₂²	semidirect
367. #60864	C₈₉	direct (N × H)
375. C₂×#533	C₂×C₈₉	semidirect
377. #3235	C₂×C₈₉	semidirect
378. #3234	C₂×C₈₉	semidirect
379. #3228	C₂×C₈₉	semidirect
380. #3227	C₂×C₈₉	semidirect
381. #3226	C₂×C₈₉	semidirect
382. #3165	C₂×C₈₉	semidirect
383. #3138	C₂×C₈₉	semidirect
384. #3094	C₂×C₈₉	semidirect
385. #3077	C₂×C₈₉	semidirect
386. #2920	C₂×C₈₉	semidirect
387. C₈₉	#60864	direct (N × H)
395. #533	C₂²×C₈₉	semidirect
396. #533	C₂²×C₈₉	semidirect
406. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
407. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
409. C₂×#125	C₂²×C₈₉	semidirect
421. #501	C₂²×C₈₉	semidirect
422. #500	C₂²×C₈₉	semidirect
423. #498	C₂²×C₈₉	semidirect
424. #490	C₂²×C₈₉	semidirect
425. #486	C₂²×C₈₉	semidirect
426. #486	C₂²×C₈₉	semidirect
427. #482	C₂²×C₈₉	semidirect
428. #481	C₂²×C₈₉	semidirect
429. #480	C₂²×C₈₉	semidirect
430. #478	C₂²×C₈₉	semidirect
431. #476	C₂²×C₈₉	semidirect
432. #474	C₂²×C₈₉	semidirect
433. #432	C₂²×C₈₉	semidirect
434. #432	C₂²×C₈₉	semidirect
435. #431	C₂²×C₈₉	semidirect
436. #431	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#3235	2
C₈₉×#3234	2
C₈₉×#3228	2
C₈₉×#3227	2
C₈₉×#3226	2
C₈₉×#3165	2
C₈₉×#3138	2
C₈₉×#3094	2
C₈₉×#3077	2
C₈₉×#2920	2
#60864	89

Subgroups — C89×#60864 #36438712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60864 #36438712