Finite Group Databasebeta

← #18069161

Subgroups — #18069161

Order 4864.

248 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564428C211yesmaximal, characteristic
2#14561575C211yesmaximal, characteristic, complemented
3C19×#1322C211yesmaximal, characteristic, complemented
4C2×C4×D76C411yescharacteristic
5C2×(C2×D19)⋊C8—21no—
6C2×(C2×D19)⋊C8—21no—
7C2×C4×C19⋊C8C411yescharacteristic
8C22⋊(C19⋊C16)—21no—
9C2×C19×C4⋊C8C2211yescharacteristic
10C19×C22⋊C16—21no—
11C22×D76C811yescharacteristic
12C22×C4×D19—21no—
13C22×C8×C19D411yescharacteristic
14C22×C8×C19D411yescharacteristic
15C2×C42×C19C2×C411yescharacteristic
16C2×(C2×D19)⋊C4—21no—
17C2×C4⋊Dic19C811yescharacteristic
18C22×C19⋊C8—21no—
19C4×D76—41no—
20C4×D76—41no—
21C2×C16×C19—41no—
22C19×C4⋊C8—41no—
23(C2×D19)⋊C8—42no—
24(C2×D19)⋊C8—42no—
25C2×C19⋊C16—41no—
26C4×C19⋊C8—41no—
27C23×D19—21no—
28C22×C4×C19C22⋊C411yescharacteristic
29C22×C4×C19C2×C811yescharacteristic
30C22×C4×C19M1611yescharacteristic
31C22×Dic19—21no—
32C2×D76—21no—
33C2×D76—41no—
34C2×D76—41no—
35C2×D76C1612yescomplemented
36C2×C4×D19—41no—
37C2×C4×D19—41no—
38C2×C4×D19—41no—
39C2×C4×D19—41no—
40C2×C4×D19—41no—
41C2×C4×D19—41no—
42C2×C8×C19—21no—
43C2×C8×C19—21no—
44C2×C8×C19—41no—
45C2×C8×C19—41no—
46C42×C19—21no—
47C42×C19—21no—
48(C2×D19)⋊C4—42no—
49C4⋊Dic19—41no—
50C2×C19⋊C8—22no—
51C2×C19⋊C8—41no—
52C2×C19⋊C8—41no—
53C16×C19—81no—
54C19⋊C16—81no—
55#7056—191nomaximal, Sylow
56C23×C19C22⋊C811yescharacteristic
57C22×D19—22no—
58C22×D19—41no—
59C22×D19—41no—
60C22×D19—41no—
61C22×D19—41no—
62C22×D19—41no—
63C22×D19—41no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—41no—
70C2×C4×C19#9911yescharacteristic
71C2×C4×C19#10011yescharacteristic
72C2×C4×C19C2×C1611yescharacteristic
73C2×C4×C19M3211yescharacteristic
74C2×Dic19—41no—
75C2×Dic19—41no—
76C2×Dic19—41no—
77D76—42no—
78D76—42no—
79C4×D19—81no—
80C4×D19—81no—
81C4×D19—81no—
82C4×D19—81no—
83C8×C19—41no—
84C8×C19—41no—
85C19⋊C8—42no—
86#1954—191no—
87#1322—191no—
88#1322D1911yescharacteristic, complemented
89C22×C19—21no—
90C22×C19—21no—
91C22×C19#32311yescharacteristic
92C22×C19C22⋊C1611yescharacteristic
93C22×C19#34911yescharacteristic
94C2×D19—42no—
95C2×D19—42no—
96C2×D19—42no—
97C2×D19—81no—
98C2×D19—81no—
99C2×D19—81no—
100C2×D19—81no—
101C4×C19—21no—
102C4×C19—21no—
103C4×C19—21no—
104C4×C19—41no—
105C4×C19#35311yescharacteristic
106C4×C19#35511yescharacteristic
107Dic19—81no—
108C2×C4×D4—191no—
109C2×C4⋊C8C2×D1911yescharacteristic
110C2×C22⋊C8—381no—
111C2×C22⋊C8—381no—
112C2×C4×C8—191no—
113C22⋊C16—21no—
114C22⋊C16—381no—
115C2×C19—21no—
116C2×C19—21no—
117C2×C19#131411yescharacteristic
118C2×C19#131811yescharacteristic
119C2×C19#132111yescharacteristic
120D19—82no—
121C22×D4—191no—
122C23×C4—381no—
123C22×C8—381no—
124C22×C8D7611yescharacteristic
125C22×C8C22⋊D1911yescharacteristic
126C4×D4—761no—
127C4×D4—761no—
128C2×C4⋊C4—191no—
129C2×C22⋊C4—381no—
130C2×C42C4×D1911yescharacteristic
131C2×C16—41no—
132C2×C16—761no—
133C4⋊C8—41no—
134C22⋊C8—762no—
135C22⋊C8—762no—
136C4×C8—761no—
137C19#705611yescharacteristic, complemented, Sylow
138C24—381no—
139C2×D4—192no—
140C2×D4—381no—
141C2×D4—761no—
142C2×D4—761no—
143C22×C4—381no—
144C22×C4—761no—
145C22×C4—761no—
146C22×C4—761no—
147C22×C4—761no—
148C22×C4—761no—
149C22×C4—761no—
150C22×C4C8×D1911yescharacteristic
151C22×C4#6451511yescharacteristic
152C22×C4(C2×D19)⋊C411yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—382no—
158C2×C8—761no—
159C2×C8—761no—
160C4⋊C4—761no—
161C22⋊C4—762no—
162C42—21no—
163C42—21no—
164C16—81no—
165C16—1521no—
166C23—382no—
167C23—761no—
168C23—761no—
169C23—761no—
170C23—761no—
171C23—761no—
172C23—761no—
173C23(C2×D19)⋊C811yescharacteristic
174D4—762no—
175D4—762no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—761no—
183C2×C4—761no—
184C2×C4—761no—
185C2×C4—1521no—
186C2×C4—1521no—
187C2×C4—1521no—
188C2×C4—1521no—
189C2×C4C16×D1911yescharacteristic
190C2×C4#1059725511yescharacteristic
191C2×C4#1059726311yescharacteristic
192C2×C4#1059728011yescharacteristic
193C8—41no—
194C8—41no—
195C8—762no—
196C22—21no—
197C22—21no—
198C22—762no—
199C22—762no—
200C22—762no—
201C22—1521no—
202C22—1521no—
203C22—1521no—
204C22—1521no—
205C22#1192626711yescharacteristic
206C22(C2×D19)⋊C1611yescharacteristic
207C22#1192632511yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—1521no—
213C4#1192633611yescharacteristic
214C4#1192634011yescharacteristic
215C2—21no—
216C2—21no—
217C2—1522no—
218C2#1456155811yescharacteristic
219C2#1456156611yescharacteristic
220C2#1456157211yescharacteristic
subgroupG/H
centerC2×C4#10597263
commutatorC2×C4×C19C2×C16
FrattiniC2×C4⋊C8C2×D19
FittingC19×#1322C2
socleC22×C19#323
prime radicalC22×D76C8
cosocleC2×C19×C4⋊C8C22
hypercenter#1322D19
hypocenterC19#7056
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #14561575C2semidirect
3. C19×#1322C2semidirect
35. C2×D76C16semidirect
88. #1322D19semidirect
137. C19#7056semidirect

Maximal subgroups

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

subgroupindex
#145644282
#145615752
C19×#13222
#705619