Subgroups — C₂×C₈₉×#3037 #36438259

Order 22784.

2810 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3037	C₂	1	16	yes	maximal, direct product factor
5	C₂×#464×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₂×#462×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#460×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#423×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#417×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×#137×C₈₉	—	2	16	no	—
13	C₂×#137×C₈₉	C₂²	1	16	yes	complemented
14	C₂²×Q₁₆×C₈₉	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₈₉	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
17	#532×C₈₉	—	2	4	no	—
18	#532×C₈₉	C₂²	1	8	yes	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#121×C₈₉	—	2	1	no	—
23	C₂×#121×C₈₉	—	2	1	no	—
24	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
26	C₂×C₄×Q₈×C₈₉	—	2	4	no	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
30	C₂×C₄×D₄×C₈₉	—	2	1	no	—
31	C₂×C₄×D₄×C₈₉	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₈₉	—	2	1	no	—
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#464×C₈₉	C₂²	1	32	yes	complemented
37	#462×C₈₉	C₂²	1	16	yes	complemented
38	#460×C₈₉	C₂²	1	16	yes	complemented
39	#423×C₈₉	C₂²	1	8	yes	complemented
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
42	#417×C₈₉	C₂²	1	16	yes	complemented
43	C₂×#103×C₈₉	C₂²	1	4	yes	—
44	C₂×#102×C₈₉	C₂²	1	4	yes	—
45	C₂×#41×C₈₉	—	2	4	no	—
46	C₂×#41×C₈₉	—	2	8	no	—
47	C₂×#41×C₈₉	—	2	8	no	—
48	C₂×#41×C₈₉	C₂³	1	8	yes	—
49	C₂²×Q₈×C₈₉	—	2	2	no	—
50	C₂²×Q₈×C₈₉	—	2	1	no	—
51	C₂²×Q₈×C₈₉	—	2	4	no	—
52	C₂²×Q₈×C₈₉	D₄	1	8	yes	complemented
53	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
54	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
55	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
56	C₂²×D₄×C₈₉	—	2	2	no	—
57	C₂²×D₄×C₈₉	—	2	1	no	—
58	C₂²×D₄×C₈₉	—	2	1	no	—
59	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₈₉	—	2	1	no	—
61	C₂³×C₄×C₈₉	—	2	1	no	—
62	C₂³×C₄×C₈₉	—	2	2	no	—
63	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	#137×C₈₉	—	2	64	no	—
67	C₂×Q₁₆×C₈₉	—	2	16	no	—
68	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
69	C₂×SD₁₆×C₈₉	—	2	16	no	—
70	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
71	C₂×M₁₆×C₈₉	—	2	8	no	—
72	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
73	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
74	C₄⋊Q₈×C₈₉	—	2	2	no	—
75	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
76	#127×C₈₉	—	2	2	no	—
77	#127×C₈₉	C₂³	1	4	yes	—
78	#124×C₈₉	—	2	4	no	—
79	#124×C₈₉	C₂³	1	8	yes	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	—	2	8	no	—
82	C₄×Q₈×C₈₉	—	2	4	no	—
83	C₄×Q₈×C₈₉	—	2	4	no	—
84	C₄×Q₈×C₈₉	—	2	8	no	—
85	C₄×Q₈×C₈₉	—	2	8	no	—
86	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
87	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₄×D₄×C₈₉	—	2	8	no	—
90	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
101	C₂×C₄²×C₈₉	—	2	2	no	—
102	C₂×C₄²×C₈₉	—	2	2	no	—
103	C₂×C₄²×C₈₉	—	2	8	no	—
104	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	D₄	1	4	yes	—
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
110	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
111	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
112	#103×C₈₉	C₂³	1	16	yes	—
113	#102×C₈₉	C₂³	1	16	yes	—
114	C₂⁴×C₈₉	—	2	2	no	—
115	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
116	#41×C₈₉	—	2	16	no	—
117	#41×C₈₉	—	2	16	no	—
118	#41×C₈₉	—	4	16	no	—
119	C₂×Q₈×C₈₉	—	2	8	no	—
120	C₂×Q₈×C₈₉	—	2	16	no	—
121	C₂×Q₈×C₈₉	—	2	4	no	—
122	C₂×Q₈×C₈₉	—	2	2	no	—
123	C₂×Q₈×C₈₉	—	2	2	no	—
124	C₂×Q₈×C₈₉	—	2	4	no	—
125	C₂×Q₈×C₈₉	—	2	8	no	—
126	C₂×Q₈×C₈₉	—	2	4	no	—
127	C₂×Q₈×C₈₉	—	2	4	no	—
128	C₂×Q₈×C₈₉	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₈₉	C₂×D₄	1	16	yes	complemented
130	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
132	C₂×D₄×C₈₉	—	2	8	no	—
133	C₂×D₄×C₈₉	—	2	4	no	—
134	C₂×D₄×C₈₉	—	2	4	no	—
135	C₂×D₄×C₈₉	—	2	4	no	—
136	C₂×D₄×C₈₉	—	2	2	no	—
137	C₂×D₄×C₈₉	—	2	4	no	—
138	C₂×D₄×C₈₉	—	4	4	no	—
139	C₂×D₄×C₈₉	—	4	8	no	—
140	C₂×D₄×C₈₉	—	4	4	no	—
141	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₈₉	—	2	8	no	—
143	C₂²×C₄×C₈₉	—	2	4	no	—
144	C₂²×C₄×C₈₉	—	2	2	no	—
145	C₂²×C₄×C₈₉	—	2	4	no	—
146	C₂²×C₄×C₈₉	—	2	4	no	—
147	C₂²×C₄×C₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	2	no	—
149	C₂²×C₄×C₈₉	—	2	8	no	—
150	C₂²×C₄×C₈₉	—	4	2	no	—
151	C₂²×C₄×C₈₉	—	4	4	no	—
152	C₂²×C₄×C₈₉	—	4	8	no	—
153	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	4	yes	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	#41	1	4	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₈₉	—	2	32	no	—
166	SD₁₆×C₈₉	—	2	32	no	—
167	M₁₆×C₈₉	—	2	16	no	—
168	C₂×C₈×C₈₉	—	2	8	no	—
169	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
170	C₄⋊C₄×C₈₉	—	2	8	no	—
171	C₄⋊C₄×C₈₉	—	2	8	no	—
172	C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₄⋊C₄×C₈₉	—	2	2	no	—
174	C₄⋊C₄×C₈₉	—	2	4	no	—
175	C₄⋊C₄×C₈₉	—	2	4	no	—
176	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
177	C₂²⋊C₄×C₈₉	—	2	8	no	—
178	C₂²⋊C₄×C₈₉	—	2	8	no	—
179	C₄²×C₈₉	—	2	8	no	—
180	C₄²×C₈₉	—	2	8	no	—
181	C₄²×C₈₉	C₂×D₄	1	4	yes	—
182	C₄²×C₈₉	C₂×D₄	1	4	yes	—
183	C₄²×C₈₉	C₂×D₄	1	2	yes	—
184	C₄²×C₈₉	C₂×D₄	1	2	yes	—
185	C₄²×C₈₉	C₂⁴	1	2	yes	—
186	C₄²×C₈₉	C₂⁴	1	2	yes	—
187	C₂³×C₈₉	—	2	2	no	—
188	C₂³×C₈₉	—	2	2	no	—
189	C₂³×C₈₉	—	2	4	no	—
190	C₂³×C₈₉	—	4	4	no	—
191	C₂³×C₈₉	—	4	4	no	—
192	C₂³×C₈₉	—	4	4	no	—
193	C₂³×C₈₉	#121	1	4	yes	—
194	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
195	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₈₉	—	2	8	no	—
197	Q₈×C₈₉	—	2	16	no	—
198	Q₈×C₈₉	—	2	4	no	—
199	Q₈×C₈₉	—	2	4	no	—
200	Q₈×C₈₉	—	2	4	no	—
201	Q₈×C₈₉	—	4	4	no	—
202	Q₈×C₈₉	C₂²×D₄	1	8	yes	—
203	D₄×C₈₉	—	2	4	no	—
204	D₄×C₈₉	—	2	4	no	—
205	D₄×C₈₉	—	4	8	no	—
206	D₄×C₈₉	—	4	16	no	—
207	D₄×C₈₉	—	4	4	no	—
208	D₄×C₈₉	—	4	8	no	—
209	C₂×C₄×C₈₉	—	2	8	no	—
210	C₂×C₄×C₈₉	—	2	16	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	4	no	—
215	C₂×C₄×C₈₉	—	2	8	no	—
216	C₂×C₄×C₈₉	—	2	4	no	—
217	C₂×C₄×C₈₉	—	2	4	no	—
218	C₂×C₄×C₈₉	—	4	4	no	—
219	C₂×C₄×C₈₉	—	4	8	no	—
220	C₂×C₄×C₈₉	—	4	4	no	—
221	C₂×C₄×C₈₉	—	4	4	no	—
222	C₂×C₄×C₈₉	—	4	16	no	—
223	C₂×C₄×C₈₉	#121	1	4	yes	—
224	C₂×C₄×C₈₉	#121	1	8	yes	—
225	C₂×C₄×C₈₉	#137	1	4	yes	complemented
226	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
235	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
236	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
237	C₈×C₈₉	—	2	8	no	—
238	C₂²×C₈₉	—	2	8	no	—
239	C₂²×C₈₉	—	2	2	no	—
240	C₂²×C₈₉	—	2	2	no	—
241	C₂²×C₈₉	—	4	4	no	—
242	C₂²×C₈₉	—	4	4	no	—
243	C₂²×C₈₉	—	4	4	no	—
244	C₂²×C₈₉	—	8	8	no	—
245	C₂²×C₈₉	C₂×#121	1	4	yes	—
246	C₂²×C₈₉	C₂×#121	1	2	yes	—
247	C₂²×C₈₉	C₂×#137	1	2	yes	—
248	C₂²×C₈₉	#575	1	2	yes	—
249	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₈₉	—	2	8	no	—
251	C₄×C₈₉	—	2	2	no	—
252	C₄×C₈₉	—	2	2	no	—
253	C₄×C₈₉	—	2	2	no	—
254	C₄×C₈₉	—	4	4	no	—
255	C₄×C₈₉	—	4	4	no	—
256	C₄×C₈₉	C₂×#121	1	4	yes	—
257	C₄×C₈₉	C₂×#121	1	2	yes	—
258	C₄×C₈₉	C₂×#137	1	4	yes	complemented
259	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
261	C₂×#3037	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂×C₈₉	—	2	4	no	—
263	C₂×C₈₉	—	8	4	no	—
264	C₂×C₈₉	#3037	1	4	yes	direct product factor
265	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
266	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
267	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
268	C₂²×#137	C₂×C₈₉	1	2	yes	complemented
269	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
270	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
271	#3037	C₂×C₈₉	1	16	yes	direct product factor
272	C₂×#464	C₂×C₈₉	1	4	yes	complemented
273	C₂×#462	C₂×C₈₉	1	2	yes	complemented
274	C₂×#460	C₂×C₈₉	1	2	yes	complemented
275	C₂×#423	C₂×C₈₉	1	1	yes	characteristic, complemented
276	C₂×#417	C₂×C₈₉	1	2	yes	complemented
277	C₈₉	C₂×#3037	1	1	yes	characteristic, direct product factor, Sylow
278	C₂²×#41	C₂²×C₈₉	1	2	yes	—
279	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
280	C₂×#137	—	2	16	no	—
281	C₂×#137	C₂²×C₈₉	1	16	yes	complemented
282	C₂²×Q₁₆	C₂²×C₈₉	1	4	yes	—
283	C₂²×SD₁₆	C₂²×C₈₉	1	4	yes	—
284	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
285	#532	—	2	4	no	—
286	#532	C₂²×C₈₉	1	8	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
288	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
289	C₂×#124	C₂²×C₈₉	1	2	yes	—
290	C₂×#121	—	2	1	no	—
291	C₂×#121	—	2	1	no	—
292	C₂×C₄×Q₈	—	2	1	no	—
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×Q₈	—	2	4	no	—
295	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	—	2	1	no	—
300	C₂²×C₄⋊C₄	—	2	1	no	—
301	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
302	C₂²×C₄²	—	2	1	no	—
303	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
304	#464	C₂²×C₈₉	1	32	yes	complemented
305	#462	C₂²×C₈₉	1	16	yes	complemented
306	#460	C₂²×C₈₉	1	16	yes	complemented
307	#423	C₂²×C₈₉	1	8	yes	complemented
308	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
309	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
310	#417	C₂²×C₈₉	1	16	yes	complemented
311	C₂×#103	C₂²×C₈₉	1	4	yes	—
312	C₂×#102	C₂²×C₈₉	1	4	yes	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	C₂³×C₈₉	1	8	yes	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	2	4	no	—
320	C₂²×Q₈	D₄×C₈₉	1	8	yes	complemented
321	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
322	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
323	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	—	2	2	no	—
331	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
334	#137	—	2	64	no	—
335	C₂×Q₁₆	—	2	16	no	—
336	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
337	C₂×SD₁₆	—	2	16	no	—
338	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
339	C₂×M₁₆	—	2	8	no	—
340	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
341	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
344	#127	—	2	2	no	—
345	#127	C₂³×C₈₉	1	4	yes	—
346	#124	—	2	4	no	—
347	#124	C₂³×C₈₉	1	8	yes	—
348	#121	—	2	8	no	—
349	#121	—	2	8	no	—
350	C₄×Q₈	—	2	4	no	—
351	C₄×Q₈	—	2	4	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×Q₈	—	2	8	no	—
354	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
355	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	8	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	8	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	8	no	—
372	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
373	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
374	C₂×C₄²	D₄×C₈₉	1	4	yes	—
375	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
378	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
379	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
380	#103	C₂³×C₈₉	1	16	yes	—
381	#102	C₂³×C₈₉	1	16	yes	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
384	#41	—	2	16	no	—
385	#41	—	2	16	no	—
386	#41	—	4	16	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	16	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	C₂×D₄×C₈₉	1	8	yes	—
397	C₂×Q₈	C₂×D₄×C₈₉	1	16	yes	complemented
398	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
399	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	8	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
429	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
430	C₂²×C₄	#41×C₈₉	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
433	Q₁₆	—	2	32	no	—
434	SD₁₆	—	2	32	no	—
435	M₁₆	—	2	16	no	—
436	C₂×C₈	—	2	8	no	—
437	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₄²	—	2	8	no	—
448	C₄²	—	2	8	no	—
449	C₄²	C₂×D₄×C₈₉	1	4	yes	—
450	C₄²	C₂×D₄×C₈₉	1	4	yes	—
451	C₄²	C₂×D₄×C₈₉	1	2	yes	—
452	C₄²	C₂×D₄×C₈₉	1	2	yes	—
453	C₄²	C₂⁴×C₈₉	1	2	yes	—
454	C₄²	C₂⁴×C₈₉	1	2	yes	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	#121×C₈₉	1	4	yes	—
462	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
463	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
464	Q₈	—	2	8	no	—
465	Q₈	—	2	16	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	4	no	—
470	Q₈	C₂²×D₄×C₈₉	1	8	yes	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	16	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	8	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	#121×C₈₉	1	4	yes	—
492	C₂×C₄	#121×C₈₉	1	8	yes	—
493	C₂×C₄	#137×C₈₉	1	4	yes	complemented
494	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
502	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
503	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
504	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
505	C₈	—	2	8	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	8	8	no	—
513	C₂²	C₂×#121×C₈₉	1	4	yes	—
514	C₂²	C₂×#121×C₈₉	1	2	yes	—
515	C₂²	C₂×#137×C₈₉	1	2	yes	—
516	C₂²	#575×C₈₉	1	2	yes	—
517	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	8	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	C₂×#121×C₈₉	1	4	yes	—
525	C₄	C₂×#121×C₈₉	1	2	yes	—
526	C₄	C₂×#137×C₈₉	1	4	yes	complemented
527	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
528	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
529	C₂	—	2	4	no	—
530	C₂	—	8	4	no	—
531	C₂	C₈₉×#3037	1	4	yes	direct product factor
532	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
533	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
534	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
1. C₂²×#137×C₈₉	C₂	semidirect
3. C₂²×C₄×Q₈×C₈₉	C₂	semidirect
4. C₈₉×#3037	C₂	direct (N × H)
5. C₂×#464×C₈₉	C₂	semidirect
6. C₂×#462×C₈₉	C₂	semidirect
7. C₂×#460×C₈₉	C₂	semidirect
8. C₂×#423×C₈₉	C₂	semidirect
9. C₂×#417×C₈₉	C₂	semidirect
13. C₂×#137×C₈₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
36. #464×C₈₉	C₂²	semidirect
37. #462×C₈₉	C₂²	semidirect
38. #460×C₈₉	C₂²	semidirect
39. #423×C₈₉	C₂²	semidirect
42. #417×C₈₉	C₂²	semidirect
52. C₂²×Q₈×C₈₉	D₄	semidirect
129. C₂×Q₈×C₈₉	C₂×D₄	semidirect
225. C₂×C₄×C₈₉	#137	semidirect
258. C₄×C₈₉	C₂×#137	semidirect
261. C₂×#3037	C₈₉	direct (N × H)
264. C₂×C₈₉	#3037	direct (N × H)
268. C₂²×#137	C₂×C₈₉	semidirect
270. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
271. #3037	C₂×C₈₉	direct (N × H)
272. C₂×#464	C₂×C₈₉	semidirect
273. C₂×#462	C₂×C₈₉	semidirect
274. C₂×#460	C₂×C₈₉	semidirect
275. C₂×#423	C₂×C₈₉	semidirect
276. C₂×#417	C₂×C₈₉	semidirect
277. C₈₉	C₂×#3037	direct (N × H)
281. C₂×#137	C₂²×C₈₉	semidirect
297. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
304. #464	C₂²×C₈₉	semidirect
305. #462	C₂²×C₈₉	semidirect
306. #460	C₂²×C₈₉	semidirect
307. #423	C₂²×C₈₉	semidirect
310. #417	C₂²×C₈₉	semidirect
320. C₂²×Q₈	D₄×C₈₉	semidirect
397. C₂×Q₈	C₂×D₄×C₈₉	semidirect
493. C₂×C₄	#137×C₈₉	semidirect
526. C₄	C₂×#137×C₈₉	semidirect
531. C₂	C₈₉×#3037	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₈₉	2
C₂×#532×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#3037	2
C₂×#464×C₈₉	2
C₂×#462×C₈₉	2
C₂×#460×C₈₉	2
C₂×#423×C₈₉	2
C₂×#417×C₈₉	2
C₂×#3037	89

Subgroups — C2×C89×#3037 #36438259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3037 #36438259