Finite Group Databasebeta

← #14562948

Subgroups — #14562948

Order 2432.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#11927298C211yesmaximal, characteristic
2#11926954C211yesmaximal, characteristic, complemented
3#11926953C211yesmaximal, characteristic, complemented
4#11926938C211yesmaximal, characteristic
5#11926285C211yesmaximal, characteristic, complemented
6#11926283C211yesmaximal, characteristic
7C19×#330C211yesmaximal, characteristic, complemented
8C19×#125C2211yescharacteristic
9C2×Dic76—21no—
10C2×#64516—21no—
11#10597344—21no—
12#10597344—21no—
13#10597343—21no—
14#10597342—21no—
15#10597340—21no—
16#10597334—21no—
17#10597321C2211yescharacteristic
18#10597316C2211yescharacteristic
19#10597315C2211yescharacteristic
20C19×#97C2211yescharacteristic
21C19×#97C2211yescharacteristic
22#10597275—21no—
23#10597274—21no—
24#10597265—21no—
25#10597264—21no—
26#10597260C2211yescharacteristic
27C2×D76D411yescharacteristic
28C2×C4×D19—21no—
29C2×Dic38—21no—
30C2×Dic38—21no—
31C2×Dic38D411yescharacteristic
32C2×C8×C19—21no—
33C2×C8×C19—21no—
34C4⋊C4×C19—21no—
35C4⋊C4×C19—21no—
36C4⋊C4×C19D411yescharacteristic
37C4⋊C4×C19D411yescharacteristic
38C42×C19C2311yescharacteristic
39(C2×D19)⋊C4—21no—
40(C2×D19)⋊C4—21no—
41(C2×D19)⋊C4—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44C4⋊Dic19—21no—
45C4⋊Dic19—21no—
46C4⋊Dic19—21no—
47C4⋊Dic19D411yescharacteristic
48C4⋊Dic19D411yescharacteristic
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52C4×Dic19—21no—
53C2×C19⋊C8—21no—
54Dic76—42no—
55#64516—42no—
56C22×D19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19C2×D411yescharacteristic
60C2×C4×C19C2×D411yescharacteristic
61C2×C4×C19C2×D411yescharacteristic
62C2×Dic19—21no—
63C2×Dic19—21no—
64C2×Dic19—21no—
65C2×Dic19—41no—
66D76—41no—
67C4×D19—81no—
68Dic38—41no—
69Dic38—41no—
70Dic38—41no—
71Dic38—81no—
72C8×C19—22no—
73C8×C19—22no—
74C19⋊C8—22no—
75#1660—191nomaximal, Sylow
76C22×C19#12011yescharacteristic
77C2×D19—41no—
78C2×D19—41no—
79C2×D19—41no—
80C4×C19—21no—
81C4×C19—21no—
82C4×C19—21no—
83C4×C19—41no—
84C4×C19—41no—
85Dic19—41no—
86Dic19—41no—
87Dic19—41no—
88Dic19—81no—
89#563—191no—
90#501—191no—
91#501—191no—
92#497—191no—
93#330—191no—
94#330D1911yescharacteristic, complemented
95#329—191no—
96C2×C19#45311yescharacteristic
97C2×C19#45611yescharacteristic
98C2×C19#45611yescharacteristic
99D19—81no—
100C2×Q16—381no—
101C2×SD16—381no—
102C4⋊Q8—191no—
103C4⋊Q8—381no—
104#126—381no—
105#126—381no—
106#125—191no—
107#125C2×D1911yescharacteristic
108#124—191no—
109#123—381no—
110C22⋊Q8—381no—
111C22⋊Q8—381no—
112#107—381no—
113#107—381no—
114#106—381no—
115#106—381no—
116#97—191no—
117#97C2×D1911yescharacteristic
118#97C2×D1911yescharacteristic
119C19#166011yescharacteristic, complemented, Sylow
120C2×Q8—191no—
121C2×Q8—381no—
122C2×Q8—381no—
123C2×D4—191no—
124C22×C4—381no—
125Q16—762no—
126SD16—762no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—381no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—191no—
133C4⋊C4—191no—
134C4⋊C4—381no—
135C4⋊C4—381no—
136C4⋊C4—381no—
137C4⋊C4—381no—
138C4⋊C4—381no—
139C4⋊C4—381no—
140C4⋊C4D7611yescharacteristic
141C4⋊C4D7611yescharacteristic
142C22⋊C4—381no—
143C22⋊C4—381no—
144C22⋊C4—381no—
145C22⋊C4—381no—
146C22⋊C4—381no—
147C42—381no—
148C42C22×D1911yescharacteristic
149C23—381no—
150Q8—761no—
151Q8—761no—
152Q8—761no—
153Q8—1521no—
154D4—761no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—381no—
158C2×C4—381no—
159C2×C4—381no—
160C2×C4—761no—
161C2×C4—1521no—
162C2×C4C2×D7611yescharacteristic
163C2×C4D4×D1911yescharacteristic
164C2×C4D4×D1911yescharacteristic
165C8—22no—
166C8—22no—
167C8—382no—
168C22—761no—
169C22—761no—
170C22—761no—
171C22#1059732811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—761no—
178C4—761no—
179C4—761no—
180C4—1521no—
181C2—1521no—
182C2#1192671311yescharacteristic
183C2#1192672811yescharacteristic
184C2#1192672911yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#330C2
socleC22×C19#120
prime radicalC2×D76D4
hypercenter#330D19
hypocenterC19#1660
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11926954C2semidirect
3. #11926953C2semidirect
5. #11926285C2semidirect
7. C19×#330C2semidirect
94. #330D19semidirect
119. C19#1660semidirect

Maximal subgroups

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

subgroupindex
#119272982
#119269542
#119269532
#119269382
#119262852
#119262832
C19×#3302
#166019