Subgroups — C₈₉×#35540 #36413388

Order 22784.

2962 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2483	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2422	C₂	1	8	yes	maximal, complemented
5	C₈₉×#2420	C₂	1	8	yes	maximal, complemented
6	C₈₉×#2405	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2317	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2280	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
14	C₂×#121×C₈₉	—	2	8	no	—
15	C₂×#121×C₈₉	C₂²	1	8	yes	—
16	#518×C₈₉	—	2	8	no	—
17	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
18	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
19	C₂×#117×C₈₉	C₂²	1	2	yes	—
20	C₂×#117×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
23	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
24	#397×C₈₉	C₂²	1	16	yes	complemented
25	#394×C₈₉	C₂²	1	16	yes	complemented
26	#390×C₈₉	C₂²	1	8	yes	complemented
27	#389×C₈₉	C₂²	1	8	yes	complemented
28	#386×C₈₉	C₂²	1	8	yes	complemented
29	#385×C₈₉	C₂²	1	8	yes	—
30	#385×C₈₉	C₂²	1	8	yes	complemented
31	#384×C₈₉	C₂²	1	4	yes	complemented
32	#382×C₈₉	C₂²	1	4	yes	complemented
33	#381×C₈₉	C₂²	1	4	yes	—
34	#381×C₈₉	C₂²	1	8	yes	complemented
35	#380×C₈₉	C₂²	1	4	yes	complemented
36	#380×C₈₉	C₂²	1	4	yes	complemented
37	#379×C₈₉	C₂²	1	4	yes	—
38	#379×C₈₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
40	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
41	C₂⁵×C₈₉	C₂³	1	2	yes	—
42	C₂²×D₄×C₈₉	—	2	8	no	—
43	C₂²×D₄×C₈₉	—	2	8	no	—
44	C₂²×D₄×C₈₉	—	4	8	no	—
45	C₂²×D₄×C₈₉	D₄	1	8	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
47	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₈₉	—	2	4	no	—
49	C₂³×C₄×C₈₉	—	2	8	no	—
50	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	#123×C₈₉	—	4	16	no	—
57	#121×C₈₉	—	2	32	no	—
58	C₄×D₄×C₈₉	—	2	16	no	—
59	C₄×D₄×C₈₉	—	2	16	no	—
60	#117×C₈₉	—	2	8	no	—
61	#117×C₈₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
78	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
80	#95×C₈₉	C₂³	1	8	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	#95×C₈₉	C₂³	1	16	yes	—
83	C₂⁴×C₈₉	—	2	2	no	—
84	C₂⁴×C₈₉	—	2	4	no	—
85	C₂⁴×C₈₉	—	2	8	no	—
86	C₂⁴×C₈₉	—	2	4	no	—
87	C₂⁴×C₈₉	—	4	2	no	—
88	C₂⁴×C₈₉	—	4	4	no	—
89	C₂⁴×C₈₉	—	4	4	no	—
90	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
91	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
92	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
93	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₈₉	—	2	16	no	—
95	C₂×D₄×C₈₉	—	2	16	no	—
96	C₂×D₄×C₈₉	—	2	32	no	—
97	C₂×D₄×C₈₉	—	2	8	no	—
98	C₂×D₄×C₈₉	—	2	8	no	—
99	C₂×D₄×C₈₉	—	4	8	no	—
100	C₂×D₄×C₈₉	—	4	32	no	—
101	C₂×D₄×C₈₉	C₂×D₄	1	16	yes	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	—	2	4	no	—
104	C₂²×C₄×C₈₉	—	2	4	no	—
105	C₂²×C₄×C₈₉	—	2	8	no	—
106	C₂²×C₄×C₈₉	—	2	8	no	—
107	C₂²×C₄×C₈₉	—	2	8	no	—
108	C₂²×C₄×C₈₉	—	2	8	no	—
109	C₂²×C₄×C₈₉	—	2	8	no	—
110	C₂²×C₄×C₈₉	—	4	4	no	—
111	C₂²×C₄×C₈₉	—	4	8	no	—
112	C₂²×C₄×C₈₉	—	4	8	no	—
113	C₂²×C₄×C₈₉	—	4	16	no	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₈₉	#41	1	8	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
122	C₄⋊C₄×C₈₉	—	2	8	no	—
123	C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₄⋊C₄×C₈₉	—	2	4	no	—
125	C₄⋊C₄×C₈₉	—	2	8	no	—
126	C₄⋊C₄×C₈₉	—	4	16	no	—
127	C₂²⋊C₄×C₈₉	—	2	8	no	—
128	C₂²⋊C₄×C₈₉	—	2	16	no	—
129	C₂²⋊C₄×C₈₉	—	2	16	no	—
130	C₂²⋊C₄×C₈₉	—	2	8	no	—
131	C₂²⋊C₄×C₈₉	—	2	16	no	—
132	C₂²⋊C₄×C₈₉	—	4	8	no	—
133	C₂²⋊C₄×C₈₉	—	4	8	no	—
134	C₂²⋊C₄×C₈₉	—	4	8	no	—
135	C₄²×C₈₉	—	2	8	no	—
136	C₄²×C₈₉	—	2	8	no	—
137	C₂³×C₈₉	—	2	2	no	—
138	C₂³×C₈₉	—	2	2	no	—
139	C₂³×C₈₉	—	2	8	no	—
140	C₂³×C₈₉	—	2	2	no	—
141	C₂³×C₈₉	—	2	4	no	—
142	C₂³×C₈₉	—	2	8	no	—
143	C₂³×C₈₉	—	2	8	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	—	2	4	no	—
146	C₂³×C₈₉	—	2	8	no	—
147	C₂³×C₈₉	—	2	16	no	—
148	C₂³×C₈₉	—	4	8	no	—
149	C₂³×C₈₉	—	4	8	no	—
150	C₂³×C₈₉	—	4	16	no	—
151	C₂³×C₈₉	—	4	4	no	—
152	C₂³×C₈₉	—	4	4	no	—
153	C₂³×C₈₉	—	8	16	no	—
154	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
155	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
156	C₂³×C₈₉	C₂×#41	1	4	yes	—
157	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
158	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
159	D₄×C₈₉	—	2	32	no	—
160	D₄×C₈₉	—	4	32	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	2	8	no	—
166	C₂×C₄×C₈₉	—	2	4	no	—
167	C₂×C₄×C₈₉	—	2	8	no	—
168	C₂×C₄×C₈₉	—	2	8	no	—
169	C₂×C₄×C₈₉	—	2	8	no	—
170	C₂×C₄×C₈₉	—	2	8	no	—
171	C₂×C₄×C₈₉	—	2	8	no	—
172	C₂×C₄×C₈₉	—	4	8	no	—
173	C₂×C₄×C₈₉	—	4	4	no	—
174	C₂×C₄×C₈₉	—	4	16	no	—
175	C₂×C₄×C₈₉	—	8	8	no	—
176	C₂×C₄×C₈₉	—	8	8	no	—
177	C₂×C₄×C₈₉	#123	1	16	yes	complemented
178	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
179	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
180	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	2	8	no	—
184	C₂²×C₈₉	—	2	8	no	—
185	C₂²×C₈₉	—	2	8	no	—
186	C₂²×C₈₉	—	2	4	no	—
187	C₂²×C₈₉	—	2	8	no	—
188	C₂²×C₈₉	—	2	8	no	—
189	C₂²×C₈₉	—	4	16	no	—
190	C₂²×C₈₉	—	4	2	no	—
191	C₂²×C₈₉	—	4	2	no	—
192	C₂²×C₈₉	—	4	4	no	—
193	C₂²×C₈₉	—	4	16	no	—
194	C₂²×C₈₉	—	8	16	no	—
195	C₂²×C₈₉	C₂×#123	1	4	yes	—
196	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
197	C₂²×C₈₉	C₂²×#41	1	2	yes	—
198	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
199	C₂²×C₈₉	#585	1	2	yes	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	4	no	—
202	C₄×C₈₉	—	4	4	no	—
203	C₄×C₈₉	—	4	4	no	—
204	C₄×C₈₉	—	4	8	no	—
205	C₄×C₈₉	C₂×#123	1	8	yes	—
206	#35540	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	—	2	4	no	—
208	C₂×C₈₉	—	4	4	no	—
209	C₂×C₈₉	—	4	8	no	—
210	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
211	C₂×C₈₉	#3484	1	1	yes	characteristic
212	C₂×C₈₉	#3485	1	1	yes	characteristic
213	C₂×C₈₉	#3494	1	4	yes	—
214	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic
215	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
216	#2483	C₂×C₈₉	1	4	yes	complemented
217	#2422	C₂×C₈₉	1	8	yes	complemented
218	#2420	C₂×C₈₉	1	8	yes	complemented
219	#2405	C₂×C₈₉	1	4	yes	complemented
220	#2317	C₂×C₈₉	1	2	yes	complemented
221	#2309	C₂×C₈₉	1	1	yes	characteristic, complemented
222	#2280	C₂×C₈₉	1	2	yes	complemented
223	C₈₉	#35540	1	1	yes	characteristic, direct product factor, Sylow
224	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
225	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
226	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
227	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
228	C₂×#121	—	2	8	no	—
229	C₂×#121	C₂²×C₈₉	1	8	yes	—
230	#518	—	2	8	no	—
231	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
232	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
233	C₂×#117	C₂²×C₈₉	1	2	yes	—
234	C₂×#117	C₂²×C₈₉	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
238	#397	C₂²×C₈₉	1	16	yes	complemented
239	#394	C₂²×C₈₉	1	16	yes	complemented
240	#390	C₂²×C₈₉	1	8	yes	complemented
241	#389	C₂²×C₈₉	1	8	yes	complemented
242	#386	C₂²×C₈₉	1	8	yes	complemented
243	#385	C₂²×C₈₉	1	8	yes	—
244	#385	C₂²×C₈₉	1	8	yes	complemented
245	#384	C₂²×C₈₉	1	4	yes	complemented
246	#382	C₂²×C₈₉	1	4	yes	complemented
247	#381	C₂²×C₈₉	1	4	yes	—
248	#381	C₂²×C₈₉	1	8	yes	complemented
249	#380	C₂²×C₈₉	1	4	yes	complemented
250	#380	C₂²×C₈₉	1	4	yes	complemented
251	#379	C₂²×C₈₉	1	4	yes	—
252	#379	C₂²×C₈₉	1	4	yes	—
253	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
254	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
255	C₂⁵	C₂³×C₈₉	1	2	yes	—
256	C₂²×D₄	—	2	8	no	—
257	C₂²×D₄	—	2	8	no	—
258	C₂²×D₄	—	4	8	no	—
259	C₂²×D₄	D₄×C₈₉	1	8	yes	—
260	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
261	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
262	C₂³×C₄	—	2	4	no	—
263	C₂³×C₄	—	2	8	no	—
264	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
265	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
266	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
267	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
268	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
269	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
270	#123	—	4	16	no	—
271	#121	—	2	32	no	—
272	C₄×D₄	—	2	16	no	—
273	C₄×D₄	—	2	16	no	—
274	#117	—	2	8	no	—
275	#117	—	2	8	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
282	C₂×C₂²⋊C₄	—	2	16	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
292	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
293	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
294	#95	C₂³×C₈₉	1	8	yes	—
295	#95	C₂³×C₈₉	1	8	yes	—
296	#95	C₂³×C₈₉	1	16	yes	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	4	2	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×D₄×C₈₉	1	8	yes	—
305	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
306	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
307	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	16	no	—
310	C₂×D₄	—	2	32	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	32	no	—
315	C₂×D₄	C₂×D₄×C₈₉	1	16	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	16	no	—
328	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
329	C₂²×C₄	#41×C₈₉	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
333	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	4	16	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	16	no	—
346	C₂²⋊C₄	—	4	8	no	—
347	C₂²⋊C₄	—	4	8	no	—
348	C₂²⋊C₄	—	4	8	no	—
349	C₄²	—	2	8	no	—
350	C₄²	—	2	8	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	16	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	8	16	no	—
368	C₂³	C₂²×D₄×C₈₉	1	8	yes	—
369	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
370	C₂³	C₂×#41×C₈₉	1	4	yes	—
371	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
372	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
373	D₄	—	2	32	no	—
374	D₄	—	4	32	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	8	8	no	—
390	C₂×C₄	—	8	8	no	—
391	C₂×C₄	#123×C₈₉	1	16	yes	complemented
392	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
393	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
394	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	8	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	4	16	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	16	no	—
408	C₂²	—	8	16	no	—
409	C₂²	C₂×#123×C₈₉	1	4	yes	—
410	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
411	C₂²	C₂²×#41×C₈₉	1	2	yes	—
412	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
413	C₂²	#585×C₈₉	1	2	yes	—
414	C₄	—	4	2	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	8	no	—
419	C₄	C₂×#123×C₈₉	1	8	yes	—
420	C₂	—	2	4	no	—
421	C₂	—	4	4	no	—
422	C₂	—	4	8	no	—
423	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
424	C₂	C₈₉×#3484	1	1	yes	characteristic
425	C₂	C₈₉×#3485	1	1	yes	characteristic
426	C₂	C₈₉×#3494	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#121×C₈₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2483	C₂	semidirect
4. C₈₉×#2422	C₂	semidirect
5. C₈₉×#2420	C₂	semidirect
6. C₈₉×#2405	C₂	semidirect
7. C₈₉×#2317	C₂	semidirect
8. C₈₉×#2309	C₂	semidirect
9. C₈₉×#2280	C₂	semidirect
13. C₂×#123×C₈₉	C₂²	semidirect
17. C₂×C₄×D₄×C₈₉	C₂²	semidirect
18. C₂×C₄×D₄×C₈₉	C₂²	semidirect
24. #397×C₈₉	C₂²	semidirect
25. #394×C₈₉	C₂²	semidirect
26. #390×C₈₉	C₂²	semidirect
27. #389×C₈₉	C₂²	semidirect
28. #386×C₈₉	C₂²	semidirect
30. #385×C₈₉	C₂²	semidirect
31. #384×C₈₉	C₂²	semidirect
32. #382×C₈₉	C₂²	semidirect
34. #381×C₈₉	C₂²	semidirect
35. #380×C₈₉	C₂²	semidirect
36. #380×C₈₉	C₂²	semidirect
39. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
177. C₂×C₄×C₈₉	#123	semidirect
206. #35540	C₈₉	direct (N × H)
215. C₂×#518	C₂×C₈₉	semidirect
216. #2483	C₂×C₈₉	semidirect
217. #2422	C₂×C₈₉	semidirect
218. #2420	C₂×C₈₉	semidirect
219. #2405	C₂×C₈₉	semidirect
220. #2317	C₂×C₈₉	semidirect
221. #2309	C₂×C₈₉	semidirect
222. #2280	C₂×C₈₉	semidirect
223. C₈₉	#35540	direct (N × H)
227. C₂×#123	C₂²×C₈₉	semidirect
231. C₂×C₄×D₄	C₂²×C₈₉	semidirect
232. C₂×C₄×D₄	C₂²×C₈₉	semidirect
238. #397	C₂²×C₈₉	semidirect
239. #394	C₂²×C₈₉	semidirect
240. #390	C₂²×C₈₉	semidirect
241. #389	C₂²×C₈₉	semidirect
242. #386	C₂²×C₈₉	semidirect
244. #385	C₂²×C₈₉	semidirect
245. #384	C₂²×C₈₉	semidirect
246. #382	C₂²×C₈₉	semidirect
248. #381	C₂²×C₈₉	semidirect
249. #380	C₂²×C₈₉	semidirect
250. #380	C₂²×C₈₉	semidirect
253. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
391. C₂×C₄	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2483	2
C₈₉×#2422	2
C₈₉×#2420	2
C₈₉×#2405	2
C₈₉×#2317	2
C₈₉×#2309	2
C₈₉×#2280	2
#35540	89

Subgroups — C89×#35540 #36413388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35540 #36413388