Subgroups — C₈₉×#20525 #36398373

Order 22784.

1354 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#407×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1753	C₂	1	4	yes	maximal, complemented
5	C₈₉×#1752	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊C₄×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊C₈×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
11	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
13	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
14	#407×C₈₉	C₄	1	8	yes	complemented
15	C₂×C₂²⋊C₈×C₈₉	C₄	1	8	yes	complemented
16	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
21	C₂×#97×C₈₉	C₂²	1	4	yes	complemented
22	C₂×C₄×C₈×C₈₉	C₂²	1	4	yes	complemented
23	C₄×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
28	C₂×#95×C₈₉	C₄	1	2	yes	—
29	#336×C₈₉	C₂²	1	4	yes	complemented
30	#336×C₈₉	C₂²	1	4	yes	complemented
31	C₂⁵×C₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₈₉	—	4	4	no	—
33	C₂³×C₄×C₈₉	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₈₉	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₈₉	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₈₉	—	4	4	no	—
43	C₂×M₁₆×C₈₉	C₂×C₄	1	8	yes	complemented
44	C₂²×C₈×C₈₉	—	4	4	no	—
45	C₂²×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
46	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
48	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
49	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
52	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₈₉	—	4	4	no	—
54	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
57	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
58	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
59	C₂²⋊C₈×C₈₉	C₂×C₄	1	8	yes	—
60	C₂²⋊C₈×C₈₉	C₂×C₄	1	8	yes	complemented
61	C₂²⋊C₈×C₈₉	C₂×C₄	1	8	yes	complemented
62	#97×C₈₉	—	4	4	no	—
63	C₄×C₈×C₈₉	—	4	4	no	—
64	#95×C₈₉	C₂×C₄	1	2	yes	—
65	#95×C₈₉	C₂×C₄	1	4	yes	—
66	#95×C₈₉	C₂×C₄	1	2	yes	—
67	C₂⁴×C₈₉	—	2	4	no	—
68	C₂⁴×C₈₉	—	2	4	no	—
69	C₂⁴×C₈₉	—	4	2	no	—
70	C₂⁴×C₈₉	C₄²	1	4	yes	—
71	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	—	2	4	no	—
75	C₂²×C₄×C₈₉	—	2	4	no	—
76	C₂²×C₄×C₈₉	—	2	4	no	—
77	C₂²×C₄×C₈₉	—	2	8	no	—
78	C₂²×C₄×C₈₉	—	2	8	no	—
79	C₂²×C₄×C₈₉	—	4	8	no	—
80	C₂²×C₄×C₈₉	—	4	8	no	—
81	C₂²×C₄×C₈₉	—	4	4	no	—
82	C₂²×C₄×C₈₉	—	4	2	no	—
83	C₂²×C₄×C₈₉	—	4	2	no	—
84	C₂²×C₄×C₈₉	—	4	2	no	—
85	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
86	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
87	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
88	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₈₉	—	4	8	no	—
101	C₂×C₈×C₈₉	—	2	4	no	—
102	C₂×C₈×C₈₉	—	2	4	no	—
103	C₂×C₈×C₈₉	—	2	4	no	—
104	C₂×C₈×C₈₉	—	2	4	no	—
105	C₂×C₈×C₈₉	—	4	8	no	—
106	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
109	C₂²⋊C₄×C₈₉	—	2	4	no	—
110	C₂²⋊C₄×C₈₉	—	2	8	no	—
111	C₂²⋊C₄×C₈₉	M₁₆	1	8	yes	complemented
112	C₄²×C₈₉	—	2	4	no	—
113	C₄²×C₈₉	—	2	4	no	—
114	C₄²×C₈₉	—	4	4	no	—
115	C₂³×C₈₉	—	2	2	no	—
116	C₂³×C₈₉	—	2	2	no	—
117	C₂³×C₈₉	—	2	2	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	—	2	2	no	—
120	C₂³×C₈₉	—	2	2	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	—	2	8	no	—
123	C₂³×C₈₉	—	2	8	no	—
124	C₂³×C₈₉	—	4	4	no	—
125	C₂³×C₈₉	—	4	16	no	—
126	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
127	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
128	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
129	C₂³×C₈₉	C₂×M₁₆	1	4	yes	—
130	C₂³×C₈₉	#131	1	4	yes	—
131	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	—	2	4	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	4	no	—
138	C₂×C₄×C₈₉	—	2	4	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	2	4	no	—
141	C₂×C₄×C₈₉	—	2	4	no	—
142	C₂×C₄×C₈₉	—	2	4	no	—
143	C₂×C₄×C₈₉	—	2	4	no	—
144	C₂×C₄×C₈₉	—	2	4	no	—
145	C₂×C₄×C₈₉	—	2	4	no	—
146	C₂×C₄×C₈₉	—	4	4	no	—
147	C₂×C₄×C₈₉	—	4	4	no	—
148	C₂×C₄×C₈₉	—	4	4	no	—
149	C₂×C₄×C₈₉	—	4	16	no	—
150	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₈₉	C₂×M₁₆	1	8	yes	—
154	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
157	C₈×C₈₉	—	2	4	no	—
158	C₈×C₈₉	—	2	4	no	—
159	C₈×C₈₉	—	2	8	no	—
160	C₂²×C₈₉	—	2	2	no	—
161	C₂²×C₈₉	—	2	2	no	—
162	C₂²×C₈₉	—	2	8	no	—
163	C₂²×C₈₉	—	2	8	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	—	2	2	no	—
168	C₂²×C₈₉	—	2	2	no	—
169	C₂²×C₈₉	—	4	16	no	—
170	C₂²×C₈₉	—	4	4	no	—
171	C₂²×C₈₉	C₄×M₁₆	1	4	yes	—
172	C₂²×C₈₉	#405	1	4	yes	—
173	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
174	C₂²×C₈₉	#518	1	2	yes	—
175	C₂²×C₈₉	C₂²×M₁₆	1	2	yes	—
176	C₂²×C₈₉	C₂×#131	1	2	yes	—
177	C₄×C₈₉	—	2	8	no	—
178	C₄×C₈₉	—	2	2	no	—
179	C₄×C₈₉	—	2	2	no	—
180	C₄×C₈₉	—	2	2	no	—
181	C₄×C₈₉	—	4	4	no	—
182	C₄×C₈₉	#518	1	2	yes	—
183	C₄×C₈₉	#518	1	2	yes	—
184	#20525	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₈₉	—	2	4	no	—
186	C₂×C₈₉	—	2	4	no	—
187	C₂×C₈₉	—	4	2	no	—
188	C₂×C₈₉	#2273	1	1	yes	characteristic
189	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
190	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
191	C₂×C₈₉	#2974	1	4	yes	—
192	C₂×#407	C₂×C₈₉	1	1	yes	characteristic
193	C₂²×C₂²⋊C₈	C₂×C₈₉	1	1	yes	characteristic
194	C₂×C₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic
195	#1753	C₂×C₈₉	1	4	yes	complemented
196	#1752	C₂×C₈₉	1	2	yes	complemented
197	C₈×C₂²⋊C₄	C₂×C₈₉	1	2	yes	complemented
198	#1749	C₂×C₈₉	1	2	yes	complemented
199	C₄×C₂²⋊C₈	C₂×C₈₉	1	2	yes	complemented
200	C₈₉	#20525	1	1	yes	characteristic, direct product factor, Sylow
201	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
203	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₄×C₈₉	1	2	yes	—
205	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
206	#407	C₄×C₈₉	1	8	yes	complemented
207	C₂×C₂²⋊C₈	C₄×C₈₉	1	8	yes	complemented
208	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
209	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
210	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
212	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
213	C₂×#97	C₂²×C₈₉	1	4	yes	complemented
214	C₂×C₄×C₈	C₂²×C₈₉	1	4	yes	complemented
215	C₄×C₂²⋊C₄	C₄×C₈₉	1	2	yes	—
216	C₄×C₂²⋊C₄	C₄×C₈₉	1	2	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
220	C₂×#95	C₄×C₈₉	1	2	yes	—
221	#336	C₂²×C₈₉	1	4	yes	complemented
222	#336	C₂²×C₈₉	1	4	yes	complemented
223	C₂⁵	C₂×C₄×C₈₉	1	1	yes	characteristic
224	C₂³×C₄	—	4	4	no	—
225	C₂³×C₄	C₂×C₄×C₈₉	1	4	yes	—
226	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
228	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₈₉	1	4	yes	—
230	C₂³×C₄	C₂×C₄×C₈₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
234	C₂×M₁₆	—	4	4	no	—
235	C₂×M₁₆	C₂×C₄×C₈₉	1	8	yes	complemented
236	C₂²×C₈	—	4	4	no	—
237	C₂²×C₈	C₂×C₄×C₈₉	1	8	yes	complemented
238	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
240	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
241	C₂×C₂²⋊C₄	—	2	8	no	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	4	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
245	C₂×C₄²	—	4	4	no	—
246	C₂×C₄²	C₂×C₄×C₈₉	1	4	yes	—
247	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
248	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
249	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
250	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
251	C₂²⋊C₈	C₂×C₄×C₈₉	1	8	yes	—
252	C₂²⋊C₈	C₂×C₄×C₈₉	1	8	yes	complemented
253	C₂²⋊C₈	C₂×C₄×C₈₉	1	8	yes	complemented
254	#97	—	4	4	no	—
255	C₄×C₈	—	4	4	no	—
256	#95	C₂×C₄×C₈₉	1	2	yes	—
257	#95	C₂×C₄×C₈₉	1	4	yes	—
258	#95	C₂×C₄×C₈₉	1	2	yes	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	4	2	no	—
262	C₂⁴	C₄²×C₈₉	1	4	yes	—
263	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
264	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
265	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₄²×C₈₉	1	4	yes	—
278	C₂²×C₄	C₄²×C₈₉	1	4	yes	—
279	C₂²×C₄	C₄²×C₈₉	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
281	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
291	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
292	M₁₆	—	4	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	8	no	—
298	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
299	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
300	C₂×C₈	C₂²×C₄×C₈₉	1	8	yes	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	8	no	—
303	C₂²⋊C₄	M₁₆×C₈₉	1	8	yes	complemented
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	4	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	16	no	—
318	C₂³	C₂×C₄²×C₈₉	1	2	yes	—
319	C₂³	C₂×C₄²×C₈₉	1	2	yes	—
320	C₂³	C₂×C₄²×C₈₉	1	2	yes	—
321	C₂³	C₂×M₁₆×C₈₉	1	4	yes	—
322	C₂³	#131×C₈₉	1	4	yes	—
323	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	16	no	—
342	C₂×C₄	C₂×C₄²×C₈₉	1	2	yes	—
343	C₂×C₄	C₂×C₄²×C₈₉	1	2	yes	—
344	C₂×C₄	C₂×C₄²×C₈₉	1	2	yes	—
345	C₂×C₄	C₂×M₁₆×C₈₉	1	8	yes	—
346	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
348	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	—	2	8	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	8	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	4	4	no	—
363	C₂²	C₄×M₁₆×C₈₉	1	4	yes	—
364	C₂²	#405×C₈₉	1	4	yes	—
365	C₂²	C₂²×C₄²×C₈₉	1	1	yes	characteristic
366	C₂²	#518×C₈₉	1	2	yes	—
367	C₂²	C₂²×M₁₆×C₈₉	1	2	yes	—
368	C₂²	C₂×#131×C₈₉	1	2	yes	—
369	C₄	—	2	8	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	4	no	—
374	C₄	#518×C₈₉	1	2	yes	—
375	C₄	#518×C₈₉	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	2	4	no	—
378	C₂	—	4	2	no	—
379	C₂	C₈₉×#2273	1	1	yes	characteristic
380	C₂	C₂×C₄×M₁₆×C₈₉	1	1	yes	characteristic
381	C₂	C₂×#405×C₈₉	1	1	yes	characteristic
382	C₂	C₈₉×#2974	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂⁵×C₈₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1753	C₂	semidirect
5. C₈₉×#1752	C₂	semidirect
6. C₈×C₂²⋊C₄×C₈₉	C₂	semidirect
7. C₈₉×#1749	C₂	semidirect
8. C₄×C₂²⋊C₈×C₈₉	C₂	semidirect
14. #407×C₈₉	C₄	semidirect
15. C₂×C₂²⋊C₈×C₈₉	C₄	semidirect
21. C₂×#97×C₈₉	C₂²	semidirect
22. C₂×C₄×C₈×C₈₉	C₂²	semidirect
29. #336×C₈₉	C₂²	semidirect
30. #336×C₈₉	C₂²	semidirect
43. C₂×M₁₆×C₈₉	C₂×C₄	semidirect
45. C₂²×C₈×C₈₉	C₂×C₄	semidirect
60. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
61. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
111. C₂²⋊C₄×C₈₉	M₁₆	semidirect
184. #20525	C₈₉	direct (N × H)
195. #1753	C₂×C₈₉	semidirect
196. #1752	C₂×C₈₉	semidirect
197. C₈×C₂²⋊C₄	C₂×C₈₉	semidirect
198. #1749	C₂×C₈₉	semidirect
199. C₄×C₂²⋊C₈	C₂×C₈₉	semidirect
200. C₈₉	#20525	direct (N × H)
206. #407	C₄×C₈₉	semidirect
207. C₂×C₂²⋊C₈	C₄×C₈₉	semidirect
213. C₂×#97	C₂²×C₈₉	semidirect
214. C₂×C₄×C₈	C₂²×C₈₉	semidirect
221. #336	C₂²×C₈₉	semidirect
222. #336	C₂²×C₈₉	semidirect
235. C₂×M₁₆	C₂×C₄×C₈₉	semidirect
237. C₂²×C₈	C₂×C₄×C₈₉	semidirect
252. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect
253. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect
303. C₂²⋊C₄	M₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#407×C₈₉	2
C₂²×C₂²⋊C₈×C₈₉	2
C₂×C₄×C₂²⋊C₄×C₈₉	2
C₈₉×#1753	2
C₈₉×#1752	2
C₈×C₂²⋊C₄×C₈₉	2
C₈₉×#1749	2
C₄×C₂²⋊C₈×C₈₉	2
#20525	89

Subgroups — C89×#20525 #36398373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#20525 #36398373