Subgroups — C₈₉×#24832 #36402680

Order 22784.

776 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#477×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2568	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2351	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2085	C₂	1	2	yes	maximal
6	C₈₉×#2068	C₂	1	2	yes	maximal
7	C₈₉×#1993	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1878	C₂	1	2	yes	maximal
10	C₈₉×#1805	C₂	1	2	yes	maximal
11	C₈₉×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	#477×C₈₉	—	2	4	no	—
18	#441×C₈₉	—	2	4	no	—
19	C₂×#107×C₈₉	C₂²	1	2	yes	—
20	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
23	C₂×#103×C₈₉	C₂²	1	2	yes	—
24	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₈₉	C₂²	1	2	yes	—
27	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
28	#400×C₈₉	—	2	1	no	—
29	#400×C₈₉	—	2	1	no	—
30	#391×C₈₉	—	2	2	no	—
31	#391×C₈₉	C₂²	1	2	yes	—
32	#389×C₈₉	—	2	2	no	—
33	#389×C₈₉	C₂²	1	2	yes	—
34	#382×C₈₉	—	2	1	no	—
35	#382×C₈₉	C₂²	1	2	yes	—
36	#382×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	#340×C₈₉	C₂²	1	2	yes	—
40	#340×C₈₉	C₂²	1	2	yes	—
41	#340×C₈₉	C₂²	1	2	yes	—
42	#336×C₈₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₈₉	—	2	1	no	—
44	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₈₉	—	2	2	no	—
47	C₂×Q₁₆×C₈₉	—	2	2	no	—
48	C₂×Q₁₆×C₈₉	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₈₉	—	2	2	no	—
53	C₄⋊Q₈×C₈₉	—	2	2	no	—
54	C₄×Q₈×C₈₉	—	2	2	no	—
55	C₄×Q₈×C₈₉	—	2	4	no	—
56	C₄×Q₈×C₈₉	—	2	2	no	—
57	C₄×Q₈×C₈₉	—	2	2	no	—
58	C₄×Q₈×C₈₉	—	4	2	no	—
59	C₄×Q₈×C₈₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	—	2	1	no	—
71	C₂×C₄²×C₈₉	—	2	2	no	—
72	C₂×C₄²×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	#107×C₈₉	—	2	4	no	—
76	#106×C₈₉	—	2	2	no	—
77	C₄⋊C₈×C₈₉	—	2	2	no	—
78	C₄⋊C₈×C₈₉	—	4	2	no	—
79	#103×C₈₉	—	2	2	no	—
80	#103×C₈₉	—	2	4	no	—
81	#103×C₈₉	—	2	2	no	—
82	#103×C₈₉	—	4	2	no	—
83	#97×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	1	no	—
85	#95×C₈₉	—	2	2	no	—
86	#95×C₈₉	—	2	1	no	—
87	#95×C₈₉	—	2	2	no	—
88	#95×C₈₉	—	2	2	no	—
89	#95×C₈₉	—	2	2	no	—
90	#95×C₈₉	—	2	2	no	—
91	#95×C₈₉	D₄	1	1	yes	characteristic
92	#95×C₈₉	D₄	1	1	yes	characteristic
93	C₂×Q₈×C₈₉	—	2	1	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	2	1	no	—
96	C₂×Q₈×C₈₉	—	2	1	no	—
97	C₂×Q₈×C₈₉	—	2	1	no	—
98	C₂×Q₈×C₈₉	—	2	1	no	—
99	C₂×Q₈×C₈₉	—	2	1	no	—
100	C₂×Q₈×C₈₉	—	2	1	no	—
101	C₂×Q₈×C₈₉	—	4	4	no	—
102	C₂×Q₈×C₈₉	—	4	2	no	—
103	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
105	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₈₉	#41	1	2	yes	—
107	C₂²×C₄×C₈₉	—	2	1	no	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₈₉	—	2	8	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
128	C₄⋊C₄×C₈₉	—	2	4	no	—
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	—	2	2	no	—
132	C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₄⋊C₄×C₈₉	—	2	2	no	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	4	2	no	—
137	C₄⋊C₄×C₈₉	—	4	4	no	—
138	C₄⋊C₄×C₈₉	—	4	4	no	—
139	C₄⋊C₄×C₈₉	—	4	2	no	—
140	C₄⋊C₄×C₈₉	—	4	2	no	—
141	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
142	C₄²×C₈₉	—	2	4	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	4	4	no	—
146	C₄²×C₈₉	—	4	2	no	—
147	C₄²×C₈₉	C₂×D₄	1	2	yes	—
148	C₄²×C₈₉	#41	1	2	yes	—
149	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₈₉	—	2	2	no	—
151	Q₈×C₈₉	—	2	2	no	—
152	Q₈×C₈₉	—	2	2	no	—
153	Q₈×C₈₉	—	2	2	no	—
154	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	4	1	no	—
156	Q₈×C₈₉	—	4	1	no	—
157	Q₈×C₈₉	—	8	4	no	—
158	Q₈×C₈₉	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	2	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	4	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	#121	1	2	yes	—
183	C₂×C₄×C₈₉	#121	1	2	yes	—
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	4	1	no	—
192	C₈×C₈₉	—	4	2	no	—
193	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂²×C₈₉	#546	1	1	yes	characteristic
195	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
196	C₂²×C₈₉	#575	1	2	yes	—
197	C₂²×C₈₉	#578	1	2	yes	—
198	C₄×C₈₉	—	2	4	no	—
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	—	4	2	no	—
204	C₄×C₈₉	—	4	2	no	—
205	C₄×C₈₉	—	8	2	no	—
206	C₄×C₈₉	—	8	1	no	—
207	C₄×C₈₉	—	8	2	no	—
208	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₄×C₈₉	#537	1	1	yes	characteristic
210	C₄×C₈₉	#552	1	1	yes	characteristic
211	C₄×C₈₉	#554	1	1	yes	characteristic
212	#24832	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂×C₈₉	#2417	1	1	yes	characteristic
214	C₂×C₈₉	#3040	1	1	yes	characteristic
215	C₂×C₈₉	#3044	1	1	yes	characteristic
216	C₂×C₈₉	#3313	1	2	yes	—
217	C₂×C₈₉	#3390	1	2	yes	—
218	C₂×#477	C₂×C₈₉	1	1	yes	characteristic
219	C₂×#441	C₂×C₈₉	1	1	yes	characteristic
220	#2568	C₂×C₈₉	1	1	yes	characteristic
221	#2351	C₂×C₈₉	1	1	yes	characteristic
222	#2085	C₂×C₈₉	1	2	yes	—
223	#2068	C₂×C₈₉	1	2	yes	—
224	#1993	C₂×C₈₉	1	1	yes	characteristic
225	#1940	C₂×C₈₉	1	1	yes	characteristic
226	#1878	C₂×C₈₉	1	2	yes	—
227	#1805	C₂×C₈₉	1	1	yes	characteristic
228	#1805	C₂×C₈₉	1	2	yes	—
229	C₈₉	#24832	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
235	#477	—	2	4	no	—
236	#441	—	2	4	no	—
237	C₂×#107	C₂²×C₈₉	1	2	yes	—
238	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
241	C₂×#103	C₂²×C₈₉	1	2	yes	—
242	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
243	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
244	C₂×#103	C₂²×C₈₉	1	2	yes	—
245	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
246	#400	—	2	1	no	—
247	#400	—	2	1	no	—
248	#391	—	2	2	no	—
249	#391	C₂²×C₈₉	1	2	yes	—
250	#389	—	2	2	no	—
251	#389	C₂²×C₈₉	1	2	yes	—
252	#382	—	2	1	no	—
253	#382	C₂²×C₈₉	1	2	yes	—
254	#382	C₂²×C₈₉	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	2	1	no	—
256	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
257	#340	C₂²×C₈₉	1	2	yes	—
258	#340	C₂²×C₈₉	1	2	yes	—
259	#340	C₂²×C₈₉	1	2	yes	—
260	#336	C₂²×C₈₉	1	2	yes	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	Q₈×C₈₉	1	4	yes	complemented
267	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
268	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	4	2	no	—
277	C₄×Q₈	D₄×C₈₉	1	4	yes	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
292	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
293	#107	—	2	4	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	4	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	4	no	—
299	#103	—	2	2	no	—
300	#103	—	4	2	no	—
301	#97	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	D₄×C₈₉	1	1	yes	characteristic
310	#95	D₄×C₈₉	1	1	yes	characteristic
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
322	C₂×Q₈	C₂×Q₈×C₈₉	1	2	yes	—
323	C₂×Q₈	C₂×Q₈×C₈₉	1	2	yes	—
324	C₂×Q₈	#41×C₈₉	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
336	Q₁₆	—	2	8	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂×Q₈×C₈₉	1	2	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₂×D₄×C₈₉	1	2	yes	—
366	C₄²	#41×C₈₉	1	2	yes	—
367	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	4	no	—
376	Q₈	C₂²⋊Q₈×C₈₉	1	4	yes	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	#121×C₈₉	1	2	yes	—
401	C₂×C₄	#121×C₈₉	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
406	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
407	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
412	C₂²	#546×C₈₉	1	1	yes	characteristic
413	C₂²	D₄×Q₈×C₈₉	1	1	yes	characteristic
414	C₂²	#575×C₈₉	1	2	yes	—
415	C₂²	#578×C₈₉	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	2	no	—
426	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
427	C₄	#537×C₈₉	1	1	yes	characteristic
428	C₄	#552×C₈₉	1	1	yes	characteristic
429	C₄	#554×C₈₉	1	1	yes	characteristic
430	C₂	C₈₉×#2417	1	1	yes	characteristic
431	C₂	C₈₉×#3040	1	1	yes	characteristic
432	C₂	C₈₉×#3044	1	1	yes	characteristic
433	C₂	C₈₉×#3313	1	2	yes	—
434	C₂	C₈₉×#3390	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
48. C₂×Q₁₆×C₈₉	Q₈	semidirect
212. #24832	C₈₉	direct (N × H)
229. C₈₉	#24832	direct (N × H)
266. C₂×Q₁₆	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#477×C₈₉	2
C₂×#441×C₈₉	2
C₈₉×#2568	2
C₈₉×#2351	2
C₈₉×#2085	2
C₈₉×#2068	2
C₈₉×#1993	2
C₈₉×#1940	2
C₈₉×#1878	2
C₈₉×#1805	2
#24832	89

Subgroups — C89×#24832 #36402680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24832 #36402680