Subgroups — C₈₉×#29375 #36407223

Order 22784.

778 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2042	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2015	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1926	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1839	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
32	#391×C₈₉	C₂²	1	1	yes	characteristic
33	#391×C₈₉	C₂²	1	1	yes	characteristic
34	#391×C₈₉	C₂²	1	1	yes	characteristic
35	#390×C₈₉	C₂²	1	1	yes	characteristic
36	#389×C₈₉	C₂²	1	1	yes	characteristic
37	#389×C₈₉	C₂²	1	1	yes	characteristic
38	#388×C₈₉	—	2	1	no	—
39	#388×C₈₉	—	2	1	no	—
40	#387×C₈₉	—	2	1	no	—
41	#387×C₈₉	—	2	1	no	—
42	#382×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
44	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
46	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
47	#376×C₈₉	—	2	1	no	—
48	C₄³×C₈₉	C₂²	1	1	yes	characteristic
49	#340×C₈₉	C₂²	1	1	yes	characteristic
50	#340×C₈₉	C₂²	1	1	yes	characteristic
51	#340×C₈₉	C₂²	1	1	yes	characteristic
52	#340×C₈₉	C₂²	1	1	yes	characteristic
53	#336×C₈₉	C₂²	1	1	yes	characteristic
54	#336×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	—	2	1	no	—
63	C₂×Q₁₆×C₈₉	—	2	2	no	—
64	C₂×Q₁₆×C₈₉	—	2	2	no	—
65	C₂×Q₁₆×C₈₉	—	4	1	no	—
66	C₂×SD₁₆×C₈₉	—	2	2	no	—
67	C₂×SD₁₆×C₈₉	—	2	2	no	—
68	C₂×SD₁₆×C₈₉	—	4	1	no	—
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	#124×C₈₉	—	2	2	no	—
74	#124×C₈₉	—	2	2	no	—
75	C₄×Q₈×C₈₉	—	2	2	no	—
76	C₄×Q₈×C₈₉	—	2	2	no	—
77	C₄×Q₈×C₈₉	—	4	1	no	—
78	C₄×Q₈×C₈₉	—	4	1	no	—
79	C₄×D₄×C₈₉	—	4	1	no	—
80	C₄×D₄×C₈₉	—	4	1	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄²×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	—	2	1	no	—
98	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	#107×C₈₉	—	4	1	no	—
106	#106×C₈₉	—	4	1	no	—
107	#103×C₈₉	—	2	2	no	—
108	#103×C₈₉	—	2	2	no	—
109	#103×C₈₉	—	4	1	no	—
110	#103×C₈₉	—	4	1	no	—
111	#103×C₈₉	—	4	1	no	—
112	#102×C₈₉	—	2	2	no	—
113	#102×C₈₉	—	2	2	no	—
114	#102×C₈₉	—	4	1	no	—
115	#95×C₈₉	—	2	1	no	—
116	#95×C₈₉	—	2	1	no	—
117	#95×C₈₉	—	2	1	no	—
118	#95×C₈₉	—	2	1	no	—
119	#95×C₈₉	—	2	1	no	—
120	#95×C₈₉	—	2	1	no	—
121	#95×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	1	no	—
123	#95×C₈₉	—	2	1	no	—
124	#95×C₈₉	—	2	1	no	—
125	#95×C₈₉	—	2	1	no	—
126	C₂⁴×C₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	1	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×Q₈×C₈₉	—	2	1	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	#41	1	2	yes	—
138	C₂×Q₈×C₈₉	#41	1	2	yes	—
139	C₂×D₄×C₈₉	—	2	1	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	1	no	—
142	C₂×D₄×C₈₉	—	2	1	no	—
143	C₂×D₄×C₈₉	—	2	1	no	—
144	C₂×D₄×C₈₉	#41	1	2	yes	—
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	4	2	no	—
153	C₂²×C₄×C₈₉	—	4	2	no	—
154	C₂²×C₄×C₈₉	—	4	2	no	—
155	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	Q₁₆×C₈₉	—	4	4	no	—
163	SD₁₆×C₈₉	—	4	4	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	—	2	1	no	—
167	C₂×C₈×C₈₉	—	2	1	no	—
168	C₂×C₈×C₈₉	—	2	1	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	—	2	1	no	—
172	C₂×C₈×C₈₉	—	2	1	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	2	1	no	—
186	C₄⋊C₄×C₈₉	—	4	2	no	—
187	C₄⋊C₄×C₈₉	—	4	2	no	—
188	C₄⋊C₄×C₈₉	—	4	2	no	—
189	C₄⋊C₄×C₈₉	#41	1	2	yes	—
190	C₂²⋊C₄×C₈₉	—	2	4	no	—
191	C₂²⋊C₄×C₈₉	—	2	4	no	—
192	C₂²⋊C₄×C₈₉	—	4	2	no	—
193	C₂²⋊C₄×C₈₉	—	4	2	no	—
194	C₂²⋊C₄×C₈₉	—	4	2	no	—
195	C₄²×C₈₉	—	2	4	no	—
196	C₄²×C₈₉	—	2	2	no	—
197	C₄²×C₈₉	—	2	2	no	—
198	C₄²×C₈₉	—	2	1	no	—
199	C₄²×C₈₉	—	2	1	no	—
200	C₄²×C₈₉	—	2	1	no	—
201	C₄²×C₈₉	—	2	1	no	—
202	C₄²×C₈₉	—	2	1	no	—
203	C₄²×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	—	4	1	no	—
205	C₄²×C₈₉	—	4	1	no	—
206	C₄²×C₈₉	—	4	2	no	—
207	C₄²×C₈₉	—	4	2	no	—
208	C₂³×C₈₉	—	2	2	no	—
209	C₂³×C₈₉	—	4	1	no	—
210	C₂³×C₈₉	—	4	1	no	—
211	C₂³×C₈₉	—	4	1	no	—
212	C₂³×C₈₉	—	4	1	no	—
213	C₂³×C₈₉	—	4	1	no	—
214	C₂³×C₈₉	—	4	1	no	—
215	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₈₉	—	2	2	no	—
217	Q₈×C₈₉	—	2	2	no	—
218	Q₈×C₈₉	—	2	2	no	—
219	Q₈×C₈₉	—	2	2	no	—
220	Q₈×C₈₉	—	4	1	no	—
221	Q₈×C₈₉	—	4	1	no	—
222	Q₈×C₈₉	—	4	1	no	—
223	Q₈×C₈₉	—	4	1	no	—
224	D₄×C₈₉	—	2	2	no	—
225	D₄×C₈₉	—	2	2	no	—
226	D₄×C₈₉	—	4	1	no	—
227	D₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	1	no	—
242	C₂×C₄×C₈₉	—	2	1	no	—
243	C₂×C₄×C₈₉	—	2	1	no	—
244	C₂×C₄×C₈₉	—	2	1	no	—
245	C₂×C₄×C₈₉	—	2	1	no	—
246	C₂×C₄×C₈₉	—	2	1	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	—	4	1	no	—
250	C₂×C₄×C₈₉	—	4	1	no	—
251	C₂×C₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	—	4	1	no	—
253	C₂×C₄×C₈₉	—	4	1	no	—
254	C₂×C₄×C₈₉	—	4	1	no	—
255	C₂×C₄×C₈₉	—	4	1	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	1	no	—
258	C₂×C₄×C₈₉	—	4	1	no	—
259	C₂×C₄×C₈₉	—	4	1	no	—
260	C₂×C₄×C₈₉	—	4	1	no	—
261	C₂×C₄×C₈₉	—	4	1	no	—
262	C₂×C₄×C₈₉	—	4	1	no	—
263	C₂×C₄×C₈₉	—	4	1	no	—
264	C₂×C₄×C₈₉	—	4	1	no	—
265	C₂×C₄×C₈₉	—	8	4	no	—
266	C₂×C₄×C₈₉	#135	1	2	yes	—
267	C₂×C₄×C₈₉	#137	1	2	yes	—
268	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₈×C₈₉	—	4	1	no	—
275	C₈×C₈₉	—	4	1	no	—
276	C₈×C₈₉	—	4	1	no	—
277	C₈×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	—	4	2	no	—
279	C₂²×C₈₉	—	4	2	no	—
280	C₂²×C₈₉	—	4	2	no	—
281	C₂²×C₈₉	—	8	1	no	—
282	C₂²×C₈₉	—	8	1	no	—
283	C₂²×C₈₉	—	8	1	no	—
284	C₂²×C₈₉	—	8	1	no	—
285	C₂²×C₈₉	#525	1	1	yes	characteristic
286	C₂²×C₈₉	#525	1	1	yes	characteristic
287	C₂²×C₈₉	#535	1	1	yes	characteristic
288	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
289	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
290	C₂²×C₈₉	#575	1	1	yes	characteristic
291	C₂²×C₈₉	#575	1	1	yes	characteristic
292	C₄×C₈₉	—	2	2	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	4	1	no	—
295	C₄×C₈₉	—	4	2	no	—
296	C₄×C₈₉	—	4	1	no	—
297	C₄×C₈₉	—	4	2	no	—
298	C₄×C₈₉	—	4	2	no	—
299	C₄×C₈₉	—	4	1	no	—
300	C₄×C₈₉	—	4	1	no	—
301	C₄×C₈₉	—	8	1	no	—
302	C₄×C₈₉	—	8	1	no	—
303	C₄×C₈₉	—	8	1	no	—
304	C₄×C₈₉	—	8	1	no	—
305	C₄×C₈₉	#551	1	1	yes	characteristic
306	C₄×C₈₉	#551	1	1	yes	characteristic
307	C₄×C₈₉	#553	1	1	yes	characteristic
308	C₄×C₈₉	#553	1	1	yes	characteristic
309	#29375	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₂×C₈₉	—	8	2	no	—
311	C₂×C₈₉	#2598	1	1	yes	characteristic
312	C₂×C₈₉	#3102	1	1	yes	characteristic
313	C₂×C₈₉	#3107	1	1	yes	characteristic
314	C₂×C₈₉	#3111	1	1	yes	characteristic
315	C₂×C₈₉	#3117	1	1	yes	characteristic
316	C₂×C₈₉	#3211	1	1	yes	characteristic
317	C₂×C₈₉	#3216	1	1	yes	characteristic
318	C₄×#124	C₂×C₈₉	1	1	yes	characteristic
319	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
320	#2101	C₂×C₈₉	1	1	yes	characteristic, complemented
321	#2097	C₂×C₈₉	1	1	yes	characteristic, complemented
322	#2042	C₂×C₈₉	1	1	yes	characteristic
323	#2015	C₂×C₈₉	1	1	yes	characteristic
324	#1928	C₂×C₈₉	1	1	yes	characteristic, complemented
325	#1926	C₂×C₈₉	1	1	yes	characteristic
326	#1880	C₂×C₈₉	1	1	yes	characteristic
327	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
328	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
329	#1877	C₂×C₈₉	1	1	yes	characteristic
330	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
331	#1862	C₂×C₈₉	1	1	yes	characteristic
332	#1839	C₂×C₈₉	1	1	yes	characteristic, complemented
333	C₈₉	#29375	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
335	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
336	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
338	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
340	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
341	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
342	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
343	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
344	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
345	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
346	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
347	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
348	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
349	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
350	#391	C₂²×C₈₉	1	1	yes	characteristic
351	#391	C₂²×C₈₉	1	1	yes	characteristic
352	#391	C₂²×C₈₉	1	1	yes	characteristic
353	#390	C₂²×C₈₉	1	1	yes	characteristic
354	#389	C₂²×C₈₉	1	1	yes	characteristic
355	#389	C₂²×C₈₉	1	1	yes	characteristic
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#382	C₂²×C₈₉	1	1	yes	characteristic
361	C₄×C₄⋊C₄	—	2	1	no	—
362	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
363	C₄×C₂²⋊C₄	—	2	1	no	—
364	C₄×C₂²⋊C₄	—	2	1	no	—
365	#376	—	2	1	no	—
366	C₄³	C₂²×C₈₉	1	1	yes	characteristic
367	#340	C₂²×C₈₉	1	1	yes	characteristic
368	#340	C₂²×C₈₉	1	1	yes	characteristic
369	#340	C₂²×C₈₉	1	1	yes	characteristic
370	#340	C₂²×C₈₉	1	1	yes	characteristic
371	#336	C₂²×C₈₉	1	1	yes	characteristic
372	#336	C₂²×C₈₉	1	1	yes	characteristic
373	#336	C₂²×C₈₉	1	1	yes	characteristic
374	#336	C₂²×C₈₉	1	1	yes	characteristic
375	#336	C₂²×C₈₉	1	1	yes	characteristic
376	#336	C₂²×C₈₉	1	1	yes	characteristic
377	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂×Q₁₆	—	2	2	no	—
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	—	4	1	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	4	1	no	—
387	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
391	#124	—	2	2	no	—
392	#124	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	4	1	no	—
396	C₄×Q₈	—	4	1	no	—
397	C₄×D₄	—	4	1	no	—
398	C₄×D₄	—	4	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
417	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
418	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
419	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
423	#107	—	4	1	no	—
424	#106	—	4	1	no	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	4	1	no	—
428	#103	—	4	1	no	—
429	#103	—	4	1	no	—
430	#102	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	4	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	C₂⁴	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	#41×C₈₉	1	2	yes	—
456	C₂×Q₈	#41×C₈₉	1	2	yes	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	#41×C₈₉	1	2	yes	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
480	Q₁₆	—	4	4	no	—
481	SD₁₆	—	4	4	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	#41×C₈₉	1	2	yes	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	4	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	8	4	no	—
584	C₂×C₄	#135×C₈₉	1	2	yes	—
585	C₂×C₄	#137×C₈₉	1	2	yes	—
586	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
587	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
588	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
590	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
591	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	#525×C₈₉	1	1	yes	characteristic
604	C₂²	#525×C₈₉	1	1	yes	characteristic
605	C₂²	#535×C₈₉	1	1	yes	characteristic
606	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
607	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
608	C₂²	#575×C₈₉	1	1	yes	characteristic
609	C₂²	#575×C₈₉	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	#551×C₈₉	1	1	yes	characteristic
624	C₄	#551×C₈₉	1	1	yes	characteristic
625	C₄	#553×C₈₉	1	1	yes	characteristic
626	C₄	#553×C₈₉	1	1	yes	characteristic
627	C₂	—	8	2	no	—
628	C₂	C₈₉×#2598	1	1	yes	characteristic
629	C₂	C₈₉×#3102	1	1	yes	characteristic
630	C₂	C₈₉×#3107	1	1	yes	characteristic
631	C₂	C₈₉×#3111	1	1	yes	characteristic
632	C₂	C₈₉×#3117	1	1	yes	characteristic
633	C₂	C₈₉×#3211	1	1	yes	characteristic
634	C₂	C₈₉×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₈₉×#2295	C₂	semidirect
3. C₈₉×#2101	C₂	semidirect
4. C₈₉×#2097	C₂	semidirect
7. C₈₉×#1928	C₂	semidirect
10. C₈₉×#1878	C₂	semidirect
11. C₈₉×#1878	C₂	semidirect
13. C₈₉×#1865	C₂	semidirect
15. C₈₉×#1839	C₂	semidirect
309. #29375	C₈₉	direct (N × H)
319. #2295	C₂×C₈₉	semidirect
320. #2101	C₂×C₈₉	semidirect
321. #2097	C₂×C₈₉	semidirect
324. #1928	C₂×C₈₉	semidirect
327. #1878	C₂×C₈₉	semidirect
328. #1878	C₂×C₈₉	semidirect
330. #1865	C₂×C₈₉	semidirect
332. #1839	C₂×C₈₉	semidirect
333. C₈₉	#29375	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#124×C₈₉	2
C₈₉×#2295	2
C₈₉×#2101	2
C₈₉×#2097	2
C₈₉×#2042	2
C₈₉×#2015	2
C₈₉×#1928	2
C₈₉×#1926	2
C₈₉×#1880	2
C₈₉×#1878	2
C₈₉×#1877	2
C₈₉×#1865	2
C₈₉×#1862	2
C₈₉×#1839	2
#29375	89

Subgroups — C89×#29375 #36407223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29375 #36407223