Subgroups — C₈₉×#60032 #36437880

Order 22784.

2212 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2736	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2668	C₂	1	3	yes	maximal, complemented
3	C₈₉×#2578	C₂	1	6	yes	maximal, complemented
4	C₈₉×#2564	C₂	1	3	yes	maximal, complemented
5	C₈₉×#2535	C₂	1	3	yes	maximal, complemented
6	C₈₉×#2517	C₂	1	3	yes	maximal, complemented
7	C₈₉×#2463	C₂	1	3	yes	maximal, complemented
8	C₈₉×#2364	C₂	1	6	yes	maximal, complemented
9	C₄×#120×C₈₉	C₂	1	3	yes	maximal, complemented
10	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
12	C₂×#121×C₈₉	C₂²	1	6	yes	—
13	C₂×#120×C₈₉	C₂²	1	3	yes	—
14	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
16	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	complemented
17	#400×C₈₉	C₂²	1	3	yes	complemented
18	#399×C₈₉	C₂²	1	3	yes	—
19	#397×C₈₉	C₂²	1	6	yes	—
20	#397×C₈₉	C₂²	1	3	yes	—
21	#397×C₈₉	C₂²	1	3	yes	complemented
22	#395×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#394×C₈₉	C₂²	1	6	yes	—
24	#393×C₈₉	C₂²	1	3	yes	—
25	#392×C₈₉	C₂²	1	3	yes	—
26	#392×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#388×C₈₉	C₂²	1	6	yes	—
28	#388×C₈₉	C₂²	1	6	yes	complemented
29	#387×C₈₉	C₂²	1	6	yes	complemented
30	#387×C₈₉	C₂²	1	6	yes	complemented
31	#387×C₈₉	C₂²	1	6	yes	complemented
32	#386×C₈₉	C₂²	1	6	yes	—
33	#386×C₈₉	C₂²	1	3	yes	—
34	#386×C₈₉	C₂²	1	6	yes	—
35	#386×C₈₉	C₂²	1	6	yes	—
36	#386×C₈₉	C₂²	1	6	yes	complemented
37	#385×C₈₉	C₂²	1	6	yes	—
38	#385×C₈₉	C₂²	1	3	yes	—
39	#383×C₈₉	C₂²	1	2	yes	complemented
40	#382×C₈₉	C₂²	1	3	yes	complemented
41	#380×C₈₉	C₂²	1	6	yes	complemented
42	#379×C₈₉	C₂²	1	3	yes	—
43	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	—
44	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
45	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	complemented
46	C₂×#95×C₈₉	C₂²	1	3	yes	complemented
47	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
51	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
52	C₂³×C₄×C₈₉	—	4	6	no	—
53	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
57	C₂²⋊Q₈×C₈₉	—	4	6	no	—
58	#121×C₈₉	—	2	24	no	—
59	#120×C₈₉	—	2	12	no	—
60	C₄×D₄×C₈₉	—	4	6	no	—
61	C₄×D₄×C₈₉	—	4	6	no	—
62	C₄×D₄×C₈₉	—	4	12	no	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
68	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
78	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
79	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
80	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
81	#95×C₈₉	C₂³	1	6	yes	—
82	#95×C₈₉	C₂³	1	3	yes	—
83	#95×C₈₉	C₂³	1	3	yes	—
84	#95×C₈₉	C₂³	1	6	yes	—
85	#95×C₈₉	C₂³	1	6	yes	—
86	#95×C₈₉	C₂³	1	6	yes	—
87	#95×C₈₉	C₂³	1	6	yes	—
88	#95×C₈₉	C₂³	1	1	yes	characteristic
89	#95×C₈₉	C₂³	1	3	yes	—
90	#95×C₈₉	C₂³	1	6	yes	—
91	C₂⁴×C₈₉	—	2	6	no	—
92	C₂⁴×C₈₉	—	4	3	no	—
93	C₂⁴×C₈₉	—	4	1	no	—
94	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
95	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
96	C₂×Q₈×C₈₉	—	4	3	no	—
97	C₂×D₄×C₈₉	—	2	12	no	—
98	C₂×D₄×C₈₉	—	2	12	no	—
99	C₂×D₄×C₈₉	—	2	12	no	—
100	C₂×D₄×C₈₉	—	4	3	no	—
101	C₂×D₄×C₈₉	—	4	3	no	—
102	C₂×D₄×C₈₉	—	4	6	no	—
103	C₂×D₄×C₈₉	—	4	3	no	—
104	C₂×D₄×C₈₉	#41	1	12	yes	—
105	C₂²×C₄×C₈₉	—	2	12	no	—
106	C₂²×C₄×C₈₉	—	2	6	no	—
107	C₂²×C₄×C₈₉	—	2	12	no	—
108	C₂²×C₄×C₈₉	—	2	6	no	—
109	C₂²×C₄×C₈₉	—	4	3	no	—
110	C₂²×C₄×C₈₉	—	4	6	no	—
111	C₂²×C₄×C₈₉	—	4	6	no	—
112	C₂²×C₄×C₈₉	—	4	6	no	—
113	C₂²×C₄×C₈₉	—	4	6	no	—
114	C₂²×C₄×C₈₉	—	4	16	no	—
115	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
122	C₄⋊C₄×C₈₉	—	2	12	no	—
123	C₄⋊C₄×C₈₉	—	2	12	no	—
124	C₄⋊C₄×C₈₉	—	4	3	no	—
125	C₄⋊C₄×C₈₉	—	4	3	no	—
126	C₄⋊C₄×C₈₉	—	4	3	no	—
127	C₂²⋊C₄×C₈₉	—	2	6	no	—
128	C₂²⋊C₄×C₈₉	—	2	12	no	—
129	C₂²⋊C₄×C₈₉	—	2	12	no	—
130	C₂²⋊C₄×C₈₉	—	2	12	no	—
131	C₂²⋊C₄×C₈₉	—	2	12	no	—
132	C₂²⋊C₄×C₈₉	—	4	3	no	—
133	C₂²⋊C₄×C₈₉	—	4	3	no	—
134	C₂²⋊C₄×C₈₉	—	4	3	no	—
135	C₂²⋊C₄×C₈₉	—	4	6	no	—
136	C₂²⋊C₄×C₈₉	—	4	6	no	—
137	C₄²×C₈₉	—	2	6	no	—
138	C₄²×C₈₉	—	4	2	no	—
139	C₄²×C₈₉	—	4	6	no	—
140	C₂³×C₈₉	—	2	6	no	—
141	C₂³×C₈₉	—	2	6	no	—
142	C₂³×C₈₉	—	2	6	no	—
143	C₂³×C₈₉	—	2	3	no	—
144	C₂³×C₈₉	—	2	6	no	—
145	C₂³×C₈₉	—	2	3	no	—
146	C₂³×C₈₉	—	2	3	no	—
147	C₂³×C₈₉	—	2	3	no	—
148	C₂³×C₈₉	—	4	12	no	—
149	C₂³×C₈₉	—	4	12	no	—
150	C₂³×C₈₉	—	4	4	no	—
151	C₂³×C₈₉	C₂×#41	1	6	yes	—
152	C₂³×C₈₉	C₂×#41	1	6	yes	—
153	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
154	Q₈×C₈₉	—	8	2	no	—
155	D₄×C₈₉	—	4	12	no	—
156	D₄×C₈₉	—	4	12	no	—
157	D₄×C₈₉	—	4	24	no	—
158	C₂×C₄×C₈₉	—	2	3	no	—
159	C₂×C₄×C₈₉	—	2	6	no	—
160	C₂×C₄×C₈₉	—	2	3	no	—
161	C₂×C₄×C₈₉	—	2	6	no	—
162	C₂×C₄×C₈₉	—	2	6	no	—
163	C₂×C₄×C₈₉	—	2	6	no	—
164	C₂×C₄×C₈₉	—	2	6	no	—
165	C₂×C₄×C₈₉	—	2	3	no	—
166	C₂×C₄×C₈₉	—	2	6	no	—
167	C₂×C₄×C₈₉	—	2	6	no	—
168	C₂×C₄×C₈₉	—	2	6	no	—
169	C₂×C₄×C₈₉	—	2	3	no	—
170	C₂×C₄×C₈₉	—	2	3	no	—
171	C₂×C₄×C₈₉	—	2	6	no	—
172	C₂×C₄×C₈₉	—	4	12	no	—
173	C₂×C₄×C₈₉	—	4	12	no	—
174	C₂×C₄×C₈₉	—	8	12	no	—
175	C₂×C₄×C₈₉	—	8	6	no	—
176	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
177	C₂×C₄×C₈₉	H(5,𝔽₂)	1	6	yes	—
178	C₂²×C₈₉	—	2	12	no	—
179	C₂²×C₈₉	—	2	12	no	—
180	C₂²×C₈₉	—	2	6	no	—
181	C₂²×C₈₉	—	2	6	no	—
182	C₂²×C₈₉	—	4	16	no	—
183	C₂²×C₈₉	—	4	3	no	—
184	C₂²×C₈₉	—	4	3	no	—
185	C₂²×C₈₉	—	4	6	no	—
186	C₂²×C₈₉	—	4	6	no	—
187	C₂²×C₈₉	—	4	3	no	—
188	C₂²×C₈₉	—	4	3	no	—
189	C₂²×C₈₉	C₂²×#41	1	3	yes	—
190	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	3	yes	—
191	C₂²×C₈₉	#585	1	1	yes	characteristic
192	C₄×C₈₉	—	2	6	no	—
193	C₄×C₈₉	—	2	6	no	—
194	C₄×C₈₉	—	4	6	no	—
195	C₄×C₈₉	—	4	3	no	—
196	C₄×C₈₉	—	4	6	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	—	4	3	no	—
199	#60032	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₈₉	—	4	6	no	—
201	C₂×C₈₉	—	4	6	no	—
202	C₂×C₈₉	#3481	1	3	yes	—
203	C₂×C₈₉	#3505	1	3	yes	—
204	C₂×C₈₉	#3532	1	1	yes	characteristic
205	#2736	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#2668	C₂×C₈₉	1	3	yes	complemented
207	#2578	C₂×C₈₉	1	6	yes	complemented
208	#2564	C₂×C₈₉	1	3	yes	complemented
209	#2535	C₂×C₈₉	1	3	yes	complemented
210	#2517	C₂×C₈₉	1	3	yes	complemented
211	#2463	C₂×C₈₉	1	3	yes	complemented
212	#2364	C₂×C₈₉	1	6	yes	complemented
213	C₄×#120	C₂×C₈₉	1	3	yes	complemented
214	C₈₉	#60032	1	1	yes	characteristic, direct product factor, Sylow
215	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
217	C₂×#121	C₂²×C₈₉	1	6	yes	—
218	C₂×#120	C₂²×C₈₉	1	3	yes	—
219	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
220	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
221	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	complemented
222	#400	C₂²×C₈₉	1	3	yes	complemented
223	#399	C₂²×C₈₉	1	3	yes	—
224	#397	C₂²×C₈₉	1	6	yes	—
225	#397	C₂²×C₈₉	1	3	yes	—
226	#397	C₂²×C₈₉	1	3	yes	complemented
227	#395	C₂²×C₈₉	1	1	yes	characteristic, complemented
228	#394	C₂²×C₈₉	1	6	yes	—
229	#393	C₂²×C₈₉	1	3	yes	—
230	#392	C₂²×C₈₉	1	3	yes	—
231	#392	C₂²×C₈₉	1	1	yes	characteristic, complemented
232	#388	C₂²×C₈₉	1	6	yes	—
233	#388	C₂²×C₈₉	1	6	yes	complemented
234	#387	C₂²×C₈₉	1	6	yes	complemented
235	#387	C₂²×C₈₉	1	6	yes	complemented
236	#387	C₂²×C₈₉	1	6	yes	complemented
237	#386	C₂²×C₈₉	1	6	yes	—
238	#386	C₂²×C₈₉	1	6	yes	—
239	#386	C₂²×C₈₉	1	6	yes	—
240	#386	C₂²×C₈₉	1	3	yes	—
241	#386	C₂²×C₈₉	1	6	yes	complemented
242	#385	C₂²×C₈₉	1	6	yes	—
243	#385	C₂²×C₈₉	1	3	yes	—
244	#383	C₂²×C₈₉	1	2	yes	complemented
245	#382	C₂²×C₈₉	1	3	yes	complemented
246	#380	C₂²×C₈₉	1	6	yes	complemented
247	#379	C₂²×C₈₉	1	3	yes	—
248	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	complemented
251	C₂×#95	C₂²×C₈₉	1	3	yes	complemented
252	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
253	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
255	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
256	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
257	C₂³×C₄	—	4	6	no	—
258	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
259	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
260	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
261	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
262	C₂²⋊Q₈	—	4	6	no	—
263	#121	—	2	24	no	—
264	#120	—	2	12	no	—
265	C₄×D₄	—	4	6	no	—
266	C₄×D₄	—	4	6	no	—
267	C₄×D₄	—	4	12	no	—
268	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
269	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
270	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
271	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
272	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
283	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
284	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
285	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
286	#95	C₂³×C₈₉	1	6	yes	—
287	#95	C₂³×C₈₉	1	3	yes	—
288	#95	C₂³×C₈₉	1	3	yes	—
289	#95	C₂³×C₈₉	1	6	yes	—
290	#95	C₂³×C₈₉	1	6	yes	—
291	#95	C₂³×C₈₉	1	6	yes	—
292	#95	C₂³×C₈₉	1	6	yes	—
293	#95	C₂³×C₈₉	1	1	yes	characteristic
294	#95	C₂³×C₈₉	1	3	yes	—
295	#95	C₂³×C₈₉	1	6	yes	—
296	C₂⁴	—	2	6	no	—
297	C₂⁴	—	4	3	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
300	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
301	C₂×Q₈	—	4	3	no	—
302	C₂×D₄	—	2	12	no	—
303	C₂×D₄	—	2	12	no	—
304	C₂×D₄	—	2	12	no	—
305	C₂×D₄	—	4	3	no	—
306	C₂×D₄	—	4	3	no	—
307	C₂×D₄	—	4	6	no	—
308	C₂×D₄	—	4	3	no	—
309	C₂×D₄	#41×C₈₉	1	12	yes	—
310	C₂²×C₄	—	2	12	no	—
311	C₂²×C₄	—	2	6	no	—
312	C₂²×C₄	—	2	12	no	—
313	C₂²×C₄	—	2	6	no	—
314	C₂²×C₄	—	4	3	no	—
315	C₂²×C₄	—	4	6	no	—
316	C₂²×C₄	—	4	6	no	—
317	C₂²×C₄	—	4	6	no	—
318	C₂²×C₄	—	4	6	no	—
319	C₂²×C₄	—	4	16	no	—
320	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
321	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
322	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
323	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
325	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
326	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
327	C₄⋊C₄	—	2	12	no	—
328	C₄⋊C₄	—	2	12	no	—
329	C₄⋊C₄	—	4	3	no	—
330	C₄⋊C₄	—	4	3	no	—
331	C₄⋊C₄	—	4	3	no	—
332	C₂²⋊C₄	—	2	6	no	—
333	C₂²⋊C₄	—	2	12	no	—
334	C₂²⋊C₄	—	2	12	no	—
335	C₂²⋊C₄	—	2	12	no	—
336	C₂²⋊C₄	—	2	12	no	—
337	C₂²⋊C₄	—	4	3	no	—
338	C₂²⋊C₄	—	4	3	no	—
339	C₂²⋊C₄	—	4	6	no	—
340	C₂²⋊C₄	—	4	6	no	—
341	C₂²⋊C₄	—	4	3	no	—
342	C₄²	—	2	6	no	—
343	C₄²	—	4	6	no	—
344	C₄²	—	4	2	no	—
345	C₂³	—	2	6	no	—
346	C₂³	—	2	6	no	—
347	C₂³	—	2	6	no	—
348	C₂³	—	2	3	no	—
349	C₂³	—	2	6	no	—
350	C₂³	—	2	3	no	—
351	C₂³	—	2	3	no	—
352	C₂³	—	2	3	no	—
353	C₂³	—	4	12	no	—
354	C₂³	—	4	12	no	—
355	C₂³	—	4	4	no	—
356	C₂³	C₂×#41×C₈₉	1	6	yes	—
357	C₂³	C₂×#41×C₈₉	1	6	yes	—
358	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
359	Q₈	—	8	2	no	—
360	D₄	—	4	12	no	—
361	D₄	—	4	12	no	—
362	D₄	—	4	24	no	—
363	C₂×C₄	—	2	3	no	—
364	C₂×C₄	—	2	6	no	—
365	C₂×C₄	—	2	3	no	—
366	C₂×C₄	—	2	6	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	6	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	3	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	3	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	4	12	no	—
378	C₂×C₄	—	4	12	no	—
379	C₂×C₄	—	8	12	no	—
380	C₂×C₄	—	8	6	no	—
381	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
382	C₂×C₄	H(5,𝔽₂)×C₈₉	1	6	yes	—
383	C₂²	—	2	12	no	—
384	C₂²	—	2	12	no	—
385	C₂²	—	2	6	no	—
386	C₂²	—	2	6	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	4	3	no	—
389	C₂²	—	4	3	no	—
390	C₂²	—	4	6	no	—
391	C₂²	—	4	6	no	—
392	C₂²	—	4	3	no	—
393	C₂²	—	4	3	no	—
394	C₂²	C₂²×#41×C₈₉	1	3	yes	—
395	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	3	yes	—
396	C₂²	#585×C₈₉	1	1	yes	characteristic
397	C₄	—	2	6	no	—
398	C₄	—	2	6	no	—
399	C₄	—	4	6	no	—
400	C₄	—	4	3	no	—
401	C₄	—	4	6	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	3	no	—
404	C₂	—	4	6	no	—
405	C₂	—	4	6	no	—
406	C₂	C₈₉×#3481	1	3	yes	—
407	C₂	C₈₉×#3505	1	3	yes	—
408	C₂	C₈₉×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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
1. C₈₉×#2736	C₂	semidirect
2. C₈₉×#2668	C₂	semidirect
3. C₈₉×#2578	C₂	semidirect
4. C₈₉×#2564	C₂	semidirect
5. C₈₉×#2535	C₂	semidirect
6. C₈₉×#2517	C₂	semidirect
7. C₈₉×#2463	C₂	semidirect
8. C₈₉×#2364	C₂	semidirect
9. C₄×#120×C₈₉	C₂	semidirect
11. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
16. C₂×C₄×D₄×C₈₉	C₂²	semidirect
17. #400×C₈₉	C₂²	semidirect
21. #397×C₈₉	C₂²	semidirect
22. #395×C₈₉	C₂²	semidirect
26. #392×C₈₉	C₂²	semidirect
28. #388×C₈₉	C₂²	semidirect
29. #387×C₈₉	C₂²	semidirect
30. #387×C₈₉	C₂²	semidirect
31. #387×C₈₉	C₂²	semidirect
36. #386×C₈₉	C₂²	semidirect
39. #383×C₈₉	C₂²	semidirect
40. #382×C₈₉	C₂²	semidirect
41. #380×C₈₉	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
46. C₂×#95×C₈₉	C₂²	semidirect
199. #60032	C₈₉	direct (N × H)
205. #2736	C₂×C₈₉	semidirect
206. #2668	C₂×C₈₉	semidirect
207. #2578	C₂×C₈₉	semidirect
208. #2564	C₂×C₈₉	semidirect
209. #2535	C₂×C₈₉	semidirect
210. #2517	C₂×C₈₉	semidirect
211. #2463	C₂×C₈₉	semidirect
212. #2364	C₂×C₈₉	semidirect
213. C₄×#120	C₂×C₈₉	semidirect
214. C₈₉	#60032	direct (N × H)
216. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
221. C₂×C₄×D₄	C₂²×C₈₉	semidirect
222. #400	C₂²×C₈₉	semidirect
226. #397	C₂²×C₈₉	semidirect
227. #395	C₂²×C₈₉	semidirect
231. #392	C₂²×C₈₉	semidirect
233. #388	C₂²×C₈₉	semidirect
234. #387	C₂²×C₈₉	semidirect
235. #387	C₂²×C₈₉	semidirect
236. #387	C₂²×C₈₉	semidirect
241. #386	C₂²×C₈₉	semidirect
244. #383	C₂²×C₈₉	semidirect
245. #382	C₂²×C₈₉	semidirect
246. #380	C₂²×C₈₉	semidirect
250. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
251. C₂×#95	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2736	2
C₈₉×#2668	2
C₈₉×#2578	2
C₈₉×#2564	2
C₈₉×#2535	2
C₈₉×#2517	2
C₈₉×#2463	2
C₈₉×#2364	2
C₄×#120×C₈₉	2
#60032	89

Subgroups — C89×#60032 #36437880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60032 #36437880