Finite Group Databasebeta

← #14562784

Subgroups — #14562784

Order 2432.

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

normal subgroups only

This group has 234 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#11926894C211yesmaximal, characteristic, complemented
3#11926831C211yesmaximal, characteristic, complemented
4#11926291C211yesmaximal, characteristic, complemented
5D4⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
6#11926271C211yesmaximal, characteristic, complemented
7C19×#476C211yesmaximal, characteristic, complemented
8C2×#64543—21no—
9C19×C4⋊Q8C2211yescharacteristic
10C4×D4×C19C2211yescharacteristic
11#10597376—21no—
12C2×C4⋊Dic19—21no—
13#10597343—21no—
14#10597332—22no—
15C4×D76C2211yescharacteristic
16#10597315C2211yescharacteristic
17C19×#106—21no—
18C19×C4⋊C8C2211yescharacteristic
19C19×#102—21no—
20#10597292—22no—
21#10597266—21no—
22#10597265—21no—
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(C2×D19)⋊C4—22no—
42(C2×D19)⋊C4—21no—
43C4⋊Dic19—22no—
44C4⋊Dic19—21no—
45C4⋊Dic19D411yescharacteristic
46C4⋊Dic19D412yes—
47C2×C19⋊C8—21no—
48C2×C19⋊C8—21no—
49C23×C19—21no—
50C22×D19—21no—
51Q8×C19—42no—
52D4×C19—21no—
53D4×C19SD1612yes—
54C2×C4×C19—21no—
55C2×C4×C19—41no—
56C2×C4×C19—41no—
57C2×C4×C19—41no—
58C2×C4×C19C2×D411yescharacteristic
59C2×C4×C19C2×D411yescharacteristic
60C2×C4×C19C2×D411yescharacteristic
61C22⋊D19—44no—
62C2×Dic19—22no—
63C2×Dic19—21no—
64C2×Dic19—44no—
65D76—21no—
66D76—21no—
67C4×D19—41no—
68C4×D19—41no—
69Dic38—41no—
70Dic38—41no—
71C8×C19—41no—
72C19⋊C8—41no—
73C19⋊C8—41no—
74#1635—191nomaximal, Sylow
75C22×C19—22no—
76C22×C19—41no—
77C22×C19—41no—
78C22×C19#12011yescharacteristic
79C2×D19—41no—
80C2×D19—41no—
81C2×D19—41no—
82C4×C19—21no—
83C4×C19—41no—
84C4×C19—81no—
85C4×C19C2×SD1611yescharacteristic
86C4×C19#13511yescharacteristic
87C4×C19AGL(1,ℤ/8)11yescharacteristic
88C4×C19#13711yescharacteristic
89Dic19—42no—
90Dic19—41no—
91#547—191no—
92#487—191no—
93#476—191no—
94#476D1911yescharacteristic, complemented
95#332—191no—
96D4⋊C8—191no—
97D4⋊C8—191no—
98C2×C19—42no—
99C2×C19#45011yescharacteristic
100C2×C19#45211yescharacteristic
101C2×C19#45411yescharacteristic
102D19—81no—
103C2×#41—381no—
104C4⋊Q8—191no—
105C4⋊Q8C2×D1911yescharacteristic
106#123—382no—
107C22⋊Q8—381no—
108#121—381no—
109C4×D4—191no—
110C4×D4C2×D1911yescharacteristic
111C2×C4⋊C4—381no—
112#106—21no—
113#106—381no—
114C4⋊C8—191no—
115C4⋊C8C2×D1911yescharacteristic
116#103—382no—
117#102—21no—
118#102—381no—
119C4×C8—191no—
120C19#163511yescharacteristic, complemented, Sylow
121#41—762no—
122#41—762no—
123C2×Q8—21no—
124C2×Q8—381no—
125C2×D4—191no—
126C2×D4—382no—
127C2×D4C22⋊D1911yescharacteristic
128C22×C4—21no—
129C22×C4—382no—
130C22×C4—381no—
131C2×C8—21no—
132C2×C8—381no—
133C2×C8—381no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—192no—
137C4⋊C4—191no—
138C4⋊C4—382no—
139C4⋊C4—381no—
140C4⋊C4C22⋊D1911yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—382no—
143C22⋊C4—381no—
144C42C22×D1911yescharacteristic
145C23—21no—
146C23—381no—
147Q8—42no—
148Q8—761no—
149Q8—761no—
150D4—21no—
151D4—381no—
152D4—381no—
153D4—764no—
154D4#6452712yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—381no—
160C2×C4—382no—
161C2×C4—764no—
162C2×C4—761no—
163C2×C4—761no—
164C2×C4D4×D1911yescharacteristic
165C2×C4D4×D1911yescharacteristic
166C2×C4C2×C22⋊D1911yescharacteristic
167C8—41no—
168C8—761no—
169C8—761no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—761no—
174C22—761no—
175C22—761no—
176C22#1059738311yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—761no—
181C4—762no—
182C4#1059736111yescharacteristic
183C4#1059736211yescharacteristic
184C4C2×#6452711yescharacteristic
185C4#1059739511yescharacteristic
186C2—42no—
187C2—1521no—
188C2#1192669411yescharacteristic
189C2#1192670311yescharacteristic
190C2#1192671511yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#476C2
socleC22×C19#120
prime radical#11927198C2
hypercenter#476D19
hypocenterC19#1635
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #11926894C2semidirect
3. #11926831C2semidirect
4. #11926291C2semidirect
5. D4⋊(C19⋊C8)C2semidirect
6. #11926271C2semidirect
7. C19×#476C2semidirect
94. #476D19semidirect
120. C19#1635semidirect

Maximal subgroups

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

subgroupindex
#119271982
#119268942
#119268312
#119262912
D4⋊(C19⋊C8)2
#119262712
C19×#4762
#163519