Subgroups — C₈₉×#19397 #36397245

Order 22784.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3206	C₂	1	1	yes	maximal, characteristic
2	C₂×#475×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3037	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1680	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1666	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1540	C₂	1	1	yes	maximal, characteristic
10	C₂×#137×C₈₉	—	2	1	no	—
11	#532×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	#492×C₈₉	C₂²	1	2	yes	—
15	#487×C₈₉	C₂²	1	2	yes	—
16	#475×C₈₉	—	2	2	no	—
17	#475×C₈₉	C₂²	1	4	yes	—
18	#464×C₈₉	—	2	2	no	—
19	#462×C₈₉	C₂²	1	2	yes	—
20	#461×C₈₉	—	2	2	no	—
21	#460×C₈₉	C₂²	1	2	yes	—
22	#448×C₈₉	—	2	2	no	—
23	C₈×Q₈×C₈₉	—	2	2	no	—
24	C₈×Q₈×C₈₉	C₂²	1	4	yes	—
25	#431×C₈₉	—	2	2	no	—
26	#431×C₈₉	C₂²	1	1	yes	characteristic
27	#431×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₈₉	—	2	1	no	—
29	#423×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
31	#417×C₈₉	—	2	1	no	—
32	C₂×#103×C₈₉	—	2	1	no	—
33	#334×C₈₉	C₂²	1	4	yes	—
34	#332×C₈₉	C₂²	1	2	yes	—
35	#332×C₈₉	C₂²	1	4	yes	—
36	#331×C₈₉	C₂²	1	2	yes	—
37	C₂×#41×C₈₉	—	2	1	no	—
38	C₂²×Q₈×C₈₉	—	2	1	no	—
39	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
40	#137×C₈₉	—	4	4	no	—
41	C₂×Q₁₆×C₈₉	—	2	2	no	—
42	C₂×SD₁₆×C₈₉	—	2	2	no	—
43	C₂×SD₁₆×C₈₉	—	2	4	no	—
44	C₂×M₁₆×C₈₉	—	2	1	no	—
45	C₂²×C₈×C₈₉	—	2	1	no	—
46	C₄⋊Q₈×C₈₉	—	2	1	no	—
47	C₄⋊Q₈×C₈₉	—	2	1	no	—
48	C₄⋊Q₈×C₈₉	—	2	1	no	—
49	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
51	#127×C₈₉	C₂³	1	1	yes	characteristic
52	#124×C₈₉	—	2	1	no	—
53	#121×C₈₉	—	2	1	no	—
54	#121×C₈₉	—	2	1	no	—
55	C₄×Q₈×C₈₉	—	2	1	no	—
56	C₄×Q₈×C₈₉	—	2	1	no	—
57	C₄×Q₈×C₈₉	D₄	1	2	yes	—
58	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
59	C₄×D₄×C₈₉	—	2	1	no	—
60	C₄×D₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	—	2	1	no	—
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	#106×C₈₉	—	2	4	no	—
68	C₄⋊C₈×C₈₉	—	2	4	no	—
69	C₄⋊C₈×C₈₉	—	2	1	no	—
70	C₄⋊C₈×C₈₉	—	2	1	no	—
71	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
72	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
73	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
74	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
75	#103×C₈₉	—	2	4	no	—
76	#103×C₈₉	—	2	4	no	—
77	#103×C₈₉	—	2	2	no	—
78	#102×C₈₉	—	2	2	no	—
79	C₂²⋊C₈×C₈₉	—	2	1	no	—
80	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
81	C₄×C₈×C₈₉	—	2	4	no	—
82	C₄×C₈×C₈₉	—	2	1	no	—
83	C₄×C₈×C₈₉	C₂³	1	2	yes	—
84	#41×C₈₉	—	4	2	no	—
85	#41×C₈₉	—	4	2	no	—
86	C₂×Q₈×C₈₉	—	2	1	no	—
87	C₂×Q₈×C₈₉	—	2	2	no	—
88	C₂×Q₈×C₈₉	—	2	1	no	—
89	C₂×Q₈×C₈₉	—	2	2	no	—
90	C₂×Q₈×C₈₉	—	4	1	no	—
91	C₂×Q₈×C₈₉	—	8	2	no	—
92	C₂×Q₈×C₈₉	SD₁₆	1	4	yes	complemented
93	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₈₉	—	2	1	no	—
95	C₂×D₄×C₈₉	—	2	1	no	—
96	C₂×D₄×C₈₉	—	2	1	no	—
97	C₂×D₄×C₈₉	—	4	1	no	—
98	C₂²×C₄×C₈₉	—	2	1	no	—
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	4	1	no	—
101	C₂²×C₄×C₈₉	—	4	1	no	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
105	Q₁₆×C₈₉	—	4	4	no	—
106	SD₁₆×C₈₉	—	4	4	no	—
107	SD₁₆×C₈₉	—	8	4	no	—
108	M₁₆×C₈₉	—	4	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	2	no	—
111	C₂×C₈×C₈₉	—	2	2	no	—
112	C₂×C₈×C₈₉	—	4	2	no	—
113	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
114	C₄⋊C₄×C₈₉	—	2	2	no	—
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₄⋊C₄×C₈₉	—	2	2	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	—	2	1	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₈₉	—	4	1	no	—
125	C₂²⋊C₄×C₈₉	—	4	1	no	—
126	C₄²×C₈₉	—	2	2	no	—
127	C₄²×C₈₉	—	2	2	no	—
128	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₈₉	#41	1	1	yes	characteristic
131	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
132	C₂³×C₈₉	—	4	1	no	—
133	C₂³×C₈₉	#121	1	1	yes	characteristic
134	Q₈×C₈₉	—	2	2	no	—
135	Q₈×C₈₉	—	2	4	no	—
136	Q₈×C₈₉	—	4	1	no	—
137	Q₈×C₈₉	—	4	1	no	—
138	Q₈×C₈₉	—	4	4	no	—
139	Q₈×C₈₉	—	8	2	no	—
140	Q₈×C₈₉	C₂×SD₁₆	1	4	yes	—
141	D₄×C₈₉	—	4	1	no	—
142	D₄×C₈₉	—	4	1	no	—
143	D₄×C₈₉	—	4	2	no	—
144	D₄×C₈₉	—	8	1	no	—
145	D₄×C₈₉	—	8	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	4	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	8	1	no	—
154	C₂×C₄×C₈₉	—	8	2	no	—
155	C₂×C₄×C₈₉	—	8	2	no	—
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₈₉	#135	1	2	yes	—
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
164	C₈×C₈₉	—	2	4	no	—
165	C₈×C₈₉	—	4	2	no	—
166	C₈×C₈₉	—	4	2	no	—
167	C₈×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	8	1	no	—
171	C₂²×C₈₉	—	8	1	no	—
172	C₂²×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	#465	1	2	yes	—
174	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	2	4	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	4	2	no	—
180	C₄×C₈₉	—	8	2	no	—
181	C₄×C₈₉	—	8	1	no	—
182	C₄×C₈₉	#465	1	2	yes	—
183	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
184	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
185	C₄×C₈₉	#577	1	2	yes	—
186	#19397	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₈₉	—	2	2	no	—
188	C₂×C₈₉	—	16	1	no	—
189	C₂×C₈₉	#3043	1	1	yes	characteristic
190	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
191	C₂×C₈₉	#3069	1	1	yes	characteristic
192	#3206	C₂×C₈₉	1	1	yes	characteristic
193	C₂×#475	C₂×C₈₉	1	1	yes	characteristic, complemented
194	#3037	C₂×C₈₉	1	1	yes	characteristic
195	#2982	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#1680	C₂×C₈₉	1	4	yes	complemented
197	#1666	C₂×C₈₉	1	4	yes	complemented
198	#1570	C₂×C₈₉	1	1	yes	characteristic, complemented
199	#1549	C₂×C₈₉	1	1	yes	characteristic, complemented
200	#1540	C₂×C₈₉	1	1	yes	characteristic
201	C₈₉	#19397	1	1	yes	characteristic, direct product factor, Sylow
202	C₂×#137	—	2	1	no	—
203	#532	C₂²×C₈₉	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
206	#492	C₂²×C₈₉	1	2	yes	—
207	#487	C₂²×C₈₉	1	2	yes	—
208	#475	—	2	2	no	—
209	#475	C₂²×C₈₉	1	4	yes	—
210	#464	—	2	2	no	—
211	#462	C₂²×C₈₉	1	2	yes	—
212	#461	—	2	2	no	—
213	#460	C₂²×C₈₉	1	2	yes	—
214	#448	—	2	2	no	—
215	C₈×Q₈	—	2	2	no	—
216	C₈×Q₈	C₂²×C₈₉	1	4	yes	—
217	#431	—	2	2	no	—
218	#431	C₂²×C₈₉	1	1	yes	characteristic
219	#431	C₂²×C₈₉	1	1	yes	characteristic
220	C₂×#106	—	2	1	no	—
221	#423	C₂²×C₈₉	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
223	#417	—	2	1	no	—
224	C₂×#103	—	2	1	no	—
225	#334	C₂²×C₈₉	1	4	yes	—
226	#332	C₂²×C₈₉	1	2	yes	—
227	#332	C₂²×C₈₉	1	4	yes	—
228	#331	C₂²×C₈₉	1	2	yes	—
229	C₂×#41	—	2	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
232	#137	—	4	4	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
243	#127	C₂³×C₈₉	1	1	yes	characteristic
244	#124	—	2	1	no	—
245	#121	—	2	1	no	—
246	#121	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	D₄×C₈₉	1	2	yes	—
250	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
259	#106	—	2	4	no	—
260	C₄⋊C₈	—	2	4	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
264	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
265	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
266	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
267	#103	—	2	4	no	—
268	#103	—	2	4	no	—
269	#103	—	2	2	no	—
270	#102	—	2	2	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	D₄×C₈₉	1	2	yes	—
273	C₄×C₈	—	2	4	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂³×C₈₉	1	2	yes	—
276	#41	—	4	2	no	—
277	#41	—	4	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	8	2	no	—
284	C₂×Q₈	SD₁₆×C₈₉	1	4	yes	complemented
285	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
296	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
297	Q₁₆	—	4	4	no	—
298	SD₁₆	—	4	4	no	—
299	SD₁₆	—	8	4	no	—
300	M₁₆	—	4	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
322	C₄²	#41×C₈₉	1	1	yes	characteristic
323	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
324	C₂³	—	4	1	no	—
325	C₂³	#121×C₈₉	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	4	1	no	—
329	Q₈	—	4	1	no	—
330	Q₈	—	4	4	no	—
331	Q₈	—	8	2	no	—
332	Q₈	C₂×SD₁₆×C₈₉	1	4	yes	—
333	D₄	—	4	1	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	2	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
349	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
350	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
351	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
352	C₂×C₄	#135×C₈₉	1	2	yes	—
353	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	#465×C₈₉	1	2	yes	—
366	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	1	no	—
374	C₄	#465×C₈₉	1	2	yes	—
375	C₄	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
376	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
377	C₄	#577×C₈₉	1	2	yes	—
378	C₂	—	2	2	no	—
379	C₂	—	16	1	no	—
380	C₂	C₈₉×#3043	1	1	yes	characteristic
381	C₂	C₂×#465×C₈₉	1	1	yes	characteristic
382	C₂	C₈₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	#532×C₈₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#475×C₈₉	C₂	semidirect
4. C₈₉×#2982	C₂	semidirect
5. C₈₉×#1680	C₂	semidirect
6. C₈₉×#1666	C₂	semidirect
7. C₈₉×#1570	C₂	semidirect
8. C₈₉×#1549	C₂	semidirect
92. C₂×Q₈×C₈₉	SD₁₆	semidirect
186. #19397	C₈₉	direct (N × H)
193. C₂×#475	C₂×C₈₉	semidirect
195. #2982	C₂×C₈₉	semidirect
196. #1680	C₂×C₈₉	semidirect
197. #1666	C₂×C₈₉	semidirect
198. #1570	C₂×C₈₉	semidirect
199. #1549	C₂×C₈₉	semidirect
201. C₈₉	#19397	direct (N × H)
284. C₂×Q₈	SD₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3206	2
C₂×#475×C₈₉	2
C₈₉×#3037	2
C₈₉×#2982	2
C₈₉×#1680	2
C₈₉×#1666	2
C₈₉×#1570	2
C₈₉×#1549	2
C₈₉×#1540	2
#19397	89

Subgroups — C89×#19397 #36397245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19397 #36397245