Finite Group Databasebeta

← #14564407

Subgroups — #14564407

Order 2432.

200 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#10597279C211yesmaximal, characteristic
2#11926567C211yesmaximal, characteristic
3C2×Dic19⋊C8C211yesmaximal, characteristic
4M16×Dic19C211yesmaximal, characteristic
5#11926309C211yesmaximal, characteristic
6#11926308C211yesmaximal, characteristic
7C2×C19×#108C211yesmaximal, characteristic
8C2×M16×C19C2211yescharacteristic
9C2×M16×C19C2211yescharacteristic
10C22×C8×C19C2211yescharacteristic
11C2×C4×Dic19C2211yescharacteristic
12C2×#64520C2211yescharacteristic
13C2×#64520C2211yescharacteristic
14C22×C19⋊C8C2211yescharacteristic
15C19×#108—22no—
16#10597279—22no—
17#10597272—21no—
18Dic19⋊C8—21no—
19Dic19⋊C8—21no—
20Dic19⋊C8C412yes—
21Dic19⋊C8C412yes—
22C8×Dic19—21no—
23C22×C4×C19C2311yescharacteristic
24C22×Dic19Q811yescharacteristic
25C22×Dic19Q811yescharacteristic
26M16×C19—21no—
27M16×C19—21no—
28M16×C19—21no—
29M16×C19D412yes—
30C2×C8×C19—21no—
31C2×C8×C19—21no—
32C2×C8×C19—21no—
33C2×C8×C19—21no—
34C2×C8×C19C2×C412yes—
35C4×Dic19C2×C411yescharacteristic
36C4×Dic19C2×C411yescharacteristic
37C4×Dic19D411yescharacteristic
38C4×Dic19D411yescharacteristic
39#64520—21no—
40#64520—21no—
41#64520—21no—
42#64520Q812yes—
43C2×C19⋊C8—21no—
44C2×C19⋊C8—21no—
45C2×C19⋊C8—21no—
46C2×C19⋊C8—21no—
47C2×C19⋊C8C2×C412yes—
48C23×C19C2×Q811yescharacteristic
49C2×C4×C19C22×C411yescharacteristic
50C2×C4×C19C2×D411yescharacteristic
51C2×C4×C19C2×D411yescharacteristic
52C2×C4×C19C2×Q811yescharacteristic
53C2×C4×C19#4111yescharacteristic
54C2×C4×C19#4111yescharacteristic
55C2×Dic19—22no—
56C2×Dic19—41no—
57C2×Dic19C4⋊C411yescharacteristic
58C2×Dic19C4⋊C411yescharacteristic
59C2×Dic19C4⋊C411yescharacteristic
60C2×Dic19C4⋊C411yescharacteristic
61C8×C19—22no—
62C8×C19—22no—
63C8×C19—41no—
64C19⋊C8—22no—
65C19⋊C8—22no—
66C19⋊C8—41no—
67#1950—191nomaximal, Sylow
68C22×C19—21no—
69C22×C19—21no—
70C22×C19C2×C4⋊C411yescharacteristic
71C22×C19#12511yescharacteristic
72C22×C19C4⋊Q811yescharacteristic
73C4×C19C4×D411yescharacteristic
74C4×C19C4×Q811yescharacteristic
75C4×C19#12111yescharacteristic
76C4×C19C22⋊Q811yescharacteristic
77Dic19—21no—
78Dic19—21no—
79Dic19—21no—
80Dic19#10812yescomplemented
81C2×#108—191no—
82C2×#108D1911yescharacteristic
83#423—191no—
84C2×C4⋊C8—191no—
85C4×M16—191no—
86#341—191no—
87#341—191no—
88C2×C19—21no—
89C2×C19—21no—
90C2×C19#38911yescharacteristic
91C2×C19C2×#10811yescharacteristic
92C2×C19#43011yescharacteristic
93C2×M16—191no—
94C2×M16—191no—
95C2×M16C2×D1911yescharacteristic
96C2×M16C2×D1911yescharacteristic
97C22×C8—191no—
98C22×C8C2×D1911yescharacteristic
99C2×C42—191no—
100#108—22no—
101#108—382no—
102C4⋊C8—192no—
103C4⋊C8—192no—
104C4⋊C8—381no—
105C4⋊C8—381no—
106#97—381no—
107C4×C8—381no—
108C19#195011yescharacteristic, complemented, Sylow
109C22×C4—191no—
110C22×C4—191no—
111C22×C4C22×D1911yescharacteristic
112M16—21no—
113M16—21no—
114M16—21no—
115M16—192no—
116M16—381no—
117M16—381no—
118M16—381no—
119M16C22⋊D1912yes—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—192no—
125C2×C8—381no—
126C2×C8—381no—
127C2×C8—381no—
128C2×C8—381no—
129C2×C8C4×D1912yes—
130C42—191no—
131C42—191no—
132C42—191no—
133C42—191no—
134C23Q8×D1911yescharacteristic
135C2×C4—191no—
136C2×C4—191no—
137C2×C4—191no—
138C2×C4—191no—
139C2×C4—382no—
140C2×C4—761no—
141C2×C4C2×C4×D1911yescharacteristic
142C2×C4#6454111yescharacteristic
143C2×C4D4×D1911yescharacteristic
144C2×C4#6454311yescharacteristic
145C2×C4Q8×D1911yescharacteristic
146C2×C4C2×C22⋊D1911yescharacteristic
147C8—22no—
148C8—22no—
149C8—41no—
150C8—382no—
151C8—382no—
152C8—761no—
153C22—21no—
154C22—21no—
155C22#1059733511yescharacteristic
156C22C4⋊C4×D1911yescharacteristic
157C22#1059739011yescharacteristic
158C4—192no—
159C4—381no—
160C4—381no—
161C4—381no—
162C4#1059733311yescharacteristic
163C4#1059734211yescharacteristic
164C4C4×C22⋊D1911yescharacteristic
165C4#1059738511yescharacteristic
166C2—21no—
167C2—21no—
168C2#1192643911yescharacteristic
169C2#108×D1911yescharacteristic
170C2#1192659111yescharacteristic
subgroupG/H
centerC2×C4D4×D19
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC2×C19×#108C2
socleC22×C19C2×C4⋊C4
prime radicalC23×C19C2×Q8
cosocleC22×C4×C19C23
hypercenterC2×#108D19
hypocenterC19#1950
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
80. Dic19#108semidirect
108. C19#1950semidirect

Maximal subgroups

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

subgroupindex
C2×#105972792
#119265672
C2×Dic19⋊C82
M16×Dic192
#119263092
#119263082
C2×C19×#1082
#195019