Subgroups — C₈₉×#25033 #36402881

Order 22784.

794 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#467×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2421	C₂	1	2	yes	maximal
4	C₈₉×#2074	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2035	C₂	1	2	yes	maximal
6	C₈₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1865	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
16	#467×C₈₉	—	2	4	no	—
17	C₄×Q₁₆×C₈₉	—	2	4	no	—
18	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	2	yes	—
22	C₂×#103×C₈₉	C₂²	1	2	yes	—
23	C₂×#103×C₈₉	C₂²	1	2	yes	—
24	C₂×#103×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	#400×C₈₉	—	2	2	no	—
29	#397×C₈₉	—	2	2	no	—
30	#391×C₈₉	C₂²	1	2	yes	—
31	#389×C₈₉	C₂²	1	2	yes	—
32	#388×C₈₉	—	2	2	no	—
33	#387×C₈₉	—	2	2	no	—
34	#382×C₈₉	C₂²	1	2	yes	—
35	#380×C₈₉	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	#340×C₈₉	C₂²	1	2	yes	—
38	#340×C₈₉	C₂²	1	2	yes	—
39	#336×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₈₉	—	2	2	no	—
44	C₂×Q₁₆×C₈₉	—	2	2	no	—
45	C₂×Q₁₆×C₈₉	D₄	1	4	yes	—
46	C₂²×C₈×C₈₉	—	2	2	no	—
47	C₂²×C₈×C₈₉	—	2	2	no	—
48	C₂²×C₈×C₈₉	—	2	2	no	—
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²⋊Q₈×C₈₉	—	2	4	no	—
54	C₂²⋊Q₈×C₈₉	—	4	2	no	—
55	C₄×Q₈×C₈₉	—	2	4	no	—
56	C₄×Q₈×C₈₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	—	2	2	no	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#107×C₈₉	—	2	2	no	—
71	#107×C₈₉	—	2	2	no	—
72	#107×C₈₉	—	2	2	no	—
73	#106×C₈₉	—	4	2	no	—
74	#103×C₈₉	—	2	4	no	—
75	#103×C₈₉	—	2	4	no	—
76	#103×C₈₉	—	2	4	no	—
77	C₂²⋊C₈×C₈₉	—	2	2	no	—
78	C₄×C₈×C₈₉	—	2	2	no	—
79	C₄×C₈×C₈₉	—	2	2	no	—
80	#95×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	2	no	—
82	#95×C₈₉	—	2	2	no	—
83	#95×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	2	no	—
85	#95×C₈₉	—	2	2	no	—
86	#95×C₈₉	D₄	1	1	yes	characteristic
87	#95×C₈₉	D₄	1	1	yes	characteristic
88	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₈₉	—	2	2	no	—
90	C₂×Q₈×C₈₉	—	2	2	no	—
91	C₂×Q₈×C₈₉	—	2	2	no	—
92	C₂×Q₈×C₈₉	—	2	2	no	—
93	C₂×Q₈×C₈₉	—	2	2	no	—
94	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	2	1	no	—
97	C₂²×C₄×C₈₉	—	2	1	no	—
98	C₂²×C₄×C₈₉	—	2	1	no	—
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	2	1	no	—
101	C₂²×C₄×C₈₉	—	2	1	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	—	2	2	no	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₈₉	—	2	8	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	—	2	1	no	—
115	C₂×C₈×C₈₉	—	2	1	no	—
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	4	4	no	—
121	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₈₉	#41	1	2	yes	—
123	C₂×C₈×C₈₉	#41	1	2	yes	—
124	C₂×C₈×C₈₉	#41	1	2	yes	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	4	4	no	—
132	C₄⋊C₄×C₈₉	—	4	4	no	—
133	C₄⋊C₄×C₈₉	—	4	4	no	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₂²⋊C₄×C₈₉	—	4	4	no	—
137	C₂²⋊C₄×C₈₉	—	4	4	no	—
138	C₄²×C₈₉	—	2	1	no	—
139	C₄²×C₈₉	—	2	1	no	—
140	C₄²×C₈₉	—	2	1	no	—
141	C₄²×C₈₉	—	2	1	no	—
142	C₄²×C₈₉	—	4	4	no	—
143	C₂³×C₈₉	—	2	1	no	—
144	C₂³×C₈₉	—	2	1	no	—
145	C₂³×C₈₉	—	2	1	no	—
146	C₂³×C₈₉	—	2	1	no	—
147	C₂³×C₈₉	—	2	1	no	—
148	C₂³×C₈₉	—	2	1	no	—
149	C₂³×C₈₉	#135	1	2	yes	—
150	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₈₉	—	2	4	no	—
152	Q₈×C₈₉	—	2	4	no	—
153	Q₈×C₈₉	—	4	2	no	—
154	Q₈×C₈₉	—	4	2	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	1	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	—	4	2	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	—	4	2	no	—
184	C₂×C₄×C₈₉	—	4	2	no	—
185	C₂×C₄×C₈₉	#135	1	2	yes	—
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₈₉	—	2	2	no	—
193	C₈×C₈₉	—	4	1	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	#123	1	4	yes	—
196	C₂²×C₈₉	—	2	2	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	2	2	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	#532	1	1	yes	characteristic
204	C₂²×C₈₉	D₄²	1	1	yes	characteristic
205	C₂²×C₈₉	#547	1	1	yes	characteristic
206	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
207	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
208	C₂²×C₈₉	#578	1	1	yes	characteristic
209	C₂²×C₈₉	#578	1	1	yes	characteristic
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	—	4	1	no	—
212	C₄×C₈₉	—	4	1	no	—
213	C₄×C₈₉	—	4	1	no	—
214	C₄×C₈₉	—	4	4	no	—
215	C₄×C₈₉	—	4	1	no	—
216	C₄×C₈₉	—	8	2	no	—
217	C₄×C₈₉	—	8	2	no	—
218	C₄×C₈₉	—	8	2	no	—
219	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
220	C₄×C₈₉	#542	1	1	yes	characteristic
221	C₄×C₈₉	#547	1	1	yes	characteristic
222	C₄×C₈₉	#553	1	1	yes	characteristic
223	#25033	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₈₉	—	4	2	no	—
225	C₂×C₈₉	#2422	1	1	yes	characteristic
226	C₂×C₈₉	#3168	1	1	yes	characteristic
227	C₂×C₈₉	#3177	1	1	yes	characteristic
228	C₂×C₈₉	#3285	1	1	yes	characteristic
229	C₂×C₈₉	#3285	1	1	yes	characteristic
230	C₂×C₈₉	#3336	1	1	yes	characteristic
231	C₂×C₈₉	#3342	1	1	yes	characteristic
232	C₂×#467	C₂×C₈₉	1	1	yes	characteristic
233	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
234	#2421	C₂×C₈₉	1	2	yes	—
235	#2074	C₂×C₈₉	1	2	yes	complemented
236	#2035	C₂×C₈₉	1	2	yes	—
237	#1969	C₂×C₈₉	1	1	yes	characteristic, complemented
238	#1942	C₂×C₈₉	1	1	yes	characteristic, complemented
239	#1865	C₂×C₈₉	1	2	yes	complemented
240	#1846	C₂×C₈₉	1	1	yes	characteristic, complemented
241	#1808	C₂×C₈₉	1	1	yes	characteristic
242	C₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic
243	C₈₉	#25033	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
248	#467	—	2	4	no	—
249	C₄×Q₁₆	—	2	4	no	—
250	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
252	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×#106	C₂²×C₈₉	1	2	yes	—
254	C₂×#103	C₂²×C₈₉	1	2	yes	—
255	C₂×#103	C₂²×C₈₉	1	2	yes	—
256	C₂×#103	C₂²×C₈₉	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
260	#400	—	2	2	no	—
261	#397	—	2	2	no	—
262	#391	C₂²×C₈₉	1	2	yes	—
263	#389	C₂²×C₈₉	1	2	yes	—
264	#388	—	2	2	no	—
265	#387	—	2	2	no	—
266	#382	C₂²×C₈₉	1	2	yes	—
267	#380	C₂²×C₈₉	1	2	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
269	#340	C₂²×C₈₉	1	2	yes	—
270	#340	C₂²×C₈₉	1	2	yes	—
271	#336	C₂²×C₈₉	1	1	yes	characteristic
272	#336	C₂²×C₈₉	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
274	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	D₄×C₈₉	1	4	yes	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	4	2	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	4	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#107	—	2	2	no	—
305	#106	—	4	2	no	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#103	—	2	4	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	D₄×C₈₉	1	1	yes	characteristic
319	#95	D₄×C₈₉	1	1	yes	characteristic
320	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
343	Q₁₆	—	2	8	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
354	C₂×C₈	#41×C₈₉	1	2	yes	—
355	C₂×C₈	#41×C₈₉	1	2	yes	—
356	C₂×C₈	#41×C₈₉	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	4	4	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	#135×C₈₉	1	2	yes	—
382	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	#135×C₈₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
422	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
423	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	#123×C₈₉	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	#532×C₈₉	1	1	yes	characteristic
436	C₂²	D₄²×C₈₉	1	1	yes	characteristic
437	C₂²	#547×C₈₉	1	1	yes	characteristic
438	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
439	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
440	C₂²	#578×C₈₉	1	1	yes	characteristic
441	C₂²	#578×C₈₉	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
452	C₄	#542×C₈₉	1	1	yes	characteristic
453	C₄	#547×C₈₉	1	1	yes	characteristic
454	C₄	#553×C₈₉	1	1	yes	characteristic
455	C₂	—	4	2	no	—
456	C₂	C₈₉×#2422	1	1	yes	characteristic
457	C₂	C₈₉×#3168	1	1	yes	characteristic
458	C₂	C₈₉×#3177	1	1	yes	characteristic
459	C₂	C₈₉×#3285	1	1	yes	characteristic
460	C₂	C₈₉×#3285	1	1	yes	characteristic
461	C₂	C₈₉×#3336	1	1	yes	characteristic
462	C₂	C₈₉×#3342	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
4. C₈₉×#2074	C₂	semidirect
6. C₈₉×#1969	C₂	semidirect
7. C₈₉×#1942	C₂	semidirect
8. C₈₉×#1865	C₂	semidirect
9. C₈₉×#1846	C₂	semidirect
223. #25033	C₈₉	direct (N × H)
233. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
235. #2074	C₂×C₈₉	semidirect
237. #1969	C₂×C₈₉	semidirect
238. #1942	C₂×C₈₉	semidirect
239. #1865	C₂×C₈₉	semidirect
240. #1846	C₂×C₈₉	semidirect
243. C₈₉	#25033	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#467×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₈₉×#2421	2
C₈₉×#2074	2
C₈₉×#2035	2
C₈₉×#1969	2
C₈₉×#1942	2
C₈₉×#1865	2
C₈₉×#1846	2
C₈₉×#1808	2
C₈×C₂²⋊C₄×C₈₉	2
#25033	89

Subgroups — C89×#25033 #36402881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25033 #36402881