Subgroups — C₂×C₈₉×#3234 #36438695

Order 22784.

2050 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3234	C₂	1	16	yes	maximal, direct product factor
4	C₂×#501×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#490×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#481×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#480×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#478×C₈₉	C₂	1	4	yes	maximal, complemented
9	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	—	2	1	no	—
11	#532×C₈₉	—	2	4	no	—
12	#532×C₈₉	C₂²	1	8	yes	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₈₉	—	2	1	no	—
16	C₂×#125×C₈₉	—	2	1	no	—
17	C₂×#125×C₈₉	—	2	4	no	—
18	C₂×#125×C₈₉	C₂²	1	2	yes	—
19	C₂×#125×C₈₉	C₂²	1	2	yes	—
20	C₂×#125×C₈₉	C₂²	1	8	yes	complemented
21	C₂×#124×C₈₉	—	2	1	no	—
22	C₂×#121×C₈₉	—	2	1	no	—
23	C₂×#121×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₈₉	—	2	1	no	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#501×C₈₉	C₂²	1	16	yes	complemented
32	#490×C₈₉	C₂²	1	16	yes	complemented
33	#481×C₈₉	C₂²	1	16	yes	complemented
34	#480×C₈₉	C₂²	1	16	yes	complemented
35	#478×C₈₉	C₂²	1	32	yes	complemented
36	#432×C₈₉	C₂²	1	8	yes	complemented
37	C₂×#107×C₈₉	C₂²	1	4	yes	—
38	C₂×#106×C₈₉	C₂²	1	4	yes	—
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
40	C₂×#102×C₈₉	C₂²	1	4	yes	—
41	C₂×#102×C₈₉	C₂²	1	4	yes	—
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×#97×C₈₉	C₂²	1	2	yes	—
44	C₂×#41×C₈₉	—	2	8	no	—
45	C₂×#41×C₈₉	—	4	8	no	—
46	C₂²×Q₈×C₈₉	—	2	1	no	—
47	C₂²×D₄×C₈₉	—	2	2	no	—
48	C₂²×D₄×C₈₉	—	2	1	no	—
49	C₂²×D₄×C₈₉	—	2	1	no	—
50	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	C₂³×C₄×C₈₉	—	2	1	no	—
53	C₂³×C₄×C₈₉	—	2	2	no	—
54	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
58	C₄⋊Q₈×C₈₉	—	2	2	no	—
59	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
60	#127×C₈₉	—	2	2	no	—
61	#127×C₈₉	C₂³	1	4	yes	—
62	#125×C₈₉	—	2	4	no	—
63	#125×C₈₉	—	2	4	no	—
64	#125×C₈₉	—	2	8	no	—
65	#125×C₈₉	—	2	8	no	—
66	#125×C₈₉	C₂³	1	8	yes	—
67	#125×C₈₉	C₂³	1	8	yes	—
68	#124×C₈₉	—	2	8	no	—
69	#121×C₈₉	—	2	8	no	—
70	#121×C₈₉	—	2	4	no	—
71	#121×C₈₉	C₂³	1	8	yes	—
72	C₄×D₄×C₈₉	—	2	8	no	—
73	C₄×D₄×C₈₉	—	2	4	no	—
74	C₄×D₄×C₈₉	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
93	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	D₄	1	4	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
99	#107×C₈₉	C₂³	1	16	yes	—
100	#106×C₈₉	C₂³	1	16	yes	—
101	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
102	#102×C₈₉	C₂³	1	16	yes	—
103	#102×C₈₉	C₂³	1	16	yes	—
104	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
105	#97×C₈₉	C₂³	1	8	yes	—
106	C₂⁴×C₈₉	—	2	2	no	—
107	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
108	#41×C₈₉	—	4	32	no	—
109	C₂×Q₈×C₈₉	—	2	4	no	—
110	C₂×Q₈×C₈₉	—	4	4	no	—
111	C₂×D₄×C₈₉	—	2	8	no	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	4	no	—
114	C₂×D₄×C₈₉	—	2	4	no	—
115	C₂×D₄×C₈₉	—	2	8	no	—
116	C₂×D₄×C₈₉	—	4	4	no	—
117	C₂×D₄×C₈₉	—	4	4	no	—
118	C₂×D₄×C₈₉	—	4	8	no	—
119	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₈₉	—	2	4	no	—
121	C₂²×C₄×C₈₉	—	2	4	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	2	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	8	no	—
128	C₂²×C₄×C₈₉	—	4	2	no	—
129	C₂²×C₄×C₈₉	—	4	8	no	—
130	C₂²×C₄×C₈₉	—	4	4	no	—
131	C₂²×C₄×C₈₉	—	4	4	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₈₉	—	2	8	no	—
143	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
144	C₄⋊C₄×C₈₉	—	2	8	no	—
145	C₄⋊C₄×C₈₉	—	2	8	no	—
146	C₄⋊C₄×C₈₉	—	2	8	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	4	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	2	4	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
156	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₄²×C₈₉	C₂×D₄	1	4	yes	—
160	C₄²×C₈₉	C₂×D₄	1	2	yes	—
161	C₄²×C₈₉	C₂×D₄	1	4	yes	—
162	C₄²×C₈₉	C₂×D₄	1	2	yes	—
163	C₄²×C₈₉	C₂⁴	1	2	yes	—
164	C₄²×C₈₉	C₂⁴	1	2	yes	—
165	C₂³×C₈₉	—	2	2	no	—
166	C₂³×C₈₉	—	2	2	no	—
167	C₂³×C₈₉	—	2	4	no	—
168	C₂³×C₈₉	—	4	4	no	—
169	C₂³×C₈₉	—	4	4	no	—
170	C₂³×C₈₉	—	4	4	no	—
171	C₂³×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₈₉	—	4	8	no	—
175	D₄×C₈₉	—	2	8	no	—
176	D₄×C₈₉	—	4	8	no	—
177	D₄×C₈₉	—	4	8	no	—
178	D₄×C₈₉	—	4	16	no	—
179	D₄×C₈₉	—	4	4	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	2	2	no	—
183	C₂×C₄×C₈₉	—	2	8	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	4	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	—	4	4	no	—
192	C₂×C₄×C₈₉	—	4	16	no	—
193	C₂×C₄×C₈₉	—	4	8	no	—
194	C₂×C₄×C₈₉	—	4	8	no	—
195	C₂×C₄×C₈₉	—	4	4	no	—
196	C₂×C₄×C₈₉	—	4	4	no	—
197	C₂×C₄×C₈₉	—	4	4	no	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
205	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
206	C₈×C₈₉	—	2	8	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	2	8	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	4	4	no	—
211	C₂²×C₈₉	—	4	4	no	—
212	C₂²×C₈₉	—	4	4	no	—
213	C₂²×C₈₉	—	8	8	no	—
214	C₂²×C₈₉	#536	1	2	yes	—
215	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
216	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₂²×C₈₉	#575	1	2	yes	—
218	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
219	C₄×C₈₉	—	2	2	no	—
220	C₄×C₈₉	—	2	2	no	—
221	C₄×C₈₉	—	2	2	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	—	4	4	no	—
225	C₄×C₈₉	—	4	4	no	—
226	C₄×C₈₉	—	4	4	no	—
227	C₄×C₈₉	#536	1	2	yes	—
228	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
229	C₂×#3234	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₈₉	—	2	4	no	—
231	C₂×C₈₉	—	8	4	no	—
232	C₂×C₈₉	#3234	1	4	yes	direct product factor
233	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
234	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
236	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
237	C₂²×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
238	#3234	C₂×C₈₉	1	16	yes	direct product factor
239	C₂×#501	C₂×C₈₉	1	2	yes	complemented
240	C₂×#490	C₂×C₈₉	1	2	yes	complemented
241	C₂×#481	C₂×C₈₉	1	2	yes	complemented
242	C₂×#480	C₂×C₈₉	1	2	yes	complemented
243	C₂×#478	C₂×C₈₉	1	4	yes	complemented
244	C₂×#432	C₂×C₈₉	1	1	yes	characteristic, complemented
245	C₈₉	C₂×#3234	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#41	—	2	1	no	—
247	#532	—	2	4	no	—
248	#532	C₂²×C₈₉	1	8	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×#125	—	2	1	no	—
252	C₂×#125	—	2	1	no	—
253	C₂×#125	—	2	4	no	—
254	C₂×#125	C₂²×C₈₉	1	2	yes	—
255	C₂×#125	C₂²×C₈₉	1	2	yes	—
256	C₂×#125	C₂²×C₈₉	1	8	yes	complemented
257	C₂×#124	—	2	1	no	—
258	C₂×#121	—	2	1	no	—
259	C₂×#121	C₂²×C₈₉	1	2	yes	—
260	C₂×C₄×D₄	—	2	1	no	—
261	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
262	C₂²×C₄⋊C₄	—	2	1	no	—
263	C₂²×C₄⋊C₄	—	2	1	no	—
264	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
266	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
267	#501	C₂²×C₈₉	1	16	yes	complemented
268	#490	C₂²×C₈₉	1	16	yes	complemented
269	#481	C₂²×C₈₉	1	16	yes	complemented
270	#480	C₂²×C₈₉	1	16	yes	complemented
271	#478	C₂²×C₈₉	1	32	yes	complemented
272	#432	C₂²×C₈₉	1	8	yes	complemented
273	C₂×#107	C₂²×C₈₉	1	4	yes	—
274	C₂×#106	C₂²×C₈₉	1	4	yes	—
275	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
276	C₂×#102	C₂²×C₈₉	1	4	yes	—
277	C₂×#102	C₂²×C₈₉	1	4	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
279	C₂×#97	C₂²×C₈₉	1	2	yes	—
280	C₂×#41	—	2	8	no	—
281	C₂×#41	—	4	8	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
296	#127	—	2	2	no	—
297	#127	C₂³×C₈₉	1	4	yes	—
298	#125	—	2	4	no	—
299	#125	—	2	4	no	—
300	#125	—	2	8	no	—
301	#125	—	2	8	no	—
302	#125	C₂³×C₈₉	1	8	yes	—
303	#125	C₂³×C₈₉	1	8	yes	—
304	#124	—	2	8	no	—
305	#121	—	2	8	no	—
306	#121	—	2	4	no	—
307	#121	C₂³×C₈₉	1	8	yes	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	C₂³×C₈₉	1	8	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	8	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
330	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
331	C₂×C₄²	D₄×C₈₉	1	4	yes	—
332	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
335	#107	C₂³×C₈₉	1	16	yes	—
336	#106	C₂³×C₈₉	1	16	yes	—
337	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
338	#102	C₂³×C₈₉	1	16	yes	—
339	#102	C₂³×C₈₉	1	16	yes	—
340	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
341	#97	C₂³×C₈₉	1	8	yes	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
344	#41	—	4	32	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
375	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₄²	C₂×D₄×C₈₉	1	4	yes	—
396	C₄²	C₂×D₄×C₈₉	1	2	yes	—
397	C₄²	C₂×D₄×C₈₉	1	4	yes	—
398	C₄²	C₂×D₄×C₈₉	1	2	yes	—
399	C₄²	C₂⁴×C₈₉	1	2	yes	—
400	C₄²	C₂⁴×C₈₉	1	2	yes	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	4	no	—
407	C₂³	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
408	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
409	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
410	Q₈	—	4	8	no	—
411	D₄	—	2	8	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	16	no	—
415	D₄	—	4	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
440	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
441	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
442	C₈	—	2	8	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	8	no	—
450	C₂²	#536×C₈₉	1	2	yes	—
451	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
452	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
453	C₂²	#575×C₈₉	1	2	yes	—
454	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	#536×C₈₉	1	2	yes	—
464	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
465	C₂	—	2	4	no	—
466	C₂	—	8	4	no	—
467	C₂	C₈₉×#3234	1	4	yes	direct product factor
468	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
469	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
470	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#125×C₈₉	C₂	semidirect
3. C₈₉×#3234	C₂	direct (N × H)
4. C₂×#501×C₈₉	C₂	semidirect
5. C₂×#490×C₈₉	C₂	semidirect
6. C₂×#481×C₈₉	C₂	semidirect
7. C₂×#480×C₈₉	C₂	semidirect
8. C₂×#478×C₈₉	C₂	semidirect
9. C₂×#432×C₈₉	C₂	semidirect
20. C₂×#125×C₈₉	C₂²	semidirect
31. #501×C₈₉	C₂²	semidirect
32. #490×C₈₉	C₂²	semidirect
33. #481×C₈₉	C₂²	semidirect
34. #480×C₈₉	C₂²	semidirect
35. #478×C₈₉	C₂²	semidirect
36. #432×C₈₉	C₂²	semidirect
229. C₂×#3234	C₈₉	direct (N × H)
232. C₂×C₈₉	#3234	direct (N × H)
237. C₂²×#125	C₂×C₈₉	semidirect
238. #3234	C₂×C₈₉	direct (N × H)
239. C₂×#501	C₂×C₈₉	semidirect
240. C₂×#490	C₂×C₈₉	semidirect
241. C₂×#481	C₂×C₈₉	semidirect
242. C₂×#480	C₂×C₈₉	semidirect
243. C₂×#478	C₂×C₈₉	semidirect
244. C₂×#432	C₂×C₈₉	semidirect
245. C₈₉	C₂×#3234	direct (N × H)
256. C₂×#125	C₂²×C₈₉	semidirect
267. #501	C₂²×C₈₉	semidirect
268. #490	C₂²×C₈₉	semidirect
269. #481	C₂²×C₈₉	semidirect
270. #480	C₂²×C₈₉	semidirect
271. #478	C₂²×C₈₉	semidirect
272. #432	C₂²×C₈₉	semidirect
467. C₂	C₈₉×#3234	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×#532×C₈₉	2
C₂²×#125×C₈₉	2
C₈₉×#3234	2
C₂×#501×C₈₉	2
C₂×#490×C₈₉	2
C₂×#481×C₈₉	2
C₂×#480×C₈₉	2
C₂×#478×C₈₉	2
C₂×#432×C₈₉	2
C₂×#3234	89

Subgroups — C2×C89×#3234 #36438695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3234 #36438695