Subgroups — C₂×C₈₉×#3178 #36438531

Order 22784.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3178	C₂	1	16	yes	maximal, direct product factor
4	C₂×#501×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#497×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#488×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#487×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#467×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#465×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#405×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#542×C₈₉	—	2	4	no	—
24	#542×C₈₉	C₂²	1	8	yes	—
25	#541×C₈₉	—	2	4	no	—
26	#541×C₈₉	C₂²	1	8	yes	complemented
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#126×C₈₉	—	2	1	no	—
30	C₂×#126×C₈₉	—	2	1	no	—
31	C₂×#126×C₈₉	—	2	1	no	—
32	C₂×#125×C₈₉	—	2	1	no	—
33	C₂×#125×C₈₉	—	2	1	no	—
34	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#124×C₈₉	—	2	1	no	—
36	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#123×C₈₉	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	8	yes	complemented
49	#497×C₈₉	C₂²	1	8	yes	complemented
50	#488×C₈₉	C₂²	1	8	yes	complemented
51	#487×C₈₉	C₂²	1	8	yes	complemented
52	#470×C₈₉	C₂²	1	8	yes	complemented
53	#468×C₈₉	C₂²	1	8	yes	—
54	#467×C₈₉	C₂²	1	8	yes	complemented
55	#465×C₈₉	C₂²	1	8	yes	—
56	#441×C₈₉	C₂²	1	8	yes	complemented
57	#440×C₈₉	C₂²	1	8	yes	complemented
58	C₄×Q₁₆×C₈₉	C₂²	1	8	yes	complemented
59	C₄×SD₁₆×C₈₉	C₂²	1	8	yes	complemented
60	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
64	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
68	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
71	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
72	#405×C₈₉	C₂²	1	8	yes	complemented
73	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
74	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₈₉	—	2	1	no	—
78	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	—	2	1	no	—
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×Q₁₆×C₈₉	—	2	4	no	—
86	C₂×Q₁₆×C₈₉	—	2	4	no	—
87	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₈₉	—	2	4	no	—
90	C₂×SD₁₆×C₈₉	—	2	4	no	—
91	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
93	C₂×M₁₆×C₈₉	—	2	4	no	—
94	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
95	C₂²×C₈×C₈₉	—	2	4	no	—
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₈₉	—	2	2	no	—
102	C₄⋊Q₈×C₈₉	—	2	2	no	—
103	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
105	#126×C₈₉	—	2	8	no	—
106	#126×C₈₉	—	2	8	no	—
107	#126×C₈₉	—	2	8	no	—
108	#125×C₈₉	—	2	8	no	—
109	#125×C₈₉	—	2	8	no	—
110	#125×C₈₉	—	2	2	no	—
111	#125×C₈₉	C₂³	1	4	yes	—
112	#124×C₈₉	—	2	8	no	—
113	#124×C₈₉	—	2	2	no	—
114	#124×C₈₉	C₂³	1	4	yes	—
115	#123×C₈₉	—	2	8	no	—
116	C₂²⋊Q₈×C₈₉	—	2	2	no	—
117	C₂²⋊Q₈×C₈₉	—	2	2	no	—
118	C₂²⋊Q₈×C₈₉	—	2	2	no	—
119	C₂²⋊Q₈×C₈₉	—	2	8	no	—
120	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
121	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
122	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
123	#121×C₈₉	—	2	2	no	—
124	#121×C₈₉	C₂³	1	4	yes	—
125	C₄×Q₈×C₈₉	—	2	2	no	—
126	C₄×Q₈×C₈₉	—	2	2	no	—
127	C₄×Q₈×C₈₉	—	2	2	no	—
128	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
129	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
130	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
131	C₄×D₄×C₈₉	—	2	2	no	—
132	C₄×D₄×C₈₉	C₂³	1	4	yes	—
133	#117×C₈₉	D₄	1	4	yes	—
134	#117×C₈₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
136	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	—	2	1	no	—
162	C₂×C₄²×C₈₉	—	2	1	no	—
163	C₂×C₄²×C₈₉	—	2	1	no	—
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	#107×C₈₉	C₂³	1	4	yes	—
167	#107×C₈₉	C₂³	1	4	yes	—
168	#106×C₈₉	C₂³	1	4	yes	—
169	#106×C₈₉	C₂³	1	4	yes	—
170	#103×C₈₉	C₂³	1	4	yes	—
171	#103×C₈₉	C₂³	1	4	yes	—
172	#103×C₈₉	C₂³	1	4	yes	—
173	#103×C₈₉	C₂³	1	4	yes	—
174	#103×C₈₉	C₂³	1	4	yes	—
175	#103×C₈₉	C₂³	1	4	yes	—
176	#102×C₈₉	C₂³	1	4	yes	—
177	#102×C₈₉	C₂³	1	4	yes	—
178	#97×C₈₉	C₂³	1	4	yes	—
179	#97×C₈₉	C₂³	1	4	yes	—
180	C₄×C₈×C₈₉	C₂³	1	4	yes	—
181	C₄×C₈×C₈₉	C₂³	1	4	yes	—
182	C₂⁴×C₈₉	—	2	1	no	—
183	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₈₉	—	2	1	no	—
185	C₂×Q₈×C₈₉	—	2	1	no	—
186	C₂×Q₈×C₈₉	—	2	1	no	—
187	C₂×Q₈×C₈₉	—	2	4	no	—
188	C₂×Q₈×C₈₉	—	2	2	no	—
189	C₂×Q₈×C₈₉	—	2	2	no	—
190	C₂×Q₈×C₈₉	—	2	2	no	—
191	C₂×Q₈×C₈₉	—	2	2	no	—
192	C₂×Q₈×C₈₉	—	2	2	no	—
193	C₂×Q₈×C₈₉	—	2	2	no	—
194	C₂×Q₈×C₈₉	—	8	2	no	—
195	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
198	C₂×D₄×C₈₉	—	2	4	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	2	no	—
201	C₂×D₄×C₈₉	—	2	2	no	—
202	C₂×D₄×C₈₉	—	8	2	no	—
203	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₈₉	—	2	2	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	1	no	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	8	2	no	—
215	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
223	Q₁₆×C₈₉	—	2	8	no	—
224	Q₁₆×C₈₉	—	2	8	no	—
225	SD₁₆×C₈₉	—	2	8	no	—
226	SD₁₆×C₈₉	—	2	8	no	—
227	M₁₆×C₈₉	—	2	8	no	—
228	C₂×C₈×C₈₉	—	2	2	no	—
229	C₂×C₈×C₈₉	—	2	2	no	—
230	C₂×C₈×C₈₉	—	2	8	no	—
231	C₂×C₈×C₈₉	#41	1	4	yes	—
232	C₂×C₈×C₈₉	#41	1	4	yes	—
233	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
234	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
235	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
236	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	1	no	—
249	C₄⋊C₄×C₈₉	—	2	1	no	—
250	C₄⋊C₄×C₈₉	—	2	1	no	—
251	C₄⋊C₄×C₈₉	—	2	1	no	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
266	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	C₂×D₄	1	2	yes	—
271	C₄²×C₈₉	C₂×D₄	1	2	yes	—
272	C₄²×C₈₉	C₂⁴	1	2	yes	—
273	C₄²×C₈₉	C₂⁴	1	2	yes	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	2	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	4	2	no	—
279	C₂³×C₈₉	—	4	2	no	—
280	C₂³×C₈₉	—	4	2	no	—
281	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₈₉	—	2	2	no	—
284	Q₈×C₈₉	—	2	2	no	—
285	Q₈×C₈₉	—	2	2	no	—
286	Q₈×C₈₉	—	2	2	no	—
287	Q₈×C₈₉	—	2	2	no	—
288	Q₈×C₈₉	—	2	2	no	—
289	Q₈×C₈₉	—	4	2	no	—
290	Q₈×C₈₉	—	4	2	no	—
291	Q₈×C₈₉	—	4	2	no	—
292	Q₈×C₈₉	—	8	4	no	—
293	D₄×C₈₉	—	2	2	no	—
294	D₄×C₈₉	—	2	2	no	—
295	D₄×C₈₉	—	4	2	no	—
296	D₄×C₈₉	—	8	4	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	4	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	4	2	no	—
313	C₂×C₄×C₈₉	—	4	2	no	—
314	C₂×C₄×C₈₉	—	4	2	no	—
315	C₂×C₄×C₈₉	—	4	2	no	—
316	C₂×C₄×C₈₉	—	4	2	no	—
317	C₂×C₄×C₈₉	—	4	2	no	—
318	C₂×C₄×C₈₉	—	4	2	no	—
319	C₂×C₄×C₈₉	—	8	4	no	—
320	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
327	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
328	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
329	C₈×C₈₉	—	2	2	no	—
330	C₈×C₈₉	—	2	2	no	—
331	C₈×C₈₉	C₂×#41	1	4	yes	—
332	C₈×C₈₉	C₂×#41	1	4	yes	—
333	C₂²×C₈₉	—	2	2	no	—
334	C₂²×C₈₉	—	2	2	no	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	4	4	no	—
337	C₂²×C₈₉	—	4	2	no	—
338	C₂²×C₈₉	—	4	2	no	—
339	C₂²×C₈₉	—	4	2	no	—
340	C₂²×C₈₉	—	8	4	no	—
341	C₂²×C₈₉	#532	1	2	yes	—
342	C₂²×C₈₉	#577	1	2	yes	—
343	C₂²×C₈₉	#578	1	2	yes	—
344	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₈₉	—	2	2	no	—
346	C₄×C₈₉	—	2	2	no	—
347	C₄×C₈₉	—	2	2	no	—
348	C₄×C₈₉	—	2	2	no	—
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	2	no	—
352	C₄×C₈₉	—	4	2	no	—
353	C₄×C₈₉	—	4	2	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	2	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	#532	1	2	yes	—
358	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
360	C₂×#3178	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₈₉	—	4	2	no	—
362	C₂×C₈₉	—	8	2	no	—
363	C₂×C₈₉	#3178	1	4	yes	direct product factor
364	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
365	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
366	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
367	C₂×#542	C₂×C₈₉	1	1	yes	characteristic
368	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
369	#3178	C₂×C₈₉	1	16	yes	direct product factor
370	C₂×#501	C₂×C₈₉	1	1	yes	characteristic, complemented
371	C₂×#497	C₂×C₈₉	1	1	yes	characteristic, complemented
372	C₂×#488	C₂×C₈₉	1	1	yes	characteristic, complemented
373	C₂×#487	C₂×C₈₉	1	1	yes	characteristic, complemented
374	C₂×#470	C₂×C₈₉	1	1	yes	characteristic, complemented
375	C₂×#468	C₂×C₈₉	1	1	yes	characteristic
376	C₂×#467	C₂×C₈₉	1	1	yes	characteristic, complemented
377	C₂×#465	C₂×C₈₉	1	1	yes	characteristic
378	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
379	C₂×#440	C₂×C₈₉	1	1	yes	characteristic, complemented
380	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
381	C₂×C₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
382	C₂×#405	C₂×C₈₉	1	1	yes	characteristic, complemented
383	C₈₉	C₂×#3178	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
385	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
386	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
388	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
389	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
390	#542	—	2	4	no	—
391	#542	C₂²×C₈₉	1	8	yes	—
392	#541	—	2	4	no	—
393	#541	C₂²×C₈₉	1	8	yes	complemented
394	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
396	C₂×#126	—	2	1	no	—
397	C₂×#126	—	2	1	no	—
398	C₂×#126	—	2	1	no	—
399	C₂×#125	—	2	1	no	—
400	C₂×#125	—	2	1	no	—
401	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
402	C₂×#124	—	2	1	no	—
403	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#123	—	2	1	no	—
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
415	#501	C₂²×C₈₉	1	8	yes	complemented
416	#497	C₂²×C₈₉	1	8	yes	complemented
417	#488	C₂²×C₈₉	1	8	yes	complemented
418	#487	C₂²×C₈₉	1	8	yes	complemented
419	#470	C₂²×C₈₉	1	8	yes	complemented
420	#468	C₂²×C₈₉	1	8	yes	—
421	#467	C₂²×C₈₉	1	8	yes	complemented
422	#465	C₂²×C₈₉	1	8	yes	—
423	#441	C₂²×C₈₉	1	8	yes	complemented
424	#440	C₂²×C₈₉	1	8	yes	complemented
425	C₄×Q₁₆	C₂²×C₈₉	1	8	yes	complemented
426	C₄×SD₁₆	C₂²×C₈₉	1	8	yes	complemented
427	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
439	#405	C₂²×C₈₉	1	8	yes	complemented
440	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
452	C₂×Q₁₆	—	2	4	no	—
453	C₂×Q₁₆	—	2	4	no	—
454	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
455	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
456	C₂×SD₁₆	—	2	4	no	—
457	C₂×SD₁₆	—	2	4	no	—
458	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
459	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
460	C₂×M₁₆	—	2	4	no	—
461	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
462	C₂²×C₈	—	2	4	no	—
463	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
465	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
471	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
472	#126	—	2	8	no	—
473	#126	—	2	8	no	—
474	#126	—	2	8	no	—
475	#125	—	2	8	no	—
476	#125	—	2	8	no	—
477	#125	—	2	2	no	—
478	#125	C₂³×C₈₉	1	4	yes	—
479	#124	—	2	8	no	—
480	#124	—	2	2	no	—
481	#124	C₂³×C₈₉	1	4	yes	—
482	#123	—	2	8	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	8	no	—
487	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
489	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
490	#121	—	2	2	no	—
491	#121	C₂³×C₈₉	1	4	yes	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
496	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
497	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	C₂³×C₈₉	1	4	yes	—
500	#117	D₄×C₈₉	1	4	yes	—
501	#117	C₂³×C₈₉	1	4	yes	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
533	#107	C₂³×C₈₉	1	4	yes	—
534	#107	C₂³×C₈₉	1	4	yes	—
535	#106	C₂³×C₈₉	1	4	yes	—
536	#106	C₂³×C₈₉	1	4	yes	—
537	#103	C₂³×C₈₉	1	4	yes	—
538	#103	C₂³×C₈₉	1	4	yes	—
539	#103	C₂³×C₈₉	1	4	yes	—
540	#103	C₂³×C₈₉	1	4	yes	—
541	#103	C₂³×C₈₉	1	4	yes	—
542	#103	C₂³×C₈₉	1	4	yes	—
543	#102	C₂³×C₈₉	1	4	yes	—
544	#102	C₂³×C₈₉	1	4	yes	—
545	#97	C₂³×C₈₉	1	4	yes	—
546	#97	C₂³×C₈₉	1	4	yes	—
547	C₄×C₈	C₂³×C₈₉	1	4	yes	—
548	C₄×C₈	C₂³×C₈₉	1	4	yes	—
549	C₂⁴	—	2	1	no	—
550	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	8	2	no	—
562	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
563	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
564	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	8	2	no	—
570	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	8	2	no	—
582	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
590	Q₁₆	—	2	8	no	—
591	Q₁₆	—	2	8	no	—
592	SD₁₆	—	2	8	no	—
593	SD₁₆	—	2	8	no	—
594	M₁₆	—	2	8	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	8	no	—
598	C₂×C₈	#41×C₈₉	1	4	yes	—
599	C₂×C₈	#41×C₈₉	1	4	yes	—
600	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
601	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
602	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
603	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
621	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
633	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	C₂×D₄×C₈₉	1	2	yes	—
638	C₄²	C₂×D₄×C₈₉	1	2	yes	—
639	C₄²	C₂⁴×C₈₉	1	2	yes	—
640	C₄²	C₂⁴×C₈₉	1	2	yes	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
649	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	8	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	8	4	no	—
687	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
693	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
694	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
695	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	2	2	no	—
698	C₈	C₂×#41×C₈₉	1	4	yes	—
699	C₈	C₂×#41×C₈₉	1	4	yes	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	8	4	no	—
708	C₂²	#532×C₈₉	1	2	yes	—
709	C₂²	#577×C₈₉	1	2	yes	—
710	C₂²	#578×C₈₉	1	2	yes	—
711	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	#532×C₈₉	1	2	yes	—
725	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
726	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	C₈₉×#3178	1	4	yes	direct product factor
730	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
731	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
732	C₂	C₂×#578×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#3178	C₂	direct (N × H)
4. C₂×#501×C₈₉	C₂	semidirect
5. C₂×#497×C₈₉	C₂	semidirect
6. C₂×#488×C₈₉	C₂	semidirect
7. C₂×#487×C₈₉	C₂	semidirect
8. C₂×#470×C₈₉	C₂	semidirect
10. C₂×#467×C₈₉	C₂	semidirect
12. C₂×#441×C₈₉	C₂	semidirect
13. C₂×#440×C₈₉	C₂	semidirect
14. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
15. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
16. C₂×#405×C₈₉	C₂	semidirect
26. #541×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #497×C₈₉	C₂²	semidirect
50. #488×C₈₉	C₂²	semidirect
51. #487×C₈₉	C₂²	semidirect
52. #470×C₈₉	C₂²	semidirect
54. #467×C₈₉	C₂²	semidirect
56. #441×C₈₉	C₂²	semidirect
57. #440×C₈₉	C₂²	semidirect
58. C₄×Q₁₆×C₈₉	C₂²	semidirect
59. C₄×SD₁₆×C₈₉	C₂²	semidirect
72. #405×C₈₉	C₂²	semidirect
360. C₂×#3178	C₈₉	direct (N × H)
363. C₂×C₈₉	#3178	direct (N × H)
368. C₂×#541	C₂×C₈₉	semidirect
369. #3178	C₂×C₈₉	direct (N × H)
370. C₂×#501	C₂×C₈₉	semidirect
371. C₂×#497	C₂×C₈₉	semidirect
372. C₂×#488	C₂×C₈₉	semidirect
373. C₂×#487	C₂×C₈₉	semidirect
374. C₂×#470	C₂×C₈₉	semidirect
376. C₂×#467	C₂×C₈₉	semidirect
378. C₂×#441	C₂×C₈₉	semidirect
379. C₂×#440	C₂×C₈₉	semidirect
380. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
381. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
382. C₂×#405	C₂×C₈₉	semidirect
383. C₈₉	C₂×#3178	direct (N × H)
393. #541	C₂²×C₈₉	semidirect
415. #501	C₂²×C₈₉	semidirect
416. #497	C₂²×C₈₉	semidirect
417. #488	C₂²×C₈₉	semidirect
418. #487	C₂²×C₈₉	semidirect
419. #470	C₂²×C₈₉	semidirect
421. #467	C₂²×C₈₉	semidirect
423. #441	C₂²×C₈₉	semidirect
424. #440	C₂²×C₈₉	semidirect
425. C₄×Q₁₆	C₂²×C₈₉	semidirect
426. C₄×SD₁₆	C₂²×C₈₉	semidirect
439. #405	C₂²×C₈₉	semidirect
729. C₂	C₈₉×#3178	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×#542×C₈₉	2
C₂×#541×C₈₉	2
C₈₉×#3178	2
C₂×#501×C₈₉	2
C₂×#497×C₈₉	2
C₂×#488×C₈₉	2
C₂×#487×C₈₉	2
C₂×#470×C₈₉	2
C₂×#468×C₈₉	2
C₂×#467×C₈₉	2
C₂×#465×C₈₉	2
C₂×#441×C₈₉	2
C₂×#440×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₂×#405×C₈₉	2
C₂×#3178	89

Subgroups — C2×C89×#3178 #36438531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3178 #36438531