Subgroups — C₈₉×#60797 #36438645

Order 22784.

2062 conjugacy classes of subgroups.

The subgroup lattice has 710 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	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3225	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3224	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3223	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3222	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3221	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3220	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3035	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×#433×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	2	yes	—
17	C₂×#135×C₈₉	C₂²	1	4	yes	complemented
18	C₂×#135×C₈₉	C₂²	1	4	yes	complemented
19	#542×C₈₉	C₂²	1	4	yes	complemented
20	#541×C₈₉	C₂²	1	2	yes	complemented
21	#540×C₈₉	C₂²	1	2	yes	complemented
22	#539×C₈₉	—	2	2	no	—
23	#538×C₈₉	—	2	2	no	—
24	#537×C₈₉	—	2	2	no	—
25	#536×C₈₉	C₂²	1	2	yes	—
26	#536×C₈₉	C₂²	1	2	yes	—
27	#535×C₈₉	C₂²	1	2	yes	—
28	#535×C₈₉	C₂²	1	2	yes	—
29	#534×C₈₉	—	2	2	no	—
30	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#532×C₈₉	C₂²	1	1	yes	characteristic
32	#532×C₈₉	C₂²	1	1	yes	characteristic
33	#532×C₈₉	C₂²	1	2	yes	—
34	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	#529×C₈₉	—	2	4	no	—
36	#525×C₈₉	—	2	4	no	—
37	#525×C₈₉	C₂²	1	2	yes	—
38	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	#497×C₈₉	C₂²	1	2	yes	complemented
41	#497×C₈₉	C₂²	1	2	yes	complemented
42	#496×C₈₉	C₂²	1	2	yes	complemented
43	#496×C₈₉	C₂²	1	2	yes	complemented
44	#495×C₈₉	C₂²	1	4	yes	complemented
45	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#491×C₈₉	C₂²	1	2	yes	complemented
50	#490×C₈₉	C₂²	1	2	yes	complemented
51	#489×C₈₉	C₂²	1	4	yes	complemented
52	#488×C₈₉	C₂²	1	2	yes	complemented
53	#488×C₈₉	C₂²	1	2	yes	complemented
54	#487×C₈₉	C₂²	1	2	yes	complemented
55	#486×C₈₉	C₂²	1	2	yes	complemented
56	#464×C₈₉	C₂²	1	4	yes	complemented
57	#464×C₈₉	C₂²	1	4	yes	complemented
58	#463×C₈₉	C₂²	1	4	yes	complemented
59	#463×C₈₉	C₂²	1	4	yes	complemented
60	#462×C₈₉	C₂²	1	4	yes	complemented
61	#461×C₈₉	C₂²	1	4	yes	complemented
62	#460×C₈₉	C₂²	1	4	yes	complemented
63	#459×C₈₉	C₂²	1	4	yes	complemented
64	#452×C₈₉	C₂²	1	4	yes	—
65	#452×C₈₉	C₂²	1	4	yes	—
66	#451×C₈₉	C₂²	1	4	yes	complemented
67	#450×C₈₉	C₂²	1	4	yes	complemented
68	#449×C₈₉	C₂²	1	4	yes	—
69	#449×C₈₉	C₂²	1	4	yes	—
70	#448×C₈₉	C₂²	1	4	yes	complemented
71	#447×C₈₉	C₂²	1	4	yes	complemented
72	#433×C₈₉	C₂²	1	2	yes	complemented
73	#433×C₈₉	C₂²	1	2	yes	complemented
74	#433×C₈₉	C₂²	1	4	yes	complemented
75	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
76	#416×C₈₉	C₂²	1	4	yes	complemented
77	#416×C₈₉	C₂²	1	4	yes	complemented
78	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
79	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×#41×C₈₉	—	2	2	no	—
82	C₂×#41×C₈₉	—	2	2	no	—
83	C₂×#41×C₈₉	—	4	8	no	—
84	C₂×#41×C₈₉	C₂³	1	2	yes	—
85	C₂×#41×C₈₉	C₂³	1	2	yes	—
86	C₂×#41×C₈₉	C₂³	1	2	yes	—
87	C₂×#41×C₈₉	C₂³	1	2	yes	—
88	C₂×#41×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₈₉	—	2	2	no	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	—	2	2	no	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	#135×C₈₉	—	4	8	no	—
95	#135×C₈₉	—	4	8	no	—
96	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
102	C₂×D₈×C₈₉	C₂³	1	4	yes	—
103	C₂×D₈×C₈₉	C₂³	1	4	yes	—
104	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
105	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
111	#127×C₈₉	C₂³	1	2	yes	—
112	#127×C₈₉	C₂³	1	1	yes	characteristic
113	#127×C₈₉	C₂³	1	1	yes	characteristic
114	#127×C₈₉	C₂³	1	1	yes	characteristic
115	#126×C₈₉	—	2	4	no	—
116	#126×C₈₉	—	2	4	no	—
117	#125×C₈₉	—	2	4	no	—
118	#125×C₈₉	C₂³	1	2	yes	—
119	#124×C₈₉	—	2	4	no	—
120	#124×C₈₉	C₂³	1	2	yes	—
121	#124×C₈₉	C₂³	1	2	yes	—
122	#124×C₈₉	C₂³	1	2	yes	—
123	#124×C₈₉	C₂³	1	2	yes	—
124	#124×C₈₉	C₂³	1	2	yes	—
125	#123×C₈₉	—	2	2	no	—
126	#123×C₈₉	—	2	4	no	—
127	#123×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	4	no	—
130	C₂²⋊Q₈×C₈₉	—	2	2	no	—
131	C₂²⋊Q₈×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	—	2	4	no	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
135	#121×C₈₉	—	2	4	no	—
136	#121×C₈₉	—	2	2	no	—
137	#121×C₈₉	—	2	2	no	—
138	#121×C₈₉	—	2	2	no	—
139	#121×C₈₉	—	2	4	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	C₂³	1	4	yes	—
143	#120×C₈₉	—	2	2	no	—
144	#120×C₈₉	—	2	4	no	—
145	#120×C₈₉	—	2	4	no	—
146	C₄×Q₈×C₈₉	—	2	2	no	—
147	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
148	C₄×D₄×C₈₉	—	2	4	no	—
149	C₄×D₄×C₈₉	—	2	4	no	—
150	C₄×D₄×C₈₉	—	2	4	no	—
151	C₄×D₄×C₈₉	—	2	2	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	C₂³	1	4	yes	—
155	#117×C₈₉	—	2	2	no	—
156	#117×C₈₉	D₄	1	4	yes	—
157	#117×C₈₉	C₂³	1	2	yes	—
158	#117×C₈₉	C₂³	1	2	yes	—
159	#117×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
162	C₂×C₄²×C₈₉	—	2	2	no	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
166	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
167	#103×C₈₉	C₂³	1	4	yes	—
168	#103×C₈₉	C₂³	1	4	yes	—
169	#103×C₈₉	C₂³	1	4	yes	—
170	#103×C₈₉	C₂³	1	4	yes	—
171	#102×C₈₉	C₂³	1	4	yes	—
172	#102×C₈₉	C₂³	1	4	yes	—
173	#102×C₈₉	C₂³	1	4	yes	—
174	#102×C₈₉	C₂³	1	4	yes	—
175	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
177	#97×C₈₉	C₂³	1	2	yes	—
178	#97×C₈₉	C₂³	1	2	yes	—
179	C₄×C₈×C₈₉	C₂³	1	2	yes	—
180	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
182	C₂⁴×C₈₉	—	2	2	no	—
183	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
184	#41×C₈₉	—	2	8	no	—
185	#41×C₈₉	—	2	8	no	—
186	#41×C₈₉	—	2	8	no	—
187	#41×C₈₉	—	4	4	no	—
188	#41×C₈₉	—	4	4	no	—
189	#41×C₈₉	—	4	8	no	—
190	#41×C₈₉	—	4	8	no	—
191	C₂×Q₈×C₈₉	—	2	2	no	—
192	C₂×Q₈×C₈₉	—	2	2	no	—
193	C₂×Q₈×C₈₉	—	4	4	no	—
194	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
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	2	no	—
201	C₂×D₄×C₈₉	—	2	2	no	—
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	2	2	no	—
204	C₂×D₄×C₈₉	—	2	4	no	—
205	C₂×D₄×C₈₉	—	2	2	no	—
206	C₂×D₄×C₈₉	—	2	2	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	4	4	no	—
209	C₂×D₄×C₈₉	—	4	8	no	—
210	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	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	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	4	8	no	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₈₉	—	4	4	no	—
229	Q₁₆×C₈₉	—	4	4	no	—
230	SD₁₆×C₈₉	—	4	4	no	—
231	SD₁₆×C₈₉	—	4	4	no	—
232	SD₁₆×C₈₉	—	4	4	no	—
233	SD₁₆×C₈₉	—	4	4	no	—
234	D₈×C₈₉	—	4	4	no	—
235	D₈×C₈₉	—	4	4	no	—
236	C₂×C₈×C₈₉	—	2	4	no	—
237	C₂×C₈×C₈₉	—	2	4	no	—
238	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
239	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
240	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	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	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	2	no	—
249	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
252	C₂²⋊C₄×C₈₉	—	2	2	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
263	C₄²×C₈₉	—	2	4	no	—
264	C₄²×C₈₉	—	2	2	no	—
265	C₄²×C₈₉	C₂×D₄	1	2	yes	—
266	C₄²×C₈₉	C₂×D₄	1	2	yes	—
267	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₄²×C₈₉	C₂⁴	1	2	yes	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	2	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	4	2	no	—
275	C₂³×C₈₉	—	4	4	no	—
276	C₂³×C₈₉	—	8	4	no	—
277	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
278	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₈₉	—	2	4	no	—
280	Q₈×C₈₉	—	2	4	no	—
281	Q₈×C₈₉	—	2	4	no	—
282	Q₈×C₈₉	—	4	4	no	—
283	Q₈×C₈₉	—	8	2	no	—
284	D₄×C₈₉	—	2	4	no	—
285	D₄×C₈₉	—	2	4	no	—
286	D₄×C₈₉	—	2	4	no	—
287	D₄×C₈₉	—	4	4	no	—
288	D₄×C₈₉	—	4	4	no	—
289	D₄×C₈₉	—	4	4	no	—
290	D₄×C₈₉	—	4	4	no	—
291	D₄×C₈₉	—	4	4	no	—
292	D₄×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	8	4	no	—
294	D₄×C₈₉	—	8	2	no	—
295	D₄×C₈₉	—	8	2	no	—
296	D₄×C₈₉	—	8	2	no	—
297	D₄×C₈₉	—	8	4	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	4	no	—
300	C₂×C₄×C₈₉	—	2	4	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
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	—	4	2	no	—
306	C₂×C₄×C₈₉	—	4	2	no	—
307	C₂×C₄×C₈₉	—	4	4	no	—
308	C₂×C₄×C₈₉	—	4	4	no	—
309	C₂×C₄×C₈₉	—	4	4	no	—
310	C₂×C₄×C₈₉	—	4	4	no	—
311	C₂×C₄×C₈₉	—	4	4	no	—
312	C₂×C₄×C₈₉	—	4	4	no	—
313	C₂×C₄×C₈₉	—	8	4	no	—
314	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
321	C₈×C₈₉	—	2	2	no	—
322	C₈×C₈₉	—	2	4	no	—
323	C₈×C₈₉	—	2	2	no	—
324	C₂²×C₈₉	—	2	2	no	—
325	C₂²×C₈₉	—	2	4	no	—
326	C₂²×C₈₉	—	2	2	no	—
327	C₂²×C₈₉	—	4	4	no	—
328	C₂²×C₈₉	—	4	4	no	—
329	C₂²×C₈₉	—	4	4	no	—
330	C₂²×C₈₉	—	4	2	no	—
331	C₂²×C₈₉	—	4	2	no	—
332	C₂²×C₈₉	—	4	2	no	—
333	C₂²×C₈₉	—	8	2	no	—
334	C₂²×C₈₉	—	8	8	no	—
335	C₂²×C₈₉	#535	1	2	yes	—
336	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₈₉	—	2	4	no	—
338	C₄×C₈₉	—	2	2	no	—
339	C₄×C₈₉	—	2	2	no	—
340	C₄×C₈₉	—	2	2	no	—
341	C₄×C₈₉	—	4	4	no	—
342	C₄×C₈₉	—	4	2	no	—
343	C₄×C₈₉	—	4	2	no	—
344	C₄×C₈₉	—	4	2	no	—
345	C₄×C₈₉	#535	1	2	yes	—
346	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
347	#60797	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂×C₈₉	—	2	2	no	—
349	C₂×C₈₉	—	4	2	no	—
350	C₂×C₈₉	—	8	2	no	—
351	C₂×C₈₉	—	8	2	no	—
352	C₂×C₈₉	—	8	2	no	—
353	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
354	C₂×C₈₉	#3584	1	2	yes	—
355	#3455	C₂×C₈₉	1	1	yes	characteristic, complemented
356	#3449	C₂×C₈₉	1	1	yes	characteristic, complemented
357	#3225	C₂×C₈₉	1	4	yes	complemented
358	#3224	C₂×C₈₉	1	4	yes	complemented
359	#3223	C₂×C₈₉	1	2	yes	complemented
360	#3222	C₂×C₈₉	1	2	yes	complemented
361	#3221	C₂×C₈₉	1	2	yes	complemented
362	#3220	C₂×C₈₉	1	2	yes	complemented
363	#3150	C₂×C₈₉	1	1	yes	characteristic, complemented
364	#3147	C₂×C₈₉	1	1	yes	characteristic, complemented
365	#3135	C₂×C₈₉	1	1	yes	characteristic, complemented
366	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
367	#3035	C₂×C₈₉	1	4	yes	complemented
368	#3002	C₂×C₈₉	1	4	yes	complemented
369	C₂×#433	C₂×C₈₉	1	1	yes	characteristic, complemented
370	C₈₉	#60797	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²×#41	C₂²×C₈₉	1	2	yes	—
372	C₂×#135	C₂²×C₈₉	1	4	yes	complemented
373	C₂×#135	C₂²×C₈₉	1	4	yes	complemented
374	#542	C₂²×C₈₉	1	4	yes	complemented
375	#541	C₂²×C₈₉	1	2	yes	complemented
376	#540	C₂²×C₈₉	1	2	yes	complemented
377	#539	—	2	2	no	—
378	#538	—	2	2	no	—
379	#537	—	2	2	no	—
380	#536	C₂²×C₈₉	1	2	yes	—
381	#536	C₂²×C₈₉	1	2	yes	—
382	#535	C₂²×C₈₉	1	2	yes	—
383	#535	C₂²×C₈₉	1	2	yes	—
384	#534	—	2	2	no	—
385	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
386	#532	C₂²×C₈₉	1	1	yes	characteristic
387	#532	C₂²×C₈₉	1	1	yes	characteristic
388	#532	C₂²×C₈₉	1	2	yes	—
389	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
390	#529	—	2	4	no	—
391	#525	—	2	4	no	—
392	#525	C₂²×C₈₉	1	2	yes	—
393	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
394	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
395	#497	C₂²×C₈₉	1	2	yes	complemented
396	#497	C₂²×C₈₉	1	2	yes	complemented
397	#496	C₂²×C₈₉	1	2	yes	complemented
398	#496	C₂²×C₈₉	1	2	yes	complemented
399	#495	C₂²×C₈₉	1	4	yes	complemented
400	#494	C₂²×C₈₉	1	1	yes	characteristic, complemented
401	#493	C₂²×C₈₉	1	1	yes	characteristic, complemented
402	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
403	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
404	#491	C₂²×C₈₉	1	2	yes	complemented
405	#490	C₂²×C₈₉	1	2	yes	complemented
406	#489	C₂²×C₈₉	1	4	yes	complemented
407	#488	C₂²×C₈₉	1	2	yes	complemented
408	#488	C₂²×C₈₉	1	2	yes	complemented
409	#487	C₂²×C₈₉	1	2	yes	complemented
410	#486	C₂²×C₈₉	1	2	yes	complemented
411	#464	C₂²×C₈₉	1	4	yes	complemented
412	#464	C₂²×C₈₉	1	4	yes	complemented
413	#463	C₂²×C₈₉	1	4	yes	complemented
414	#463	C₂²×C₈₉	1	4	yes	complemented
415	#462	C₂²×C₈₉	1	4	yes	complemented
416	#461	C₂²×C₈₉	1	4	yes	complemented
417	#460	C₂²×C₈₉	1	4	yes	complemented
418	#459	C₂²×C₈₉	1	4	yes	complemented
419	#452	C₂²×C₈₉	1	4	yes	—
420	#452	C₂²×C₈₉	1	4	yes	—
421	#451	C₂²×C₈₉	1	4	yes	complemented
422	#450	C₂²×C₈₉	1	4	yes	complemented
423	#449	C₂²×C₈₉	1	4	yes	—
424	#449	C₂²×C₈₉	1	4	yes	—
425	#448	C₂²×C₈₉	1	4	yes	complemented
426	#447	C₂²×C₈₉	1	4	yes	complemented
427	#433	C₂²×C₈₉	1	2	yes	complemented
428	#433	C₂²×C₈₉	1	2	yes	complemented
429	#433	C₂²×C₈₉	1	4	yes	complemented
430	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
431	#416	C₂²×C₈₉	1	4	yes	complemented
432	#416	C₂²×C₈₉	1	4	yes	complemented
433	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
434	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
435	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
436	C₂×#41	—	2	2	no	—
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	4	8	no	—
439	C₂×#41	C₂³×C₈₉	1	2	yes	—
440	C₂×#41	C₂³×C₈₉	1	2	yes	—
441	C₂×#41	C₂³×C₈₉	1	2	yes	—
442	C₂×#41	C₂³×C₈₉	1	2	yes	—
443	C₂×#41	C₂³×C₈₉	1	2	yes	—
444	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
447	C₂³×C₄	—	2	2	no	—
448	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
449	#135	—	4	8	no	—
450	#135	—	4	8	no	—
451	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
452	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
453	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
454	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
456	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
457	C₂×D₈	C₂³×C₈₉	1	4	yes	—
458	C₂×D₈	C₂³×C₈₉	1	4	yes	—
459	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
460	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
461	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
462	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
466	#127	C₂³×C₈₉	1	2	yes	—
467	#127	C₂³×C₈₉	1	1	yes	characteristic
468	#127	C₂³×C₈₉	1	1	yes	characteristic
469	#127	C₂³×C₈₉	1	1	yes	characteristic
470	#126	—	2	4	no	—
471	#126	—	2	4	no	—
472	#125	—	2	4	no	—
473	#125	C₂³×C₈₉	1	2	yes	—
474	#124	—	2	4	no	—
475	#124	C₂³×C₈₉	1	2	yes	—
476	#124	C₂³×C₈₉	1	2	yes	—
477	#124	C₂³×C₈₉	1	2	yes	—
478	#124	C₂³×C₈₉	1	2	yes	—
479	#124	C₂³×C₈₉	1	2	yes	—
480	#123	—	2	2	no	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
490	#121	—	2	4	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	4	no	—
495	#121	—	2	4	no	—
496	#121	—	2	4	no	—
497	#121	C₂³×C₈₉	1	4	yes	—
498	#120	—	2	2	no	—
499	#120	—	2	4	no	—
500	#120	—	2	4	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	C₂³×C₈₉	1	4	yes	—
510	#117	—	2	2	no	—
511	#117	D₄×C₈₉	1	4	yes	—
512	#117	C₂³×C₈₉	1	2	yes	—
513	#117	C₂³×C₈₉	1	2	yes	—
514	#117	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
516	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
517	C₂×C₄²	—	2	2	no	—
518	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
521	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
522	#103	C₂³×C₈₉	1	4	yes	—
523	#103	C₂³×C₈₉	1	4	yes	—
524	#103	C₂³×C₈₉	1	4	yes	—
525	#103	C₂³×C₈₉	1	4	yes	—
526	#102	C₂³×C₈₉	1	4	yes	—
527	#102	C₂³×C₈₉	1	4	yes	—
528	#102	C₂³×C₈₉	1	4	yes	—
529	#102	C₂³×C₈₉	1	4	yes	—
530	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
531	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
532	#97	C₂³×C₈₉	1	2	yes	—
533	#97	C₂³×C₈₉	1	2	yes	—
534	C₄×C₈	C₂³×C₈₉	1	2	yes	—
535	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
536	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
537	C₂⁴	—	2	2	no	—
538	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
539	#41	—	2	8	no	—
540	#41	—	2	8	no	—
541	#41	—	2	8	no	—
542	#41	—	4	4	no	—
543	#41	—	4	4	no	—
544	#41	—	4	8	no	—
545	#41	—	4	8	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	4	no	—
549	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
550	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
551	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	8	no	—
565	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
566	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
567	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	4	8	no	—
577	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
583	Q₁₆	—	4	4	no	—
584	Q₁₆	—	4	4	no	—
585	SD₁₆	—	4	4	no	—
586	SD₁₆	—	4	4	no	—
587	SD₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	no	—
589	D₈	—	4	4	no	—
590	D₈	—	4	4	no	—
591	C₂×C₈	—	2	4	no	—
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
594	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
595	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
605	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
606	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
617	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	C₂×D₄×C₈₉	1	2	yes	—
621	C₄²	C₂×D₄×C₈₉	1	2	yes	—
622	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
623	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
624	C₄²	C₂⁴×C₈₉	1	2	yes	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	8	4	no	—
632	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
633	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
634	Q₈	—	2	4	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	2	4	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	8	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	4	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
674	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
675	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
676	C₈	—	2	2	no	—
677	C₈	—	2	4	no	—
678	C₈	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	8	no	—
690	C₂²	#535×C₈₉	1	2	yes	—
691	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	#535×C₈₉	1	2	yes	—
701	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
702	C₂	—	2	2	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	—	8	2	no	—
706	C₂	—	8	2	no	—
707	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
708	C₂	C₈₉×#3584	1	2	yes	—

	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 ◁ 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. C₈₉×#3449	C₂	semidirect
3. C₈₉×#3225	C₂	semidirect
4. C₈₉×#3224	C₂	semidirect
5. C₈₉×#3223	C₂	semidirect
6. C₈₉×#3222	C₂	semidirect
7. C₈₉×#3221	C₂	semidirect
8. C₈₉×#3220	C₂	semidirect
9. C₈₉×#3150	C₂	semidirect
10. C₈₉×#3147	C₂	semidirect
11. C₈₉×#3135	C₂	semidirect
12. C₈₉×#3131	C₂	semidirect
13. C₈₉×#3035	C₂	semidirect
14. C₈₉×#3002	C₂	semidirect
15. C₂×#433×C₈₉	C₂	semidirect
17. C₂×#135×C₈₉	C₂²	semidirect
18. C₂×#135×C₈₉	C₂²	semidirect
19. #542×C₈₉	C₂²	semidirect
20. #541×C₈₉	C₂²	semidirect
21. #540×C₈₉	C₂²	semidirect
30. #533×C₈₉	C₂²	semidirect
34. #532×C₈₉	C₂²	semidirect
38. C₄×#41×C₈₉	C₂²	semidirect
40. #497×C₈₉	C₂²	semidirect
41. #497×C₈₉	C₂²	semidirect
42. #496×C₈₉	C₂²	semidirect
43. #496×C₈₉	C₂²	semidirect
44. #495×C₈₉	C₂²	semidirect
45. #494×C₈₉	C₂²	semidirect
46. #493×C₈₉	C₂²	semidirect
47. #492×C₈₉	C₂²	semidirect
48. #492×C₈₉	C₂²	semidirect
49. #491×C₈₉	C₂²	semidirect
50. #490×C₈₉	C₂²	semidirect
51. #489×C₈₉	C₂²	semidirect
52. #488×C₈₉	C₂²	semidirect
53. #488×C₈₉	C₂²	semidirect
54. #487×C₈₉	C₂²	semidirect
55. #486×C₈₉	C₂²	semidirect
56. #464×C₈₉	C₂²	semidirect
57. #464×C₈₉	C₂²	semidirect
58. #463×C₈₉	C₂²	semidirect
59. #463×C₈₉	C₂²	semidirect
60. #462×C₈₉	C₂²	semidirect
61. #461×C₈₉	C₂²	semidirect
62. #460×C₈₉	C₂²	semidirect
63. #459×C₈₉	C₂²	semidirect
66. #451×C₈₉	C₂²	semidirect
67. #450×C₈₉	C₂²	semidirect
70. #448×C₈₉	C₂²	semidirect
71. #447×C₈₉	C₂²	semidirect
72. #433×C₈₉	C₂²	semidirect
73. #433×C₈₉	C₂²	semidirect
74. #433×C₈₉	C₂²	semidirect
75. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
76. #416×C₈₉	C₂²	semidirect
77. #416×C₈₉	C₂²	semidirect
79. C₂×#97×C₈₉	C₂²	semidirect
80. C₂×C₄×C₈×C₈₉	C₂²	semidirect
347. #60797	C₈₉	direct (N × H)
355. #3455	C₂×C₈₉	semidirect
356. #3449	C₂×C₈₉	semidirect
357. #3225	C₂×C₈₉	semidirect
358. #3224	C₂×C₈₉	semidirect
359. #3223	C₂×C₈₉	semidirect
360. #3222	C₂×C₈₉	semidirect
361. #3221	C₂×C₈₉	semidirect
362. #3220	C₂×C₈₉	semidirect
363. #3150	C₂×C₈₉	semidirect
364. #3147	C₂×C₈₉	semidirect
365. #3135	C₂×C₈₉	semidirect
366. #3131	C₂×C₈₉	semidirect
367. #3035	C₂×C₈₉	semidirect
368. #3002	C₂×C₈₉	semidirect
369. C₂×#433	C₂×C₈₉	semidirect
370. C₈₉	#60797	direct (N × H)
372. C₂×#135	C₂²×C₈₉	semidirect
373. C₂×#135	C₂²×C₈₉	semidirect
374. #542	C₂²×C₈₉	semidirect
375. #541	C₂²×C₈₉	semidirect
376. #540	C₂²×C₈₉	semidirect
385. #533	C₂²×C₈₉	semidirect
389. #532	C₂²×C₈₉	semidirect
393. C₄×#41	C₂²×C₈₉	semidirect
395. #497	C₂²×C₈₉	semidirect
396. #497	C₂²×C₈₉	semidirect
397. #496	C₂²×C₈₉	semidirect
398. #496	C₂²×C₈₉	semidirect
399. #495	C₂²×C₈₉	semidirect
400. #494	C₂²×C₈₉	semidirect
401. #493	C₂²×C₈₉	semidirect
402. #492	C₂²×C₈₉	semidirect
403. #492	C₂²×C₈₉	semidirect
404. #491	C₂²×C₈₉	semidirect
405. #490	C₂²×C₈₉	semidirect
406. #489	C₂²×C₈₉	semidirect
407. #488	C₂²×C₈₉	semidirect
408. #488	C₂²×C₈₉	semidirect
409. #487	C₂²×C₈₉	semidirect
410. #486	C₂²×C₈₉	semidirect
411. #464	C₂²×C₈₉	semidirect
412. #464	C₂²×C₈₉	semidirect
413. #463	C₂²×C₈₉	semidirect
414. #463	C₂²×C₈₉	semidirect
415. #462	C₂²×C₈₉	semidirect
416. #461	C₂²×C₈₉	semidirect
417. #460	C₂²×C₈₉	semidirect
418. #459	C₂²×C₈₉	semidirect
421. #451	C₂²×C₈₉	semidirect
422. #450	C₂²×C₈₉	semidirect
425. #448	C₂²×C₈₉	semidirect
426. #447	C₂²×C₈₉	semidirect
427. #433	C₂²×C₈₉	semidirect
428. #433	C₂²×C₈₉	semidirect
429. #433	C₂²×C₈₉	semidirect
430. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
431. #416	C₂²×C₈₉	semidirect
432. #416	C₂²×C₈₉	semidirect
434. C₂×#97	C₂²×C₈₉	semidirect
435. C₂×C₄×C₈	C₂²×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
C₈₉×#3449	2
C₈₉×#3225	2
C₈₉×#3224	2
C₈₉×#3223	2
C₈₉×#3222	2
C₈₉×#3221	2
C₈₉×#3220	2
C₈₉×#3150	2
C₈₉×#3147	2
C₈₉×#3135	2
C₈₉×#3131	2
C₈₉×#3035	2
C₈₉×#3002	2
C₂×#433×C₈₉	2
#60797	89

Subgroups — C89×#60797 #36438645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60797 #36438645