Subgroups — C₈₉×#60971 #36438819

Order 22784.

1780 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×#533×C₈₉	C₂	1	2	yes	maximal
2	C₈₉×#3255	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3229	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3209	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3195	C₂	1	4	yes	maximal
6	C₈₉×#3185	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3113	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic
9	#533×C₈₉	—	2	2	no	—
10	#533×C₈₉	—	2	2	no	—
11	#533×C₈₉	—	2	2	no	—
12	#533×C₈₉	—	2	2	no	—
13	#533×C₈₉	C₂²	1	4	yes	—
14	#533×C₈₉	C₂²	1	4	yes	—
15	#533×C₈₉	C₂²	1	4	yes	—
16	#533×C₈₉	C₂²	1	4	yes	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×#125×C₈₉	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₈₉	—	2	2	no	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
24	C₂×#117×C₈₉	—	2	2	no	—
25	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
26	#498×C₈₉	C₂²	1	4	yes	complemented
27	#494×C₈₉	C₂²	1	4	yes	complemented
28	#487×C₈₉	C₂²	1	8	yes	complemented
29	#483×C₈₉	C₂²	1	16	yes	—
30	#475×C₈₉	C₂²	1	16	yes	complemented
31	#470×C₈₉	C₂²	1	16	yes	—
32	#462×C₈₉	C₂²	1	16	yes	complemented
33	#451×C₈₉	C₂²	1	16	yes	—
34	#441×C₈₉	C₂²	1	16	yes	complemented
35	#432×C₈₉	C₂²	1	4	yes	—
36	#431×C₈₉	C₂²	1	4	yes	—
37	#423×C₈₉	C₂²	1	2	yes	—
38	#407×C₈₉	C₂²	1	2	yes	—
39	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
40	C₂²×Q₈×C₈₉	—	2	2	no	—
41	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₈₉	D₄	1	2	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
45	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₈₉	—	2	2	no	—
47	C₄⋊Q₈×C₈₉	—	2	2	no	—
48	C₄⋊Q₈×C₈₉	—	2	2	no	—
49	C₄⋊Q₈×C₈₉	—	2	2	no	—
50	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
51	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
52	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
54	#125×C₈₉	—	2	4	no	—
55	#125×C₈₉	—	2	4	no	—
56	#125×C₈₉	—	2	4	no	—
57	#125×C₈₉	—	2	4	no	—
58	C₂²⋊Q₈×C₈₉	—	2	4	no	—
59	C₂²⋊Q₈×C₈₉	—	2	4	no	—
60	C₂²⋊Q₈×C₈₉	—	2	4	no	—
61	C₂²⋊Q₈×C₈₉	—	2	4	no	—
62	C₂²⋊Q₈×C₈₉	—	2	4	no	—
63	C₂²⋊Q₈×C₈₉	—	2	4	no	—
64	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
65	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
66	C₄×Q₈×C₈₉	—	2	4	no	—
67	C₄×Q₈×C₈₉	—	2	4	no	—
68	C₄×Q₈×C₈₉	—	2	4	no	—
69	C₄×Q₈×C₈₉	—	2	4	no	—
70	C₄×Q₈×C₈₉	—	2	4	no	—
71	C₄×Q₈×C₈₉	—	2	4	no	—
72	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
73	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
74	#117×C₈₉	—	2	4	no	—
75	#117×C₈₉	—	2	4	no	—
76	#117×C₈₉	—	2	4	no	—
77	#117×C₈₉	—	2	4	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
85	C₂×C₄²×C₈₉	—	2	4	no	—
86	C₂×C₄²×C₈₉	D₄	1	2	yes	—
87	C₂×C₄²×C₈₉	D₄	1	2	yes	—
88	C₂×C₄²×C₈₉	D₄	1	2	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
93	#106×C₈₉	C₂³	1	16	yes	—
94	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
95	#103×C₈₉	C₂³	1	32	yes	—
96	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
97	#97×C₈₉	C₂³	1	4	yes	—
98	C₄×C₈×C₈₉	C₂³	1	4	yes	—
99	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₈₉	—	2	4	no	—
101	C₂×Q₈×C₈₉	—	2	4	no	—
102	C₂×Q₈×C₈₉	—	2	4	no	—
103	C₂×Q₈×C₈₉	—	4	8	no	—
104	C₂×Q₈×C₈₉	—	4	8	no	—
105	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₈₉	—	2	8	no	—
107	C₂²×C₄×C₈₉	—	2	4	no	—
108	C₂²×C₄×C₈₉	—	2	4	no	—
109	C₂²×C₄×C₈₉	—	4	2	no	—
110	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₈₉	—	4	16	no	—
121	M₁₆×C₈₉	—	4	4	no	—
122	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
123	C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₄⋊C₄×C₈₉	—	2	4	no	—
125	C₄⋊C₄×C₈₉	—	2	4	no	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	2	4	no	—
128	C₄⋊C₄×C₈₉	—	2	4	no	—
129	C₄⋊C₄×C₈₉	—	2	8	no	—
130	C₄⋊C₄×C₈₉	—	2	8	no	—
131	C₄⋊C₄×C₈₉	—	2	8	no	—
132	C₄⋊C₄×C₈₉	—	2	8	no	—
133	C₄⋊C₄×C₈₉	—	2	4	no	—
134	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
135	C₂²⋊C₄×C₈₉	—	2	8	no	—
136	C₂²⋊C₄×C₈₉	—	2	8	no	—
137	C₄²×C₈₉	—	2	8	no	—
138	C₄²×C₈₉	—	2	8	no	—
139	C₄²×C₈₉	C₂×D₄	1	2	yes	—
140	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₈₉	C₂×D₄	1	2	yes	—
142	C₄²×C₈₉	C₂×D₄	1	2	yes	—
143	C₄²×C₈₉	C₂×D₄	1	2	yes	—
144	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₈₉	C₂×D₄	1	2	yes	—
146	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₄²×C₈₉	C₂⁴	1	2	yes	—
149	C₂³×C₈₉	—	2	4	no	—
150	C₂³×C₈₉	—	4	1	no	—
151	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
152	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
153	Q₈×C₈₉	—	2	16	no	—
154	Q₈×C₈₉	—	4	8	no	—
155	Q₈×C₈₉	—	4	8	no	—
156	Q₈×C₈₉	—	4	8	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	4	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	2	8	no	—
165	C₂×C₄×C₈₉	—	2	8	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	8	no	—
169	C₂×C₄×C₈₉	—	4	8	no	—
170	C₂×C₄×C₈₉	#137	1	8	yes	—
171	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
178	C₈×C₈₉	—	2	8	no	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	2	2	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	4	4	no	—
184	C₂²×C₈₉	C₂×#137	1	4	yes	—
185	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	2	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	4	8	no	—
191	C₄×C₈₉	—	4	8	no	—
192	C₄×C₈₉	C₂×#137	1	4	yes	—
193	C₄×C₈₉	C₂×#137	1	4	yes	—
194	C₄×C₈₉	#585	1	2	yes	—
195	#60971	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₈₉	—	2	4	no	—
197	C₂×C₈₉	—	4	1	no	—
198	C₂×C₈₉	#3449	1	1	yes	characteristic
199	C₂×C₈₉	C₂²×#137	1	2	yes	—
200	C₂×#533	C₂×C₈₉	1	2	yes	—
201	#3255	C₂×C₈₉	1	4	yes	complemented
202	#3229	C₂×C₈₉	1	4	yes	complemented
203	#3209	C₂×C₈₉	1	4	yes	complemented
204	#3195	C₂×C₈₉	1	4	yes	—
205	#3185	C₂×C₈₉	1	4	yes	complemented
206	#3113	C₂×C₈₉	1	8	yes	complemented
207	#2920	C₂×C₈₉	1	1	yes	characteristic
208	C₈₉	#60971	1	1	yes	characteristic, direct product factor, Sylow
209	#533	—	2	2	no	—
210	#533	—	2	2	no	—
211	#533	—	2	2	no	—
212	#533	—	2	2	no	—
213	#533	C₂²×C₈₉	1	4	yes	—
214	#533	C₂²×C₈₉	1	4	yes	—
215	#533	C₂²×C₈₉	1	4	yes	—
216	#533	C₂²×C₈₉	1	4	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
219	C₂×#125	—	2	2	no	—
220	C₂×C₂²⋊Q₈	—	2	2	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
222	C₂×C₄×Q₈	—	2	2	no	—
223	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
224	C₂×#117	—	2	2	no	—
225	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
226	#498	C₂²×C₈₉	1	4	yes	complemented
227	#494	C₂²×C₈₉	1	4	yes	complemented
228	#487	C₂²×C₈₉	1	8	yes	complemented
229	#483	C₂²×C₈₉	1	16	yes	—
230	#475	C₂²×C₈₉	1	16	yes	complemented
231	#470	C₂²×C₈₉	1	16	yes	—
232	#462	C₂²×C₈₉	1	16	yes	complemented
233	#451	C₂²×C₈₉	1	16	yes	—
234	#441	C₂²×C₈₉	1	16	yes	complemented
235	#432	C₂²×C₈₉	1	4	yes	—
236	#431	C₂²×C₈₉	1	4	yes	—
237	#423	C₂²×C₈₉	1	2	yes	—
238	#407	C₂²×C₈₉	1	2	yes	—
239	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
242	C₂³×C₄	D₄×C₈₉	1	2	yes	—
243	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
244	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
245	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
251	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
252	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
253	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
254	#125	—	2	4	no	—
255	#125	—	2	4	no	—
256	#125	—	2	4	no	—
257	#125	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	4	no	—
264	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
265	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
273	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
274	#117	—	2	4	no	—
275	#117	—	2	4	no	—
276	#117	—	2	4	no	—
277	#117	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	D₄×C₈₉	1	2	yes	—
287	C₂×C₄²	D₄×C₈₉	1	2	yes	—
288	C₂×C₄²	D₄×C₈₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
293	#106	C₂³×C₈₉	1	16	yes	—
294	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
295	#103	C₂³×C₈₉	1	32	yes	—
296	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
297	#97	C₂³×C₈₉	1	4	yes	—
298	C₄×C₈	C₂³×C₈₉	1	4	yes	—
299	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	8	no	—
304	C₂×Q₈	—	4	8	no	—
305	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
320	Q₁₆	—	4	16	no	—
321	M₁₆	—	4	4	no	—
322	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	8	no	—
339	C₄²	C₂×D₄×C₈₉	1	2	yes	—
340	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₈₉	1	2	yes	—
342	C₄²	C₂×D₄×C₈₉	1	2	yes	—
343	C₄²	C₂×D₄×C₈₉	1	2	yes	—
344	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₈₉	1	2	yes	—
346	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
347	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
348	C₄²	C₂⁴×C₈₉	1	2	yes	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
353	Q₈	—	2	16	no	—
354	Q₈	—	4	8	no	—
355	Q₈	—	4	8	no	—
356	Q₈	—	4	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	#137×C₈₉	1	8	yes	—
371	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
377	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
378	C₈	—	2	8	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₂×#137×C₈₉	1	4	yes	—
385	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	8	no	—
391	C₄	—	4	8	no	—
392	C₄	C₂×#137×C₈₉	1	4	yes	—
393	C₄	C₂×#137×C₈₉	1	4	yes	—
394	C₄	#585×C₈₉	1	2	yes	—
395	C₂	—	2	4	no	—
396	C₂	—	4	1	no	—
397	C₂	C₈₉×#3449	1	1	yes	characteristic
398	C₂	C₂²×#137×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3255	C₂	semidirect
3. C₈₉×#3229	C₂	semidirect
4. C₈₉×#3209	C₂	semidirect
6. C₈₉×#3185	C₂	semidirect
7. C₈₉×#3113	C₂	semidirect
26. #498×C₈₉	C₂²	semidirect
27. #494×C₈₉	C₂²	semidirect
28. #487×C₈₉	C₂²	semidirect
30. #475×C₈₉	C₂²	semidirect
32. #462×C₈₉	C₂²	semidirect
34. #441×C₈₉	C₂²	semidirect
195. #60971	C₈₉	direct (N × H)
201. #3255	C₂×C₈₉	semidirect
202. #3229	C₂×C₈₉	semidirect
203. #3209	C₂×C₈₉	semidirect
205. #3185	C₂×C₈₉	semidirect
206. #3113	C₂×C₈₉	semidirect
208. C₈₉	#60971	direct (N × H)
226. #498	C₂²×C₈₉	semidirect
227. #494	C₂²×C₈₉	semidirect
228. #487	C₂²×C₈₉	semidirect
230. #475	C₂²×C₈₉	semidirect
232. #462	C₂²×C₈₉	semidirect
234. #441	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₈₉×#3255	2
C₈₉×#3229	2
C₈₉×#3209	2
C₈₉×#3195	2
C₈₉×#3185	2
C₈₉×#3113	2
C₈₉×#2920	2
#60971	89

Subgroups — C89×#60971 #36438819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60971 #36438819