Subgroups — C₈₉×#25047 #36402895

Order 22784.

792 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2423	C₂	1	2	yes	maximal
4	C₈₉×#2072	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×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1865	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1809	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×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	#470×C₈₉	—	2	4	no	—
17	#441×C₈₉	—	2	4	no	—
18	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#106×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×#97×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	#399×C₈₉	—	2	2	no	—
29	#398×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	#384×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	C₂×M₁₆×C₈₉	—	2	2	no	—
47	C₂×M₁₆×C₈₉	—	2	2	no	—
48	C₂×M₁₆×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	—	2	2	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
68	C₂×C₄²×C₈₉	—	2	2	no	—
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	#106×C₈₉	—	2	2	no	—
73	#106×C₈₉	—	2	2	no	—
74	#106×C₈₉	—	4	2	no	—
75	#103×C₈₉	—	2	4	no	—
76	#103×C₈₉	—	2	4	no	—
77	#103×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	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₈₉	—	2	2	no	—
88	C₂×Q₈×C₈₉	—	2	2	no	—
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	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₈₉	—	2	2	no	—
94	C₂²×C₄×C₈₉	—	2	1	no	—
95	C₂²×C₄×C₈₉	—	2	1	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	2	no	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
107	Q₁₆×C₈₉	—	2	8	no	—
108	M₁₆×C₈₉	—	4	4	no	—
109	C₂×C₈×C₈₉	—	2	1	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	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	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₈₉	#41	1	2	yes	—
119	C₂×C₈×C₈₉	#41	1	2	yes	—
120	C₂×C₈×C₈₉	#41	1	2	yes	—
121	C₄⋊C₄×C₈₉	—	2	2	no	—
122	C₄⋊C₄×C₈₉	—	2	2	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	4	4	no	—
128	C₄⋊C₄×C₈₉	—	4	4	no	—
129	C₄⋊C₄×C₈₉	—	4	4	no	—
130	C₄⋊C₄×C₈₉	—	8	2	no	—
131	C₄⋊C₄×C₈₉	—	8	2	no	—
132	C₂²⋊C₄×C₈₉	—	2	4	no	—
133	C₂²⋊C₄×C₈₉	—	4	4	no	—
134	C₂²⋊C₄×C₈₉	—	8	2	no	—
135	C₄²×C₈₉	—	2	1	no	—
136	C₄²×C₈₉	—	2	1	no	—
137	C₄²×C₈₉	—	2	1	no	—
138	C₄²×C₈₉	—	2	1	no	—
139	C₄²×C₈₉	—	4	4	no	—
140	C₂³×C₈₉	—	2	1	no	—
141	C₂³×C₈₉	—	2	1	no	—
142	C₂³×C₈₉	—	2	1	no	—
143	C₂³×C₈₉	—	2	2	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₈₉	—	2	4	no	—
147	Q₈×C₈₉	—	2	4	no	—
148	Q₈×C₈₉	—	4	2	no	—
149	Q₈×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	#137	1	4	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₈₉	—	2	2	no	—
182	C₈×C₈₉	—	4	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	#123	1	4	yes	—
185	C₂²×C₈₉	—	4	2	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	2	no	—
190	C₂²×C₈₉	#532	1	1	yes	characteristic
191	C₂²×C₈₉	D₄²	1	1	yes	characteristic
192	C₂²×C₈₉	#547	1	1	yes	characteristic
193	C₂²×C₈₉	C₂×#137	1	2	yes	—
194	C₂²×C₈₉	#577	1	2	yes	—
195	C₄×C₈₉	—	2	4	no	—
196	C₄×C₈₉	—	4	1	no	—
197	C₄×C₈₉	—	4	4	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	8	2	no	—
200	C₄×C₈₉	—	8	2	no	—
201	C₄×C₈₉	—	8	2	no	—
202	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
203	C₄×C₈₉	#542	1	1	yes	characteristic
204	C₄×C₈₉	#547	1	1	yes	characteristic
205	C₄×C₈₉	#553	1	1	yes	characteristic
206	#25047	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	—	8	1	no	—
208	C₂×C₈₉	#2422	1	1	yes	characteristic
209	C₂×C₈₉	#3173	1	1	yes	characteristic
210	C₂×C₈₉	#3185	1	1	yes	characteristic
211	C₂×C₈₉	#3278	1	2	yes	—
212	C₂×C₈₉	#3344	1	2	yes	—
213	C₂×#470	C₂×C₈₉	1	1	yes	characteristic
214	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
215	#2423	C₂×C₈₉	1	2	yes	—
216	#2072	C₂×C₈₉	1	2	yes	complemented
217	#2035	C₂×C₈₉	1	2	yes	—
218	#1969	C₂×C₈₉	1	1	yes	characteristic, complemented
219	#1943	C₂×C₈₉	1	1	yes	characteristic, complemented
220	#1865	C₂×C₈₉	1	2	yes	complemented
221	#1844	C₂×C₈₉	1	1	yes	characteristic, complemented
222	#1809	C₂×C₈₉	1	1	yes	characteristic
223	#1753	C₂×C₈₉	1	1	yes	characteristic
224	C₈₉	#25047	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
229	#470	—	2	4	no	—
230	#441	—	2	4	no	—
231	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
233	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
234	C₂×#106	C₂²×C₈₉	1	2	yes	—
235	C₂×#103	C₂²×C₈₉	1	2	yes	—
236	C₂×#103	C₂²×C₈₉	1	2	yes	—
237	C₂×#103	C₂²×C₈₉	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
239	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
241	#399	—	2	2	no	—
242	#398	—	2	2	no	—
243	#391	C₂²×C₈₉	1	2	yes	—
244	#389	C₂²×C₈₉	1	2	yes	—
245	#388	—	2	2	no	—
246	#387	—	2	2	no	—
247	#384	C₂²×C₈₉	1	2	yes	—
248	#380	C₂²×C₈₉	1	2	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
250	#340	C₂²×C₈₉	1	2	yes	—
251	#340	C₂²×C₈₉	1	2	yes	—
252	#336	C₂²×C₈₉	1	1	yes	characteristic
253	#336	C₂²×C₈₉	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	D₄×C₈₉	1	4	yes	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	—	4	2	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	4	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
284	#107	—	2	2	no	—
285	#106	—	2	2	no	—
286	#106	—	2	2	no	—
287	#106	—	4	2	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	#103	—	2	4	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	D₄×C₈₉	1	2	yes	—
299	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
320	Q₁₆	—	2	8	no	—
321	M₁₆	—	4	4	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
331	C₂×C₈	#41×C₈₉	1	2	yes	—
332	C₂×C₈	#41×C₈₉	1	2	yes	—
333	C₂×C₈	#41×C₈₉	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	8	2	no	—
344	C₄⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	4	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	#137×C₈₉	1	4	yes	—
388	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
392	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
393	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	#123×C₈₉	1	4	yes	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	#532×C₈₉	1	1	yes	characteristic
404	C₂²	D₄²×C₈₉	1	1	yes	characteristic
405	C₂²	#547×C₈₉	1	1	yes	characteristic
406	C₂²	C₂×#137×C₈₉	1	2	yes	—
407	C₂²	#577×C₈₉	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
416	C₄	#542×C₈₉	1	1	yes	characteristic
417	C₄	#547×C₈₉	1	1	yes	characteristic
418	C₄	#553×C₈₉	1	1	yes	characteristic
419	C₂	—	8	1	no	—
420	C₂	C₈₉×#2422	1	1	yes	characteristic
421	C₂	C₈₉×#3173	1	1	yes	characteristic
422	C₂	C₈₉×#3185	1	1	yes	characteristic
423	C₂	C₈₉×#3278	1	2	yes	—
424	C₂	C₈₉×#3344	1	2	yes	—

	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×#441×C₈₉	C₂	semidirect
4. C₈₉×#2072	C₂	semidirect
6. C₈₉×#1969	C₂	semidirect
7. C₈₉×#1943	C₂	semidirect
8. C₈₉×#1865	C₂	semidirect
9. C₈₉×#1844	C₂	semidirect
206. #25047	C₈₉	direct (N × H)
214. C₂×#441	C₂×C₈₉	semidirect
216. #2072	C₂×C₈₉	semidirect
218. #1969	C₂×C₈₉	semidirect
219. #1943	C₂×C₈₉	semidirect
220. #1865	C₂×C₈₉	semidirect
221. #1844	C₂×C₈₉	semidirect
224. C₈₉	#25047	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×#470×C₈₉	2
C₂×#441×C₈₉	2
C₈₉×#2423	2
C₈₉×#2072	2
C₈₉×#2035	2
C₈₉×#1969	2
C₈₉×#1943	2
C₈₉×#1865	2
C₈₉×#1844	2
C₈₉×#1809	2
C₈₉×#1753	2
#25047	89

Subgroups — C89×#25047 #36402895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25047 #36402895