Finite Group Databasebeta

← #14571906

Subgroups — #14571906

Order 2432.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#11926486C212yesmaximal
2#11926485C212yesmaximal
3#11926482C212yesmaximal
4#11926464C211yesmaximal, characteristic
5#11926464C212yesmaximal
6#11926463C212yesmaximal
7#11926409C211yesmaximal, characteristic
8#11926408C212yesmaximal
9C19×#395C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2212yes—
14C2×C4⋊Dic19C2211yescharacteristic
15C2×Dic19⋊C4C2212yes—
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×C4×Dic19C2211yescharacteristic
20C19×#95C2212yes—
21C19×#95C2211yescharacteristic
22C19⋊#95C2212yes—
23C19⋊#95C2212yes—
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C2×Q8×C19—42no—
32C2×Q8×C19—41no—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C2×Dic38—42no—
43C2×Dic38—41no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—42no—
46C4⋊Dic19—41no—
47Dic19⋊C4—42no—
48Dic19⋊C4—42no—
49Dic19⋊C4—42no—
50Dic19⋊C4—42no—
51C4×Dic19Q814yescomplemented
52C23×C19C2411yescharacteristic
53Q8×C19—44no—
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—22no—
59C2×C4×C19—22no—
60C2×C4×C19—22no—
61C2×C4×C19—21no—
62C2×C4×C19—22no—
63C2×C4×C19—21no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19C2×Q812yes—
67C2×Dic19—22no—
68C2×Dic19—22no—
69C2×Dic19—22no—
70C2×Dic19—22no—
71C2×Dic19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—24no—
76C2×Dic19—22no—
77C2×Dic19C2×Q814yes—
78Dic38—44no—
79#2844—191nomaximal, Sylow
80C22×C19C22×Q811yescharacteristic
81C22×C19H(5,𝔽2)12yes—
82C22×C19H(5,𝔽2)11yescharacteristic
83C22×C192−1+412yes—
84C22×C192−1+411yescharacteristic
85C4×C19—22no—
86C4×C19—41no—
87C4×C19—42no—
88C4×C19—41no—
89C4×C19—42no—
90Dic19—24no—
91Dic19—42no—
92Dic19—42no—
93Dic19—42no—
94#400—192no—
95#400—192no—
96#400—192no—
97#395—192no—
98#395—192no—
99#395—191no—
100#395D1911yescharacteristic
101#382—191no—
102#382—192no—
103C2×C19#54412yes—
104C2×C19#54411yescharacteristic
105C2×C19H(3,𝔽4)11yescharacteristic
106C2×C19#56311yescharacteristic
107C2×C19#56312yes—
108C22×Q8—191no—
109C22×Q8C2×D1911yescharacteristic
110C2×C4⋊C4—192no—
111C2×C4⋊C4—192no—
112C2×C4⋊C4—191no—
113C2×C4⋊C4—192no—
114C2×C4⋊C4—192no—
115C2×C4⋊C4C2×D1911yescharacteristic
116C2×C4⋊C4C2×D1912yes—
117C2×C42—191no—
118#95—192no—
119#95—192no—
120#95—192no—
121#95—192no—
122#95—192no—
123#95—191no—
124#95—192no—
125#95—192no—
126#95—192no—
127#95C2×D1912yes—
128#95C2×D1911yescharacteristic
129C19#284411yescharacteristic, complemented, Sylow
130C2×Q8—42no—
131C2×Q8—41no—
132C2×Q8—762no—
133C2×Q8—761no—
134C22×C4—192no—
135C22×C4—192no—
136C22×C4—192no—
137C22×C4—192no—
138C22×C4C22×D1912yes—
139C22×C4C22×D1911yescharacteristic
140C22×C4C22×D1911yescharacteristic
141C22×C4C22×D1912yes—
142C22×C4C22×D1911yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—762no—
146C4⋊C4—762no—
147C4⋊C4—762no—
148C4⋊C4—762no—
149C4⋊C4—761no—
150C42—194no—
151C23C23×D1911yescharacteristic
152Q8—44no—
153Q8—764no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—194no—
167C2×C4—382no—
168C2×C4—382no—
169C2×C4—382no—
170C2×C4—382no—
171C2×C4—382no—
172C2×C4—382no—
173C2×C4—382no—
174C2×C4—384no—
175C2×C4—382no—
176C2×C4—382no—
177C2×C4Q8×D1912yes—
178C22#1059743012yes—
179C22#1059743011yescharacteristic
180C22C2×Q8×D1911yescharacteristic
181C22#1059743312yes—
182C22#1059743611yescharacteristic
183C4—22no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—42no—
188C4—384no—
189C4—762no—
190C4—762no—
191C4—762no—
192C2#1192717112yes—
193C2#1192717311yescharacteristic
194C2#1192728711yescharacteristic
195C2#1192729311yescharacteristic
196C2#1192729512yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#395C2
hypercenter#395D19
hypocenterC19#2844
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic19Q8semidirect
129. C19#2844semidirect

Maximal subgroups

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

subgroupindex
#119264862
#119264852
#119264822
#119264642
#119264632
#119264092
#119264082
C19×#3952
#284419