Finite Group Databasebeta

← #14571897

Subgroups — #14571897

Order 2432.

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

normal subgroups only

This group has 396 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#11926485C212yesmaximal, complemented
2#11926477C212yesmaximal, complemented
3#11926474C212yesmaximal, complemented
4#11926467C212yesmaximal
5#11926464C212yesmaximal, complemented
6#11926456C211yesmaximal, characteristic
7#11926405C211yesmaximal, characteristic
8#11926402C212yesmaximal
9C19×#399C211yesmaximal, characteristic
10C23×Dic19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2211yescharacteristic
18C2×C4⋊Dic19C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C19×#95C2211yescharacteristic
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C24×C19C2311yescharacteristic
32C22×C4×C19C2311yescharacteristic
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×Dic19—41no—
37C22×Dic19—41no—
38C22×Dic19Q814yescomplemented
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C2×Dic38—41no—
44C2×Dic38—42no—
45C4⋊C4×C19—41no—
46C4⋊C4×C19—42no—
47C22⋊C4×C19—42no—
48C22⋊C4×C19—41no—
49C22⋊Dic19—41no—
50C22⋊Dic19—42no—
51C4⋊Dic19—42no—
52Dic19⋊C4—42no—
53Dic19⋊C4—42no—
54Dic19⋊C4—42no—
55Dic19⋊C4—42no—
56C23×C19—22no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19—22no—
60C23×C19C2×Q812yes—
61C23×C19C2411yescharacteristic
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—44no—
84C2×Dic19C2×Q814yes—
85Dic38—44no—
86#2841—191nomaximal, Sylow
87C22×C19—22no—
88C22×C19—24no—
89C22×C19—41no—
90C22×C19—42no—
91C22×C19—41no—
92C22×C19C22×Q811yescharacteristic
93C22×C19H(5,𝔽2)11yescharacteristic
94C22×C19H(5,𝔽2)12yes—
95C22×C19H(5,𝔽2)11yescharacteristic
96C22×C192−1+412yes—
97C4×C19—41no—
98C4×C19—42no—
99C4×C19—42no—
100C4×C19—41no—
101Dic19—24no—
102Dic19—42no—
103Dic19—42no—
104Dic19—42no—
105#400—192no—
106#399D1911yescharacteristic
107#398—192no—
108#398—192no—
109#396—192no—
110#395—192no—
111#393—191no—
112#381—191no—
113#380—192no—
114C2×C19—42no—
115C2×C19#54311yescharacteristic
116C2×C19#54412yes—
117C2×C19#56011yescharacteristic
118C2×C19#56212yes—
119C2×C19#56311yescharacteristic
120C22×Q8—191no—
121C23×C4—191no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—192no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4C2×D1912yes—
128C2×C4⋊C4C2×D1911yescharacteristic
129C2×C22⋊C4—192no—
130C2×C22⋊C4—191no—
131C2×C22⋊C4C2×D1912yes—
132C2×C22⋊C4C2×D1911yescharacteristic
133#95—192no—
134#95—192no—
135#95—192no—
136#95—192no—
137#95—191no—
138#95—192no—
139#95—192no—
140#95C2×D1911yescharacteristic
141C19#284111yescharacteristic, complemented, Sylow
142C24C22×D1911yescharacteristic
143C2×Q8—761no—
144C2×Q8—762no—
145C22×C4—192no—
146C22×C4—194no—
147C22×C4—192no—
148C22×C4—192no—
149C22×C4—192no—
150C22×C4—761no—
151C22×C4—761no—
152C22×C4C22×D1911yescharacteristic
153C22×C4C22×D1911yescharacteristic
154C22×C4C22×D1912yes—
155C22×C4C22×D1912yes—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—762no—
159C4⋊C4—762no—
160C4⋊C4—762no—
161C4⋊C4—762no—
162C4⋊C4—762no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—762no—
166C22⋊C4—761no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D1912yes—
172C23C23×D1911yescharacteristic
173Q8—764no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—194no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—764no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22#1059743011yescharacteristic
203C22#1059743012yes—
204C22C2×Q8×D1911yescharacteristic
205C22#1059743511yescharacteristic
206C22#1059743612yes—
207C4—41no—
208C4—41no—
209C4—42no—
210C4—42no—
211C4—384no—
212C4—762no—
213C4—762no—
214C4—762no—
215C2—42no—
216C2#1192716911yescharacteristic
217C2#1192717312yes—
218C2#1192728111yescharacteristic
219C2#1192729112yes—
220C2#1192729711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC24×C19C23
hypercenter#399D19
hypocenterC19#2841
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #11926485C2semidirect
2. #11926477C2semidirect
3. #11926474C2semidirect
5. #11926464C2semidirect
38. C22×Dic19Q8semidirect
141. C19#2841semidirect

Maximal subgroups

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

subgroupindex
#119264852
#119264772
#119264742
#119264672
#119264642
#119264562
#119264052
#119264022
C19×#3992
#284119