Subgroups — C₈₉×#10549 #36388397

Order 22784.

502 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3151	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#331×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
9	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
10	#532×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
12	#496×C₈₉	—	2	2	no	—
13	#493×C₈₉	—	2	1	no	—
14	#492×C₈₉	—	2	1	no	—
15	#431×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#108×C₈₉	—	2	1	no	—
17	#423×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	#341×C₈₉	—	2	1	no	—
22	#332×C₈₉	—	2	1	no	—
23	#331×C₈₉	—	2	2	no	—
24	#331×C₈₉	—	2	1	no	—
25	#331×C₈₉	—	2	2	no	—
26	D₄⋊C₈×C₈₉	—	2	2	no	—
27	C₂×#41×C₈₉	—	2	1	no	—
28	C₂²×D₄×C₈₉	—	2	1	no	—
29	C₂²×D₄×C₈₉	—	2	1	no	—
30	C₂²×D₄×C₈₉	—	2	1	no	—
31	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
32	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
33	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
34	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
35	C₂×SD₁₆×C₈₉	—	2	2	no	—
36	C₂×SD₁₆×C₈₉	—	2	2	no	—
37	C₂×D₈×C₈₉	—	2	2	no	—
38	C₂×D₈×C₈₉	—	2	2	no	—
39	C₂×M₁₆×C₈₉	—	2	1	no	—
40	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	—	2	1	no	—
43	C₂²×C₈×C₈₉	—	2	1	no	—
44	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
45	#127×C₈₉	—	2	1	no	—
46	#127×C₈₉	—	2	1	no	—
47	#127×C₈₉	—	2	1	no	—
48	#127×C₈₉	D₄	1	1	yes	characteristic
49	#127×C₈₉	D₄	1	2	yes	—
50	#124×C₈₉	—	2	1	no	—
51	#121×C₈₉	—	2	1	no	—
52	#121×C₈₉	—	2	1	no	—
53	C₄×D₄×C₈₉	—	2	1	no	—
54	C₄×D₄×C₈₉	—	2	1	no	—
55	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
56	#108×C₈₉	—	4	2	no	—
57	C₄⋊C₈×C₈₉	—	2	1	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	D₄	1	2	yes	—
64	C₂²⋊C₈×C₈₉	—	2	1	no	—
65	#97×C₈₉	—	2	1	no	—
66	C₄×C₈×C₈₉	—	2	1	no	—
67	C₄×C₈×C₈₉	—	2	1	no	—
68	C₂⁴×C₈₉	—	4	1	no	—
69	#41×C₈₉	—	4	1	no	—
70	#41×C₈₉	—	4	1	no	—
71	#41×C₈₉	—	4	1	no	—
72	#41×C₈₉	—	4	1	no	—
73	C₂×Q₈×C₈₉	—	2	1	no	—
74	C₂×D₄×C₈₉	—	2	1	no	—
75	C₂×D₄×C₈₉	—	2	2	no	—
76	C₂×D₄×C₈₉	—	2	1	no	—
77	C₂×D₄×C₈₉	—	2	2	no	—
78	C₂×D₄×C₈₉	—	2	1	no	—
79	C₂×D₄×C₈₉	—	2	2	no	—
80	C₂×D₄×C₈₉	—	4	1	no	—
81	C₂×D₄×C₈₉	—	4	1	no	—
82	C₂×D₄×C₈₉	—	4	1	no	—
83	C₂×D₄×C₈₉	—	4	1	no	—
84	C₂×D₄×C₈₉	—	4	1	no	—
85	C₂×D₄×C₈₉	—	4	1	no	—
86	C₂×D₄×C₈₉	—	4	1	no	—
87	C₂×D₄×C₈₉	—	4	1	no	—
88	C₂×D₄×C₈₉	—	8	1	no	—
89	C₂×D₄×C₈₉	—	8	1	no	—
90	C₂×D₄×C₈₉	—	8	2	no	—
91	C₂²×C₄×C₈₉	—	4	1	no	—
92	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
95	SD₁₆×C₈₉	—	4	4	no	—
96	SD₁₆×C₈₉	—	4	4	no	—
97	D₈×C₈₉	—	4	4	no	—
98	D₈×C₈₉	—	4	4	no	—
99	M₁₆×C₈₉	—	2	1	no	—
100	M₁₆×C₈₉	—	2	1	no	—
101	M₁₆×C₈₉	—	4	1	no	—
102	M₁₆×C₈₉	—	4	1	no	—
103	M₁₆×C₈₉	D₈	1	2	yes	—
104	M₁₆×C₈₉	SD₁₆	1	2	yes	—
105	C₂×C₈×C₈₉	—	2	1	no	—
106	C₂×C₈×C₈₉	—	2	1	no	—
107	C₂×C₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	—	4	1	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₂×C₈×C₈₉	—	4	1	no	—
112	C₂×C₈×C₈₉	—	4	1	no	—
113	C₂×C₈×C₈₉	—	8	1	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₂²⋊C₄×C₈₉	—	4	1	no	—
117	C₂²⋊C₄×C₈₉	—	4	1	no	—
118	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₈₉	#41	1	1	yes	characteristic
122	C₂³×C₈₉	—	4	1	no	—
123	C₂³×C₈₉	—	4	2	no	—
124	C₂³×C₈₉	—	8	2	no	—
125	C₂³×C₈₉	—	8	2	no	—
126	C₂³×C₈₉	—	8	1	no	—
127	C₂³×C₈₉	—	8	1	no	—
128	C₂³×C₈₉	#124	1	1	yes	characteristic
129	Q₈×C₈₉	—	4	1	no	—
130	Q₈×C₈₉	—	4	1	no	—
131	D₄×C₈₉	—	4	1	no	—
132	D₄×C₈₉	—	4	2	no	—
133	D₄×C₈₉	—	4	1	no	—
134	D₄×C₈₉	—	4	2	no	—
135	D₄×C₈₉	—	4	1	no	—
136	D₄×C₈₉	—	4	1	no	—
137	D₄×C₈₉	—	8	1	no	—
138	D₄×C₈₉	—	8	2	no	—
139	D₄×C₈₉	—	8	2	no	—
140	D₄×C₈₉	—	8	2	no	—
141	D₄×C₈₉	—	8	1	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	—	8	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	8	1	no	—
152	C₂×C₄×C₈₉	—	8	1	no	—
153	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₈×C₈₉	—	2	2	no	—
164	C₈×C₈₉	—	2	2	no	—
165	C₈×C₈₉	—	4	2	no	—
166	C₈×C₈₉	—	8	1	no	—
167	C₈×C₈₉	—	8	1	no	—
168	C₈×C₈₉	—	8	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	8	2	no	—
172	C₂²×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	—	8	1	no	—
174	C₂²×C₈₉	—	8	2	no	—
175	C₂²×C₈₉	—	8	1	no	—
176	C₂²×C₈₉	—	8	2	no	—
177	C₂²×C₈₉	—	16	2	no	—
178	C₂²×C₈₉	—	16	2	no	—
179	C₂²×C₈₉	#394	1	1	yes	characteristic
180	C₂²×C₈₉	#486	1	1	yes	characteristic
181	C₂²×C₈₉	#490	1	1	yes	characteristic
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	8	1	no	—
186	C₄×C₈₉	#447	1	1	yes	characteristic
187	C₄×C₈₉	#450	1	1	yes	characteristic
188	C₄×C₈₉	#459	1	1	yes	characteristic
189	C₄×C₈₉	#460	1	1	yes	characteristic
190	C₄×C₈₉	#471	1	1	yes	characteristic
191	C₄×C₈₉	#472	1	1	yes	characteristic
192	#10549	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₈₉	—	2	1	no	—
194	C₂×C₈₉	—	2	1	no	—
195	C₂×C₈₉	—	16	1	no	—
196	C₂×C₈₉	—	16	2	no	—
197	C₂×C₈₉	#2041	1	1	yes	characteristic
198	C₂×C₈₉	#2048	1	1	yes	characteristic
199	C₂×C₈₉	#2051	1	1	yes	characteristic
200	#3151	C₂×C₈₉	1	1	yes	characteristic
201	#1950	C₂×C₈₉	1	1	yes	characteristic, complemented
202	#1547	C₂×C₈₉	1	1	yes	characteristic, complemented
203	#1545	C₂×C₈₉	1	1	yes	characteristic, complemented
204	C₂×#331	C₂×C₈₉	1	1	yes	characteristic, complemented
205	#1480	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#1283	C₂×C₈₉	1	1	yes	characteristic, complemented
207	C₈₉	#10549	1	1	yes	characteristic, direct product factor, Sylow
208	C₂×AGL(1,ℤ/8)	—	2	1	no	—
209	C₂×AGL(1,ℤ/8)	—	2	1	no	—
210	#532	C₂²×C₈₉	1	1	yes	characteristic
211	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
212	#496	—	2	2	no	—
213	#493	—	2	1	no	—
214	#492	—	2	1	no	—
215	#431	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×#108	—	2	1	no	—
217	#423	C₂²×C₈₉	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
220	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
221	#341	—	2	1	no	—
222	#332	—	2	1	no	—
223	#331	—	2	2	no	—
224	#331	—	2	1	no	—
225	#331	—	2	2	no	—
226	D₄⋊C₈	—	2	2	no	—
227	C₂×#41	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	AGL(1,ℤ/8)	—	4	2	no	—
232	AGL(1,ℤ/8)	—	4	2	no	—
233	AGL(1,ℤ/8)	—	4	2	no	—
234	AGL(1,ℤ/8)	—	4	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
241	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	D₄×C₈₉	1	2	yes	—
249	#127	D₄×C₈₉	1	1	yes	characteristic
250	#124	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
256	#108	—	4	2	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
264	C₂²⋊C₈	—	2	1	no	—
265	#97	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₂⁴	—	4	1	no	—
269	#41	—	4	1	no	—
270	#41	—	4	1	no	—
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	8	1	no	—
289	C₂×D₄	—	8	1	no	—
290	C₂×D₄	—	8	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
293	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
294	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	D₈	—	4	4	no	—
298	D₈	—	4	4	no	—
299	M₁₆	—	2	1	no	—
300	M₁₆	—	2	1	no	—
301	M₁₆	—	4	1	no	—
302	M₁₆	—	4	1	no	—
303	M₁₆	D₈×C₈₉	1	2	yes	—
304	M₁₆	SD₁₆×C₈₉	1	2	yes	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	8	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
321	C₄²	#41×C₈₉	1	1	yes	characteristic
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	8	2	no	—
325	C₂³	—	8	2	no	—
326	C₂³	—	8	1	no	—
327	C₂³	—	8	1	no	—
328	C₂³	#124×C₈₉	1	1	yes	characteristic
329	Q₈	—	4	1	no	—
330	Q₈	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	2	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	1	no	—
342	D₄	—	8	1	no	—
343	D₄	—	8	1	no	—
344	D₄	—	8	1	no	—
345	D₄	—	8	1	no	—
346	D₄	—	8	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
354	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
355	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
356	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
357	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
358	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
360	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
361	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
362	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	8	1	no	—
367	C₈	—	8	1	no	—
368	C₈	—	8	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	16	2	no	—
378	C₂²	—	16	2	no	—
379	C₂²	#394×C₈₉	1	1	yes	characteristic
380	C₂²	#486×C₈₉	1	1	yes	characteristic
381	C₂²	#490×C₈₉	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	8	1	no	—
386	C₄	#447×C₈₉	1	1	yes	characteristic
387	C₄	#450×C₈₉	1	1	yes	characteristic
388	C₄	#459×C₈₉	1	1	yes	characteristic
389	C₄	#460×C₈₉	1	1	yes	characteristic
390	C₄	#471×C₈₉	1	1	yes	characteristic
391	C₄	#472×C₈₉	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	—	16	1	no	—
395	C₂	—	16	2	no	—
396	C₂	C₈₉×#2041	1	1	yes	characteristic
397	C₂	C₈₉×#2048	1	1	yes	characteristic
398	C₂	C₈₉×#2051	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₈₉×#3151	C₂
LCS	G ▷ C₂×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×#1950	C₂	semidirect
3. C₈₉×#1547	C₂	semidirect
4. C₈₉×#1545	C₂	semidirect
5. C₂×#331×C₈₉	C₂	semidirect
6. C₈₉×#1480	C₂	semidirect
7. C₈₉×#1283	C₂	semidirect
192. #10549	C₈₉	direct (N × H)
201. #1950	C₂×C₈₉	semidirect
202. #1547	C₂×C₈₉	semidirect
203. #1545	C₂×C₈₉	semidirect
204. C₂×#331	C₂×C₈₉	semidirect
205. #1480	C₂×C₈₉	semidirect
206. #1283	C₂×C₈₉	semidirect
207. C₈₉	#10549	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×#3151	2
C₈₉×#1950	2
C₈₉×#1547	2
C₈₉×#1545	2
C₂×#331×C₈₉	2
C₈₉×#1480	2
C₈₉×#1283	2
#10549	89

Subgroups — C89×#10549 #36388397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#10549 #36388397