Subgroups — #14577428

Order 2432.

1540 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927206	C₂	1	4	yes	maximal, complemented
4	#11927189	C₂	1	12	yes	maximal, complemented
5	#11927120	C₂	1	3	yes	maximal, complemented
6	#11927113	C₂	1	3	yes	maximal, complemented
7	#11927094	C₂	1	3	yes	maximal, complemented
8	C₂×#10597321	C₂	1	3	yes	maximal, complemented
9	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
11	#10597436	—	2	8	no	—
12	#10597435	—	2	8	no	—
13	C₂×#64545	C₂²	1	2	yes	—
14	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
15	C₂×#64543	C₂²	1	6	yes	complemented
16	C₂×D₄×D₁₉	C₂²	1	6	yes	—
17	C₂×#64541	C₂²	1	3	yes	—
18	C₂×#64541	C₂²	1	3	yes	complemented
19	C₂²×D₇₆	C₂²	1	3	yes	—
20	C₂²×Dic₃₈	C₂²	1	3	yes	complemented
21	C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
22	C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
23	C₁₉×#117	C₂²	1	3	yes	complemented
24	C₂×C₄²×C₁₉	C₂²	1	3	yes	complemented
25	#10597376	C₂²	1	12	yes	complemented
26	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	12	yes	complemented
27	#10597343	C₂²	1	12	yes	complemented
28	#10597341	C₂²	1	12	yes	complemented
29	#10597332	C₂²	1	12	yes	complemented
30	#10597328	C₂²	1	12	yes	complemented
31	#10597321	C₂²	1	3	yes	complemented
32	#10597321	C₂²	1	6	yes	complemented
33	#10597321	C₂²	1	12	yes	complemented
34	#10597321	C₂²	1	1	yes	characteristic, complemented
35	#10597320	C₂²	1	3	yes	complemented
36	C₄×D₇₆	C₂²	1	12	yes	complemented
37	#10597315	C₂²	1	3	yes	complemented
38	C₂³×D₁₉	C₂³	1	6	yes	—
39	#41×C₁₉	D₄	1	8	yes	complemented
40	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×D₄×C₁₉	C₂³	1	3	yes	—
42	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
43	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
44	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
45	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
46	C₂²×Dic₁₉	C₂³	1	6	yes	—
47	#64545	—	2	8	no	—
48	Q₈×D₁₉	—	2	8	no	—
49	#64543	—	2	24	no	—
50	D₄×D₁₉	—	2	24	no	—
51	#64541	—	2	12	no	—
52	#64541	—	2	12	no	—
53	C₂×D₇₆	—	2	12	no	—
54	C₂×D₇₆	C₂³	1	3	yes	—
55	C₂×D₇₆	C₂³	1	6	yes	—
56	C₂×D₇₆	C₂³	1	1	yes	characteristic
57	C₂×D₇₆	C₂³	1	12	yes	—
58	C₂×C₄×D₁₉	C₂³	1	6	yes	—
59	C₂×C₄×D₁₉	C₂³	1	6	yes	—
60	C₂×Dic₃₈	—	2	12	no	—
61	C₂×Dic₃₈	C₂³	1	3	yes	—
62	C₂×Dic₃₈	C₂³	1	6	yes	—
63	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
65	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
66	C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₄²×C₁₉	C₂³	1	3	yes	—
68	C₄²×C₁₉	C₂³	1	6	yes	—
69	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
70	(C₂×D₁₉)⋊C₄	C₂³	1	12	yes	—
71	(C₂×D₁₉)⋊C₄	C₂³	1	24	yes	—
72	C₄⋊Dic₁₉	C₂³	1	12	yes	—
73	C₂³×C₁₉	C₂⁴	1	3	yes	—
74	C₂²×D₁₉	—	2	12	no	—
75	C₂²×D₁₉	—	4	12	no	—
76	C₂²×D₁₉	C₂⁴	1	6	yes	—
77	C₂²×D₁₉	C₂⁴	1	2	yes	—
78	Q₈×C₁₉	C₂×D₄	1	4	yes	—
79	D₄×C₁₉	C₂×D₄	1	12	yes	—
80	C₂×C₄×C₁₉	—	4	6	no	—
81	C₂×C₄×C₁₉	C₂×D₄	1	12	yes	—
82	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
83	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
84	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
86	C₂²⋊D₁₉	—	2	12	no	—
87	C₂²⋊D₁₉	—	2	12	no	—
88	C₂×Dic₁₉	—	2	12	no	—
89	C₂×Dic₁₉	C₂⁴	1	2	yes	—
90	C₂×Dic₁₉	C₂⁴	1	6	yes	—
91	D₇₆	—	2	6	no	—
92	D₇₆	—	2	12	no	—
93	D₇₆	—	2	2	no	—
94	D₇₆	—	4	12	no	—
95	C₄×D₁₉	—	2	12	no	—
96	C₄×D₁₉	—	2	12	no	—
97	Dic₃₈	—	2	6	no	—
98	Dic₃₈	—	2	12	no	—
99	Dic₃₈	—	2	2	no	—
100	#3500	—	19	1	no	maximal, Sylow
101	C₂²×C₁₉	—	2	6	no	—
102	C₂²×C₁₉	C₂²×D₄	1	6	yes	—
103	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
104	C₂×D₁₉	—	2	2	no	—
105	C₂×D₁₉	—	2	6	no	—
106	C₂×D₁₉	—	2	4	no	—
107	C₂×D₁₉	—	2	12	no	—
108	C₂×D₁₉	—	8	12	no	—
109	C₄×C₁₉	—	2	6	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	C₂²×D₄	1	2	yes	—
112	C₄×C₁₉	C₂²×D₄	1	6	yes	—
113	Dic₁₉	—	2	6	no	—
114	Dic₁₉	—	2	2	no	—
115	C₂×2₋¹⁺⁴	—	19	1	no	—
116	C₂×H(5,𝔽₂)	—	19	1	no	—
117	#548	—	19	4	no	—
118	#546	—	19	12	no	—
119	#536	—	19	3	no	—
120	#535	—	19	3	no	—
121	#532	—	19	3	no	—
122	C₂×#124	—	19	3	no	—
123	C₄×#41	D₁₉	1	1	yes	characteristic, complemented
124	C₂×C₁₉	—	2	6	no	—
125	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
126	C₂×C₁₉	#585	1	2	yes	—
127	D₁₉	—	4	2	no	—
128	D₁₉	—	4	6	no	—
129	2₋¹⁺⁴	—	38	8	no	—
130	H(5,𝔽₂)	—	38	8	no	—
131	C₂×#41	—	19	2	no	—
132	C₂×#41	—	19	6	no	—
133	C₂×#41	—	19	3	no	—
134	C₂×#41	—	19	3	no	—
135	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
136	C₂²×Q₈	—	19	2	no	—
137	C₂²×Q₈	—	19	3	no	—
138	C₂²×D₄	—	19	6	no	—
139	C₂²×D₄	—	19	3	no	—
140	C₄⋊Q₈	—	19	3	no	—
141	#127	—	19	3	no	—
142	#124	—	19	3	no	—
143	#124	—	19	6	no	—
144	#124	—	19	12	no	—
145	#124	—	19	1	no	—
146	#123	—	19	12	no	—
147	C₂²⋊Q₈	—	19	12	no	—
148	#121	—	19	12	no	—
149	#121	—	19	12	no	—
150	#120	—	19	12	no	—
151	C₄×Q₈	C₂×D₁₉	1	2	yes	complemented
152	C₄×D₄	—	19	12	no	—
153	C₄×D₄	C₂×D₁₉	1	6	yes	complemented
154	#117	C₂×D₁₉	1	3	yes	complemented
155	C₂×C₂²⋊C₄	—	19	12	no	—
156	C₂×C₄²	C₂×D₁₉	1	3	yes	complemented
157	C₁₉	#3500	1	1	yes	characteristic, complemented, Sylow
158	C₂⁴	—	19	6	no	—
159	#41	—	38	8	no	—
160	#41	—	38	24	no	—
161	#41	—	38	12	no	—
162	#41	—	38	12	no	—
163	#41	D₇₆	1	8	yes	complemented
164	C₂×Q₈	—	19	6	no	—
165	C₂×Q₈	—	19	3	no	—
166	C₂×Q₈	—	19	1	no	—
167	C₂×Q₈	—	38	8	no	—
168	C₂×Q₈	—	38	12	no	—
169	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
170	C₂×D₄	—	19	6	no	—
171	C₂×D₄	—	19	6	no	—
172	C₂×D₄	—	19	6	no	—
173	C₂×D₄	—	19	3	no	—
174	C₂×D₄	—	19	1	no	—
175	C₂×D₄	—	19	12	no	—
176	C₂×D₄	—	38	24	no	—
177	C₂×D₄	—	38	12	no	—
178	C₂×D₄	C₂²×D₁₉	1	3	yes	—
179	C₂²×C₄	—	19	6	no	—
180	C₂²×C₄	—	19	6	no	—
181	C₂²×C₄	—	19	6	no	—
182	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
183	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
184	C₄⋊C₄	—	19	12	no	—
185	C₄⋊C₄	C₂²×D₁₉	1	6	yes	—
186	C₂²⋊C₄	—	19	12	no	—
187	C₂²⋊C₄	—	19	24	no	—
188	C₂²⋊C₄	—	19	4	no	—
189	C₂²⋊C₄	C₂²×D₁₉	1	6	yes	—
190	C₄²	C₂²×D₁₉	1	1	yes	characteristic
191	C₄²	C₂²×D₁₉	1	3	yes	—
192	C₄²	C₂²×D₁₉	1	6	yes	—
193	C₂³	—	19	6	no	—
194	C₂³	—	19	2	no	—
195	C₂³	—	38	12	no	—
196	C₂³	—	76	12	no	—
197	C₂³	C₂³×D₁₉	1	3	yes	—
198	Q₈	—	38	12	no	—
199	Q₈	—	38	6	no	—
200	Q₈	—	38	2	no	—
201	Q₈	C₂×D₇₆	1	4	yes	—
202	D₄	—	38	12	no	—
203	D₄	—	38	12	no	—
204	D₄	—	38	12	no	—
205	D₄	—	38	6	no	—
206	D₄	—	38	2	no	—
207	D₄	—	76	12	no	—
208	D₄	C₂×D₇₆	1	12	yes	—
209	C₂×C₄	—	4	6	no	—
210	C₂×C₄	—	19	6	no	—
211	C₂×C₄	—	19	2	no	—
212	C₂×C₄	—	38	12	no	—
213	C₂×C₄	—	38	12	no	—
214	C₂×C₄	—	38	12	no	—
215	C₂×C₄	C₂×D₇₆	1	12	yes	—
216	C₂×C₄	C₂³×D₁₉	1	2	yes	—
217	C₂×C₄	C₂³×D₁₉	1	6	yes	—
218	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
219	C₂×C₄	C₂³×D₁₉	1	3	yes	—
220	C₂²	—	2	6	no	—
221	C₂²	—	38	2	no	—
222	C₂²	—	38	6	no	—
223	C₂²	—	38	4	no	—
224	C₂²	—	38	12	no	—
225	C₂²	—	152	12	no	—
226	C₂²	C₂²×D₇₆	1	6	yes	—
227	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
228	C₄	—	2	2	no	—
229	C₄	—	2	6	no	—
230	C₄	—	38	2	no	—
231	C₄	—	38	6	no	—
232	C₄	C₂²×D₇₆	1	6	yes	—
233	C₄	C₂²×D₇₆	1	2	yes	—
234	C₂	—	2	6	no	—
235	C₂	—	76	6	no	—
236	C₂	—	76	2	no	—
237	C₂	C₂³×D₇₆	1	1	yes	characteristic
238	C₂	#11927380	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₄×#41×C₁₉	C₂
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	#3500
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#10597436	C₂	semidirect
2. C₂×#10597435	C₂	semidirect
3. #11927206	C₂	semidirect
4. #11927189	C₂	semidirect
5. #11927120	C₂	semidirect
6. #11927113	C₂	semidirect
7. #11927094	C₂	semidirect
8. C₂×#10597321	C₂	semidirect
9. C₄×#41×C₁₉	C₂	semidirect
14. C₂×Q₈×D₁₉	C₂²	semidirect
15. C₂×#64543	C₂²	semidirect
18. C₂×#64541	C₂²	semidirect
20. C₂²×Dic₃₈	C₂²	semidirect
21. C₄×Q₈×C₁₉	C₂²	semidirect
22. C₄×D₄×C₁₉	C₂²	semidirect
23. C₁₉×#117	C₂²	semidirect
24. C₂×C₄²×C₁₉	C₂²	semidirect
25. #10597376	C₂²	semidirect
26. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
27. #10597343	C₂²	semidirect
28. #10597341	C₂²	semidirect
29. #10597332	C₂²	semidirect
30. #10597328	C₂²	semidirect
31. #10597321	C₂²	semidirect
32. #10597321	C₂²	semidirect
33. #10597321	C₂²	semidirect
34. #10597321	C₂²	semidirect
35. #10597320	C₂²	semidirect
36. C₄×D₇₆	C₂²	semidirect
37. #10597315	C₂²	semidirect
39. #41×C₁₉	D₄	semidirect
123. C₄×#41	D₁₉	semidirect
151. C₄×Q₈	C₂×D₁₉	semidirect
153. C₄×D₄	C₂×D₁₉	semidirect
154. #117	C₂×D₁₉	semidirect
156. C₂×C₄²	C₂×D₁₉	semidirect
157. C₁₉	#3500	semidirect
163. #41	D₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597436	2
C₂×#10597435	2
#11927206	2
#11927189	2
#11927120	2
#11927113	2
#11927094	2
C₂×#10597321	2
C₄×#41×C₁₉	2
#3500	19