Subgroups — C₈₉×#7857 #36385705

Order 22784.

592 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2283	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1274	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
6	#432×C₈₉	—	2	1	no	—
7	#432×C₈₉	—	2	1	no	—
8	#431×C₈₉	—	2	1	no	—
9	#431×C₈₉	—	2	1	no	—
10	#431×C₈₉	C₄	1	2	yes	complemented
11	#431×C₈₉	C₄	1	2	yes	complemented
12	#431×C₈₉	C₂²	1	2	yes	—
13	#431×C₈₉	C₂²	1	2	yes	—
14	#423×C₈₉	—	2	1	no	—
15	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
16	#407×C₈₉	—	2	1	no	—
17	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
18	C₄×M₁₆×C₈₉	C₄	1	2	yes	complemented
19	C₂×C₄×C₈×C₈₉	C₄	1	2	yes	complemented
20	#383×C₈₉	—	2	1	no	—
21	#382×C₈₉	—	2	1	no	—
22	#381×C₈₉	—	2	1	no	—
23	#380×C₈₉	—	2	1	no	—
24	C₄×C₄⋊C₄×C₈₉	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
26	#376×C₈₉	C₂²	1	2	yes	—
27	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₈₉	—	2	2	no	—
31	C₂²×C₈×C₈₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
34	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
47	C₄⋊C₈×C₈₉	—	2	2	no	—
48	C₄⋊C₈×C₈₉	—	2	2	no	—
49	C₄⋊C₈×C₈₉	—	2	2	no	—
50	C₄⋊C₈×C₈₉	—	2	2	no	—
51	C₂²⋊C₈×C₈₉	—	2	2	no	—
52	C₂²⋊C₈×C₈₉	—	2	2	no	—
53	C₂²⋊C₈×C₈₉	—	2	2	no	—
54	C₂²⋊C₈×C₈₉	—	2	2	no	—
55	#97×C₈₉	—	2	2	no	—
56	C₄×C₈×C₈₉	—	2	2	no	—
57	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
58	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
59	#95×C₈₉	—	2	2	no	—
60	#95×C₈₉	—	2	2	no	—
61	#95×C₈₉	—	2	2	no	—
62	#95×C₈₉	—	2	2	no	—
63	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₈₉	—	2	4	no	—
65	C₂²×C₄×C₈₉	—	2	4	no	—
66	C₂²×C₄×C₈₉	—	4	2	no	—
67	C₂²×C₄×C₈₉	—	4	2	no	—
68	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
86	M₁₆×C₈₉	—	4	4	no	—
87	C₂×C₈×C₈₉	—	2	4	no	—
88	C₂×C₈×C₈₉	—	2	4	no	—
89	C₂×C₈×C₈₉	—	4	4	no	—
90	C₄⋊C₄×C₈₉	—	4	4	no	—
91	C₂²⋊C₄×C₈₉	—	4	4	no	—
92	C₄²×C₈₉	—	2	8	no	—
93	C₄²×C₈₉	C₄²	1	1	yes	characteristic
94	C₄²×C₈₉	C₄²	1	1	yes	characteristic
95	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
109	C₂³×C₈₉	—	2	2	no	—
110	C₂³×C₈₉	—	2	2	no	—
111	C₂³×C₈₉	—	4	1	no	—
112	C₂³×C₈₉	#95	1	1	yes	characteristic
113	C₂³×C₈₉	#95	1	1	yes	characteristic
114	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₈₉	—	2	2	no	—
116	C₂×C₄×C₈₉	—	2	2	no	—
117	C₂×C₄×C₈₉	—	2	2	no	—
118	C₂×C₄×C₈₉	—	2	2	no	—
119	C₂×C₄×C₈₉	—	2	2	no	—
120	C₂×C₄×C₈₉	—	2	2	no	—
121	C₂×C₄×C₈₉	—	2	2	no	—
122	C₂×C₄×C₈₉	—	2	2	no	—
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	2	no	—
125	C₂×C₄×C₈₉	—	4	1	no	—
126	C₂×C₄×C₈₉	—	4	1	no	—
127	C₂×C₄×C₈₉	—	4	1	no	—
128	C₂×C₄×C₈₉	—	4	1	no	—
129	C₂×C₄×C₈₉	—	4	1	no	—
130	C₂×C₄×C₈₉	—	4	1	no	—
131	C₂×C₄×C₈₉	—	4	1	no	—
132	C₂×C₄×C₈₉	—	4	4	no	—
133	C₂×C₄×C₈₉	—	4	4	no	—
134	C₂×C₄×C₈₉	—	4	4	no	—
135	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
136	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
137	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
138	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#131	1	4	yes	—
148	C₈×C₈₉	—	4	4	no	—
149	C₈×C₈₉	—	4	4	no	—
150	C₂²×C₈₉	—	2	1	no	—
151	C₂²×C₈₉	—	2	1	no	—
152	C₂²×C₈₉	—	2	1	no	—
153	C₂²×C₈₉	—	2	1	no	—
154	C₂²×C₈₉	—	2	1	no	—
155	C₂²×C₈₉	—	2	1	no	—
156	C₂²×C₈₉	—	2	1	no	—
157	C₂²×C₈₉	—	4	4	no	—
158	C₂²×C₈₉	H(3,ℤ/4)	1	2	yes	—
159	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
160	C₂²×C₈₉	#408	1	2	yes	—
161	C₄×C₈₉	—	2	1	no	—
162	C₄×C₈₉	—	2	1	no	—
163	C₄×C₈₉	—	2	1	no	—
164	C₄×C₈₉	—	2	1	no	—
165	C₄×C₈₉	—	2	1	no	—
166	C₄×C₈₉	—	2	1	no	—
167	C₄×C₈₉	—	2	1	no	—
168	C₄×C₈₉	—	2	1	no	—
169	C₄×C₈₉	—	2	1	no	—
170	C₄×C₈₉	—	8	4	no	—
171	C₄×C₈₉	H(3,ℤ/4)	1	2	yes	—
172	C₄×C₈₉	#405	1	2	yes	—
173	C₄×C₈₉	#424	1	2	yes	—
174	#7857	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₈₉	—	2	2	no	—
176	C₂×C₈₉	—	2	2	no	—
177	C₂×C₈₉	—	4	1	no	—
178	C₂×C₈₉	#1729	1	1	yes	characteristic
179	C₂×C₈₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
180	C₂×C₈₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
181	#2920	C₂×C₈₉	1	1	yes	characteristic
182	C₂×#431	C₂×C₈₉	1	1	yes	characteristic
183	#2283	C₂×C₈₉	1	1	yes	characteristic
184	#1274	C₂×C₈₉	1	4	yes	complemented
185	C₈₉	#7857	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
187	#432	—	2	1	no	—
188	#432	—	2	1	no	—
189	#431	—	2	1	no	—
190	#431	—	2	1	no	—
191	#431	C₄×C₈₉	1	2	yes	complemented
192	#431	C₄×C₈₉	1	2	yes	complemented
193	#431	C₂²×C₈₉	1	2	yes	—
194	#431	C₂²×C₈₉	1	2	yes	—
195	#423	—	2	1	no	—
196	C₂×C₄⋊C₈	—	2	1	no	—
197	#407	—	2	1	no	—
198	C₂×C₂²⋊C₈	—	2	1	no	—
199	C₄×M₁₆	C₄×C₈₉	1	2	yes	complemented
200	C₂×C₄×C₈	C₄×C₈₉	1	2	yes	complemented
201	#383	—	2	1	no	—
202	#382	—	2	1	no	—
203	#381	—	2	1	no	—
204	#380	—	2	1	no	—
205	C₄×C₄⋊C₄	C₄×C₈₉	1	2	yes	—
206	C₄×C₂²⋊C₄	C₄×C₈₉	1	2	yes	—
207	#376	C₂²×C₈₉	1	2	yes	—
208	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
209	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
210	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
211	C₂×M₁₆	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₂²⋊C₄	—	2	2	no	—
215	C₂×C₄²	C₂×C₄×C₈₉	1	4	yes	—
216	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
224	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
225	C₂×C₄²	Q₈×C₈₉	1	1	yes	characteristic
226	C₂×C₄²	Q₈×C₈₉	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	#97	—	2	2	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	C₂×C₄×C₈₉	1	4	yes	—
239	C₄×C₈	C₂×C₄×C₈₉	1	4	yes	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	C₂⁴	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	C₄²×C₈₉	1	1	yes	characteristic
250	C₂²×C₄	C₄²×C₈₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
252	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
253	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
254	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
257	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊C₄×C₈₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
267	M₁₆	—	4	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	4	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₂²⋊C₄	—	4	4	no	—
273	C₄²	—	2	8	no	—
274	C₄²	C₄²×C₈₉	1	1	yes	characteristic
275	C₄²	C₄²×C₈₉	1	1	yes	characteristic
276	C₄²	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
277	C₄²	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
278	C₄²	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
279	C₄²	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
280	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
281	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
282	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
283	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
284	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
285	C₄²	C₄⋊C₄×C₈₉	1	1	yes	characteristic
286	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
287	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
288	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
289	C₄²	C₂×Q₈×C₈₉	1	1	yes	characteristic
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	4	1	no	—
293	C₂³	#95×C₈₉	1	1	yes	characteristic
294	C₂³	#95×C₈₉	1	1	yes	characteristic
295	C₂³	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
317	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
318	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
319	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
320	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
321	C₂×C₄	#95×C₈₉	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄²×C₈₉	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	1	yes	characteristic
328	C₂×C₄	#131×C₈₉	1	4	yes	—
329	C₈	—	4	4	no	—
330	C₈	—	4	4	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	4	4	no	—
339	C₂²	H(3,ℤ/4)×C₈₉	1	2	yes	—
340	C₂²	C₂×#95×C₈₉	1	1	yes	characteristic
341	C₂²	#408×C₈₉	1	2	yes	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	8	4	no	—
352	C₄	H(3,ℤ/4)×C₈₉	1	2	yes	—
353	C₄	#405×C₈₉	1	2	yes	—
354	C₄	#424×C₈₉	1	2	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	1	no	—
358	C₂	C₈₉×#1729	1	1	yes	characteristic
359	C₂	C₂×H(3,ℤ/4)×C₈₉	1	1	yes	characteristic
360	C₂	C₂×H(3,ℤ/4)×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
socle	C₂²×C₈₉	C₂×#95
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1274	C₂	semidirect
10. #431×C₈₉	C₄	semidirect
11. #431×C₈₉	C₄	semidirect
18. C₄×M₁₆×C₈₉	C₄	semidirect
19. C₂×C₄×C₈×C₈₉	C₄	semidirect
174. #7857	C₈₉	direct (N × H)
184. #1274	C₂×C₈₉	semidirect
185. C₈₉	#7857	direct (N × H)
191. #431	C₄×C₈₉	semidirect
192. #431	C₄×C₈₉	semidirect
199. C₄×M₁₆	C₄×C₈₉	semidirect
200. C₂×C₄×C₈	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2920	2
C₂×#431×C₈₉	2
C₈₉×#2283	2
C₈₉×#1274	2
#7857	89

Subgroups — C89×#7857 #36385705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7857 #36385705