Subgroups — #26024593

Order 11392.

476 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668004	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15667991	C₂	1	1	yes	maximal, characteristic
3	#19151539	C₂	1	2	yes	maximal, complemented
4	#19151526	C₂	1	2	yes	maximal
5	#19151504	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151504	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151486	C₂	1	2	yes	maximal
8	#19151462	C₂	1	2	yes	maximal, complemented
9	#19151458	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	#15668004	—	2	4	no	—
14	#15667991	—	2	4	no	—
15	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
18	C₂×#13083553	C₂²	1	2	yes	—
19	C₂×#13083553	C₂²	1	2	yes	—
20	C₂×#13083553	C₂²	1	2	yes	—
21	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	—
23	C₂×C₄×Dic₈₉	C₂²	1	2	yes	—
24	#15667919	C₂²	1	2	yes	—
25	#15667919	C₂²	1	2	yes	—
26	#15667919	C₂²	1	2	yes	—
27	#15667919	C₂²	1	2	yes	—
28	#15667919	C₂²	1	2	yes	—
29	#15667919	C₂²	1	2	yes	—
30	C₂³×C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	#95×C₈₉	C₂²	1	1	yes	characteristic
36	#95×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×Dic₁₇₈	—	2	2	no	—
38	C₂×Dic₁₇₈	—	2	2	no	—
39	C₂×Dic₁₇₈	—	2	2	no	—
40	C₂²×Dic₈₉	C₂³	1	2	yes	—
41	C₂²×Dic₈₉	C₂³	1	2	yes	—
42	C₂²×Dic₈₉	C₂³	1	2	yes	—
43	C₂²×Dic₈₉	C₂³	1	2	yes	—
44	C₄⋊Dic₈₉	—	2	2	no	—
45	C₄⋊Dic₈₉	—	2	2	no	—
46	C₄⋊Dic₈₉	D₄	1	4	yes	—
47	#13083553	—	2	4	no	—
48	#13083553	—	2	4	no	—
49	#13083553	—	2	4	no	—
50	C₂²⋊Dic₈₉	—	2	4	no	—
51	C₂²⋊Dic₈₉	—	2	4	no	—
52	C₄×Dic₈₉	—	2	4	no	—
53	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₈₉	—	2	2	no	—
55	C₂²×C₄×C₈₉	—	2	2	no	—
56	C₂²×C₄×C₈₉	—	2	2	no	—
57	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²⋊C₄×C₈₉	—	2	2	no	—
64	C₂²⋊C₄×C₈₉	—	2	2	no	—
65	C₄²×C₈₉	—	2	2	no	—
66	C₄²×C₈₉	—	2	2	no	—
67	C₂³×C₈₉	—	2	1	no	—
68	C₂³×C₈₉	—	2	1	no	—
69	C₂³×C₈₉	—	2	1	no	—
70	C₂³×C₈₉	—	2	1	no	—
71	C₂³×C₈₉	—	2	1	no	—
72	C₂³×C₈₉	—	2	1	no	—
73	C₂³×C₈₉	#41	1	2	yes	—
74	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
75	C₂×C₄×C₈₉	—	2	1	no	—
76	C₂×C₄×C₈₉	—	2	1	no	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	2	1	no	—
81	C₂×C₄×C₈₉	—	2	1	no	—
82	C₂×C₄×C₈₉	—	2	1	no	—
83	C₂×C₄×C₈₉	—	2	1	no	—
84	C₂×C₄×C₈₉	—	2	1	no	—
85	C₂×C₄×C₈₉	—	2	1	no	—
86	C₂×C₄×C₈₉	—	2	1	no	—
87	C₂×C₄×C₈₉	—	2	1	no	—
88	C₂×C₄×C₈₉	—	2	1	no	—
89	C₂×C₄×C₈₉	—	4	4	no	—
90	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
91	C₂×C₄×C₈₉	#41	1	2	yes	—
92	C₂×C₄×C₈₉	#41	1	2	yes	—
93	C₂×C₄×C₈₉	#41	1	2	yes	—
94	C₂×Dic₈₉	—	2	2	no	—
95	C₂×Dic₈₉	—	2	2	no	—
96	C₂×Dic₈₉	—	2	2	no	—
97	C₂×Dic₈₉	—	2	2	no	—
98	C₂×Dic₈₉	—	2	2	no	—
99	C₂×Dic₈₉	—	2	2	no	—
100	C₂×Dic₈₉	—	2	2	no	—
101	C₂×Dic₈₉	—	2	2	no	—
102	C₂×Dic₈₉	—	2	2	no	—
103	C₂×Dic₈₉	—	2	2	no	—
104	C₂×Dic₈₉	—	2	2	no	—
105	C₂×Dic₈₉	C₂×D₄	1	4	yes	—
106	Dic₁₇₈	—	4	4	no	—
107	C₂²×C₈₉	—	2	2	no	—
108	C₂²×C₈₉	—	2	2	no	—
109	C₂²×C₈₉	—	2	2	no	—
110	C₂²×C₈₉	—	4	1	no	—
111	C₂²×C₈₉	—	4	1	no	—
112	C₂²×C₈₉	—	4	1	no	—
113	C₂²×C₈₉	—	4	1	no	—
114	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
115	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
116	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
117	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
118	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
119	C₂²×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
120	C₂²×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
121	C₄×C₈₉	—	2	2	no	—
122	C₄×C₈₉	—	4	1	no	—
123	C₄×C₈₉	—	4	1	no	—
124	C₄×C₈₉	—	4	1	no	—
125	C₄×C₈₉	—	4	1	no	—
126	C₄×C₈₉	#124	1	4	yes	—
127	Dic₈₉	—	2	4	no	—
128	Dic₈₉	—	4	2	no	—
129	Dic₈₉	—	4	2	no	—
130	Dic₈₉	—	4	2	no	—
131	C₂×C₈₉	—	4	2	no	—
132	C₂×C₈₉	C₂×#124	1	1	yes	characteristic
133	C₂×C₈₉	#529	1	1	yes	characteristic
134	C₂×C₈₉	#541	1	1	yes	characteristic
135	C₂×C₈₉	#547	1	1	yes	characteristic
136	C₂×C₈₉	#548	1	1	yes	characteristic
137	C₂×C₈₉	#552	1	1	yes	characteristic
138	C₂×C₈₉	#552	1	1	yes	characteristic
139	#2489	—	89	1	no	maximal, Sylow
140	C₈₉	#2489	1	1	yes	characteristic, complemented, Sylow
141	C₂×#125	—	89	1	no	—
142	C₂×C₂²⋊Q₈	—	89	1	no	—
143	#400	—	89	2	no	—
144	#397	—	89	2	no	—
145	#391	—	89	1	no	—
146	#391	—	89	1	no	—
147	#388	—	89	2	no	—
148	#382	—	89	2	no	—
149	#380	—	89	1	no	—
150	C₄×C₄⋊C₄	—	89	1	no	—
151	C₄×C₂²⋊C₄	D₈₉	1	1	yes	characteristic
152	C₂²×Q₈	—	89	1	no	—
153	C₂³×C₄	C₂×D₈₉	1	1	yes	characteristic
154	#125	—	178	4	no	—
155	C₂²⋊Q₈	—	178	4	no	—
156	C₂×C₄⋊C₄	—	89	1	no	—
157	C₂×C₄⋊C₄	—	89	2	no	—
158	C₂×C₄⋊C₄	—	89	1	no	—
159	C₂×C₄⋊C₄	—	89	2	no	—
160	C₂×C₄⋊C₄	—	89	2	no	—
161	C₂×C₄⋊C₄	—	89	1	no	—
162	C₂×C₂²⋊C₄	—	89	2	no	—
163	C₂×C₂²⋊C₄	—	89	2	no	—
164	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
166	C₂×C₄²	—	89	2	no	—
167	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
168	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
169	#95	—	89	2	no	—
170	#95	—	89	2	no	—
171	#95	—	89	2	no	—
172	#95	—	89	2	no	—
173	#95	—	89	2	no	—
174	#95	—	89	2	no	—
175	#95	C₂×D₈₉	1	1	yes	characteristic
176	#95	C₂×D₈₉	1	1	yes	characteristic
177	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
178	C₂×Q₈	—	178	2	no	—
179	C₂×Q₈	—	178	2	no	—
180	C₂×Q₈	—	178	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	89	2	no	—
185	C₂²×C₄	—	89	2	no	—
186	C₂²×C₄	—	89	2	no	—
187	C₂²×C₄	—	89	2	no	—
188	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
190	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
191	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
192	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
193	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
194	C₄⋊C₄	—	89	4	no	—
195	C₄⋊C₄	—	178	4	no	—
196	C₄⋊C₄	—	178	4	no	—
197	C₄⋊C₄	—	178	4	no	—
198	C₄⋊C₄	—	178	2	no	—
199	C₄⋊C₄	—	178	2	no	—
200	C₂²⋊C₄	—	2	2	no	—
201	C₂²⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	178	4	no	—
203	C₂²⋊C₄	—	178	4	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	178	4	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	—	2	1	no	—
211	C₂³	—	2	1	no	—
212	C₂³	—	2	1	no	—
213	C₂³	#13083574	1	2	yes	—
214	C₂³	C₂³×D₈₉	1	1	yes	characteristic
215	Q₈	—	356	4	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	4	4	no	—
231	C₂×C₄	—	89	4	no	—
232	C₂×C₄	—	178	2	no	—
233	C₂×C₄	—	178	2	no	—
234	C₂×C₄	—	178	2	no	—
235	C₂×C₄	—	178	2	no	—
236	C₂×C₄	—	178	2	no	—
237	C₂×C₄	—	178	2	no	—
238	C₂×C₄	—	178	2	no	—
239	C₂×C₄	—	178	2	no	—
240	C₂×C₄	—	178	2	no	—
241	C₂×C₄	—	178	2	no	—
242	C₂×C₄	—	178	2	no	—
243	C₂×C₄	D₄×D₈₉	1	2	yes	—
244	C₂×C₄	#13083573	1	2	yes	—
245	C₂×C₄	#13083574	1	2	yes	—
246	C₂×C₄	#13083574	1	2	yes	—
247	C₂²	—	2	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	4	1	no	—
251	C₂²	—	4	1	no	—
252	C₂²	—	4	1	no	—
253	C₂²	—	4	1	no	—
254	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
255	C₂²	C₂×#13083573	1	1	yes	characteristic
256	C₂²	C₂×#13083574	1	1	yes	characteristic
257	C₂²	C₂×#13083574	1	1	yes	characteristic
258	C₂²	C₂×#13083574	1	1	yes	characteristic
259	C₂²	#15668059	1	1	yes	characteristic
260	C₂²	#15668059	1	1	yes	characteristic
261	C₄	—	2	2	no	—
262	C₄	—	4	1	no	—
263	C₄	—	4	1	no	—
264	C₄	—	4	1	no	—
265	C₄	—	4	1	no	—
266	C₄	—	356	2	no	—
267	C₄	—	356	2	no	—
268	C₄	—	356	2	no	—
269	C₄	—	178	4	no	—
270	C₄	#15667998	1	4	yes	—
271	C₂	—	4	2	no	—
272	C₂	C₂×#15667998	1	1	yes	characteristic
273	C₂	#19152132	1	1	yes	characteristic
274	C₂	#19152210	1	1	yes	characteristic
275	C₂	#19152253	1	1	yes	characteristic
276	C₂	#19152257	1	1	yes	characteristic
277	C₂	#19152288	1	1	yes	characteristic
278	C₂	#19152288	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁴
Fitting	C₄×C₂²⋊C₄×C₈₉	C₂
prime radical	C₂⁴×C₈₉	C₂³
hypercenter	C₄×C₂²⋊C₄	D₈₉
hypocenter	C₈₉	#2489
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15668004	C₂	semidirect
3. #19151539	C₂	semidirect
5. #19151504	C₂	semidirect
6. #19151504	C₂	semidirect
8. #19151462	C₂	semidirect
10. C₄×C₄⋊Dic₈₉	C₂	semidirect
140. C₈₉	#2489	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668004	2
C₂×#15667991	2
#19151539	2
#19151526	2
#19151504	2
#19151486	2
#19151462	2
#19151458	2
C₄×C₄⋊Dic₈₉	2
C₄×C₂²⋊C₄×C₈₉	2
#2489	89