Subgroups — C₈₉×#23643 #36401491

Order 22784.

1014 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#408×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2077	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2077	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2076	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2075	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#340×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	#428×C₈₉	—	2	4	no	—
20	C₂×#107×C₈₉	C₂²	1	2	yes	—
21	C₂×#106×C₈₉	C₂²	1	2	yes	—
22	#408×C₈₉	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
25	#391×C₈₉	—	2	1	no	—
26	#391×C₈₉	—	2	1	no	—
27	#390×C₈₉	—	2	1	no	—
28	#390×C₈₉	—	2	1	no	—
29	#386×C₈₉	—	2	2	no	—
30	#386×C₈₉	—	2	2	no	—
31	#380×C₈₉	C₂²	1	2	yes	—
32	#380×C₈₉	C₂²	1	2	yes	—
33	#380×C₈₉	C₂²	1	2	yes	—
34	#380×C₈₉	C₂²	1	2	yes	—
35	#340×C₈₉	C₂²	1	1	yes	characteristic
36	#340×C₈₉	C₂²	1	2	yes	—
37	#340×C₈₉	C₂²	1	2	yes	—
38	#340×C₈₉	C₂²	1	1	yes	characteristic
39	#340×C₈₉	C₂²	1	2	yes	—
40	#340×C₈₉	C₂²	1	2	yes	—
41	#340×C₈₉	C₂²	1	1	yes	characteristic
42	#340×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#41×C₈₉	—	2	2	no	—
44	C₂×#41×C₈₉	—	2	2	no	—
45	C₂×#41×C₈₉	—	2	2	no	—
46	C₂×#41×C₈₉	—	2	2	no	—
47	C₂×#41×C₈₉	—	2	2	no	—
48	C₂×#41×C₈₉	—	2	2	no	—
49	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₈₉	D₄	1	2	yes	—
51	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	—	2	1	no	—
53	C₂³×C₄×C₈₉	—	2	1	no	—
54	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₈₉	—	2	2	no	—
57	C₂×M₁₆×C₈₉	—	2	2	no	—
58	C₂×M₁₆×C₈₉	D₄	1	4	yes	—
59	C₂²×C₈×C₈₉	—	2	2	no	—
60	C₂²×C₈×C₈₉	—	2	2	no	—
61	C₂²×C₈×C₈₉	—	2	2	no	—
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
65	#117×C₈₉	—	2	2	no	—
66	#117×C₈₉	—	2	2	no	—
67	#117×C₈₉	—	2	2	no	—
68	#117×C₈₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
87	C₂×C₄²×C₈₉	—	2	1	no	—
88	C₂×C₄²×C₈₉	—	2	1	no	—
89	#107×C₈₉	—	2	4	no	—
90	#106×C₈₉	—	2	4	no	—
91	C₂²⋊C₈×C₈₉	—	2	4	no	—
92	C₂²⋊C₈×C₈₉	—	2	4	no	—
93	#95×C₈₉	—	2	2	no	—
94	#95×C₈₉	—	2	2	no	—
95	#95×C₈₉	—	2	2	no	—
96	#95×C₈₉	—	2	2	no	—
97	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
98	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
99	#41×C₈₉	—	4	4	no	—
100	#41×C₈₉	—	4	4	no	—
101	#41×C₈₉	—	4	4	no	—
102	#41×C₈₉	—	4	4	no	—
103	C₂×Q₈×C₈₉	—	2	2	no	—
104	C₂×Q₈×C₈₉	—	2	2	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	4	no	—
107	C₂×D₄×C₈₉	—	2	4	no	—
108	C₂×D₄×C₈₉	—	2	4	no	—
109	C₂×D₄×C₈₉	—	2	2	no	—
110	C₂×D₄×C₈₉	—	2	2	no	—
111	C₂×D₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	—	2	1	no	—
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	—	2	2	no	—
123	C₂²×C₄×C₈₉	—	2	2	no	—
124	C₂²×C₄×C₈₉	—	4	2	no	—
125	C₂²×C₄×C₈₉	—	4	2	no	—
126	C₂²×C₄×C₈₉	—	8	1	no	—
127	C₂²×C₄×C₈₉	—	8	1	no	—
128	C₂²×C₄×C₈₉	—	8	1	no	—
129	C₂²×C₄×C₈₉	—	8	1	no	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	#41	1	2	yes	—
134	C₂²×C₄×C₈₉	#41	1	2	yes	—
135	C₂²×C₄×C₈₉	#41	1	2	yes	—
136	C₂²×C₄×C₈₉	#41	1	2	yes	—
137	C₂²×C₄×C₈₉	#41	1	2	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₈₉	—	2	8	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	4	4	no	—
149	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	—	2	2	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	4	2	no	—
163	C₄⋊C₄×C₈₉	—	4	2	no	—
164	C₂²⋊C₄×C₈₉	—	4	2	no	—
165	C₂²⋊C₄×C₈₉	—	4	2	no	—
166	C₂²⋊C₄×C₈₉	—	8	2	no	—
167	C₂²⋊C₄×C₈₉	—	8	2	no	—
168	C₂²⋊C₄×C₈₉	—	8	2	no	—
169	C₂²⋊C₄×C₈₉	—	8	2	no	—
170	C₄²×C₈₉	—	4	2	no	—
171	C₄²×C₈₉	—	4	2	no	—
172	C₂³×C₈₉	—	2	1	no	—
173	C₂³×C₈₉	—	2	1	no	—
174	C₂³×C₈₉	—	2	1	no	—
175	C₂³×C₈₉	—	2	1	no	—
176	C₂³×C₈₉	—	2	2	no	—
177	C₂³×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	2	2	no	—
179	C₂³×C₈₉	—	2	2	no	—
180	C₂³×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	#121	1	2	yes	—
184	C₂³×C₈₉	#123	1	2	yes	—
185	C₂³×C₈₉	#123	1	2	yes	—
186	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₈₉	—	4	4	no	—
188	D₄×C₈₉	—	4	8	no	—
189	D₄×C₈₉	—	4	4	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	4	2	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	4	2	no	—
203	C₂×C₄×C₈₉	—	4	1	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	4	2	no	—
206	C₂×C₄×C₈₉	—	4	2	no	—
207	C₂×C₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	—	4	2	no	—
210	C₂×C₄×C₈₉	—	4	2	no	—
211	C₂×C₄×C₈₉	—	4	1	no	—
212	C₂×C₄×C₈₉	—	4	1	no	—
213	C₂×C₄×C₈₉	—	4	1	no	—
214	C₂×C₄×C₈₉	—	4	1	no	—
215	C₂×C₄×C₈₉	—	8	4	no	—
216	C₂×C₄×C₈₉	—	8	4	no	—
217	C₂×C₄×C₈₉	#121	1	2	yes	—
218	C₂×C₄×C₈₉	#123	1	4	yes	—
219	C₂×C₄×C₈₉	#123	1	2	yes	—
220	C₂×C₄×C₈₉	#123	1	2	yes	—
221	C₂×C₄×C₈₉	#124	1	4	yes	—
222	C₂×C₄×C₈₉	#126	1	4	yes	—
223	C₂×C₄×C₈₉	#126	1	4	yes	—
224	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
230	C₈×C₈₉	—	2	4	no	—
231	C₈×C₈₉	—	4	1	no	—
232	C₈×C₈₉	—	4	1	no	—
233	C₂²×C₈₉	—	2	2	no	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	2	2	no	—
236	C₂²×C₈₉	—	2	2	no	—
237	C₂²×C₈₉	—	2	2	no	—
238	C₂²×C₈₉	—	2	2	no	—
239	C₂²×C₈₉	—	4	2	no	—
240	C₂²×C₈₉	—	4	2	no	—
241	C₂²×C₈₉	—	4	2	no	—
242	C₂²×C₈₉	—	4	2	no	—
243	C₂²×C₈₉	—	4	2	no	—
244	C₂²×C₈₉	—	4	2	no	—
245	C₂²×C₈₉	—	4	2	no	—
246	C₂²×C₈₉	#397	1	4	yes	—
247	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
248	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
249	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
250	C₂²×C₈₉	#576	1	1	yes	characteristic
251	C₂²×C₈₉	#577	1	1	yes	characteristic
252	C₂²×C₈₉	#577	1	1	yes	characteristic
253	C₂²×C₈₉	#578	1	1	yes	characteristic
254	C₄×C₈₉	—	4	2	no	—
255	C₄×C₈₉	—	8	2	no	—
256	C₄×C₈₉	—	8	1	no	—
257	C₄×C₈₉	—	8	1	no	—
258	C₄×C₈₉	—	8	1	no	—
259	C₄×C₈₉	—	8	2	no	—
260	C₄×C₈₉	—	8	1	no	—
261	C₄×C₈₉	#397	1	4	yes	—
262	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
263	C₄×C₈₉	C₂×#124	1	1	yes	characteristic
264	C₄×C₈₉	C₂×#126	1	1	yes	characteristic
265	C₄×C₈₉	C₂×#126	1	1	yes	characteristic
266	#23643	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂×C₈₉	—	2	4	no	—
268	C₂×C₈₉	—	8	2	no	—
269	C₂×C₈₉	C₂×#397	1	1	yes	characteristic
270	C₂×C₈₉	#3062	1	1	yes	characteristic
271	C₂×C₈₉	#3063	1	1	yes	characteristic
272	C₂×C₈₉	#3096	1	1	yes	characteristic
273	C₂×C₈₉	#3097	1	1	yes	characteristic
274	C₂×C₈₉	#3098	1	1	yes	characteristic
275	C₂×C₈₉	#3099	1	1	yes	characteristic
276	C₂×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
277	C₂×#408	C₂×C₈₉	1	1	yes	characteristic
278	#2311	C₂×C₈₉	1	1	yes	characteristic
279	#2311	C₂×C₈₉	1	1	yes	characteristic
280	#2077	C₂×C₈₉	1	2	yes	complemented
281	#2077	C₂×C₈₉	1	2	yes	complemented
282	#2076	C₂×C₈₉	1	2	yes	complemented
283	#2075	C₂×C₈₉	1	2	yes	complemented
284	#1736	C₂×C₈₉	1	1	yes	characteristic, complemented
285	#1735	C₂×C₈₉	1	1	yes	characteristic, complemented
286	C₂×#340	C₂×C₈₉	1	1	yes	characteristic, complemented
287	C₈₉	#23643	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
289	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
290	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
291	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
292	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
295	#428	—	2	4	no	—
296	C₂×#107	C₂²×C₈₉	1	2	yes	—
297	C₂×#106	C₂²×C₈₉	1	2	yes	—
298	#408	—	2	4	no	—
299	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
300	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
301	#391	—	2	1	no	—
302	#391	—	2	1	no	—
303	#390	—	2	1	no	—
304	#390	—	2	1	no	—
305	#386	—	2	2	no	—
306	#386	—	2	2	no	—
307	#380	C₂²×C₈₉	1	2	yes	—
308	#380	C₂²×C₈₉	1	2	yes	—
309	#380	C₂²×C₈₉	1	2	yes	—
310	#380	C₂²×C₈₉	1	2	yes	—
311	#340	C₂²×C₈₉	1	1	yes	characteristic
312	#340	C₂²×C₈₉	1	2	yes	—
313	#340	C₂²×C₈₉	1	2	yes	—
314	#340	C₂²×C₈₉	1	1	yes	characteristic
315	#340	C₂²×C₈₉	1	2	yes	—
316	#340	C₂²×C₈₉	1	2	yes	—
317	#340	C₂²×C₈₉	1	1	yes	characteristic
318	#340	C₂²×C₈₉	1	1	yes	characteristic
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
326	C₂²×D₄	D₄×C₈₉	1	2	yes	—
327	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
331	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	D₄×C₈₉	1	4	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	#107	—	2	4	no	—
366	#106	—	2	4	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
374	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	4	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	8	1	no	—
403	C₂²×C₄	—	8	1	no	—
404	C₂²×C₄	—	8	1	no	—
405	C₂²×C₄	—	8	1	no	—
406	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
409	C₂²×C₄	#41×C₈₉	1	2	yes	—
410	C₂²×C₄	#41×C₈₉	1	2	yes	—
411	C₂²×C₄	#41×C₈₉	1	2	yes	—
412	C₂²×C₄	#41×C₈₉	1	2	yes	—
413	C₂²×C₄	#41×C₈₉	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
415	M₁₆	—	2	8	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	4	4	no	—
425	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	8	2	no	—
443	C₂²⋊C₄	—	8	2	no	—
444	C₂²⋊C₄	—	8	2	no	—
445	C₂²⋊C₄	—	8	2	no	—
446	C₄²	—	4	2	no	—
447	C₄²	—	4	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	#121×C₈₉	1	2	yes	—
460	C₂³	#123×C₈₉	1	2	yes	—
461	C₂³	#123×C₈₉	1	2	yes	—
462	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
463	Q₈	—	4	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	#121×C₈₉	1	2	yes	—
494	C₂×C₄	#123×C₈₉	1	2	yes	—
495	C₂×C₄	#123×C₈₉	1	2	yes	—
496	C₂×C₄	#123×C₈₉	1	4	yes	—
497	C₂×C₄	#124×C₈₉	1	4	yes	—
498	C₂×C₄	#126×C₈₉	1	4	yes	—
499	C₂×C₄	#126×C₈₉	1	4	yes	—
500	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#397×C₈₉	1	4	yes	—
523	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
524	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
525	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
526	C₂²	#576×C₈₉	1	1	yes	characteristic
527	C₂²	#577×C₈₉	1	1	yes	characteristic
528	C₂²	#577×C₈₉	1	1	yes	characteristic
529	C₂²	#578×C₈₉	1	1	yes	characteristic
530	C₄	—	4	2	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	2	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	#397×C₈₉	1	4	yes	—
538	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
539	C₄	C₂×#124×C₈₉	1	1	yes	characteristic
540	C₄	C₂×#126×C₈₉	1	1	yes	characteristic
541	C₄	C₂×#126×C₈₉	1	1	yes	characteristic
542	C₂	—	2	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₂×#397×C₈₉	1	1	yes	characteristic
545	C₂	C₈₉×#3062	1	1	yes	characteristic
546	C₂	C₈₉×#3063	1	1	yes	characteristic
547	C₂	C₈₉×#3096	1	1	yes	characteristic
548	C₂	C₈₉×#3097	1	1	yes	characteristic
549	C₂	C₈₉×#3098	1	1	yes	characteristic
550	C₂	C₈₉×#3099	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₈₉	C₂	semidirect
5. C₈₉×#2077	C₂	semidirect
6. C₈₉×#2077	C₂	semidirect
7. C₈₉×#2076	C₂	semidirect
8. C₈₉×#2075	C₂	semidirect
9. C₈₉×#1736	C₂	semidirect
10. C₈₉×#1735	C₂	semidirect
11. C₂×#340×C₈₉	C₂	semidirect
266. #23643	C₈₉	direct (N × H)
276. C₂×#428	C₂×C₈₉	semidirect
280. #2077	C₂×C₈₉	semidirect
281. #2077	C₂×C₈₉	semidirect
282. #2076	C₂×C₈₉	semidirect
283. #2075	C₂×C₈₉	semidirect
284. #1736	C₂×C₈₉	semidirect
285. #1735	C₂×C₈₉	semidirect
286. C₂×#340	C₂×C₈₉	semidirect
287. C₈₉	#23643	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#428×C₈₉	2
C₂×#408×C₈₉	2
C₈₉×#2311	2
C₈₉×#2077	2
C₈₉×#2076	2
C₈₉×#2075	2
C₈₉×#1736	2
C₈₉×#1735	2
C₂×#340×C₈₉	2
#23643	89

Subgroups — C89×#23643 #36401491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23643 #36401491