Subgroups — #14577502

Order 2432.

1012 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927279	C₂	1	2	yes	maximal, complemented
2	#11927273	C₂	1	2	yes	maximal, complemented
3	#11927268	C₂	1	2	yes	maximal, complemented
4	#11927267	C₂	1	4	yes	maximal, complemented
5	#11927255	C₂	1	2	yes	maximal, complemented
6	#11927232	C₂	1	4	yes	maximal, complemented
7	#11927143	C₂	1	4	yes	maximal, complemented
8	#11927120	C₂	1	2	yes	maximal, complemented
9	#11927094	C₂	1	1	yes	maximal, characteristic
10	#11927080	C₂	1	4	yes	maximal, complemented
11	#11927024	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#64541	C₂²	1	2	yes	—
15	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
16	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#125	C₂²	1	2	yes	—
19	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#117	C₂²	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	#10597393	C₂²	1	4	yes	—
26	#10597392	C₂²	1	8	yes	—
27	Q₈×Dic₁₉	C₂²	1	4	yes	—
28	#10597376	C₂²	1	2	yes	—
29	#10597376	C₂²	1	2	yes	—
30	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
32	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
33	#10597344	C₂²	1	8	yes	—
34	#10597344	C₂²	1	8	yes	—
35	#10597343	C₂²	1	4	yes	—
36	#10597343	C₂²	1	4	yes	—
37	#10597340	C₂²	1	8	yes	—
38	#10597339	C₂²	1	4	yes	—
39	#10597338	C₂²	1	8	yes	—
40	#10597338	C₂²	1	4	yes	—
41	C₄⋊C₄×D₁₉	C₂²	1	4	yes	—
42	#10597336	C₂²	1	4	yes	—
43	#10597336	C₂²	1	8	yes	—
44	#10597332	C₂²	1	8	yes	—
45	(C₂²⋊D₁₉)⋊C₄	C₂²	1	8	yes	—
46	#10597321	C₂²	1	2	yes	—
47	#10597321	C₂²	1	4	yes	—
48	#10597320	C₂²	1	1	yes	characteristic
49	C₄×D₇₆	C₂²	1	2	yes	—
50	C₄×D₇₆	C₂²	1	2	yes	—
51	C₄×D₇₆	C₂²	1	4	yes	—
52	#10597315	C₂²	1	1	yes	characteristic
53	#10597315	C₂²	1	4	yes	—
54	C₄×Dic₃₈	C₂²	1	2	yes	—
55	C₄×Dic₃₈	C₂²	1	2	yes	—
56	C₄×Dic₃₈	C₂²	1	2	yes	—
57	C₄×Dic₃₈	C₂²	1	2	yes	—
58	C₄×Dic₃₈	C₂²	1	4	yes	—
59	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
65	C₂²×Dic₁₉	C₂³	1	2	yes	—
66	C₂²×Dic₁₉	C₂³	1	2	yes	—
67	#64541	—	2	8	no	—
68	C₂×D₇₆	C₂³	1	2	yes	—
69	C₂×D₇₆	C₂³	1	2	yes	—
70	C₂×D₇₆	C₂³	1	2	yes	—
71	C₂×C₄×D₁₉	C₂³	1	4	yes	—
72	C₂×C₄×D₁₉	C₂³	1	8	yes	—
73	C₂×Dic₃₈	—	2	4	no	—
74	C₂×Dic₃₈	C₂³	1	2	yes	—
75	C₂×Dic₃₈	C₂³	1	2	yes	—
76	C₂×Dic₃₈	C₂³	1	2	yes	—
77	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₄²×C₁₉	C₂³	1	4	yes	—
89	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
90	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
91	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
92	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
93	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
94	C₄⋊Dic₁₉	C₂³	1	2	yes	—
95	C₄⋊Dic₁₉	C₂³	1	2	yes	—
96	C₄⋊Dic₁₉	C₂³	1	8	yes	—
97	C₄⋊Dic₁₉	C₂³	1	8	yes	—
98	C₄⋊Dic₁₉	C₂³	1	2	yes	—
99	C₄⋊Dic₁₉	C₂³	1	2	yes	—
100	Dic₁₉⋊C₄	C₂³	1	4	yes	—
101	Dic₁₉⋊C₄	C₂³	1	8	yes	—
102	Dic₁₉⋊C₄	C₂³	1	4	yes	—
103	C₄×Dic₁₉	C₂³	1	4	yes	—
104	C₄×Dic₁₉	C₂³	1	8	yes	—
105	C₄×Dic₁₉	C₂³	1	4	yes	—
106	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂²×D₁₉	C₂⁴	1	4	yes	—
108	Q₈×C₁₉	—	2	4	no	—
109	Q₈×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	#41	1	4	yes	—
113	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
115	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
118	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂²⋊D₁₉	—	2	8	no	—
122	C₂×Dic₁₉	—	2	4	no	—
123	C₂×Dic₁₉	—	4	2	no	—
124	C₂×Dic₁₉	C₂⁴	1	4	yes	—
125	C₂×Dic₁₉	C₂⁴	1	4	yes	—
126	C₂×Dic₁₉	C₂⁴	1	4	yes	—
127	D₇₆	—	2	4	no	—
128	D₇₆	—	2	4	no	—
129	D₇₆	—	4	2	no	—
130	C₄×D₁₉	—	2	8	no	—
131	C₄×D₁₉	—	4	8	no	—
132	Dic₃₈	—	2	4	no	—
133	Dic₃₈	—	2	4	no	—
134	Dic₃₈	—	2	4	no	—
135	#3507	—	19	1	no	maximal, Sylow
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	C₂×#41	1	2	yes	—
139	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
140	C₂×D₁₉	—	2	4	no	—
141	C₂×D₁₉	—	2	4	no	—
142	C₂×D₁₉	—	2	4	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	4	no	—
145	C₄×C₁₉	—	2	4	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	C₂×#41	1	2	yes	—
149	C₄×C₁₉	C₂×#41	1	2	yes	—
150	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
151	Dic₁₉	—	2	4	no	—
152	Dic₁₉	—	2	4	no	—
153	Dic₁₉	—	2	4	no	—
154	#559	—	19	2	no	—
155	#557	—	19	2	no	—
156	#556	—	19	2	no	—
157	#556	—	19	4	no	—
158	#554	—	19	2	no	—
159	#552	—	19	4	no	—
160	#539	—	19	4	no	—
161	#536	—	19	2	no	—
162	#533	D₁₉	1	1	yes	characteristic, complemented
163	#532	—	19	1	no	—
164	#529	—	19	4	no	—
165	#520	—	19	2	no	—
166	C₂×C₄×Q₈	—	19	1	no	—
167	C₂×C₁₉	—	2	2	no	—
168	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
169	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
170	C₂×C₁₉	#585	1	1	yes	characteristic
171	D₁₉	—	4	4	no	—
172	C₂×#41	—	19	2	no	—
173	C₂²×Q₈	—	19	1	no	—
174	C₄⋊Q₈	—	19	1	no	—
175	C₄⋊Q₈	—	19	4	no	—
176	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
177	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
178	#127	—	19	1	no	—
179	#126	—	19	8	no	—
180	#126	—	19	8	no	—
181	#125	—	19	4	no	—
182	#125	—	19	8	no	—
183	#125	C₂×D₁₉	1	2	yes	—
184	#124	—	19	4	no	—
185	#124	—	19	2	no	—
186	#124	—	19	4	no	—
187	#123	—	19	8	no	—
188	#123	—	19	8	no	—
189	C₂²⋊Q₈	—	19	8	no	—
190	C₂²⋊Q₈	—	19	4	no	—
191	C₂²⋊Q₈	—	19	4	no	—
192	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
193	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
194	#121	—	19	2	no	—
195	#121	—	19	2	no	—
196	C₄×Q₈	—	19	4	no	—
197	C₄×Q₈	—	19	2	no	—
198	C₄×Q₈	—	19	2	no	—
199	C₄×Q₈	—	19	2	no	—
200	C₄×Q₈	—	19	2	no	—
201	C₄×Q₈	—	19	4	no	—
202	C₄×Q₈	C₂×D₁₉	1	2	yes	—
203	C₄×Q₈	C₂×D₁₉	1	2	yes	—
204	C₄×D₄	—	19	4	no	—
205	C₄×D₄	—	19	8	no	—
206	C₄×D₄	—	19	4	no	—
207	C₄×D₄	—	19	2	no	—
208	C₄×D₄	—	19	2	no	—
209	#117	—	19	4	no	—
210	#117	—	19	8	no	—
211	#117	C₂×D₁₉	1	2	yes	—
212	C₂×C₄⋊C₄	—	19	1	no	—
213	C₂×C₄⋊C₄	—	19	2	no	—
214	C₂×C₄⋊C₄	—	19	4	no	—
215	C₂×C₄²	—	19	2	no	—
216	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
217	C₁₉	#3507	1	1	yes	characteristic, complemented, Sylow
218	#41	—	38	8	no	—
219	C₂×Q₈	—	19	2	no	—
220	C₂×Q₈	—	19	2	no	—
221	C₂×Q₈	—	19	2	no	—
222	C₂×Q₈	—	38	4	no	—
223	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
224	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
225	C₂×D₄	—	19	4	no	—
226	C₂×D₄	—	19	2	no	—
227	C₂×D₄	—	19	2	no	—
228	C₂×D₄	—	19	2	no	—
229	C₂²×C₄	—	19	2	no	—
230	C₂²×C₄	—	19	2	no	—
231	C₂²×C₄	—	19	4	no	—
232	C₂²×C₄	—	19	8	no	—
233	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
234	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
235	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
236	C₄⋊C₄	—	19	8	no	—
237	C₄⋊C₄	—	19	4	no	—
238	C₄⋊C₄	—	19	4	no	—
239	C₄⋊C₄	—	19	2	no	—
240	C₄⋊C₄	—	19	2	no	—
241	C₄⋊C₄	—	19	8	no	—
242	C₄⋊C₄	—	19	2	no	—
243	C₄⋊C₄	—	19	2	no	—
244	C₄⋊C₄	—	19	8	no	—
245	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
246	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
247	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
248	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
249	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
250	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
251	C₂²⋊C₄	—	19	4	no	—
252	C₂²⋊C₄	—	19	8	no	—
253	C₂²⋊C₄	—	19	8	no	—
254	C₂²⋊C₄	—	19	4	no	—
255	C₂²⋊C₄	—	19	8	no	—
256	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
257	C₄²	—	19	4	no	—
258	C₄²	—	19	4	no	—
259	C₄²	—	19	8	no	—
260	C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	C₄²	C₂²×D₁₉	1	1	yes	characteristic
262	C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	C₄²	C₂²×D₁₉	1	1	yes	characteristic
264	C₄²	C₂²×D₁₉	1	4	yes	—
265	C₂³	—	19	4	no	—
266	C₂³	C₂³×D₁₉	1	1	yes	characteristic
267	Q₈	—	2	4	no	—
268	Q₈	—	4	2	no	—
269	Q₈	—	38	4	no	—
270	Q₈	—	38	4	no	—
271	Q₈	—	38	4	no	—
272	D₄	—	38	8	no	—
273	D₄	—	38	4	no	—
274	D₄	—	38	4	no	—
275	D₄	—	76	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	1	no	—
278	C₂×C₄	—	19	4	no	—
279	C₂×C₄	—	19	4	no	—
280	C₂×C₄	—	19	4	no	—
281	C₂×C₄	—	38	4	no	—
282	C₂×C₄	—	38	8	no	—
283	C₂×C₄	—	76	8	no	—
284	C₂×C₄	—	76	2	no	—
285	C₂×C₄	#64545	1	4	yes	—
286	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
287	C₂×C₄	C₂³×D₁₉	1	4	yes	—
288	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
289	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
290	C₂×C₄	C₂³×D₁₉	1	4	yes	—
291	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
292	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
293	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
294	C₂²	—	2	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	—	38	4	no	—
297	C₂²	—	38	4	no	—
298	C₂²	—	38	4	no	—
299	C₂²	C₂×#64545	1	2	yes	—
300	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
301	C₄	—	2	1	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	2	4	no	—
306	C₄	—	38	4	no	—
307	C₄	—	38	4	no	—
308	C₄	—	38	4	no	—
309	C₄	C₂×#64545	1	2	yes	—
310	C₄	C₂×#64545	1	2	yes	—
311	C₄	#10597436	1	2	yes	—
312	C₂	—	2	2	no	—
313	C₂	—	76	4	no	—
314	C₂	C₂²×#64545	1	1	yes	characteristic
315	C₂	C₂×#10597436	1	1	yes	characteristic
316	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#533	C₂
prime radical	#11927094	C₂
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3507
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #11927279	C₂	semidirect
2. #11927273	C₂	semidirect
3. #11927268	C₂	semidirect
4. #11927267	C₂	semidirect
5. #11927255	C₂	semidirect
6. #11927232	C₂	semidirect
7. #11927143	C₂	semidirect
8. #11927120	C₂	semidirect
10. #11927080	C₂	semidirect
11. #11927024	C₂	semidirect
12. C₂×C₄×Dic₃₈	C₂	semidirect
13. C₁₉×#533	C₂	semidirect
162. #533	D₁₉	semidirect
217. C₁₉	#3507	semidirect

Maximal subgroups

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

subgroup	index
#11927279	2
#11927273	2
#11927268	2
#11927267	2
#11927255	2
#11927232	2
#11927143	2
#11927120	2
#11927094	2
#11927080	2
#11927024	2
C₂×C₄×Dic₃₈	2
C₁₉×#533	2
#3507	19