Subgroups — C₈₉×#9325 #36387173

Order 22784.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3109	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2275	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1505	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1300	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1285	C₂	1	1	yes	maximal, characteristic, complemented
8	#532×C₈₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₈₉	—	2	1	no	—
10	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	#481×C₈₉	—	2	1	no	—
12	#476×C₈₉	C₄	1	2	yes	complemented
13	#459×C₈₉	C₄	1	2	yes	complemented
14	#447×C₈₉	—	2	1	no	—
15	#442×C₈₉	—	2	2	no	—
16	#432×C₈₉	C₂²	1	1	yes	characteristic
17	#432×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#104×C₈₉	—	2	2	no	—
19	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₈₉	—	2	2	no	—
23	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
24	#376×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#95×C₈₉	—	2	1	no	—
26	#327×C₈₉	—	2	1	no	—
27	#327×C₈₉	—	2	1	no	—
28	D₄⋊C₈×C₈₉	—	2	2	no	—
29	C₂×#41×C₈₉	—	2	1	no	—
30	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₈₉	—	2	2	no	—
32	C₂³×C₄×C₈₉	—	2	1	no	—
33	C₂×D₈×C₈₉	—	2	2	no	—
34	C₂×M₁₆×C₈₉	—	2	1	no	—
35	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
36	#127×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
37	#124×C₈₉	—	2	1	no	—
38	#121×C₈₉	—	2	1	no	—
39	#121×C₈₉	—	2	1	no	—
40	C₄×D₄×C₈₉	—	2	8	no	—
41	C₄×D₄×C₈₉	—	2	1	no	—
42	C₄×D₄×C₈₉	—	2	1	no	—
43	C₄×D₄×C₈₉	—	2	1	no	—
44	C₄×D₄×C₈₉	—	2	1	no	—
45	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₈₉	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
51	C₂×C₄²×C₈₉	—	2	1	no	—
52	C₂×C₄²×C₈₉	—	2	2	no	—
53	C₂×C₄²×C₈₉	D₄	1	2	yes	—
54	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
55	#106×C₈₉	—	2	2	no	—
56	C₄⋊C₈×C₈₉	—	2	1	no	—
57	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
58	#104×C₈₉	—	4	4	no	—
59	#102×C₈₉	—	2	2	no	—
60	#102×C₈₉	—	2	2	no	—
61	C₂²⋊C₈×C₈₉	—	2	1	no	—
62	C₂²⋊C₈×C₈₉	—	2	1	no	—
63	#97×C₈₉	—	2	1	no	—
64	#97×C₈₉	—	2	1	no	—
65	#97×C₈₉	—	2	1	no	—
66	C₄×C₈×C₈₉	—	2	1	no	—
67	#95×C₈₉	—	2	2	no	—
68	#95×C₈₉	—	2	1	no	—
69	#95×C₈₉	—	2	1	no	—
70	#95×C₈₉	D₄	1	1	yes	characteristic
71	#95×C₈₉	D₄	1	1	yes	characteristic
72	C₂⁴×C₈₉	—	2	1	no	—
73	#41×C₈₉	—	4	2	no	—
74	#41×C₈₉	—	4	2	no	—
75	C₂×Q₈×C₈₉	—	2	1	no	—
76	C₂×D₄×C₈₉	—	2	4	no	—
77	C₂×D₄×C₈₉	—	2	1	no	—
78	C₂×D₄×C₈₉	—	2	1	no	—
79	C₂×D₄×C₈₉	—	2	1	no	—
80	C₂×D₄×C₈₉	—	2	1	no	—
81	C₂×D₄×C₈₉	—	4	1	no	—
82	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₈₉	—	2	1	no	—
84	C₂²×C₄×C₈₉	—	2	1	no	—
85	C₂²×C₄×C₈₉	—	2	2	no	—
86	C₂²×C₄×C₈₉	—	2	1	no	—
87	C₂²×C₄×C₈₉	—	2	8	no	—
88	C₂²×C₄×C₈₉	—	2	2	no	—
89	C₂²×C₄×C₈₉	—	2	2	no	—
90	C₂²×C₄×C₈₉	—	4	1	no	—
91	C₂²×C₄×C₈₉	—	8	2	no	—
92	C₂²×C₄×C₈₉	—	8	2	no	—
93	C₂²×C₄×C₈₉	—	8	2	no	—
94	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
97	D₈×C₈₉	—	4	4	no	—
98	M₁₆×C₈₉	—	2	2	no	—
99	M₁₆×C₈₉	—	4	1	no	—
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	4	1	no	—
102	C₂×C₈×C₈₉	—	4	1	no	—
103	C₄⋊C₄×C₈₉	—	2	4	no	—
104	C₄⋊C₄×C₈₉	—	2	1	no	—
105	C₄⋊C₄×C₈₉	—	2	1	no	—
106	C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₈₉	—	2	8	no	—
109	C₂²⋊C₄×C₈₉	—	2	2	no	—
110	C₂²⋊C₄×C₈₉	—	2	2	no	—
111	C₂²⋊C₄×C₈₉	—	4	1	no	—
112	C₂²⋊C₄×C₈₉	—	4	1	no	—
113	C₄²×C₈₉	—	2	4	no	—
114	C₄²×C₈₉	—	4	2	no	—
115	C₄²×C₈₉	—	8	2	no	—
116	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₈₉	#41	1	1	yes	characteristic
119	C₄²×C₈₉	#41	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	4	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	—	4	2	no	—
123	C₂³×C₈₉	—	4	1	no	—
124	C₂³×C₈₉	—	4	1	no	—
125	C₂³×C₈₉	—	4	1	no	—
126	C₂³×C₈₉	#120	1	1	yes	characteristic
127	Q₈×C₈₉	—	4	2	no	—
128	D₄×C₈₉	—	2	4	no	—
129	D₄×C₈₉	—	2	2	no	—
130	D₄×C₈₉	—	4	2	no	—
131	D₄×C₈₉	—	4	2	no	—
132	D₄×C₈₉	—	8	1	no	—
133	D₄×C₈₉	—	8	1	no	—
134	D₄×C₈₉	—	8	1	no	—
135	D₄×C₈₉	#104	1	4	yes	complemented
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	4	no	—
142	C₂×C₄×C₈₉	—	2	2	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	—	4	2	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	8	2	no	—
153	C₂×C₄×C₈₉	—	8	2	no	—
154	C₂×C₄×C₈₉	—	8	2	no	—
155	C₂×C₄×C₈₉	—	8	8	no	—
156	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
162	C₈×C₈₉	—	4	2	no	—
163	C₈×C₈₉	—	4	2	no	—
164	C₈×C₈₉	—	8	1	no	—
165	C₂²×C₈₉	—	2	1	no	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	2	4	no	—
168	C₂²×C₈₉	—	4	4	no	—
169	C₂²×C₈₉	—	4	4	no	—
170	C₂²×C₈₉	—	4	2	no	—
171	C₂²×C₈₉	—	4	2	no	—
172	C₂²×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	—	8	1	no	—
174	C₂²×C₈₉	—	8	1	no	—
175	C₂²×C₈₉	#386	1	1	yes	characteristic
176	C₂²×C₈₉	#453	1	1	yes	characteristic
177	C₂²×C₈₉	#454	1	1	yes	characteristic
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	4	2	no	—
184	C₄×C₈₉	—	4	4	no	—
185	C₄×C₈₉	—	4	2	no	—
186	C₄×C₈₉	—	4	2	no	—
187	C₄×C₈₉	—	8	1	no	—
188	C₄×C₈₉	C₂×#104	1	2	yes	—
189	#9325	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₈₉	—	2	1	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	—	4	4	no	—
193	C₂×C₈₉	—	16	1	no	—
194	C₂×C₈₉	#1883	1	1	yes	characteristic
195	C₂×C₈₉	#1896	1	1	yes	characteristic
196	C₂×C₈₉	#1904	1	1	yes	characteristic
197	#3109	C₂×C₈₉	1	1	yes	characteristic
198	#2275	C₂×C₈₉	1	1	yes	characteristic, complemented
199	#1980	C₂×C₈₉	1	1	yes	characteristic, complemented
200	#1505	C₂×C₈₉	1	1	yes	characteristic, complemented
201	#1490	C₂×C₈₉	1	1	yes	characteristic, complemented
202	#1300	C₂×C₈₉	1	1	yes	characteristic, complemented
203	#1285	C₂×C₈₉	1	1	yes	characteristic, complemented
204	C₈₉	#9325	1	1	yes	characteristic, direct product factor, Sylow
205	#532	C₂²×C₈₉	1	1	yes	characteristic
206	C₂×C₄×D₄	—	2	1	no	—
207	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
208	#481	—	2	1	no	—
209	#476	C₄×C₈₉	1	2	yes	complemented
210	#459	C₄×C₈₉	1	2	yes	complemented
211	#447	—	2	1	no	—
212	#442	—	2	2	no	—
213	#432	C₂²×C₈₉	1	1	yes	characteristic
214	#432	C₂²×C₈₉	1	1	yes	characteristic
215	C₂×#104	—	2	2	no	—
216	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	—	2	1	no	—
218	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	—	2	2	no	—
220	C₄×C₂²⋊C₄	—	2	1	no	—
221	#376	C₂²×C₈₉	1	1	yes	characteristic
222	C₂×#95	—	2	1	no	—
223	#327	—	2	1	no	—
224	#327	—	2	1	no	—
225	D₄⋊C₈	—	2	2	no	—
226	C₂×#41	—	2	1	no	—
227	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	2	1	no	—
230	C₂×D₈	—	2	2	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₄⋊Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
233	#127	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
234	#124	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	—	2	1	no	—
237	C₄×D₄	—	2	8	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
243	C₄×D₄	D₄×C₈₉	1	2	yes	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	D₄×C₈₉	1	2	yes	—
251	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
252	#106	—	2	2	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	C₂×C₄×C₈₉	1	2	yes	complemented
255	#104	—	4	4	no	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	#97	—	2	1	no	—
261	#97	—	2	1	no	—
262	#97	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	#95	—	2	2	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	D₄×C₈₉	1	1	yes	characteristic
268	#95	D₄×C₈₉	1	1	yes	characteristic
269	C₂⁴	—	2	1	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	8	2	no	—
289	C₂²×C₄	—	8	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
294	D₈	—	4	4	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	4	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
305	C₂²⋊C₄	—	2	8	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	8	2	no	—
313	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
315	C₄²	#41×C₈₉	1	1	yes	characteristic
316	C₄²	#41×C₈₉	1	1	yes	characteristic
317	C₂³	—	2	4	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	#120×C₈₉	1	1	yes	characteristic
324	Q₈	—	4	2	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	8	1	no	—
330	D₄	—	8	1	no	—
331	D₄	—	8	1	no	—
332	D₄	#104×C₈₉	1	4	yes	complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	8	no	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
354	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
355	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
356	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
357	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
358	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
359	C₈	—	4	2	no	—
360	C₈	—	4	2	no	—
361	C₈	—	8	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	#386×C₈₉	1	1	yes	characteristic
373	C₂²	#453×C₈₉	1	1	yes	characteristic
374	C₂²	#454×C₈₉	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	C₂×#104×C₈₉	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	4	4	no	—
389	C₂	—	16	1	no	—
390	C₂	C₈₉×#1883	1	1	yes	characteristic
391	C₂	C₈₉×#1896	1	1	yes	characteristic
392	C₂	C₈₉×#1904	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	C₈₉×#3109	C₂
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. C₈₉×#2275	C₂	semidirect
3. C₈₉×#1980	C₂	semidirect
4. C₈₉×#1505	C₂	semidirect
5. C₈₉×#1490	C₂	semidirect
6. C₈₉×#1300	C₂	semidirect
7. C₈₉×#1285	C₂	semidirect
12. #476×C₈₉	C₄	semidirect
13. #459×C₈₉	C₄	semidirect
35. C₄⋊Q₈×C₈₉	C₂×C₄	semidirect
36. #127×C₈₉	C₂×C₄	semidirect
57. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
135. D₄×C₈₉	#104	semidirect
189. #9325	C₈₉	direct (N × H)
198. #2275	C₂×C₈₉	semidirect
199. #1980	C₂×C₈₉	semidirect
200. #1505	C₂×C₈₉	semidirect
201. #1490	C₂×C₈₉	semidirect
202. #1300	C₂×C₈₉	semidirect
203. #1285	C₂×C₈₉	semidirect
204. C₈₉	#9325	direct (N × H)
209. #476	C₄×C₈₉	semidirect
210. #459	C₄×C₈₉	semidirect
232. C₄⋊Q₈	C₂×C₄×C₈₉	semidirect
233. #127	C₂×C₄×C₈₉	semidirect
254. C₄⋊C₈	C₂×C₄×C₈₉	semidirect
332. D₄	#104×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3109	2
C₈₉×#2275	2
C₈₉×#1980	2
C₈₉×#1505	2
C₈₉×#1490	2
C₈₉×#1300	2
C₈₉×#1285	2
#9325	89

Subgroups — C89×#9325 #36387173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9325 #36387173