Finite Group Databasebeta

← #14564477

Subgroups — #14564477

Order 2432.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10597390C211yesmaximal, characteristic
2#11926567C211yesmaximal, characteristic
3C2×#10597293C211yesmaximal, characteristic
4C2×#10597281C211yesmaximal, characteristic
5C2×#10597281C211yesmaximal, characteristic
6M16×Dic19C211yesmaximal, characteristic
7C2×C19×#101C211yesmaximal, characteristic
8C22×Q8×C19C2211yescharacteristic
9C22×Dic38C2211yescharacteristic
10C2×M16×C19C2211yescharacteristic
11C2×M16×C19C2211yescharacteristic
12#10597390—21no—
13#10597390—22no—
14#10597390—21no—
15C2×Dic19⋊C4C414yes—
16C2×C4×Dic19C2211yescharacteristic
17C2×#64520C2211yescharacteristic
18C2×#64520C2211yescharacteristic
19C19×#101—22no—
20#10597293—22no—
21#10597281—22no—
22#10597281—22no—
23#10597272—21no—
24Dic19⋊C8—22no—
25C8×Dic19—21no—
26C2×Q8×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19—21no—
29C2×Q8×C19—21no—
30C2×Q8×C19—21no—
31C2×Q8×C19—21no—
32C22×C4×C19C2×C412yes—
33C22×C4×C19C2311yescharacteristic
34C22×Dic19C2×C412yes—
35C22×Dic19C2×C412yes—
36C2×Dic38—21no—
37C2×Dic38—21no—
38C2×Dic38—21no—
39C2×Dic38—21no—
40C2×Dic38—21no—
41C2×Dic38—21no—
42M16×C19—21no—
43M16×C19—21no—
44M16×C19—21no—
45M16×C19D412yes—
46C2×C8×C19—21no—
47C2×C8×C19—21no—
48Dic19⋊C4—24no—
49Dic19⋊C4—24no—
50C4×Dic19D411yescharacteristic
51C4×Dic19D412yes—
52C4×Dic19D411yescharacteristic
53#64520—21no—
54#64520—21no—
55#64520—21no—
56#64520D412yes—
57C2×C19⋊C8—21no—
58C2×C19⋊C8—21no—
59C23×C19C22×C411yescharacteristic
60Q8×C19—41no—
61Q8×C19—41no—
62Q8×C19—41no—
63Q8×C19—41no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19C2×D411yescharacteristic
68C2×C4×C19C2×D411yescharacteristic
69C2×C4×C19C2×D411yescharacteristic
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19#4111yescharacteristic
72C2×C4×C19#4111yescharacteristic
73C2×Dic19—24no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19C22⋊C412yes—
78C2×Dic19C22⋊C412yes—
79Dic38—41no—
80Dic38—41no—
81Dic38—41no—
82Dic38—41no—
83C8×C19—22no—
84C8×C19—41no—
85C19⋊C8—22no—
86C19⋊C8—41no—
87#1966—191nomaximal, Sylow
88C22×C19—22no—
89C22×C19C2×C22⋊C411yescharacteristic
90C22×C19C4×D411yescharacteristic
91C22×C19C4×D411yescharacteristic
92C4×C19—42no—
93C4×C19#12111yescharacteristic
94C4×C19#12111yescharacteristic
95C4×C19#12411yescharacteristic
96C4×C19#12711yescharacteristic
97Dic19—22no—
98Dic19—42no—
99Dic19#10114yescomplemented
100C2×C4⋊Q8—191no—
101#423—191no—
102C2×#101—191no—
103C2×#101—191no—
104C2×#101—191no—
105C2×#101D1911yescharacteristic
106C4×M16—191no—
107C2×C19—21no—
108C2×C19—21no—
109C2×C19#39011yescharacteristic
110C2×C19C2×#10112yes—
111C22×Q8—191no—
112C22×Q8C2×D1911yescharacteristic
113C2×M16—191no—
114C2×M16—191no—
115C2×M16C2×D1911yescharacteristic
116C2×M16C2×D1911yescharacteristic
117C4⋊Q8—381no—
118C4⋊Q8—381no—
119C4⋊Q8—382no—
120C2×C4⋊C4—194no—
121C2×C42—191no—
122C4⋊C8—382no—
123#101—22no—
124#101—382no—
125#101—382no—
126#101—382no—
127#97—381no—
128C4×C8—381no—
129C19#196611yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—381no—
137C2×Q8—381no—
138C2×Q8—381no—
139C2×Q8—381no—
140C2×Q8—381no—
141C2×Q8—381no—
142C22×C4—192no—
143C22×C4—192no—
144C22×C4C4×D1912yes—
145C22×C4C22×D1911yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—192no—
150M16—381no—
151M16—381no—
152M16—381no—
153M16C22⋊D1912yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—381no—
157C2×C8—381no—
158C4⋊C4—384no—
159C4⋊C4—384no—
160C42—191no—
161C42—191no—
162C42—192no—
163C23C2×C4×D1911yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—761no—
169Q8—761no—
170Q8—761no—
171Q8—761no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—192no—
176C2×C4—192no—
177C2×C4—384no—
178C2×C4—382no—
179C2×C4—382no—
180C2×C4—382no—
181C2×C4#6454111yescharacteristic
182C2×C4D4×D1911yescharacteristic
183C2×C4D4×D1911yescharacteristic
184C2×C4D4×D1911yescharacteristic
185C2×C4#6454311yescharacteristic
186C2×C4C2×C22⋊D1911yescharacteristic
187C8—22no—
188C8—41no—
189C8—382no—
190C8—761no—
191C22—22no—
192C22C22⋊C4×D1911yescharacteristic
193C22(C22⋊D19)⋊C411yescharacteristic
194C22C4×C22⋊D1911yescharacteristic
195C4—42no—
196C4—194no—
197C4—382no—
198C4—762no—
199C4#1059733011yescharacteristic
200C4#1059733111yescharacteristic
201C4#1059738511yescharacteristic
202C4#1059738611yescharacteristic
203C2—21no—
204C2—21no—
205C2#1192644411yescharacteristic
206C2#101×D1912yes—
subgroupG/H
centerC22C22⋊C4×D19
commutator, prime radicalC23×C19C22×C4
FrattiniC22×C4C22×D19
FittingC2×C19×#101C2
socleC22×C19C2×C22⋊C4
cosocleC22×C4×C19C23
hypercenterC2×#101D19
hypocenterC19#1966
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
99. Dic19#101semidirect
129. C19#1966semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
#119265672
C2×#105972932
C2×#105972812
M16×Dic192
C2×C19×#1012
#196619