Subgroups — #14573937

Order 2432.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927157	C₂	1	1	yes	maximal, characteristic
2	#11927020	C₂	1	1	yes	maximal, characteristic
3	#11926888	C₂	1	1	yes	maximal, characteristic
4	#11926887	C₂	1	1	yes	maximal, characteristic
5	#11926848	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926755	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926754	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926701	C₂	1	1	yes	maximal, characteristic
9	#11926701	C₂	1	1	yes	maximal, characteristic
10	#11926650	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926648	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926638	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926636	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926604	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×#64528	C₂²	1	1	yes	characteristic
21	C₂×#64528	C₂²	1	1	yes	characteristic
22	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
23	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
24	#10597344	—	2	1	no	—
25	#10597344	—	2	1	no	—
26	#10597343	C₂²	1	1	yes	characteristic
27	#10597343	C₂²	1	1	yes	characteristic
28	#10597338	—	2	1	no	—
29	#10597338	C₂²	1	1	yes	characteristic
30	#10597336	—	2	1	no	—
31	#10597336	—	2	1	no	—
32	#10597333	—	2	1	no	—
33	#10597333	C₂²	1	1	yes	characteristic
34	#10597333	C₂²	1	1	yes	characteristic
35	#10597333	C₂²	1	1	yes	characteristic
36	#10597318	—	2	1	no	—
37	#10597318	C₂²	1	1	yes	characteristic
38	#10597315	C₂²	1	1	yes	characteristic
39	C₄×Dic₃₈	—	2	1	no	—
40	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
41	C₁₉×#107	C₂²	1	1	yes	characteristic
42	C₁₉×#106	C₂²	1	1	yes	characteristic
43	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₁₉×#103	C₂²	1	1	yes	characteristic
46	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
48	#10597273	C₂²	1	1	yes	characteristic
49	#10597273	C₂²	1	1	yes	characteristic
50	#10597272	C₂²	1	1	yes	characteristic
51	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
52	#10597267	C₂²	1	1	yes	characteristic
53	#10597267	C₂²	1	1	yes	characteristic
54	#10597267	C₂²	1	1	yes	characteristic
55	#10597267	C₂²	1	1	yes	characteristic
56	#10597265	C₂²	1	1	yes	characteristic
57	#10597264	C₂²	1	1	yes	characteristic
58	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	Q₈×D₁₉	—	2	2	no	—
61	Q₈×D₁₉	—	2	2	no	—
62	C₂×C₄×D₁₉	—	2	1	no	—
63	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
64	C₂×Dic₃₈	—	2	1	no	—
65	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
66	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
67	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₄²×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	#64528	—	2	2	no	—
79	#64528	—	2	2	no	—
80	(C₂×D₁₉)⋊C₄	—	2	1	no	—
81	(C₂×D₁₉)⋊C₄	—	2	1	no	—
82	(C₂×D₁₉)⋊C₄	—	2	1	no	—
83	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
84	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
85	C₄⋊Dic₁₉	—	2	1	no	—
86	C₄⋊Dic₁₉	—	2	1	no	—
87	C₄⋊Dic₁₉	—	2	1	no	—
88	C₄⋊Dic₁₉	—	2	1	no	—
89	C₄⋊Dic₁₉	—	2	1	no	—
90	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
91	Dic₁₉⋊C₄	—	2	1	no	—
92	Dic₁₉⋊C₄	—	2	1	no	—
93	Dic₁₉⋊C₄	—	2	1	no	—
94	Dic₁₉⋊C₄	—	2	1	no	—
95	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
96	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
97	C₄×Dic₁₉	—	2	1	no	—
98	C₄×Dic₁₉	—	2	1	no	—
99	C₄×Dic₁₉	—	2	1	no	—
100	C₄×Dic₁₉	—	2	1	no	—
101	C₄×Dic₁₉	—	2	1	no	—
102	C₄×Dic₁₉	—	2	1	no	—
103	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	Dic₇₆	—	2	2	no	—
107	Dic₇₆	—	2	2	no	—
108	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
109	Q₈×C₁₉	—	2	1	no	—
110	Q₈×C₁₉	#41	1	2	yes	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	1	no	—
120	C₂×Dic₁₉	—	2	1	no	—
121	C₂×Dic₁₉	—	2	1	no	—
122	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄×D₁₉	—	2	4	no	—
126	C₄×D₁₉	—	2	1	no	—
127	C₄×D₁₉	—	2	1	no	—
128	Dic₃₈	—	2	4	no	—
129	Dic₃₈	—	2	1	no	—
130	Dic₃₈	—	2	1	no	—
131	Dic₃₈	—	2	1	no	—
132	Dic₃₈	—	2	1	no	—
133	Dic₃₈	—	2	1	no	—
134	Dic₃₈	#41	1	2	yes	—
135	C₈×C₁₉	—	2	1	no	—
136	C₈×C₁₉	—	2	1	no	—
137	C₁₉⋊C₈	—	2	1	no	—
138	C₁₉⋊C₈	—	2	1	no	—
139	#3127	—	19	1	no	maximal, Sylow
140	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	C₂×D₁₉	—	2	1	no	—
142	C₂×D₁₉	—	2	1	no	—
143	C₂×D₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	4	1	no	—
148	C₄×C₁₉	—	4	1	no	—
149	C₄×C₁₉	—	4	1	no	—
150	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
151	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
152	Dic₁₉	—	2	1	no	—
153	Dic₁₉	—	2	2	no	—
154	Dic₁₉	—	2	1	no	—
155	Dic₁₉	—	2	1	no	—
156	Dic₁₉	—	4	1	no	—
157	Dic₁₉	—	4	1	no	—
158	Dic₁₉	—	4	1	no	—
159	#541	—	19	1	no	—
160	#519	—	19	1	no	—
161	#485	—	19	1	no	—
162	#485	—	19	1	no	—
163	#479	—	19	1	no	—
164	#479	D₁₉	1	1	yes	characteristic, complemented
165	#462	—	19	1	no	—
166	#462	—	19	1	no	—
167	#451	—	19	1	no	—
168	#451	—	19	1	no	—
169	#441	—	19	1	no	—
170	#441	—	19	1	no	—
171	C₄×Q₁₆	—	19	1	no	—
172	C₄×Q₁₆	—	19	1	no	—
173	#433	—	19	1	no	—
174	C₂×C₁₉	#525	1	1	yes	characteristic
175	C₂×C₁₉	#578	1	1	yes	characteristic
176	C₂×C₁₉	#578	1	1	yes	characteristic
177	D₁₉	—	4	1	no	—
178	C₂²×Q₈	—	19	1	no	—
179	C₂×Q₁₆	—	19	1	no	—
180	C₂×Q₁₆	—	19	1	no	—
181	C₂×Q₁₆	—	19	1	no	—
182	C₂×Q₁₆	—	19	1	no	—
183	C₄⋊Q₈	—	19	1	no	—
184	#126	—	38	1	no	—
185	#126	—	38	1	no	—
186	#125	—	38	1	no	—
187	#125	—	38	1	no	—
188	#125	C₂×D₁₉	1	1	yes	characteristic
189	C₂²⋊Q₈	—	19	1	no	—
190	C₂²⋊Q₈	—	19	1	no	—
191	C₄×Q₈	—	19	1	no	—
192	C₄×Q₈	—	19	1	no	—
193	C₄×Q₈	—	19	1	no	—
194	C₄×Q₈	—	19	1	no	—
195	C₄×Q₈	—	19	1	no	—
196	C₄×Q₈	—	38	1	no	—
197	C₄×Q₈	—	38	1	no	—
198	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
199	#117	—	19	1	no	—
200	#117	—	19	1	no	—
201	#117	—	38	1	no	—
202	#117	—	38	1	no	—
203	#107	—	19	1	no	—
204	#107	C₂×D₁₉	1	1	yes	characteristic
205	#106	—	19	1	no	—
206	#106	C₂×D₁₉	1	1	yes	characteristic
207	C₄⋊C₈	—	19	1	no	—
208	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
209	#103	—	19	1	no	—
210	#103	—	19	1	no	—
211	#103	—	19	1	no	—
212	#103	—	19	1	no	—
213	#103	—	19	1	no	—
214	#103	—	19	1	no	—
215	#103	C₂×D₁₉	1	1	yes	characteristic
216	#103	C₂×D₁₉	1	1	yes	characteristic
217	C₂²⋊C₈	—	19	1	no	—
218	C₂²⋊C₈	—	19	1	no	—
219	#97	—	19	1	no	—
220	C₄×C₈	—	19	1	no	—
221	C₁₉	#3127	1	1	yes	characteristic, complemented, Sylow
222	C₂×Q₈	—	19	1	no	—
223	C₂×Q₈	—	19	1	no	—
224	C₂×Q₈	—	19	1	no	—
225	C₂×Q₈	—	38	1	no	—
226	C₂×Q₈	—	38	2	no	—
227	C₂×Q₈	—	38	2	no	—
228	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
229	C₂²×C₄	—	19	1	no	—
230	C₂²×C₄	—	38	1	no	—
231	Q₁₆	—	38	2	no	—
232	Q₁₆	—	38	2	no	—
233	Q₁₆	—	38	2	no	—
234	Q₁₆	—	38	2	no	—
235	C₂×C₈	—	19	1	no	—
236	C₂×C₈	—	19	1	no	—
237	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
238	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	19	1	no	—
243	C₄⋊C₄	—	19	1	no	—
244	C₄⋊C₄	—	19	1	no	—
245	C₄⋊C₄	—	38	1	no	—
246	C₄⋊C₄	—	38	1	no	—
247	C₄⋊C₄	—	38	1	no	—
248	C₄⋊C₄	—	38	1	no	—
249	C₄⋊C₄	—	38	1	no	—
250	C₄⋊C₄	—	38	1	no	—
251	C₄⋊C₄	—	38	1	no	—
252	C₄⋊C₄	—	38	1	no	—
253	C₄⋊C₄	—	38	1	no	—
254	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
255	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
256	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
257	C₂²⋊C₄	—	19	1	no	—
258	C₂²⋊C₄	—	19	1	no	—
259	C₂²⋊C₄	—	38	1	no	—
260	C₂²⋊C₄	—	38	1	no	—
261	C₂²⋊C₄	—	38	1	no	—
262	C₄²	—	2	1	no	—
263	C₄²	—	19	1	no	—
264	C₄²	—	38	1	no	—
265	C₄²	—	38	1	no	—
266	C₄²	—	38	1	no	—
267	C₄²	—	38	1	no	—
268	C₄²	—	38	1	no	—
269	C₄²	—	38	1	no	—
270	C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	C₂³	—	19	1	no	—
272	Q₈	—	2	1	no	—
273	Q₈	—	19	2	no	—
274	Q₈	—	38	4	no	—
275	Q₈	—	38	1	no	—
276	Q₈	—	38	1	no	—
277	Q₈	—	38	1	no	—
278	Q₈	—	38	1	no	—
279	Q₈	—	38	1	no	—
280	Q₈	#64545	1	2	yes	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	19	1	no	—
286	C₂×C₄	—	19	1	no	—
287	C₂×C₄	—	19	1	no	—
288	C₂×C₄	—	38	4	no	—
289	C₂×C₄	—	38	1	no	—
290	C₂×C₄	—	38	1	no	—
291	C₂×C₄	—	38	1	no	—
292	C₂×C₄	—	38	1	no	—
293	C₂×C₄	—	38	1	no	—
294	C₂×C₄	—	38	1	no	—
295	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
296	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
297	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
298	C₈	—	2	1	no	—
299	C₈	—	2	1	no	—
300	C₈	—	38	1	no	—
301	C₈	—	38	1	no	—
302	C₂²	—	38	1	no	—
303	C₂²	—	38	1	no	—
304	C₂²	—	38	1	no	—
305	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
306	C₄	—	2	2	no	—
307	C₄	—	2	1	no	—
308	C₄	—	2	1	no	—
309	C₄	—	4	1	no	—
310	C₄	—	4	1	no	—
311	C₄	—	4	1	no	—
312	C₄	—	38	1	no	—
313	C₄	—	38	2	no	—
314	C₄	—	38	1	no	—
315	C₄	—	38	1	no	—
316	C₄	—	76	1	no	—
317	C₄	—	76	1	no	—
318	C₄	—	76	1	no	—
319	C₄	C₂×#64545	1	1	yes	characteristic
320	C₄	#41×D₁₉	1	1	yes	characteristic
321	C₂	—	76	1	no	—
322	C₂	#11927057	1	1	yes	characteristic
323	C₂	#11927358	1	1	yes	characteristic
324	C₂	#11927360	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#479	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#479	D₁₉
hypocenter	C₁₉	#3127
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #479

Complements

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

N	H ≅ G/N	type
5. #11926848	C₂	semidirect
6. #11926755	C₂	semidirect
7. #11926754	C₂	semidirect
10. #11926650	C₂	semidirect
11. #11926648	C₂	semidirect
12. #11926638	C₂	semidirect
13. #11926636	C₂	semidirect
15. C₁₉×#479	C₂	semidirect
164. #479	D₁₉	semidirect
221. C₁₉	#3127	semidirect

Maximal subgroups

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

subgroup	index
#11927157	2
#11927020	2
#11926888	2
#11926887	2
#11926848	2
#11926755	2
#11926754	2
#11926701	2
#11926650	2
#11926648	2
#11926638	2
#11926636	2
#11926604	2
C₁₉×#479	2
#3127	19