Finite Group Databasebeta

← #14574841

Subgroups — #14574841

Order 2432.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#11927101C211yesmaximal, characteristic
2#11926954C212yesmaximal, complemented
3#11926914C212yesmaximal, complemented
4#11926879C212yesmaximal
5#11926874C212yesmaximal
6#11926848C214yesmaximal, complemented
7#11926601C211yesmaximal, characteristic
8C2×C19×#125C211yesmaximal, characteristic
9C19×#125—21no—
10C19×#125—21no—
11C19×#125C2212yes—
12C19×#125C2212yes—
13C2×C4⋊C4×C19—21no—
14C2×C4⋊C4×C19—21no—
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C42×C19C2211yescharacteristic
18#10597372—21no—
19#10597370—21no—
20#10597370C2212yes—
21#10597316—21no—
22#10597315C2211yescharacteristic
23#10597315C2211yescharacteristic
24C4×Dic38—21no—
25C4×Dic38C2212yes—
26C22⋊(C19⋊C8)C2212yes—
27#10597267C2214yes—
28#10597267C2214yes—
29#10597265C2214yes—
30#10597264C2214yes—
31C4⋊(C19⋊C8)C2212yes—
32#10597260C2212yes—
33C22×C4×C19—21no—
34C22×C4×C19—21no—
35C22×C4×C19D411yescharacteristic
36C22×C4×C19D411yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C2×Dic38—21no—
39C2×Dic38C2312yes—
40C4⋊C4×C19—22no—
41C4⋊C4×C19—22no—
42C4⋊C4×C19—22no—
43C4⋊C4×C19—22no—
44C4⋊C4×C19—21no—
45C4⋊C4×C19—21no—
46C4⋊C4×C19C2312yes—
47C4⋊C4×C19C2312yes—
48C42×C19D411yescharacteristic
49C42×C19D411yescharacteristic
50C42×C19C2311yescharacteristic
51C42×C19C2311yescharacteristic
52C22⋊Dic19—22no—
53C4⋊Dic19—21no—
54C4⋊Dic19—21no—
55C4⋊Dic19—21no—
56C4⋊Dic19C2312yes—
57Dic19⋊C4—22no—
58Dic19⋊C4—22no—
59C4×Dic19—22no—
60C2×C19⋊C8C2314yes—
61C23×C19C2×D411yescharacteristic
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—41no—
67C2×C4×C19—42no—
68C2×C4×C19—42no—
69C2×C4×C19C2×D411yescharacteristic
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19C2×D411yescharacteristic
74C2×C4×C19C2411yescharacteristic
75C2×Dic19—22no—
76C2×Dic19—22no—
77Dic38—24no—
78Dic38—42no—
79C19⋊C8—24no—
80#3236—191nomaximal, Sylow
81C22×C19—21no—
82C22×C19—21no—
83C22×C19#13712yes—
84C22×C19C22×D411yescharacteristic
85C4×C19—21no—
86C4×C19—21no—
87C4×C19—21no—
88C4×C19—21no—
89C4×C19—21no—
90C4×C19—42no—
91C4×C19—42no—
92C4×C192−1+412yes—
93Dic19—42no—
94Dic19—42no—
95#533—191no—
96C2×#125D1911yescharacteristic
97#501—192no—
98#491—192no—
99#484—192no—
100#483—192no—
101#479—194no—
102#432—191no—
103C2×C19—22no—
104C2×C19#53611yescharacteristic
105C2×C19C2×#13711yescharacteristic
106C2×C19#57511yescharacteristic
107C4⋊Q8—191no—
108C4⋊Q8—191no—
109#125—21no—
110#125—21no—
111#125—381no—
112#125C2×D1912yes—
113#125C2×D1912yes—
114C22⋊Q8—192no—
115C22⋊Q8—381no—
116C4×Q8—192no—
117C4×Q8—381no—
118#117—381no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4C2×D1911yescharacteristic
122C2×C4⋊C4C2×D1911yescharacteristic
123C2×C42C2×D1911yescharacteristic
124#107—194no—
125#106—194no—
126C4⋊C8—192no—
127#103—194no—
128#103—194no—
129C22⋊C8—192no—
130#97—192no—
131C19#323611yescharacteristic, complemented, Sylow
132C2×Q8—192no—
133C2×Q8—381no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D1911yescharacteristic
137C22×C4C22⋊D1911yescharacteristic
138C22×C4C22×D1911yescharacteristic
139C2×C8—194no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—192no—
147C4⋊C4—382no—
148C4⋊C4—382no—
149C4⋊C4—381no—
150C4⋊C4—381no—
151C4⋊C4—381no—
152C4⋊C4C22×D1912yes—
153C4⋊C4C22×D1912yes—
154C22⋊C4—382no—
155C42—382no—
156C42C22⋊D1911yescharacteristic
157C42C22⋊D1911yescharacteristic
158C42C22×D1911yescharacteristic
159C42C22×D1911yescharacteristic
160C23C2×C22⋊D1911yescharacteristic
161Q8—384no—
162Q8—762no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—382no—
171C2×C4—382no—
172C2×C4C2×C22⋊D1911yescharacteristic
173C2×C4C2×C22⋊D1911yescharacteristic
174C2×C4C2×C22⋊D1911yescharacteristic
175C2×C4C2×C22⋊D1911yescharacteristic
176C2×C4C2×C22⋊D1911yescharacteristic
177C2×C4C23×D1911yescharacteristic
178C8—384no—
179C22—21no—
180C22—21no—
181C22#1059739712yes—
182C22C22×C22⋊D1911yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—762no—
191C4—762no—
192C4#1059743312yes—
193C2—22no—
194C2#1192711811yescharacteristic
195C2C2×#1059739711yescharacteristic
196C2#1192734211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#125C2
socleC22×C19C22×D4
prime radicalC23×C19C2×D4
hypercenterC2×#125D19
hypocenterC19#3236
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #11926954C2semidirect
3. #11926914C2semidirect
6. #11926848C2semidirect
131. C19#3236semidirect

Maximal subgroups

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

subgroupindex
#119271012
#119269542
#119269142
#119268792
#119268742
#119268482
#119266012
C2×C19×#1252
#323619