Subgroups — C₈₉×#35367 #36413215

Order 22784.

4050 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	C₂×#543×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2561	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2472	C₂	1	16	yes	maximal, complemented
5	C₈₉×#2435	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2308	C₂	1	2	yes	maximal, complemented
7	C₂×#379×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
12	#543×C₈₉	—	2	8	no	—
13	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
14	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
15	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
16	C₂×#120×C₈₉	—	2	8	no	—
17	C₂×#120×C₈₉	C₂²	1	8	yes	—
18	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
23	#397×C₈₉	C₂²	1	8	yes	complemented
24	#394×C₈₉	C₂²	1	16	yes	complemented
25	#393×C₈₉	C₂²	1	8	yes	complemented
26	#390×C₈₉	C₂²	1	8	yes	complemented
27	#388×C₈₉	C₂²	1	16	yes	complemented
28	#386×C₈₉	C₂²	1	8	yes	complemented
29	#386×C₈₉	C₂²	1	8	yes	complemented
30	#381×C₈₉	C₂²	1	4	yes	complemented
31	#379×C₈₉	C₂²	1	8	yes	—
32	#379×C₈₉	C₂²	1	8	yes	complemented
33	#379×C₈₉	C₂²	1	4	yes	complemented
34	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
35	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
36	C₂⁵×C₈₉	—	2	4	no	—
37	C₂⁵×C₈₉	—	2	8	no	—
38	C₂⁵×C₈₉	—	4	8	no	—
39	C₂⁵×C₈₉	C₂³	1	2	yes	—
40	C₂⁵×C₈₉	C₂³	1	4	yes	—
41	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
42	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	C₂³	1	4	yes	complemented
44	C₂²×D₄×C₈₉	—	2	4	no	—
45	C₂²×D₄×C₈₉	—	2	8	no	—
46	C₂²×D₄×C₈₉	—	2	8	no	—
47	C₂²×D₄×C₈₉	—	4	8	no	—
48	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
54	#124×C₈₉	—	4	16	no	—
55	C₂²⋊Q₈×C₈₉	—	2	16	no	—
56	C₂²⋊Q₈×C₈₉	—	2	32	no	—
57	#120×C₈₉	—	2	32	no	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	complemented
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
60	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
61	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₈₉	—	4	16	no	—
64	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	complemented
74	C₂×C₄²×C₈₉	C₂³	1	8	yes	complemented
75	#95×C₈₉	C₂³	1	8	yes	complemented
76	#95×C₈₉	C₂³	1	16	yes	complemented
77	C₂⁴×C₈₉	—	2	4	no	—
78	C₂⁴×C₈₉	—	2	8	no	—
79	C₂⁴×C₈₉	—	2	16	no	—
80	C₂⁴×C₈₉	—	2	8	no	—
81	C₂⁴×C₈₉	—	2	8	no	—
82	C₂⁴×C₈₉	—	2	2	no	—
83	C₂⁴×C₈₉	—	2	8	no	—
84	C₂⁴×C₈₉	—	2	8	no	—
85	C₂⁴×C₈₉	—	2	4	no	—
86	C₂⁴×C₈₉	—	4	4	no	—
87	C₂⁴×C₈₉	—	4	8	no	—
88	C₂⁴×C₈₉	—	4	4	no	—
89	C₂⁴×C₈₉	—	4	4	no	—
90	C₂⁴×C₈₉	—	4	32	no	—
91	C₂⁴×C₈₉	—	4	64	no	—
92	C₂⁴×C₈₉	—	4	16	no	—
93	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
94	C₂⁴×C₈₉	#41	1	8	yes	—
95	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
96	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
97	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
98	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
99	C₂×Q₈×C₈₉	—	2	8	no	—
100	C₂×Q₈×C₈₉	—	4	8	no	—
101	C₂×D₄×C₈₉	—	2	8	no	—
102	C₂×D₄×C₈₉	—	2	8	no	—
103	C₂×D₄×C₈₉	—	2	8	no	—
104	C₂×D₄×C₈₉	—	2	16	no	—
105	C₂×D₄×C₈₉	—	2	16	no	—
106	C₂×D₄×C₈₉	—	4	8	no	—
107	C₂×D₄×C₈₉	—	4	32	no	—
108	C₂×D₄×C₈₉	—	4	16	no	—
109	C₂²×C₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	2	4	no	—
111	C₂²×C₄×C₈₉	—	2	8	no	—
112	C₂²×C₄×C₈₉	—	2	8	no	—
113	C₂²×C₄×C₈₉	—	4	4	no	—
114	C₂²×C₄×C₈₉	—	4	8	no	—
115	C₂²×C₄×C₈₉	—	4	8	no	—
116	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₈₉	—	2	16	no	—
122	C₄⋊C₄×C₈₉	—	2	8	no	—
123	C₂²⋊C₄×C₈₉	—	2	8	no	—
124	C₂²⋊C₄×C₈₉	—	2	8	no	—
125	C₂²⋊C₄×C₈₉	—	2	8	no	—
126	C₂²⋊C₄×C₈₉	—	2	8	no	—
127	C₂²⋊C₄×C₈₉	—	2	32	no	—
128	C₂²⋊C₄×C₈₉	—	2	16	no	—
129	C₂²⋊C₄×C₈₉	—	4	16	no	—
130	C₂²⋊C₄×C₈₉	—	4	16	no	—
131	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
132	C₄²×C₈₉	—	4	8	no	—
133	C₂³×C₈₉	—	2	8	no	—
134	C₂³×C₈₉	—	2	4	no	—
135	C₂³×C₈₉	—	2	16	no	—
136	C₂³×C₈₉	—	2	32	no	—
137	C₂³×C₈₉	—	2	4	no	—
138	C₂³×C₈₉	—	2	8	no	—
139	C₂³×C₈₉	—	2	8	no	—
140	C₂³×C₈₉	—	2	4	no	—
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	2	8	no	—
144	C₂³×C₈₉	—	4	8	no	—
145	C₂³×C₈₉	—	4	16	no	—
146	C₂³×C₈₉	—	4	32	no	—
147	C₂³×C₈₉	—	4	32	no	—
148	C₂³×C₈₉	—	4	32	no	—
149	C₂³×C₈₉	—	4	8	no	—
150	C₂³×C₈₉	—	4	16	no	—
151	C₂³×C₈₉	—	4	8	no	—
152	C₂³×C₈₉	—	4	128	no	—
153	C₂³×C₈₉	—	4	8	no	—
154	C₂³×C₈₉	—	4	16	no	—
155	C₂³×C₈₉	—	4	4	no	—
156	C₂³×C₈₉	—	8	8	no	—
157	C₂³×C₈₉	#124	1	16	yes	complemented
158	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
159	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
160	C₂³×C₈₉	C₂×#41	1	4	yes	—
161	C₂³×C₈₉	C₂×#41	1	4	yes	—
162	C₂³×C₈₉	C₂×#41	1	4	yes	—
163	C₂³×C₈₉	H(5,𝔽₂)	1	8	yes	—
164	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
165	Q₈×C₈₉	—	8	8	no	—
166	D₄×C₈₉	—	4	32	no	—
167	D₄×C₈₉	—	4	16	no	—
168	C₂×C₄×C₈₉	—	2	8	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	8	no	—
171	C₂×C₄×C₈₉	—	2	8	no	—
172	C₂×C₄×C₈₉	—	2	4	no	—
173	C₂×C₄×C₈₉	—	2	16	no	—
174	C₂×C₄×C₈₉	—	2	16	no	—
175	C₂×C₄×C₈₉	—	4	8	no	—
176	C₂×C₄×C₈₉	—	4	4	no	—
177	C₂×C₄×C₈₉	—	8	8	no	—
178	C₂×C₄×C₈₉	—	8	8	no	—
179	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
180	C₂²×C₈₉	—	2	4	no	—
181	C₂²×C₈₉	—	2	8	no	—
182	C₂²×C₈₉	—	2	8	no	—
183	C₂²×C₈₉	—	2	8	no	—
184	C₂²×C₈₉	—	2	8	no	—
185	C₂²×C₈₉	—	2	8	no	—
186	C₂²×C₈₉	—	2	16	no	—
187	C₂²×C₈₉	—	4	16	no	—
188	C₂²×C₈₉	—	4	32	no	—
189	C₂²×C₈₉	—	4	64	no	—
190	C₂²×C₈₉	—	4	4	no	—
191	C₂²×C₈₉	—	4	4	no	—
192	C₂²×C₈₉	—	4	8	no	—
193	C₂²×C₈₉	—	4	2	no	—
194	C₂²×C₈₉	—	4	4	no	—
195	C₂²×C₈₉	—	4	8	no	—
196	C₂²×C₈₉	—	8	8	no	—
197	C₂²×C₈₉	C₂×#124	1	4	yes	—
198	C₂²×C₈₉	C₂×#124	1	8	yes	—
199	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
200	C₂²×C₈₉	C₂²×#41	1	2	yes	—
201	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
202	C₄×C₈₉	—	2	8	no	—
203	C₄×C₈₉	—	4	2	no	—
204	C₄×C₈₉	—	4	8	no	—
205	C₄×C₈₉	—	4	8	no	—
206	#35367	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	—	2	4	no	—
208	C₂×C₈₉	—	2	8	no	—
209	C₂×C₈₉	—	4	8	no	—
210	C₂×C₈₉	—	8	2	no	—
211	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
212	C₂×C₈₉	#3484	1	2	yes	—
213	C₂×C₈₉	#3490	1	4	yes	—
214	C₂×#543	C₂×C₈₉	1	1	yes	characteristic, complemented
215	C₂²×#120	C₂×C₈₉	1	1	yes	characteristic
216	#2561	C₂×C₈₉	1	4	yes	complemented
217	#2472	C₂×C₈₉	1	16	yes	complemented
218	#2435	C₂×C₈₉	1	4	yes	complemented
219	#2308	C₂×C₈₉	1	2	yes	complemented
220	C₂×#379	C₂×C₈₉	1	2	yes	complemented
221	#2273	C₂×C₈₉	1	1	yes	characteristic, complemented
222	C₈₉	#35367	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁶	C₂²×C₈₉	1	1	yes	characteristic
224	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
225	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
226	#543	—	2	8	no	—
227	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
228	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
229	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
230	C₂×#120	—	2	8	no	—
231	C₂×#120	C₂²×C₈₉	1	8	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
237	#397	C₂²×C₈₉	1	8	yes	complemented
238	#394	C₂²×C₈₉	1	16	yes	complemented
239	#393	C₂²×C₈₉	1	8	yes	complemented
240	#390	C₂²×C₈₉	1	8	yes	complemented
241	#388	C₂²×C₈₉	1	16	yes	complemented
242	#386	C₂²×C₈₉	1	8	yes	complemented
243	#386	C₂²×C₈₉	1	8	yes	complemented
244	#381	C₂²×C₈₉	1	4	yes	complemented
245	#379	C₂²×C₈₉	1	8	yes	—
246	#379	C₂²×C₈₉	1	8	yes	complemented
247	#379	C₂²×C₈₉	1	4	yes	complemented
248	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
249	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
250	C₂⁵	—	2	4	no	—
251	C₂⁵	—	2	8	no	—
252	C₂⁵	—	4	8	no	—
253	C₂⁵	C₂³×C₈₉	1	2	yes	—
254	C₂⁵	C₂³×C₈₉	1	4	yes	—
255	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
256	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₈₉	1	4	yes	complemented
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	2	8	no	—
260	C₂²×D₄	—	2	8	no	—
261	C₂²×D₄	—	4	8	no	—
262	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
263	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
264	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
265	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
266	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
267	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
268	#124	—	4	16	no	—
269	C₂²⋊Q₈	—	2	16	no	—
270	C₂²⋊Q₈	—	2	32	no	—
271	#120	—	2	32	no	—
272	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	complemented
273	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
274	C₂×C₂²⋊C₄	—	2	8	no	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	2	8	no	—
277	C₂×C₂²⋊C₄	—	4	16	no	—
278	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	complemented
288	C₂×C₄²	C₂³×C₈₉	1	8	yes	complemented
289	#95	C₂³×C₈₉	1	8	yes	complemented
290	#95	C₂³×C₈₉	1	16	yes	complemented
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	16	no	—
294	C₂⁴	—	2	8	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	8	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	—	4	32	no	—
305	C₂⁴	—	4	64	no	—
306	C₂⁴	—	4	16	no	—
307	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
308	C₂⁴	#41×C₈₉	1	8	yes	—
309	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
310	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
311	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
312	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
313	C₂×Q₈	—	2	8	no	—
314	C₂×Q₈	—	4	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	16	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	4	8	no	—
321	C₂×D₄	—	4	32	no	—
322	C₂×D₄	—	4	16	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	8	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
333	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
334	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
335	C₄⋊C₄	—	2	16	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	32	no	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	—	4	16	no	—
345	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
346	C₄²	—	4	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	16	no	—
350	C₂³	—	2	32	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	4	8	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	4	32	no	—
361	C₂³	—	4	32	no	—
362	C₂³	—	4	32	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	128	no	—
367	C₂³	—	4	8	no	—
368	C₂³	—	4	16	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	8	8	no	—
371	C₂³	#124×C₈₉	1	16	yes	complemented
372	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
373	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
374	C₂³	C₂×#41×C₈₉	1	4	yes	—
375	C₂³	C₂×#41×C₈₉	1	4	yes	—
376	C₂³	C₂×#41×C₈₉	1	4	yes	—
377	C₂³	H(5,𝔽₂)×C₈₉	1	8	yes	—
378	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
379	Q₈	—	8	8	no	—
380	D₄	—	4	32	no	—
381	D₄	—	4	16	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	16	no	—
388	C₂×C₄	—	2	16	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	8	8	no	—
392	C₂×C₄	—	8	8	no	—
393	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	8	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	16	no	—
401	C₂²	—	4	16	no	—
402	C₂²	—	4	32	no	—
403	C₂²	—	4	64	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	8	8	no	—
411	C₂²	C₂×#124×C₈₉	1	4	yes	—
412	C₂²	C₂×#124×C₈₉	1	8	yes	—
413	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
414	C₂²	C₂²×#41×C₈₉	1	2	yes	—
415	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
416	C₄	—	2	8	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	8	no	—
419	C₄	—	4	8	no	—
420	C₂	—	2	4	no	—
421	C₂	—	2	8	no	—
422	C₂	—	4	8	no	—
423	C₂	—	8	2	no	—
424	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
425	C₂	C₈₉×#3484	1	2	yes	—
426	C₂	C₈₉×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#120×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
1. C₂×#543×C₈₉	C₂	semidirect
3. C₈₉×#2561	C₂	semidirect
4. C₈₉×#2472	C₂	semidirect
5. C₈₉×#2435	C₂	semidirect
6. C₈₉×#2308	C₂	semidirect
7. C₂×#379×C₈₉	C₂	semidirect
8. C₈₉×#2273	C₂	semidirect
13. C₂×#124×C₈₉	C₂²	semidirect
14. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
15. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
23. #397×C₈₉	C₂²	semidirect
24. #394×C₈₉	C₂²	semidirect
25. #393×C₈₉	C₂²	semidirect
26. #390×C₈₉	C₂²	semidirect
27. #388×C₈₉	C₂²	semidirect
28. #386×C₈₉	C₂²	semidirect
29. #386×C₈₉	C₂²	semidirect
30. #381×C₈₉	C₂²	semidirect
32. #379×C₈₉	C₂²	semidirect
33. #379×C₈₉	C₂²	semidirect
34. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
35. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
43. C₂²×Q₈×C₈₉	C₂³	semidirect
58. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
59. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
73. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
74. C₂×C₄²×C₈₉	C₂³	semidirect
75. #95×C₈₉	C₂³	semidirect
76. #95×C₈₉	C₂³	semidirect
157. C₂³×C₈₉	#124	semidirect
206. #35367	C₈₉	direct (N × H)
214. C₂×#543	C₂×C₈₉	semidirect
216. #2561	C₂×C₈₉	semidirect
217. #2472	C₂×C₈₉	semidirect
218. #2435	C₂×C₈₉	semidirect
219. #2308	C₂×C₈₉	semidirect
220. C₂×#379	C₂×C₈₉	semidirect
221. #2273	C₂×C₈₉	semidirect
222. C₈₉	#35367	direct (N × H)
227. C₂×#124	C₂²×C₈₉	semidirect
228. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
229. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
236. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
237. #397	C₂²×C₈₉	semidirect
238. #394	C₂²×C₈₉	semidirect
239. #393	C₂²×C₈₉	semidirect
240. #390	C₂²×C₈₉	semidirect
241. #388	C₂²×C₈₉	semidirect
242. #386	C₂²×C₈₉	semidirect
243. #386	C₂²×C₈₉	semidirect
244. #381	C₂²×C₈₉	semidirect
246. #379	C₂²×C₈₉	semidirect
247. #379	C₂²×C₈₉	semidirect
248. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
249. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
257. C₂²×Q₈	C₂³×C₈₉	semidirect
272. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
273. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
287. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
288. C₂×C₄²	C₂³×C₈₉	semidirect
289. #95	C₂³×C₈₉	semidirect
290. #95	C₂³×C₈₉	semidirect
371. C₂³	#124×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#543×C₈₉	2
C₂²×#120×C₈₉	2
C₈₉×#2561	2
C₈₉×#2472	2
C₈₉×#2435	2
C₈₉×#2308	2
C₂×#379×C₈₉	2
C₈₉×#2273	2
#35367	89

Subgroups — C89×#35367 #36413215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35367 #36413215