Subgroups — C₈₉×#9359 #36387207

Order 22784.

540 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1299	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₈₉	C₄	1	2	yes	—
9	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
10	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
11	#460×C₈₉	—	2	1	no	—
12	#460×C₈₉	—	2	1	no	—
13	#459×C₈₉	—	2	1	no	—
14	#459×C₈₉	—	2	1	no	—
15	#446×C₈₉	—	2	1	no	—
16	#435×C₈₉	—	2	2	no	—
17	C₈×D₄×C₈₉	—	2	1	no	—
18	#432×C₈₉	—	2	1	no	—
19	#431×C₈₉	C₂²	1	1	yes	characteristic
20	#423×C₈₉	C₂²	1	1	yes	characteristic
21	#423×C₈₉	C₂²	1	1	yes	characteristic
22	#423×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
24	#418×C₈₉	C₄	1	2	yes	—
25	C₂×#100×C₈₉	—	2	2	no	—
26	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	#331×C₈₉	—	2	1	no	—
28	#331×C₈₉	—	2	1	no	—
29	Q₈⋊C₈×C₈₉	—	2	1	no	—
30	D₄⋊C₈×C₈₉	—	2	1	no	—
31	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	—	2	1	no	—
34	C₂²×D₄×C₈₉	C₂×C₄	1	2	yes	—
35	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
36	C₂×SD₁₆×C₈₉	—	2	2	no	—
37	C₂×D₈×C₈₉	—	2	2	no	—
38	C₂×M₁₆×C₈₉	—	2	1	no	—
39	C₂×M₁₆×C₈₉	—	2	1	no	—
40	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
42	C₂²×C₈×C₈₉	—	2	2	no	—
43	#127×C₈₉	—	2	1	no	—
44	#127×C₈₉	—	2	1	no	—
45	#127×C₈₉	—	2	1	no	—
46	#127×C₈₉	—	2	1	no	—
47	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
49	C₄×D₄×C₈₉	—	2	1	no	—
50	C₄×D₄×C₈₉	—	2	1	no	—
51	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
52	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
53	#117×C₈₉	—	2	1	no	—
54	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	—	2	1	no	—
56	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₈₉	—	2	2	no	—
58	C₄⋊C₈×C₈₉	—	2	1	no	—
59	C₄⋊C₈×C₈₉	—	2	1	no	—
60	C₄⋊C₈×C₈₉	—	2	1	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	D₄	1	1	yes	characteristic
65	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
66	#102×C₈₉	—	2	2	no	—
67	#102×C₈₉	—	2	2	no	—
68	#100×C₈₉	—	4	4	no	—
69	C₂²⋊C₈×C₈₉	—	2	2	no	—
70	C₂²⋊C₈×C₈₉	—	2	1	no	—
71	#97×C₈₉	—	2	2	no	—
72	#97×C₈₉	—	2	1	no	—
73	C₄×C₈×C₈₉	—	2	1	no	—
74	C₄×C₈×C₈₉	—	2	1	no	—
75	C₂⁴×C₈₉	—	2	2	no	—
76	#41×C₈₉	—	2	2	no	—
77	#41×C₈₉	—	4	1	no	—
78	C₂×Q₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₈₉	—	2	1	no	—
80	C₂×D₄×C₈₉	—	2	2	no	—
81	C₂×D₄×C₈₉	—	2	2	no	—
82	C₂×D₄×C₈₉	—	4	2	no	—
83	C₂×D₄×C₈₉	—	4	2	no	—
84	C₂×D₄×C₈₉	—	4	2	no	—
85	C₂×D₄×C₈₉	—	4	2	no	—
86	C₂×D₄×C₈₉	—	4	1	no	—
87	C₂×D₄×C₈₉	—	4	1	no	—
88	C₂×D₄×C₈₉	—	4	1	no	—
89	C₂×D₄×C₈₉	—	4	1	no	—
90	C₂×D₄×C₈₉	—	8	1	no	—
91	C₂×D₄×C₈₉	—	8	1	no	—
92	C₂×D₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	—	2	1	no	—
94	C₂²×C₄×C₈₉	—	2	1	no	—
95	C₂²×C₄×C₈₉	—	2	1	no	—
96	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
99	SD₁₆×C₈₉	—	4	4	no	—
100	D₈×C₈₉	—	4	4	no	—
101	M₁₆×C₈₉	—	2	2	no	—
102	M₁₆×C₈₉	—	4	1	no	—
103	M₁₆×C₈₉	—	4	2	no	—
104	M₁₆×C₈₉	—	4	2	no	—
105	M₁₆×C₈₉	—	8	1	no	—
106	C₂×C₈×C₈₉	—	2	2	no	—
107	C₂×C₈×C₈₉	—	2	1	no	—
108	C₂×C₈×C₈₉	—	2	1	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₂×C₈×C₈₉	—	4	1	no	—
112	C₂×C₈×C₈₉	—	8	2	no	—
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₄²×C₈₉	—	2	1	no	—
121	C₄²×C₈₉	—	2	1	no	—
122	C₄²×C₈₉	—	2	1	no	—
123	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₈₉	#41	1	1	yes	characteristic
127	C₂³×C₈₉	—	2	1	no	—
128	C₂³×C₈₉	—	4	4	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	8	2	no	—
131	C₂³×C₈₉	—	8	2	no	—
132	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
133	Q₈×C₈₉	—	2	1	no	—
134	Q₈×C₈₉	—	2	1	no	—
135	D₄×C₈₉	—	2	1	no	—
136	D₄×C₈₉	—	4	2	no	—
137	D₄×C₈₉	—	4	2	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	8	2	no	—
140	D₄×C₈₉	—	8	2	no	—
141	D₄×C₈₉	—	8	2	no	—
142	D₄×C₈₉	—	8	1	no	—
143	D₄×C₈₉	—	8	1	no	—
144	D₄×C₈₉	—	8	1	no	—
145	D₄×C₈₉	—	8	1	no	—
146	D₄×C₈₉	#100	1	2	yes	complemented
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	1	no	—
161	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	—	4	2	no	—
169	C₈×C₈₉	—	4	1	no	—
170	C₈×C₈₉	—	4	2	no	—
171	C₈×C₈₉	—	4	1	no	—
172	C₈×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	—	2	1	no	—
175	C₂²×C₈₉	—	2	2	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	4	1	no	—
178	C₂²×C₈₉	—	4	1	no	—
179	C₂²×C₈₉	—	8	2	no	—
180	C₂²×C₈₉	—	8	2	no	—
181	C₂²×C₈₉	—	8	2	no	—
182	C₂²×C₈₉	—	16	4	no	—
183	C₂²×C₈₉	#386	1	1	yes	characteristic
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	4	1	no	—
188	C₄×C₈₉	—	4	1	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	C₂×#100	1	1	yes	characteristic
191	C₄×C₈₉	#413	1	1	yes	characteristic
192	C₄×C₈₉	#453	1	1	yes	characteristic
193	C₄×C₈₉	#454	1	1	yes	characteristic
194	C₄×C₈₉	#471	1	1	yes	characteristic
195	C₄×C₈₉	#472	1	1	yes	characteristic
196	#9359	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₈₉	—	4	1	no	—
198	C₂×C₈₉	—	4	2	no	—
199	C₂×C₈₉	—	16	2	no	—
200	C₂×C₈₉	#1883	1	1	yes	characteristic
201	C₂×C₈₉	#1900	1	1	yes	characteristic
202	C₂×C₈₉	#1907	1	1	yes	characteristic
203	#3038	C₂×C₈₉	1	1	yes	characteristic
204	#2990	C₂×C₈₉	1	1	yes	characteristic, complemented
205	#1965	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#1545	C₂×C₈₉	1	1	yes	characteristic, complemented
207	#1489	C₂×C₈₉	1	1	yes	characteristic, complemented
208	#1309	C₂×C₈₉	1	1	yes	characteristic, complemented
209	#1299	C₂×C₈₉	1	1	yes	characteristic, complemented
210	C₈₉	#9359	1	1	yes	characteristic, direct product factor, Sylow
211	C₂×AGL(1,ℤ/8)	C₄×C₈₉	1	2	yes	—
212	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
213	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
214	#460	—	2	1	no	—
215	#460	—	2	1	no	—
216	#459	—	2	1	no	—
217	#459	—	2	1	no	—
218	#446	—	2	1	no	—
219	#435	—	2	2	no	—
220	C₈×D₄	—	2	1	no	—
221	#432	—	2	1	no	—
222	#431	C₂²×C₈₉	1	1	yes	characteristic
223	#423	C₂²×C₈₉	1	1	yes	characteristic
224	#423	C₂²×C₈₉	1	1	yes	characteristic
225	#423	C₂²×C₈₉	1	1	yes	characteristic
226	C₂×C₄⋊C₈	—	2	1	no	—
227	#418	C₄×C₈₉	1	2	yes	—
228	C₂×#100	—	2	2	no	—
229	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
230	#331	—	2	1	no	—
231	#331	—	2	1	no	—
232	Q₈⋊C₈	—	2	1	no	—
233	D₄⋊C₈	—	2	1	no	—
234	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	C₂×C₄×C₈₉	1	2	yes	—
238	AGL(1,ℤ/8)	—	4	4	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
244	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
245	C₂²×C₈	—	2	2	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	—	2	1	no	—
250	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
251	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
255	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
256	#117	—	2	1	no	—
257	#117	C₂×C₄×C₈₉	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
268	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#100	—	4	4	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	#97	—	2	2	no	—
275	#97	—	2	1	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₂⁴	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	C₂×Q₈	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	8	1	no	—
294	C₂×D₄	—	8	1	no	—
295	C₂×D₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
301	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
302	SD₁₆	—	4	4	no	—
303	D₈	—	4	4	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	4	1	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	2	no	—
308	M₁₆	—	8	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	8	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
319	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
329	C₄²	#41×C₈₉	1	1	yes	characteristic
330	C₂³	—	2	1	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	2	no	—
345	D₄	—	8	1	no	—
346	D₄	—	8	1	no	—
347	D₄	—	8	1	no	—
348	D₄	—	8	1	no	—
349	D₄	#100×C₈₉	1	2	yes	complemented
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
366	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
367	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
368	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
369	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	1	no	—
375	C₈	—	8	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	16	4	no	—
386	C₂²	#386×C₈₉	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	C₂×#100×C₈₉	1	1	yes	characteristic
394	C₄	#413×C₈₉	1	1	yes	characteristic
395	C₄	#453×C₈₉	1	1	yes	characteristic
396	C₄	#454×C₈₉	1	1	yes	characteristic
397	C₄	#471×C₈₉	1	1	yes	characteristic
398	C₄	#472×C₈₉	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	2	no	—
401	C₂	—	16	2	no	—
402	C₂	C₈₉×#1883	1	1	yes	characteristic
403	C₂	C₈₉×#1900	1	1	yes	characteristic
404	C₂	C₈₉×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₈₉×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#2990	C₂	semidirect
3. C₈₉×#1965	C₂	semidirect
4. C₈₉×#1545	C₂	semidirect
5. C₈₉×#1489	C₂	semidirect
6. C₈₉×#1309	C₂	semidirect
7. C₈₉×#1299	C₂	semidirect
146. D₄×C₈₉	#100	semidirect
196. #9359	C₈₉	direct (N × H)
204. #2990	C₂×C₈₉	semidirect
205. #1965	C₂×C₈₉	semidirect
206. #1545	C₂×C₈₉	semidirect
207. #1489	C₂×C₈₉	semidirect
208. #1309	C₂×C₈₉	semidirect
209. #1299	C₂×C₈₉	semidirect
210. C₈₉	#9359	direct (N × H)
349. D₄	#100×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3038	2
C₈₉×#2990	2
C₈₉×#1965	2
C₈₉×#1545	2
C₈₉×#1489	2
C₈₉×#1309	2
C₈₉×#1299	2
#9359	89

Subgroups — C89×#9359 #36387207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9359 #36387207