Finite Group Databasebeta

← #14562640

Subgroups — #14562640

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#11926858C212yesmaximal, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926279C212yesmaximal, complemented
5C19×#324C211yesmaximal, characteristic, complemented
6C2×#64541—21no—
7C2×C4⋊C4×C19C2211yescharacteristic
8#10597376—21no—
9#10597376C2212yes—
10C2×C4⋊Dic19C2211yescharacteristic
11C2×Dic19⋊C4—21no—
12#10597343—22no—
13#10597341—22no—
14C19×C22⋊C8C2212yes—
15C19⋊#95—21no—
16C19⋊#95C2211yescharacteristic
17#10597278—22no—
18#10597275—22no—
19C22×C4×C19D411yescharacteristic
20C22×C4×C19D411yescharacteristic
21C22×C4×C19C2311yescharacteristic
22C2×C22⋊D19—22no—
23C22×Dic19—21no—
24C22×Dic19—21no—
25#64541—42no—
26#64541—42no—
27C2×D76—21no—
28C2×D76—21no—
29C2×D76D412yes—
30C2×C4×D19—22no—
31C2×Dic38—21no—
32C2×C8×C19—22no—
33C4⋊C4×C19—22no—
34(C2×D19)⋊C4—22no—
35(C2×D19)⋊C4—22no—
36C4⋊Dic19—21no—
37C4⋊Dic19—22no—
38C4⋊Dic19D412yes—
39Dic19⋊C4—42no—
40C23×C19C2×D411yescharacteristic
41C22×D19—22no—
42C2×C4×C19—21no—
43C2×C4×C19—21no—
44C2×C4×C19—21no—
45C2×C4×C19—41no—
46C2×C4×C19—41no—
47C2×C4×C19D812yes—
48C2×C4×C19C2×D412yes—
49C22⋊D19—42no—
50C22⋊D19—42no—
51C2×Dic19—22no—
52C2×Dic19—22no—
53C2×Dic19—41no—
54C2×Dic19—41no—
55C2×Dic19—41no—
56C2×Dic19—41no—
57C2×Dic19—41no—
58D76—42no—
59D76—42no—
60D76—81no—
61C4×D19—44no—
62Dic38—42no—
63C8×C19—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—41no—
76Dic19—42no—
77Dic19—42no—
78Dic19—81no—
79#537—191no—
80#480—192no—
81#398—191no—
82#327—192no—
83#324D1911yescharacteristic, complemented
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—191no—
96C2×C4⋊C4—381no—
97C2×C4⋊C4C2×D1911yescharacteristic
98#107—382no—
99#102—382no—
100C22⋊C8C2×D1912yes—
101#95—191no—
102#95—381no—
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—382no—
112C22×C4—381no—
113C22×C4—381no—
114C22×C4D7611yescharacteristic
115C22×C4D7611yescharacteristic
116C22×C4C22×D1911yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—192no—
120C4⋊C4—381no—
121C4⋊C4—382no—
122C4⋊C4—762no—
123C22⋊C4—382no—
124C22⋊C4—382no—
125C23—382no—
126C23C2×D7611yescharacteristic
127Q8—762no—
128D4—762no—
129D4—762no—
130D4—762no—
131D4—762no—
132D4—1521no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—382no—
139C2×C4—382no—
140C2×C4—764no—
141C2×C4—761no—
142C2×C4—761no—
143C2×C4—761no—
144C2×C4—761no—
145C2×C4—761no—
146C2×C4D15212yes—
147C2×C4D4×D1912yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—762no—
152C22—762no—
153C22—762no—
154C22#1059732811yescharacteristic
155C22C2×D15211yescharacteristic
156C22#1059735411yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—762no—
161C4—762no—
162C4—1521no—
163C2—21no—
164C2—21no—
165C2—1522no—
166C2#1192668011yescharacteristic
167C2#1192672911yescharacteristic
168C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#324C2
socleC22×C19#120
prime radical#11927125C2
hypercenter#324D19
hypocenterC19#1610
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #11926858C2semidirect
3. #11926474C2semidirect
4. #11926279C2semidirect
5. C19×#324C2semidirect
83. #324D19semidirect
103. C19#1610semidirect

Maximal subgroups

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

subgroupindex
#119271252
#119268582
#119264742
#119262792
C19×#3242
#161019