Subgroups — C₈₉×#35223 #36413071

Order 22784.

3534 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂³×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2847	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2618	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2417	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2416	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2311	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
13	#537×C₈₉	—	2	8	no	—
14	#525×C₈₉	—	2	16	no	—
15	C₂×#123×C₈₉	C₂²	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
18	C₂×#121×C₈₉	C₂²	1	4	yes	—
19	C₂×#121×C₈₉	C₂²	1	4	yes	—
20	C₂×#121×C₈₉	C₂²	1	8	yes	—
21	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
22	C₂×#120×C₈₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	—
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₈₉	—	2	8	no	—
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	#398×C₈₉	C₂²	1	8	yes	complemented
31	#396×C₈₉	C₂²	1	16	yes	complemented
32	#394×C₈₉	C₂²	1	8	yes	complemented
33	#391×C₈₉	C₂²	1	4	yes	complemented
34	#390×C₈₉	C₂²	1	4	yes	complemented
35	#389×C₈₉	C₂²	1	8	yes	complemented
36	#386×C₈₉	C₂²	1	8	yes	—
37	#386×C₈₉	C₂²	1	16	yes	—
38	#380×C₈₉	C₂²	1	4	yes	—
39	#380×C₈₉	C₂²	1	8	yes	—
40	#380×C₈₉	C₂²	1	8	yes	complemented
41	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
42	C₂×#41×C₈₉	—	2	8	no	—
43	C₂×#41×C₈₉	—	2	8	no	—
44	C₂×#41×C₈₉	—	2	8	no	—
45	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
47	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₈₉	—	2	4	no	—
51	C₂³×C₄×C₈₉	—	2	4	no	—
52	C₂³×C₄×C₈₉	—	2	8	no	—
53	C₂³×C₄×C₈₉	—	4	8	no	—
54	C₂³×C₄×C₈₉	D₄	1	8	yes	complemented
55	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	#123×C₈₉	—	2	16	no	—
63	C₂²⋊Q₈×C₈₉	—	2	16	no	—
64	C₂²⋊Q₈×C₈₉	—	2	16	no	—
65	#121×C₈₉	—	2	16	no	—
66	#121×C₈₉	—	2	16	no	—
67	#121×C₈₉	—	2	16	no	—
68	#121×C₈₉	—	4	16	no	—
69	#120×C₈₉	—	2	16	no	—
70	C₄×D₄×C₈₉	—	2	32	no	—
71	#117×C₈₉	—	2	8	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₈₉	—	2	32	no	—
75	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
88	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
89	#95×C₈₉	C₂³	1	16	yes	—
90	#95×C₈₉	C₂³	1	8	yes	—
91	C₂⁴×C₈₉	—	2	2	no	—
92	C₂⁴×C₈₉	—	2	2	no	—
93	C₂⁴×C₈₉	—	2	4	no	—
94	C₂⁴×C₈₉	—	2	4	no	—
95	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
96	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
97	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
98	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
99	#41×C₈₉	—	4	32	no	—
100	C₂×Q₈×C₈₉	—	2	4	no	—
101	C₂×Q₈×C₈₉	—	2	4	no	—
102	C₂×Q₈×C₈₉	—	2	4	no	—
103	C₂×D₄×C₈₉	—	2	16	no	—
104	C₂×D₄×C₈₉	—	2	8	no	—
105	C₂×D₄×C₈₉	—	2	8	no	—
106	C₂×D₄×C₈₉	—	2	8	no	—
107	C₂×D₄×C₈₉	—	2	16	no	—
108	C₂×D₄×C₈₉	—	2	16	no	—
109	C₂×D₄×C₈₉	—	2	4	no	—
110	C₂×D₄×C₈₉	—	2	4	no	—
111	C₂×D₄×C₈₉	—	2	8	no	—
112	C₂×D₄×C₈₉	—	2	4	no	—
113	C₂×D₄×C₈₉	—	4	8	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	32	no	—
117	C₂²×C₄×C₈₉	—	2	8	no	—
118	C₂²×C₄×C₈₉	—	2	8	no	—
119	C₂²×C₄×C₈₉	—	2	4	no	—
120	C₂²×C₄×C₈₉	—	2	16	no	—
121	C₂²×C₄×C₈₉	—	2	16	no	—
122	C₂²×C₄×C₈₉	—	2	8	no	—
123	C₂²×C₄×C₈₉	—	2	8	no	—
124	C₂²×C₄×C₈₉	—	2	8	no	—
125	C₂²×C₄×C₈₉	—	4	4	no	—
126	C₂²×C₄×C₈₉	—	4	8	no	—
127	C₂²×C₄×C₈₉	—	4	4	no	—
128	C₂²×C₄×C₈₉	—	4	32	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	#41	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₈₉	—	2	16	no	—
142	C₄⋊C₄×C₈₉	—	2	8	no	—
143	C₄⋊C₄×C₈₉	—	2	8	no	—
144	C₄⋊C₄×C₈₉	—	2	16	no	—
145	C₄⋊C₄×C₈₉	—	2	8	no	—
146	C₄⋊C₄×C₈₉	—	4	8	no	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
148	C₂²⋊C₄×C₈₉	—	2	8	no	—
149	C₂²⋊C₄×C₈₉	—	2	16	no	—
150	C₂²⋊C₄×C₈₉	—	2	16	no	—
151	C₂²⋊C₄×C₈₉	—	2	16	no	—
152	C₂²⋊C₄×C₈₉	—	4	16	no	—
153	C₄²×C₈₉	—	2	8	no	—
154	C₂³×C₈₉	—	2	8	no	—
155	C₂³×C₈₉	—	2	8	no	—
156	C₂³×C₈₉	—	2	16	no	—
157	C₂³×C₈₉	—	2	8	no	—
158	C₂³×C₈₉	—	2	16	no	—
159	C₂³×C₈₉	—	2	2	no	—
160	C₂³×C₈₉	—	2	2	no	—
161	C₂³×C₈₉	—	2	2	no	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	—	2	2	no	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	4	no	—
166	C₂³×C₈₉	—	2	4	no	—
167	C₂³×C₈₉	—	2	4	no	—
168	C₂³×C₈₉	—	2	8	no	—
169	C₂³×C₈₉	—	2	8	no	—
170	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
173	C₂³×C₈₉	C₂×#41	1	2	yes	—
174	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
175	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
176	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
177	Q₈×C₈₉	—	4	8	no	—
178	D₄×C₈₉	—	4	16	no	—
179	D₄×C₈₉	—	4	32	no	—
180	D₄×C₈₉	—	4	8	no	—
181	D₄×C₈₉	—	8	8	no	—
182	C₂×C₄×C₈₉	—	2	8	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	8	no	—
186	C₂×C₄×C₈₉	—	2	32	no	—
187	C₂×C₄×C₈₉	—	2	8	no	—
188	C₂×C₄×C₈₉	—	2	4	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	2	4	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	8	no	—
194	C₂×C₄×C₈₉	—	2	8	no	—
195	C₂×C₄×C₈₉	—	4	8	no	—
196	C₂×C₄×C₈₉	—	4	32	no	—
197	C₂×C₄×C₈₉	—	4	8	no	—
198	C₂×C₄×C₈₉	—	4	16	no	—
199	C₂×C₄×C₈₉	#121	1	16	yes	complemented
200	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
202	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
205	C₂²×C₈₉	—	2	32	no	—
206	C₂²×C₈₉	—	2	4	no	—
207	C₂²×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	4	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	2	4	no	—
211	C₂²×C₈₉	—	2	2	no	—
212	C₂²×C₈₉	—	2	4	no	—
213	C₂²×C₈₉	—	2	4	no	—
214	C₂²×C₈₉	—	2	4	no	—
215	C₂²×C₈₉	—	2	4	no	—
216	C₂²×C₈₉	—	4	4	no	—
217	C₂²×C₈₉	—	4	8	no	—
218	C₂²×C₈₉	—	4	4	no	—
219	C₂²×C₈₉	—	4	4	no	—
220	C₂²×C₈₉	—	4	8	no	—
221	C₂²×C₈₉	C₂×#121	1	4	yes	—
222	C₂²×C₈₉	#537	1	8	yes	complemented
223	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
224	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
225	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
226	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
227	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
228	C₄×C₈₉	—	2	4	no	—
229	C₄×C₈₉	—	2	8	no	—
230	C₄×C₈₉	—	4	4	no	—
231	C₄×C₈₉	—	4	8	no	—
232	C₄×C₈₉	—	4	4	no	—
233	C₄×C₈₉	C₂×#121	1	8	yes	—
234	#35223	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₈₉	—	2	4	no	—
236	C₂×C₈₉	—	2	8	no	—
237	C₂×C₈₉	—	8	4	no	—
238	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
239	C₂×C₈₉	C₂×#537	1	2	yes	—
240	C₂×C₈₉	#3484	1	1	yes	characteristic
241	C₂×C₈₉	#3486	1	1	yes	characteristic
242	C₂×C₈₉	#3492	1	2	yes	—
243	C₂×#537	C₂×C₈₉	1	1	yes	characteristic, complemented
244	C₂×#525	C₂×C₈₉	1	2	yes	complemented
245	C₂³×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
246	#2847	C₂×C₈₉	1	4	yes	complemented
247	#2618	C₂×C₈₉	1	4	yes	complemented
248	#2417	C₂×C₈₉	1	8	yes	complemented
249	#2416	C₂×C₈₉	1	8	yes	complemented
250	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#2311	C₂×C₈₉	1	2	yes	complemented
252	C₈₉	#35223	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×#41	C₂²×C₈₉	1	2	yes	—
254	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
256	#537	—	2	8	no	—
257	#525	—	2	16	no	—
258	C₂×#123	C₂²×C₈₉	1	4	yes	—
259	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
261	C₂×#121	C₂²×C₈₉	1	4	yes	—
262	C₂×#121	C₂²×C₈₉	1	4	yes	—
263	C₂×#121	C₂²×C₈₉	1	8	yes	—
264	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
265	C₂×#120	C₂²×C₈₉	1	4	yes	—
266	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	—
267	C₂×#117	C₂²×C₈₉	1	2	yes	—
268	C₂²×C₄⋊C₄	—	2	8	no	—
269	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
272	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
273	#398	C₂²×C₈₉	1	8	yes	complemented
274	#396	C₂²×C₈₉	1	16	yes	complemented
275	#394	C₂²×C₈₉	1	8	yes	complemented
276	#391	C₂²×C₈₉	1	4	yes	complemented
277	#390	C₂²×C₈₉	1	4	yes	complemented
278	#389	C₂²×C₈₉	1	8	yes	complemented
279	#386	C₂²×C₈₉	1	8	yes	—
280	#386	C₂²×C₈₉	1	16	yes	—
281	#380	C₂²×C₈₉	1	4	yes	—
282	#380	C₂²×C₈₉	1	8	yes	—
283	#380	C₂²×C₈₉	1	8	yes	complemented
284	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
285	C₂×#41	—	2	8	no	—
286	C₂×#41	—	2	8	no	—
287	C₂×#41	—	2	8	no	—
288	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
289	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
290	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
291	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
292	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
293	C₂³×C₄	—	2	4	no	—
294	C₂³×C₄	—	2	4	no	—
295	C₂³×C₄	—	2	8	no	—
296	C₂³×C₄	—	4	8	no	—
297	C₂³×C₄	D₄×C₈₉	1	8	yes	complemented
298	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
299	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
300	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
301	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
303	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
304	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
305	#123	—	2	16	no	—
306	C₂²⋊Q₈	—	2	16	no	—
307	C₂²⋊Q₈	—	2	16	no	—
308	#121	—	2	16	no	—
309	#121	—	2	16	no	—
310	#121	—	2	16	no	—
311	#121	—	4	16	no	—
312	#120	—	2	16	no	—
313	C₄×D₄	—	2	32	no	—
314	#117	—	2	8	no	—
315	C₂×C₄⋊C₄	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	32	no	—
318	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
319	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
331	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
332	#95	C₂³×C₈₉	1	16	yes	—
333	#95	C₂³×C₈₉	1	8	yes	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
339	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
340	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
341	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
342	#41	—	4	32	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×D₄	—	2	16	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	16	no	—
351	C₂×D₄	—	2	16	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	32	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	2	16	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	8	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	32	no	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	—
373	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
375	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
377	C₂²×C₄	#41×C₈₉	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
379	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
384	C₄⋊C₄	—	2	16	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	16	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	16	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₂²⋊C₄	—	2	16	no	—
395	C₂²⋊C₄	—	4	16	no	—
396	C₄²	—	2	8	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	16	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	8	no	—
413	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
414	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
415	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
416	C₂³	C₂×#41×C₈₉	1	2	yes	—
417	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
418	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
419	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
420	Q₈	—	4	8	no	—
421	D₄	—	4	16	no	—
422	D₄	—	4	32	no	—
423	D₄	—	4	8	no	—
424	D₄	—	8	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	32	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	32	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	16	no	—
442	C₂×C₄	#121×C₈₉	1	16	yes	complemented
443	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
444	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
445	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
446	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
447	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
448	C₂²	—	2	32	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	8	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	8	no	—
464	C₂²	C₂×#121×C₈₉	1	4	yes	—
465	C₂²	#537×C₈₉	1	8	yes	complemented
466	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
467	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
468	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
469	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
470	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
471	C₄	—	2	4	no	—
472	C₄	—	2	8	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	8	no	—
475	C₄	—	4	4	no	—
476	C₄	C₂×#121×C₈₉	1	8	yes	—
477	C₂	—	2	4	no	—
478	C₂	—	2	8	no	—
479	C₂	—	8	4	no	—
480	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
481	C₂	C₂×#537×C₈₉	1	2	yes	—
482	C₂	C₈₉×#3484	1	1	yes	characteristic
483	C₂	C₈₉×#3486	1	1	yes	characteristic
484	C₂	C₈₉×#3492	1	2	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×#537×C₈₉	C₂	semidirect
2. C₂×#525×C₈₉	C₂	semidirect
3. C₂³×C₄⋊C₄×C₈₉	C₂	semidirect
4. C₈₉×#2847	C₂	semidirect
5. C₈₉×#2618	C₂	semidirect
6. C₈₉×#2417	C₂	semidirect
7. C₈₉×#2416	C₂	semidirect
8. C₈₉×#2316	C₂	semidirect
9. C₈₉×#2311	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
21. C₂×#121×C₈₉	C₂²	semidirect
30. #398×C₈₉	C₂²	semidirect
31. #396×C₈₉	C₂²	semidirect
32. #394×C₈₉	C₂²	semidirect
33. #391×C₈₉	C₂²	semidirect
34. #390×C₈₉	C₂²	semidirect
35. #389×C₈₉	C₂²	semidirect
40. #380×C₈₉	C₂²	semidirect
54. C₂³×C₄×C₈₉	D₄	semidirect
75. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
199. C₂×C₄×C₈₉	#121	semidirect
222. C₂²×C₈₉	#537	semidirect
234. #35223	C₈₉	direct (N × H)
243. C₂×#537	C₂×C₈₉	semidirect
244. C₂×#525	C₂×C₈₉	semidirect
245. C₂³×C₄⋊C₄	C₂×C₈₉	semidirect
246. #2847	C₂×C₈₉	semidirect
247. #2618	C₂×C₈₉	semidirect
248. #2417	C₂×C₈₉	semidirect
249. #2416	C₂×C₈₉	semidirect
250. #2316	C₂×C₈₉	semidirect
251. #2311	C₂×C₈₉	semidirect
252. C₈₉	#35223	direct (N × H)
260. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
264. C₂×#121	C₂²×C₈₉	semidirect
273. #398	C₂²×C₈₉	semidirect
274. #396	C₂²×C₈₉	semidirect
275. #394	C₂²×C₈₉	semidirect
276. #391	C₂²×C₈₉	semidirect
277. #390	C₂²×C₈₉	semidirect
278. #389	C₂²×C₈₉	semidirect
283. #380	C₂²×C₈₉	semidirect
297. C₂³×C₄	D₄×C₈₉	semidirect
318. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
442. C₂×C₄	#121×C₈₉	semidirect
465. C₂²	#537×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₈₉	2
C₂×#525×C₈₉	2
C₂³×C₄⋊C₄×C₈₉	2
C₈₉×#2847	2
C₈₉×#2618	2
C₈₉×#2417	2
C₈₉×#2416	2
C₈₉×#2316	2
C₈₉×#2311	2
#35223	89

Subgroups — C89×#35223 #36413071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35223 #36413071