Subgroups — C₈₉×#29152 #36407000

Order 22784.

798 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×#2660	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2025	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2023	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1961	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1836	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1804	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1802	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#102×C₈₉	C₂²	1	2	yes	—
18	C₂×#102×C₈₉	C₂²	1	2	yes	—
19	C₂×#102×C₈₉	C₂²	1	2	yes	—
20	C₂×#102×C₈₉	C₂²	1	2	yes	—
21	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#398×C₈₉	—	2	2	no	—
24	#395×C₈₉	—	2	2	no	—
25	#390×C₈₉	C₂²	1	2	yes	—
26	#386×C₈₉	—	2	2	no	—
27	#386×C₈₉	—	2	2	no	—
28	#384×C₈₉	C₂²	1	1	yes	characteristic
29	#384×C₈₉	C₂²	1	1	yes	characteristic
30	#382×C₈₉	C₂²	1	1	yes	characteristic
31	#382×C₈₉	C₂²	1	1	yes	characteristic
32	#382×C₈₉	C₂²	1	1	yes	characteristic
33	#376×C₈₉	C₂²	1	1	yes	characteristic
34	#340×C₈₉	C₂²	1	2	yes	—
35	#340×C₈₉	C₂²	1	2	yes	—
36	#340×C₈₉	C₂²	1	2	yes	—
37	#340×C₈₉	C₂²	1	2	yes	—
38	#336×C₈₉	C₂²	1	2	yes	—
39	C₂²×Q₈×C₈₉	—	2	1	no	—
40	C₂²×D₄×C₈₉	—	2	2	no	—
41	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₈₉	—	2	2	no	—
43	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₈₉	—	4	2	no	—
46	#127×C₈₉	—	2	2	no	—
47	#127×C₈₉	Q₈	1	4	yes	complemented
48	#125×C₈₉	—	4	2	no	—
49	C₄×D₄×C₈₉	—	2	4	no	—
50	C₄×D₄×C₈₉	—	2	4	no	—
51	C₂×C₄⋊C₄×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	2	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₈₉	—	2	4	no	—
68	#102×C₈₉	—	4	2	no	—
69	#102×C₈₉	—	4	2	no	—
70	#102×C₈₉	—	4	2	no	—
71	#102×C₈₉	—	4	2	no	—
72	#97×C₈₉	—	2	2	no	—
73	C₄×C₈×C₈₉	—	2	2	no	—
74	#95×C₈₉	—	2	2	no	—
75	#95×C₈₉	—	2	2	no	—
76	#95×C₈₉	—	2	2	no	—
77	#95×C₈₉	D₄	1	2	yes	—
78	#95×C₈₉	D₄	1	2	yes	—
79	C₂⁴×C₈₉	—	2	2	no	—
80	C₂×Q₈×C₈₉	—	4	2	no	—
81	C₂×Q₈×C₈₉	—	8	2	no	—
82	C₂×D₄×C₈₉	—	2	8	no	—
83	C₂×D₄×C₈₉	—	2	2	no	—
84	C₂×D₄×C₈₉	—	2	2	no	—
85	C₂×D₄×C₈₉	—	2	2	no	—
86	C₂×D₄×C₈₉	—	2	2	no	—
87	C₂×D₄×C₈₉	—	2	2	no	—
88	C₂×D₄×C₈₉	—	8	2	no	—
89	C₂×D₄×C₈₉	—	8	2	no	—
90	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₈₉	—	2	1	no	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
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	—	4	4	no	—
97	C₂²×C₄×C₈₉	—	8	2	no	—
98	C₂²×C₄×C₈₉	—	8	2	no	—
99	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	2	2	no	—
107	C₂×C₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₄⋊C₄×C₈₉	—	2	2	no	—
111	C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₄⋊C₄×C₈₉	—	2	2	no	—
113	C₄⋊C₄×C₈₉	—	2	2	no	—
114	C₄⋊C₄×C₈₉	—	2	2	no	—
115	C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₄⋊C₄×C₈₉	—	4	2	no	—
117	C₄⋊C₄×C₈₉	—	4	2	no	—
118	C₄⋊C₄×C₈₉	—	4	2	no	—
119	C₄⋊C₄×C₈₉	—	8	2	no	—
120	C₄⋊C₄×C₈₉	—	8	2	no	—
121	C₂²⋊C₄×C₈₉	—	4	4	no	—
122	C₂²⋊C₄×C₈₉	—	8	2	no	—
123	C₂²⋊C₄×C₈₉	—	8	2	no	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
126	C₄²×C₈₉	#41	1	2	yes	—
127	C₄²×C₈₉	#41	1	4	yes	—
128	C₂³×C₈₉	—	2	4	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	—	4	2	no	—
132	C₂³×C₈₉	—	4	2	no	—
133	C₂³×C₈₉	—	4	2	no	—
134	C₂³×C₈₉	—	4	2	no	—
135	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₈₉	—	8	4	no	—
137	D₄×C₈₉	—	2	4	no	—
138	D₄×C₈₉	—	2	4	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	—	4	2	no	—
141	D₄×C₈₉	—	8	8	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	4	2	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	—	4	1	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	8	8	no	—
162	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
163	C₂×C₄×C₈₉	#124	1	4	yes	—
164	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
166	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
168	C₈×C₈₉	—	4	2	no	—
169	C₈×C₈₉	—	4	2	no	—
170	C₂²×C₈₉	—	4	4	no	—
171	C₂²×C₈₉	—	4	4	no	—
172	C₂²×C₈₉	—	4	4	no	—
173	C₂²×C₈₉	—	8	2	no	—
174	C₂²×C₈₉	—	8	2	no	—
175	C₂²×C₈₉	—	8	2	no	—
176	C₂²×C₈₉	—	8	2	no	—
177	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₂²×C₈₉	C₂×#124	1	1	yes	characteristic
179	C₂²×C₈₉	#535	1	1	yes	characteristic
180	C₂²×C₈₉	#576	1	2	yes	—
181	C₂²×C₈₉	#577	1	2	yes	—
182	C₄×C₈₉	—	2	4	no	—
183	C₄×C₈₉	—	2	4	no	—
184	C₄×C₈₉	—	4	1	no	—
185	C₄×C₈₉	—	4	1	no	—
186	C₄×C₈₉	—	8	2	no	—
187	C₄×C₈₉	—	8	1	no	—
188	C₄×C₈₉	—	8	1	no	—
189	C₄×C₈₉	—	8	1	no	—
190	C₄×C₈₉	—	8	1	no	—
191	C₄×C₈₉	#554	1	2	yes	—
192	C₄×C₈₉	#555	1	2	yes	—
193	#29152	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₈₉	—	8	4	no	—
195	C₂×C₈₉	#2563	1	1	yes	characteristic
196	C₂×C₈₉	#3081	1	2	yes	—
197	C₂×C₈₉	#3136	1	2	yes	—
198	C₂×C₈₉	#3220	1	1	yes	characteristic
199	C₂×C₈₉	#3221	1	1	yes	characteristic
200	#2660	C₂×C₈₉	1	1	yes	characteristic, complemented
201	#2328	C₂×C₈₉	1	1	yes	characteristic
202	#2025	C₂×C₈₉	1	2	yes	complemented
203	#2023	C₂×C₈₉	1	2	yes	complemented
204	#1961	C₂×C₈₉	1	1	yes	characteristic
205	#1957	C₂×C₈₉	1	1	yes	characteristic
206	#1836	C₂×C₈₉	1	1	yes	characteristic, complemented
207	#1835	C₂×C₈₉	1	1	yes	characteristic, complemented
208	#1804	C₂×C₈₉	1	2	yes	complemented
209	#1802	C₂×C₈₉	1	2	yes	complemented
210	#1768	C₂×C₈₉	1	1	yes	characteristic, complemented
211	C₈₉	#29152	1	1	yes	characteristic, direct product factor, Sylow
212	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
213	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
214	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
217	C₂×#102	C₂²×C₈₉	1	2	yes	—
218	C₂×#102	C₂²×C₈₉	1	2	yes	—
219	C₂×#102	C₂²×C₈₉	1	2	yes	—
220	C₂×#102	C₂²×C₈₉	1	2	yes	—
221	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
223	#398	—	2	2	no	—
224	#395	—	2	2	no	—
225	#390	C₂²×C₈₉	1	2	yes	—
226	#386	—	2	2	no	—
227	#386	—	2	2	no	—
228	#384	C₂²×C₈₉	1	1	yes	characteristic
229	#384	C₂²×C₈₉	1	1	yes	characteristic
230	#382	C₂²×C₈₉	1	1	yes	characteristic
231	#382	C₂²×C₈₉	1	1	yes	characteristic
232	#382	C₂²×C₈₉	1	1	yes	characteristic
233	#376	C₂²×C₈₉	1	1	yes	characteristic
234	#340	C₂²×C₈₉	1	2	yes	—
235	#340	C₂²×C₈₉	1	2	yes	—
236	#340	C₂²×C₈₉	1	2	yes	—
237	#340	C₂²×C₈₉	1	2	yes	—
238	#336	C₂²×C₈₉	1	2	yes	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
244	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
245	C₄⋊Q₈	—	4	2	no	—
246	#127	—	2	2	no	—
247	#127	Q₈×C₈₉	1	4	yes	complemented
248	#125	—	4	2	no	—
249	C₄×D₄	—	2	4	no	—
250	C₄×D₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	4	no	—
268	#102	—	4	2	no	—
269	#102	—	4	2	no	—
270	#102	—	4	2	no	—
271	#102	—	4	2	no	—
272	#97	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	D₄×C₈₉	1	2	yes	—
278	#95	D₄×C₈₉	1	2	yes	—
279	C₂⁴	—	2	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	8	2	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	8	2	no	—
289	C₂×D₄	—	8	2	no	—
290	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	—	8	2	no	—
299	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₄⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₂²⋊C₄	—	8	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
326	C₄²	#41×C₈₉	1	2	yes	—
327	C₄²	#41×C₈₉	1	4	yes	—
328	C₂³	—	2	4	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
336	Q₈	—	8	4	no	—
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	8	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	8	no	—
362	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
363	C₂×C₄	#124×C₈₉	1	4	yes	—
364	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
366	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
367	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
378	C₂²	C₂×#124×C₈₉	1	1	yes	characteristic
379	C₂²	#535×C₈₉	1	1	yes	characteristic
380	C₂²	#576×C₈₉	1	2	yes	—
381	C₂²	#577×C₈₉	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₄	#554×C₈₉	1	2	yes	—
392	C₄	#555×C₈₉	1	2	yes	—
393	C₂	—	8	4	no	—
394	C₂	C₈₉×#2563	1	1	yes	characteristic
395	C₂	C₈₉×#3081	1	2	yes	—
396	C₂	C₈₉×#3136	1	2	yes	—
397	C₂	C₈₉×#3220	1	1	yes	characteristic
398	C₂	C₈₉×#3221	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#127×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ #376×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2660	C₂	semidirect
3. C₈₉×#2025	C₂	semidirect
4. C₈₉×#2023	C₂	semidirect
7. C₈₉×#1836	C₂	semidirect
8. C₈₉×#1835	C₂	semidirect
9. C₈₉×#1804	C₂	semidirect
10. C₈₉×#1802	C₂	semidirect
11. C₈₉×#1768	C₂	semidirect
47. #127×C₈₉	Q₈	semidirect
193. #29152	C₈₉	direct (N × H)
200. #2660	C₂×C₈₉	semidirect
202. #2025	C₂×C₈₉	semidirect
203. #2023	C₂×C₈₉	semidirect
206. #1836	C₂×C₈₉	semidirect
207. #1835	C₂×C₈₉	semidirect
208. #1804	C₂×C₈₉	semidirect
209. #1802	C₂×C₈₉	semidirect
210. #1768	C₂×C₈₉	semidirect
211. C₈₉	#29152	direct (N × H)
247. #127	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2660	2
C₈₉×#2328	2
C₈₉×#2025	2
C₈₉×#2023	2
C₈₉×#1961	2
C₈₉×#1957	2
C₈₉×#1836	2
C₈₉×#1835	2
C₈₉×#1804	2
C₈₉×#1802	2
C₈₉×#1768	2
#29152	89

Subgroups — C89×#29152 #36407000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29152 #36407000