Subgroups — C₈₉×#25048 #36402896

Order 22784.

888 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2420	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2073	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2033	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1862	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#121×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
16	#469×C₈₉	—	2	4	no	—
17	#442×C₈₉	—	2	4	no	—
18	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₈₉	C₂²	1	2	yes	—
20	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₈₉	C₂²	1	2	yes	—
23	C₂×#102×C₈₉	C₂²	1	2	yes	—
24	C₂×#102×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	#397×C₈₉	—	2	2	no	—
29	#394×C₈₉	—	2	2	no	—
30	#390×C₈₉	C₂²	1	2	yes	—
31	#389×C₈₉	C₂²	1	2	yes	—
32	#386×C₈₉	—	2	2	no	—
33	#382×C₈₉	C₂²	1	2	yes	—
34	#381×C₈₉	—	2	2	no	—
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×D₄×C₈₉	—	2	2	no	—
42	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₈₉	—	2	2	no	—
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₈₉	—	2	2	no	—
46	C₂×D₈×C₈₉	—	2	2	no	—
47	C₂×D₈×C₈₉	D₄	1	4	yes	—
48	C₂×M₁₆×C₈₉	—	2	2	no	—
49	C₂×M₁₆×C₈₉	—	2	2	no	—
50	C₂×M₁₆×C₈₉	—	2	2	no	—
51	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
55	#121×C₈₉	—	2	4	no	—
56	#121×C₈₉	—	4	2	no	—
57	C₄×D₄×C₈₉	—	2	4	no	—
58	C₄×D₄×C₈₉	—	4	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	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
71	#107×C₈₉	—	2	2	no	—
72	#107×C₈₉	—	4	2	no	—
73	#106×C₈₉	—	2	2	no	—
74	#106×C₈₉	—	2	2	no	—
75	#102×C₈₉	—	2	4	no	—
76	#102×C₈₉	—	2	4	no	—
77	#102×C₈₉	—	2	4	no	—
78	C₂²⋊C₈×C₈₉	—	2	2	no	—
79	#97×C₈₉	—	2	2	no	—
80	C₄×C₈×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	D₄	1	2	yes	—
86	C₂⁴×C₈₉	—	2	2	no	—
87	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂×D₄×C₈₉	—	2	2	no	—
89	C₂×D₄×C₈₉	—	2	2	no	—
90	C₂×D₄×C₈₉	—	2	2	no	—
91	C₂×D₄×C₈₉	—	2	2	no	—
92	C₂×D₄×C₈₉	—	2	2	no	—
93	C₂×D₄×C₈₉	—	4	4	no	—
94	C₂×D₄×C₈₉	—	4	4	no	—
95	C₂×D₄×C₈₉	—	8	2	no	—
96	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
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	1	no	—
103	C₂²×C₄×C₈₉	—	2	2	no	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	—	2	2	no	—
106	C₂²×C₄×C₈₉	—	4	4	no	—
107	C₂²×C₄×C₈₉	—	4	4	no	—
108	C₂²×C₄×C₈₉	—	8	2	no	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
113	D₈×C₈₉	—	2	8	no	—
114	M₁₆×C₈₉	—	4	4	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	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₈₉	#41	1	2	yes	—
125	C₂×C₈×C₈₉	#41	1	2	yes	—
126	C₂×C₈×C₈₉	#41	1	2	yes	—
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	—	2	2	no	—
132	C₄⋊C₄×C₈₉	—	2	2	no	—
133	C₄⋊C₄×C₈₉	—	8	2	no	—
134	C₂²⋊C₄×C₈₉	—	4	2	no	—
135	C₂²⋊C₄×C₈₉	—	4	4	no	—
136	C₂²⋊C₄×C₈₉	—	4	4	no	—
137	C₂²⋊C₄×C₈₉	—	8	2	no	—
138	C₂²⋊C₄×C₈₉	—	8	2	no	—
139	C₂²⋊C₄×C₈₉	—	8	2	no	—
140	C₄²×C₈₉	—	2	1	no	—
141	C₄²×C₈₉	—	2	1	no	—
142	C₄²×C₈₉	—	2	1	no	—
143	C₄²×C₈₉	—	2	1	no	—
144	C₂³×C₈₉	—	2	1	no	—
145	C₂³×C₈₉	—	2	4	no	—
146	C₂³×C₈₉	—	2	1	no	—
147	C₂³×C₈₉	—	2	1	no	—
148	C₂³×C₈₉	—	2	2	no	—
149	C₂³×C₈₉	—	2	2	no	—
150	C₂³×C₈₉	—	4	2	no	—
151	C₂³×C₈₉	—	4	2	no	—
152	C₂³×C₈₉	—	4	2	no	—
153	C₂³×C₈₉	—	4	2	no	—
154	C₂³×C₈₉	—	4	2	no	—
155	C₂³×C₈₉	—	4	2	no	—
156	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	D₄×C₈₉	—	2	4	no	—
158	D₄×C₈₉	—	2	4	no	—
159	D₄×C₈₉	—	4	2	no	—
160	D₄×C₈₉	—	4	2	no	—
161	D₄×C₈₉	—	8	8	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	1	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	—	4	1	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	2	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	—	8	8	no	—
185	C₂×C₄×C₈₉	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	4	1	no	—
193	C₈×C₈₉	—	4	1	no	—
194	C₈×C₈₉	#123	1	4	yes	—
195	C₂²×C₈₉	—	4	2	no	—
196	C₂²×C₈₉	—	4	1	no	—
197	C₂²×C₈₉	—	4	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	4	no	—
200	C₂²×C₈₉	—	4	4	no	—
201	C₂²×C₈₉	—	4	2	no	—
202	C₂²×C₈₉	—	4	4	no	—
203	C₂²×C₈₉	—	8	2	no	—
204	C₂²×C₈₉	—	8	2	no	—
205	C₂²×C₈₉	—	8	2	no	—
206	C₂²×C₈₉	—	8	2	no	—
207	C₂²×C₈₉	#532	1	1	yes	characteristic
208	C₂²×C₈₉	D₄²	1	1	yes	characteristic
209	C₂²×C₈₉	#547	1	1	yes	characteristic
210	C₂²×C₈₉	#575	1	2	yes	—
211	C₂²×C₈₉	#576	1	2	yes	—
212	C₄×C₈₉	—	4	2	no	—
213	C₄×C₈₉	—	4	1	no	—
214	C₄×C₈₉	—	4	2	no	—
215	C₄×C₈₉	—	8	2	no	—
216	C₄×C₈₉	—	8	2	no	—
217	C₄×C₈₉	—	8	2	no	—
218	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
219	C₄×C₈₉	#542	1	1	yes	characteristic
220	C₄×C₈₉	#547	1	1	yes	characteristic
221	C₄×C₈₉	#553	1	1	yes	characteristic
222	#25048	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂×C₈₉	—	8	1	no	—
224	C₂×C₈₉	—	8	4	no	—
225	C₂×C₈₉	#2422	1	1	yes	characteristic
226	C₂×C₈₉	#3176	1	1	yes	characteristic
227	C₂×C₈₉	#3183	1	1	yes	characteristic
228	C₂×C₈₉	#3273	1	2	yes	—
229	C₂×C₈₉	#3347	1	2	yes	—
230	C₂×#469	C₂×C₈₉	1	1	yes	characteristic
231	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
232	#2420	C₂×C₈₉	1	2	yes	complemented
233	#2073	C₂×C₈₉	1	2	yes	complemented
234	#2033	C₂×C₈₉	1	2	yes	complemented
235	#1970	C₂×C₈₉	1	1	yes	characteristic, complemented
236	#1943	C₂×C₈₉	1	1	yes	characteristic, complemented
237	#1862	C₂×C₈₉	1	2	yes	complemented
238	#1846	C₂×C₈₉	1	1	yes	characteristic, complemented
239	#1809	C₂×C₈₉	1	1	yes	characteristic, complemented
240	#1753	C₂×C₈₉	1	1	yes	characteristic, complemented
241	C₈₉	#25048	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
243	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
244	C₂×#121	C₂²×C₈₉	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
246	#469	—	2	4	no	—
247	#442	—	2	4	no	—
248	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
249	C₂×#107	C₂²×C₈₉	1	2	yes	—
250	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
252	C₂×#102	C₂²×C₈₉	1	2	yes	—
253	C₂×#102	C₂²×C₈₉	1	2	yes	—
254	C₂×#102	C₂²×C₈₉	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
256	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
258	#397	—	2	2	no	—
259	#394	—	2	2	no	—
260	#390	C₂²×C₈₉	1	2	yes	—
261	#389	C₂²×C₈₉	1	2	yes	—
262	#386	—	2	2	no	—
263	#382	C₂²×C₈₉	1	2	yes	—
264	#381	—	2	2	no	—
265	#380	C₂²×C₈₉	1	2	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
267	#340	C₂²×C₈₉	1	2	yes	—
268	#340	C₂²×C₈₉	1	2	yes	—
269	#336	C₂²×C₈₉	1	1	yes	characteristic
270	#336	C₂²×C₈₉	1	1	yes	characteristic
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	D₄×C₈₉	1	4	yes	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	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	#121	—	2	4	no	—
286	#121	—	4	2	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	4	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
299	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
301	#107	—	2	2	no	—
302	#107	—	4	2	no	—
303	#106	—	2	2	no	—
304	#106	—	2	2	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₈₉	1	2	yes	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
327	C₂²×C₄	—	2	1	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	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
343	D₈	—	2	8	no	—
344	M₁₆	—	4	4	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	—	2	1	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	—	8	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	8	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	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	—	8	8	no	—
415	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
419	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
420	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	#123×C₈₉	1	4	yes	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	#532×C₈₉	1	1	yes	characteristic
438	C₂²	D₄²×C₈₉	1	1	yes	characteristic
439	C₂²	#547×C₈₉	1	1	yes	characteristic
440	C₂²	#575×C₈₉	1	2	yes	—
441	C₂²	#576×C₈₉	1	2	yes	—
442	C₄	—	4	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
449	C₄	#542×C₈₉	1	1	yes	characteristic
450	C₄	#547×C₈₉	1	1	yes	characteristic
451	C₄	#553×C₈₉	1	1	yes	characteristic
452	C₂	—	8	1	no	—
453	C₂	—	8	4	no	—
454	C₂	C₈₉×#2422	1	1	yes	characteristic
455	C₂	C₈₉×#3176	1	1	yes	characteristic
456	C₂	C₈₉×#3183	1	1	yes	characteristic
457	C₂	C₈₉×#3273	1	2	yes	—
458	C₂	C₈₉×#3347	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#469×C₈₉	C₂
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×#442×C₈₉	C₂	semidirect
3. C₈₉×#2420	C₂	semidirect
4. C₈₉×#2073	C₂	semidirect
5. C₈₉×#2033	C₂	semidirect
6. C₈₉×#1970	C₂	semidirect
7. C₈₉×#1943	C₂	semidirect
8. C₈₉×#1862	C₂	semidirect
9. C₈₉×#1846	C₂	semidirect
10. C₈₉×#1809	C₂	semidirect
11. C₈₉×#1753	C₂	semidirect
222. #25048	C₈₉	direct (N × H)
231. C₂×#442	C₂×C₈₉	semidirect
232. #2420	C₂×C₈₉	semidirect
233. #2073	C₂×C₈₉	semidirect
234. #2033	C₂×C₈₉	semidirect
235. #1970	C₂×C₈₉	semidirect
236. #1943	C₂×C₈₉	semidirect
237. #1862	C₂×C₈₉	semidirect
238. #1846	C₂×C₈₉	semidirect
239. #1809	C₂×C₈₉	semidirect
240. #1753	C₂×C₈₉	semidirect
241. C₈₉	#25048	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×#469×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×#2420	2
C₈₉×#2073	2
C₈₉×#2033	2
C₈₉×#1970	2
C₈₉×#1943	2
C₈₉×#1862	2
C₈₉×#1846	2
C₈₉×#1809	2
C₈₉×#1753	2
#25048	89

Subgroups — C89×#25048 #36402896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25048 #36402896