Subgroups — C₈₉×#34331 #36412179

Order 22784.

2436 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2367	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2367	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2366	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2359	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2354	C₂	1	2	yes	maximal, complemented
8	Q₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2349	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2335	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2326	C₂	1	2	yes	maximal, complemented
12	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₄×#124×C₈₉	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2293	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2275	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₄	1	16	yes	complemented
19	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#124×C₈₉	C₂²	1	2	yes	—
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#123×C₈₉	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
35	C₂×#117×C₈₉	C₂²	1	4	yes	—
36	#391×C₈₉	C₂²	1	1	yes	characteristic
37	#391×C₈₉	C₂²	1	1	yes	characteristic
38	#391×C₈₉	C₂²	1	2	yes	—
39	#390×C₈₉	C₂²	1	2	yes	—
40	#390×C₈₉	C₂²	1	2	yes	—
41	#390×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#390×C₈₉	C₂²	1	2	yes	—
44	#389×C₈₉	C₂²	1	1	yes	characteristic
45	#389×C₈₉	C₂²	1	1	yes	characteristic
46	#389×C₈₉	C₂²	1	4	yes	—
47	#389×C₈₉	C₂²	1	2	yes	—
48	#388×C₈₉	C₂²	1	4	yes	—
49	#388×C₈₉	C₂²	1	4	yes	—
50	#388×C₈₉	C₂²	1	4	yes	—
51	#388×C₈₉	C₂²	1	4	yes	—
52	#388×C₈₉	C₂²	1	4	yes	—
53	#388×C₈₉	C₂²	1	4	yes	—
54	#387×C₈₉	C₂²	1	2	yes	—
55	#387×C₈₉	C₂²	1	2	yes	—
56	#387×C₈₉	C₂²	1	4	yes	—
57	#386×C₈₉	C₂²	1	4	yes	—
58	#385×C₈₉	C₂²	1	4	yes	—
59	#385×C₈₉	C₂²	1	4	yes	—
60	#385×C₈₉	C₂²	1	4	yes	—
61	#384×C₈₉	C₂²	1	1	yes	characteristic
62	#384×C₈₉	C₂²	1	2	yes	—
63	#382×C₈₉	C₂²	1	2	yes	—
64	#380×C₈₉	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
80	#376×C₈₉	C₂²	1	2	yes	—
81	C₂×#95×C₈₉	C₂²	1	4	yes	—
82	C₄³×C₈₉	C₂²	1	1	yes	characteristic
83	C₄³×C₈₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
90	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
92	#127×C₈₉	C₂×C₄	1	8	yes	—
93	#124×C₈₉	C₂×C₄	1	16	yes	complemented
94	#124×C₈₉	C₂×C₄	1	16	yes	complemented
95	#123×C₈₉	C₂×C₄	1	32	yes	complemented
96	C₄×Q₈×C₈₉	—	2	4	no	—
97	C₄×Q₈×C₈₉	—	2	4	no	—
98	C₄×Q₈×C₈₉	—	4	4	no	—
99	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
100	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
101	C₄×D₄×C₈₉	—	2	8	no	—
102	C₄×D₄×C₈₉	—	2	8	no	—
103	C₄×D₄×C₈₉	—	4	4	no	—
104	C₄×D₄×C₈₉	—	4	4	no	—
105	C₄×D₄×C₈₉	—	4	4	no	—
106	C₄×D₄×C₈₉	C₂×C₄	1	16	yes	complemented
107	C₄×D₄×C₈₉	C₂×C₄	1	16	yes	complemented
108	#117×C₈₉	—	4	8	no	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
147	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	#95×C₈₉	C₂³	1	2	yes	—
153	#95×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	#95×C₈₉	C₂³	1	4	yes	—
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	2	yes	—
158	#95×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	2	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	#95×C₈₉	C₂³	1	2	yes	—
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₈₉	—	2	2	no	—
168	C₂×Q₈×C₈₉	—	2	2	no	—
169	C₂×Q₈×C₈₉	—	2	2	no	—
170	C₂×Q₈×C₈₉	—	2	2	no	—
171	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₈₉	—	2	4	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	—	4	2	no	—
178	C₂×D₄×C₈₉	—	4	2	no	—
179	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
180	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
181	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
182	C₂²×C₄×C₈₉	—	2	8	no	—
183	C₂²×C₄×C₈₉	—	2	8	no	—
184	C₂²×C₄×C₈₉	—	4	4	no	—
185	C₂²×C₄×C₈₉	—	4	4	no	—
186	C₂²×C₄×C₈₉	—	4	4	no	—
187	C₂²×C₄×C₈₉	—	4	4	no	—
188	C₂²×C₄×C₈₉	—	4	4	no	—
189	C₂²×C₄×C₈₉	—	4	4	no	—
190	C₂²×C₄×C₈₉	C₂²×C₄	1	16	yes	—
191	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₈₉	—	2	4	no	—
208	C₄⋊C₄×C₈₉	—	2	4	no	—
209	C₄⋊C₄×C₈₉	—	2	4	no	—
210	C₄⋊C₄×C₈₉	—	2	2	no	—
211	C₄⋊C₄×C₈₉	—	2	4	no	—
212	C₄⋊C₄×C₈₉	—	2	2	no	—
213	C₄⋊C₄×C₈₉	—	2	4	no	—
214	C₄⋊C₄×C₈₉	—	2	2	no	—
215	C₄⋊C₄×C₈₉	—	4	2	no	—
216	C₄⋊C₄×C₈₉	—	4	4	no	—
217	C₄⋊C₄×C₈₉	—	4	2	no	—
218	C₄⋊C₄×C₈₉	—	4	4	no	—
219	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
222	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
223	C₄⋊C₄×C₈₉	#41	1	4	yes	—
224	C₂²⋊C₄×C₈₉	—	2	8	no	—
225	C₂²⋊C₄×C₈₉	—	2	8	no	—
226	C₂²⋊C₄×C₈₉	—	2	8	no	—
227	C₂²⋊C₄×C₈₉	—	4	4	no	—
228	C₂²⋊C₄×C₈₉	—	4	4	no	—
229	C₂²⋊C₄×C₈₉	—	4	4	no	—
230	C₂²⋊C₄×C₈₉	C₂²×C₄	1	16	yes	—
231	C₂²⋊C₄×C₈₉	C₂²×C₄	1	16	yes	—
232	C₂²⋊C₄×C₈₉	C₂²×C₄	1	16	yes	—
233	C₄²×C₈₉	—	2	4	no	—
234	C₄²×C₈₉	—	2	4	no	—
235	C₄²×C₈₉	—	2	2	no	—
236	C₄²×C₈₉	—	2	4	no	—
237	C₄²×C₈₉	—	2	4	no	—
238	C₄²×C₈₉	—	2	2	no	—
239	C₄²×C₈₉	—	2	2	no	—
240	C₄²×C₈₉	—	2	4	no	—
241	C₄²×C₈₉	—	2	2	no	—
242	C₄²×C₈₉	—	4	2	no	—
243	C₄²×C₈₉	—	4	1	no	—
244	C₄²×C₈₉	—	4	4	no	—
245	C₄²×C₈₉	—	4	4	no	—
246	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
247	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
248	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
249	C₄²×C₈₉	#41	1	4	yes	—
250	C₂³×C₈₉	—	2	4	no	—
251	C₂³×C₈₉	—	2	4	no	—
252	C₂³×C₈₉	—	2	4	no	—
253	C₂³×C₈₉	—	2	4	no	—
254	C₂³×C₈₉	—	2	4	no	—
255	C₂³×C₈₉	—	2	4	no	—
256	C₂³×C₈₉	C₂³×C₄	1	8	yes	—
257	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
258	Q₈×C₈₉	—	2	8	no	—
259	Q₈×C₈₉	—	2	8	no	—
260	D₄×C₈₉	—	2	16	no	—
261	D₄×C₈₉	—	2	16	no	—
262	D₄×C₈₉	—	4	8	no	—
263	C₂×C₄×C₈₉	—	2	1	no	—
264	C₂×C₄×C₈₉	—	2	2	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	2	2	no	—
268	C₂×C₄×C₈₉	—	2	1	no	—
269	C₂×C₄×C₈₉	—	2	1	no	—
270	C₂×C₄×C₈₉	—	2	1	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	2	2	no	—
273	C₂×C₄×C₈₉	—	2	1	no	—
274	C₂×C₄×C₈₉	—	2	1	no	—
275	C₂×C₄×C₈₉	—	2	2	no	—
276	C₂×C₄×C₈₉	—	2	1	no	—
277	C₂×C₄×C₈₉	—	2	2	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	1	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	4	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	4	no	—
291	C₂×C₄×C₈₉	—	2	4	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	4	16	no	—
297	C₂×C₄×C₈₉	—	8	8	no	—
298	C₂×C₄×C₈₉	—	8	8	no	—
299	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
307	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
308	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
309	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
310	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
311	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
314	C₂²×C₈₉	—	2	8	no	—
315	C₂²×C₈₉	—	2	8	no	—
316	C₂²×C₈₉	—	2	8	no	—
317	C₂²×C₈₉	—	4	4	no	—
318	C₂²×C₈₉	—	4	4	no	—
319	C₂²×C₈₉	—	4	4	no	—
320	C₂²×C₈₉	—	4	4	no	—
321	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
322	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	C₂²×C₈₉	#585	1	1	yes	characteristic
328	C₄×C₈₉	—	2	4	no	—
329	C₄×C₈₉	—	2	4	no	—
330	C₄×C₈₉	—	2	4	no	—
331	C₄×C₈₉	—	2	4	no	—
332	C₄×C₈₉	—	2	2	no	—
333	C₄×C₈₉	—	2	2	no	—
334	C₄×C₈₉	—	2	2	no	—
335	C₄×C₈₉	—	2	4	no	—
336	C₄×C₈₉	—	2	2	no	—
337	C₄×C₈₉	—	4	2	no	—
338	C₄×C₈₉	—	4	4	no	—
339	C₄×C₈₉	—	4	1	no	—
340	C₄×C₈₉	—	4	2	no	—
341	C₄×C₈₉	—	4	2	no	—
342	C₄×C₈₉	C₄×#41	1	4	yes	—
343	C₄×C₈₉	#520	1	4	yes	—
344	#34331	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₈₉	—	4	8	no	—
346	C₂×C₈₉	C₂×C₄×#41	1	1	yes	characteristic
347	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
348	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₈₉	#3507	1	1	yes	characteristic
350	C₂×C₈₉	#3508	1	1	yes	characteristic
351	C₂×C₈₉	#3514	1	1	yes	characteristic
352	C₂×C₈₉	#3522	1	1	yes	characteristic
353	C₂×#559	C₂×C₈₉	1	1	yes	characteristic
354	#2367	C₂×C₈₉	1	2	yes	complemented
355	#2367	C₂×C₈₉	1	2	yes	complemented
356	#2366	C₂×C₈₉	1	1	yes	characteristic
357	#2359	C₂×C₈₉	1	4	yes	complemented
358	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
359	#2354	C₂×C₈₉	1	2	yes	complemented
360	Q₈×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
361	#2349	C₂×C₈₉	1	2	yes	complemented
362	#2335	C₂×C₈₉	1	4	yes	complemented
363	#2326	C₂×C₈₉	1	2	yes	complemented
364	C₄×#127	C₂×C₈₉	1	1	yes	characteristic
365	C₄×#124	C₂×C₈₉	1	2	yes	complemented
366	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
367	#2293	C₂×C₈₉	1	2	yes	complemented
368	#2275	C₂×C₈₉	1	2	yes	complemented
369	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
370	C₈₉	#34331	1	1	yes	characteristic, direct product factor, Sylow
371	#559	C₄×C₈₉	1	16	yes	complemented
372	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
373	C₂×#124	C₂²×C₈₉	1	2	yes	—
374	C₂×#124	C₂²×C₈₉	1	2	yes	—
375	C₂×#123	C₂²×C₈₉	1	4	yes	—
376	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
379	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
388	C₂×#117	C₂²×C₈₉	1	4	yes	—
389	#391	C₂²×C₈₉	1	2	yes	—
390	#391	C₂²×C₈₉	1	1	yes	characteristic
391	#391	C₂²×C₈₉	1	1	yes	characteristic
392	#390	C₂²×C₈₉	1	2	yes	—
393	#390	C₂²×C₈₉	1	2	yes	—
394	#390	C₂²×C₈₉	1	2	yes	—
395	#390	C₂²×C₈₉	1	2	yes	—
396	#390	C₂²×C₈₉	1	2	yes	—
397	#389	C₂²×C₈₉	1	4	yes	—
398	#389	C₂²×C₈₉	1	1	yes	characteristic
399	#389	C₂²×C₈₉	1	2	yes	—
400	#389	C₂²×C₈₉	1	1	yes	characteristic
401	#388	C₂²×C₈₉	1	4	yes	—
402	#388	C₂²×C₈₉	1	4	yes	—
403	#388	C₂²×C₈₉	1	4	yes	—
404	#388	C₂²×C₈₉	1	4	yes	—
405	#388	C₂²×C₈₉	1	4	yes	—
406	#388	C₂²×C₈₉	1	4	yes	—
407	#387	C₂²×C₈₉	1	2	yes	—
408	#387	C₂²×C₈₉	1	4	yes	—
409	#387	C₂²×C₈₉	1	2	yes	—
410	#386	C₂²×C₈₉	1	4	yes	—
411	#385	C₂²×C₈₉	1	4	yes	—
412	#385	C₂²×C₈₉	1	4	yes	—
413	#385	C₂²×C₈₉	1	4	yes	—
414	#384	C₂²×C₈₉	1	1	yes	characteristic
415	#384	C₂²×C₈₉	1	2	yes	—
416	#382	C₂²×C₈₉	1	2	yes	—
417	#380	C₂²×C₈₉	1	4	yes	—
418	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
425	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
429	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
433	#376	C₂²×C₈₉	1	2	yes	—
434	C₂×#95	C₂²×C₈₉	1	4	yes	—
435	C₄³	C₂²×C₈₉	1	1	yes	characteristic
436	C₄³	C₂²×C₈₉	1	2	yes	—
437	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
439	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
440	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
441	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
442	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
443	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
444	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
445	#127	C₂×C₄×C₈₉	1	8	yes	—
446	#124	C₂×C₄×C₈₉	1	16	yes	complemented
447	#124	C₂×C₄×C₈₉	1	16	yes	complemented
448	#123	C₂×C₄×C₈₉	1	32	yes	complemented
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	2	4	no	—
451	C₄×Q₈	—	4	4	no	—
452	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
453	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	—	4	4	no	—
457	C₄×D₄	—	4	4	no	—
458	C₄×D₄	—	4	4	no	—
459	C₄×D₄	C₂×C₄×C₈₉	1	16	yes	complemented
460	C₄×D₄	C₂×C₄×C₈₉	1	16	yes	complemented
461	#117	—	4	8	no	—
462	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
489	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
492	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
494	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
496	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
498	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
499	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
500	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
505	#95	C₂³×C₈₉	1	2	yes	—
506	#95	C₂³×C₈₉	1	2	yes	—
507	#95	C₂³×C₈₉	1	4	yes	—
508	#95	C₂³×C₈₉	1	4	yes	—
509	#95	C₂³×C₈₉	1	2	yes	—
510	#95	C₂³×C₈₉	1	2	yes	—
511	#95	C₂³×C₈₉	1	2	yes	—
512	#95	C₂³×C₈₉	1	2	yes	—
513	#95	C₂³×C₈₉	1	4	yes	—
514	#95	C₂³×C₈₉	1	2	yes	—
515	#95	C₂³×C₈₉	1	2	yes	—
516	#95	C₂³×C₈₉	1	4	yes	—
517	#95	C₂³×C₈₉	1	2	yes	—
518	#95	C₂³×C₈₉	1	2	yes	—
519	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
525	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
534	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	8	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	C₂²×C₄×C₈₉	1	16	yes	—
544	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
575	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
576	C₄⋊C₄	#41×C₈₉	1	4	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	C₂²×C₄×C₈₉	1	16	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₈₉	1	16	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₈₉	1	16	yes	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	2	no	—
598	C₄²	—	4	1	no	—
599	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
600	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
601	C₄²	C₂²×C₄×C₈₉	1	4	yes	—
602	C₄²	#41×C₈₉	1	4	yes	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	4	no	—
609	C₂³	C₂³×C₄×C₈₉	1	8	yes	—
610	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
611	Q₈	—	2	8	no	—
612	Q₈	—	2	8	no	—
613	D₄	—	2	16	no	—
614	D₄	—	2	16	no	—
615	D₄	—	4	8	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	8	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
660	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
661	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
662	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
664	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
665	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
666	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
667	C₂²	—	2	8	no	—
668	C₂²	—	2	8	no	—
669	C₂²	—	2	8	no	—
670	C₂²	—	4	4	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	4	no	—
674	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
675	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
676	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
677	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
678	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
679	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
680	C₂²	#585×C₈₉	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	C₄×#41×C₈₉	1	4	yes	—
696	C₄	#520×C₈₉	1	4	yes	—
697	C₂	—	4	8	no	—
698	C₂	C₂×C₄×#41×C₈₉	1	1	yes	characteristic
699	C₂	C₂×#520×C₈₉	1	1	yes	characteristic
700	C₂	C₄×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
701	C₂	C₈₉×#3507	1	1	yes	characteristic
702	C₂	C₈₉×#3508	1	1	yes	characteristic
703	C₂	C₈₉×#3514	1	1	yes	characteristic
704	C₂	C₈₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#127×C₈₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2367	C₂	semidirect
3. C₈₉×#2367	C₂	semidirect
5. C₈₉×#2359	C₂	semidirect
6. C₈₉×#2355	C₂	semidirect
7. C₈₉×#2354	C₂	semidirect
8. Q₈×C₄⋊C₄×C₈₉	C₂	semidirect
9. C₈₉×#2349	C₂	semidirect
10. C₈₉×#2335	C₂	semidirect
11. C₈₉×#2326	C₂	semidirect
13. C₄×#124×C₈₉	C₂	semidirect
14. C₈₉×#2295	C₂	semidirect
15. C₈₉×#2293	C₂	semidirect
16. C₈₉×#2275	C₂	semidirect
17. C₄²×Q₈×C₈₉	C₂	semidirect
18. #559×C₈₉	C₄	semidirect
93. #124×C₈₉	C₂×C₄	semidirect
94. #124×C₈₉	C₂×C₄	semidirect
95. #123×C₈₉	C₂×C₄	semidirect
99. C₄×Q₈×C₈₉	C₂×C₄	semidirect
100. C₄×Q₈×C₈₉	C₂×C₄	semidirect
106. C₄×D₄×C₈₉	C₂×C₄	semidirect
107. C₄×D₄×C₈₉	C₂×C₄	semidirect
344. #34331	C₈₉	direct (N × H)
354. #2367	C₂×C₈₉	semidirect
355. #2367	C₂×C₈₉	semidirect
357. #2359	C₂×C₈₉	semidirect
358. #2355	C₂×C₈₉	semidirect
359. #2354	C₂×C₈₉	semidirect
360. Q₈×C₄⋊C₄	C₂×C₈₉	semidirect
361. #2349	C₂×C₈₉	semidirect
362. #2335	C₂×C₈₉	semidirect
363. #2326	C₂×C₈₉	semidirect
365. C₄×#124	C₂×C₈₉	semidirect
366. #2295	C₂×C₈₉	semidirect
367. #2293	C₂×C₈₉	semidirect
368. #2275	C₂×C₈₉	semidirect
369. C₄²×Q₈	C₂×C₈₉	semidirect
370. C₈₉	#34331	direct (N × H)
371. #559	C₄×C₈₉	semidirect
446. #124	C₂×C₄×C₈₉	semidirect
447. #124	C₂×C₄×C₈₉	semidirect
448. #123	C₂×C₄×C₈₉	semidirect
452. C₄×Q₈	C₂×C₄×C₈₉	semidirect
453. C₄×Q₈	C₂×C₄×C₈₉	semidirect
459. C₄×D₄	C₂×C₄×C₈₉	semidirect
460. C₄×D₄	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₈₉	2
C₈₉×#2367	2
C₈₉×#2366	2
C₈₉×#2359	2
C₈₉×#2355	2
C₈₉×#2354	2
Q₈×C₄⋊C₄×C₈₉	2
C₈₉×#2349	2
C₈₉×#2335	2
C₈₉×#2326	2
C₄×#127×C₈₉	2
C₄×#124×C₈₉	2
C₈₉×#2295	2
C₈₉×#2293	2
C₈₉×#2275	2
C₄²×Q₈×C₈₉	2
#34331	89

Subgroups — C89×#34331 #36412179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#34331 #36412179