Subgroups — C₂×C₈₉×#2851 #36414464

Order 22784.

3182 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2851	C₂	1	16	yes	maximal, direct product factor
4	C₂×#389×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#387×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₂×#385×C₈₉	C₂	1	4	yes	maximal
7	C₂×#382×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#380×C₈₉	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#125×C₈₉	—	2	8	no	—
12	C₂×#125×C₈₉	C₂²	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
18	C₂²×C₄²×C₈₉	—	2	8	no	—
19	C₂²×C₄²×C₈₉	C₂²	1	8	yes	—
20	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
23	#389×C₈₉	C₂²	1	16	yes	complemented
24	#387×C₈₉	C₂²	1	32	yes	complemented
25	#385×C₈₉	C₂²	1	32	yes	—
26	#382×C₈₉	C₂²	1	8	yes	complemented
27	#380×C₈₉	C₂²	1	16	yes	—
28	C₂×#95×C₈₉	C₂²	1	4	yes	—
29	C₂×#95×C₈₉	C₂²	1	4	yes	—
30	C₂×#95×C₈₉	C₂²	1	4	yes	—
31	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₈₉	—	2	8	no	—
33	C₂³×C₄×C₈₉	—	2	8	no	—
34	C₂³×C₄×C₈₉	—	2	4	no	—
35	C₂³×C₄×C₈₉	—	2	8	no	—
36	C₂³×C₄×C₈₉	—	2	4	no	—
37	C₂³×C₄×C₈₉	Q₈	1	8	yes	—
38	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
39	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
46	#125×C₈₉	—	2	32	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
52	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
53	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
55	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
57	C₂×C₄²×C₈₉	—	2	8	no	—
58	C₂×C₄²×C₈₉	—	2	4	no	—
59	C₂×C₄²×C₈₉	—	2	32	no	—
60	C₂×C₄²×C₈₉	D₄	1	8	yes	—
61	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
62	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
63	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
64	#95×C₈₉	C₂³	1	16	yes	—
65	#95×C₈₉	C₂³	1	16	yes	—
66	#95×C₈₉	C₂³	1	16	yes	—
67	C₂⁴×C₈₉	—	2	2	no	—
68	C₂⁴×C₈₉	—	2	2	no	—
69	C₂⁴×C₈₉	—	2	4	no	—
70	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
71	C₂⁴×C₈₉	#41	1	8	yes	—
72	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
73	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	—	2	64	no	—
75	C₂²×C₄×C₈₉	—	2	2	no	—
76	C₂²×C₄×C₈₉	—	2	4	no	—
77	C₂²×C₄×C₈₉	—	2	16	no	—
78	C₂²×C₄×C₈₉	—	2	2	no	—
79	C₂²×C₄×C₈₉	—	2	4	no	—
80	C₂²×C₄×C₈₉	—	2	4	no	—
81	C₂²×C₄×C₈₉	—	2	4	no	—
82	C₂²×C₄×C₈₉	—	2	32	no	—
83	C₂²×C₄×C₈₉	—	2	16	no	—
84	C₂²×C₄×C₈₉	—	2	8	no	—
85	C₂²×C₄×C₈₉	—	2	16	no	—
86	C₂²×C₄×C₈₉	—	2	8	no	—
87	C₂²×C₄×C₈₉	—	2	8	no	—
88	C₂²×C₄×C₈₉	—	2	8	no	—
89	C₂²×C₄×C₈₉	—	2	8	no	—
90	C₂²×C₄×C₈₉	—	2	8	no	—
91	C₂²×C₄×C₈₉	—	2	8	no	—
92	C₂²×C₄×C₈₉	—	2	8	no	—
93	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₈₉	C₂×Q₈	1	16	yes	—
97	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₈₉	#41	1	8	yes	—
99	C₂²×C₄×C₈₉	#41	1	4	yes	—
100	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
106	C₄⋊C₄×C₈₉	—	2	32	no	—
107	C₄⋊C₄×C₈₉	—	2	16	no	—
108	C₄⋊C₄×C₈₉	—	2	32	no	—
109	C₄⋊C₄×C₈₉	—	2	16	no	—
110	C₂²⋊C₄×C₈₉	—	2	32	no	—
111	C₄²×C₈₉	—	2	16	no	—
112	C₄²×C₈₉	—	2	8	no	—
113	C₄²×C₈₉	C₂×D₄	1	16	yes	—
114	C₂³×C₈₉	—	2	8	no	—
115	C₂³×C₈₉	—	2	16	no	—
116	C₂³×C₈₉	—	2	16	no	—
117	C₂³×C₈₉	—	2	8	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	—	2	2	no	—
120	C₂³×C₈₉	—	2	4	no	—
121	C₂³×C₈₉	#125	1	16	yes	complemented
122	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
123	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
124	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
125	C₂³×C₈₉	C₂×#41	1	8	yes	—
126	C₂³×C₈₉	C₂×#41	1	2	yes	—
127	C₂³×C₈₉	C₂×#41	1	4	yes	—
128	C₂³×C₈₉	C₂×#41	1	4	yes	—
129	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
130	C₂×C₄×C₈₉	—	2	64	no	—
131	C₂×C₄×C₈₉	—	2	8	no	—
132	C₂×C₄×C₈₉	—	2	16	no	—
133	C₂×C₄×C₈₉	—	2	16	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	2	4	no	—
138	C₂×C₄×C₈₉	—	2	4	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	2	32	no	—
141	C₂×C₄×C₈₉	—	2	8	no	—
142	C₂×C₄×C₈₉	—	2	8	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	2	8	no	—
145	C₂×C₄×C₈₉	—	2	8	no	—
146	C₂×C₄×C₈₉	—	2	8	no	—
147	C₂×C₄×C₈₉	—	4	16	no	—
148	C₂×C₄×C₈₉	—	4	16	no	—
149	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	—
150	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
153	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
154	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
155	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
156	C₂²×C₈₉	—	2	32	no	—
157	C₂²×C₈₉	—	2	4	no	—
158	C₂²×C₈₉	—	2	8	no	—
159	C₂²×C₈₉	—	2	8	no	—
160	C₂²×C₈₉	—	2	4	no	—
161	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
162	C₂²×C₈₉	#525	1	8	yes	—
163	C₂²×C₈₉	C₂×#125	1	4	yes	—
164	C₂²×C₈₉	C₂×#125	1	8	yes	complemented
165	C₂²×C₈₉	#529	1	8	yes	—
166	C₂²×C₈₉	#533	1	4	yes	—
167	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
168	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
169	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
170	C₂²×C₈₉	C₂²×#41	1	2	yes	—
171	C₂²×C₈₉	C₂²×#41	1	2	yes	—
172	C₄×C₈₉	—	2	4	no	—
173	C₄×C₈₉	—	2	8	no	—
174	C₄×C₈₉	—	2	8	no	—
175	C₄×C₈₉	—	4	8	no	—
176	C₄×C₈₉	—	4	8	no	—
177	C₄×C₈₉	C₂×C₂²⋊Q₈	1	8	yes	—
178	C₂×#2851	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₈₉	—	2	8	no	—
180	C₂×C₈₉	#2851	1	8	yes	direct product factor
181	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₈₉	C₂×#525	1	2	yes	—
183	C₂×C₈₉	C₂²×#125	1	1	yes	characteristic
184	C₂×C₈₉	C₂×#529	1	2	yes	—
185	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
186	C₂²×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
187	C₂³×C₄²	C₂×C₈₉	1	1	yes	characteristic
188	#2851	C₂×C₈₉	1	16	yes	direct product factor
189	C₂×#389	C₂×C₈₉	1	2	yes	complemented
190	C₂×#387	C₂×C₈₉	1	4	yes	complemented
191	C₂×#385	C₂×C₈₉	1	4	yes	—
192	C₂×#382	C₂×C₈₉	1	1	yes	characteristic, complemented
193	C₂×#380	C₂×C₈₉	1	2	yes	—
194	C₈₉	C₂×#2851	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
196	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
197	C₂×#125	—	2	8	no	—
198	C₂×#125	C₂²×C₈₉	1	8	yes	complemented
199	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
200	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
204	C₂²×C₄²	—	2	8	no	—
205	C₂²×C₄²	C₂²×C₈₉	1	8	yes	—
206	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
207	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
208	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
209	#389	C₂²×C₈₉	1	16	yes	complemented
210	#387	C₂²×C₈₉	1	32	yes	complemented
211	#385	C₂²×C₈₉	1	32	yes	—
212	#382	C₂²×C₈₉	1	8	yes	complemented
213	#380	C₂²×C₈₉	1	16	yes	—
214	C₂×#95	C₂²×C₈₉	1	4	yes	—
215	C₂×#95	C₂²×C₈₉	1	4	yes	—
216	C₂×#95	C₂²×C₈₉	1	4	yes	—
217	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	2	8	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	8	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	Q₈×C₈₉	1	8	yes	—
224	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
225	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
226	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
227	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
228	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
230	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
232	#125	—	2	32	no	—
233	C₂×C₄⋊C₄	—	2	16	no	—
234	C₂×C₄⋊C₄	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
238	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
239	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
240	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
241	C₂×C₂²⋊C₄	—	2	16	no	—
242	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
243	C₂×C₄²	—	2	8	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	32	no	—
246	C₂×C₄²	D₄×C₈₉	1	8	yes	—
247	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
248	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
249	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
250	#95	C₂³×C₈₉	1	16	yes	—
251	#95	C₂³×C₈₉	1	16	yes	—
252	#95	C₂³×C₈₉	1	16	yes	—
253	C₂⁴	—	2	2	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
257	C₂⁴	#41×C₈₉	1	8	yes	—
258	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
259	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
260	C₂²×C₄	—	2	64	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	16	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	32	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
280	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
282	C₂²×C₄	C₂×Q₈×C₈₉	1	16	yes	—
283	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
284	C₂²×C₄	#41×C₈₉	1	8	yes	—
285	C₂²×C₄	#41×C₈₉	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
287	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
291	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
292	C₄⋊C₄	—	2	32	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	32	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	2	32	no	—
297	C₄²	—	2	16	no	—
298	C₄²	—	2	8	no	—
299	C₄²	C₂×D₄×C₈₉	1	16	yes	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	16	no	—
302	C₂³	—	2	16	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	#125×C₈₉	1	16	yes	complemented
308	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
309	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
310	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
311	C₂³	C₂×#41×C₈₉	1	8	yes	—
312	C₂³	C₂×#41×C₈₉	1	2	yes	—
313	C₂³	C₂×#41×C₈₉	1	4	yes	—
314	C₂³	C₂×#41×C₈₉	1	4	yes	—
315	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
316	C₂×C₄	—	2	64	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	16	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	32	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	—
336	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
337	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
338	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
339	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
340	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
341	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
342	C₂²	—	2	32	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	2	4	no	—
347	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
348	C₂²	#525×C₈₉	1	8	yes	—
349	C₂²	C₂×#125×C₈₉	1	4	yes	—
350	C₂²	C₂×#125×C₈₉	1	8	yes	complemented
351	C₂²	#529×C₈₉	1	8	yes	—
352	C₂²	#533×C₈₉	1	4	yes	—
353	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
354	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
355	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
356	C₂²	C₂²×#41×C₈₉	1	2	yes	—
357	C₂²	C₂²×#41×C₈₉	1	2	yes	—
358	C₄	—	2	4	no	—
359	C₄	—	2	8	no	—
360	C₄	—	2	8	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₂²⋊Q₈×C₈₉	1	8	yes	—
364	C₂	—	2	8	no	—
365	C₂	C₈₉×#2851	1	8	yes	direct product factor
366	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
367	C₂	C₂×#525×C₈₉	1	2	yes	—
368	C₂	C₂²×#125×C₈₉	1	1	yes	characteristic
369	C₂	C₂×#529×C₈₉	1	2	yes	—
370	C₂	C₂×#533×C₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#125×C₈₉	C₂	semidirect
3. C₈₉×#2851	C₂	direct (N × H)
4. C₂×#389×C₈₉	C₂	semidirect
5. C₂×#387×C₈₉	C₂	semidirect
7. C₂×#382×C₈₉	C₂	semidirect
12. C₂×#125×C₈₉	C₂²	semidirect
23. #389×C₈₉	C₂²	semidirect
24. #387×C₈₉	C₂²	semidirect
26. #382×C₈₉	C₂²	semidirect
121. C₂³×C₈₉	#125	semidirect
164. C₂²×C₈₉	C₂×#125	semidirect
178. C₂×#2851	C₈₉	direct (N × H)
180. C₂×C₈₉	#2851	direct (N × H)
186. C₂²×#125	C₂×C₈₉	semidirect
188. #2851	C₂×C₈₉	direct (N × H)
189. C₂×#389	C₂×C₈₉	semidirect
190. C₂×#387	C₂×C₈₉	semidirect
192. C₂×#382	C₂×C₈₉	semidirect
194. C₈₉	C₂×#2851	direct (N × H)
198. C₂×#125	C₂²×C₈₉	semidirect
209. #389	C₂²×C₈₉	semidirect
210. #387	C₂²×C₈₉	semidirect
212. #382	C₂²×C₈₉	semidirect
307. C₂³	#125×C₈₉	semidirect
350. C₂²	C₂×#125×C₈₉	semidirect
365. C₂	C₈₉×#2851	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#125×C₈₉	2
C₂³×C₄²×C₈₉	2
C₈₉×#2851	2
C₂×#389×C₈₉	2
C₂×#387×C₈₉	2
C₂×#385×C₈₉	2
C₂×#382×C₈₉	2
C₂×#380×C₈₉	2
C₂×#2851	89

Subgroups — C2×C89×#2851 #36414464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2851 #36414464