Subgroups — C₈₉×#22838 #36400686

Order 22784.

732 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1955	C₂	1	2	yes	maximal
3	C₈₉×#1924	C₂	1	2	yes	maximal, complemented
4	C₈₉×#1923	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1818	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1771	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1750	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₈₉	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
18	C₂×#97×C₈₉	C₂²	1	2	yes	—
19	C₂×#97×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
21	#390×C₈₉	C₄	1	1	yes	characteristic
22	#390×C₈₉	C₄	1	1	yes	characteristic
23	#389×C₈₉	C₄	1	1	yes	characteristic
24	#389×C₈₉	C₄	1	1	yes	characteristic
25	#388×C₈₉	C₄	1	2	yes	—
26	#388×C₈₉	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
29	C₄³×C₈₉	C₂²	1	1	yes	characteristic
30	#336×C₈₉	C₂²	1	1	yes	characteristic
31	#336×C₈₉	C₂²	1	2	yes	—
32	#336×C₈₉	C₂²	1	2	yes	—
33	#336×C₈₉	C₂²	1	2	yes	—
34	#336×C₈₉	C₂²	1	1	yes	characteristic
35	#336×C₈₉	C₂²	1	1	yes	characteristic
36	#336×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
43	C₄×D₄×C₈₉	—	2	2	no	—
44	C₄×D₄×C₈₉	—	2	2	no	—
45	#117×C₈₉	—	4	2	no	—
46	#117×C₈₉	—	4	2	no	—
47	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₈₉	—	2	4	no	—
66	C₄⋊C₈×C₈₉	—	2	4	no	—
67	C₂²⋊C₈×C₈₉	—	2	4	no	—
68	C₂²⋊C₈×C₈₉	—	2	4	no	—
69	C₂²⋊C₈×C₈₉	—	4	2	no	—
70	C₂²⋊C₈×C₈₉	—	4	2	no	—
71	#97×C₈₉	—	2	4	no	—
72	#97×C₈₉	—	4	2	no	—
73	C₄×C₈×C₈₉	—	4	2	no	—
74	#95×C₈₉	C₂×C₄	1	2	yes	—
75	#95×C₈₉	C₂×C₄	1	2	yes	—
76	#95×C₈₉	C₂×C₄	1	2	yes	—
77	C₂⁴×C₈₉	C₂²×C₄	1	2	yes	—
78	C₂×D₄×C₈₉	—	2	2	no	—
79	C₂×D₄×C₈₉	—	4	1	no	—
80	C₂×D₄×C₈₉	—	4	1	no	—
81	C₂²×C₄×C₈₉	—	2	2	no	—
82	C₂²×C₄×C₈₉	—	2	2	no	—
83	C₂²×C₄×C₈₉	—	2	2	no	—
84	C₂²×C₄×C₈₉	—	2	2	no	—
85	C₂²×C₄×C₈₉	—	2	2	no	—
86	C₂²×C₄×C₈₉	—	2	2	no	—
87	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₈₉	—	2	2	no	—
98	C₂×C₈×C₈₉	—	2	2	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	2	2	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	2	2	no	—
107	C₂×C₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	#41	1	4	yes	—
109	C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₄⋊C₄×C₈₉	—	4	1	no	—
111	C₄⋊C₄×C₈₉	—	4	1	no	—
112	C₄⋊C₄×C₈₉	—	4	2	no	—
113	C₄⋊C₄×C₈₉	—	4	2	no	—
114	C₂²⋊C₄×C₈₉	—	2	4	no	—
115	C₂²⋊C₄×C₈₉	—	2	4	no	—
116	C₂²⋊C₄×C₈₉	—	4	2	no	—
117	C₂²⋊C₄×C₈₉	—	4	2	no	—
118	C₂²⋊C₄×C₈₉	—	4	2	no	—
119	C₄²×C₈₉	—	2	2	no	—
120	C₄²×C₈₉	—	2	2	no	—
121	C₄²×C₈₉	—	2	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	—	4	1	no	—
126	C₄²×C₈₉	—	4	1	no	—
127	C₄²×C₈₉	#41	1	2	yes	—
128	C₄²×C₈₉	#41	1	2	yes	—
129	C₂³×C₈₉	—	2	2	no	—
130	C₂³×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	—	2	2	no	—
132	C₂³×C₈₉	—	2	2	no	—
133	C₂³×C₈₉	—	2	2	no	—
134	C₂³×C₈₉	—	2	2	no	—
135	C₂³×C₈₉	—	2	2	no	—
136	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
137	D₄×C₈₉	—	4	4	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	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	1	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	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	#117	1	2	yes	—
167	C₂×C₄×C₈₉	#117	1	2	yes	—
168	C₂×C₄×C₈₉	#131	1	2	yes	—
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
173	C₈×C₈₉	—	2	4	no	—
174	C₈×C₈₉	—	4	2	no	—
175	C₈×C₈₉	—	4	2	no	—
176	C₈×C₈₉	—	4	2	no	—
177	C₂²×C₈₉	—	4	2	no	—
178	C₂²×C₈₉	—	4	2	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	—	4	2	no	—
182	C₂²×C₈₉	—	4	2	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
185	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
186	C₂²×C₈₉	#518	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
188	C₂²×C₈₉	#568	1	1	yes	characteristic
189	C₂²×C₈₉	#568	1	1	yes	characteristic
190	C₂²×C₈₉	#568	1	1	yes	characteristic
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	—	2	2	no	—
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	4	2	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	—	4	1	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	#553	1	2	yes	—
201	C₄×C₈₉	#559	1	2	yes	—
202	#22838	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₈₉	—	8	2	no	—
204	C₂×C₈₉	#2357	1	1	yes	characteristic
205	C₂×C₈₉	#2921	1	1	yes	characteristic
206	C₂×C₈₉	#2925	1	1	yes	characteristic
207	C₂×C₈₉	#2967	1	1	yes	characteristic
208	C₂×C₈₉	#2968	1	1	yes	characteristic
209	C₂×C₈₉	#2980	1	1	yes	characteristic
210	C₂×C₈₉	#2981	1	1	yes	characteristic
211	#2293	C₂×C₈₉	1	1	yes	characteristic
212	#1955	C₂×C₈₉	1	2	yes	—
213	#1924	C₂×C₈₉	1	2	yes	complemented
214	#1923	C₂×C₈₉	1	2	yes	complemented
215	#1831	C₂×C₈₉	1	1	yes	characteristic, complemented
216	#1818	C₂×C₈₉	1	2	yes	complemented
217	#1771	C₂×C₈₉	1	2	yes	complemented
218	#1767	C₂×C₈₉	1	1	yes	characteristic, complemented
219	#1750	C₂×C₈₉	1	2	yes	complemented
220	C₈₉	#22838	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
222	C₂×#117	C₂²×C₈₉	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
229	C₂×#97	C₂²×C₈₉	1	2	yes	—
230	C₂×#97	C₂²×C₈₉	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
232	#390	C₄×C₈₉	1	1	yes	characteristic
233	#390	C₄×C₈₉	1	1	yes	characteristic
234	#389	C₄×C₈₉	1	1	yes	characteristic
235	#389	C₄×C₈₉	1	1	yes	characteristic
236	#388	C₄×C₈₉	1	2	yes	—
237	#388	C₄×C₈₉	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
239	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
240	C₄³	C₂²×C₈₉	1	1	yes	characteristic
241	#336	C₂²×C₈₉	1	1	yes	characteristic
242	#336	C₂²×C₈₉	1	2	yes	—
243	#336	C₂²×C₈₉	1	2	yes	—
244	#336	C₂²×C₈₉	1	2	yes	—
245	#336	C₂²×C₈₉	1	1	yes	characteristic
246	#336	C₂²×C₈₉	1	1	yes	characteristic
247	#336	C₂²×C₈₉	1	1	yes	characteristic
248	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
251	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
253	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	#117	—	4	2	no	—
257	#117	—	4	2	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
268	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
274	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
276	C₄⋊C₈	—	2	4	no	—
277	C₄⋊C₈	—	2	4	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	4	2	no	—
281	C₂²⋊C₈	—	4	2	no	—
282	#97	—	2	4	no	—
283	#97	—	4	2	no	—
284	C₄×C₈	—	4	2	no	—
285	#95	C₂×C₄×C₈₉	1	2	yes	—
286	#95	C₂×C₄×C₈₉	1	2	yes	—
287	#95	C₂×C₄×C₈₉	1	2	yes	—
288	C₂⁴	C₂²×C₄×C₈₉	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	#41×C₈₉	1	4	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	#41×C₈₉	1	2	yes	—
339	C₄²	#41×C₈₉	1	2	yes	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	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	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	#117×C₈₉	1	2	yes	—
378	C₂×C₄	#117×C₈₉	1	2	yes	—
379	C₂×C₄	#131×C₈₉	1	2	yes	—
380	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
382	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
383	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×#117×C₈₉	1	1	yes	characteristic
396	C₂²	C₄×#41×C₈₉	1	1	yes	characteristic
397	C₂²	#518×C₈₉	1	1	yes	characteristic
398	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
399	C₂²	#568×C₈₉	1	1	yes	characteristic
400	C₂²	#568×C₈₉	1	1	yes	characteristic
401	C₂²	#568×C₈₉	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	2	no	—
411	C₄	#553×C₈₉	1	2	yes	—
412	C₄	#559×C₈₉	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	C₈₉×#2357	1	1	yes	characteristic
415	C₂	C₈₉×#2921	1	1	yes	characteristic
416	C₂	C₈₉×#2925	1	1	yes	characteristic
417	C₂	C₈₉×#2967	1	1	yes	characteristic
418	C₂	C₈₉×#2968	1	1	yes	characteristic
419	C₂	C₈₉×#2980	1	1	yes	characteristic
420	C₂	C₈₉×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₈₉×#1924	C₂	semidirect
4. C₈₉×#1923	C₂	semidirect
5. C₈₉×#1831	C₂	semidirect
6. C₈₉×#1818	C₂	semidirect
7. C₈₉×#1771	C₂	semidirect
8. C₈₉×#1767	C₂	semidirect
9. C₈₉×#1750	C₂	semidirect
202. #22838	C₈₉	direct (N × H)
213. #1924	C₂×C₈₉	semidirect
214. #1923	C₂×C₈₉	semidirect
215. #1831	C₂×C₈₉	semidirect
216. #1818	C₂×C₈₉	semidirect
217. #1771	C₂×C₈₉	semidirect
218. #1767	C₂×C₈₉	semidirect
219. #1750	C₂×C₈₉	semidirect
220. C₈₉	#22838	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2293	2
C₈₉×#1955	2
C₈₉×#1924	2
C₈₉×#1923	2
C₈₉×#1831	2
C₈₉×#1818	2
C₈₉×#1771	2
C₈₉×#1767	2
C₈₉×#1750	2
#22838	89

Subgroups — C89×#22838 #36400686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22838 #36400686