Subgroups — C₈₉×#19387 #36397235

Order 22784.

654 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2972	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1683	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1669	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1571	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	#533×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
13	#494×C₈₉	C₂²	1	2	yes	complemented
14	#487×C₈₉	C₂²	1	2	yes	complemented
15	#478×C₈₉	—	2	2	no	—
16	#476×C₈₉	C₂²	1	2	yes	—
17	#474×C₈₉	—	2	2	no	—
18	#474×C₈₉	C₂²	1	4	yes	—
19	#474×C₈₉	C₂²	1	2	yes	—
20	#462×C₈₉	—	2	2	no	—
21	#451×C₈₉	—	2	2	no	—
22	C₈×D₄×C₈₉	—	2	2	no	—
23	C₈×D₄×C₈₉	C₂²	1	4	yes	—
24	#431×C₈₉	C₂²	1	1	yes	characteristic
25	#431×C₈₉	C₂²	1	1	yes	characteristic
26	#428×C₈₉	—	2	1	no	—
27	C₂×#107×C₈₉	—	2	1	no	—
28	#423×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
30	#418×C₈₉	—	2	1	no	—
31	C₂×#102×C₈₉	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
33	#335×C₈₉	C₂²	1	4	yes	complemented
34	#333×C₈₉	C₂²	1	2	yes	complemented
35	#332×C₈₉	C₂²	1	2	yes	complemented
36	#332×C₈₉	C₂²	1	4	yes	complemented
37	C₂²×Q₈×C₈₉	—	2	1	no	—
38	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₈₉	—	2	1	no	—
40	C₂×Q₁₆×C₈₉	—	2	4	no	—
41	C₂×M₁₆×C₈₉	—	2	1	no	—
42	C₂²×C₈×C₈₉	—	2	1	no	—
43	C₂²×C₈×C₈₉	—	2	4	no	—
44	C₄⋊Q₈×C₈₉	—	2	1	no	—
45	C₄⋊Q₈×C₈₉	—	2	1	no	—
46	C₄⋊Q₈×C₈₉	—	2	1	no	—
47	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
50	#125×C₈₉	—	2	1	no	—
51	C₂²⋊Q₈×C₈₉	—	2	1	no	—
52	C₂²⋊Q₈×C₈₉	—	2	1	no	—
53	C₄×Q₈×C₈₉	—	2	1	no	—
54	C₄×Q₈×C₈₉	—	2	1	no	—
55	C₄×D₄×C₈₉	—	2	1	no	—
56	C₄×D₄×C₈₉	—	2	1	no	—
57	C₄×D₄×C₈₉	D₄	1	2	yes	—
58	C₄×D₄×C₈₉	C₂³	1	2	yes	—
59	#117×C₈₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	#107×C₈₉	—	2	4	no	—
66	#107×C₈₉	—	2	2	no	—
67	#106×C₈₉	—	2	2	no	—
68	C₄⋊C₈×C₈₉	—	2	1	no	—
69	C₄⋊C₈×C₈₉	—	2	1	no	—
70	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
71	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
72	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
73	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
74	#103×C₈₉	—	2	4	no	—
75	#102×C₈₉	—	2	4	no	—
76	#102×C₈₉	—	2	2	no	—
77	#102×C₈₉	—	2	2	no	—
78	C₂²⋊C₈×C₈₉	—	2	1	no	—
79	C₂²⋊C₈×C₈₉	—	2	4	no	—
80	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
81	C₄×C₈×C₈₉	—	2	1	no	—
82	C₄×C₈×C₈₉	C₂³	1	2	yes	—
83	C₂⁴×C₈₉	—	2	1	no	—
84	C₂×Q₈×C₈₉	—	2	2	no	—
85	C₂×Q₈×C₈₉	—	2	1	no	—
86	C₂×Q₈×C₈₉	—	2	1	no	—
87	C₂×Q₈×C₈₉	—	4	1	no	—
88	C₂×Q₈×C₈₉	—	8	2	no	—
89	C₂×D₄×C₈₉	—	2	1	no	—
90	C₂×D₄×C₈₉	—	2	2	no	—
91	C₂×D₄×C₈₉	Q₁₆	1	4	yes	complemented
92	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₈₉	—	2	1	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	4	1	no	—
97	C₂²×C₄×C₈₉	—	8	2	no	—
98	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
101	Q₁₆×C₈₉	—	8	4	no	—
102	M₁₆×C₈₉	—	4	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	4	2	no	—
107	C₂×C₈×C₈₉	—	8	4	no	—
108	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	—	2	2	no	—
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	—	4	1	no	—
117	C₄⋊C₄×C₈₉	—	4	1	no	—
118	C₄⋊C₄×C₈₉	—	4	1	no	—
119	C₄⋊C₄×C₈₉	—	4	1	no	—
120	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
121	C₂²⋊C₄×C₈₉	—	2	2	no	—
122	C₂²⋊C₄×C₈₉	—	2	2	no	—
123	C₂²⋊C₄×C₈₉	—	4	1	no	—
124	C₄²×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₈₉	#41	1	1	yes	characteristic
128	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
129	C₂³×C₈₉	—	2	2	no	—
130	C₂³×C₈₉	—	2	4	no	—
131	C₂³×C₈₉	—	8	1	no	—
132	C₂³×C₈₉	—	8	1	no	—
133	C₂³×C₈₉	#121	1	1	yes	characteristic
134	Q₈×C₈₉	—	4	2	no	—
135	Q₈×C₈₉	—	4	4	no	—
136	Q₈×C₈₉	—	8	1	no	—
137	Q₈×C₈₉	—	8	2	no	—
138	D₄×C₈₉	—	2	2	no	—
139	D₄×C₈₉	—	2	4	no	—
140	D₄×C₈₉	C₂×Q₁₆	1	4	yes	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	2	no	—
148	C₂×C₄×C₈₉	—	8	2	no	—
149	C₂×C₄×C₈₉	—	8	1	no	—
150	C₂×C₄×C₈₉	—	8	2	no	—
151	C₂×C₄×C₈₉	#121	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×Q₁₆	1	2	yes	—
155	C₂×C₄×C₈₉	#135	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
159	C₈×C₈₉	—	2	4	no	—
160	C₈×C₈₉	—	4	2	no	—
161	C₈×C₈₉	—	4	2	no	—
162	C₈×C₈₉	—	4	2	no	—
163	C₂²×C₈₉	—	2	1	no	—
164	C₂²×C₈₉	—	2	1	no	—
165	C₂²×C₈₉	—	2	4	no	—
166	C₂²×C₈₉	—	4	2	no	—
167	C₂²×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	—	8	4	no	—
169	C₂²×C₈₉	#467	1	2	yes	—
170	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
171	C₄×C₈₉	—	2	1	no	—
172	C₄×C₈₉	—	2	1	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	4	2	no	—
175	C₄×C₈₉	—	8	2	no	—
176	C₄×C₈₉	—	8	1	no	—
177	C₄×C₈₉	—	8	1	no	—
178	C₄×C₈₉	#467	1	2	yes	—
179	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
180	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
181	C₄×C₈₉	#576	1	2	yes	—
182	#19387	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₈₉	—	2	2	no	—
184	C₂×C₈₉	—	4	4	no	—
185	C₂×C₈₉	#3041	1	1	yes	characteristic
186	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
187	C₂×C₈₉	#3069	1	1	yes	characteristic
188	#3209	C₂×C₈₉	1	1	yes	characteristic, complemented
189	#3077	C₂×C₈₉	1	1	yes	characteristic
190	C₂×#474	C₂×C₈₉	1	1	yes	characteristic
191	#2972	C₂×C₈₉	1	1	yes	characteristic
192	#1683	C₂×C₈₉	1	4	yes	complemented
193	#1669	C₂×C₈₉	1	4	yes	complemented
194	#1571	C₂×C₈₉	1	1	yes	characteristic, complemented
195	#1549	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#1542	C₂×C₈₉	1	1	yes	characteristic, complemented
197	C₈₉	#19387	1	1	yes	characteristic, direct product factor, Sylow
198	#533	C₂²×C₈₉	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
201	#494	C₂²×C₈₉	1	2	yes	complemented
202	#487	C₂²×C₈₉	1	2	yes	complemented
203	#478	—	2	2	no	—
204	#476	C₂²×C₈₉	1	2	yes	—
205	#474	—	2	2	no	—
206	#474	C₂²×C₈₉	1	2	yes	—
207	#474	C₂²×C₈₉	1	4	yes	—
208	#462	—	2	2	no	—
209	#451	—	2	2	no	—
210	C₈×D₄	—	2	2	no	—
211	C₈×D₄	C₂²×C₈₉	1	4	yes	—
212	#431	C₂²×C₈₉	1	1	yes	characteristic
213	#431	C₂²×C₈₉	1	1	yes	characteristic
214	#428	—	2	1	no	—
215	C₂×#107	—	2	1	no	—
216	#423	C₂²×C₈₉	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
218	#418	—	2	1	no	—
219	C₂×#102	—	2	1	no	—
220	C₂×C₂²⋊C₈	—	2	2	no	—
221	#335	C₂²×C₈₉	1	4	yes	complemented
222	#333	C₂²×C₈₉	1	2	yes	complemented
223	#332	C₂²×C₈₉	1	2	yes	complemented
224	#332	C₂²×C₈₉	1	4	yes	complemented
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
227	C₂³×C₄	—	2	1	no	—
228	C₂×Q₁₆	—	2	4	no	—
229	C₂×M₁₆	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	4	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
236	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
238	#125	—	2	1	no	—
239	C₂²⋊Q₈	—	2	1	no	—
240	C₂²⋊Q₈	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	D₄×C₈₉	1	2	yes	—
246	C₄×D₄	C₂³×C₈₉	1	2	yes	—
247	#117	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
253	#107	—	2	4	no	—
254	#107	—	2	2	no	—
255	#106	—	2	2	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
259	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
260	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
261	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
262	#103	—	2	4	no	—
263	#102	—	2	4	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	4	no	—
268	C₂²⋊C₈	D₄×C₈₉	1	2	yes	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	C₂³×C₈₉	1	2	yes	—
271	C₂⁴	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	8	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	Q₁₆×C₈₉	1	4	yes	complemented
280	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	8	2	no	—
286	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
288	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
289	Q₁₆	—	8	4	no	—
290	M₁₆	—	4	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	8	4	no	—
296	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
315	C₄²	#41×C₈₉	1	1	yes	characteristic
316	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	8	1	no	—
321	C₂³	#121×C₈₉	1	1	yes	characteristic
322	Q₈	—	4	2	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	8	1	no	—
325	Q₈	—	8	2	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	C₂×Q₁₆×C₈₉	1	4	yes	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
340	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
341	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
342	C₂×C₄	C₂×Q₁₆×C₈₉	1	2	yes	—
343	C₂×C₄	#135×C₈₉	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	8	4	no	—
357	C₂²	#467×C₈₉	1	2	yes	—
358	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	1	no	—
366	C₄	#467×C₈₉	1	2	yes	—
367	C₄	C₂²×Q₁₆×C₈₉	1	1	yes	characteristic
368	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
369	C₄	#576×C₈₉	1	2	yes	—
370	C₂	—	2	2	no	—
371	C₂	—	4	4	no	—
372	C₂	C₈₉×#3041	1	1	yes	characteristic
373	C₂	C₂×#467×C₈₉	1	1	yes	characteristic
374	C₂	C₈₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₂²×D₄×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
1. C₈₉×#3209	C₂	semidirect
5. C₈₉×#1683	C₂	semidirect
6. C₈₉×#1669	C₂	semidirect
7. C₈₉×#1571	C₂	semidirect
8. C₈₉×#1549	C₂	semidirect
9. C₈₉×#1542	C₂	semidirect
13. #494×C₈₉	C₂²	semidirect
14. #487×C₈₉	C₂²	semidirect
33. #335×C₈₉	C₂²	semidirect
34. #333×C₈₉	C₂²	semidirect
35. #332×C₈₉	C₂²	semidirect
36. #332×C₈₉	C₂²	semidirect
91. C₂×D₄×C₈₉	Q₁₆	semidirect
182. #19387	C₈₉	direct (N × H)
188. #3209	C₂×C₈₉	semidirect
192. #1683	C₂×C₈₉	semidirect
193. #1669	C₂×C₈₉	semidirect
194. #1571	C₂×C₈₉	semidirect
195. #1549	C₂×C₈₉	semidirect
196. #1542	C₂×C₈₉	semidirect
197. C₈₉	#19387	direct (N × H)
201. #494	C₂²×C₈₉	semidirect
202. #487	C₂²×C₈₉	semidirect
221. #335	C₂²×C₈₉	semidirect
222. #333	C₂²×C₈₉	semidirect
223. #332	C₂²×C₈₉	semidirect
224. #332	C₂²×C₈₉	semidirect
279. C₂×D₄	Q₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3209	2
C₈₉×#3077	2
C₂×#474×C₈₉	2
C₈₉×#2972	2
C₈₉×#1683	2
C₈₉×#1669	2
C₈₉×#1571	2
C₈₉×#1549	2
C₈₉×#1542	2
#19387	89

Subgroups — C89×#19387 #36397235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19387 #36397235