Subgroups — C₈₉×#10270 #36388118

Order 22784.

594 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	C₂×#487×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1954	C₂	1	1	yes	maximal, characteristic
5	C₂×#332×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#332×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₈₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	#487×C₈₉	—	2	2	no	—
13	#487×C₈₉	—	2	2	no	—
14	#474×C₈₉	—	2	2	no	—
15	#474×C₈₉	—	2	2	no	—
16	#461×C₈₉	—	2	2	no	—
17	#461×C₈₉	—	2	2	no	—
18	C₂×#107×C₈₉	—	2	1	no	—
19	C₂×C₄⋊C₈×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×#103×C₈₉	—	2	2	no	—
23	C₂×#103×C₈₉	—	2	1	no	—
24	C₂×#102×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	#332×C₈₉	—	2	2	no	—
28	#332×C₈₉	—	2	2	no	—
29	C₂²×Q₈×C₈₉	—	2	1	no	—
30	C₂²×Q₈×C₈₉	—	2	1	no	—
31	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₈₉	—	2	1	no	—
33	C₂×SD₁₆×C₈₉	—	2	4	no	—
34	C₂×SD₁₆×C₈₉	—	4	2	no	—
35	C₂×SD₁₆×C₈₉	—	4	2	no	—
36	C₂²×C₈×C₈₉	—	2	1	no	—
37	C₂²×C₈×C₈₉	—	2	1	no	—
38	C₂²×C₈×C₈₉	—	2	1	no	—
39	C₂²×C₈×C₈₉	D₄	1	2	yes	—
40	C₄⋊Q₈×C₈₉	—	2	1	no	—
41	C₄⋊Q₈×C₈₉	—	2	1	no	—
42	C₄⋊Q₈×C₈₉	—	2	1	no	—
43	C₄⋊Q₈×C₈₉	—	2	1	no	—
44	C₄⋊Q₈×C₈₉	—	2	1	no	—
45	C₄⋊Q₈×C₈₉	—	2	1	no	—
46	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
47	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
48	C₄×D₄×C₈₉	—	2	1	no	—
49	C₄×D₄×C₈₉	—	2	1	no	—
50	C₄×D₄×C₈₉	—	2	1	no	—
51	C₄×D₄×C₈₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
59	#107×C₈₉	—	2	4	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	2	yes	—
65	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
66	#103×C₈₉	—	2	4	no	—
67	#103×C₈₉	—	2	8	no	—
68	#102×C₈₉	—	2	4	no	—
69	C₂²⋊C₈×C₈₉	—	4	4	no	—
70	C₄×C₈×C₈₉	—	2	1	no	—
71	C₄×C₈×C₈₉	—	2	1	no	—
72	C₂⁴×C₈₉	—	2	1	no	—
73	C₂×Q₈×C₈₉	—	2	2	no	—
74	C₂×Q₈×C₈₉	—	2	2	no	—
75	C₂×Q₈×C₈₉	—	4	1	no	—
76	C₂×Q₈×C₈₉	—	4	1	no	—
77	C₂×Q₈×C₈₉	—	4	1	no	—
78	C₂×Q₈×C₈₉	—	4	2	no	—
79	C₂×Q₈×C₈₉	—	4	1	no	—
80	C₂×Q₈×C₈₉	—	4	1	no	—
81	C₂×Q₈×C₈₉	—	4	2	no	—
82	C₂×Q₈×C₈₉	—	4	1	no	—
83	C₂×D₄×C₈₉	—	2	1	no	—
84	C₂×D₄×C₈₉	—	2	1	no	—
85	C₂×D₄×C₈₉	—	2	1	no	—
86	C₂×D₄×C₈₉	—	2	1	no	—
87	C₂×D₄×C₈₉	—	2	1	no	—
88	C₂×D₄×C₈₉	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₈₉	—	2	1	no	—
90	C₂²×C₄×C₈₉	—	4	1	no	—
91	C₂²×C₄×C₈₉	—	4	1	no	—
92	C₂²×C₄×C₈₉	—	4	1	no	—
93	C₂²×C₄×C₈₉	—	4	1	no	—
94	C₂²×C₄×C₈₉	—	4	2	no	—
95	C₂²×C₄×C₈₉	—	4	2	no	—
96	C₂²×C₄×C₈₉	C₂×D₄	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	8	no	—
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	2	2	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	4	1	no	—
106	C₂×C₈×C₈₉	—	4	1	no	—
107	C₂×C₈×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	—	4	1	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	2	no	—
111	C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₄⋊C₄×C₈₉	—	2	2	no	—
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₄⋊C₄×C₈₉	—	4	1	no	—
118	C₄⋊C₄×C₈₉	—	4	1	no	—
119	C₄⋊C₄×C₈₉	—	4	1	no	—
120	C₄⋊C₄×C₈₉	—	4	1	no	—
121	C₂²⋊C₄×C₈₉	—	4	1	no	—
122	C₂²⋊C₄×C₈₉	—	4	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	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₈₉	—	2	2	no	—
128	C₂³×C₈₉	—	4	1	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	4	1	no	—
131	C₂³×C₈₉	—	4	2	no	—
132	C₂³×C₈₉	#121	1	1	yes	characteristic
133	Q₈×C₈₉	—	4	4	no	—
134	Q₈×C₈₉	—	4	2	no	—
135	Q₈×C₈₉	—	4	2	no	—
136	Q₈×C₈₉	—	8	1	no	—
137	Q₈×C₈₉	—	8	1	no	—
138	Q₈×C₈₉	—	8	1	no	—
139	Q₈×C₈₉	—	8	1	no	—
140	D₄×C₈₉	—	2	2	no	—
141	D₄×C₈₉	—	2	2	no	—
142	D₄×C₈₉	—	4	1	no	—
143	D₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	2	no	—
147	C₂×C₄×C₈₉	—	4	2	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	8	2	no	—
150	C₂×C₄×C₈₉	—	8	1	no	—
151	C₂×C₄×C₈₉	—	8	1	no	—
152	C₂×C₄×C₈₉	—	8	2	no	—
153	C₂×C₄×C₈₉	—	8	1	no	—
154	C₂×C₄×C₈₉	—	8	1	no	—
155	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#135	1	2	yes	—
164	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	—	4	2	no	—
169	C₈×C₈₉	—	4	2	no	—
170	C₈×C₈₉	—	8	1	no	—
171	C₂²×C₈₉	—	4	4	no	—
172	C₂²×C₈₉	—	4	2	no	—
173	C₂²×C₈₉	—	8	2	no	—
174	C₂²×C₈₉	—	8	1	no	—
175	C₂²×C₈₉	—	8	1	no	—
176	C₂²×C₈₉	#392	1	1	yes	characteristic
177	C₂²×C₈₉	#463	1	2	yes	—
178	C₂²×C₈₉	#465	1	1	yes	characteristic
179	C₂²×C₈₉	#468	1	1	yes	characteristic
180	C₂²×C₈₉	#473	1	2	yes	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	8	2	no	—
184	C₄×C₈₉	—	8	1	no	—
185	C₄×C₈₉	—	8	2	no	—
186	C₄×C₈₉	#448	1	1	yes	characteristic
187	C₄×C₈₉	#449	1	1	yes	characteristic
188	C₄×C₈₉	#449	1	2	yes	—
189	C₄×C₈₉	#450	1	1	yes	characteristic
190	C₄×C₈₉	#452	1	1	yes	characteristic
191	C₄×C₈₉	#495	1	1	yes	characteristic
192	C₄×C₈₉	#496	1	1	yes	characteristic
193	#10270	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₈₉	—	8	2	no	—
195	C₂×C₈₉	#1679	1	2	yes	—
196	C₂×C₈₉	#1699	1	2	yes	—
197	C₂×C₈₉	#2000	1	1	yes	characteristic
198	C₂×C₈₉	#2012	1	1	yes	characteristic
199	C₂×C₈₉	#2020	1	1	yes	characteristic
200	C₂×#487	C₂×C₈₉	1	1	yes	characteristic, complemented
201	C₂×#474	C₂×C₈₉	1	1	yes	characteristic
202	C₂×#461	C₂×C₈₉	1	1	yes	characteristic
203	#1954	C₂×C₈₉	1	1	yes	characteristic
204	C₂×#332	C₂×C₈₉	1	1	yes	characteristic, complemented
205	C₂×#332	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#1277	C₂×C₈₉	1	1	yes	characteristic, complemented
207	C₈₉	#10270	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²×SD₁₆	—	2	1	no	—
209	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
212	#487	—	2	2	no	—
213	#487	—	2	2	no	—
214	#474	—	2	2	no	—
215	#474	—	2	2	no	—
216	#461	—	2	2	no	—
217	#461	—	2	2	no	—
218	C₂×#107	—	2	1	no	—
219	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
222	C₂×#103	—	2	2	no	—
223	C₂×#103	—	2	1	no	—
224	C₂×#102	—	2	1	no	—
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
227	#332	—	2	2	no	—
228	#332	—	2	2	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	—	4	2	no	—
235	C₂×SD₁₆	—	4	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	D₄×C₈₉	1	2	yes	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	D₄×C₈₉	1	2	yes	—
247	C₄⋊Q₈	D₄×C₈₉	1	2	yes	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
259	#107	—	2	4	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
265	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
266	#103	—	2	4	no	—
267	#103	—	2	8	no	—
268	#102	—	2	4	no	—
269	C₂²⋊C₈	—	4	4	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	SD₁₆×C₈₉	1	2	yes	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
298	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
299	SD₁₆	—	4	8	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	#121×C₈₉	1	1	yes	characteristic
333	Q₈	—	4	4	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	1	no	—
337	Q₈	—	8	1	no	—
338	Q₈	—	8	1	no	—
339	Q₈	—	8	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
356	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
357	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
358	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
359	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
360	C₂×C₄	#127×C₈₉	1	1	yes	characteristic
361	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
362	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
363	C₂×C₄	#135×C₈₉	1	2	yes	—
364	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
365	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
366	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
367	C₈	—	4	2	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	8	1	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	#392×C₈₉	1	1	yes	characteristic
377	C₂²	#463×C₈₉	1	2	yes	—
378	C₂²	#465×C₈₉	1	1	yes	characteristic
379	C₂²	#468×C₈₉	1	1	yes	characteristic
380	C₂²	#473×C₈₉	1	2	yes	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	#448×C₈₉	1	1	yes	characteristic
387	C₄	#449×C₈₉	1	1	yes	characteristic
388	C₄	#449×C₈₉	1	2	yes	—
389	C₄	#450×C₈₉	1	1	yes	characteristic
390	C₄	#452×C₈₉	1	1	yes	characteristic
391	C₄	#495×C₈₉	1	1	yes	characteristic
392	C₄	#496×C₈₉	1	1	yes	characteristic
393	C₂	—	8	2	no	—
394	C₂	C₈₉×#1679	1	2	yes	—
395	C₂	C₈₉×#1699	1	2	yes	—
396	C₂	C₈₉×#2000	1	1	yes	characteristic
397	C₂	C₈₉×#2012	1	1	yes	characteristic
398	C₂	C₈₉×#2020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂²×D₄×C₈₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#487×C₈₉	C₂	semidirect
5. C₂×#332×C₈₉	C₂	semidirect
6. C₂×#332×C₈₉	C₂	semidirect
7. C₈₉×#1277	C₂	semidirect
193. #10270	C₈₉	direct (N × H)
200. C₂×#487	C₂×C₈₉	semidirect
204. C₂×#332	C₂×C₈₉	semidirect
205. C₂×#332	C₂×C₈₉	semidirect
206. #1277	C₂×C₈₉	semidirect
207. C₈₉	#10270	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#487×C₈₉	2
C₂×#474×C₈₉	2
C₂×#461×C₈₉	2
C₈₉×#1954	2
C₂×#332×C₈₉	2
C₈₉×#1277	2
#10270	89

Subgroups — C89×#10270 #36388118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#10270 #36388118