Finite Group Databasebeta

← #14562637

Subgroups — #14562637

Order 2432.

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

normal subgroups only

This group has 254 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#11927125C211yesmaximal, characteristic
2#11926857C212yesmaximal, complemented
3#11926277C212yesmaximal, complemented
4#11926270C211yesmaximal, characteristic, complemented
5C19×#398C211yesmaximal, characteristic, complemented
6C2×#64541—21no—
7C2×C4⋊C4×C19—21no—
8C2×C4⋊C4×C19C2211yescharacteristic
9C2×C4⋊C4×C19C2211yescharacteristic
10#10597376—21no—
11#10597376C2212yes—
12#10597343—22no—
13#10597341—22no—
14C19×#95—21no—
15C19×#95C2211yescharacteristic
16C22⋊(C19⋊C8)C2212yes—
17#10597266—22no—
18#10597264—22no—
19C22×C4×C19—21no—
20C22×C4×C19—21no—
21C22×C4×C19D411yescharacteristic
22C22×C4×C19D411yescharacteristic
23C22×C4×C19C2311yescharacteristic
24C2×C22⋊D19—22no—
25#64541—42no—
26#64541—42no—
27C2×D76—21no—
28C2×D76—21no—
29C2×D76D412yes—
30C2×C4×D19—22no—
31C2×Dic38—21no—
32C4⋊C4×C19—22no—
33C4⋊C4×C19—22no—
34C4⋊C4×C19—42no—
35(C2×D19)⋊C4—22no—
36(C2×D19)⋊C4—22no—
37C4⋊Dic19—21no—
38C4⋊Dic19D412yes—
39C2×C19⋊C8—22no—
40C23×C19C2×D411yescharacteristic
41C22×D19—22no—
42C2×C4×C19—21no—
43C2×C4×C19—21no—
44C2×C4×C19—22no—
45C2×C4×C19—21no—
46C2×C4×C19—41no—
47C2×C4×C19—41no—
48C2×C4×C19—41no—
49C2×C4×C19—41no—
50C2×C4×C19—41no—
51C2×C4×C19—41no—
52C2×C4×C19—41no—
53C2×C4×C19D812yes—
54C2×C4×C19C2×D412yes—
55C22⋊D19—42no—
56C22⋊D19—42no—
57C2×Dic19—22no—
58D76—42no—
59D76—42no—
60D76—81no—
61C4×D19—44no—
62Dic38—42no—
63C19⋊C8—42no—
64#1610—191nomaximal, Sylow
65C22×C19—21no—
66C22×C19—21no—
67C22×C19#12011yescharacteristic
68C22×C19C2×D811yescharacteristic
69C22×C19AGL(1,ℤ/8)11yescharacteristic
70C2×D19—42no—
71C2×D19—42no—
72C2×D19—42no—
73C4×C19—22no—
74C4×C19—22no—
75C4×C19—42no—
76C4×C19—41no—
77C4×C19—81no—
78Dic19—42no—
79#537—191no—
80#480—192no—
81#398D1911yescharacteristic, complemented
82#327—192no—
83#324—191no—
84C2×C19—21no—
85C2×C19—21no—
86C2×C19#44711yescharacteristic
87C2×C19#45611yescharacteristic
88C2×C19#45811yescharacteristic
89D19—82no—
90C2×#41—381no—
91C22⋊Q8—382no—
92#121—192no—
93#121—382no—
94#121—381no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D1911yescharacteristic
97C2×C4⋊C4C2×D1911yescharacteristic
98#107—382no—
99#102—382no—
100C22⋊C8—192no—
101#95—21no—
102#95C2×D1911yescharacteristic
103C19#161011yescharacteristic, complemented, Sylow
104#41—762no—
105#41—762no—
106C2×Q8—381no—
107C2×D4—192no—
108C2×D4—381no—
109C2×D4—381no—
110C2×D4—382no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—382no—
114C22×C4C22⋊D1911yescharacteristic
115C22×C4C22⋊D1911yescharacteristic
116C22×C4C22×D1911yescharacteristic
117C2×C8—382no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—192no—
122C4⋊C4—381no—
123C22⋊C4—382no—
124C22⋊C4—382no—
125C23—382no—
126C23C2×C22⋊D1911yescharacteristic
127Q8—762no—
128D4—762no—
129D4—762no—
130D4—762no—
131D4—762no—
132D4—1521no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—382no—
145C2×C4—764no—
146C2×C4#6452512yes—
147C2×C4D4×D1912yes—
148C8—762no—
149C22—21no—
150C22—21no—
151C22—762no—
152C22—762no—
153C22—762no—
154C22C2×#6452511yescharacteristic
155C22#1059738311yescharacteristic
156C22#1059739511yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—762no—
163C2—21no—
164C2—21no—
165C2—1522no—
166C2#1192667711yescharacteristic
167C2#1192672611yescharacteristic
168C2#1192673311yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#398C2
socleC22×C19#120
prime radical#11927125C2
hypercenter#398D19
hypocenterC19#1610
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #11926857C2semidirect
3. #11926277C2semidirect
4. #11926270C2semidirect
5. C19×#398C2semidirect
81. #398D19semidirect
103. C19#1610semidirect

Maximal subgroups

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

subgroupindex
#119271252
#119268572
#119262772
#119262702
C19×#3982
#161019