Subgroups — C₈₉×#35329 #36413177

Order 22784.

3662 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₂×#535×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2858	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2658	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2657	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2540	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2539	C₂	1	8	yes	maximal, complemented
10	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₉	C₂²	1	2	yes	—
12	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	#536×C₈₉	—	2	16	no	—
15	#535×C₈₉	—	2	16	no	—
16	#532×C₈₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#127×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#124×C₈₉	—	2	8	no	—
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#124×C₈₉	C₂²	1	4	yes	—
24	C₂×#124×C₈₉	C₂²	1	2	yes	—
25	C₂×#124×C₈₉	C₂²	1	4	yes	—
26	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
27	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
28	C₂×#123×C₈₉	C₂²	1	8	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
30	C₂×#121×C₈₉	C₂²	1	4	yes	—
31	C₂×#121×C₈₉	C₂²	1	8	yes	—
32	C₂×#120×C₈₉	C₂²	1	8	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
36	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
37	#399×C₈₉	C₂²	1	16	yes	complemented
38	#392×C₈₉	C₂²	1	16	yes	complemented
39	#390×C₈₉	C₂²	1	32	yes	complemented
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
42	#376×C₈₉	C₂²	1	2	yes	complemented
43	C₄³×C₈₉	C₂²	1	2	yes	complemented
44	C₂⁵×C₈₉	C₂³	1	2	yes	—
45	C₂×#41×C₈₉	—	2	8	no	—
46	C₂×#41×C₈₉	—	2	8	no	—
47	C₂×#41×C₈₉	—	2	8	no	—
48	C₂²×Q₈×C₈₉	—	2	4	no	—
49	C₂²×Q₈×C₈₉	—	2	8	no	—
50	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
52	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
53	C₂²×D₄×C₈₉	—	2	4	no	—
54	C₂²×D₄×C₈₉	—	2	8	no	—
55	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
56	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	—	2	4	no	—
66	C₄⋊Q₈×C₈₉	—	2	16	no	—
67	#127×C₈₉	—	2	16	no	—
68	#127×C₈₉	—	2	4	no	—
69	#124×C₈₉	—	2	16	no	—
70	#124×C₈₉	—	2	8	no	—
71	#124×C₈₉	—	2	8	no	—
72	#124×C₈₉	—	2	16	no	—
73	#124×C₈₉	—	2	8	no	—
74	#124×C₈₉	—	2	16	no	—
75	#123×C₈₉	—	2	32	no	—
76	C₂²⋊Q₈×C₈₉	—	2	32	no	—
77	#121×C₈₉	—	2	16	no	—
78	#121×C₈₉	—	2	32	no	—
79	#120×C₈₉	—	2	32	no	—
80	C₄×D₄×C₈₉	—	2	16	no	—
81	#117×C₈₉	D₄	1	16	yes	complemented
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
89	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
93	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
98	#95×C₈₉	C₂³	1	8	yes	—
99	C₂⁴×C₈₉	—	2	4	no	—
100	C₂⁴×C₈₉	—	2	8	no	—
101	C₂⁴×C₈₉	—	4	8	no	—
102	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
103	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
104	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
105	#41×C₈₉	—	4	32	no	—
106	C₂×Q₈×C₈₉	—	2	8	no	—
107	C₂×Q₈×C₈₉	—	2	4	no	—
108	C₂×Q₈×C₈₉	—	2	4	no	—
109	C₂×Q₈×C₈₉	—	2	4	no	—
110	C₂×Q₈×C₈₉	—	2	8	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×Q₈×C₈₉	—	2	4	no	—
113	C₂×Q₈×C₈₉	—	4	16	no	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	8	no	—
116	C₂×D₄×C₈₉	—	2	8	no	—
117	C₂×D₄×C₈₉	—	2	8	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	4	no	—
120	C₂×D₄×C₈₉	—	2	4	no	—
121	C₂×D₄×C₈₉	—	2	4	no	—
122	C₂×D₄×C₈₉	—	2	8	no	—
123	C₂×D₄×C₈₉	—	2	4	no	—
124	C₂×D₄×C₈₉	—	2	4	no	—
125	C₂×D₄×C₈₉	—	2	32	no	—
126	C₂×D₄×C₈₉	—	4	8	no	—
127	C₂×D₄×C₈₉	—	4	32	no	—
128	C₂×D₄×C₈₉	—	4	16	no	—
129	C₂²×C₄×C₈₉	—	2	4	no	—
130	C₂²×C₄×C₈₉	—	2	8	no	—
131	C₂²×C₄×C₈₉	—	2	8	no	—
132	C₂²×C₄×C₈₉	—	2	8	no	—
133	C₂²×C₄×C₈₉	—	2	8	no	—
134	C₂²×C₄×C₈₉	—	4	4	no	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
136	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	—	2	8	no	—
146	C₄⋊C₄×C₈₉	—	2	32	no	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
148	C₂²⋊C₄×C₈₉	—	2	16	no	—
149	C₂²⋊C₄×C₈₉	—	2	16	no	—
150	C₂²⋊C₄×C₈₉	—	2	16	no	—
151	C₂²⋊C₄×C₈₉	—	2	32	no	—
152	C₂²⋊C₄×C₈₉	—	2	32	no	—
153	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
154	C₄²×C₈₉	—	4	8	no	—
155	C₄²×C₈₉	C₂×D₄	1	8	yes	—
156	C₄²×C₈₉	C₂×D₄	1	4	yes	—
157	C₄²×C₈₉	C₂×D₄	1	4	yes	—
158	C₄²×C₈₉	C₂×D₄	1	16	yes	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	2	4	no	—
161	C₂³×C₈₉	—	2	4	no	—
162	C₂³×C₈₉	—	2	4	no	—
163	C₂³×C₈₉	—	2	8	no	—
164	C₂³×C₈₉	—	2	4	no	—
165	C₂³×C₈₉	—	2	16	no	—
166	C₂³×C₈₉	—	2	16	no	—
167	C₂³×C₈₉	—	4	16	no	—
168	C₂³×C₈₉	—	4	8	no	—
169	C₂³×C₈₉	—	8	16	no	—
170	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
171	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
173	Q₈×C₈₉	—	4	8	no	—
174	Q₈×C₈₉	—	4	8	no	—
175	Q₈×C₈₉	—	4	8	no	—
176	D₄×C₈₉	—	4	16	no	—
177	D₄×C₈₉	—	4	16	no	—
178	D₄×C₈₉	—	4	8	no	—
179	D₄×C₈₉	—	4	8	no	—
180	D₄×C₈₉	—	4	8	no	—
181	D₄×C₈₉	—	8	32	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	16	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	8	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	4	8	no	—
191	C₂×C₄×C₈₉	—	4	8	no	—
192	C₂×C₄×C₈₉	—	4	16	no	—
193	C₂×C₄×C₈₉	#127	1	16	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
201	C₂²×C₈₉	—	2	4	no	—
202	C₂²×C₈₉	—	2	8	no	—
203	C₂²×C₈₉	—	4	4	no	—
204	C₂²×C₈₉	—	4	4	no	—
205	C₂²×C₈₉	—	4	8	no	—
206	C₂²×C₈₉	—	4	8	no	—
207	C₂²×C₈₉	—	4	8	no	—
208	C₂²×C₈₉	—	4	16	no	—
209	C₂²×C₈₉	—	4	8	no	—
210	C₂²×C₈₉	—	8	16	no	—
211	C₂²×C₈₉	C₂×#127	1	4	yes	—
212	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
214	C₂²×C₈₉	#585	1	4	yes	—
215	C₄×C₈₉	—	2	4	no	—
216	C₄×C₈₉	—	2	4	no	—
217	C₄×C₈₉	—	2	16	no	—
218	C₄×C₈₉	—	4	4	no	—
219	C₄×C₈₉	—	4	4	no	—
220	C₄×C₈₉	C₂×#127	1	4	yes	—
221	C₄×C₈₉	C₂×#127	1	4	yes	—
222	#35329	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂×C₈₉	—	2	4	no	—
224	C₂×C₈₉	—	8	4	no	—
225	C₂×C₈₉	—	8	4	no	—
226	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
227	C₂×C₈₉	#3449	1	2	yes	—
228	C₂×C₈₉	#3500	1	4	yes	—
229	C₂×#536	C₂×C₈₉	1	2	yes	complemented
230	C₂×#535	C₂×C₈₉	1	2	yes	complemented
231	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
232	C₂²×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#2858	C₂×C₈₉	1	4	yes	complemented
234	#2658	C₂×C₈₉	1	2	yes	complemented
235	#2657	C₂×C₈₉	1	2	yes	complemented
236	#2540	C₂×C₈₉	1	8	yes	complemented
237	#2539	C₂×C₈₉	1	8	yes	complemented
238	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#35329	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×#41	C₂²×C₈₉	1	2	yes	—
241	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
242	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
243	#536	—	2	16	no	—
244	#535	—	2	16	no	—
245	#532	—	2	8	no	—
246	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
247	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
248	C₂×#127	C₂²×C₈₉	1	4	yes	—
249	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
250	C₂×#124	—	2	8	no	—
251	C₂×#124	C₂²×C₈₉	1	2	yes	—
252	C₂×#124	C₂²×C₈₉	1	4	yes	—
253	C₂×#124	C₂²×C₈₉	1	2	yes	—
254	C₂×#124	C₂²×C₈₉	1	4	yes	—
255	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
256	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
257	C₂×#123	C₂²×C₈₉	1	8	yes	—
258	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
259	C₂×#121	C₂²×C₈₉	1	4	yes	—
260	C₂×#121	C₂²×C₈₉	1	8	yes	—
261	C₂×#120	C₂²×C₈₉	1	8	yes	—
262	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
263	C₂×#117	C₂²×C₈₉	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
265	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
266	#399	C₂²×C₈₉	1	16	yes	complemented
267	#392	C₂²×C₈₉	1	16	yes	complemented
268	#390	C₂²×C₈₉	1	32	yes	complemented
269	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
270	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
271	#376	C₂²×C₈₉	1	2	yes	complemented
272	C₄³	C₂²×C₈₉	1	2	yes	complemented
273	C₂⁵	C₂³×C₈₉	1	2	yes	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	—	2	8	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	—	2	8	no	—
279	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
280	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
281	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
282	C₂²×D₄	—	2	4	no	—
283	C₂²×D₄	—	2	8	no	—
284	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
285	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
286	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
287	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
288	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
289	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
290	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
291	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
292	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
293	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	16	no	—
296	#127	—	2	16	no	—
297	#127	—	2	4	no	—
298	#124	—	2	16	no	—
299	#124	—	2	8	no	—
300	#124	—	2	8	no	—
301	#124	—	2	16	no	—
302	#124	—	2	8	no	—
303	#124	—	2	16	no	—
304	#123	—	2	32	no	—
305	C₂²⋊Q₈	—	2	32	no	—
306	#121	—	2	16	no	—
307	#121	—	2	32	no	—
308	#120	—	2	32	no	—
309	C₄×D₄	—	2	16	no	—
310	#117	D₄×C₈₉	1	16	yes	complemented
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
313	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
314	C₂×C₂²⋊C₄	—	2	16	no	—
315	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
321	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
322	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
323	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
324	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
327	#95	C₂³×C₈₉	1	8	yes	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	4	8	no	—
331	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
332	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
333	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
334	#41	—	4	32	no	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	8	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	4	16	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	32	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	4	32	no	—
357	C₂×D₄	—	4	16	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
365	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
367	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
371	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	32	no	—
376	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
377	C₂²⋊C₄	—	2	16	no	—
378	C₂²⋊C₄	—	2	16	no	—
379	C₂²⋊C₄	—	2	16	no	—
380	C₂²⋊C₄	—	2	32	no	—
381	C₂²⋊C₄	—	2	32	no	—
382	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
383	C₄²	—	4	8	no	—
384	C₄²	C₂×D₄×C₈₉	1	8	yes	—
385	C₄²	C₂×D₄×C₈₉	1	4	yes	—
386	C₄²	C₂×D₄×C₈₉	1	4	yes	—
387	C₄²	C₂×D₄×C₈₉	1	16	yes	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	16	no	—
395	C₂³	—	2	16	no	—
396	C₂³	—	4	16	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	8	16	no	—
399	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
400	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
401	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
402	Q₈	—	4	8	no	—
403	Q₈	—	4	8	no	—
404	Q₈	—	4	8	no	—
405	D₄	—	4	16	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	8	32	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	16	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	16	no	—
422	C₂×C₄	#127×C₈₉	1	16	yes	—
423	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
424	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
426	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	8	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	8	no	—
437	C₂²	—	4	16	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	8	16	no	—
440	C₂²	C₂×#127×C₈₉	1	4	yes	—
441	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
442	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
443	C₂²	#585×C₈₉	1	4	yes	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	16	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	4	no	—
449	C₄	C₂×#127×C₈₉	1	4	yes	—
450	C₄	C₂×#127×C₈₉	1	4	yes	—
451	C₂	—	2	4	no	—
452	C₂	—	8	4	no	—
453	C₂	—	8	4	no	—
454	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
455	C₂	C₈₉×#3449	1	2	yes	—
456	C₂	C₈₉×#3500	1	4	yes	—

	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. C₂×#536×C₈₉	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₂×#532×C₈₉	C₂	semidirect
4. C₂²×#124×C₈₉	C₂	semidirect
5. C₈₉×#2858	C₂	semidirect
6. C₈₉×#2658	C₂	semidirect
7. C₈₉×#2657	C₂	semidirect
8. C₈₉×#2540	C₂	semidirect
9. C₈₉×#2539	C₂	semidirect
10. C₄×#117×C₈₉	C₂	semidirect
17. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
20. C₂×#127×C₈₉	C₂²	semidirect
26. C₂×#124×C₈₉	C₂²	semidirect
27. C₂×#124×C₈₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₄×D₄×C₈₉	C₂²	semidirect
37. #399×C₈₉	C₂²	semidirect
38. #392×C₈₉	C₂²	semidirect
39. #390×C₈₉	C₂²	semidirect
40. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
42. #376×C₈₉	C₂²	semidirect
43. C₄³×C₈₉	C₂²	semidirect
81. #117×C₈₉	D₄	semidirect
92. C₂×C₄²×C₈₉	D₄	semidirect
222. #35329	C₈₉	direct (N × H)
229. C₂×#536	C₂×C₈₉	semidirect
230. C₂×#535	C₂×C₈₉	semidirect
231. C₂×#532	C₂×C₈₉	semidirect
232. C₂²×#124	C₂×C₈₉	semidirect
233. #2858	C₂×C₈₉	semidirect
234. #2658	C₂×C₈₉	semidirect
235. #2657	C₂×C₈₉	semidirect
236. #2540	C₂×C₈₉	semidirect
237. #2539	C₂×C₈₉	semidirect
238. C₄×#117	C₂×C₈₉	semidirect
239. C₈₉	#35329	direct (N × H)
246. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
247. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
249. C₂×#127	C₂²×C₈₉	semidirect
255. C₂×#124	C₂²×C₈₉	semidirect
256. C₂×#124	C₂²×C₈₉	semidirect
258. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
262. C₂×C₄×D₄	C₂²×C₈₉	semidirect
266. #399	C₂²×C₈₉	semidirect
267. #392	C₂²×C₈₉	semidirect
268. #390	C₂²×C₈₉	semidirect
269. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
271. #376	C₂²×C₈₉	semidirect
272. C₄³	C₂²×C₈₉	semidirect
310. #117	D₄×C₈₉	semidirect
321. C₂×C₄²	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₈₉	2
C₂×#535×C₈₉	2
C₂×#532×C₈₉	2
C₂²×#124×C₈₉	2
C₈₉×#2858	2
C₈₉×#2658	2
C₈₉×#2657	2
C₈₉×#2540	2
C₈₉×#2539	2
C₄×#117×C₈₉	2
#35329	89

Subgroups — C89×#35329 #36413177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35329 #36413177