Subgroups — C₂×C₈₉×#3377 #36439163

Order 22784.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3377	C₂	1	16	yes	maximal, direct product factor
4	C₂×#491×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#488×C₈₉	C₂	1	1	yes	maximal, characteristic
7	C₂×#479×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#477×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#478×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#462×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#446×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#440×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Q₁₆×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	#557×C₈₉	—	2	4	no	—
21	#557×C₈₉	C₂²	1	8	yes	complemented
22	#556×C₈₉	—	2	4	no	—
23	#556×C₈₉	C₂²	1	8	yes	—
24	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₈₉	—	2	1	no	—
28	C₂×#126×C₈₉	—	2	1	no	—
29	C₂×#125×C₈₉	—	2	1	no	—
30	C₂×#125×C₈₉	—	2	1	no	—
31	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
36	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
37	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#117×C₈₉	—	2	1	no	—
45	#491×C₈₉	C₂²	1	8	yes	complemented
46	#489×C₈₉	C₂²	1	8	yes	—
47	#488×C₈₉	C₂²	1	8	yes	—
48	#479×C₈₉	C₂²	1	8	yes	complemented
49	#478×C₈₉	C₂²	1	8	yes	—
50	#477×C₈₉	C₂²	1	8	yes	complemented
51	#464×C₈₉	C₂²	1	8	yes	—
52	#464×C₈₉	C₂²	1	8	yes	—
53	#462×C₈₉	C₂²	1	8	yes	complemented
54	#446×C₈₉	C₂²	1	8	yes	complemented
55	#441×C₈₉	C₂²	1	8	yes	complemented
56	#440×C₈₉	C₂²	1	8	yes	—
57	C₄×Q₁₆×C₈₉	C₂²	1	8	yes	complemented
58	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×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×#103×C₈₉	C₂²	1	1	yes	characteristic
71	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
73	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
74	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×#97×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	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	—	2	1	no	—
84	C₂×Q₁₆×C₈₉	—	2	4	no	—
85	C₂×Q₁₆×C₈₉	—	2	4	no	—
86	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
87	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
88	C₂×SD₁₆×C₈₉	—	2	4	no	—
89	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊Q₈×C₈₉	—	2	8	no	—
95	C₄⋊Q₈×C₈₉	—	2	2	no	—
96	C₄⋊Q₈×C₈₉	—	2	2	no	—
97	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
99	#126×C₈₉	—	2	8	no	—
100	#126×C₈₉	—	2	8	no	—
101	#125×C₈₉	—	2	8	no	—
102	#125×C₈₉	—	2	8	no	—
103	#125×C₈₉	—	2	2	no	—
104	#125×C₈₉	—	2	2	no	—
105	#125×C₈₉	C₂³	1	4	yes	—
106	#125×C₈₉	C₂³	1	4	yes	—
107	#124×C₈₉	—	2	2	no	—
108	#124×C₈₉	—	2	2	no	—
109	#124×C₈₉	C₂³	1	4	yes	—
110	#124×C₈₉	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₈₉	—	2	8	no	—
112	C₄×Q₈×C₈₉	—	2	8	no	—
113	C₄×Q₈×C₈₉	—	2	2	no	—
114	C₄×Q₈×C₈₉	—	2	2	no	—
115	C₄×Q₈×C₈₉	—	2	2	no	—
116	C₄×Q₈×C₈₉	—	2	2	no	—
117	C₄×Q₈×C₈₉	—	2	2	no	—
118	C₄×Q₈×C₈₉	D₄	1	4	yes	—
119	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
120	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
121	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
122	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
123	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
124	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
125	C₄×D₄×C₈₉	—	2	2	no	—
126	C₄×D₄×C₈₉	C₂³	1	4	yes	—
127	#117×C₈₉	—	2	8	no	—
128	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₂×C₄²×C₈₉	—	2	1	no	—
153	C₂×C₄²×C₈₉	—	2	1	no	—
154	C₂×C₄²×C₈₉	—	2	1	no	—
155	C₂×C₄²×C₈₉	—	2	1	no	—
156	C₂×C₄²×C₈₉	—	2	1	no	—
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
160	#107×C₈₉	C₂³	1	4	yes	—
161	#107×C₈₉	C₂³	1	4	yes	—
162	#106×C₈₉	C₂³	1	4	yes	—
163	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
164	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
165	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
166	#103×C₈₉	C₂³	1	4	yes	—
167	#103×C₈₉	C₂³	1	4	yes	—
168	#103×C₈₉	C₂³	1	4	yes	—
169	#103×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	#102×C₈₉	C₂³	1	4	yes	—
174	#102×C₈₉	C₂³	1	4	yes	—
175	#102×C₈₉	C₂³	1	4	yes	—
176	#97×C₈₉	C₂³	1	4	yes	—
177	#97×C₈₉	C₂³	1	4	yes	—
178	C₄×C₈×C₈₉	C₂³	1	4	yes	—
179	C₂⁴×C₈₉	—	2	1	no	—
180	C₂×Q₈×C₈₉	—	2	1	no	—
181	C₂×Q₈×C₈₉	—	2	1	no	—
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×Q₈×C₈₉	—	2	4	no	—
184	C₂×Q₈×C₈₉	—	2	2	no	—
185	C₂×Q₈×C₈₉	—	2	2	no	—
186	C₂×Q₈×C₈₉	—	2	2	no	—
187	C₂×Q₈×C₈₉	—	2	2	no	—
188	C₂×Q₈×C₈₉	—	2	2	no	—
189	C₂×Q₈×C₈₉	—	4	2	no	—
190	C₂×Q₈×C₈₉	—	4	4	no	—
191	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
192	C₂×Q₈×C₈₉	#41	1	4	yes	—
193	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
194	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	2	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	C₂²×C₄×C₈₉	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	4	no	—
208	C₂²×C₄×C₈₉	—	4	4	no	—
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
216	Q₁₆×C₈₉	—	2	8	no	—
217	Q₁₆×C₈₉	—	2	8	no	—
218	SD₁₆×C₈₉	—	2	8	no	—
219	C₂×C₈×C₈₉	—	2	2	no	—
220	C₂×C₈×C₈₉	—	2	2	no	—
221	C₂×C₈×C₈₉	—	2	2	no	—
222	C₂×C₈×C₈₉	—	2	2	no	—
223	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
224	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
225	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
226	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
227	C₄⋊C₄×C₈₉	—	2	4	no	—
228	C₄⋊C₄×C₈₉	—	2	4	no	—
229	C₄⋊C₄×C₈₉	—	2	4	no	—
230	C₄⋊C₄×C₈₉	—	2	4	no	—
231	C₄⋊C₄×C₈₉	—	2	4	no	—
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	no	—
235	C₄⋊C₄×C₈₉	—	2	4	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	1	no	—
240	C₄⋊C₄×C₈₉	—	2	1	no	—
241	C₄⋊C₄×C₈₉	—	2	1	no	—
242	C₄⋊C₄×C₈₉	—	2	1	no	—
243	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
245	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
250	C₂²⋊C₄×C₈₉	—	2	4	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₄²×C₈₉	—	2	4	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	—	2	4	no	—
258	C₄²×C₈₉	—	2	4	no	—
259	C₄²×C₈₉	—	2	4	no	—
260	C₄²×C₈₉	C₂×D₄	1	2	yes	—
261	C₄²×C₈₉	C₂×D₄	1	2	yes	—
262	C₄²×C₈₉	C₂×D₄	1	2	yes	—
263	C₄²×C₈₉	C₂⁴	1	2	yes	—
264	C₄²×C₈₉	C₂⁴	1	2	yes	—
265	C₄²×C₈₉	C₂⁴	1	2	yes	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	4	2	no	—
268	C₂³×C₈₉	—	4	2	no	—
269	C₂³×C₈₉	—	4	2	no	—
270	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₈₉	—	2	4	no	—
272	Q₈×C₈₉	—	2	2	no	—
273	Q₈×C₈₉	—	2	2	no	—
274	Q₈×C₈₉	—	2	2	no	—
275	Q₈×C₈₉	—	2	2	no	—
276	Q₈×C₈₉	—	2	2	no	—
277	Q₈×C₈₉	—	4	4	no	—
278	Q₈×C₈₉	—	4	8	no	—
279	Q₈×C₈₉	—	4	2	no	—
280	Q₈×C₈₉	—	4	2	no	—
281	Q₈×C₈₉	C₂×#41	1	4	yes	—
282	D₄×C₈₉	—	2	2	no	—
283	D₄×C₈₉	—	2	2	no	—
284	D₄×C₈₉	—	4	2	no	—
285	C₂×C₄×C₈₉	—	2	4	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	4	8	no	—
300	C₂×C₄×C₈₉	—	4	2	no	—
301	C₂×C₄×C₈₉	—	4	2	no	—
302	C₂×C₄×C₈₉	—	4	2	no	—
303	C₂×C₄×C₈₉	—	4	2	no	—
304	C₂×C₄×C₈₉	—	4	2	no	—
305	C₂×C₄×C₈₉	—	4	2	no	—
306	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
314	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
315	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
316	C₈×C₈₉	—	2	2	no	—
317	C₈×C₈₉	—	2	2	no	—
318	C₈×C₈₉	—	2	2	no	—
319	C₈×C₈₉	—	2	2	no	—
320	C₂²×C₈₉	—	4	2	no	—
321	C₂²×C₈₉	—	4	2	no	—
322	C₂²×C₈₉	—	4	2	no	—
323	C₂²×C₈₉	—	8	4	no	—
324	C₂²×C₈₉	#548	1	2	yes	—
325	C₂²×C₈₉	#575	1	2	yes	—
326	C₂²×C₈₉	#578	1	2	yes	—
327	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₈₉	—	2	4	no	—
329	C₄×C₈₉	—	2	2	no	—
330	C₄×C₈₉	—	2	2	no	—
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	2	no	—
333	C₄×C₈₉	—	2	2	no	—
334	C₄×C₈₉	—	2	2	no	—
335	C₄×C₈₉	—	4	2	no	—
336	C₄×C₈₉	—	4	2	no	—
337	C₄×C₈₉	—	4	2	no	—
338	C₄×C₈₉	—	4	2	no	—
339	C₄×C₈₉	—	4	2	no	—
340	C₄×C₈₉	—	4	2	no	—
341	C₄×C₈₉	#548	1	2	yes	—
342	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
343	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂×#3377	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₈₉	—	8	2	no	—
346	C₂×C₈₉	#3377	1	4	yes	direct product factor
347	C₂×C₈₉	C₂×#548	1	1	yes	characteristic
348	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
349	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
350	C₂×#557	C₂×C₈₉	1	1	yes	characteristic, complemented
351	C₂×#556	C₂×C₈₉	1	1	yes	characteristic
352	#3377	C₂×C₈₉	1	16	yes	direct product factor
353	C₂×#491	C₂×C₈₉	1	1	yes	characteristic, complemented
354	C₂×#489	C₂×C₈₉	1	1	yes	characteristic
355	C₂×#488	C₂×C₈₉	1	1	yes	characteristic
356	C₂×#479	C₂×C₈₉	1	1	yes	characteristic, complemented
357	C₂×#477	C₂×C₈₉	1	1	yes	characteristic, complemented
358	C₂×#478	C₂×C₈₉	1	1	yes	characteristic
359	C₂×#464	C₂×C₈₉	1	1	yes	characteristic
360	C₂×#464	C₂×C₈₉	1	1	yes	characteristic
361	C₂×#462	C₂×C₈₉	1	1	yes	characteristic, complemented
362	C₂×#446	C₂×C₈₉	1	1	yes	characteristic, complemented
363	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
364	C₂×#440	C₂×C₈₉	1	1	yes	characteristic
365	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
366	C₈₉	C₂×#3377	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
368	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
370	#557	—	2	4	no	—
371	#557	C₂²×C₈₉	1	8	yes	complemented
372	#556	—	2	4	no	—
373	#556	C₂²×C₈₉	1	8	yes	—
374	C₂×C₄⋊Q₈	—	2	1	no	—
375	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
376	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
377	C₂×#126	—	2	1	no	—
378	C₂×#126	—	2	1	no	—
379	C₂×#125	—	2	1	no	—
380	C₂×#125	—	2	1	no	—
381	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
382	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
383	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
384	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
385	C₂×C₂²⋊Q₈	—	2	1	no	—
386	C₂×C₄×Q₈	—	2	1	no	—
387	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
394	C₂×#117	—	2	1	no	—
395	#491	C₂²×C₈₉	1	8	yes	complemented
396	#489	C₂²×C₈₉	1	8	yes	—
397	#488	C₂²×C₈₉	1	8	yes	—
398	#479	C₂²×C₈₉	1	8	yes	complemented
399	#478	C₂²×C₈₉	1	8	yes	—
400	#477	C₂²×C₈₉	1	8	yes	complemented
401	#464	C₂²×C₈₉	1	8	yes	—
402	#464	C₂²×C₈₉	1	8	yes	—
403	#462	C₂²×C₈₉	1	8	yes	complemented
404	#446	C₂²×C₈₉	1	8	yes	complemented
405	#441	C₂²×C₈₉	1	8	yes	complemented
406	#440	C₂²×C₈₉	1	8	yes	—
407	C₄×Q₁₆	C₂²×C₈₉	1	8	yes	complemented
408	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
433	C₂³×C₄	—	2	1	no	—
434	C₂×Q₁₆	—	2	4	no	—
435	C₂×Q₁₆	—	2	4	no	—
436	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
437	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
438	C₂×SD₁₆	—	2	4	no	—
439	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
440	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
444	C₄⋊Q₈	—	2	8	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	—	2	2	no	—
447	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
448	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
449	#126	—	2	8	no	—
450	#126	—	2	8	no	—
451	#125	—	2	8	no	—
452	#125	—	2	8	no	—
453	#125	—	2	2	no	—
454	#125	—	2	2	no	—
455	#125	C₂³×C₈₉	1	4	yes	—
456	#125	C₂³×C₈₉	1	4	yes	—
457	#124	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	C₂³×C₈₉	1	4	yes	—
460	#124	C₂³×C₈₉	1	4	yes	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₄×Q₈	—	2	8	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	D₄×C₈₉	1	4	yes	—
469	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
470	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
471	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
472	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
473	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
474	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	C₂³×C₈₉	1	4	yes	—
477	#117	—	2	8	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	—	2	1	no	—
507	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
510	#107	C₂³×C₈₉	1	4	yes	—
511	#107	C₂³×C₈₉	1	4	yes	—
512	#106	C₂³×C₈₉	1	4	yes	—
513	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
514	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
515	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
516	#103	C₂³×C₈₉	1	4	yes	—
517	#103	C₂³×C₈₉	1	4	yes	—
518	#103	C₂³×C₈₉	1	4	yes	—
519	#103	C₂³×C₈₉	1	4	yes	—
520	#103	C₂³×C₈₉	1	4	yes	—
521	#103	C₂³×C₈₉	1	4	yes	—
522	#103	C₂³×C₈₉	1	4	yes	—
523	#102	C₂³×C₈₉	1	4	yes	—
524	#102	C₂³×C₈₉	1	4	yes	—
525	#102	C₂³×C₈₉	1	4	yes	—
526	#97	C₂³×C₈₉	1	4	yes	—
527	#97	C₂³×C₈₉	1	4	yes	—
528	C₄×C₈	C₂³×C₈₉	1	4	yes	—
529	C₂⁴	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
542	C₂×Q₈	#41×C₈₉	1	4	yes	—
543	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
544	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
545	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
566	Q₁₆	—	2	8	no	—
567	Q₁₆	—	2	8	no	—
568	SD₁₆	—	2	8	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
574	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
575	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
576	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
594	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
595	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
596	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
597	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
598	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
599	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	C₂×D₄×C₈₉	1	2	yes	—
611	C₄²	C₂×D₄×C₈₉	1	2	yes	—
612	C₄²	C₂×D₄×C₈₉	1	2	yes	—
613	C₄²	C₂⁴×C₈₉	1	2	yes	—
614	C₄²	C₂⁴×C₈₉	1	2	yes	—
615	C₄²	C₂⁴×C₈₉	1	2	yes	—
616	C₂³	—	2	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
621	Q₈	—	2	4	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	2	2	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	4	4	no	—
628	Q₈	—	4	8	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	2	no	—
631	Q₈	C₂×#41×C₈₉	1	4	yes	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	4	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
664	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
665	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
666	C₈	—	2	2	no	—
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	8	4	no	—
674	C₂²	#548×C₈₉	1	2	yes	—
675	C₂²	#575×C₈₉	1	2	yes	—
676	C₂²	#578×C₈₉	1	2	yes	—
677	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	4	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	#548×C₈₉	1	2	yes	—
692	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
693	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
694	C₂	—	8	2	no	—
695	C₂	C₈₉×#3377	1	4	yes	direct product factor
696	C₂	C₂×#548×C₈₉	1	1	yes	characteristic
697	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
698	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	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#557×C₈₉	C₂	semidirect
3. C₈₉×#3377	C₂	direct (N × H)
4. C₂×#491×C₈₉	C₂	semidirect
7. C₂×#479×C₈₉	C₂	semidirect
8. C₂×#477×C₈₉	C₂	semidirect
12. C₂×#462×C₈₉	C₂	semidirect
13. C₂×#446×C₈₉	C₂	semidirect
14. C₂×#441×C₈₉	C₂	semidirect
16. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
21. #557×C₈₉	C₂²	semidirect
45. #491×C₈₉	C₂²	semidirect
48. #479×C₈₉	C₂²	semidirect
50. #477×C₈₉	C₂²	semidirect
53. #462×C₈₉	C₂²	semidirect
54. #446×C₈₉	C₂²	semidirect
55. #441×C₈₉	C₂²	semidirect
57. C₄×Q₁₆×C₈₉	C₂²	semidirect
344. C₂×#3377	C₈₉	direct (N × H)
346. C₂×C₈₉	#3377	direct (N × H)
350. C₂×#557	C₂×C₈₉	semidirect
352. #3377	C₂×C₈₉	direct (N × H)
353. C₂×#491	C₂×C₈₉	semidirect
356. C₂×#479	C₂×C₈₉	semidirect
357. C₂×#477	C₂×C₈₉	semidirect
361. C₂×#462	C₂×C₈₉	semidirect
362. C₂×#446	C₂×C₈₉	semidirect
363. C₂×#441	C₂×C₈₉	semidirect
365. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
366. C₈₉	C₂×#3377	direct (N × H)
371. #557	C₂²×C₈₉	semidirect
395. #491	C₂²×C₈₉	semidirect
398. #479	C₂²×C₈₉	semidirect
400. #477	C₂²×C₈₉	semidirect
403. #462	C₂²×C₈₉	semidirect
404. #446	C₂²×C₈₉	semidirect
405. #441	C₂²×C₈₉	semidirect
407. C₄×Q₁₆	C₂²×C₈₉	semidirect
695. C₂	C₈₉×#3377	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×#557×C₈₉	2
C₂×#556×C₈₉	2
C₈₉×#3377	2
C₂×#491×C₈₉	2
C₂×#489×C₈₉	2
C₂×#488×C₈₉	2
C₂×#479×C₈₉	2
C₂×#477×C₈₉	2
C₂×#478×C₈₉	2
C₂×#464×C₈₉	2
C₂×#462×C₈₉	2
C₂×#446×C₈₉	2
C₂×#441×C₈₉	2
C₂×#440×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₂×#3377	89

Subgroups — C2×C89×#3377 #36439163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3377 #36439163