Subgroups — #26031463

Order 11392.

322 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152151	C₂	1	1	yes	maximal, characteristic
2	#19152150	C₂	1	1	yes	maximal, characteristic
3	#19152006	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152005	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151965	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151965	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151940	C₂	1	1	yes	maximal, characteristic
8	#19151939	C₂	1	1	yes	maximal, characteristic
9	#19151936	C₂	1	1	yes	maximal, characteristic
10	#19151892	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151891	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151882	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151881	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151652	C₂	1	1	yes	maximal, characteristic
15	#485×C₈₉	C₂	1	1	yes	maximal, characteristic
16	#15668011	C₂²	1	1	yes	characteristic
17	#15668011	C₂²	1	1	yes	characteristic
18	#15668011	C₂²	1	1	yes	characteristic
19	#15668010	C₂²	1	1	yes	characteristic
20	#15668003	C₂²	1	1	yes	characteristic
21	#15668003	C₂²	1	1	yes	characteristic
22	#15668002	—	2	1	no	—
23	#15667991	C₂²	1	1	yes	characteristic
24	#15667989	—	2	1	no	—
25	#15667989	—	2	1	no	—
26	#15667989	—	2	1	no	—
27	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
28	C₄×Dic₁₇₈	—	2	1	no	—
29	C₄×Dic₁₇₈	—	2	1	no	—
30	#15667977	—	2	1	no	—
31	#15667977	C₂²	1	1	yes	characteristic
32	#15667971	C₂²	1	1	yes	characteristic
33	#15667968	—	2	1	no	—
34	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
35	#15667946	C₂²	1	1	yes	characteristic
36	#15667945	C₂²	1	1	yes	characteristic
37	#15667945	C₂²	1	1	yes	characteristic
38	#15667944	C₂²	1	1	yes	characteristic
39	#15667943	C₂²	1	1	yes	characteristic
40	#15667943	C₂²	1	1	yes	characteristic
41	#15667941	C₂²	1	1	yes	characteristic
42	#15667941	C₂²	1	1	yes	characteristic
43	#15667937	C₂²	1	1	yes	characteristic
44	#15667937	C₂²	1	1	yes	characteristic
45	#15667936	C₂²	1	1	yes	characteristic
46	#15667936	C₂²	1	1	yes	characteristic
47	#15667935	C₂²	1	1	yes	characteristic
48	#15667935	C₂²	1	1	yes	characteristic
49	C₂²⋊#10623494	C₂²	1	1	yes	characteristic
50	#15667922	C₂²	1	1	yes	characteristic
51	#15667922	C₂²	1	1	yes	characteristic
52	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
53	#117×C₈₉	C₂²	1	1	yes	characteristic
54	#107×C₈₉	C₂²	1	1	yes	characteristic
55	#106×C₈₉	C₂²	1	1	yes	characteristic
56	#103×C₈₉	C₂²	1	1	yes	characteristic
57	#103×C₈₉	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×Dic₁₇₈	—	2	1	no	—
60	C₂×Dic₁₇₈	—	2	1	no	—
61	C₂×Dic₁₇₈	—	2	1	no	—
62	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
64	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
65	C₂×#10623494	C₂³	1	1	yes	characteristic
66	C₂×#10623494	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₈₉	—	2	1	no	—
68	C₄⋊Dic₈₉	—	2	1	no	—
69	C₄⋊Dic₈₉	—	2	1	no	—
70	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
71	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
72	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
73	#13083553	—	2	1	no	—
74	#13083553	—	2	1	no	—
75	#13083553	—	2	1	no	—
76	#13083553	—	2	1	no	—
77	#13083553	—	2	1	no	—
78	#13083553	—	2	1	no	—
79	#13083553	—	2	1	no	—
80	#13083553	—	2	1	no	—
81	#13083553	—	2	1	no	—
82	C₂²⋊Dic₈₉	—	2	1	no	—
83	C₂²⋊Dic₈₉	—	2	1	no	—
84	C₄×Dic₈₉	—	2	1	no	—
85	C₄×Dic₈₉	—	2	1	no	—
86	C₄×Dic₈₉	—	2	1	no	—
87	C₄×Dic₈₉	D₄	1	1	yes	characteristic
88	C₄×Dic₈₉	D₄	1	1	yes	characteristic
89	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
90	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₈₉	—	2	1	no	—
100	C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₄²×C₈₉	—	2	1	no	—
102	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
103	Q₈×C₈₉	—	2	1	no	—
104	Q₈×C₈₉	—	2	1	no	—
105	C₂×C₄×C₈₉	—	2	1	no	—
106	C₂×C₄×C₈₉	—	2	1	no	—
107	C₂×C₄×C₈₉	—	2	1	no	—
108	C₂×C₄×C₈₉	—	2	1	no	—
109	C₂×C₄×C₈₉	—	2	1	no	—
110	C₂×C₄×C₈₉	—	2	1	no	—
111	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
113	C₂×Dic₈₉	—	2	2	no	—
114	C₂×Dic₈₉	—	2	1	no	—
115	C₂×Dic₈₉	—	2	1	no	—
116	C₂×Dic₈₉	—	2	1	no	—
117	C₂×Dic₈₉	—	2	1	no	—
118	C₂×Dic₈₉	—	4	1	no	—
119	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
123	Dic₁₇₈	—	2	1	no	—
124	Dic₁₇₈	—	2	1	no	—
125	Dic₁₇₈	—	4	2	no	—
126	Dic₁₇₈	—	4	2	no	—
127	Dic₁₇₈	—	4	2	no	—
128	C₈×C₈₉	—	2	1	no	—
129	C₈×C₈₉	—	2	1	no	—
130	#10623494	—	2	1	no	—
131	#10623494	—	2	1	no	—
132	C₂²×C₈₉	—	2	1	no	—
133	C₂²×C₈₉	—	2	1	no	—
134	C₂²×C₈₉	—	2	1	no	—
135	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
136	C₄×C₈₉	—	2	1	no	—
137	C₄×C₈₉	—	4	1	no	—
138	C₄×C₈₉	—	4	1	no	—
139	C₄×C₈₉	—	4	1	no	—
140	C₄×C₈₉	—	4	1	no	—
141	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
142	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
143	Dic₈₉	—	2	1	no	—
144	Dic₈₉	—	2	1	no	—
145	Dic₈₉	—	2	1	no	—
146	Dic₈₉	—	4	1	no	—
147	Dic₈₉	—	4	1	no	—
148	Dic₈₉	—	4	1	no	—
149	Dic₈₉	—	4	1	no	—
150	Dic₈₉	#137	1	2	yes	—
151	C₂×C₈₉	—	4	1	no	—
152	C₂×C₈₉	#536	1	1	yes	characteristic
153	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
154	C₂×C₈₉	#575	1	1	yes	characteristic
155	#3237	—	89	1	no	maximal, Sylow
156	C₈₉	#3237	1	1	yes	characteristic, complemented, Sylow
157	#533	—	89	1	no	—
158	#533	—	89	1	no	—
159	#501	—	89	1	no	—
160	#501	—	89	1	no	—
161	#491	—	89	1	no	—
162	#491	—	89	1	no	—
163	#485	—	89	1	no	—
164	#485	—	89	1	no	—
165	#485	—	89	1	no	—
166	#485	D₈₉	1	1	yes	characteristic
167	#477	—	89	1	no	—
168	#477	—	89	1	no	—
169	#475	—	89	1	no	—
170	#475	—	89	1	no	—
171	#432	—	89	1	no	—
172	C₄⋊Q₈	—	89	1	no	—
173	C₄⋊Q₈	—	89	1	no	—
174	C₄⋊Q₈	—	89	1	no	—
175	C₄⋊Q₈	—	89	1	no	—
176	#125	—	89	1	no	—
177	#125	—	89	1	no	—
178	#125	—	178	1	no	—
179	C₂²⋊Q₈	—	89	1	no	—
180	C₂²⋊Q₈	—	178	1	no	—
181	C₂²⋊Q₈	—	178	1	no	—
182	C₂²⋊Q₈	—	178	1	no	—
183	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
184	C₄×Q₈	—	89	1	no	—
185	C₄×Q₈	—	89	1	no	—
186	C₄×Q₈	—	178	1	no	—
187	C₄×Q₈	—	178	1	no	—
188	C₄×Q₈	—	178	1	no	—
189	#117	—	89	1	no	—
190	#117	—	178	1	no	—
191	#117	C₂×D₈₉	1	1	yes	characteristic
192	C₂×C₄²	—	89	1	no	—
193	#107	—	89	1	no	—
194	#107	—	89	1	no	—
195	#107	—	89	1	no	—
196	#107	C₂×D₈₉	1	1	yes	characteristic
197	#106	—	89	1	no	—
198	#106	—	89	1	no	—
199	#106	—	89	1	no	—
200	#106	C₂×D₈₉	1	1	yes	characteristic
201	C₄⋊C₈	—	89	1	no	—
202	C₄⋊C₈	—	89	1	no	—
203	#103	—	89	1	no	—
204	#103	—	89	1	no	—
205	#103	—	89	1	no	—
206	#103	—	89	1	no	—
207	#103	—	89	1	no	—
208	#103	—	89	1	no	—
209	#103	C₂×D₈₉	1	1	yes	characteristic
210	#103	C₂×D₈₉	1	1	yes	characteristic
211	C₂²⋊C₈	—	89	1	no	—
212	C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
213	#97	—	89	1	no	—
214	#97	—	89	1	no	—
215	C₂×Q₈	—	89	1	no	—
216	C₂×Q₈	—	178	1	no	—
217	C₂×Q₈	—	178	1	no	—
218	C₂×Q₈	—	178	1	no	—
219	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
220	C₂²×C₄	—	89	1	no	—
221	C₂²×C₄	—	89	1	no	—
222	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
223	C₂×C₈	—	89	1	no	—
224	C₂×C₈	—	89	1	no	—
225	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
226	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
227	C₄⋊C₄	—	2	1	no	—
228	C₄⋊C₄	—	89	1	no	—
229	C₄⋊C₄	—	89	1	no	—
230	C₄⋊C₄	—	89	1	no	—
231	C₄⋊C₄	—	178	1	no	—
232	C₄⋊C₄	—	178	1	no	—
233	C₄⋊C₄	—	178	1	no	—
234	C₄⋊C₄	—	178	1	no	—
235	C₄⋊C₄	—	178	1	no	—
236	C₄⋊C₄	—	178	1	no	—
237	C₄⋊C₄	—	178	1	no	—
238	C₄⋊C₄	—	178	1	no	—
239	C₄⋊C₄	—	178	1	no	—
240	C₄⋊C₄	—	178	1	no	—
241	C₄⋊C₄	—	178	1	no	—
242	C₄⋊C₄	—	178	1	no	—
243	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
244	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
245	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
246	C₂²⋊C₄	—	2	1	no	—
247	C₂²⋊C₄	—	2	1	no	—
248	C₂²⋊C₄	—	178	1	no	—
249	C₂²⋊C₄	—	178	1	no	—
250	C₄²	—	2	1	no	—
251	C₄²	—	89	1	no	—
252	C₄²	—	89	1	no	—
253	C₄²	—	89	1	no	—
254	C₄²	—	89	1	no	—
255	C₄²	—	178	1	no	—
256	C₄²	—	178	1	no	—
257	C₄²	—	178	1	no	—
258	C₂³	D₄×D₈₉	1	1	yes	characteristic
259	Q₈	—	2	1	no	—
260	Q₈	—	2	1	no	—
261	Q₈	—	356	2	no	—
262	Q₈	—	356	2	no	—
263	Q₈	—	356	2	no	—
264	Q₈	—	178	1	no	—
265	Q₈	—	178	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	89	1	no	—
273	C₂×C₄	—	89	1	no	—
274	C₂×C₄	—	89	1	no	—
275	C₂×C₄	—	89	1	no	—
276	C₂×C₄	—	356	1	no	—
277	C₂×C₄	—	178	2	no	—
278	C₂×C₄	—	178	1	no	—
279	C₂×C₄	—	178	1	no	—
280	C₂×C₄	—	178	1	no	—
281	C₂×C₄	—	178	1	no	—
282	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
283	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
284	C₈	—	2	1	no	—
285	C₈	—	2	1	no	—
286	C₈	—	178	1	no	—
287	C₈	—	178	1	no	—
288	C₂²	—	2	1	no	—
289	C₂²	—	2	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
292	C₄	—	2	1	no	—
293	C₄	—	4	1	no	—
294	C₄	—	4	1	no	—
295	C₄	—	4	1	no	—
296	C₄	—	4	1	no	—
297	C₄	—	89	2	no	—
298	C₄	—	356	1	no	—
299	C₄	—	356	1	no	—
300	C₄	—	356	1	no	—
301	C₄	—	356	1	no	—
302	C₄	—	178	1	no	—
303	C₄	—	178	1	no	—
304	C₄	—	178	1	no	—
305	C₄	#15668059	1	1	yes	characteristic
306	C₄	#15668059	1	1	yes	characteristic
307	C₂	—	4	1	no	—
308	C₂	#19152170	1	1	yes	characteristic
309	C₂	#137×D₈₉	1	1	yes	characteristic
310	C₂	#19152395	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#485×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂³×C₈₉	C₂×D₄
hypercenter	#485	D₈₉
hypocenter	C₈₉	#3237
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #485

Complements

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

N	H ≅ G/N	type
3. #19152006	C₂	semidirect
4. #19152005	C₂	semidirect
5. #19151965	C₂	semidirect
6. #19151965	C₂	semidirect
10. #19151892	C₂	semidirect
11. #19151891	C₂	semidirect
12. #19151882	C₂	semidirect
13. #19151881	C₂	semidirect
156. C₈₉	#3237	semidirect

Maximal subgroups

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

subgroup	index
#19152151	2
#19152150	2
#19152006	2
#19152005	2
#19151965	2
#19151940	2
#19151939	2
#19151936	2
#19151892	2
#19151891	2
#19151882	2
#19151881	2
#19151652	2
#485×C₈₉	2
#3237	89