Subgroups — C₈₉×#8461 #36386309

Order 22784.

682 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3507	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1551	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1530	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
8	#559×C₈₉	—	2	1	no	—
9	#557×C₈₉	—	2	1	no	—
10	#556×C₈₉	—	2	1	no	—
11	#556×C₈₉	—	2	2	no	—
12	#554×C₈₉	—	2	1	no	—
13	#552×C₈₉	—	2	2	no	—
14	#539×C₈₉	—	2	2	no	—
15	#536×C₈₉	C₄	1	2	yes	—
16	#533×C₈₉	C₂²	1	1	yes	characteristic
17	#532×C₈₉	C₂²	1	1	yes	characteristic
18	#529×C₈₉	—	2	2	no	—
19	#520×C₈₉	C₄	1	2	yes	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	#432×C₈₉	C₂²	1	1	yes	characteristic
22	#432×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
25	#336×C₈₉	—	2	2	no	—
26	#333×C₈₉	—	2	1	no	—
27	#332×C₈₉	—	2	1	no	—
28	#332×C₈₉	—	2	1	no	—
29	#331×C₈₉	—	2	1	no	—
30	#330×C₈₉	—	2	2	no	—
31	#329×C₈₉	—	2	2	no	—
32	#324×C₈₉	—	2	2	no	—
33	C₂×#41×C₈₉	C₂×C₄	1	2	yes	—
34	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₈₉	—	2	1	no	—
36	C₂²×C₈×C₈₉	—	2	1	no	—
37	C₄⋊Q₈×C₈₉	—	2	2	no	—
38	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
39	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
40	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
41	#127×C₈₉	D₄	1	1	yes	characteristic
42	#126×C₈₉	—	2	4	no	—
43	#126×C₈₉	—	2	4	no	—
44	#125×C₈₉	—	2	2	no	—
45	#125×C₈₉	—	2	4	no	—
46	#125×C₈₉	D₄	1	2	yes	—
47	#124×C₈₉	—	2	2	no	—
48	#124×C₈₉	—	2	2	no	—
49	#124×C₈₉	D₄	1	2	yes	—
50	#123×C₈₉	—	2	4	no	—
51	#123×C₈₉	—	2	4	no	—
52	C₂²⋊Q₈×C₈₉	—	2	4	no	—
53	C₂²⋊Q₈×C₈₉	—	2	1	no	—
54	C₂²⋊Q₈×C₈₉	—	2	1	no	—
55	C₂²⋊Q₈×C₈₉	—	2	2	no	—
56	C₂²⋊Q₈×C₈₉	—	2	2	no	—
57	#121×C₈₉	—	2	1	no	—
58	#121×C₈₉	—	2	1	no	—
59	C₄×Q₈×C₈₉	—	2	2	no	—
60	C₄×Q₈×C₈₉	—	2	2	no	—
61	C₄×Q₈×C₈₉	—	2	1	no	—
62	C₄×Q₈×C₈₉	—	2	1	no	—
63	C₄×Q₈×C₈₉	—	2	1	no	—
64	C₄×Q₈×C₈₉	—	2	1	no	—
65	C₄×Q₈×C₈₉	—	2	1	no	—
66	C₄×Q₈×C₈₉	—	2	1	no	—
67	C₄×D₄×C₈₉	—	2	2	no	—
68	C₄×D₄×C₈₉	—	2	2	no	—
69	C₄×D₄×C₈₉	—	2	4	no	—
70	C₄×D₄×C₈₉	—	2	1	no	—
71	C₄×D₄×C₈₉	—	2	1	no	—
72	#117×C₈₉	—	2	4	no	—
73	#117×C₈₉	—	2	2	no	—
74	#117×C₈₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
78	C₂×C₄²×C₈₉	D₄	1	2	yes	—
79	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₈₉	—	2	1	no	—
81	C₄⋊C₈×C₈₉	—	2	1	no	—
82	C₄⋊C₈×C₈₉	—	2	1	no	—
83	C₄⋊C₈×C₈₉	—	2	1	no	—
84	C₂²⋊C₈×C₈₉	—	2	1	no	—
85	C₂²⋊C₈×C₈₉	—	2	1	no	—
86	#97×C₈₉	—	2	1	no	—
87	#97×C₈₉	—	2	1	no	—
88	#97×C₈₉	—	2	1	no	—
89	#97×C₈₉	—	2	1	no	—
90	#41×C₈₉	—	4	4	no	—
91	C₂×Q₈×C₈₉	—	2	1	no	—
92	C₂×Q₈×C₈₉	—	2	1	no	—
93	C₂×Q₈×C₈₉	—	2	1	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	4	2	no	—
96	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₈₉	—	2	2	no	—
98	C₂×D₄×C₈₉	—	2	1	no	—
99	C₂×D₄×C₈₉	—	2	1	no	—
100	C₂×D₄×C₈₉	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₈₉	—	2	4	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₂×C₈×C₈₉	—	4	2	no	—
112	C₂×C₈×C₈₉	—	4	1	no	—
113	C₂×C₈×C₈₉	—	4	1	no	—
114	C₂×C₈×C₈₉	—	4	1	no	—
115	C₄⋊C₄×C₈₉	—	2	4	no	—
116	C₄⋊C₄×C₈₉	—	2	4	no	—
117	C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₄⋊C₄×C₈₉	—	2	2	no	—
122	C₄⋊C₄×C₈₉	—	2	2	no	—
123	C₄⋊C₄×C₈₉	—	2	1	no	—
124	C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₄⋊C₄×C₈₉	—	2	1	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
129	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
130	C₂²⋊C₄×C₈₉	—	2	4	no	—
131	C₂²⋊C₄×C₈₉	—	2	4	no	—
132	C₂²⋊C₄×C₈₉	—	2	4	no	—
133	C₂²⋊C₄×C₈₉	—	2	2	no	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₄²×C₈₉	—	2	4	no	—
137	C₄²×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	—	2	2	no	—
139	C₄²×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	Q₈×C₈₉	—	4	2	no	—
147	Q₈×C₈₉	—	4	2	no	—
148	Q₈×C₈₉	—	4	2	no	—
149	Q₈×C₈₉	—	4	1	no	—
150	Q₈×C₈₉	—	4	1	no	—
151	Q₈×C₈₉	—	8	1	no	—
152	D₄×C₈₉	—	4	2	no	—
153	D₄×C₈₉	—	4	4	no	—
154	D₄×C₈₉	—	4	1	no	—
155	D₄×C₈₉	—	4	1	no	—
156	D₄×C₈₉	—	8	1	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	4	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	4	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	8	4	no	—
170	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
176	C₈×C₈₉	—	4	2	no	—
177	C₈×C₈₉	—	8	1	no	—
178	C₈×C₈₉	—	8	1	no	—
179	C₈×C₈₉	—	8	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	4	2	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	—	4	2	no	—
185	C₂²×C₈₉	#379	1	1	yes	characteristic
186	C₂²×C₈₉	#413	1	2	yes	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	4	2	no	—
193	C₄×C₈₉	—	4	2	no	—
194	C₄×C₈₉	—	4	2	no	—
195	C₄×C₈₉	—	4	2	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	#454	1	1	yes	characteristic
198	C₄×C₈₉	#456	1	1	yes	characteristic
199	#8461	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₈₉	—	2	2	no	—
201	C₂×C₈₉	—	8	2	no	—
202	C₂×C₈₉	#1785	1	1	yes	characteristic
203	C₂×C₈₉	#1793	1	1	yes	characteristic
204	C₂×C₈₉	#1794	1	1	yes	characteristic
205	#3507	C₂×C₈₉	1	1	yes	characteristic
206	#1985	C₂×C₈₉	1	1	yes	characteristic, complemented
207	#1552	C₂×C₈₉	1	1	yes	characteristic, complemented
208	#1551	C₂×C₈₉	1	1	yes	characteristic
209	#1531	C₂×C₈₉	1	1	yes	characteristic, complemented
210	#1530	C₂×C₈₉	1	1	yes	characteristic
211	#1467	C₂×C₈₉	1	1	yes	characteristic, complemented
212	C₈₉	#8461	1	1	yes	characteristic, direct product factor, Sylow
213	#559	—	2	1	no	—
214	#557	—	2	1	no	—
215	#556	—	2	1	no	—
216	#556	—	2	2	no	—
217	#554	—	2	1	no	—
218	#552	—	2	2	no	—
219	#539	—	2	2	no	—
220	#536	C₄×C₈₉	1	2	yes	—
221	#533	C₂²×C₈₉	1	1	yes	characteristic
222	#532	C₂²×C₈₉	1	1	yes	characteristic
223	#529	—	2	2	no	—
224	#520	C₄×C₈₉	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
226	#432	C₂²×C₈₉	1	1	yes	characteristic
227	#432	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
229	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
230	#336	—	2	2	no	—
231	#333	—	2	1	no	—
232	#332	—	2	1	no	—
233	#332	—	2	1	no	—
234	#331	—	2	1	no	—
235	#330	—	2	2	no	—
236	#329	—	2	2	no	—
237	#324	—	2	2	no	—
238	C₂×#41	C₂×C₄×C₈₉	1	2	yes	—
239	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
244	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
245	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
246	#127	D₄×C₈₉	1	1	yes	characteristic
247	#126	—	2	4	no	—
248	#126	—	2	4	no	—
249	#125	—	2	2	no	—
250	#125	—	2	4	no	—
251	#125	D₄×C₈₉	1	2	yes	—
252	#124	—	2	2	no	—
253	#124	—	2	2	no	—
254	#124	D₄×C₈₉	1	2	yes	—
255	#123	—	2	4	no	—
256	#123	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	#121	—	2	1	no	—
263	#121	—	2	1	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	#117	—	2	4	no	—
278	#117	—	2	2	no	—
279	#117	C₂×C₄×C₈₉	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
283	C₂×C₄²	D₄×C₈₉	1	2	yes	—
284	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	1	no	—
292	#97	—	2	1	no	—
293	#97	—	2	1	no	—
294	#97	—	2	1	no	—
295	#41	—	4	4	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	C₂²⋊C₄×C₈₉	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂²⋊C₄×C₈₉	1	2	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
309	C₂²×C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
334	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	2	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
349	C₂³	—	2	2	no	—
350	C₂³	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	8	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	8	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
377	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
378	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
379	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
380	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
381	C₈	—	4	2	no	—
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₈	—	8	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	#379×C₈₉	1	1	yes	characteristic
391	C₂²	#413×C₈₉	1	2	yes	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	#454×C₈₉	1	1	yes	characteristic
403	C₄	#456×C₈₉	1	1	yes	characteristic
404	C₂	—	2	2	no	—
405	C₂	—	8	2	no	—
406	C₂	C₈₉×#1785	1	1	yes	characteristic
407	C₂	C₈₉×#1793	1	1	yes	characteristic
408	C₂	C₈₉×#1794	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	#532×C₈₉	C₂²
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×#1985	C₂	semidirect
3. C₈₉×#1552	C₂	semidirect
5. C₈₉×#1531	C₂	semidirect
7. C₈₉×#1467	C₂	semidirect
199. #8461	C₈₉	direct (N × H)
206. #1985	C₂×C₈₉	semidirect
207. #1552	C₂×C₈₉	semidirect
209. #1531	C₂×C₈₉	semidirect
211. #1467	C₂×C₈₉	semidirect
212. C₈₉	#8461	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×#3507	2
C₈₉×#1985	2
C₈₉×#1552	2
C₈₉×#1551	2
C₈₉×#1531	2
C₈₉×#1530	2
C₈₉×#1467	2
#8461	89

Subgroups — C89×#8461 #36386309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#8461 #36386309