Subgroups — C₈₉×#11176 #36389024

Order 22784.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2896	C₂	1	1	yes	maximal, characteristic
2	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#410×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×H(3,ℤ/4)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
15	#419×C₈₉	—	2	1	no	—
16	#418×C₈₉	—	2	1	no	—
17	#417×C₈₉	—	2	2	no	—
18	#416×C₈₉	—	2	2	no	—
19	#416×C₈₉	—	2	2	no	—
20	#416×C₈₉	C₄	1	4	yes	complemented
21	C₂×#103×C₈₉	—	2	1	no	—
22	C₂×#102×C₈₉	—	2	1	no	—
23	#410×C₈₉	—	2	2	no	—
24	#410×C₈₉	—	2	2	no	—
25	C₂×#99×C₈₉	—	2	2	no	—
26	#342×C₈₉	—	2	2	no	—
27	#340×C₈₉	—	2	2	no	—
28	H(3,ℤ/4)×C₈₉	—	2	2	no	—
29	#336×C₈₉	—	2	2	no	—
30	C₂×#41×C₈₉	—	2	1	no	—
31	C₂×#41×C₈₉	—	2	1	no	—
32	C₂×#41×C₈₉	—	2	1	no	—
33	C₂×#41×C₈₉	—	2	1	no	—
34	C₂×#41×C₈₉	—	2	1	no	—
35	C₂×#41×C₈₉	—	2	1	no	—
36	C₂×#41×C₈₉	—	2	1	no	—
37	C₂×#41×C₈₉	—	2	1	no	—
38	C₂×#41×C₈₉	—	2	1	no	—
39	C₂×#41×C₈₉	—	2	1	no	—
40	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₈₉	D₄	1	2	yes	—
42	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₈₉	—	2	1	no	—
44	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	—	2	1	no	—
46	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₈₉	—	2	1	no	—
48	C₂×M₁₆×C₈₉	—	2	1	no	—
49	C₂×M₁₆×C₈₉	—	2	1	no	—
50	C₂×M₁₆×C₈₉	—	2	1	no	—
51	C₂×M₁₆×C₈₉	—	2	1	no	—
52	C₂×M₁₆×C₈₉	—	2	1	no	—
53	C₂²×C₈×C₈₉	—	2	1	no	—
54	C₂²×C₈×C₈₉	—	2	1	no	—
55	C₂²×C₈×C₈₉	—	2	1	no	—
56	C₂²×C₈×C₈₉	—	2	1	no	—
57	C₂²×C₈×C₈₉	—	2	1	no	—
58	C₂²×C₈×C₈₉	—	2	1	no	—
59	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₈₉	D₄	1	2	yes	—
61	#117×C₈₉	—	2	1	no	—
62	#117×C₈₉	—	2	1	no	—
63	#117×C₈₉	—	2	1	no	—
64	#117×C₈₉	—	2	1	no	—
65	#117×C₈₉	—	2	1	no	—
66	#117×C₈₉	—	2	1	no	—
67	#117×C₈₉	—	2	1	no	—
68	#117×C₈₉	—	2	1	no	—
69	#117×C₈₉	—	2	1	no	—
70	#117×C₈₉	—	2	1	no	—
71	#117×C₈₉	—	2	1	no	—
72	#117×C₈₉	—	2	1	no	—
73	#117×C₈₉	—	2	1	no	—
74	#117×C₈₉	—	2	1	no	—
75	#117×C₈₉	C₂×C₄	1	2	yes	—
76	#117×C₈₉	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
85	C₂×C₄²×C₈₉	—	2	1	no	—
86	C₂×C₄²×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	—	2	1	no	—
88	C₂×C₄²×C₈₉	—	2	1	no	—
89	#103×C₈₉	—	2	4	no	—
90	#103×C₈₉	—	2	4	no	—
91	#102×C₈₉	—	2	4	no	—
92	#102×C₈₉	—	2	4	no	—
93	#99×C₈₉	—	2	8	no	—
94	C₂⁴×C₈₉	—	2	1	no	—
95	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
96	#41×C₈₉	—	2	2	no	—
97	#41×C₈₉	—	2	2	no	—
98	#41×C₈₉	—	2	2	no	—
99	#41×C₈₉	—	2	2	no	—
100	#41×C₈₉	—	2	2	no	—
101	#41×C₈₉	—	2	2	no	—
102	#41×C₈₉	—	2	2	no	—
103	#41×C₈₉	—	2	2	no	—
104	#41×C₈₉	—	4	1	no	—
105	#41×C₈₉	—	4	1	no	—
106	#41×C₈₉	—	4	1	no	—
107	#41×C₈₉	—	4	1	no	—
108	#41×C₈₉	—	4	1	no	—
109	#41×C₈₉	—	4	1	no	—
110	#41×C₈₉	—	4	1	no	—
111	#41×C₈₉	—	4	1	no	—
112	C₂×Q₈×C₈₉	—	2	1	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	—	2	1	no	—
117	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	—	2	1	no	—
125	C₂×D₄×C₈₉	—	4	1	no	—
126	C₂×D₄×C₈₉	—	4	1	no	—
127	C₂×D₄×C₈₉	—	4	1	no	—
128	C₂×D₄×C₈₉	—	4	1	no	—
129	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	2	2	no	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	C₂²×C₄×C₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	—	4	1	no	—
136	C₂²×C₄×C₈₉	—	4	1	no	—
137	C₂²×C₄×C₈₉	—	4	1	no	—
138	C₂²×C₄×C₈₉	—	4	1	no	—
139	C₂²×C₄×C₈₉	—	4	1	no	—
140	C₂²×C₄×C₈₉	—	4	1	no	—
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
155	M₁₆×C₈₉	—	4	1	no	—
156	M₁₆×C₈₉	—	4	1	no	—
157	M₁₆×C₈₉	—	4	1	no	—
158	M₁₆×C₈₉	—	4	1	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	2	no	—
162	C₂×C₈×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	—	2	2	no	—
165	C₂×C₈×C₈₉	—	4	1	no	—
166	C₂×C₈×C₈₉	—	4	1	no	—
167	C₂×C₈×C₈₉	—	4	1	no	—
168	C₂×C₈×C₈₉	—	4	1	no	—
169	C₄⋊C₄×C₈₉	—	2	2	no	—
170	C₄⋊C₄×C₈₉	—	2	2	no	—
171	C₄⋊C₄×C₈₉	—	2	2	no	—
172	C₄⋊C₄×C₈₉	—	2	2	no	—
173	C₄⋊C₄×C₈₉	—	4	1	no	—
174	C₄⋊C₄×C₈₉	—	4	1	no	—
175	C₄⋊C₄×C₈₉	—	4	1	no	—
176	C₄⋊C₄×C₈₉	—	4	1	no	—
177	C₂²⋊C₄×C₈₉	—	2	2	no	—
178	C₂²⋊C₄×C₈₉	—	2	2	no	—
179	C₂²⋊C₄×C₈₉	—	2	2	no	—
180	C₂²⋊C₄×C₈₉	—	2	2	no	—
181	C₂²⋊C₄×C₈₉	—	4	1	no	—
182	C₂²⋊C₄×C₈₉	—	4	1	no	—
183	C₂²⋊C₄×C₈₉	—	4	1	no	—
184	C₂²⋊C₄×C₈₉	—	4	1	no	—
185	C₄²×C₈₉	—	2	2	no	—
186	C₄²×C₈₉	—	2	2	no	—
187	C₄²×C₈₉	—	4	1	no	—
188	C₄²×C₈₉	—	4	1	no	—
189	C₄²×C₈₉	—	4	1	no	—
190	C₄²×C₈₉	—	4	1	no	—
191	C₄²×C₈₉	—	4	1	no	—
192	C₄²×C₈₉	—	4	1	no	—
193	C₂³×C₈₉	—	2	2	no	—
194	C₂³×C₈₉	—	4	2	no	—
195	C₂³×C₈₉	—	4	1	no	—
196	C₂³×C₈₉	—	4	1	no	—
197	C₂³×C₈₉	—	8	2	no	—
198	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₈₉	#120	1	1	yes	characteristic
200	C₂³×C₈₉	#121	1	1	yes	characteristic
201	C₂³×C₈₉	#121	1	1	yes	characteristic
202	C₂³×C₈₉	#121	1	1	yes	characteristic
203	C₂³×C₈₉	#123	1	1	yes	characteristic
204	C₂³×C₈₉	#124	1	1	yes	characteristic
205	Q₈×C₈₉	—	2	2	no	—
206	Q₈×C₈₉	—	2	2	no	—
207	Q₈×C₈₉	—	4	1	no	—
208	Q₈×C₈₉	—	4	1	no	—
209	D₄×C₈₉	—	2	2	no	—
210	D₄×C₈₉	—	2	2	no	—
211	D₄×C₈₉	—	4	2	no	—
212	D₄×C₈₉	—	4	2	no	—
213	D₄×C₈₉	—	4	2	no	—
214	D₄×C₈₉	—	4	2	no	—
215	D₄×C₈₉	—	4	1	no	—
216	D₄×C₈₉	—	4	1	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	4	1	no	—
219	C₂×C₄×C₈₉	—	4	1	no	—
220	C₂×C₄×C₈₉	—	4	2	no	—
221	C₂×C₄×C₈₉	—	4	2	no	—
222	C₂×C₄×C₈₉	—	4	2	no	—
223	C₂×C₄×C₈₉	—	4	2	no	—
224	C₂×C₄×C₈₉	—	4	4	no	—
225	C₂×C₄×C₈₉	—	4	2	no	—
226	C₂×C₄×C₈₉	—	4	2	no	—
227	C₂×C₄×C₈₉	—	4	2	no	—
228	C₂×C₄×C₈₉	—	4	2	no	—
229	C₂×C₄×C₈₉	—	8	2	no	—
230	C₂×C₄×C₈₉	—	8	2	no	—
231	C₂×C₄×C₈₉	—	8	2	no	—
232	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
234	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
245	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
246	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
247	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
248	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
249	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
250	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
251	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
252	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
253	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
254	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
255	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
256	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
257	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
258	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
259	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
260	C₈×C₈₉	—	4	2	no	—
261	C₈×C₈₉	—	4	2	no	—
262	C₂²×C₈₉	—	2	2	no	—
263	C₂²×C₈₉	—	2	2	no	—
264	C₂²×C₈₉	—	2	2	no	—
265	C₂²×C₈₉	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	4	1	no	—
269	C₂²×C₈₉	—	4	2	no	—
270	C₂²×C₈₉	—	8	2	no	—
271	C₂²×C₈₉	—	8	2	no	—
272	C₂²×C₈₉	—	8	2	no	—
273	C₂²×C₈₉	#386	1	1	yes	characteristic
274	C₂²×C₈₉	#388	1	1	yes	characteristic
275	C₂²×C₈₉	#388	1	1	yes	characteristic
276	C₂²×C₈₉	#394	1	1	yes	characteristic
277	C₂²×C₈₉	#394	1	1	yes	characteristic
278	C₂²×C₈₉	#394	1	1	yes	characteristic
279	C₂²×C₈₉	#397	1	1	yes	characteristic
280	C₄×C₈₉	—	4	2	no	—
281	C₄×C₈₉	—	8	2	no	—
282	C₄×C₈₉	—	8	2	no	—
283	C₄×C₈₉	—	8	2	no	—
284	C₄×C₈₉	—	8	2	no	—
285	C₄×C₈₉	#381	1	1	yes	characteristic
286	C₄×C₈₉	#386	1	1	yes	characteristic
287	C₄×C₈₉	#388	1	1	yes	characteristic
288	C₄×C₈₉	#388	1	1	yes	characteristic
289	C₄×C₈₉	#394	1	1	yes	characteristic
290	C₄×C₈₉	#397	1	1	yes	characteristic
291	C₄×C₈₉	#397	1	1	yes	characteristic
292	C₄×C₈₉	#397	1	1	yes	characteristic
293	#11176	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂×C₈₉	—	2	1	no	—
295	C₂×C₈₉	—	2	1	no	—
296	C₂×C₈₉	—	2	1	no	—
297	C₂×C₈₉	—	2	1	no	—
298	C₂×C₈₉	—	2	1	no	—
299	C₂×C₈₉	—	2	1	no	—
300	C₂×C₈₉	—	8	2	no	—
301	C₂×C₈₉	#1440	1	1	yes	characteristic
302	C₂×C₈₉	#2053	1	2	yes	—
303	#2896	C₂×C₈₉	1	1	yes	characteristic
304	C₂×#416	C₂×C₈₉	1	1	yes	characteristic
305	C₂×#410	C₂×C₈₉	1	1	yes	characteristic
306	#1740	C₂×C₈₉	1	1	yes	characteristic, complemented
307	#1735	C₂×C₈₉	1	1	yes	characteristic, complemented
308	C₂×H(3,ℤ/4)	C₂×C₈₉	1	1	yes	characteristic, complemented
309	#1729	C₂×C₈₉	1	1	yes	characteristic, complemented
310	C₈₉	#11176	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
313	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
315	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
316	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
317	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
318	#419	—	2	1	no	—
319	#418	—	2	1	no	—
320	#417	—	2	2	no	—
321	#416	—	2	2	no	—
322	#416	—	2	2	no	—
323	#416	C₄×C₈₉	1	4	yes	complemented
324	C₂×#103	—	2	1	no	—
325	C₂×#102	—	2	1	no	—
326	#410	—	2	2	no	—
327	#410	—	2	2	no	—
328	C₂×#99	—	2	2	no	—
329	#342	—	2	2	no	—
330	#340	—	2	2	no	—
331	H(3,ℤ/4)	—	2	2	no	—
332	#336	—	2	2	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	C₂×C₄×C₈₉	1	2	yes	—
344	C₂×#41	D₄×C₈₉	1	2	yes	—
345	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
363	C₂²×C₈	D₄×C₈₉	1	2	yes	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	C₂×C₄×C₈₉	1	2	yes	—
379	#117	D₄×C₈₉	1	2	yes	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	#103	—	2	4	no	—
393	#103	—	2	4	no	—
394	#102	—	2	4	no	—
395	#102	—	2	4	no	—
396	#99	—	2	8	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₂²⋊C₄×C₈₉	1	2	yes	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
450	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
451	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
452	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
453	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
454	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
455	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
456	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
457	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
458	M₁₆	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	4	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	4	1	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	4	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	—	4	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	—	4	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	8	2	no	—
501	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
502	C₂³	#120×C₈₉	1	1	yes	characteristic
503	C₂³	#121×C₈₉	1	1	yes	characteristic
504	C₂³	#121×C₈₉	1	1	yes	characteristic
505	C₂³	#121×C₈₉	1	1	yes	characteristic
506	C₂³	#123×C₈₉	1	1	yes	characteristic
507	C₂³	#124×C₈₉	1	1	yes	characteristic
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
536	C₂×C₄	#117×C₈₉	1	1	yes	characteristic
537	C₂×C₄	#117×C₈₉	1	1	yes	characteristic
538	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
539	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
540	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
541	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
542	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
543	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
544	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
545	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
546	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
547	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
548	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
549	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
550	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
551	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
552	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
553	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
554	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
555	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
556	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
557	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
558	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
559	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
560	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
561	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
562	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
563	C₈	—	4	2	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	#386×C₈₉	1	1	yes	characteristic
577	C₂²	#388×C₈₉	1	1	yes	characteristic
578	C₂²	#388×C₈₉	1	1	yes	characteristic
579	C₂²	#394×C₈₉	1	1	yes	characteristic
580	C₂²	#394×C₈₉	1	1	yes	characteristic
581	C₂²	#394×C₈₉	1	1	yes	characteristic
582	C₂²	#397×C₈₉	1	1	yes	characteristic
583	C₄	—	4	2	no	—
584	C₄	—	8	2	no	—
585	C₄	—	8	2	no	—
586	C₄	—	8	2	no	—
587	C₄	—	8	2	no	—
588	C₄	#381×C₈₉	1	1	yes	characteristic
589	C₄	#386×C₈₉	1	1	yes	characteristic
590	C₄	#388×C₈₉	1	1	yes	characteristic
591	C₄	#388×C₈₉	1	1	yes	characteristic
592	C₄	#394×C₈₉	1	1	yes	characteristic
593	C₄	#397×C₈₉	1	1	yes	characteristic
594	C₄	#397×C₈₉	1	1	yes	characteristic
595	C₄	#397×C₈₉	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	8	2	no	—
603	C₂	C₈₉×#1440	1	1	yes	characteristic
604	C₂	C₈₉×#2053	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₉	#124
commutator	C₂²×C₄	C₂²×C₄×C₈₉
Frattini, cosocle	C₂³×C₄	C₂³×C₈₉
socle	C₂²×C₈₉	#394
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1740	C₂	semidirect
5. C₈₉×#1735	C₂	semidirect
6. C₂×H(3,ℤ/4)×C₈₉	C₂	semidirect
7. C₈₉×#1729	C₂	semidirect
20. #416×C₈₉	C₄	semidirect
293. #11176	C₈₉	direct (N × H)
306. #1740	C₂×C₈₉	semidirect
307. #1735	C₂×C₈₉	semidirect
308. C₂×H(3,ℤ/4)	C₂×C₈₉	semidirect
309. #1729	C₂×C₈₉	semidirect
310. C₈₉	#11176	direct (N × H)
323. #416	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2896	2
C₂×#416×C₈₉	2
C₂×#410×C₈₉	2
C₈₉×#1740	2
C₈₉×#1735	2
C₂×H(3,ℤ/4)×C₈₉	2
C₈₉×#1729	2
#11176	89

Subgroups — C89×#11176 #36389024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#11176 #36389024