Subgroups — C₂×C₈₉×#3359 #36439144

Order 22784.

2058 conjugacy classes of subgroups.

The subgroup lattice has 332 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×D₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3359	C₂	1	16	yes	maximal, direct product factor
4	C₂×#487×C₈₉	C₂	1	3	yes	maximal, complemented
5	C₂×#475×C₈₉	C₂	1	3	yes	maximal, complemented
6	C₂×#461×C₈₉	C₂	1	3	yes	maximal
7	C₂×C₈×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₈₉	C₂	1	3	yes	maximal
9	C₂³×Q₈×C₈₉	—	2	1	no	—
10	C₂²×SD₁₆×C₈₉	C₂²	1	3	yes	—
11	#557×C₈₉	—	2	4	no	—
12	#557×C₈₉	C₂²	1	8	yes	complemented
13	D₄×Q₈×C₈₉	—	2	4	no	—
14	D₄×Q₈×C₈₉	C₂²	1	8	yes	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
17	C₂×#125×C₈₉	—	2	3	no	—
18	C₂×C₂²⋊Q₈×C₈₉	—	2	3	no	—
19	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	3	yes	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
23	#487×C₈₉	C₂²	1	24	yes	complemented
24	#475×C₈₉	C₂²	1	24	yes	complemented
25	#461×C₈₉	C₂²	1	24	yes	—
26	C₈×Q₈×C₈₉	C₂²	1	8	yes	complemented
27	C₄×SD₁₆×C₈₉	C₂²	1	24	yes	—
28	C₂×#106×C₈₉	C₂²	1	3	yes	—
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	3	yes	—
30	C₂×#103×C₈₉	C₂²	1	6	yes	—
31	C₂×#103×C₈₉	C₂²	1	3	yes	—
32	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
34	C₂²×Q₈×C₈₉	—	2	8	no	—
35	C₂²×Q₈×C₈₉	—	2	3	no	—
36	C₂²×Q₈×C₈₉	—	4	8	no	—
37	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
39	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₈₉	—	2	3	no	—
41	C₂×SD₁₆×C₈₉	—	2	12	no	—
42	C₂×SD₁₆×C₈₉	C₂³	1	12	yes	—
43	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
45	C₄⋊Q₈×C₈₉	—	2	6	no	—
46	C₄⋊Q₈×C₈₉	—	2	6	no	—
47	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
48	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
49	#125×C₈₉	—	2	24	no	—
50	C₂²⋊Q₈×C₈₉	—	2	24	no	—
51	C₄×Q₈×C₈₉	—	2	8	no	—
52	C₄×Q₈×C₈₉	—	2	6	no	—
53	C₄×Q₈×C₈₉	D₄	1	4	yes	—
54	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
55	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
56	C₄×D₄×C₈₉	—	2	6	no	—
57	C₄×D₄×C₈₉	C₂³	1	12	yes	—
58	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
62	C₂×C₄⋊C₄×C₈₉	D₄	1	3	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
66	C₂×C₄²×C₈₉	—	2	3	no	—
67	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
68	#106×C₈₉	C₂³	1	12	yes	—
69	C₄⋊C₈×C₈₉	C₂³	1	12	yes	—
70	#103×C₈₉	C₂³	1	12	yes	—
71	#103×C₈₉	C₂³	1	24	yes	—
72	#102×C₈₉	C₂³	1	4	yes	—
73	C₄×C₈×C₈₉	C₂³	1	12	yes	—
74	C₂⁴×C₈₉	—	2	1	no	—
75	C₂×Q₈×C₈₉	—	2	3	no	—
76	C₂×Q₈×C₈₉	—	2	12	no	—
77	C₂×Q₈×C₈₉	—	2	6	no	—
78	C₂×Q₈×C₈₉	—	2	6	no	—
79	C₂×Q₈×C₈₉	—	4	32	no	—
80	C₂×Q₈×C₈₉	—	4	12	no	—
81	C₂×Q₈×C₈₉	SD₁₆	1	8	yes	complemented
82	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
83	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
84	C₂×D₄×C₈₉	—	2	1	no	—
85	C₂×D₄×C₈₉	—	2	2	no	—
86	C₂×D₄×C₈₉	#41	1	4	yes	—
87	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
88	C₂²×C₄×C₈₉	—	2	1	no	—
89	C₂²×C₄×C₈₉	—	2	3	no	—
90	C₂²×C₄×C₈₉	—	2	3	no	—
91	C₂²×C₄×C₈₉	—	2	12	no	—
92	C₂²×C₄×C₈₉	—	4	12	no	—
93	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
94	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
96	SD₁₆×C₈₉	—	2	24	no	—
97	C₂×C₈×C₈₉	—	2	6	no	—
98	C₂×C₈×C₈₉	—	2	2	no	—
99	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
100	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
101	C₄⋊C₄×C₈₉	—	2	12	no	—
102	C₄⋊C₄×C₈₉	—	2	12	no	—
103	C₄⋊C₄×C₈₉	—	2	12	no	—
104	C₄⋊C₄×C₈₉	—	2	12	no	—
105	C₄⋊C₄×C₈₉	—	2	3	no	—
106	C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₄⋊C₄×C₈₉	C₂×D₄	1	12	yes	—
108	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
109	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
110	C₂²⋊C₄×C₈₉	—	2	12	no	—
111	C₄²×C₈₉	—	2	12	no	—
112	C₄²×C₈₉	C₂×D₄	1	6	yes	—
113	C₄²×C₈₉	C₂⁴	1	6	yes	—
114	C₂³×C₈₉	—	2	4	no	—
115	C₂³×C₈₉	—	2	2	no	—
116	C₂³×C₈₉	—	4	2	no	—
117	C₂³×C₈₉	—	4	2	no	—
118	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₈₉	—	2	6	no	—
120	Q₈×C₈₉	—	2	6	no	—
121	Q₈×C₈₉	—	4	6	no	—
122	Q₈×C₈₉	—	4	24	no	—
123	Q₈×C₈₉	C₂×SD₁₆	1	16	yes	complemented
124	D₄×C₈₉	—	2	4	no	—
125	D₄×C₈₉	—	2	2	no	—
126	D₄×C₈₉	C₂×#41	1	4	yes	—
127	C₂×C₄×C₈₉	—	2	6	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	2	6	no	—
130	C₂×C₄×C₈₉	—	2	6	no	—
131	C₂×C₄×C₈₉	—	4	6	no	—
132	C₂×C₄×C₈₉	—	4	6	no	—
133	C₂×C₄×C₈₉	—	4	2	no	—
134	C₂×C₄×C₈₉	—	4	24	no	—
135	C₂×C₄×C₈₉	C₂×SD₁₆	1	12	yes	—
136	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
137	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
139	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
140	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
141	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
142	C₈×C₈₉	—	2	6	no	—
143	C₈×C₈₉	—	2	2	no	—
144	C₂²×C₈₉	—	2	4	no	—
145	C₂²×C₈₉	—	4	8	no	—
146	C₂²×C₈₉	—	4	2	no	—
147	C₂²×C₈₉	—	4	2	no	—
148	C₂²×C₈₉	#548	1	2	yes	—
149	C₂²×C₈₉	C₂²×SD₁₆	1	2	yes	—
150	C₂²×C₈₉	#578	1	2	yes	—
151	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
152	C₄×C₈₉	—	2	6	no	—
153	C₄×C₈₉	—	4	6	no	—
154	C₄×C₈₉	—	4	6	no	—
155	C₄×C₈₉	—	4	2	no	—
156	C₄×C₈₉	#548	1	2	yes	—
157	C₄×C₈₉	C₂²×SD₁₆	1	12	yes	—
158	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
159	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×#3359	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₈₉	—	4	4	no	—
162	C₂×C₈₉	#3359	1	4	yes	direct product factor
163	C₂×C₈₉	C₂×#548	1	1	yes	characteristic
164	C₂×C₈₉	C₂³×SD₁₆	1	1	yes	characteristic
165	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
166	C₂×#557	C₂×C₈₉	1	1	yes	characteristic, complemented
167	C₂×D₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
168	#3359	C₂×C₈₉	1	16	yes	direct product factor
169	C₂×#487	C₂×C₈₉	1	3	yes	complemented
170	C₂×#475	C₂×C₈₉	1	3	yes	complemented
171	C₂×#461	C₂×C₈₉	1	3	yes	—
172	C₂×C₈×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
173	C₂×C₄×SD₁₆	C₂×C₈₉	1	3	yes	—
174	C₈₉	C₂×#3359	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³×Q₈	—	2	1	no	—
176	C₂²×SD₁₆	C₂²×C₈₉	1	3	yes	—
177	#557	—	2	4	no	—
178	#557	C₂²×C₈₉	1	8	yes	complemented
179	D₄×Q₈	—	2	4	no	—
180	D₄×Q₈	C₂²×C₈₉	1	8	yes	—
181	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
182	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
183	C₂×#125	—	2	3	no	—
184	C₂×C₂²⋊Q₈	—	2	3	no	—
185	C₂×C₄×Q₈	—	2	1	no	—
186	C₂×C₄×Q₈	C₂²×C₈₉	1	3	yes	—
187	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
189	#487	C₂²×C₈₉	1	24	yes	complemented
190	#475	C₂²×C₈₉	1	24	yes	complemented
191	#461	C₂²×C₈₉	1	24	yes	—
192	C₈×Q₈	C₂²×C₈₉	1	8	yes	complemented
193	C₄×SD₁₆	C₂²×C₈₉	1	24	yes	—
194	C₂×#106	C₂²×C₈₉	1	3	yes	—
195	C₂×C₄⋊C₈	C₂²×C₈₉	1	3	yes	—
196	C₂×#103	C₂²×C₈₉	1	6	yes	—
197	C₂×#103	C₂²×C₈₉	1	3	yes	—
198	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₈₉	1	3	yes	—
200	C₂²×Q₈	—	2	8	no	—
201	C₂²×Q₈	—	2	3	no	—
202	C₂²×Q₈	—	4	8	no	—
203	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
204	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
205	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
206	C₂³×C₄	—	2	3	no	—
207	C₂×SD₁₆	—	2	12	no	—
208	C₂×SD₁₆	C₂³×C₈₉	1	12	yes	—
209	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
210	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
211	C₄⋊Q₈	—	2	6	no	—
212	C₄⋊Q₈	—	2	6	no	—
213	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
214	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
215	#125	—	2	24	no	—
216	C₂²⋊Q₈	—	2	24	no	—
217	C₄×Q₈	—	2	8	no	—
218	C₄×Q₈	—	2	6	no	—
219	C₄×Q₈	D₄×C₈₉	1	4	yes	—
220	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
221	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
222	C₄×D₄	—	2	6	no	—
223	C₄×D₄	C₂³×C₈₉	1	12	yes	—
224	C₂×C₄⋊C₄	—	2	3	no	—
225	C₂×C₄⋊C₄	—	2	3	no	—
226	C₂×C₄⋊C₄	—	2	3	no	—
227	C₂×C₄⋊C₄	—	2	3	no	—
228	C₂×C₄⋊C₄	D₄×C₈₉	1	3	yes	—
229	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
230	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	3	no	—
232	C₂×C₄²	—	2	3	no	—
233	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
234	#106	C₂³×C₈₉	1	12	yes	—
235	C₄⋊C₈	C₂³×C₈₉	1	12	yes	—
236	#103	C₂³×C₈₉	1	12	yes	—
237	#103	C₂³×C₈₉	1	24	yes	—
238	#102	C₂³×C₈₉	1	4	yes	—
239	C₄×C₈	C₂³×C₈₉	1	12	yes	—
240	C₂⁴	—	2	1	no	—
241	C₂×Q₈	—	2	3	no	—
242	C₂×Q₈	—	2	12	no	—
243	C₂×Q₈	—	2	6	no	—
244	C₂×Q₈	—	2	6	no	—
245	C₂×Q₈	—	4	32	no	—
246	C₂×Q₈	—	4	12	no	—
247	C₂×Q₈	SD₁₆×C₈₉	1	8	yes	complemented
248	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
249	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	#41×C₈₉	1	4	yes	—
253	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	3	no	—
256	C₂²×C₄	—	2	3	no	—
257	C₂²×C₄	—	2	12	no	—
258	C₂²×C₄	—	4	12	no	—
259	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
260	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
261	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
262	SD₁₆	—	2	24	no	—
263	C₂×C₈	—	2	6	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
266	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
267	C₄⋊C₄	—	2	12	no	—
268	C₄⋊C₄	—	2	12	no	—
269	C₄⋊C₄	—	2	12	no	—
270	C₄⋊C₄	—	2	12	no	—
271	C₄⋊C₄	—	2	3	no	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	C₂×D₄×C₈₉	1	12	yes	—
274	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
275	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
276	C₂²⋊C₄	—	2	12	no	—
277	C₄²	—	2	12	no	—
278	C₄²	C₂×D₄×C₈₉	1	6	yes	—
279	C₄²	C₂⁴×C₈₉	1	6	yes	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	4	2	no	—
283	C₂³	—	4	2	no	—
284	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
285	Q₈	—	2	6	no	—
286	Q₈	—	2	6	no	—
287	Q₈	—	4	6	no	—
288	Q₈	—	4	24	no	—
289	Q₈	C₂×SD₁₆×C₈₉	1	16	yes	complemented
290	D₄	—	2	4	no	—
291	D₄	—	2	2	no	—
292	D₄	C₂×#41×C₈₉	1	4	yes	—
293	C₂×C₄	—	2	6	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	6	no	—
296	C₂×C₄	—	2	6	no	—
297	C₂×C₄	—	4	6	no	—
298	C₂×C₄	—	4	6	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	24	no	—
301	C₂×C₄	C₂×SD₁₆×C₈₉	1	12	yes	—
302	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
303	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
304	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
305	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
306	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
307	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
308	C₈	—	2	6	no	—
309	C₈	—	2	2	no	—
310	C₂²	—	2	4	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	—	4	8	no	—
314	C₂²	#548×C₈₉	1	2	yes	—
315	C₂²	C₂²×SD₁₆×C₈₉	1	2	yes	—
316	C₂²	#578×C₈₉	1	2	yes	—
317	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
318	C₄	—	2	6	no	—
319	C₄	—	4	6	no	—
320	C₄	—	4	2	no	—
321	C₄	—	4	6	no	—
322	C₄	#548×C₈₉	1	2	yes	—
323	C₄	C₂²×SD₁₆×C₈₉	1	12	yes	—
324	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
325	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
326	C₂	—	4	4	no	—
327	C₂	C₈₉×#3359	1	4	yes	direct product factor
328	C₂	C₂×#548×C₈₉	1	1	yes	characteristic
329	C₂	C₂³×SD₁₆×C₈₉	1	1	yes	characteristic
330	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×#3359	C₂	direct (N × H)
4. C₂×#487×C₈₉	C₂	semidirect
5. C₂×#475×C₈₉	C₂	semidirect
7. C₂×C₈×Q₈×C₈₉	C₂	semidirect
12. #557×C₈₉	C₂²	semidirect
23. #487×C₈₉	C₂²	semidirect
24. #475×C₈₉	C₂²	semidirect
26. C₈×Q₈×C₈₉	C₂²	semidirect
81. C₂×Q₈×C₈₉	SD₁₆	semidirect
123. Q₈×C₈₉	C₂×SD₁₆	semidirect
160. C₂×#3359	C₈₉	direct (N × H)
162. C₂×C₈₉	#3359	direct (N × H)
166. C₂×#557	C₂×C₈₉	semidirect
168. #3359	C₂×C₈₉	direct (N × H)
169. C₂×#487	C₂×C₈₉	semidirect
170. C₂×#475	C₂×C₈₉	semidirect
172. C₂×C₈×Q₈	C₂×C₈₉	semidirect
174. C₈₉	C₂×#3359	direct (N × H)
178. #557	C₂²×C₈₉	semidirect
189. #487	C₂²×C₈₉	semidirect
190. #475	C₂²×C₈₉	semidirect
192. C₈×Q₈	C₂²×C₈₉	semidirect
247. C₂×Q₈	SD₁₆×C₈₉	semidirect
289. Q₈	C₂×SD₁₆×C₈₉	semidirect
327. C₂	C₈₉×#3359	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×D₄×Q₈×C₈₉	2
C₈₉×#3359	2
C₂×#487×C₈₉	2
C₂×#475×C₈₉	2
C₂×#461×C₈₉	2
C₂×C₈×Q₈×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₂×#3359	89

Subgroups — C2×C89×#3359 #36439144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3359 #36439144