Subgroups — C₈₉×#35291 #36413139

Order 22784.

1650 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2645	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2625	C₂	1	2	yes	maximal
7	C₈₉×#2514	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2509	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2508	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2495	C₂	1	2	yes	maximal
11	C₈₉×#2494	C₂	1	2	yes	maximal
12	C₈₉×#2489	C₂	1	2	yes	maximal
13	C₈₉×#2453	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2421	C₂	1	2	yes	maximal
15	C₈₉×#2323	C₂	1	2	yes	maximal
16	C₈₉×#2320	C₂	1	2	yes	maximal, complemented
17	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#401×C₈₉	C₂²	1	4	yes	—
31	#400×C₈₉	C₂²	1	4	yes	—
32	#400×C₈₉	C₂²	1	4	yes	—
33	#400×C₈₉	C₂²	1	4	yes	—
34	#400×C₈₉	C₂²	1	4	yes	—
35	#398×C₈₉	C₂²	1	4	yes	—
36	#397×C₈₉	C₂²	1	4	yes	—
37	#397×C₈₉	C₂²	1	4	yes	—
38	#391×C₈₉	C₂²	1	2	yes	—
39	#391×C₈₉	C₂²	1	2	yes	—
40	#391×C₈₉	C₂²	1	2	yes	—
41	#391×C₈₉	C₂²	1	2	yes	—
42	#391×C₈₉	C₂²	1	2	yes	—
43	#391×C₈₉	C₂²	1	2	yes	—
44	#391×C₈₉	C₂²	1	2	yes	—
45	#391×C₈₉	C₂²	1	2	yes	—
46	#389×C₈₉	C₂²	1	2	yes	—
47	#389×C₈₉	C₂²	1	2	yes	—
48	#389×C₈₉	C₂²	1	2	yes	—
49	#389×C₈₉	C₂²	1	2	yes	—
50	#389×C₈₉	C₂²	1	2	yes	—
51	#389×C₈₉	C₂²	1	2	yes	—
52	#389×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	4	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#388×C₈₉	C₂²	1	4	yes	—
60	#388×C₈₉	C₂²	1	4	yes	—
61	#387×C₈₉	C₂²	1	4	yes	—
62	#387×C₈₉	C₂²	1	4	yes	—
63	#387×C₈₉	C₂²	1	4	yes	—
64	#384×C₈₉	C₂²	1	1	yes	characteristic
65	#384×C₈₉	C₂²	1	1	yes	characteristic
66	#383×C₈₉	C₂²	1	4	yes	—
67	#382×C₈₉	C₂²	1	4	yes	—
68	#382×C₈₉	C₂²	1	2	yes	—
69	#382×C₈₉	C₂²	1	2	yes	—
70	#382×C₈₉	C₂²	1	2	yes	—
71	#380×C₈₉	C₂²	1	2	yes	—
72	#380×C₈₉	C₂²	1	2	yes	—
73	#380×C₈₉	C₂²	1	2	yes	—
74	#380×C₈₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
87	#376×C₈₉	C₂²	1	1	yes	characteristic
88	#376×C₈₉	C₂²	1	1	yes	characteristic
89	C₄³×C₈₉	C₂²	1	1	yes	characteristic
90	C₄³×C₈₉	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₈₉	C₂³	1	2	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	1	yes	characteristic
96	C₄⋊Q₈×C₈₉	—	2	4	no	—
97	C₄⋊Q₈×C₈₉	—	2	4	no	—
98	#125×C₈₉	—	4	4	no	—
99	C₂²⋊Q₈×C₈₉	—	2	8	no	—
100	C₂²⋊Q₈×C₈₉	—	4	4	no	—
101	C₄×Q₈×C₈₉	—	2	8	no	—
102	C₄×Q₈×C₈₉	—	4	4	no	—
103	#117×C₈₉	—	2	4	no	—
104	#117×C₈₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₈₉	—	2	4	no	—
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
150	#95×C₈₉	C₂³	1	1	yes	characteristic
151	#95×C₈₉	C₂³	1	1	yes	characteristic
152	#95×C₈₉	C₂³	1	1	yes	characteristic
153	#95×C₈₉	C₂³	1	1	yes	characteristic
154	#95×C₈₉	C₂³	1	1	yes	characteristic
155	#95×C₈₉	C₂³	1	1	yes	characteristic
156	#95×C₈₉	C₂³	1	1	yes	characteristic
157	#95×C₈₉	C₂³	1	1	yes	characteristic
158	#95×C₈₉	C₂³	1	4	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	#95×C₈₉	C₂³	1	4	yes	—
162	#95×C₈₉	C₂³	1	4	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	4	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₈₉	—	2	4	no	—
174	C₂×Q₈×C₈₉	—	2	4	no	—
175	C₂×Q₈×C₈₉	—	2	4	no	—
176	C₂×Q₈×C₈₉	—	2	4	no	—
177	C₂×Q₈×C₈₉	—	2	4	no	—
178	C₂×Q₈×C₈₉	—	2	4	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	2	no	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	2	no	—
187	C₂²×C₄×C₈₉	#41	1	4	yes	—
188	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	—	2	2	no	—
207	C₄⋊C₄×C₈₉	—	2	2	no	—
208	C₄⋊C₄×C₈₉	—	2	2	no	—
209	C₄⋊C₄×C₈₉	—	2	2	no	—
210	C₄⋊C₄×C₈₉	—	2	4	no	—
211	C₄⋊C₄×C₈₉	—	2	8	no	—
212	C₄⋊C₄×C₈₉	—	2	4	no	—
213	C₄⋊C₄×C₈₉	—	2	8	no	—
214	C₄⋊C₄×C₈₉	—	2	4	no	—
215	C₄⋊C₄×C₈₉	—	2	4	no	—
216	C₄⋊C₄×C₈₉	—	2	4	no	—
217	C₄⋊C₄×C₈₉	—	2	4	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	—	4	4	no	—
223	C₄⋊C₄×C₈₉	—	4	4	no	—
224	C₄⋊C₄×C₈₉	—	4	4	no	—
225	C₄⋊C₄×C₈₉	—	4	4	no	—
226	C₂²⋊C₄×C₈₉	—	2	2	no	—
227	C₂²⋊C₄×C₈₉	—	2	2	no	—
228	C₂²⋊C₄×C₈₉	—	2	8	no	—
229	C₂²⋊C₄×C₈₉	—	2	2	no	—
230	C₂²⋊C₄×C₈₉	—	2	2	no	—
231	C₂²⋊C₄×C₈₉	—	4	4	no	—
232	C₄²×C₈₉	—	2	2	no	—
233	C₄²×C₈₉	—	2	2	no	—
234	C₄²×C₈₉	—	2	2	no	—
235	C₄²×C₈₉	—	2	2	no	—
236	C₄²×C₈₉	—	2	2	no	—
237	C₄²×C₈₉	—	2	2	no	—
238	C₄²×C₈₉	—	2	8	no	—
239	C₄²×C₈₉	—	2	2	no	—
240	C₄²×C₈₉	—	2	2	no	—
241	C₄²×C₈₉	—	2	2	no	—
242	C₄²×C₈₉	—	2	2	no	—
243	C₄²×C₈₉	—	2	2	no	—
244	C₄²×C₈₉	—	2	2	no	—
245	C₄²×C₈₉	—	2	2	no	—
246	C₄²×C₈₉	—	2	2	no	—
247	C₄²×C₈₉	—	4	4	no	—
248	C₄²×C₈₉	#41	1	4	yes	—
249	C₄²×C₈₉	#41	1	4	yes	—
250	C₂³×C₈₉	—	2	1	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	1	no	—
255	C₂³×C₈₉	—	2	1	no	—
256	C₂³×C₈₉	C₂×#41	1	2	yes	—
257	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
258	Q₈×C₈₉	—	4	8	no	—
259	Q₈×C₈₉	—	4	8	no	—
260	C₂×C₄×C₈₉	—	2	1	no	—
261	C₂×C₄×C₈₉	—	2	1	no	—
262	C₂×C₄×C₈₉	—	2	1	no	—
263	C₂×C₄×C₈₉	—	2	1	no	—
264	C₂×C₄×C₈₉	—	2	1	no	—
265	C₂×C₄×C₈₉	—	2	1	no	—
266	C₂×C₄×C₈₉	—	2	8	no	—
267	C₂×C₄×C₈₉	—	2	1	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	1	no	—
272	C₂×C₄×C₈₉	—	2	1	no	—
273	C₂×C₄×C₈₉	—	2	1	no	—
274	C₂×C₄×C₈₉	—	2	1	no	—
275	C₂×C₄×C₈₉	—	2	4	no	—
276	C₂×C₄×C₈₉	—	2	4	no	—
277	C₂×C₄×C₈₉	—	2	4	no	—
278	C₂×C₄×C₈₉	—	2	4	no	—
279	C₂×C₄×C₈₉	—	2	4	no	—
280	C₂×C₄×C₈₉	—	2	4	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	1	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	4	no	—
285	C₂×C₄×C₈₉	—	2	4	no	—
286	C₂×C₄×C₈₉	—	2	4	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	1	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	4	no	—
298	C₂×C₄×C₈₉	—	2	4	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	1	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	4	no	—
303	C₂×C₄×C₈₉	—	4	4	no	—
304	C₂×C₄×C₈₉	—	4	4	no	—
305	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
306	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
307	C₂×C₄×C₈₉	C₂×#41	1	2	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	C₂×#41	1	2	yes	—
312	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
313	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
314	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
315	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
316	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
317	C₂²×C₈₉	—	2	2	no	—
318	C₂²×C₈₉	—	2	2	no	—
319	C₂²×C₈₉	—	2	2	no	—
320	C₂²×C₈₉	—	4	1	no	—
321	C₂²×C₈₉	—	4	1	no	—
322	C₂²×C₈₉	—	4	1	no	—
323	C₂²×C₈₉	—	4	1	no	—
324	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	2	no	—
333	C₄×C₈₉	—	2	2	no	—
334	C₄×C₈₉	—	4	4	no	—
335	C₄×C₈₉	—	4	1	no	—
336	C₄×C₈₉	—	4	1	no	—
337	C₄×C₈₉	—	4	4	no	—
338	C₄×C₈₉	—	4	1	no	—
339	C₄×C₈₉	—	4	1	no	—
340	C₄×C₈₉	—	4	1	no	—
341	C₄×C₈₉	—	4	1	no	—
342	C₄×C₈₉	—	4	4	no	—
343	C₄×C₈₉	—	4	1	no	—
344	C₄×C₈₉	—	4	1	no	—
345	C₄×C₈₉	—	4	4	no	—
346	C₄×C₈₉	#529	1	4	yes	—
347	C₄×C₈₉	#541	1	4	yes	—
348	C₄×C₈₉	#542	1	4	yes	—
349	#35291	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂×C₈₉	—	4	2	no	—
351	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
352	C₂×C₈₉	C₂×#541	1	1	yes	characteristic
353	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
354	C₂×C₈₉	#3509	1	1	yes	characteristic
355	C₂×C₈₉	#3509	1	1	yes	characteristic
356	C₂×C₈₉	#3511	1	1	yes	characteristic
357	C₂×C₈₉	#3511	1	1	yes	characteristic
358	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
359	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
360	#2857	C₂×C₈₉	1	1	yes	characteristic
361	#2857	C₂×C₈₉	1	1	yes	characteristic
362	#2645	C₂×C₈₉	1	2	yes	complemented
363	#2625	C₂×C₈₉	1	2	yes	—
364	#2514	C₂×C₈₉	1	2	yes	complemented
365	#2509	C₂×C₈₉	1	2	yes	complemented
366	#2508	C₂×C₈₉	1	2	yes	complemented
367	#2495	C₂×C₈₉	1	2	yes	—
368	#2494	C₂×C₈₉	1	2	yes	—
369	#2489	C₂×C₈₉	1	2	yes	—
370	#2453	C₂×C₈₉	1	2	yes	complemented
371	#2421	C₂×C₈₉	1	2	yes	—
372	#2323	C₂×C₈₉	1	2	yes	—
373	#2320	C₂×C₈₉	1	2	yes	complemented
374	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
375	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
376	C₄×#117	C₂×C₈₉	1	1	yes	characteristic
377	C₈₉	#35291	1	1	yes	characteristic, direct product factor, Sylow
378	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
379	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
380	C₂×#125	C₂²×C₈₉	1	2	yes	—
381	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
383	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
384	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
385	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
386	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
388	#401	C₂²×C₈₉	1	4	yes	—
389	#400	C₂²×C₈₉	1	4	yes	—
390	#400	C₂²×C₈₉	1	4	yes	—
391	#400	C₂²×C₈₉	1	4	yes	—
392	#400	C₂²×C₈₉	1	4	yes	—
393	#398	C₂²×C₈₉	1	4	yes	—
394	#397	C₂²×C₈₉	1	4	yes	—
395	#397	C₂²×C₈₉	1	4	yes	—
396	#391	C₂²×C₈₉	1	2	yes	—
397	#391	C₂²×C₈₉	1	2	yes	—
398	#391	C₂²×C₈₉	1	2	yes	—
399	#391	C₂²×C₈₉	1	2	yes	—
400	#391	C₂²×C₈₉	1	2	yes	—
401	#391	C₂²×C₈₉	1	2	yes	—
402	#391	C₂²×C₈₉	1	2	yes	—
403	#391	C₂²×C₈₉	1	2	yes	—
404	#389	C₂²×C₈₉	1	2	yes	—
405	#389	C₂²×C₈₉	1	2	yes	—
406	#389	C₂²×C₈₉	1	2	yes	—
407	#389	C₂²×C₈₉	1	2	yes	—
408	#389	C₂²×C₈₉	1	2	yes	—
409	#389	C₂²×C₈₉	1	2	yes	—
410	#389	C₂²×C₈₉	1	2	yes	—
411	#389	C₂²×C₈₉	1	4	yes	—
412	#389	C₂²×C₈₉	1	2	yes	—
413	#389	C₂²×C₈₉	1	2	yes	—
414	#389	C₂²×C₈₉	1	2	yes	—
415	#389	C₂²×C₈₉	1	2	yes	—
416	#389	C₂²×C₈₉	1	2	yes	—
417	#388	C₂²×C₈₉	1	4	yes	—
418	#388	C₂²×C₈₉	1	4	yes	—
419	#387	C₂²×C₈₉	1	4	yes	—
420	#387	C₂²×C₈₉	1	4	yes	—
421	#387	C₂²×C₈₉	1	4	yes	—
422	#384	C₂²×C₈₉	1	1	yes	characteristic
423	#384	C₂²×C₈₉	1	1	yes	characteristic
424	#383	C₂²×C₈₉	1	4	yes	—
425	#382	C₂²×C₈₉	1	4	yes	—
426	#382	C₂²×C₈₉	1	2	yes	—
427	#382	C₂²×C₈₉	1	2	yes	—
428	#382	C₂²×C₈₉	1	2	yes	—
429	#380	C₂²×C₈₉	1	2	yes	—
430	#380	C₂²×C₈₉	1	2	yes	—
431	#380	C₂²×C₈₉	1	2	yes	—
432	#380	C₂²×C₈₉	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
443	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
445	#376	C₂²×C₈₉	1	1	yes	characteristic
446	#376	C₂²×C₈₉	1	1	yes	characteristic
447	C₄³	C₂²×C₈₉	1	1	yes	characteristic
448	C₄³	C₂²×C₈₉	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
450	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
451	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
454	C₄⋊Q₈	—	2	4	no	—
455	C₄⋊Q₈	—	2	4	no	—
456	#125	—	4	4	no	—
457	C₂²⋊Q₈	—	2	8	no	—
458	C₂²⋊Q₈	—	4	4	no	—
459	C₄×Q₈	—	2	8	no	—
460	C₄×Q₈	—	4	4	no	—
461	#117	—	2	4	no	—
462	#117	—	2	4	no	—
463	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	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	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄²	—	2	4	no	—
490	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
495	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
506	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
508	#95	C₂³×C₈₉	1	1	yes	characteristic
509	#95	C₂³×C₈₉	1	1	yes	characteristic
510	#95	C₂³×C₈₉	1	1	yes	characteristic
511	#95	C₂³×C₈₉	1	1	yes	characteristic
512	#95	C₂³×C₈₉	1	1	yes	characteristic
513	#95	C₂³×C₈₉	1	1	yes	characteristic
514	#95	C₂³×C₈₉	1	1	yes	characteristic
515	#95	C₂³×C₈₉	1	1	yes	characteristic
516	#95	C₂³×C₈₉	1	4	yes	—
517	#95	C₂³×C₈₉	1	4	yes	—
518	#95	C₂³×C₈₉	1	4	yes	—
519	#95	C₂³×C₈₉	1	4	yes	—
520	#95	C₂³×C₈₉	1	4	yes	—
521	#95	C₂³×C₈₉	1	4	yes	—
522	#95	C₂³×C₈₉	1	4	yes	—
523	#95	C₂³×C₈₉	1	4	yes	—
524	#95	C₂³×C₈₉	1	4	yes	—
525	#95	C₂³×C₈₉	1	4	yes	—
526	#95	C₂³×C₈₉	1	4	yes	—
527	#95	C₂³×C₈₉	1	4	yes	—
528	#95	C₂³×C₈₉	1	4	yes	—
529	#95	C₂³×C₈₉	1	4	yes	—
530	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	2	4	no	—
536	C₂×Q₈	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	#41×C₈₉	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	8	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	8	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	4	4	no	—
606	C₄²	#41×C₈₉	1	4	yes	—
607	C₄²	#41×C₈₉	1	4	yes	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	C₂×#41×C₈₉	1	2	yes	—
615	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
616	Q₈	—	4	8	no	—
617	Q₈	—	4	8	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
664	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
665	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
666	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
667	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
668	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
669	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
670	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
671	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
672	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
673	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
674	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
683	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
684	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
685	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
686	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
687	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
688	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	4	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	4	no	—
704	C₄	#529×C₈₉	1	4	yes	—
705	C₄	#541×C₈₉	1	4	yes	—
706	C₄	#542×C₈₉	1	4	yes	—
707	C₂	—	4	2	no	—
708	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
709	C₂	C₂×#541×C₈₉	1	1	yes	characteristic
710	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
711	C₂	C₈₉×#3509	1	1	yes	characteristic
712	C₂	C₈₉×#3509	1	1	yes	characteristic
713	C₂	C₈₉×#3511	1	1	yes	characteristic
714	C₂	C₈₉×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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. C₈₉×#2862	C₂	semidirect
2. C₈₉×#2859	C₂	semidirect
5. C₈₉×#2645	C₂	semidirect
7. C₈₉×#2514	C₂	semidirect
8. C₈₉×#2509	C₂	semidirect
9. C₈₉×#2508	C₂	semidirect
13. C₈₉×#2453	C₂	semidirect
16. C₈₉×#2320	C₂	semidirect
17. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
18. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
349. #35291	C₈₉	direct (N × H)
358. #2862	C₂×C₈₉	semidirect
359. #2859	C₂×C₈₉	semidirect
362. #2645	C₂×C₈₉	semidirect
364. #2514	C₂×C₈₉	semidirect
365. #2509	C₂×C₈₉	semidirect
366. #2508	C₂×C₈₉	semidirect
370. #2453	C₂×C₈₉	semidirect
373. #2320	C₂×C₈₉	semidirect
374. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
375. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
377. C₈₉	#35291	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2862	2
C₈₉×#2859	2
C₈₉×#2857	2
C₈₉×#2645	2
C₈₉×#2625	2
C₈₉×#2514	2
C₈₉×#2509	2
C₈₉×#2508	2
C₈₉×#2495	2
C₈₉×#2494	2
C₈₉×#2489	2
C₈₉×#2453	2
C₈₉×#2421	2
C₈₉×#2323	2
C₈₉×#2320	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#117×C₈₉	2
#35291	89

Subgroups — C89×#35291 #36413139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35291 #36413139