Subgroups — C₈₉×#9273 #36387121

Order 22784.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3205	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#331×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#131×C₈₉	—	2	1	no	—
9	#532×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
11	#493×C₈₉	—	2	1	no	—
12	#486×C₈₉	—	2	1	no	—
13	#459×C₈₉	—	2	2	no	—
14	#447×C₈₉	C₄	1	4	yes	—
15	#436×C₈₉	—	2	1	no	—
16	#435×C₈₉	—	2	2	no	—
17	C₈×D₄×C₈₉	—	2	1	no	—
18	#431×C₈₉	C₂²	1	1	yes	characteristic
19	#423×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#100×C₈₉	—	2	1	no	—
23	C₂×#100×C₈₉	—	2	1	no	—
24	#408×C₈₉	—	2	1	no	—
25	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
26	#332×C₈₉	—	2	1	no	—
27	#331×C₈₉	—	2	1	no	—
28	#331×C₈₉	—	2	1	no	—
29	#331×C₈₉	—	2	1	no	—
30	C₂×#41×C₈₉	—	2	1	no	—
31	C₂²×D₄×C₈₉	—	2	1	no	—
32	C₂²×D₄×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	C₂×C₄	1	2	yes	—
34	C₂×D₈×C₈₉	—	2	4	no	—
35	#131×C₈₉	—	4	2	no	—
36	#131×C₈₉	—	4	2	no	—
37	C₂×M₁₆×C₈₉	—	2	2	no	—
38	C₂×M₁₆×C₈₉	—	2	1	no	—
39	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₈₉	—	2	2	no	—
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	—	2	1	no	—
49	#127×C₈₉	D₄	1	1	yes	characteristic
50	#124×C₈₉	—	2	1	no	—
51	#121×C₈₉	—	2	1	no	—
52	#121×C₈₉	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₈₉	—	2	1	no	—
54	C₄×D₄×C₈₉	D₄	1	2	yes	—
55	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₈₉	—	2	1	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	D₄	1	1	yes	characteristic
63	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
64	#102×C₈₉	—	2	4	no	—
65	#100×C₈₉	—	4	2	no	—
66	#100×C₈₉	—	4	2	no	—
67	C₂²⋊C₈×C₈₉	—	2	2	no	—
68	C₂²⋊C₈×C₈₉	—	2	2	no	—
69	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
70	#97×C₈₉	—	2	1	no	—
71	C₄×C₈×C₈₉	—	2	1	no	—
72	C₄×C₈×C₈₉	—	2	1	no	—
73	C₂⁴×C₈₉	—	2	2	no	—
74	#41×C₈₉	—	4	1	no	—
75	#41×C₈₉	—	4	1	no	—
76	#41×C₈₉	—	4	1	no	—
77	#41×C₈₉	—	4	1	no	—
78	C₂×Q₈×C₈₉	—	2	1	no	—
79	C₂×D₄×C₈₉	—	2	2	no	—
80	C₂×D₄×C₈₉	—	2	2	no	—
81	C₂×D₄×C₈₉	—	2	2	no	—
82	C₂×D₄×C₈₉	—	2	1	no	—
83	C₂×D₄×C₈₉	—	2	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	—	4	1	no	—
89	C₂×D₄×C₈₉	—	4	1	no	—
90	C₂×D₄×C₈₉	—	4	1	no	—
91	C₂×D₄×C₈₉	—	4	1	no	—
92	C₂×D₄×C₈₉	—	8	1	no	—
93	C₂×D₄×C₈₉	—	8	1	no	—
94	C₂×D₄×C₈₉	—	8	2	no	—
95	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₈₉	—	2	2	no	—
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
100	D₈×C₈₉	—	8	4	no	—
101	M₁₆×C₈₉	—	2	1	no	—
102	M₁₆×C₈₉	—	2	1	no	—
103	M₁₆×C₈₉	—	2	1	no	—
104	M₁₆×C₈₉	—	4	4	no	—
105	M₁₆×C₈₉	—	4	1	no	—
106	M₁₆×C₈₉	—	4	1	no	—
107	M₁₆×C₈₉	D₈	1	2	yes	complemented
108	C₂×C₈×C₈₉	—	2	1	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	4	4	no	—
114	C₂×C₈×C₈₉	—	4	1	no	—
115	C₂×C₈×C₈₉	—	4	1	no	—
116	C₂×C₈×C₈₉	—	4	1	no	—
117	C₂×C₈×C₈₉	—	4	1	no	—
118	C₂×C₈×C₈₉	—	8	1	no	—
119	C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₈₉	—	2	2	no	—
122	C₂²⋊C₄×C₈₉	—	2	2	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	2	no	—
128	C₂³×C₈₉	—	4	2	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	—	8	2	no	—
132	C₂³×C₈₉	—	8	2	no	—
133	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
134	Q₈×C₈₉	—	4	1	no	—
135	Q₈×C₈₉	—	4	1	no	—
136	D₄×C₈₉	—	4	2	no	—
137	D₄×C₈₉	—	4	4	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	—	4	1	no	—
141	D₄×C₈₉	—	4	1	no	—
142	D₄×C₈₉	—	4	1	no	—
143	D₄×C₈₉	—	4	1	no	—
144	D₄×C₈₉	—	8	2	no	—
145	D₄×C₈₉	—	8	2	no	—
146	D₄×C₈₉	—	8	1	no	—
147	D₄×C₈₉	—	8	1	no	—
148	D₄×C₈₉	—	8	1	no	—
149	D₄×C₈₉	—	8	1	no	—
150	D₄×C₈₉	—	8	1	no	—
151	D₄×C₈₉	—	8	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₈×C₈₉	—	2	2	no	—
169	C₈×C₈₉	—	4	2	no	—
170	C₈×C₈₉	—	4	1	no	—
171	C₈×C₈₉	—	4	1	no	—
172	C₈×C₈₉	—	4	1	no	—
173	C₈×C₈₉	—	8	1	no	—
174	C₈×C₈₉	—	8	1	no	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	4	2	no	—
178	C₂²×C₈₉	—	4	2	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	8	2	no	—
181	C₂²×C₈₉	—	8	2	no	—
182	C₂²×C₈₉	—	8	2	no	—
183	C₂²×C₈₉	—	16	2	no	—
184	C₂²×C₈₉	—	16	2	no	—
185	C₂²×C₈₉	#386	1	1	yes	characteristic
186	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
187	C₂²×C₈₉	#442	1	1	yes	characteristic
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	#447	1	1	yes	characteristic
193	C₄×C₈₉	#449	1	1	yes	characteristic
194	C₄×C₈₉	#459	1	1	yes	characteristic
195	C₄×C₈₉	#463	1	1	yes	characteristic
196	C₄×C₈₉	#471	1	1	yes	characteristic
197	C₄×C₈₉	#472	1	1	yes	characteristic
198	#9273	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₈₉	—	2	1	no	—
200	C₂×C₈₉	—	2	1	no	—
201	C₂×C₈₉	—	8	2	no	—
202	C₂×C₈₉	—	16	2	no	—
203	C₂×C₈₉	#1879	1	1	yes	characteristic
204	C₂×C₈₉	#1907	1	1	yes	characteristic
205	C₂×C₈₉	#1914	1	1	yes	characteristic
206	#3205	C₂×C₈₉	1	1	yes	characteristic
207	#2935	C₂×C₈₉	1	1	yes	characteristic, complemented
208	#1965	C₂×C₈₉	1	1	yes	characteristic, complemented
209	#1547	C₂×C₈₉	1	1	yes	characteristic, complemented
210	C₂×#331	C₂×C₈₉	1	1	yes	characteristic, complemented
211	#1301	C₂×C₈₉	1	1	yes	characteristic, complemented
212	#1283	C₂×C₈₉	1	1	yes	characteristic, complemented
213	C₈₉	#9273	1	1	yes	characteristic, direct product factor, Sylow
214	C₂×#131	—	2	1	no	—
215	#532	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
217	#493	—	2	1	no	—
218	#486	—	2	1	no	—
219	#459	—	2	2	no	—
220	#447	C₄×C₈₉	1	4	yes	—
221	#436	—	2	1	no	—
222	#435	—	2	2	no	—
223	C₈×D₄	—	2	1	no	—
224	#431	C₂²×C₈₉	1	1	yes	characteristic
225	#423	C₂²×C₈₉	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×#100	—	2	1	no	—
229	C₂×#100	—	2	1	no	—
230	#408	—	2	1	no	—
231	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
232	#332	—	2	1	no	—
233	#331	—	2	1	no	—
234	#331	—	2	1	no	—
235	#331	—	2	1	no	—
236	C₂×#41	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	C₂×C₄×C₈₉	1	2	yes	—
240	C₂×D₈	—	2	4	no	—
241	#131	—	4	2	no	—
242	#131	—	4	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
246	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
251	#127	—	2	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	D₄×C₈₉	1	1	yes	characteristic
256	#124	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	C₂×C₄×C₈₉	1	2	yes	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	D₄×C₈₉	1	2	yes	—
261	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	—	2	1	no	—
268	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
269	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
270	#102	—	2	4	no	—
271	#100	—	4	2	no	—
272	#100	—	4	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	C₂×C₄×C₈₉	1	2	yes	—
276	#97	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₂⁴	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	#41	—	4	1	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	8	1	no	—
299	C₂×D₄	—	8	1	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
306	D₈	—	8	4	no	—
307	M₁₆	—	2	1	no	—
308	M₁₆	—	2	1	no	—
309	M₁₆	—	2	1	no	—
310	M₁₆	—	4	4	no	—
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	D₈×C₈₉	1	2	yes	complemented
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	8	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
332	C₄²	#41×C₈₉	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	1	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	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	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
371	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
372	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
373	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	—	8	1	no	—
380	C₈	—	8	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	#386×C₈₉	1	1	yes	characteristic
392	C₂²	C₄×D₈×C₈₉	1	1	yes	characteristic
393	C₂²	#442×C₈₉	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	4	2	no	—
398	C₄	#447×C₈₉	1	1	yes	characteristic
399	C₄	#449×C₈₉	1	1	yes	characteristic
400	C₄	#459×C₈₉	1	1	yes	characteristic
401	C₄	#463×C₈₉	1	1	yes	characteristic
402	C₄	#471×C₈₉	1	1	yes	characteristic
403	C₄	#472×C₈₉	1	1	yes	characteristic
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	8	2	no	—
407	C₂	—	16	2	no	—
408	C₂	C₈₉×#1879	1	1	yes	characteristic
409	C₂	C₈₉×#1907	1	1	yes	characteristic
410	C₂	C₈₉×#1914	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×#3205	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×#2935	C₂	semidirect
3. C₈₉×#1965	C₂	semidirect
4. C₈₉×#1547	C₂	semidirect
5. C₂×#331×C₈₉	C₂	semidirect
6. C₈₉×#1301	C₂	semidirect
7. C₈₉×#1283	C₂	semidirect
107. M₁₆×C₈₉	D₈	semidirect
198. #9273	C₈₉	direct (N × H)
207. #2935	C₂×C₈₉	semidirect
208. #1965	C₂×C₈₉	semidirect
209. #1547	C₂×C₈₉	semidirect
210. C₂×#331	C₂×C₈₉	semidirect
211. #1301	C₂×C₈₉	semidirect
212. #1283	C₂×C₈₉	semidirect
213. C₈₉	#9273	direct (N × H)
313. M₁₆	D₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3205	2
C₈₉×#2935	2
C₈₉×#1965	2
C₈₉×#1547	2
C₂×#331×C₈₉	2
C₈₉×#1301	2
C₈₉×#1283	2
#9273	89

Subgroups — C89×#9273 #36387121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#9273 #36387121