Subgroups — #14577333

Order 2432.

1052 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927227	C₂	1	8	yes	maximal, complemented
2	#11927218	C₂	1	8	yes	maximal, complemented
3	#11927170	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927141	C₂	1	4	yes	maximal, complemented
5	#11927106	C₂	1	1	yes	maximal, characteristic
6	#11927078	C₂	1	4	yes	maximal, complemented
7	C₂×#10597375	C₂	1	2	yes	maximal, complemented
8	#11927017	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
12	C₁₉×#117	C₂²	1	8	yes	complemented
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
14	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂²	1	2	yes	complemented
17	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	#10597376	C₂²	1	4	yes	—
19	#10597375	C₂²	1	8	yes	—
20	#10597375	C₂²	1	4	yes	complemented
21	#10597375	C₂²	1	4	yes	complemented
22	C₄×C₂²⋊D₁₉	C₂²	1	8	yes	complemented
23	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
24	#10597370	C₂²	1	4	yes	complemented
25	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	complemented
26	#10597344	C₂²	1	8	yes	complemented
27	#10597342	C₂²	1	8	yes	complemented
28	#10597340	C₂²	1	8	yes	complemented
29	#10597335	C₂²	1	8	yes	complemented
30	#10597332	C₂²	1	4	yes	—
31	#10597328	C₂²	1	4	yes	—
32	(C₂²⋊D₁₉)⋊C₄	C₂²	1	8	yes	—
33	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
34	#10597324	C₂²	1	8	yes	complemented
35	#10597323	C₂²	1	4	yes	complemented
36	#10597322	C₂²	1	8	yes	complemented
37	#10597321	C₂²	1	4	yes	complemented
38	C₄×D₇₆	C₂²	1	4	yes	complemented
39	#10597318	C₂²	1	8	yes	complemented
40	#10597316	C₂²	1	4	yes	complemented
41	C₄×Dic₃₈	C₂²	1	4	yes	complemented
42	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×D₁₉	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
48	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂×C₂²⋊D₁₉	—	2	8	no	—
51	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
52	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
53	C₂²×Dic₁₉	C₂³	1	2	yes	—
54	C₂²×Dic₁₉	C₂³	1	4	yes	—
55	C₂×D₇₆	C₂³	1	4	yes	—
56	C₂×C₄×D₁₉	C₂³	1	8	yes	—
57	C₂×Dic₃₈	C₂³	1	4	yes	—
58	C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₄²×C₁₉	C₂³	1	4	yes	—
62	C₄²×C₁₉	C₂³	1	4	yes	—
63	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
64	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
65	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
66	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
67	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
68	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
69	C₄⋊Dic₁₉	C₂³	1	4	yes	—
70	C₄⋊Dic₁₉	C₂³	1	4	yes	—
71	Dic₁₉⋊C₄	C₂³	1	8	yes	—
72	Dic₁₉⋊C₄	C₂³	1	8	yes	—
73	Dic₁₉⋊C₄	C₂³	1	8	yes	—
74	Dic₁₉⋊C₄	C₂³	1	8	yes	—
75	C₄×Dic₁₉	C₂³	1	8	yes	—
76	C₂³×C₁₉	—	4	2	no	—
77	C₂³×C₁₉	#41	1	4	yes	—
78	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
79	C₂³×C₁₉	C₂⁴	1	2	yes	—
80	C₂²×D₁₉	—	2	4	no	—
81	C₂²×D₁₉	—	4	4	no	—
82	C₂²×D₁₉	C₂⁴	1	4	yes	—
83	C₂×C₄×C₁₉	—	2	8	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
89	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
90	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
91	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
92	C₂²⋊D₁₉	—	2	8	no	—
93	C₂²⋊D₁₉	—	2	8	no	—
94	C₂×Dic₁₉	—	2	4	no	—
95	C₂×Dic₁₉	—	4	4	no	—
96	C₂×Dic₁₉	C₂⁴	1	4	yes	—
97	C₂×Dic₁₉	C₂⁴	1	8	yes	—
98	D₇₆	—	4	4	no	—
99	C₄×D₁₉	—	4	8	no	—
100	Dic₃₈	—	4	4	no	—
101	#3491	—	19	1	no	maximal, Sylow
102	C₂²×C₁₉	—	2	4	no	—
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	C₂×#41	1	4	yes	—
106	C₂²×C₁₉	C₂×#41	1	2	yes	—
107	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
108	C₂×D₁₉	—	2	4	no	—
109	C₂×D₁₉	—	2	8	no	—
110	C₂×D₁₉	—	8	4	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	2	4	no	—
114	C₄×C₁₉	—	2	4	no	—
115	Dic₁₉	—	2	4	no	—
116	Dic₁₉	—	2	8	no	—
117	#552	—	19	8	no	—
118	#551	—	19	8	no	—
119	#543	—	19	1	no	—
120	#539	—	19	4	no	—
121	#534	—	19	1	no	—
122	#529	—	19	4	no	—
123	C₂×#123	—	19	2	no	—
124	#518	—	19	2	no	—
125	C₂×#117	D₁₉	1	1	yes	characteristic, complemented
126	C₂×C₁₉	—	2	4	no	—
127	C₂×C₁₉	—	2	2	no	—
128	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
129	C₂×C₁₉	#585	1	2	yes	—
130	D₁₉	—	4	4	no	—
131	C₂²×D₄	—	19	2	no	—
132	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
133	#126	—	19	8	no	—
134	#126	—	19	8	no	—
135	#125	—	19	8	no	—
136	#125	—	19	4	no	—
137	#124	—	19	4	no	—
138	#123	—	19	4	no	—
139	#123	—	19	4	no	—
140	#123	—	19	8	no	—
141	#123	—	19	8	no	—
142	#123	—	19	4	no	—
143	C₂²⋊Q₈	—	19	4	no	—
144	C₂²⋊Q₈	—	19	8	no	—
145	C₂²⋊Q₈	—	19	8	no	—
146	#121	—	19	4	no	—
147	#120	—	19	4	no	—
148	C₄×Q₈	—	19	4	no	—
149	C₄×D₄	—	19	8	no	—
150	C₄×D₄	—	19	8	no	—
151	C₄×D₄	—	19	4	no	—
152	#117	—	19	4	no	—
153	#117	—	19	8	no	—
154	#117	C₂×D₁₉	1	8	yes	complemented
155	C₂×C₄⋊C₄	—	19	4	no	—
156	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	complemented
157	C₂×C₂²⋊C₄	—	19	2	no	—
158	C₂×C₂²⋊C₄	—	19	4	no	—
159	C₂×C₂²⋊C₄	—	19	4	no	—
160	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
161	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
162	C₂×C₄²	C₂×D₁₉	1	2	yes	complemented
163	C₁₉	#3491	1	1	yes	characteristic, complemented, Sylow
164	C₂⁴	—	19	2	no	—
165	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
166	C₂×Q₈	—	19	4	no	—
167	C₂×D₄	—	19	4	no	—
168	C₂×D₄	—	19	4	no	—
169	C₂×D₄	—	19	4	no	—
170	C₂×D₄	—	38	8	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	19	2	no	—
173	C₂²×C₄	—	19	4	no	—
174	C₂²×C₄	—	19	8	no	—
175	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
177	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
179	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
180	C₄⋊C₄	—	19	8	no	—
181	C₄⋊C₄	—	19	8	no	—
182	C₄⋊C₄	—	19	8	no	—
183	C₄⋊C₄	—	19	8	no	—
184	C₄⋊C₄	—	19	4	no	—
185	C₄⋊C₄	—	19	4	no	—
186	C₄⋊C₄	C₂²×D₁₉	1	8	yes	—
187	C₂²⋊C₄	—	19	4	no	—
188	C₂²⋊C₄	—	19	4	no	—
189	C₂²⋊C₄	—	19	8	no	—
190	C₂²⋊C₄	—	19	8	no	—
191	C₂²⋊C₄	—	19	8	no	—
192	C₂²⋊C₄	—	19	8	no	—
193	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
194	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
195	C₄²	—	19	8	no	—
196	C₄²	C₂²×D₁₉	1	4	yes	—
197	C₄²	C₂²×D₁₉	1	4	yes	—
198	C₂³	—	4	2	no	—
199	C₂³	—	19	4	no	—
200	C₂³	—	38	4	no	—
201	C₂³	—	76	4	no	—
202	C₂³	#64541	1	4	yes	—
203	C₂³	C₂³×D₁₉	1	1	yes	characteristic
204	C₂³	C₂³×D₁₉	1	2	yes	—
205	Q₈	—	76	4	no	—
206	D₄	—	38	8	no	—
207	D₄	—	38	8	no	—
208	D₄	—	76	4	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	19	4	no	—
215	C₂×C₄	—	19	8	no	—
216	C₂×C₄	—	38	4	no	—
217	C₂×C₄	—	76	8	no	—
218	C₂×C₄	—	76	4	no	—
219	C₂×C₄	C₂³×D₁₉	1	4	yes	—
220	C₂×C₄	C₂³×D₁₉	1	2	yes	—
221	C₂×C₄	C₂³×D₁₉	1	4	yes	—
222	C₂×C₄	C₂³×D₁₉	1	2	yes	—
223	C₂²	—	2	2	no	—
224	C₂²	—	2	4	no	—
225	C₂²	—	4	4	no	—
226	C₂²	—	38	4	no	—
227	C₂²	—	38	8	no	—
228	C₂²	—	152	4	no	—
229	C₂²	C₂×#64541	1	4	yes	—
230	C₂²	C₂×#64541	1	2	yes	—
231	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	4	no	—
235	C₄	—	2	4	no	—
236	C₄	—	38	4	no	—
237	C₄	—	38	8	no	—
238	C₂	—	2	4	no	—
239	C₂	—	2	2	no	—
240	C₂	—	76	4	no	—
241	C₂	C₂²×#64541	1	1	yes	characteristic
242	C₂	#11927380	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₁₉×#117	C₂
prime radical	#11927106	C₂
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#3491
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #11927227	C₂	semidirect
2. #11927218	C₂	semidirect
3. #11927170	C₂	semidirect
4. #11927141	C₂	semidirect
6. #11927078	C₂	semidirect
7. C₂×#10597375	C₂	semidirect
8. #11927017	C₂	semidirect
9. C₂×C₁₉×#117	C₂	semidirect
12. C₁₉×#117	C₂²	semidirect
13. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
16. C₂×C₄²×C₁₉	C₂²	semidirect
20. #10597375	C₂²	semidirect
21. #10597375	C₂²	semidirect
22. C₄×C₂²⋊D₁₉	C₂²	semidirect
23. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
24. #10597370	C₂²	semidirect
25. C₂×Dic₁₉⋊C₄	C₂²	semidirect
26. #10597344	C₂²	semidirect
27. #10597342	C₂²	semidirect
28. #10597340	C₂²	semidirect
29. #10597335	C₂²	semidirect
33. C₂²⋊C₄×D₁₉	C₂²	semidirect
34. #10597324	C₂²	semidirect
35. #10597323	C₂²	semidirect
36. #10597322	C₂²	semidirect
37. #10597321	C₂²	semidirect
38. C₄×D₇₆	C₂²	semidirect
39. #10597318	C₂²	semidirect
40. #10597316	C₂²	semidirect
41. C₄×Dic₃₈	C₂²	semidirect
125. C₂×#117	D₁₉	semidirect
154. #117	C₂×D₁₉	semidirect
156. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
162. C₂×C₄²	C₂×D₁₉	semidirect
163. C₁₉	#3491	semidirect

Maximal subgroups

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

subgroup	index
#11927227	2
#11927218	2
#11927170	2
#11927141	2
#11927106	2
#11927078	2
C₂×#10597375	2
#11927017	2
C₂×C₁₉×#117	2
#3491	19