Subgroups — C₈₉×#35357 #36413205

Order 22784.

2758 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2534	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2477	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2465	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2463	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2449	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2409	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2406	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2404	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2322	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#123×C₈₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₈₉	—	2	8	no	—
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
24	C₂×#120×C₈₉	C₂²	1	2	yes	—
25	#520×C₈₉	—	2	8	no	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	#400×C₈₉	C₂²	1	2	yes	complemented
40	#399×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	complemented
42	#397×C₈₉	C₂²	1	2	yes	—
43	#396×C₈₉	C₂²	1	4	yes	—
44	#395×C₈₉	C₂²	1	2	yes	complemented
45	#395×C₈₉	C₂²	1	4	yes	complemented
46	#394×C₈₉	C₂²	1	4	yes	—
47	#394×C₈₉	C₂²	1	2	yes	complemented
48	#393×C₈₉	C₂²	1	2	yes	—
49	#393×C₈₉	C₂²	1	4	yes	complemented
50	#392×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	4	yes	complemented
52	#389×C₈₉	C₂²	1	4	yes	complemented
53	#388×C₈₉	C₂²	1	4	yes	—
54	#388×C₈₉	C₂²	1	4	yes	—
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#387×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#387×C₈₉	C₂²	1	4	yes	complemented
59	#387×C₈₉	C₂²	1	4	yes	complemented
60	#386×C₈₉	C₂²	1	2	yes	—
61	#386×C₈₉	C₂²	1	4	yes	—
62	#386×C₈₉	C₂²	1	2	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#386×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	2	yes	—
66	#385×C₈₉	C₂²	1	4	yes	—
67	#385×C₈₉	C₂²	1	2	yes	—
68	#385×C₈₉	C₂²	1	4	yes	complemented
69	#385×C₈₉	C₂²	1	4	yes	complemented
70	#381×C₈₉	C₂²	1	1	yes	characteristic
71	#381×C₈₉	C₂²	1	1	yes	characteristic
72	#381×C₈₉	C₂²	1	2	yes	—
73	#380×C₈₉	C₂²	1	2	yes	—
74	#379×C₈₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×#41×C₈₉	—	2	8	no	—
79	C₂×#41×C₈₉	—	2	4	no	—
80	C₂²×Q₈×C₈₉	—	2	4	no	—
81	C₂²×Q₈×C₈₉	—	4	4	no	—
82	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₈₉	—	2	4	no	—
88	C₂³×C₄×C₈₉	—	4	4	no	—
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
99	#123×C₈₉	—	2	8	no	—
100	C₂²⋊Q₈×C₈₉	—	2	16	no	—
101	C₂²⋊Q₈×C₈₉	—	2	16	no	—
102	C₂²⋊Q₈×C₈₉	—	4	8	no	—
103	#120×C₈₉	—	2	8	no	—
104	C₄×Q₈×C₈₉	—	2	8	no	—
105	C₄×D₄×C₈₉	—	2	8	no	—
106	C₄×D₄×C₈₉	—	2	8	no	—
107	C₄×D₄×C₈₉	—	2	8	no	—
108	C₄×D₄×C₈₉	—	4	8	no	—
109	#117×C₈₉	—	2	4	no	—
110	#117×C₈₉	—	2	8	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
114	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
144	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
148	#95×C₈₉	C₂³	1	4	yes	—
149	#95×C₈₉	C₂³	1	4	yes	—
150	#95×C₈₉	C₂³	1	4	yes	—
151	#95×C₈₉	C₂³	1	4	yes	—
152	#95×C₈₉	C₂³	1	2	yes	—
153	#95×C₈₉	C₂³	1	4	yes	—
154	#95×C₈₉	C₂³	1	2	yes	—
155	#95×C₈₉	C₂³	1	2	yes	—
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	4	yes	—
158	#95×C₈₉	C₂³	1	4	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	C₂⁴×C₈₉	—	2	2	no	—
161	C₂⁴×C₈₉	—	2	4	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	4	2	no	—
164	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
165	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
166	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
167	#41×C₈₉	—	2	32	no	—
168	C₂×Q₈×C₈₉	—	2	2	no	—
169	C₂×Q₈×C₈₉	—	2	8	no	—
170	C₂×Q₈×C₈₉	—	2	4	no	—
171	C₂×Q₈×C₈₉	—	2	8	no	—
172	C₂×Q₈×C₈₉	—	4	4	no	—
173	C₂×Q₈×C₈₉	—	4	16	no	—
174	C₂×D₄×C₈₉	—	2	4	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	8	no	—
178	C₂×D₄×C₈₉	—	2	8	no	—
179	C₂×D₄×C₈₉	—	2	2	no	—
180	C₂×D₄×C₈₉	—	4	4	no	—
181	C₂×D₄×C₈₉	#41	1	8	yes	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	4	no	—
184	C₂²×C₄×C₈₉	—	2	4	no	—
185	C₂²×C₄×C₈₉	—	2	4	no	—
186	C₂²×C₄×C₈₉	—	2	4	no	—
187	C₂²×C₄×C₈₉	—	2	4	no	—
188	C₂²×C₄×C₈₉	—	2	2	no	—
189	C₂²×C₄×C₈₉	—	2	2	no	—
190	C₂²×C₄×C₈₉	—	2	4	no	—
191	C₂²×C₄×C₈₉	—	2	8	no	—
192	C₂²×C₄×C₈₉	—	2	8	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	4	no	—
195	C₂²×C₄×C₈₉	—	4	2	no	—
196	C₂²×C₄×C₈₉	—	4	4	no	—
197	C₂²×C₄×C₈₉	—	4	2	no	—
198	C₂²×C₄×C₈₉	—	4	2	no	—
199	C₂²×C₄×C₈₉	—	4	4	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	4	16	no	—
202	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₈₉	—	2	2	no	—
218	C₄⋊C₄×C₈₉	—	2	4	no	—
219	C₄⋊C₄×C₈₉	—	2	4	no	—
220	C₄⋊C₄×C₈₉	—	2	4	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	8	no	—
223	C₄⋊C₄×C₈₉	—	2	2	no	—
224	C₄⋊C₄×C₈₉	—	2	8	no	—
225	C₄⋊C₄×C₈₉	—	2	8	no	—
226	C₄⋊C₄×C₈₉	—	4	4	no	—
227	C₄⋊C₄×C₈₉	—	4	4	no	—
228	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
229	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
230	C₂²⋊C₄×C₈₉	—	2	4	no	—
231	C₂²⋊C₄×C₈₉	—	2	4	no	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	8	no	—
234	C₂²⋊C₄×C₈₉	—	2	8	no	—
235	C₂²⋊C₄×C₈₉	—	2	8	no	—
236	C₂²⋊C₄×C₈₉	—	2	4	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	8	no	—
241	C₂²⋊C₄×C₈₉	—	2	8	no	—
242	C₂²⋊C₄×C₈₉	—	4	4	no	—
243	C₂²⋊C₄×C₈₉	—	4	4	no	—
244	C₄²×C₈₉	—	2	4	no	—
245	C₄²×C₈₉	—	2	4	no	—
246	C₄²×C₈₉	—	2	4	no	—
247	C₄²×C₈₉	—	4	4	no	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	2	2	no	—
250	C₂³×C₈₉	—	2	8	no	—
251	C₂³×C₈₉	—	2	2	no	—
252	C₂³×C₈₉	—	2	2	no	—
253	C₂³×C₈₉	—	2	4	no	—
254	C₂³×C₈₉	—	2	2	no	—
255	C₂³×C₈₉	—	2	4	no	—
256	C₂³×C₈₉	—	2	4	no	—
257	C₂³×C₈₉	—	2	4	no	—
258	C₂³×C₈₉	—	2	2	no	—
259	C₂³×C₈₉	—	4	16	no	—
260	C₂³×C₈₉	—	4	4	no	—
261	C₂³×C₈₉	—	4	4	no	—
262	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
263	C₂³×C₈₉	C₂×#41	1	4	yes	—
264	C₂³×C₈₉	C₂×#41	1	4	yes	—
265	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
266	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
267	Q₈×C₈₉	—	2	8	no	—
268	Q₈×C₈₉	—	4	16	no	—
269	D₄×C₈₉	—	2	8	no	—
270	D₄×C₈₉	—	2	16	no	—
271	D₄×C₈₉	—	4	16	no	—
272	C₂×C₄×C₈₉	—	2	8	no	—
273	C₂×C₄×C₈₉	—	2	16	no	—
274	C₂×C₄×C₈₉	—	2	8	no	—
275	C₂×C₄×C₈₉	—	2	2	no	—
276	C₂×C₄×C₈₉	—	2	2	no	—
277	C₂×C₄×C₈₉	—	2	2	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	4	no	—
281	C₂×C₄×C₈₉	—	2	4	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	4	no	—
288	C₂×C₄×C₈₉	—	2	4	no	—
289	C₂×C₄×C₈₉	—	2	4	no	—
290	C₂×C₄×C₈₉	—	2	4	no	—
291	C₂×C₄×C₈₉	—	2	4	no	—
292	C₂×C₄×C₈₉	—	2	4	no	—
293	C₂×C₄×C₈₉	—	2	4	no	—
294	C₂×C₄×C₈₉	—	2	4	no	—
295	C₂×C₄×C₈₉	—	2	4	no	—
296	C₂×C₄×C₈₉	—	2	4	no	—
297	C₂×C₄×C₈₉	—	4	4	no	—
298	C₂×C₄×C₈₉	—	4	4	no	—
299	C₂×C₄×C₈₉	—	4	16	no	—
300	C₂×C₄×C₈₉	—	4	4	no	—
301	C₂×C₄×C₈₉	—	4	4	no	—
302	C₂×C₄×C₈₉	—	8	4	no	—
303	C₂×C₄×C₈₉	—	8	4	no	—
304	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
306	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
309	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
310	C₂²×C₈₉	—	2	2	no	—
311	C₂²×C₈₉	—	2	2	no	—
312	C₂²×C₈₉	—	2	8	no	—
313	C₂²×C₈₉	—	2	4	no	—
314	C₂²×C₈₉	—	2	4	no	—
315	C₂²×C₈₉	—	2	8	no	—
316	C₂²×C₈₉	—	2	8	no	—
317	C₂²×C₈₉	—	4	16	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	—	4	4	no	—
323	C₂²×C₈₉	—	4	4	no	—
324	C₂²×C₈₉	#525	1	4	yes	—
325	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₈₉	C₂²×#41	1	2	yes	—
327	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
328	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
329	C₄×C₈₉	—	2	2	no	—
330	C₄×C₈₉	—	2	2	no	—
331	C₄×C₈₉	—	2	4	no	—
332	C₄×C₈₉	—	2	4	no	—
333	C₄×C₈₉	—	2	4	no	—
334	C₄×C₈₉	—	2	4	no	—
335	C₄×C₈₉	—	4	2	no	—
336	C₄×C₈₉	—	4	2	no	—
337	C₄×C₈₉	—	4	2	no	—
338	C₄×C₈₉	—	4	2	no	—
339	C₄×C₈₉	—	4	4	no	—
340	C₄×C₈₉	—	4	4	no	—
341	#35357	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂×C₈₉	—	2	4	no	—
343	C₂×C₈₉	—	4	4	no	—
344	C₂×C₈₉	—	4	4	no	—
345	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
346	C₂×C₈₉	#3484	1	1	yes	characteristic
347	C₂×C₈₉	#3486	1	1	yes	characteristic
348	C₂×C₈₉	#3520	1	4	yes	—
349	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
350	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
351	#2534	C₂×C₈₉	1	2	yes	complemented
352	#2484	C₂×C₈₉	1	1	yes	characteristic, complemented
353	#2482	C₂×C₈₉	1	1	yes	characteristic, complemented
354	#2477	C₂×C₈₉	1	4	yes	complemented
355	#2465	C₂×C₈₉	1	4	yes	complemented
356	#2463	C₂×C₈₉	1	4	yes	complemented
357	#2449	C₂×C₈₉	1	4	yes	complemented
358	#2409	C₂×C₈₉	1	2	yes	complemented
359	#2406	C₂×C₈₉	1	1	yes	characteristic, complemented
360	#2404	C₂×C₈₉	1	1	yes	characteristic
361	#2322	C₂×C₈₉	1	2	yes	complemented
362	#2313	C₂×C₈₉	1	1	yes	characteristic, complemented
363	C₄×#120	C₂×C₈₉	1	2	yes	complemented
364	C₈₉	#35357	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
367	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
368	C₂×#123	C₂²×C₈₉	1	2	yes	—
369	C₂×C₂²⋊Q₈	—	2	8	no	—
370	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
371	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
372	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
373	C₂×#120	C₂²×C₈₉	1	2	yes	—
374	#520	—	2	8	no	—
375	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
376	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
378	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
379	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
380	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
381	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
382	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
386	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
388	#400	C₂²×C₈₉	1	2	yes	complemented
389	#399	C₂²×C₈₉	1	2	yes	—
390	#398	C₂²×C₈₉	1	2	yes	complemented
391	#397	C₂²×C₈₉	1	2	yes	—
392	#396	C₂²×C₈₉	1	4	yes	—
393	#395	C₂²×C₈₉	1	2	yes	complemented
394	#395	C₂²×C₈₉	1	4	yes	complemented
395	#394	C₂²×C₈₉	1	4	yes	—
396	#394	C₂²×C₈₉	1	2	yes	complemented
397	#393	C₂²×C₈₉	1	2	yes	—
398	#393	C₂²×C₈₉	1	4	yes	complemented
399	#392	C₂²×C₈₉	1	2	yes	—
400	#391	C₂²×C₈₉	1	4	yes	complemented
401	#389	C₂²×C₈₉	1	4	yes	complemented
402	#388	C₂²×C₈₉	1	4	yes	—
403	#388	C₂²×C₈₉	1	4	yes	—
404	#388	C₂²×C₈₉	1	4	yes	complemented
405	#387	C₂²×C₈₉	1	4	yes	complemented
406	#387	C₂²×C₈₉	1	4	yes	complemented
407	#387	C₂²×C₈₉	1	4	yes	complemented
408	#387	C₂²×C₈₉	1	4	yes	complemented
409	#386	C₂²×C₈₉	1	2	yes	—
410	#386	C₂²×C₈₉	1	4	yes	—
411	#386	C₂²×C₈₉	1	2	yes	—
412	#386	C₂²×C₈₉	1	4	yes	—
413	#386	C₂²×C₈₉	1	4	yes	—
414	#385	C₂²×C₈₉	1	2	yes	—
415	#385	C₂²×C₈₉	1	2	yes	—
416	#385	C₂²×C₈₉	1	4	yes	—
417	#385	C₂²×C₈₉	1	4	yes	complemented
418	#385	C₂²×C₈₉	1	4	yes	complemented
419	#381	C₂²×C₈₉	1	1	yes	characteristic
420	#381	C₂²×C₈₉	1	1	yes	characteristic
421	#381	C₂²×C₈₉	1	2	yes	—
422	#380	C₂²×C₈₉	1	2	yes	—
423	#379	C₂²×C₈₉	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
426	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
427	C₂×#41	—	2	8	no	—
428	C₂×#41	—	2	4	no	—
429	C₂²×Q₈	—	2	4	no	—
430	C₂²×Q₈	—	4	4	no	—
431	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
433	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
435	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
436	C₂³×C₄	—	2	4	no	—
437	C₂³×C₄	—	4	4	no	—
438	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
441	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
442	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
445	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
448	#123	—	2	8	no	—
449	C₂²⋊Q₈	—	2	16	no	—
450	C₂²⋊Q₈	—	2	16	no	—
451	C₂²⋊Q₈	—	4	8	no	—
452	#120	—	2	8	no	—
453	C₄×Q₈	—	2	8	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	4	8	no	—
458	#117	—	2	4	no	—
459	#117	—	2	8	no	—
460	C₂×C₄⋊C₄	—	2	4	no	—
461	C₂×C₄⋊C₄	—	2	4	no	—
462	C₂×C₄⋊C₄	—	2	8	no	—
463	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
464	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₂²⋊C₄	—	2	4	no	—
479	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
493	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
494	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
496	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
497	#95	C₂³×C₈₉	1	4	yes	—
498	#95	C₂³×C₈₉	1	4	yes	—
499	#95	C₂³×C₈₉	1	4	yes	—
500	#95	C₂³×C₈₉	1	4	yes	—
501	#95	C₂³×C₈₉	1	2	yes	—
502	#95	C₂³×C₈₉	1	4	yes	—
503	#95	C₂³×C₈₉	1	2	yes	—
504	#95	C₂³×C₈₉	1	2	yes	—
505	#95	C₂³×C₈₉	1	2	yes	—
506	#95	C₂³×C₈₉	1	4	yes	—
507	#95	C₂³×C₈₉	1	4	yes	—
508	#95	C₂³×C₈₉	1	4	yes	—
509	C₂⁴	—	2	2	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	4	2	no	—
513	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
514	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
515	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
516	#41	—	2	32	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	8	no	—
521	C₂×Q₈	—	4	4	no	—
522	C₂×Q₈	—	4	16	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	#41×C₈₉	1	8	yes	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	4	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	16	no	—
551	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
552	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
553	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	8	no	—
574	C₄⋊C₄	—	2	8	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
578	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	—	2	8	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	4	no	—
596	C₄²	—	4	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	4	16	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	4	4	no	—
611	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
612	C₂³	C₂×#41×C₈₉	1	4	yes	—
613	C₂³	C₂×#41×C₈₉	1	4	yes	—
614	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
615	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
616	Q₈	—	2	8	no	—
617	Q₈	—	4	16	no	—
618	D₄	—	2	8	no	—
619	D₄	—	2	16	no	—
620	D₄	—	4	16	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	16	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	16	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
654	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
655	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
657	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
658	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	8	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	8	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	4	16	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	#525×C₈₉	1	4	yes	—
674	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
675	C₂²	C₂²×#41×C₈₉	1	2	yes	—
676	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
677	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	4	no	—
690	C₂	—	2	4	no	—
691	C₂	—	4	4	no	—
692	C₂	—	4	4	no	—
693	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
694	C₂	C₈₉×#3484	1	1	yes	characteristic
695	C₂	C₈₉×#3486	1	1	yes	characteristic
696	C₂	C₈₉×#3520	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2404	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₈₉	C₂	semidirect
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#2534	C₂	semidirect
4. C₈₉×#2484	C₂	semidirect
5. C₈₉×#2482	C₂	semidirect
6. C₈₉×#2477	C₂	semidirect
7. C₈₉×#2465	C₂	semidirect
8. C₈₉×#2463	C₂	semidirect
9. C₈₉×#2449	C₂	semidirect
10. C₈₉×#2409	C₂	semidirect
11. C₈₉×#2406	C₂	semidirect
13. C₈₉×#2322	C₂	semidirect
14. C₈₉×#2313	C₂	semidirect
15. C₄×#120×C₈₉	C₂	semidirect
23. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
26. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
30. C₂×C₄×D₄×C₈₉	C₂²	semidirect
32. C₂×#117×C₈₉	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
39. #400×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
44. #395×C₈₉	C₂²	semidirect
45. #395×C₈₉	C₂²	semidirect
47. #394×C₈₉	C₂²	semidirect
49. #393×C₈₉	C₂²	semidirect
51. #391×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #387×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
58. #387×C₈₉	C₂²	semidirect
59. #387×C₈₉	C₂²	semidirect
68. #385×C₈₉	C₂²	semidirect
69. #385×C₈₉	C₂²	semidirect
114. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
341. #35357	C₈₉	direct (N × H)
349. C₂²×C₂²⋊Q₈	C₂×C₈₉	semidirect
350. C₂×#520	C₂×C₈₉	semidirect
351. #2534	C₂×C₈₉	semidirect
352. #2484	C₂×C₈₉	semidirect
353. #2482	C₂×C₈₉	semidirect
354. #2477	C₂×C₈₉	semidirect
355. #2465	C₂×C₈₉	semidirect
356. #2463	C₂×C₈₉	semidirect
357. #2449	C₂×C₈₉	semidirect
358. #2409	C₂×C₈₉	semidirect
359. #2406	C₂×C₈₉	semidirect
361. #2322	C₂×C₈₉	semidirect
362. #2313	C₂×C₈₉	semidirect
363. C₄×#120	C₂×C₈₉	semidirect
364. C₈₉	#35357	direct (N × H)
372. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
375. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
379. C₂×C₄×D₄	C₂²×C₈₉	semidirect
381. C₂×#117	C₂²×C₈₉	semidirect
385. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
388. #400	C₂²×C₈₉	semidirect
390. #398	C₂²×C₈₉	semidirect
393. #395	C₂²×C₈₉	semidirect
394. #395	C₂²×C₈₉	semidirect
396. #394	C₂²×C₈₉	semidirect
398. #393	C₂²×C₈₉	semidirect
400. #391	C₂²×C₈₉	semidirect
401. #389	C₂²×C₈₉	semidirect
404. #388	C₂²×C₈₉	semidirect
405. #387	C₂²×C₈₉	semidirect
406. #387	C₂²×C₈₉	semidirect
407. #387	C₂²×C₈₉	semidirect
408. #387	C₂²×C₈₉	semidirect
417. #385	C₂²×C₈₉	semidirect
418. #385	C₂²×C₈₉	semidirect
463. C₂×C₄⋊C₄	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2534	2
C₈₉×#2484	2
C₈₉×#2482	2
C₈₉×#2477	2
C₈₉×#2465	2
C₈₉×#2463	2
C₈₉×#2449	2
C₈₉×#2409	2
C₈₉×#2406	2
C₈₉×#2404	2
C₈₉×#2322	2
C₈₉×#2313	2
C₄×#120×C₈₉	2
#35357	89

Subgroups — C89×#35357 #36413205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35357 #36413205