Subgroups — #14577521

Order 2432.

992 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927272	C₂	1	4	yes	maximal, complemented
2	#11927264	C₂	1	4	yes	maximal, complemented
3	#11927234	C₂	1	8	yes	maximal, complemented
4	#11927156	C₂	1	4	yes	maximal, complemented
5	#11927115	C₂	1	2	yes	maximal
6	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927101	C₂	1	4	yes	maximal, complemented
8	C₂×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927021	C₂	1	2	yes	maximal, complemented
10	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
11	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃₈	C₂²	1	2	yes	—
13	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₄×D₄×C₁₉	C₂²	1	4	yes	—
15	C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#117	C₂²	1	2	yes	—
17	C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
20	#10597390	C₂²	1	4	yes	—
21	#10597382	C₂²	1	4	yes	—
22	#10597381	C₂²	1	8	yes	—
23	#10597372	C₂²	1	2	yes	—
24	#10597372	C₂²	1	8	yes	—
25	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
26	#10597370	C₂²	1	8	yes	—
27	#10597370	C₂²	1	4	yes	—
28	#10597370	C₂²	1	8	yes	—
29	#10597335	C₂²	1	16	yes	—
30	#10597333	C₂²	1	8	yes	—
31	#10597325	C₂²	1	16	yes	—
32	#10597323	C₂²	1	8	yes	—
33	#10597316	C₂²	1	2	yes	—
34	#10597316	C₂²	1	8	yes	—
35	#10597315	C₂²	1	2	yes	—
36	#10597315	C₂²	1	2	yes	—
37	#10597315	C₂²	1	4	yes	—
38	#10597315	C₂²	1	2	yes	—
39	C₄×Dic₃₈	C₂²	1	8	yes	—
40	C₄×Dic₃₈	C₂²	1	8	yes	—
41	C₄×Dic₃₈	C₂²	1	4	yes	—
42	#41×C₁₉	—	2	4	no	—
43	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
49	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×Dic₁₉	C₂³	1	4	yes	—
51	C₂×Dic₃₈	—	2	8	no	—
52	C₂×Dic₃₈	C₂³	1	4	yes	—
53	C₂×Dic₃₈	C₂³	1	4	yes	—
54	C₂×Dic₃₈	C₂³	1	4	yes	—
55	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
57	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
59	C₄²×C₁₉	C₂³	1	1	yes	characteristic
60	C₄²×C₁₉	C₂³	1	2	yes	—
61	C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₄²×C₁₉	C₂³	1	2	yes	—
63	C₄²×C₁₉	C₂³	1	4	yes	—
64	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
65	C₂²⋊Dic₁₉	C₂³	1	16	yes	—
66	C₄⋊Dic₁₉	C₂³	1	4	yes	—
67	C₄⋊Dic₁₉	C₂³	1	8	yes	—
68	C₄⋊Dic₁₉	C₂³	1	4	yes	—
69	C₄⋊Dic₁₉	C₂³	1	8	yes	—
70	Dic₁₉⋊C₄	C₂³	1	16	yes	—
71	Dic₁₉⋊C₄	C₂³	1	16	yes	—
72	Dic₁₉⋊C₄	C₂³	1	8	yes	—
73	C₄×Dic₁₉	C₂³	1	4	yes	—
74	C₄×Dic₁₉	C₂³	1	16	yes	—
75	C₂³×C₁₉	C₂⁴	1	2	yes	—
76	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
77	Q₈×C₁₉	—	2	2	no	—
78	D₄×C₁₉	—	2	4	no	—
79	D₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	4	no	—
82	C₂×C₄×C₁₉	—	2	8	no	—
83	C₂×C₄×C₁₉	#41	1	4	yes	—
84	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
85	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
86	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
87	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
90	C₂×Dic₁₉	—	2	8	no	—
91	C₂×Dic₁₉	C₂⁴	1	8	yes	—
92	C₂×Dic₁₉	C₂⁴	1	8	yes	—
93	Dic₃₈	—	2	8	no	—
94	Dic₃₈	—	2	8	no	—
95	Dic₃₈	—	2	8	no	—
96	#3509	—	19	1	no	maximal, Sylow
97	C₂²×C₁₉	—	2	2	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	4	no	—
100	C₂²×C₁₉	C₂×#41	1	2	yes	—
101	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	4	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	C₂×#41	1	2	yes	—
106	C₄×C₁₉	C₂×#41	1	2	yes	—
107	C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
108	Dic₁₉	—	2	8	no	—
109	Dic₁₉	—	2	8	no	—
110	#557	—	19	4	no	—
111	#556	—	19	4	no	—
112	#552	—	19	8	no	—
113	#541	—	19	4	no	—
114	#536	—	19	2	no	—
115	#533	—	19	1	no	—
116	#533	—	19	4	no	—
117	C₂×C₄⋊Q₈	—	19	1	no	—
118	#519	—	19	2	no	—
119	C₄×#41	D₁₉	1	1	yes	characteristic
120	C₂×C₁₉	—	2	2	no	—
121	C₂×C₁₉	—	4	2	no	—
122	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
123	C₂×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
124	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
125	C₂²×Q₈	—	19	2	no	—
126	C₄⋊Q₈	—	19	4	no	—
127	C₄⋊Q₈	—	19	2	no	—
128	C₄⋊Q₈	—	19	2	no	—
129	C₄⋊Q₈	—	19	4	no	—
130	C₄⋊Q₈	—	19	2	no	—
131	#126	—	19	16	no	—
132	#125	—	19	16	no	—
133	#125	—	19	2	no	—
134	#125	—	19	8	no	—
135	#124	—	19	4	no	—
136	#123	—	19	8	no	—
137	C₂²⋊Q₈	—	19	8	no	—
138	C₂²⋊Q₈	—	19	4	no	—
139	C₂²⋊Q₈	—	19	8	no	—
140	C₄×Q₈	—	19	8	no	—
141	C₄×Q₈	—	19	8	no	—
142	C₄×Q₈	—	19	8	no	—
143	C₄×Q₈	—	19	4	no	—
144	C₄×Q₈	C₂×D₁₉	1	2	yes	—
145	C₄×D₄	C₂×D₁₉	1	4	yes	—
146	C₄×D₄	C₂×D₁₉	1	2	yes	—
147	#117	—	19	2	no	—
148	#117	—	19	8	no	—
149	#117	—	19	8	no	—
150	#117	C₂×D₁₉	1	1	yes	characteristic
151	#117	C₂×D₁₉	1	2	yes	—
152	C₂×C₄⋊C₄	—	19	4	no	—
153	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
154	C₂×C₄²	C₂×D₁₉	1	2	yes	—
155	C₁₉	#3509	1	1	yes	characteristic, complemented, Sylow
156	#41	—	2	4	no	—
157	C₂×Q₈	—	19	4	no	—
158	C₂×Q₈	—	19	4	no	—
159	C₂×Q₈	—	19	4	no	—
160	C₂×Q₈	—	38	8	no	—
161	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₁₉	1	2	yes	—
163	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	—	19	4	no	—
165	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
166	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
167	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
168	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
169	C₄⋊C₄	—	19	16	no	—
170	C₄⋊C₄	—	19	16	no	—
171	C₄⋊C₄	—	19	8	no	—
172	C₄⋊C₄	—	19	8	no	—
173	C₄⋊C₄	—	19	8	no	—
174	C₄⋊C₄	—	19	4	no	—
175	C₄⋊C₄	—	19	4	no	—
176	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
177	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
178	C₂²⋊C₄	—	19	4	no	—
179	C₂²⋊C₄	—	19	16	no	—
180	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
181	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
182	C₄²	—	19	16	no	—
183	C₄²	—	19	4	no	—
184	C₄²	C₂²×D₁₉	1	1	yes	characteristic
185	C₄²	C₂²×D₁₉	1	2	yes	—
186	C₄²	C₂²×D₁₉	1	1	yes	characteristic
187	C₄²	C₂²×D₁₉	1	4	yes	—
188	C₄²	C₂²×D₁₉	1	2	yes	—
189	C₂³	C₂³×D₁₉	1	2	yes	—
190	C₂³	C₂³×D₁₉	1	1	yes	characteristic
191	Q₈	—	2	2	no	—
192	Q₈	—	38	8	no	—
193	Q₈	—	38	8	no	—
194	Q₈	—	38	8	no	—
195	D₄	—	2	4	no	—
196	D₄	—	2	2	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	8	no	—
200	C₂×C₄	—	19	8	no	—
201	C₂×C₄	—	19	8	no	—
202	C₂×C₄	—	38	8	no	—
203	C₂×C₄	#64541	1	4	yes	—
204	C₂×C₄	C₂³×D₁₉	1	4	yes	—
205	C₂×C₄	C₂³×D₁₉	1	2	yes	—
206	C₂×C₄	C₂³×D₁₉	1	2	yes	—
207	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
209	C₂×C₄	C₂³×D₁₉	1	2	yes	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	4	no	—
213	C₂²	C₂×#64541	1	2	yes	—
214	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	4	no	—
217	C₄	—	2	2	no	—
218	C₄	—	38	8	no	—
219	C₄	—	38	8	no	—
220	C₄	C₂×#64541	1	2	yes	—
221	C₄	C₂×#64541	1	2	yes	—
222	C₄	#10597436	1	4	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	4	2	no	—
225	C₂	C₂²×#64541	1	1	yes	characteristic
226	C₂	C₂×#10597436	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₄×#41×C₁₉	C₂
prime radical	C₂×#41×C₁₉	C₂²
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	#3509
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. #11927272	C₂	semidirect
2. #11927264	C₂	semidirect
3. #11927234	C₂	semidirect
4. #11927156	C₂	semidirect
6. #11927101	C₂	semidirect
7. #11927101	C₂	semidirect
8. C₂×#10597315	C₂	semidirect
9. #11927021	C₂	semidirect
155. C₁₉	#3509	semidirect

Maximal subgroups

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

subgroup	index
#11927272	2
#11927264	2
#11927234	2
#11927156	2
#11927115	2
#11927101	2
C₂×#10597315	2
#11927021	2
C₄×#41×C₁₉	2
#3509	19