Subgroups — C₈₉×#36676 #36414524

Order 22784.

2006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2842	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2827	C₂	1	6	yes	maximal, complemented
4	C₈₉×#2826	C₂	1	3	yes	maximal, complemented
5	C₈₉×#2825	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2812	C₂	1	3	yes	maximal, complemented
7	C₈₉×#2401	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2395	C₂	1	3	yes	maximal, complemented
10	C₈₉×#2392	C₂	1	6	yes	maximal, complemented
11	C₄×#120×C₈₉	C₂	1	3	yes	maximal, complemented
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#120×C₈₉	C₂²	1	3	yes	—
14	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
15	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
16	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	complemented
17	C₂×#117×C₈₉	C₂²	1	3	yes	complemented
18	#401×C₈₉	C₂²	1	2	yes	complemented
19	#400×C₈₉	C₂²	1	6	yes	complemented
20	#400×C₈₉	C₂²	1	3	yes	complemented
21	#399×C₈₉	C₂²	1	3	yes	—
22	#399×C₈₉	C₂²	1	1	yes	characteristic
23	#399×C₈₉	C₂²	1	3	yes	complemented
24	#398×C₈₉	C₂²	1	3	yes	complemented
25	#398×C₈₉	C₂²	1	6	yes	complemented
26	#397×C₈₉	C₂²	1	6	yes	—
27	#397×C₈₉	C₂²	1	3	yes	—
28	#397×C₈₉	C₂²	1	6	yes	complemented
29	#397×C₈₉	C₂²	1	6	yes	complemented
30	#396×C₈₉	C₂²	1	2	yes	—
31	#396×C₈₉	C₂²	1	6	yes	—
32	#396×C₈₉	C₂²	1	6	yes	complemented
33	#394×C₈₉	C₂²	1	6	yes	—
34	#394×C₈₉	C₂²	1	6	yes	—
35	#394×C₈₉	C₂²	1	6	yes	—
36	#394×C₈₉	C₂²	1	6	yes	complemented
37	#392×C₈₉	C₂²	1	6	yes	—
38	#392×C₈₉	C₂²	1	3	yes	—
39	#392×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#386×C₈₉	C₂²	1	6	yes	—
41	#386×C₈₉	C₂²	1	3	yes	—
42	#385×C₈₉	C₂²	1	3	yes	—
43	#385×C₈₉	C₂²	1	6	yes	—
44	#379×C₈₉	C₂²	1	3	yes	—
45	C₄×C₄⋊C₄×C₈₉	C₂²	1	6	yes	complemented
46	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
47	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	complemented
49	#376×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
52	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
53	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₈₉	—	4	6	no	—
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
60	#120×C₈₉	—	2	12	no	—
61	C₄×D₄×C₈₉	—	4	12	no	—
62	C₄×D₄×C₈₉	—	4	6	no	—
63	C₄×D₄×C₈₉	—	4	6	no	—
64	#117×C₈₉	—	4	6	no	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	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	6	yes	—
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
78	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
80	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
83	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
84	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
85	#95×C₈₉	C₂³	1	3	yes	—
86	#95×C₈₉	C₂³	1	1	yes	characteristic
87	#95×C₈₉	C₂³	1	6	yes	—
88	#95×C₈₉	C₂³	1	6	yes	—
89	#95×C₈₉	C₂³	1	6	yes	—
90	#95×C₈₉	C₂³	1	3	yes	—
91	#95×C₈₉	C₂³	1	3	yes	—
92	#95×C₈₉	C₂³	1	6	yes	—
93	#95×C₈₉	C₂³	1	6	yes	—
94	C₂⁴×C₈₉	—	4	3	no	—
95	C₂⁴×C₈₉	—	4	3	no	—
96	C₂⁴×C₈₉	#41	1	4	yes	—
97	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
98	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
99	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
100	C₂×D₄×C₈₉	—	2	12	no	—
101	C₂×D₄×C₈₉	—	2	6	no	—
102	C₂×D₄×C₈₉	—	4	3	no	—
103	C₂×D₄×C₈₉	—	4	3	no	—
104	C₂×D₄×C₈₉	—	4	6	no	—
105	C₂×D₄×C₈₉	—	4	6	no	—
106	C₂×D₄×C₈₉	—	4	6	no	—
107	C₂×D₄×C₈₉	—	4	3	no	—
108	C₂²×C₄×C₈₉	—	2	6	no	—
109	C₂²×C₄×C₈₉	—	2	12	no	—
110	C₂²×C₄×C₈₉	—	2	12	no	—
111	C₂²×C₄×C₈₉	—	2	6	no	—
112	C₂²×C₄×C₈₉	—	4	3	no	—
113	C₂²×C₄×C₈₉	—	4	6	no	—
114	C₂²×C₄×C₈₉	—	4	16	no	—
115	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
123	C₄⋊C₄×C₈₉	—	4	6	no	—
124	C₄⋊C₄×C₈₉	—	4	6	no	—
125	C₄⋊C₄×C₈₉	—	4	3	no	—
126	C₄⋊C₄×C₈₉	—	4	3	no	—
127	C₄⋊C₄×C₈₉	—	4	3	no	—
128	C₄⋊C₄×C₈₉	—	4	3	no	—
129	C₄⋊C₄×C₈₉	—	4	6	no	—
130	C₂²⋊C₄×C₈₉	—	2	12	no	—
131	C₂²⋊C₄×C₈₉	—	2	6	no	—
132	C₂²⋊C₄×C₈₉	—	4	3	no	—
133	C₂²⋊C₄×C₈₉	—	4	6	no	—
134	C₂²⋊C₄×C₈₉	—	4	6	no	—
135	C₂²⋊C₄×C₈₉	—	4	6	no	—
136	C₂²⋊C₄×C₈₉	—	4	6	no	—
137	C₂²⋊C₄×C₈₉	—	4	6	no	—
138	C₂²⋊C₄×C₈₉	—	4	6	no	—
139	C₂²⋊C₄×C₈₉	—	4	3	no	—
140	C₂²⋊C₄×C₈₉	—	4	3	no	—
141	C₄²×C₈₉	—	2	12	no	—
142	C₄²×C₈₉	—	2	6	no	—
143	C₂³×C₈₉	—	2	6	no	—
144	C₂³×C₈₉	—	2	3	no	—
145	C₂³×C₈₉	—	2	3	no	—
146	C₂³×C₈₉	—	2	6	no	—
147	C₂³×C₈₉	—	2	3	no	—
148	C₂³×C₈₉	—	2	3	no	—
149	C₂³×C₈₉	—	2	6	no	—
150	C₂³×C₈₉	—	2	6	no	—
151	C₂³×C₈₉	—	2	3	no	—
152	C₂³×C₈₉	—	4	12	no	—
153	C₂³×C₈₉	—	4	4	no	—
154	C₂³×C₈₉	—	4	12	no	—
155	C₂³×C₈₉	C₂×#41	1	4	yes	—
156	C₂³×C₈₉	C₂×#41	1	2	yes	—
157	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
158	D₄×C₈₉	—	4	12	no	—
159	D₄×C₈₉	—	4	24	no	—
160	D₄×C₈₉	—	4	12	no	—
161	C₂×C₄×C₈₉	—	2	3	no	—
162	C₂×C₄×C₈₉	—	2	6	no	—
163	C₂×C₄×C₈₉	—	2	6	no	—
164	C₂×C₄×C₈₉	—	2	3	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	3	no	—
169	C₂×C₄×C₈₉	—	2	6	no	—
170	C₂×C₄×C₈₉	—	2	3	no	—
171	C₂×C₄×C₈₉	—	2	6	no	—
172	C₂×C₄×C₈₉	—	2	6	no	—
173	C₂×C₄×C₈₉	—	2	6	no	—
174	C₂×C₄×C₈₉	—	2	6	no	—
175	C₂×C₄×C₈₉	—	2	3	no	—
176	C₂×C₄×C₈₉	—	4	4	no	—
177	C₂×C₄×C₈₉	—	4	8	no	—
178	C₂×C₄×C₈₉	—	4	12	no	—
179	C₂×C₄×C₈₉	—	4	8	no	—
180	C₂×C₄×C₈₉	—	4	4	no	—
181	C₂×C₄×C₈₉	H(5,𝔽₂)	1	6	yes	—
182	C₂²×C₈₉	—	2	6	no	—
183	C₂²×C₈₉	—	2	12	no	—
184	C₂²×C₈₉	—	4	16	no	—
185	C₂²×C₈₉	—	4	2	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	6	no	—
188	C₂²×C₈₉	—	4	3	no	—
189	C₂²×C₈₉	—	4	3	no	—
190	C₂²×C₈₉	—	4	6	no	—
191	C₂²×C₈₉	—	4	3	no	—
192	C₂²×C₈₉	—	4	6	no	—
193	C₂²×C₈₉	—	4	3	no	—
194	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
195	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	3	yes	—
196	C₂²×C₈₉	#585	1	3	yes	—
197	C₄×C₈₉	—	4	3	no	—
198	C₄×C₈₉	—	4	6	no	—
199	C₄×C₈₉	—	4	3	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	—	4	1	no	—
202	C₄×C₈₉	—	4	6	no	—
203	C₄×C₈₉	—	4	3	no	—
204	C₄×C₈₉	#560	1	4	yes	—
205	#36676	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₈₉	—	4	2	no	—
207	C₂×C₈₉	—	4	4	no	—
208	C₂×C₈₉	—	8	3	no	—
209	C₂×C₈₉	#3459	1	3	yes	—
210	C₂×C₈₉	C₂×#560	1	1	yes	characteristic
211	C₂×C₈₉	#3529	1	3	yes	—
212	#2842	C₂×C₈₉	1	1	yes	characteristic, complemented
213	#2834	C₂×C₈₉	1	1	yes	characteristic, complemented
214	#2827	C₂×C₈₉	1	6	yes	complemented
215	#2826	C₂×C₈₉	1	3	yes	complemented
216	#2825	C₂×C₈₉	1	2	yes	complemented
217	#2812	C₂×C₈₉	1	3	yes	complemented
218	#2401	C₂×C₈₉	1	2	yes	complemented
219	#2397	C₂×C₈₉	1	1	yes	characteristic, complemented
220	#2395	C₂×C₈₉	1	3	yes	complemented
221	#2392	C₂×C₈₉	1	6	yes	complemented
222	C₄×#120	C₂×C₈₉	1	3	yes	complemented
223	C₈₉	#36676	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
225	C₂×#120	C₂²×C₈₉	1	3	yes	—
226	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
227	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
228	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	complemented
229	C₂×#117	C₂²×C₈₉	1	3	yes	complemented
230	#401	C₂²×C₈₉	1	2	yes	complemented
231	#400	C₂²×C₈₉	1	6	yes	complemented
232	#400	C₂²×C₈₉	1	3	yes	complemented
233	#399	C₂²×C₈₉	1	3	yes	—
234	#399	C₂²×C₈₉	1	1	yes	characteristic
235	#399	C₂²×C₈₉	1	3	yes	complemented
236	#398	C₂²×C₈₉	1	3	yes	complemented
237	#398	C₂²×C₈₉	1	6	yes	complemented
238	#397	C₂²×C₈₉	1	6	yes	—
239	#397	C₂²×C₈₉	1	3	yes	—
240	#397	C₂²×C₈₉	1	6	yes	complemented
241	#397	C₂²×C₈₉	1	6	yes	complemented
242	#396	C₂²×C₈₉	1	2	yes	—
243	#396	C₂²×C₈₉	1	6	yes	—
244	#396	C₂²×C₈₉	1	6	yes	complemented
245	#394	C₂²×C₈₉	1	6	yes	—
246	#394	C₂²×C₈₉	1	6	yes	—
247	#394	C₂²×C₈₉	1	6	yes	—
248	#394	C₂²×C₈₉	1	6	yes	complemented
249	#392	C₂²×C₈₉	1	6	yes	—
250	#392	C₂²×C₈₉	1	3	yes	—
251	#392	C₂²×C₈₉	1	1	yes	characteristic, complemented
252	#386	C₂²×C₈₉	1	6	yes	—
253	#386	C₂²×C₈₉	1	3	yes	—
254	#385	C₂²×C₈₉	1	3	yes	—
255	#385	C₂²×C₈₉	1	6	yes	—
256	#379	C₂²×C₈₉	1	3	yes	—
257	C₄×C₄⋊C₄	C₂²×C₈₉	1	6	yes	complemented
258	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	complemented
261	#376	C₂²×C₈₉	1	1	yes	characteristic, complemented
262	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
263	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
264	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
265	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
266	C₂³×C₄	—	4	6	no	—
267	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
268	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
272	#120	—	2	12	no	—
273	C₄×D₄	—	4	12	no	—
274	C₄×D₄	—	4	6	no	—
275	C₄×D₄	—	4	6	no	—
276	#117	—	4	6	no	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
279	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
281	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
282	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
283	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
295	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
296	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
297	#95	C₂³×C₈₉	1	3	yes	—
298	#95	C₂³×C₈₉	1	1	yes	characteristic
299	#95	C₂³×C₈₉	1	6	yes	—
300	#95	C₂³×C₈₉	1	6	yes	—
301	#95	C₂³×C₈₉	1	6	yes	—
302	#95	C₂³×C₈₉	1	3	yes	—
303	#95	C₂³×C₈₉	1	3	yes	—
304	#95	C₂³×C₈₉	1	6	yes	—
305	#95	C₂³×C₈₉	1	6	yes	—
306	C₂⁴	—	4	3	no	—
307	C₂⁴	—	4	3	no	—
308	C₂⁴	#41×C₈₉	1	4	yes	—
309	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
310	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
311	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
312	C₂×D₄	—	2	12	no	—
313	C₂×D₄	—	2	6	no	—
314	C₂×D₄	—	4	3	no	—
315	C₂×D₄	—	4	3	no	—
316	C₂×D₄	—	4	6	no	—
317	C₂×D₄	—	4	6	no	—
318	C₂×D₄	—	4	6	no	—
319	C₂×D₄	—	4	3	no	—
320	C₂²×C₄	—	2	6	no	—
321	C₂²×C₄	—	2	12	no	—
322	C₂²×C₄	—	2	12	no	—
323	C₂²×C₄	—	2	6	no	—
324	C₂²×C₄	—	4	3	no	—
325	C₂²×C₄	—	4	6	no	—
326	C₂²×C₄	—	4	16	no	—
327	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
328	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
329	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
333	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
334	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
335	C₄⋊C₄	—	4	3	no	—
336	C₄⋊C₄	—	4	3	no	—
337	C₄⋊C₄	—	4	3	no	—
338	C₄⋊C₄	—	4	3	no	—
339	C₄⋊C₄	—	4	6	no	—
340	C₄⋊C₄	—	4	6	no	—
341	C₄⋊C₄	—	4	6	no	—
342	C₂²⋊C₄	—	2	12	no	—
343	C₂²⋊C₄	—	2	6	no	—
344	C₂²⋊C₄	—	4	6	no	—
345	C₂²⋊C₄	—	4	6	no	—
346	C₂²⋊C₄	—	4	6	no	—
347	C₂²⋊C₄	—	4	6	no	—
348	C₂²⋊C₄	—	4	3	no	—
349	C₂²⋊C₄	—	4	3	no	—
350	C₂²⋊C₄	—	4	3	no	—
351	C₂²⋊C₄	—	4	6	no	—
352	C₂²⋊C₄	—	4	6	no	—
353	C₄²	—	2	12	no	—
354	C₄²	—	2	6	no	—
355	C₂³	—	2	6	no	—
356	C₂³	—	2	3	no	—
357	C₂³	—	2	3	no	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	3	no	—
360	C₂³	—	2	3	no	—
361	C₂³	—	2	6	no	—
362	C₂³	—	2	6	no	—
363	C₂³	—	2	3	no	—
364	C₂³	—	4	12	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	12	no	—
367	C₂³	C₂×#41×C₈₉	1	2	yes	—
368	C₂³	C₂×#41×C₈₉	1	4	yes	—
369	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
370	D₄	—	4	12	no	—
371	D₄	—	4	24	no	—
372	D₄	—	4	12	no	—
373	C₂×C₄	—	2	3	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	3	no	—
377	C₂×C₄	—	2	3	no	—
378	C₂×C₄	—	2	6	no	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	2	3	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	3	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	2	6	no	—
386	C₂×C₄	—	2	6	no	—
387	C₂×C₄	—	2	3	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	12	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	H(5,𝔽₂)×C₈₉	1	6	yes	—
394	C₂²	—	2	6	no	—
395	C₂²	—	2	12	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	6	no	—
400	C₂²	—	4	3	no	—
401	C₂²	—	4	3	no	—
402	C₂²	—	4	6	no	—
403	C₂²	—	4	3	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	3	no	—
406	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
407	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	3	yes	—
408	C₂²	#585×C₈₉	1	3	yes	—
409	C₄	—	4	3	no	—
410	C₄	—	4	6	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	3	no	—
414	C₄	—	4	3	no	—
415	C₄	—	4	6	no	—
416	C₄	#560×C₈₉	1	4	yes	—
417	C₂	—	4	2	no	—
418	C₂	—	4	4	no	—
419	C₂	—	8	3	no	—
420	C₂	C₈₉×#3459	1	3	yes	—
421	C₂	C₂×#560×C₈₉	1	1	yes	characteristic
422	C₂	C₈₉×#3529	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂⁵
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
1. C₈₉×#2842	C₂	semidirect
2. C₈₉×#2834	C₂	semidirect
3. C₈₉×#2827	C₂	semidirect
4. C₈₉×#2826	C₂	semidirect
5. C₈₉×#2825	C₂	semidirect
6. C₈₉×#2812	C₂	semidirect
7. C₈₉×#2401	C₂	semidirect
8. C₈₉×#2397	C₂	semidirect
9. C₈₉×#2395	C₂	semidirect
10. C₈₉×#2392	C₂	semidirect
11. C₄×#120×C₈₉	C₂	semidirect
16. C₂×C₄×D₄×C₈₉	C₂²	semidirect
17. C₂×#117×C₈₉	C₂²	semidirect
18. #401×C₈₉	C₂²	semidirect
19. #400×C₈₉	C₂²	semidirect
20. #400×C₈₉	C₂²	semidirect
23. #399×C₈₉	C₂²	semidirect
24. #398×C₈₉	C₂²	semidirect
25. #398×C₈₉	C₂²	semidirect
28. #397×C₈₉	C₂²	semidirect
29. #397×C₈₉	C₂²	semidirect
32. #396×C₈₉	C₂²	semidirect
36. #394×C₈₉	C₂²	semidirect
39. #392×C₈₉	C₂²	semidirect
45. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
48. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
49. #376×C₈₉	C₂²	semidirect
205. #36676	C₈₉	direct (N × H)
212. #2842	C₂×C₈₉	semidirect
213. #2834	C₂×C₈₉	semidirect
214. #2827	C₂×C₈₉	semidirect
215. #2826	C₂×C₈₉	semidirect
216. #2825	C₂×C₈₉	semidirect
217. #2812	C₂×C₈₉	semidirect
218. #2401	C₂×C₈₉	semidirect
219. #2397	C₂×C₈₉	semidirect
220. #2395	C₂×C₈₉	semidirect
221. #2392	C₂×C₈₉	semidirect
222. C₄×#120	C₂×C₈₉	semidirect
223. C₈₉	#36676	direct (N × H)
228. C₂×C₄×D₄	C₂²×C₈₉	semidirect
229. C₂×#117	C₂²×C₈₉	semidirect
230. #401	C₂²×C₈₉	semidirect
231. #400	C₂²×C₈₉	semidirect
232. #400	C₂²×C₈₉	semidirect
235. #399	C₂²×C₈₉	semidirect
236. #398	C₂²×C₈₉	semidirect
237. #398	C₂²×C₈₉	semidirect
240. #397	C₂²×C₈₉	semidirect
241. #397	C₂²×C₈₉	semidirect
244. #396	C₂²×C₈₉	semidirect
248. #394	C₂²×C₈₉	semidirect
251. #392	C₂²×C₈₉	semidirect
257. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
260. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
261. #376	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×#2842	2
C₈₉×#2834	2
C₈₉×#2827	2
C₈₉×#2826	2
C₈₉×#2825	2
C₈₉×#2812	2
C₈₉×#2401	2
C₈₉×#2397	2
C₈₉×#2395	2
C₈₉×#2392	2
C₄×#120×C₈₉	2
#36676	89

Subgroups — C89×#36676 #36414524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36676 #36414524