Subgroups — C₈₉×#61433 #36439281

Order 22784.

1852 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3482	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3364	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3336	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3300	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3298	C₂	1	2	yes	maximal, complemented
9	D₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3285	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3108	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3107	C₂	1	2	yes	maximal, complemented
15	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×Q₁₆×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
20	#557×C₈₉	C₂²	1	2	yes	—
21	#556×C₈₉	—	2	2	no	—
22	#556×C₈₉	C₂²	1	2	yes	—
23	#552×C₈₉	—	2	4	no	—
24	#552×C₈₉	C₂²	1	4	yes	—
25	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	#548×C₈₉	C₂²	1	4	yes	—
27	#547×C₈₉	—	2	2	no	—
28	#547×C₈₉	C₂²	1	2	yes	—
29	#533×C₈₉	—	2	2	no	—
30	#533×C₈₉	C₂²	1	2	yes	—
31	#529×C₈₉	—	2	4	no	—
32	#529×C₈₉	C₂²	1	4	yes	—
33	C₄×#41×C₈₉	—	2	2	no	—
34	C₄×#41×C₈₉	C₂²	1	2	yes	—
35	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
37	#500×C₈₉	C₂²	1	1	yes	characteristic
38	#499×C₈₉	C₂²	1	2	yes	—
39	#495×C₈₉	C₂²	1	2	yes	—
40	#494×C₈₉	C₂²	1	1	yes	characteristic
41	#488×C₈₉	C₂²	1	4	yes	—
42	#487×C₈₉	C₂²	1	2	yes	—
43	#485×C₈₉	C₂²	1	4	yes	—
44	#483×C₈₉	C₂²	1	4	yes	—
45	#480×C₈₉	C₂²	1	4	yes	—
46	#479×C₈₉	C₂²	1	4	yes	—
47	#479×C₈₉	C₂²	1	4	yes	—
48	#475×C₈₉	C₂²	1	2	yes	—
49	#474×C₈₉	C₂²	1	2	yes	—
50	#467×C₈₉	C₂²	1	2	yes	—
51	#467×C₈₉	C₂²	1	2	yes	—
52	#467×C₈₉	C₂²	1	2	yes	—
53	#466×C₈₉	C₂²	1	2	yes	—
54	#465×C₈₉	C₂²	1	4	yes	—
55	#464×C₈₉	C₂²	1	4	yes	—
56	#464×C₈₉	C₂²	1	4	yes	—
57	#462×C₈₉	C₂²	1	2	yes	—
58	#461×C₈₉	C₂²	1	2	yes	—
59	#452×C₈₉	C₂²	1	4	yes	—
60	#451×C₈₉	C₂²	1	4	yes	—
61	#448×C₈₉	C₂²	1	4	yes	—
62	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
65	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
66	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
69	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
70	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
71	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
72	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
75	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₈₉	C₂²	1	2	yes	—
79	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₈₉	C₂²	1	2	yes	—
81	#431×C₈₉	C₂²	1	1	yes	characteristic
82	#431×C₈₉	C₂²	1	2	yes	—
83	#427×C₈₉	C₂²	1	1	yes	characteristic
84	C₂×#107×C₈₉	C₂²	1	2	yes	—
85	#416×C₈₉	C₂²	1	2	yes	—
86	C₂×#103×C₈₉	C₂²	1	4	yes	—
87	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₈₉	—	2	2	no	—
90	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
91	C₂×#41×C₈₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
93	#135×C₈₉	—	2	4	no	—
94	C₂×Q₁₆×C₈₉	—	2	8	no	—
95	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
96	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₈₉	—	2	2	no	—
107	C₄⋊Q₈×C₈₉	—	2	2	no	—
108	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
110	#126×C₈₉	—	2	4	no	—
111	#126×C₈₉	—	2	4	no	—
112	#126×C₈₉	—	2	4	no	—
113	#125×C₈₉	—	2	4	no	—
114	#125×C₈₉	—	2	4	no	—
115	#125×C₈₉	—	2	2	no	—
116	#125×C₈₉	C₂³	1	4	yes	—
117	#124×C₈₉	—	2	4	no	—
118	#124×C₈₉	C₂³	1	4	yes	—
119	#123×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	4	no	—
121	#123×C₈₉	—	2	4	no	—
122	C₂²⋊Q₈×C₈₉	—	2	2	no	—
123	C₂²⋊Q₈×C₈₉	—	2	2	no	—
124	C₂²⋊Q₈×C₈₉	—	2	2	no	—
125	C₂²⋊Q₈×C₈₉	—	2	4	no	—
126	C₂²⋊Q₈×C₈₉	—	2	4	no	—
127	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
129	#121×C₈₉	—	2	4	no	—
130	#121×C₈₉	C₂³	1	4	yes	—
131	C₄×Q₈×C₈₉	—	2	2	no	—
132	C₄×Q₈×C₈₉	—	2	4	no	—
133	C₄×Q₈×C₈₉	—	2	4	no	—
134	C₄×Q₈×C₈₉	—	2	2	no	—
135	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
137	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
138	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
139	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
140	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
141	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₈₉	—	2	2	no	—
143	C₄×D₄×C₈₉	—	2	4	no	—
144	C₄×D₄×C₈₉	—	2	2	no	—
145	C₄×D₄×C₈₉	—	2	2	no	—
146	C₄×D₄×C₈₉	—	2	4	no	—
147	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
148	C₄×D₄×C₈₉	D₄	1	2	yes	—
149	C₄×D₄×C₈₉	C₂³	1	2	yes	—
150	C₄×D₄×C₈₉	C₂³	1	2	yes	—
151	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₈₉	C₂³	1	2	yes	—
153	#117×C₈₉	—	2	2	no	—
154	#117×C₈₉	—	2	2	no	—
155	#117×C₈₉	—	2	4	no	—
156	#117×C₈₉	—	2	2	no	—
157	#117×C₈₉	—	2	4	no	—
158	#117×C₈₉	D₄	1	2	yes	—
159	#117×C₈₉	D₄	1	1	yes	characteristic
160	#117×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₈₉	—	2	4	no	—
164	C₂×C₄²×C₈₉	—	2	2	no	—
165	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	#107×C₈₉	C₂³	1	1	yes	characteristic
168	#107×C₈₉	C₂³	1	2	yes	—
169	#107×C₈₉	C₂³	1	4	yes	—
170	#107×C₈₉	C₂³	1	1	yes	characteristic
171	#107×C₈₉	C₂³	1	2	yes	—
172	#106×C₈₉	C₂³	1	2	yes	—
173	#106×C₈₉	C₂³	1	4	yes	—
174	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
177	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
178	#103×C₈₉	C₂³	1	2	yes	—
179	#103×C₈₉	C₂³	1	4	yes	—
180	#103×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	4	yes	—
182	#103×C₈₉	C₂³	1	2	yes	—
183	#103×C₈₉	C₂³	1	4	yes	—
184	#103×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	2	yes	—
186	#102×C₈₉	C₂³	1	2	yes	—
187	#102×C₈₉	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
191	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₈₉	C₂³	1	2	yes	—
193	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	#41×C₈₉	—	2	4	no	—
199	#41×C₈₉	—	2	4	no	—
200	#41×C₈₉	—	4	2	no	—
201	#41×C₈₉	—	4	8	no	—
202	C₂×Q₈×C₈₉	—	2	4	no	—
203	C₂×Q₈×C₈₉	—	2	2	no	—
204	C₂×Q₈×C₈₉	—	2	8	no	—
205	C₂×Q₈×C₈₉	—	4	4	no	—
206	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
208	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	—	2	4	no	—
215	C₂²×C₄×C₈₉	—	2	4	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₈₉	—	2	8	no	—
226	Q₁₆×C₈₉	—	2	4	no	—
227	Q₁₆×C₈₉	—	4	2	no	—
228	Q₁₆×C₈₉	#41	1	4	yes	complemented
229	SD₁₆×C₈₉	—	2	4	no	—
230	SD₁₆×C₈₉	—	4	4	no	—
231	D₈×C₈₉	—	2	2	no	—
232	C₂×C₈×C₈₉	—	2	4	no	—
233	C₂×C₈×C₈₉	—	2	2	no	—
234	C₂×C₈×C₈₉	—	4	2	no	—
235	C₂×C₈×C₈₉	—	4	1	no	—
236	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
238	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
241	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	2	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	2	no	—
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	2	2	no	—
267	C₂²⋊C₄×C₈₉	—	2	2	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
273	C₄²×C₈₉	—	2	2	no	—
274	C₄²×C₈₉	—	2	4	no	—
275	C₄²×C₈₉	—	2	2	no	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	2	2	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₈₉	C₂×D₄	1	2	yes	—
281	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₈₉	C₂×D₄	1	2	yes	—
283	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₄²×C₈₉	C₂⁴	1	2	yes	—
285	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
288	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
289	Q₈×C₈₉	—	2	2	no	—
290	Q₈×C₈₉	—	2	2	no	—
291	Q₈×C₈₉	—	2	4	no	—
292	Q₈×C₈₉	—	2	4	no	—
293	Q₈×C₈₉	—	4	8	no	—
294	Q₈×C₈₉	—	4	4	no	—
295	Q₈×C₈₉	C₂×#41	1	4	yes	—
296	D₄×C₈₉	—	2	4	no	—
297	D₄×C₈₉	—	2	2	no	—
298	D₄×C₈₉	—	2	2	no	—
299	D₄×C₈₉	—	4	4	no	—
300	D₄×C₈₉	—	4	8	no	—
301	D₄×C₈₉	#135	1	4	yes	complemented
302	C₂×C₄×C₈₉	—	2	4	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	4	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	4	no	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	4	4	no	—
316	C₂×C₄×C₈₉	—	4	8	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	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
329	C₈×C₈₉	—	2	1	no	—
330	C₈×C₈₉	—	2	2	no	—
331	C₈×C₈₉	—	2	1	no	—
332	C₈×C₈₉	—	2	2	no	—
333	C₈×C₈₉	—	2	1	no	—
334	C₈×C₈₉	C₂×#41	1	2	yes	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	2	1	no	—
338	C₂²×C₈₉	—	2	1	no	—
339	C₂²×C₈₉	—	2	1	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	C₂×#135	1	4	yes	—
344	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₈₉	—	2	1	no	—
346	C₄×C₈₉	—	2	2	no	—
347	C₄×C₈₉	—	2	4	no	—
348	C₄×C₈₉	—	2	1	no	—
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	2	2	no	—
351	C₄×C₈₉	—	2	1	no	—
352	C₄×C₈₉	—	4	4	no	—
353	C₄×C₈₉	—	4	2	no	—
354	C₄×C₈₉	—	4	4	no	—
355	C₄×C₈₉	—	4	2	no	—
356	C₄×C₈₉	C₂×#135	1	2	yes	—
357	C₄×C₈₉	#578	1	2	yes	—
358	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₄×C₈₉	#585	1	1	yes	characteristic
360	#61433	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₈₉	—	2	4	no	—
362	C₂×C₈₉	—	4	1	no	—
363	C₂×C₈₉	—	8	2	no	—
364	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
365	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
366	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
367	#3482	C₂×C₈₉	1	2	yes	complemented
368	#3393	C₂×C₈₉	1	1	yes	characteristic, complemented
369	#3383	C₂×C₈₉	1	1	yes	characteristic, complemented
370	#3364	C₂×C₈₉	1	2	yes	complemented
371	#3336	C₂×C₈₉	1	2	yes	complemented
372	#3334	C₂×C₈₉	1	1	yes	characteristic, complemented
373	#3300	C₂×C₈₉	1	4	yes	complemented
374	#3298	C₂×C₈₉	1	2	yes	complemented
375	D₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
376	#3285	C₂×C₈₉	1	2	yes	complemented
377	#3170	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#3168	C₂×C₈₉	1	2	yes	complemented
379	#3108	C₂×C₈₉	1	4	yes	complemented
380	#3107	C₂×C₈₉	1	2	yes	complemented
381	C₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
382	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
383	C₂×C₄×Q₁₆	C₂×C₈₉	1	2	yes	complemented
384	C₈₉	#61433	1	1	yes	characteristic, direct product factor, Sylow
385	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
386	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
387	#557	C₂²×C₈₉	1	2	yes	—
388	#556	—	2	2	no	—
389	#556	C₂²×C₈₉	1	2	yes	—
390	#552	—	2	4	no	—
391	#552	C₂²×C₈₉	1	4	yes	—
392	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
393	#548	C₂²×C₈₉	1	4	yes	—
394	#547	—	2	2	no	—
395	#547	C₂²×C₈₉	1	2	yes	—
396	#533	—	2	2	no	—
397	#533	C₂²×C₈₉	1	2	yes	—
398	#529	—	2	4	no	—
399	#529	C₂²×C₈₉	1	4	yes	—
400	C₄×#41	—	2	2	no	—
401	C₄×#41	C₂²×C₈₉	1	2	yes	—
402	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
404	#500	C₂²×C₈₉	1	1	yes	characteristic
405	#499	C₂²×C₈₉	1	2	yes	—
406	#495	C₂²×C₈₉	1	2	yes	—
407	#494	C₂²×C₈₉	1	1	yes	characteristic
408	#488	C₂²×C₈₉	1	4	yes	—
409	#487	C₂²×C₈₉	1	2	yes	—
410	#485	C₂²×C₈₉	1	4	yes	—
411	#483	C₂²×C₈₉	1	4	yes	—
412	#480	C₂²×C₈₉	1	4	yes	—
413	#479	C₂²×C₈₉	1	4	yes	—
414	#479	C₂²×C₈₉	1	4	yes	—
415	#475	C₂²×C₈₉	1	2	yes	—
416	#474	C₂²×C₈₉	1	2	yes	—
417	#467	C₂²×C₈₉	1	2	yes	—
418	#467	C₂²×C₈₉	1	2	yes	—
419	#467	C₂²×C₈₉	1	2	yes	—
420	#466	C₂²×C₈₉	1	2	yes	—
421	#465	C₂²×C₈₉	1	4	yes	—
422	#464	C₂²×C₈₉	1	4	yes	—
423	#464	C₂²×C₈₉	1	4	yes	—
424	#462	C₂²×C₈₉	1	2	yes	—
425	#461	C₂²×C₈₉	1	2	yes	—
426	#452	C₂²×C₈₉	1	4	yes	—
427	#451	C₂²×C₈₉	1	4	yes	—
428	#448	C₂²×C₈₉	1	4	yes	—
429	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
430	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
431	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
432	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
433	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
434	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
435	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
436	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
437	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
438	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
439	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
440	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
441	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
442	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
443	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
444	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
445	C₈×D₄	C₂²×C₈₉	1	2	yes	—
446	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
447	C₈×D₄	C₂²×C₈₉	1	2	yes	—
448	#431	C₂²×C₈₉	1	1	yes	characteristic
449	#431	C₂²×C₈₉	1	2	yes	—
450	#427	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#107	C₂²×C₈₉	1	2	yes	—
452	#416	C₂²×C₈₉	1	2	yes	—
453	C₂×#103	C₂²×C₈₉	1	4	yes	—
454	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
455	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#41	—	2	2	no	—
457	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
458	C₂×#41	C₂³×C₈₉	1	2	yes	—
459	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
460	#135	—	2	4	no	—
461	C₂×Q₁₆	—	2	8	no	—
462	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
463	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
464	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
465	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
466	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
467	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
468	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
470	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
472	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
476	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
477	#126	—	2	4	no	—
478	#126	—	2	4	no	—
479	#126	—	2	4	no	—
480	#125	—	2	4	no	—
481	#125	—	2	4	no	—
482	#125	—	2	2	no	—
483	#125	C₂³×C₈₉	1	4	yes	—
484	#124	—	2	4	no	—
485	#124	C₂³×C₈₉	1	4	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	—	2	4	no	—
494	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
495	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
496	#121	—	2	4	no	—
497	#121	C₂³×C₈₉	1	4	yes	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
503	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
504	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
505	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
506	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
507	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
508	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
515	C₄×D₄	D₄×C₈₉	1	2	yes	—
516	C₄×D₄	C₂³×C₈₉	1	2	yes	—
517	C₄×D₄	C₂³×C₈₉	1	2	yes	—
518	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
519	C₄×D₄	C₂³×C₈₉	1	2	yes	—
520	#117	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	—	2	4	no	—
523	#117	—	2	2	no	—
524	#117	—	2	4	no	—
525	#117	D₄×C₈₉	1	2	yes	—
526	#117	D₄×C₈₉	1	1	yes	characteristic
527	#117	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
530	C₂×C₄²	—	2	4	no	—
531	C₂×C₄²	—	2	2	no	—
532	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
534	#107	C₂³×C₈₉	1	1	yes	characteristic
535	#107	C₂³×C₈₉	1	2	yes	—
536	#107	C₂³×C₈₉	1	4	yes	—
537	#107	C₂³×C₈₉	1	1	yes	characteristic
538	#107	C₂³×C₈₉	1	2	yes	—
539	#106	C₂³×C₈₉	1	2	yes	—
540	#106	C₂³×C₈₉	1	4	yes	—
541	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
544	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
545	#103	C₂³×C₈₉	1	2	yes	—
546	#103	C₂³×C₈₉	1	4	yes	—
547	#103	C₂³×C₈₉	1	4	yes	—
548	#103	C₂³×C₈₉	1	4	yes	—
549	#103	C₂³×C₈₉	1	2	yes	—
550	#103	C₂³×C₈₉	1	4	yes	—
551	#103	C₂³×C₈₉	1	4	yes	—
552	#102	C₂³×C₈₉	1	2	yes	—
553	#102	C₂³×C₈₉	1	2	yes	—
554	#102	C₂³×C₈₉	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
558	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₈₉	1	2	yes	—
560	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₈₉	1	2	yes	—
564	C₄×C₈	C₂³×C₈₉	1	2	yes	—
565	#41	—	2	4	no	—
566	#41	—	2	4	no	—
567	#41	—	4	2	no	—
568	#41	—	4	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	8	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
575	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
580	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
587	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
588	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
592	Q₁₆	—	2	8	no	—
593	Q₁₆	—	2	4	no	—
594	Q₁₆	—	4	2	no	—
595	Q₁₆	#41×C₈₉	1	4	yes	complemented
596	SD₁₆	—	2	4	no	—
597	SD₁₆	—	4	4	no	—
598	D₈	—	2	2	no	—
599	C₂×C₈	—	2	4	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	4	2	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
604	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
605	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
606	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
607	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
608	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
623	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
638	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
639	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₈₉	1	2	yes	—
649	C₄²	C₂×D₄×C₈₉	1	2	yes	—
650	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
651	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
652	C₄²	C₂⁴×C₈₉	1	2	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
655	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	4	8	no	—
661	Q₈	—	4	4	no	—
662	Q₈	C₂×#41×C₈₉	1	4	yes	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	#135×C₈₉	1	4	yes	complemented
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
695	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
696	C₈	—	2	1	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	2	no	—
700	C₈	—	2	1	no	—
701	C₈	C₂×#41×C₈₉	1	2	yes	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂×#135×C₈₉	1	4	yes	—
711	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₄	C₂×#135×C₈₉	1	2	yes	—
724	C₄	#578×C₈₉	1	2	yes	—
725	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
726	C₄	#585×C₈₉	1	1	yes	characteristic
727	C₂	—	2	4	no	—
728	C₂	—	4	1	no	—
729	C₂	—	8	2	no	—
730	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
731	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
732	C₂	C₂×#578×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3482	C₂	semidirect
2. C₈₉×#3393	C₂	semidirect
3. C₈₉×#3383	C₂	semidirect
4. C₈₉×#3364	C₂	semidirect
5. C₈₉×#3336	C₂	semidirect
6. C₈₉×#3334	C₂	semidirect
7. C₈₉×#3300	C₂	semidirect
8. C₈₉×#3298	C₂	semidirect
9. D₄×Q₁₆×C₈₉	C₂	semidirect
10. C₈₉×#3285	C₂	semidirect
11. C₈₉×#3170	C₂	semidirect
12. C₈₉×#3168	C₂	semidirect
13. C₈₉×#3108	C₂	semidirect
14. C₈₉×#3107	C₂	semidirect
15. C₈×#41×C₈₉	C₂	semidirect
16. C₄×#135×C₈₉	C₂	semidirect
17. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
228. Q₁₆×C₈₉	#41	semidirect
301. D₄×C₈₉	#135	semidirect
360. #61433	C₈₉	direct (N × H)
367. #3482	C₂×C₈₉	semidirect
368. #3393	C₂×C₈₉	semidirect
369. #3383	C₂×C₈₉	semidirect
370. #3364	C₂×C₈₉	semidirect
371. #3336	C₂×C₈₉	semidirect
372. #3334	C₂×C₈₉	semidirect
373. #3300	C₂×C₈₉	semidirect
374. #3298	C₂×C₈₉	semidirect
375. D₄×Q₁₆	C₂×C₈₉	semidirect
376. #3285	C₂×C₈₉	semidirect
377. #3170	C₂×C₈₉	semidirect
378. #3168	C₂×C₈₉	semidirect
379. #3108	C₂×C₈₉	semidirect
380. #3107	C₂×C₈₉	semidirect
381. C₈×#41	C₂×C₈₉	semidirect
382. C₄×#135	C₂×C₈₉	semidirect
383. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
384. C₈₉	#61433	direct (N × H)
595. Q₁₆	#41×C₈₉	semidirect
668. D₄	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3482	2
C₈₉×#3393	2
C₈₉×#3383	2
C₈₉×#3364	2
C₈₉×#3336	2
C₈₉×#3334	2
C₈₉×#3300	2
C₈₉×#3298	2
D₄×Q₁₆×C₈₉	2
C₈₉×#3285	2
C₈₉×#3170	2
C₈₉×#3168	2
C₈₉×#3108	2
C₈₉×#3107	2
C₈×#41×C₈₉	2
C₄×#135×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
#61433	89

Subgroups — C89×#61433 #36439281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61433 #36439281