Finite Group Databasebeta

← #14562918

Subgroups — #14562918

Order 2432.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#11927198C211yesmaximal, characteristic
2#11926940C211yesmaximal, characteristic, complemented
3#11926746C211yesmaximal, characteristic, complemented
4#11926291C211yesmaximal, characteristic, complemented
5D4⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
6#11926271C211yesmaximal, characteristic, complemented
7C19×#474C211yesmaximal, characteristic, complemented
8C2×#64543—21no—
9C19×C4⋊Q8C2211yescharacteristic
10C4×D4×C19C2211yescharacteristic
11C2×#64527—21no—
12#10597376—21no—
13C2×C4⋊Dic19—21no—
14#10597343—21no—
15#10597332—22no—
16C4×D76C2211yescharacteristic
17#10597315C2211yescharacteristic
18C19×#107—21no—
19C19×C4⋊C8C2211yescharacteristic
20C19×#102—21no—
21#10597292—21no—
22#10597265—22no—
23C4⋊(C19⋊C8)C2211yescharacteristic
24C4×C19⋊C8C2211yescharacteristic
25C2×Q8×C19—21no—
26C2×D4×C19D411yescharacteristic
27C22×C4×C19—21no—
28C2×C22⋊D19—22no—
29C22×Dic19—22no—
30#64543—42no—
31#64543—42no—
32C2×D76D411yescharacteristic
33C2×C4×D19—21no—
34C2×Dic38—21no—
35C2×C8×C19—21no—
36C4⋊C4×C19—21no—
37C4⋊C4×C19—21no—
38C4⋊C4×C19D411yescharacteristic
39C22⋊C4×C19—21no—
40C42×C19C2311yescharacteristic
41#64527—42no—
42(C2×D19)⋊C4—22no—
43(C2×D19)⋊C4—21no—
44C4⋊Dic19—22no—
45C4⋊Dic19—21no—
46C4⋊Dic19D412yes—
47C4⋊Dic19D411yescharacteristic
48C2×C19⋊C8—21no—
49C2×C19⋊C8—21no—
50C23×C19—21no—
51C22×D19—21no—
52Q8×C19—41no—
53Q8×C19—41no—
54D4×C19—21no—
55D4×C19SD1612yescomplemented
56C2×C4×C19—21no—
57C2×C4×C19—41no—
58C2×C4×C19—41no—
59C2×C4×C19—41no—
60C2×C4×C19C2×D411yescharacteristic
61C2×C4×C19C2×D411yescharacteristic
62C2×C4×C19C2×D411yescharacteristic
63C22⋊D19—44no—
64C2×Dic19—22no—
65C2×Dic19—21no—
66C2×Dic19—44no—
67D76—21no—
68D76—21no—
69C4×D19—41no—
70C4×D19—41no—
71Dic38—41no—
72Dic38—41no—
73C8×C19—41no—
74C19⋊C8—22no—
75C19⋊C8—41no—
76#1654—191nomaximal, Sylow
77C22×C19—22no—
78C22×C19—41no—
79C22×C19—41no—
80C22×C19#12011yescharacteristic
81C2×D19—41no—
82C2×D19—41no—
83C2×D19—41no—
84C4×C19—21no—
85C4×C19—41no—
86C4×C19—81no—
87C4×C19C2×SD1611yescharacteristic
88C4×C19#13511yescharacteristic
89C4×C19AGL(1,ℤ/8)11yescharacteristic
90C4×C19AGL(1,ℤ/8)11yescharacteristic
91Dic19—42no—
92Dic19—41no—
93#547—191no—
94#498—191no—
95#474D1911yescharacteristic, complemented
96#461—191no—
97#332—191no—
98D4⋊C8—191no—
99D4⋊C8—191no—
100C2×C19—42no—
101C2×C19#44911yescharacteristic
102C2×C19#45011yescharacteristic
103C2×C19#45611yescharacteristic
104D19—81no—
105C2×#41—381no—
106C2×SD16—381no—
107C4⋊Q8—191no—
108C4⋊Q8C2×D1911yescharacteristic
109#123—382no—
110C22⋊Q8—381no—
111#121—381no—
112C4×D4—191no—
113C4×D4C2×D1911yescharacteristic
114C2×C4⋊C4—381no—
115#107—21no—
116#106—382no—
117C4⋊C8—191no—
118C4⋊C8C2×D1911yescharacteristic
119#103—381no—
120#102—21no—
121C4×C8—191no—
122C19#165411yescharacteristic, complemented, Sylow
123#41—762no—
124#41—762no—
125C2×Q8—21no—
126C2×Q8—381no—
127C2×D4—191no—
128C2×D4—382no—
129C2×D4C22⋊D1911yescharacteristic
130C22×C4—21no—
131C22×C4—382no—
132C22×C4—381no—
133SD16—762no—
134C2×C8—21no—
135C2×C8—381no—
136C2×C8—381no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—191no—
140C4⋊C4—192no—
141C4⋊C4—382no—
142C4⋊C4—381no—
143C4⋊C4C22⋊D1911yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—382no—
146C22⋊C4—381no—
147C42C22×D1911yescharacteristic
148C23—21no—
149C23—381no—
150Q8—41no—
151Q8—41no—
152Q8—761no—
153Q8—761no—
154D4—21no—
155D4—381no—
156D4—381no—
157D4—764no—
158D4#6452712yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—381no—
164C2×C4—382no—
165C2×C4—764no—
166C2×C4—761no—
167C2×C4—761no—
168C2×C4D4×D1911yescharacteristic
169C2×C4D4×D1911yescharacteristic
170C2×C4C2×C22⋊D1911yescharacteristic
171C8—41no—
172C8—382no—
173C8—761no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—761no—
178C22—761no—
179C22—761no—
180C22#1059738311yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—761no—
185C4—762no—
186C4#1059735711yescharacteristic
187C4#1059735811yescharacteristic
188C4C2×#6452711yescharacteristic
189C4#1059739511yescharacteristic
190C2—42no—
191C2—1521no—
192C2#1192668611yescharacteristic
193C2#1192669411yescharacteristic
194C2#1192672511yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#474C2
socleC22×C19#120
prime radical#11927198C2
hypercenter#474D19
hypocenterC19#1654
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #11926940C2semidirect
3. #11926746C2semidirect
4. #11926291C2semidirect
5. D4⋊(C19⋊C8)C2semidirect
6. #11926271C2semidirect
7. C19×#474C2semidirect
55. D4×C19SD16semidirect
95. #474D19semidirect
122. C19#1654semidirect
158. D4#64527semidirect

Maximal subgroups

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

subgroupindex
#119271982
#119269402
#119267462
#119262912
D4⋊(C19⋊C8)2
#119262712
C19×#4742
#165419