Subgroups — C₈₉×#24833 #36402681

Order 22784.

868 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2349	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2083	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2068	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1877	C₂	1	2	yes	maximal
10	C₈₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1802	C₂	1	2	yes	maximal
12	C₂²×SD₁₆×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×D₄×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	#474×C₈₉	—	2	4	no	—
18	#440×C₈₉	—	2	4	no	—
19	C₂×#107×C₈₉	C₂²	1	2	yes	—
20	C₂×#107×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	1	yes	characteristic
24	C₂×#103×C₈₉	C₂²	1	2	yes	—
25	C₂×#102×C₈₉	C₂²	1	2	yes	—
26	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
28	#395×C₈₉	—	2	1	no	—
29	#395×C₈₉	—	2	1	no	—
30	#391×C₈₉	C₂²	1	2	yes	—
31	#389×C₈₉	—	2	2	no	—
32	#389×C₈₉	C₂²	1	2	yes	—
33	#385×C₈₉	—	2	2	no	—
34	#384×C₈₉	C₂²	1	2	yes	—
35	#382×C₈₉	C₂²	1	1	yes	characteristic
36	#380×C₈₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#95×C₈₉	—	2	1	no	—
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×D₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₈₉	—	2	1	no	—
47	C₂³×C₄×C₈₉	—	2	2	no	—
48	C₂×SD₁₆×C₈₉	—	2	2	no	—
49	C₂×SD₁₆×C₈₉	—	2	2	no	—
50	C₂×SD₁₆×C₈₉	Q₈	1	4	yes	complemented
51	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₈₉	—	2	2	no	—
55	C₄⋊Q₈×C₈₉	—	2	2	no	—
56	C₄×Q₈×C₈₉	—	2	2	no	—
57	C₄×Q₈×C₈₉	—	2	2	no	—
58	C₄×D₄×C₈₉	—	2	4	no	—
59	C₄×D₄×C₈₉	—	2	2	no	—
60	C₄×D₄×C₈₉	—	4	2	no	—
61	C₄×D₄×C₈₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
74	C₂×C₄²×C₈₉	—	2	1	no	—
75	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	#107×C₈₉	—	2	2	no	—
78	#107×C₈₉	—	2	4	no	—
79	C₄⋊C₈×C₈₉	—	2	2	no	—
80	C₄⋊C₈×C₈₉	—	4	2	no	—
81	#103×C₈₉	—	2	2	no	—
82	#103×C₈₉	—	4	2	no	—
83	#102×C₈₉	—	2	2	no	—
84	#102×C₈₉	—	2	4	no	—
85	#97×C₈₉	—	2	2	no	—
86	#95×C₈₉	—	2	1	no	—
87	#95×C₈₉	—	2	2	no	—
88	#95×C₈₉	—	2	1	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	C₂⁴×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	—	4	2	no	—
100	C₂×Q₈×C₈₉	—	8	2	no	—
101	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₈₉	—	2	1	no	—
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	—	2	1	no	—
105	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
107	C₂×D₄×C₈₉	#41	1	2	yes	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	4	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	4	4	no	—
115	C₂²×C₄×C₈₉	—	4	4	no	—
116	C₂²×C₄×C₈₉	—	8	2	no	—
117	C₂²×C₄×C₈₉	—	8	2	no	—
118	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
123	SD₁₆×C₈₉	—	2	8	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
133	C₄⋊C₄×C₈₉	—	2	4	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	1	no	—
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	4	2	no	—
142	C₄⋊C₄×C₈₉	—	4	2	no	—
143	C₄⋊C₄×C₈₉	—	8	2	no	—
144	C₄⋊C₄×C₈₉	—	8	2	no	—
145	C₄⋊C₄×C₈₉	—	8	2	no	—
146	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₈₉	—	2	4	no	—
148	C₂²⋊C₄×C₈₉	—	4	4	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	4	2	no	—
152	C₄²×C₈₉	C₂×D₄	1	2	yes	—
153	C₄²×C₈₉	#41	1	2	yes	—
154	C₂³×C₈₉	—	2	2	no	—
155	C₂³×C₈₉	—	2	2	no	—
156	C₂³×C₈₉	—	2	2	no	—
157	C₂³×C₈₉	—	4	2	no	—
158	C₂³×C₈₉	—	4	2	no	—
159	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₈₉	—	2	2	no	—
161	Q₈×C₈₉	—	2	2	no	—
162	Q₈×C₈₉	—	4	1	no	—
163	Q₈×C₈₉	—	4	1	no	—
164	Q₈×C₈₉	—	8	4	no	—
165	D₄×C₈₉	—	2	2	no	—
166	D₄×C₈₉	—	2	2	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
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	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	1	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	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	—	4	2	no	—
189	C₂×C₄×C₈₉	—	8	4	no	—
190	C₂×C₄×C₈₉	—	8	8	no	—
191	C₂×C₄×C₈₉	#121	1	2	yes	—
192	C₂×C₄×C₈₉	#121	1	2	yes	—
193	C₂×C₄×C₈₉	#137	1	4	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₈₉	—	2	2	no	—
201	C₈×C₈₉	—	4	1	no	—
202	C₈×C₈₉	—	4	2	no	—
203	C₂²×C₈₉	—	2	4	no	—
204	C₂²×C₈₉	—	4	4	no	—
205	C₂²×C₈₉	—	4	2	no	—
206	C₂²×C₈₉	—	4	2	no	—
207	C₂²×C₈₉	—	4	4	no	—
208	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
209	C₂²×C₈₉	#546	1	1	yes	characteristic
210	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
211	C₂²×C₈₉	C₂×#137	1	2	yes	—
212	C₂²×C₈₉	#576	1	2	yes	—
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	2	4	no	—
216	C₄×C₈₉	—	4	2	no	—
217	C₄×C₈₉	—	4	2	no	—
218	C₄×C₈₉	—	4	2	no	—
219	C₄×C₈₉	—	8	1	no	—
220	C₄×C₈₉	—	8	2	no	—
221	C₄×C₈₉	—	8	2	no	—
222	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₈₉	#537	1	1	yes	characteristic
224	C₄×C₈₉	#552	1	1	yes	characteristic
225	C₄×C₈₉	#554	1	1	yes	characteristic
226	#24833	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₈₉	—	4	4	no	—
228	C₂×C₈₉	#2417	1	1	yes	characteristic
229	C₂×C₈₉	#3039	1	1	yes	characteristic
230	C₂×C₈₉	#3041	1	1	yes	characteristic
231	C₂×C₈₉	#3314	1	2	yes	—
232	C₂×C₈₉	#3385	1	2	yes	—
233	C₂×#474	C₂×C₈₉	1	1	yes	characteristic
234	C₂×#440	C₂×C₈₉	1	1	yes	characteristic
235	#2567	C₂×C₈₉	1	1	yes	characteristic, complemented
236	#2349	C₂×C₈₉	1	1	yes	characteristic
237	#2083	C₂×C₈₉	1	2	yes	complemented
238	#2068	C₂×C₈₉	1	2	yes	complemented
239	#1993	C₂×C₈₉	1	1	yes	characteristic, complemented
240	#1940	C₂×C₈₉	1	1	yes	characteristic, complemented
241	#1877	C₂×C₈₉	1	2	yes	—
242	#1805	C₂×C₈₉	1	1	yes	characteristic, complemented
243	#1802	C₂×C₈₉	1	2	yes	—
244	C₈₉	#24833	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
250	#474	—	2	4	no	—
251	#440	—	2	4	no	—
252	C₂×#107	C₂²×C₈₉	1	2	yes	—
253	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
256	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
257	C₂×#103	C₂²×C₈₉	1	2	yes	—
258	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×#102	C₂²×C₈₉	1	2	yes	—
260	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
261	#395	—	2	1	no	—
262	#395	—	2	1	no	—
263	#391	C₂²×C₈₉	1	2	yes	—
264	#389	—	2	2	no	—
265	#389	C₂²×C₈₉	1	2	yes	—
266	#385	—	2	2	no	—
267	#384	C₂²×C₈₉	1	2	yes	—
268	#382	C₂²×C₈₉	1	1	yes	characteristic
269	#380	—	2	1	no	—
270	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
271	C₂×#95	—	2	1	no	—
272	#340	C₂²×C₈₉	1	2	yes	—
273	#340	C₂²×C₈₉	1	2	yes	—
274	#340	C₂²×C₈₉	1	2	yes	—
275	#336	C₂²×C₈₉	1	2	yes	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	Q₈×C₈₉	1	4	yes	complemented
284	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
285	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	4	2	no	—
294	C₄×D₄	D₄×C₈₉	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
309	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
310	#107	—	2	2	no	—
311	#107	—	2	4	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	4	2	no	—
314	#103	—	2	2	no	—
315	#103	—	4	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	4	no	—
318	#97	—	2	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	D₄×C₈₉	1	1	yes	characteristic
325	#95	D₄×C₈₉	1	1	yes	characteristic
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	8	2	no	—
334	C₂×Q₈	C₂×Q₈×C₈₉	1	2	yes	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
339	C₂×D₄	C₂×Q₈×C₈₉	1	2	yes	—
340	C₂×D₄	#41×C₈₉	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	8	2	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
356	SD₁₆	—	2	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	C₂×Q₈×C₈₉	1	2	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	8	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₄⋊C₄	—	8	2	no	—
379	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂×D₄×C₈₉	1	2	yes	—
386	C₄²	#41×C₈₉	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	4	1	no	—
397	Q₈	—	8	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	#121×C₈₉	1	2	yes	—
425	C₂×C₄	#121×C₈₉	1	2	yes	—
426	C₂×C₄	#137×C₈₉	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
431	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
432	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
442	C₂²	#546×C₈₉	1	1	yes	characteristic
443	C₂²	D₄×Q₈×C₈₉	1	1	yes	characteristic
444	C₂²	C₂×#137×C₈₉	1	2	yes	—
445	C₂²	#576×C₈₉	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
456	C₄	#537×C₈₉	1	1	yes	characteristic
457	C₄	#552×C₈₉	1	1	yes	characteristic
458	C₄	#554×C₈₉	1	1	yes	characteristic
459	C₂	—	4	4	no	—
460	C₂	C₈₉×#2417	1	1	yes	characteristic
461	C₂	C₈₉×#3039	1	1	yes	characteristic
462	C₂	C₈₉×#3041	1	1	yes	characteristic
463	C₂	C₈₉×#3314	1	2	yes	—
464	C₂	C₈₉×#3385	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
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
3. C₈₉×#2567	C₂	semidirect
5. C₈₉×#2083	C₂	semidirect
6. C₈₉×#2068	C₂	semidirect
7. C₈₉×#1993	C₂	semidirect
8. C₈₉×#1940	C₂	semidirect
10. C₈₉×#1805	C₂	semidirect
50. C₂×SD₁₆×C₈₉	Q₈	semidirect
226. #24833	C₈₉	direct (N × H)
235. #2567	C₂×C₈₉	semidirect
237. #2083	C₂×C₈₉	semidirect
238. #2068	C₂×C₈₉	semidirect
239. #1993	C₂×C₈₉	semidirect
240. #1940	C₂×C₈₉	semidirect
242. #1805	C₂×C₈₉	semidirect
244. C₈₉	#24833	direct (N × H)
283. C₂×SD₁₆	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×#474×C₈₉	2
C₂×#440×C₈₉	2
C₈₉×#2567	2
C₈₉×#2349	2
C₈₉×#2083	2
C₈₉×#2068	2
C₈₉×#1993	2
C₈₉×#1940	2
C₈₉×#1877	2
C₈₉×#1805	2
C₈₉×#1802	2
#24833	89

Subgroups — C89×#24833 #36402681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24833 #36402681