Subgroups — #14576932

Order 2432.

1212 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927099	C₂	1	2	yes	maximal, complemented
2	#11927095	C₂	1	2	yes	maximal, complemented
3	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927081	C₂	1	4	yes	maximal, complemented
5	#11927080	C₂	1	4	yes	maximal, complemented
6	#11927079	C₂	1	4	yes	maximal, complemented
7	#11927057	C₂	1	4	yes	maximal, complemented
8	#11927056	C₂	1	2	yes	maximal, complemented
9	C₄×#64545	C₂	1	4	yes	maximal, complemented
10	#11927012	C₂	1	2	yes	maximal, complemented
11	C₂×C₄²×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#64545	C₂²	1	4	yes	—
14	C₂×#64541	C₂²	1	2	yes	—
15	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
17	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₁₉×#125	C₂²	1	2	yes	complemented
19	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
21	C₁₉×#117	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	#10597393	C₂²	1	4	yes	complemented
24	#10597392	C₂²	1	4	yes	—
25	Q₈×Dic₁₉	C₂²	1	4	yes	complemented
26	#10597376	C₂²	1	4	yes	—
27	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
28	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
29	#10597344	C₂²	1	8	yes	complemented
30	#10597343	C₂²	1	4	yes	—
31	#10597341	C₂²	1	4	yes	—
32	#10597341	C₂²	1	4	yes	—
33	#10597340	C₂²	1	8	yes	—
34	#10597339	C₂²	1	8	yes	—
35	#10597339	C₂²	1	4	yes	complemented
36	#10597339	C₂²	1	4	yes	complemented
37	#10597338	C₂²	1	4	yes	—
38	#10597338	C₂²	1	8	yes	complemented
39	#10597336	C₂²	1	4	yes	complemented
40	#10597333	C₂²	1	4	yes	complemented
41	#10597332	C₂²	1	4	yes	—
42	#10597328	C₂²	1	4	yes	—
43	(C₂²⋊D₁₉)⋊C₄	C₂²	1	8	yes	—
44	#10597321	C₂²	1	2	yes	complemented
45	#10597320	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₇₆	C₂²	1	8	yes	—
47	C₄×D₇₆	C₂²	1	4	yes	complemented
48	#10597318	C₂²	1	4	yes	complemented
49	C₄²×D₁₉	C₂²	1	2	yes	—
50	C₄²×D₁₉	C₂²	1	2	yes	—
51	C₄²×D₁₉	C₂²	1	2	yes	—
52	C₄²×D₁₉	C₂²	1	2	yes	—
53	C₄²×D₁₉	C₂²	1	4	yes	complemented
54	#10597315	C₂²	1	1	yes	characteristic, complemented
55	C₂³×D₁₉	C₂³	1	1	yes	characteristic
56	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
57	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
60	C₂²×Dic₁₉	C₂³	1	2	yes	—
61	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
62	#64545	—	2	16	no	—
63	#64541	—	2	8	no	—
64	C₂×D₇₆	C₂³	1	4	yes	—
65	C₂×D₇₆	C₂³	1	2	yes	—
66	C₂×D₇₆	C₂³	1	8	yes	—
67	C₂×C₄×D₁₉	—	2	4	no	—
68	C₂×C₄×D₁₉	—	2	8	no	—
69	C₂×C₄×D₁₉	C₂³	1	2	yes	—
70	C₂×C₄×D₁₉	C₂³	1	2	yes	—
71	C₂×C₄×D₁₉	C₂³	1	2	yes	—
72	C₂×C₄×D₁₉	C₂³	1	2	yes	—
73	C₂×C₄×D₁₉	C₂³	1	2	yes	—
74	C₂×C₄×D₁₉	C₂³	1	4	yes	—
75	C₂×C₄×D₁₉	C₂³	1	8	yes	—
76	C₂×C₄×D₁₉	C₂³	1	2	yes	—
77	C₂×Dic₃₈	C₂³	1	2	yes	—
78	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
80	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₄²×C₁₉	C₂³	1	2	yes	—
83	C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₄²×C₁₉	C₂³	1	4	yes	—
86	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
87	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
88	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
89	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
90	C₄⋊Dic₁₉	C₂³	1	4	yes	—
91	C₄⋊Dic₁₉	C₂³	1	8	yes	—
92	Dic₁₉⋊C₄	C₂³	1	8	yes	—
93	C₄×Dic₁₉	C₂³	1	2	yes	—
94	C₄×Dic₁₉	C₂³	1	8	yes	—
95	C₄×Dic₁₉	C₂³	1	2	yes	—
96	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
97	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₉	C₂³	1	2	yes	—
99	C₄×Dic₁₉	C₂³	1	2	yes	—
100	C₄×Dic₁₉	C₂³	1	2	yes	—
101	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
102	C₂²×D₁₉	—	2	2	no	—
103	C₂²×D₁₉	—	2	4	no	—
104	C₂²×D₁₉	C₂⁴	1	4	yes	—
105	C₂²×D₁₉	C₂⁴	1	2	yes	—
106	Q₈×C₁₉	—	2	8	no	—
107	C₂×C₄×C₁₉	—	2	4	no	—
108	C₂×C₄×C₁₉	#41	1	4	yes	complemented
109	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
110	C₂×C₄×C₁₉	C₂⁴	1	8	yes	—
111	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
112	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	C₂²⋊D₁₉	—	2	8	no	—
115	C₂×Dic₁₉	—	2	2	no	—
116	C₂×Dic₁₉	—	2	4	no	—
117	C₂×Dic₁₉	C₂⁴	1	2	yes	—
118	C₂×Dic₁₉	C₂⁴	1	2	yes	—
119	C₂×Dic₁₉	C₂⁴	1	4	yes	—
120	C₂×Dic₁₉	C₂⁴	1	2	yes	—
121	D₇₆	—	2	16	no	—
122	D₇₆	—	2	4	no	—
123	D₇₆	—	2	8	no	—
124	C₄×D₁₉	—	2	4	no	—
125	C₄×D₁₉	—	2	4	no	—
126	C₄×D₁₉	—	2	4	no	—
127	C₄×D₁₉	—	2	4	no	—
128	C₄×D₁₉	—	2	8	no	—
129	C₄×D₁₉	—	2	4	no	—
130	C₄×D₁₉	—	2	16	no	—
131	C₄×D₁₉	#41	1	8	yes	complemented
132	Dic₃₈	—	2	4	no	—
133	#3444	—	19	1	no	maximal, Sylow
134	C₂²×C₁₉	—	2	2	no	—
135	C₂²×C₁₉	C₂×#41	1	2	yes	—
136	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
137	C₂×D₁₉	—	2	8	no	—
138	C₂×D₁₉	—	2	2	no	—
139	C₂×D₁₉	—	2	2	no	—
140	C₂×D₁₉	—	2	8	no	—
141	C₂×D₁₉	—	2	4	no	—
142	C₂×D₁₉	C₂×#41	1	4	yes	—
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	2	8	no	—
145	C₄×C₁₉	C₂×#41	1	2	yes	—
146	C₄×C₁₉	C₂×#41	1	2	yes	—
147	C₄×C₁₉	C₂×#41	1	4	yes	—
148	Dic₁₉	—	2	4	no	—
149	Dic₁₉	—	2	2	no	—
150	Dic₁₉	—	2	2	no	—
151	Dic₁₉	C₂×#41	1	4	yes	—
152	#533	—	19	2	no	—
153	#533	D₁₉	1	1	yes	characteristic, complemented
154	#532	—	19	2	no	—
155	#532	—	19	1	no	—
156	#529	—	19	4	no	—
157	#529	—	19	4	no	—
158	#529	—	19	4	no	—
159	#525	—	19	4	no	—
160	#525	—	19	2	no	—
161	C₄×#41	—	19	4	no	—
162	C₄×#41	—	19	2	no	—
163	C₂²×C₄²	—	19	1	no	—
164	C₂×C₁₉	—	2	2	no	—
165	C₂×C₁₉	C₂²×#41	1	2	yes	—
166	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
167	D₁₉	—	2	4	no	—
168	D₁₉	—	4	4	no	—
169	C₂×#41	—	19	4	no	—
170	C₂×#41	—	19	2	no	—
171	C₂³×C₄	—	19	2	no	—
172	C₂³×C₄	—	19	1	no	—
173	C₄⋊Q₈	—	19	1	no	—
174	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
175	#127	—	19	1	no	—
176	#126	—	19	8	no	—
177	#125	—	19	4	no	—
178	#125	C₂×D₁₉	1	2	yes	complemented
179	#124	—	19	4	no	—
180	#124	—	19	2	no	—
181	#123	—	19	8	no	—
182	#123	—	19	4	no	—
183	C₂²⋊Q₈	—	19	4	no	—
184	C₂²⋊Q₈	—	19	4	no	—
185	C₂²⋊Q₈	C₂×D₁₉	1	4	yes	—
186	#121	—	19	4	no	—
187	#121	—	19	4	no	—
188	#121	—	19	4	no	—
189	#120	—	19	4	no	—
190	C₄×Q₈	—	19	4	no	—
191	C₄×Q₈	—	19	4	no	—
192	C₄×Q₈	C₂×D₁₉	1	4	yes	complemented
193	C₄×D₄	—	19	8	no	—
194	C₄×D₄	—	19	4	no	—
195	C₄×D₄	—	19	4	no	—
196	C₄×D₄	—	19	8	no	—
197	C₄×D₄	—	19	8	no	—
198	C₄×D₄	—	19	4	no	—
199	#117	—	19	4	no	—
200	#117	—	19	8	no	—
201	#117	—	19	4	no	—
202	#117	C₂×D₁₉	1	2	yes	—
203	C₂×C₄²	—	19	1	no	—
204	C₂×C₄²	—	19	2	no	—
205	C₂×C₄²	—	19	4	no	—
206	C₂×C₄²	—	19	2	no	—
207	C₂×C₄²	—	19	2	no	—
208	C₂×C₄²	—	19	2	no	—
209	C₂×C₄²	—	19	2	no	—
210	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
211	C₁₉	#3444	1	1	yes	characteristic, complemented, Sylow
212	C₂⁴	—	19	1	no	—
213	#41	—	38	16	no	—
214	#41	—	38	8	no	—
215	C₂×Q₈	—	19	2	no	—
216	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
217	C₂×D₄	—	19	4	no	—
218	C₂×D₄	—	19	8	no	—
219	C₂×D₄	—	19	2	no	—
220	C₂×D₄	—	19	4	no	—
221	C₂²×C₄	—	19	2	no	—
222	C₂²×C₄	—	19	2	no	—
223	C₂²×C₄	—	19	1	no	—
224	C₂²×C₄	—	19	2	no	—
225	C₂²×C₄	—	19	2	no	—
226	C₂²×C₄	—	19	2	no	—
227	C₂²×C₄	—	19	2	no	—
228	C₂²×C₄	—	19	8	no	—
229	C₂²×C₄	—	19	2	no	—
230	C₂²×C₄	—	19	4	no	—
231	C₂²×C₄	—	38	8	no	—
232	C₂²×C₄	—	38	4	no	—
233	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
234	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
235	C₄⋊C₄	—	19	8	no	—
236	C₄⋊C₄	—	19	4	no	—
237	C₄⋊C₄	—	19	8	no	—
238	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
239	C₄⋊C₄	C₂²×D₁₉	1	8	yes	—
240	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
241	C₂²⋊C₄	—	19	8	no	—
242	C₂²⋊C₄	—	19	8	no	—
243	C₂²⋊C₄	—	19	8	no	—
244	C₂²⋊C₄	—	19	8	no	—
245	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
246	C₄²	—	19	2	no	—
247	C₄²	—	19	2	no	—
248	C₄²	—	19	2	no	—
249	C₄²	—	19	2	no	—
250	C₄²	—	19	2	no	—
251	C₄²	—	19	8	no	—
252	C₄²	—	19	1	no	—
253	C₄²	—	19	1	no	—
254	C₄²	C₂²×D₁₉	1	1	yes	characteristic
255	C₄²	C₂²×D₁₉	1	1	yes	characteristic
256	C₄²	C₂²×D₁₉	1	2	yes	—
257	C₄²	C₂²×D₁₉	1	4	yes	—
258	C₂³	—	19	2	no	—
259	C₂³	—	19	4	no	—
260	C₂³	—	38	4	no	—
261	C₂³	—	38	2	no	—
262	C₂³	C₂³×D₁₉	1	1	yes	characteristic
263	Q₈	—	2	8	no	—
264	Q₈	—	38	4	no	—
265	D₄	—	38	16	no	—
266	D₄	—	38	8	no	—
267	D₄	—	38	4	no	—
268	D₄	—	38	8	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	19	2	no	—
271	C₂×C₄	—	19	8	no	—
272	C₂×C₄	—	19	2	no	—
273	C₂×C₄	—	19	2	no	—
274	C₂×C₄	—	19	4	no	—
275	C₂×C₄	—	38	4	no	—
276	C₂×C₄	—	38	16	no	—
277	C₂×C₄	—	38	4	no	—
278	C₂×C₄	—	38	4	no	—
279	C₂×C₄	—	38	2	no	—
280	C₂×C₄	—	38	4	no	—
281	C₂×C₄	—	38	4	no	—
282	C₂×C₄	—	38	8	no	—
283	C₂×C₄	—	38	4	no	—
284	C₂×C₄	#64545	1	4	yes	complemented
285	C₂×C₄	C₂³×D₁₉	1	2	yes	—
286	C₂×C₄	C₂³×D₁₉	1	8	yes	—
287	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
288	C₂×C₄	C₂³×D₁₉	1	2	yes	—
289	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
290	C₂²	—	2	2	no	—
291	C₂²	—	19	4	no	—
292	C₂²	—	38	8	no	—
293	C₂²	—	38	2	no	—
294	C₂²	—	38	2	no	—
295	C₂²	—	38	8	no	—
296	C₂²	—	38	4	no	—
297	C₂²	C₂×#64545	1	2	yes	—
298	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
299	C₄	—	2	2	no	—
300	C₄	—	2	8	no	—
301	C₄	—	19	4	no	—
302	C₄	—	38	2	no	—
303	C₄	—	38	2	no	—
304	C₄	—	38	4	no	—
305	C₄	C₂×#64545	1	2	yes	—
306	C₄	C₂×#64545	1	2	yes	—
307	C₄	#41×D₁₉	1	4	yes	—
308	C₂	—	2	2	no	—
309	C₂	—	38	4	no	—
310	C₂	—	76	4	no	—
311	C₂	C₂×#41×D₁₉	1	2	yes	—
312	C₂	C₂²×#64545	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₁₉×#533	C₂
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3444
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #11927099	C₂	semidirect
2. #11927095	C₂	semidirect
3. #11927094	C₂	semidirect
4. #11927081	C₂	semidirect
5. #11927080	C₂	semidirect
6. #11927079	C₂	semidirect
7. #11927057	C₂	semidirect
8. #11927056	C₂	semidirect
9. C₄×#64545	C₂	semidirect
10. #11927012	C₂	semidirect
11. C₂×C₄²×D₁₉	C₂	semidirect
12. C₁₉×#533	C₂	semidirect
17. C₁₉×C₄⋊Q₈	C₂²	semidirect
18. C₁₉×#125	C₂²	semidirect
20. C₄×Q₈×C₁₉	C₂²	semidirect
23. #10597393	C₂²	semidirect
25. Q₈×Dic₁₉	C₂²	semidirect
29. #10597344	C₂²	semidirect
35. #10597339	C₂²	semidirect
36. #10597339	C₂²	semidirect
38. #10597338	C₂²	semidirect
39. #10597336	C₂²	semidirect
40. #10597333	C₂²	semidirect
44. #10597321	C₂²	semidirect
45. #10597320	C₂²	semidirect
47. C₄×D₇₆	C₂²	semidirect
48. #10597318	C₂²	semidirect
53. C₄²×D₁₉	C₂²	semidirect
54. #10597315	C₂²	semidirect
108. C₂×C₄×C₁₉	#41	semidirect
131. C₄×D₁₉	#41	semidirect
153. #533	D₁₉	semidirect
174. C₄⋊Q₈	C₂×D₁₉	semidirect
178. #125	C₂×D₁₉	semidirect
192. C₄×Q₈	C₂×D₁₉	semidirect
211. C₁₉	#3444	semidirect
284. C₂×C₄	#64545	semidirect

Maximal subgroups

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

subgroup	index
#11927099	2
#11927095	2
#11927094	2
#11927081	2
#11927080	2
#11927079	2
#11927057	2
#11927056	2
C₄×#64545	2
#11927012	2
C₂×C₄²×D₁₉	2
C₁₉×#533	2
#3444	19