Subgroups — C₂×C₈₉×#3116 #36438387

Order 22784.

2150 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	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3116	C₂	1	16	yes	maximal, direct product factor
4	C₂×#485×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#477×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#476×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#462×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#452×C₈₉	C₂	1	2	yes	maximal
10	C₂×#441×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₂×#440×C₈₉	C₂	1	2	yes	maximal, complemented
12	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
16	#533×C₈₉	—	2	4	no	—
17	#533×C₈₉	C₂²	1	8	yes	complemented
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₈₉	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
23	C₄×#41×C₈₉	—	2	4	no	—
24	C₄×#41×C₈₉	C₂²	1	8	yes	—
25	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	—	2	1	no	—
30	C₂×C₄×D₄×C₈₉	—	2	1	no	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	—	2	1	no	—
34	C₂×#117×C₈₉	—	2	1	no	—
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₈₉	—	2	1	no	—
37	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
38	#485×C₈₉	C₂²	1	16	yes	complemented
39	#477×C₈₉	C₂²	1	8	yes	complemented
40	#476×C₈₉	C₂²	1	8	yes	complemented
41	#462×C₈₉	C₂²	1	8	yes	complemented
42	#461×C₈₉	C₂²	1	8	yes	complemented
43	#452×C₈₉	C₂²	1	16	yes	—
44	#441×C₈₉	C₂²	1	16	yes	complemented
45	#440×C₈₉	C₂²	1	16	yes	complemented
46	#432×C₈₉	C₂²	1	8	yes	complemented
47	C₂×#107×C₈₉	C₂²	1	2	yes	—
48	C₂×#106×C₈₉	C₂²	1	2	yes	—
49	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#103×C₈₉	C₂²	1	2	yes	—
52	C₂×#103×C₈₉	C₂²	1	2	yes	—
53	C₂×#103×C₈₉	C₂²	1	2	yes	—
54	C₂×#102×C₈₉	C₂²	1	2	yes	—
55	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
56	C₂×#97×C₈₉	C₂²	1	2	yes	—
57	C₂×#41×C₈₉	—	2	4	no	—
58	C₂×#41×C₈₉	—	2	4	no	—
59	C₂×#41×C₈₉	—	2	2	no	—
60	C₂×#41×C₈₉	C₂³	1	4	yes	—
61	C₂²×Q₈×C₈₉	—	2	1	no	—
62	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
63	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	—	2	1	no	—
65	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₈₉	—	2	1	no	—
67	C₂³×C₄×C₈₉	—	2	1	no	—
68	C₂³×C₄×C₈₉	—	2	1	no	—
69	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×Q₁₆×C₈₉	—	2	8	no	—
73	C₂×Q₁₆×C₈₉	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₈₉	—	2	8	no	—
75	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
76	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
78	C₄⋊Q₈×C₈₉	—	2	2	no	—
79	C₄⋊Q₈×C₈₉	—	2	2	no	—
80	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
81	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
82	#125×C₈₉	—	2	8	no	—
83	C₂²⋊Q₈×C₈₉	—	2	8	no	—
84	C₂²⋊Q₈×C₈₉	—	2	4	no	—
85	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
86	C₄×Q₈×C₈₉	—	2	8	no	—
87	C₄×Q₈×C₈₉	—	2	2	no	—
88	C₄×Q₈×C₈₉	—	2	2	no	—
89	C₄×Q₈×C₈₉	—	2	4	no	—
90	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
91	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
92	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
93	C₄×D₄×C₈₉	—	2	8	no	—
94	C₄×D₄×C₈₉	—	2	8	no	—
95	C₄×D₄×C₈₉	—	2	2	no	—
96	C₄×D₄×C₈₉	—	2	2	no	—
97	C₄×D₄×C₈₉	C₂³	1	4	yes	—
98	C₄×D₄×C₈₉	C₂³	1	4	yes	—
99	#117×C₈₉	—	2	8	no	—
100	#117×C₈₉	—	2	2	no	—
101	#117×C₈₉	—	2	8	no	—
102	#117×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₄²×C₈₉	—	2	1	no	—
118	C₂×C₄²×C₈₉	—	2	1	no	—
119	C₂×C₄²×C₈₉	—	2	1	no	—
120	C₂×C₄²×C₈₉	—	2	2	no	—
121	C₂×C₄²×C₈₉	—	2	8	no	—
122	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	D₄	1	4	yes	—
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
128	#107×C₈₉	C₂³	1	8	yes	—
129	#106×C₈₉	C₂³	1	8	yes	—
130	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
131	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
132	#103×C₈₉	C₂³	1	8	yes	—
133	#103×C₈₉	C₂³	1	8	yes	—
134	#103×C₈₉	C₂³	1	8	yes	—
135	#102×C₈₉	C₂³	1	8	yes	—
136	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
137	#97×C₈₉	C₂³	1	8	yes	—
138	C₂⁴×C₈₉	—	2	1	no	—
139	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₈₉	—	2	16	no	—
141	#41×C₈₉	—	2	8	no	—
142	#41×C₈₉	—	2	8	no	—
143	C₂×Q₈×C₈₉	—	2	1	no	—
144	C₂×Q₈×C₈₉	—	2	2	no	—
145	C₂×Q₈×C₈₉	—	2	4	no	—
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	—	2	4	no	—
148	C₂×Q₈×C₈₉	—	2	4	no	—
149	C₂×Q₈×C₈₉	—	4	4	no	—
150	C₂×Q₈×C₈₉	#41	1	4	yes	—
151	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
152	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
153	C₂×D₄×C₈₉	—	2	8	no	—
154	C₂×D₄×C₈₉	—	2	4	no	—
155	C₂×D₄×C₈₉	—	2	1	no	—
156	C₂×D₄×C₈₉	—	2	2	no	—
157	C₂×D₄×C₈₉	#41	1	4	yes	—
158	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₈₉	—	2	8	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	2	2	no	—
164	C₂²×C₄×C₈₉	—	2	2	no	—
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	2	no	—
168	C₂²×C₄×C₈₉	—	2	2	no	—
169	C₂²×C₄×C₈₉	—	2	4	no	—
170	C₂²×C₄×C₈₉	—	2	4	no	—
171	C₂²×C₄×C₈₉	—	4	2	no	—
172	C₂²×C₄×C₈₉	—	4	4	no	—
173	C₂²×C₄×C₈₉	—	4	4	no	—
174	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
184	Q₁₆×C₈₉	—	2	16	no	—
185	SD₁₆×C₈₉	—	2	16	no	—
186	C₂×C₈×C₈₉	—	2	4	no	—
187	C₂×C₈×C₈₉	—	2	4	no	—
188	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
189	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	8	no	—
196	C₄⋊C₄×C₈₉	—	2	8	no	—
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₄⋊C₄×C₈₉	—	2	2	no	—
200	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
201	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
202	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
203	C₂²⋊C₄×C₈₉	—	2	8	no	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	2	4	no	—
207	C₄²×C₈₉	—	2	4	no	—
208	C₄²×C₈₉	—	2	4	no	—
209	C₄²×C₈₉	—	2	4	no	—
210	C₄²×C₈₉	—	2	8	no	—
211	C₄²×C₈₉	C₂×D₄	1	4	yes	—
212	C₄²×C₈₉	C₂×D₄	1	4	yes	—
213	C₄²×C₈₉	C₂×D₄	1	2	yes	—
214	C₄²×C₈₉	C₂×D₄	1	2	yes	—
215	C₄²×C₈₉	C₂⁴	1	2	yes	—
216	C₄²×C₈₉	C₂⁴	1	2	yes	—
217	C₂³×C₈₉	—	2	2	no	—
218	C₂³×C₈₉	—	2	4	no	—
219	C₂³×C₈₉	—	2	2	no	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	4	2	no	—
223	C₂³×C₈₉	—	4	2	no	—
224	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
225	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₈₉	—	2	4	no	—
227	Q₈×C₈₉	—	2	2	no	—
228	Q₈×C₈₉	—	2	4	no	—
229	Q₈×C₈₉	—	2	4	no	—
230	Q₈×C₈₉	—	4	8	no	—
231	Q₈×C₈₉	—	4	4	no	—
232	Q₈×C₈₉	C₂×#41	1	4	yes	—
233	D₄×C₈₉	—	2	16	no	—
234	D₄×C₈₉	—	2	4	no	—
235	D₄×C₈₉	—	2	2	no	—
236	D₄×C₈₉	C₂×#41	1	4	yes	—
237	C₂×C₄×C₈₉	—	2	16	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	4	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	4	no	—
245	C₂×C₄×C₈₉	—	2	8	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	2	no	—
250	C₂×C₄×C₈₉	—	2	4	no	—
251	C₂×C₄×C₈₉	—	2	4	no	—
252	C₂×C₄×C₈₉	—	4	4	no	—
253	C₂×C₄×C₈₉	—	4	8	no	—
254	C₂×C₄×C₈₉	—	4	4	no	—
255	C₂×C₄×C₈₉	—	4	2	no	—
256	C₂×C₄×C₈₉	—	4	2	no	—
257	C₂×C₄×C₈₉	—	4	4	no	—
258	C₂×C₄×C₈₉	—	4	8	no	—
259	C₂×C₄×C₈₉	#137	1	4	yes	—
260	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
267	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
268	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
269	C₈×C₈₉	—	2	4	no	—
270	C₈×C₈₉	—	2	4	no	—
271	C₂²×C₈₉	—	2	2	no	—
272	C₂²×C₈₉	—	2	4	no	—
273	C₂²×C₈₉	—	2	2	no	—
274	C₂²×C₈₉	—	2	2	no	—
275	C₂²×C₈₉	—	4	4	no	—
276	C₂²×C₈₉	—	4	8	no	—
277	C₂²×C₈₉	—	4	2	no	—
278	C₂²×C₈₉	—	4	2	no	—
279	C₂²×C₈₉	#525	1	2	yes	—
280	C₂²×C₈₉	C₂×#137	1	2	yes	—
281	C₂²×C₈₉	#575	1	2	yes	—
282	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	2	4	no	—
285	C₄×C₈₉	—	2	2	no	—
286	C₄×C₈₉	—	2	2	no	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	4	4	no	—
289	C₄×C₈₉	—	4	2	no	—
290	C₄×C₈₉	—	4	2	no	—
291	C₄×C₈₉	—	4	4	no	—
292	C₄×C₈₉	#525	1	2	yes	—
293	C₄×C₈₉	C₂×#137	1	4	yes	—
294	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
295	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
296	C₂×#3116	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂×C₈₉	—	4	2	no	—
298	C₂×C₈₉	—	4	4	no	—
299	C₂×C₈₉	#3116	1	4	yes	direct product factor
300	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
301	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
302	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
303	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
304	C₂×C₄×#41	C₂×C₈₉	1	1	yes	characteristic
305	#3116	C₂×C₈₉	1	16	yes	direct product factor
306	C₂×#485	C₂×C₈₉	1	2	yes	complemented
307	C₂×#477	C₂×C₈₉	1	1	yes	characteristic, complemented
308	C₂×#476	C₂×C₈₉	1	1	yes	characteristic, complemented
309	C₂×#462	C₂×C₈₉	1	1	yes	characteristic, complemented
310	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
311	C₂×#452	C₂×C₈₉	1	2	yes	—
312	C₂×#441	C₂×C₈₉	1	2	yes	complemented
313	C₂×#440	C₂×C₈₉	1	2	yes	complemented
314	C₂×#432	C₂×C₈₉	1	1	yes	characteristic, complemented
315	C₈₉	C₂×#3116	1	1	yes	characteristic, direct product factor, Sylow
316	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
317	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
318	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
319	#533	—	2	4	no	—
320	#533	C₂²×C₈₉	1	8	yes	complemented
321	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
322	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×#125	—	2	1	no	—
324	C₂×C₂²⋊Q₈	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
326	C₄×#41	—	2	4	no	—
327	C₄×#41	C₂²×C₈₉	1	8	yes	—
328	C₂×C₄×Q₈	—	2	1	no	—
329	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
332	C₂×C₄×D₄	—	2	1	no	—
333	C₂×C₄×D₄	—	2	1	no	—
334	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
336	C₂×#117	—	2	1	no	—
337	C₂×#117	—	2	1	no	—
338	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
339	C₂²×C₄²	—	2	1	no	—
340	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
341	#485	C₂²×C₈₉	1	16	yes	complemented
342	#477	C₂²×C₈₉	1	8	yes	complemented
343	#476	C₂²×C₈₉	1	8	yes	complemented
344	#462	C₂²×C₈₉	1	8	yes	complemented
345	#461	C₂²×C₈₉	1	8	yes	complemented
346	#452	C₂²×C₈₉	1	16	yes	—
347	#441	C₂²×C₈₉	1	16	yes	complemented
348	#440	C₂²×C₈₉	1	16	yes	complemented
349	#432	C₂²×C₈₉	1	8	yes	complemented
350	C₂×#107	C₂²×C₈₉	1	2	yes	—
351	C₂×#106	C₂²×C₈₉	1	2	yes	—
352	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
353	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
354	C₂×#103	C₂²×C₈₉	1	2	yes	—
355	C₂×#103	C₂²×C₈₉	1	2	yes	—
356	C₂×#103	C₂²×C₈₉	1	2	yes	—
357	C₂×#102	C₂²×C₈₉	1	2	yes	—
358	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
359	C₂×#97	C₂²×C₈₉	1	2	yes	—
360	C₂×#41	—	2	4	no	—
361	C₂×#41	—	2	4	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	C₂³×C₈₉	1	4	yes	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
366	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
373	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
375	C₂×Q₁₆	—	2	8	no	—
376	C₂×Q₁₆	C₂³×C₈₉	1	8	yes	—
377	C₂×SD₁₆	—	2	8	no	—
378	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
379	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
380	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
381	C₄⋊Q₈	—	2	2	no	—
382	C₄⋊Q₈	—	2	2	no	—
383	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
384	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
385	#125	—	2	8	no	—
386	C₂²⋊Q₈	—	2	8	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
389	C₄×Q₈	—	2	8	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	4	no	—
393	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
394	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
395	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
396	C₄×D₄	—	2	8	no	—
397	C₄×D₄	—	2	8	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	C₂³×C₈₉	1	4	yes	—
401	C₄×D₄	C₂³×C₈₉	1	4	yes	—
402	#117	—	2	8	no	—
403	#117	—	2	2	no	—
404	#117	—	2	8	no	—
405	#117	C₂³×C₈₉	1	4	yes	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	8	no	—
425	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
426	C₂×C₄²	D₄×C₈₉	1	4	yes	—
427	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
431	#107	C₂³×C₈₉	1	8	yes	—
432	#106	C₂³×C₈₉	1	8	yes	—
433	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
434	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
435	#103	C₂³×C₈₉	1	8	yes	—
436	#103	C₂³×C₈₉	1	8	yes	—
437	#103	C₂³×C₈₉	1	8	yes	—
438	#102	C₂³×C₈₉	1	8	yes	—
439	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
440	#97	C₂³×C₈₉	1	8	yes	—
441	C₂⁴	—	2	1	no	—
442	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
443	#41	—	2	16	no	—
444	#41	—	2	8	no	—
445	#41	—	2	8	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	2	4	no	—
452	C₂×Q₈	—	4	4	no	—
453	C₂×Q₈	#41×C₈₉	1	4	yes	—
454	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
455	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	#41×C₈₉	1	4	yes	—
461	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
481	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
483	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
484	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
487	Q₁₆	—	2	16	no	—
488	SD₁₆	—	2	16	no	—
489	C₂×C₈	—	2	4	no	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
492	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	4	no	—
513	C₄²	—	2	8	no	—
514	C₄²	C₂×D₄×C₈₉	1	4	yes	—
515	C₄²	C₂×D₄×C₈₉	1	4	yes	—
516	C₄²	C₂×D₄×C₈₉	1	2	yes	—
517	C₄²	C₂×D₄×C₈₉	1	2	yes	—
518	C₄²	C₂⁴×C₈₉	1	2	yes	—
519	C₄²	C₂⁴×C₈₉	1	2	yes	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
528	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
529	Q₈	—	2	4	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	4	no	—
532	Q₈	—	2	4	no	—
533	Q₈	—	4	8	no	—
534	Q₈	—	4	4	no	—
535	Q₈	C₂×#41×C₈₉	1	4	yes	—
536	D₄	—	2	16	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	2	no	—
539	D₄	C₂×#41×C₈₉	1	4	yes	—
540	C₂×C₄	—	2	16	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	#137×C₈₉	1	4	yes	—
563	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
564	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
569	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
570	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
571	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	2	4	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	8	no	—
582	C₂²	#525×C₈₉	1	2	yes	—
583	C₂²	C₂×#137×C₈₉	1	2	yes	—
584	C₂²	#575×C₈₉	1	2	yes	—
585	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	4	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	4	no	—
595	C₄	#525×C₈₉	1	2	yes	—
596	C₄	C₂×#137×C₈₉	1	4	yes	—
597	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
598	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
599	C₂	—	4	2	no	—
600	C₂	—	4	4	no	—
601	C₂	C₈₉×#3116	1	4	yes	direct product factor
602	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
603	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
604	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	C₂²×#41×C₈₉	C₂²
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. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3116	C₂	direct (N × H)
4. C₂×#485×C₈₉	C₂	semidirect
5. C₂×#477×C₈₉	C₂	semidirect
6. C₂×#476×C₈₉	C₂	semidirect
7. C₂×#462×C₈₉	C₂	semidirect
8. C₂×#461×C₈₉	C₂	semidirect
10. C₂×#441×C₈₉	C₂	semidirect
11. C₂×#440×C₈₉	C₂	semidirect
12. C₂×#432×C₈₉	C₂	semidirect
17. #533×C₈₉	C₂²	semidirect
38. #485×C₈₉	C₂²	semidirect
39. #477×C₈₉	C₂²	semidirect
40. #476×C₈₉	C₂²	semidirect
41. #462×C₈₉	C₂²	semidirect
42. #461×C₈₉	C₂²	semidirect
44. #441×C₈₉	C₂²	semidirect
45. #440×C₈₉	C₂²	semidirect
46. #432×C₈₉	C₂²	semidirect
296. C₂×#3116	C₈₉	direct (N × H)
299. C₂×C₈₉	#3116	direct (N × H)
303. C₂×#533	C₂×C₈₉	semidirect
305. #3116	C₂×C₈₉	direct (N × H)
306. C₂×#485	C₂×C₈₉	semidirect
307. C₂×#477	C₂×C₈₉	semidirect
308. C₂×#476	C₂×C₈₉	semidirect
309. C₂×#462	C₂×C₈₉	semidirect
310. C₂×#461	C₂×C₈₉	semidirect
312. C₂×#441	C₂×C₈₉	semidirect
313. C₂×#440	C₂×C₈₉	semidirect
314. C₂×#432	C₂×C₈₉	semidirect
315. C₈₉	C₂×#3116	direct (N × H)
320. #533	C₂²×C₈₉	semidirect
341. #485	C₂²×C₈₉	semidirect
342. #477	C₂²×C₈₉	semidirect
343. #476	C₂²×C₈₉	semidirect
344. #462	C₂²×C₈₉	semidirect
345. #461	C₂²×C₈₉	semidirect
347. #441	C₂²×C₈₉	semidirect
348. #440	C₂²×C₈₉	semidirect
349. #432	C₂²×C₈₉	semidirect
601. C₂	C₈₉×#3116	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×#533×C₈₉	2
C₂×C₄×#41×C₈₉	2
C₈₉×#3116	2
C₂×#485×C₈₉	2
C₂×#477×C₈₉	2
C₂×#476×C₈₉	2
C₂×#462×C₈₉	2
C₂×#461×C₈₉	2
C₂×#452×C₈₉	2
C₂×#441×C₈₉	2
C₂×#440×C₈₉	2
C₂×#432×C₈₉	2
C₂×#3116	89

Subgroups — C2×C89×#3116 #36438387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3116 #36438387