Subgroups — C₈₉×#9169 #36387017

Order 22784.

478 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×#3079	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#333×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1477	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#131×C₈₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
11	#477×C₈₉	—	2	1	no	—
12	#476×C₈₉	—	2	1	no	—
13	#475×C₈₉	C₄	1	2	yes	—
14	#474×C₈₉	C₄	1	2	yes	—
15	#431×C₈₉	C₂²	1	1	yes	characteristic
16	#428×C₈₉	—	2	1	no	—
17	#424×C₈₉	—	2	1	no	—
18	#424×C₈₉	—	2	2	no	—
19	#423×C₈₉	—	2	1	no	—
20	#423×C₈₉	C₂²	1	1	yes	characteristic
21	#423×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	#417×C₈₉	—	2	1	no	—
26	#333×C₈₉	—	2	1	no	—
27	#333×C₈₉	—	2	1	no	—
28	#332×C₈₉	—	2	2	no	—
29	Q₈⋊C₈×C₈₉	—	2	1	no	—
30	D₄⋊C₈×C₈₉	—	2	1	no	—
31	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
32	C₂²×Q₈×C₈₉	—	2	1	no	—
33	#131×C₈₉	—	4	2	no	—
34	#131×C₈₉	—	4	2	no	—
35	C₂×M₁₆×C₈₉	—	2	2	no	—
36	C₂×M₁₆×C₈₉	—	2	1	no	—
37	C₂×M₁₆×C₈₉	—	2	1	no	—
38	C₂²×C₈×C₈₉	—	2	2	no	—
39	C₂²×C₈×C₈₉	—	2	1	no	—
40	C₂²×C₈×C₈₉	—	2	1	no	—
41	C₄⋊Q₈×C₈₉	—	2	1	no	—
42	C₄⋊Q₈×C₈₉	—	2	1	no	—
43	C₄⋊Q₈×C₈₉	—	2	1	no	—
44	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
47	C₄×D₄×C₈₉	—	2	1	no	—
48	C₄×D₄×C₈₉	—	2	1	no	—
49	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
50	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
51	#117×C₈₉	—	2	1	no	—
52	#117×C₈₉	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄²×C₈₉	—	2	1	no	—
56	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
57	#107×C₈₉	—	2	2	no	—
58	#106×C₈₉	—	2	2	no	—
59	C₄⋊C₈×C₈₉	—	2	2	no	—
60	C₄⋊C₈×C₈₉	—	2	2	no	—
61	C₄⋊C₈×C₈₉	—	2	1	no	—
62	C₄⋊C₈×C₈₉	—	2	1	no	—
63	C₄⋊C₈×C₈₉	—	2	1	no	—
64	C₄⋊C₈×C₈₉	—	2	1	no	—
65	C₄⋊C₈×C₈₉	—	2	1	no	—
66	C₄⋊C₈×C₈₉	—	2	1	no	—
67	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
68	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
69	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
70	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
71	#103×C₈₉	—	2	2	no	—
72	#102×C₈₉	—	2	2	no	—
73	C₂²⋊C₈×C₈₉	—	2	1	no	—
74	C₄×C₈×C₈₉	—	2	1	no	—
75	#41×C₈₉	—	2	1	no	—
76	#41×C₈₉	—	2	1	no	—
77	#41×C₈₉	SD₁₆	1	2	yes	—
78	#41×C₈₉	Q₁₆	1	2	yes	—
79	C₂×Q₈×C₈₉	—	2	2	no	—
80	C₂×Q₈×C₈₉	—	4	1	no	—
81	C₂×Q₈×C₈₉	—	8	2	no	—
82	C₂×Q₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₈₉	—	2	1	no	—
84	C₂×D₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	—	2	1	no	—
86	C₂²×C₄×C₈₉	—	2	1	no	—
87	C₂²×C₄×C₈₉	—	2	1	no	—
88	C₂²×C₄×C₈₉	—	4	1	no	—
89	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
92	M₁₆×C₈₉	—	4	4	no	—
93	M₁₆×C₈₉	—	4	1	no	—
94	M₁₆×C₈₉	—	4	1	no	—
95	M₁₆×C₈₉	—	4	1	no	—
96	M₁₆×C₈₉	—	4	1	no	—
97	C₂×C₈×C₈₉	—	2	2	no	—
98	C₂×C₈×C₈₉	—	2	1	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	1	no	—
101	C₂×C₈×C₈₉	—	4	4	no	—
102	C₂×C₈×C₈₉	—	4	1	no	—
103	C₂×C₈×C₈₉	—	4	1	no	—
104	C₂×C₈×C₈₉	—	4	1	no	—
105	C₂×C₈×C₈₉	—	4	1	no	—
106	C₂×C₈×C₈₉	—	8	1	no	—
107	C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₄⋊C₄×C₈₉	—	2	2	no	—
111	C₄⋊C₄×C₈₉	—	4	1	no	—
112	C₄⋊C₄×C₈₉	—	4	1	no	—
113	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₄²×C₈₉	—	2	1	no	—
119	C₄²×C₈₉	—	2	1	no	—
120	C₄²×C₈₉	—	2	1	no	—
121	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	#123	1	1	yes	characteristic
127	Q₈×C₈₉	—	2	1	no	—
128	Q₈×C₈₉	—	8	2	no	—
129	Q₈×C₈₉	—	8	2	no	—
130	Q₈×C₈₉	#103	1	2	yes	—
131	D₄×C₈₉	—	2	2	no	—
132	D₄×C₈₉	—	2	2	no	—
133	D₄×C₈₉	—	2	1	no	—
134	D₄×C₈₉	#103	1	2	yes	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	—	8	1	no	—
147	C₂×C₄×C₈₉	—	8	2	no	—
148	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
156	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
158	C₈×C₈₉	—	4	2	no	—
159	C₈×C₈₉	—	4	1	no	—
160	C₈×C₈₉	—	4	2	no	—
161	C₈×C₈₉	—	4	1	no	—
162	C₈×C₈₉	—	8	1	no	—
163	C₈×C₈₉	—	8	1	no	—
164	C₂²×C₈₉	—	2	1	no	—
165	C₂²×C₈₉	—	2	1	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	—	4	1	no	—
168	C₂²×C₈₉	—	4	1	no	—
169	C₂²×C₈₉	#386	1	1	yes	characteristic
170	C₂²×C₈₉	#483	1	1	yes	characteristic
171	C₂²×C₈₉	#484	1	1	yes	characteristic
172	C₄×C₈₉	—	2	2	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	4	1	no	—
177	C₄×C₈₉	—	4	1	no	—
178	C₄×C₈₉	—	8	2	no	—
179	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
180	C₄×C₈₉	#417	1	1	yes	characteristic
181	C₄×C₈₉	#450	1	1	yes	characteristic
182	C₄×C₈₉	#451	1	1	yes	characteristic
183	C₄×C₈₉	#471	1	1	yes	characteristic
184	C₄×C₈₉	#473	1	1	yes	characteristic
185	#9169	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₈₉	—	2	1	no	—
187	C₂×C₈₉	—	2	1	no	—
188	C₂×C₈₉	—	4	2	no	—
189	C₂×C₈₉	#1872	1	1	yes	characteristic
190	C₂×C₈₉	#1903	1	1	yes	characteristic
191	C₂×C₈₉	#1908	1	1	yes	characteristic
192	#3079	C₂×C₈₉	1	1	yes	characteristic
193	#2906	C₂×C₈₉	1	1	yes	characteristic
194	#1549	C₂×C₈₉	1	1	yes	characteristic, complemented
195	C₂×#333	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#1477	C₂×C₈₉	1	1	yes	characteristic
197	#1301	C₂×C₈₉	1	1	yes	characteristic, complemented
198	#1292	C₂×C₈₉	1	1	yes	characteristic, complemented
199	C₈₉	#9169	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×#131	—	2	1	no	—
201	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
202	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
203	#477	—	2	1	no	—
204	#476	—	2	1	no	—
205	#475	C₄×C₈₉	1	2	yes	—
206	#474	C₄×C₈₉	1	2	yes	—
207	#431	C₂²×C₈₉	1	1	yes	characteristic
208	#428	—	2	1	no	—
209	#424	—	2	1	no	—
210	#424	—	2	2	no	—
211	#423	—	2	1	no	—
212	#423	C₂²×C₈₉	1	1	yes	characteristic
213	#423	C₂²×C₈₉	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	2	1	no	—
215	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
217	#417	—	2	1	no	—
218	#333	—	2	1	no	—
219	#333	—	2	1	no	—
220	#332	—	2	2	no	—
221	Q₈⋊C₈	—	2	1	no	—
222	D₄⋊C₈	—	2	1	no	—
223	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
224	C₂²×Q₈	—	2	1	no	—
225	#131	—	4	2	no	—
226	#131	—	4	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	—	2	1	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	C₂×C₄×C₈₉	1	2	yes	—
237	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
238	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
242	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
243	#117	—	2	1	no	—
244	#117	D₄×C₈₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
249	#107	—	2	2	no	—
250	#106	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	C₂×C₄×C₈₉	1	2	yes	—
260	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
261	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
262	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
263	#103	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	—	2	1	no	—
269	#41	SD₁₆×C₈₉	1	2	yes	—
270	#41	Q₁₆×C₈₉	1	2	yes	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	8	2	no	—
274	C₂×Q₈	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
282	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
284	M₁₆	—	4	4	no	—
285	M₁₆	—	4	1	no	—
286	M₁₆	—	4	1	no	—
287	M₁₆	—	4	1	no	—
288	M₁₆	—	4	1	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	4	4	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	8	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
306	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
307	C₂²⋊C₄	—	2	1	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
317	C₂³	—	2	1	no	—
318	C₂³	#123×C₈₉	1	1	yes	characteristic
319	Q₈	—	2	1	no	—
320	Q₈	—	8	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	#103×C₈₉	1	2	yes	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	1	no	—
326	D₄	#103×C₈₉	1	2	yes	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
343	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
344	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
345	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×Q₁₆×C₈₉	1	1	yes	characteristic
348	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
349	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
350	C₈	—	4	2	no	—
351	C₈	—	4	1	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	1	no	—
354	C₈	—	8	1	no	—
355	C₈	—	8	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	#386×C₈₉	1	1	yes	characteristic
362	C₂²	#483×C₈₉	1	1	yes	characteristic
363	C₂²	#484×C₈₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	C₂×#103×C₈₉	1	1	yes	characteristic
372	C₄	#417×C₈₉	1	1	yes	characteristic
373	C₄	#450×C₈₉	1	1	yes	characteristic
374	C₄	#451×C₈₉	1	1	yes	characteristic
375	C₄	#471×C₈₉	1	1	yes	characteristic
376	C₄	#473×C₈₉	1	1	yes	characteristic
377	C₂	—	2	1	no	—
378	C₂	—	2	1	no	—
379	C₂	—	4	2	no	—
380	C₂	C₈₉×#1872	1	1	yes	characteristic
381	C₂	C₈₉×#1903	1	1	yes	characteristic
382	C₂	C₈₉×#1908	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#386
commutator	C₄²	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂×#41×C₈₉	D₄
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
3. C₈₉×#1549	C₂	semidirect
4. C₂×#333×C₈₉	C₂	semidirect
6. C₈₉×#1301	C₂	semidirect
7. C₈₉×#1292	C₂	semidirect
185. #9169	C₈₉	direct (N × H)
194. #1549	C₂×C₈₉	semidirect
195. C₂×#333	C₂×C₈₉	semidirect
197. #1301	C₂×C₈₉	semidirect
198. #1292	C₂×C₈₉	semidirect
199. C₈₉	#9169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3079	2
C₈₉×#2906	2
C₈₉×#1549	2
C₂×#333×C₈₉	2
C₈₉×#1477	2
C₈₉×#1301	2
C₈₉×#1292	2
#9169	89

Subgroups — C89×#9169 #36387017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9169 #36387017