Finite Group Databasebeta

← #14569125

Subgroups — #14569125

Order 2432.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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#11926483C211yesmaximal, characteristic, complemented
2#11926461C212yesmaximal
3#11926445C211yesmaximal, characteristic
4#11926436C212yesmaximal, complemented
5#11926436C212yesmaximal, complemented
6#11926436C212yesmaximal, complemented
7#11926434C212yesmaximal, complemented
8C4⋊C4×Dic19C212yesmaximal, complemented
9C19×#398C211yesmaximal, characteristic, complemented
10C22×D76C2211yescharacteristic
11C2×C4⋊C4×C19C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×(C2×D19)⋊C4C2212yes—
15C2×(C2×D19)⋊C4C2212yes—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×C4⋊Dic19C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×C4×Dic19C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2212yes—
25C19×#95C2211yescharacteristic
26C19×#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C23×D19C2312yes—
32C22×C4×C19C2311yescharacteristic
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C2×D76—22no—
41C2×D76—41no—
42C2×D76—41no—
43C4⋊C4×C19—24no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—41no—
46(C2×D19)⋊C4—24no—
47(C2×D19)⋊C4—24no—
48(C2×D19)⋊C4—24no—
49(C2×D19)⋊C4—24no—
50(C2×D19)⋊C4—42no—
51(C2×D19)⋊C4—42no—
52C4⋊Dic19—24no—
53C4⋊Dic19—41no—
54C4×Dic19—24no—
55C4×Dic19—41no—
56C4×Dic19—42no—
57C23×C19C2411yescharacteristic
58C22×D19—22no—
59C22×D19—22no—
60C22×D19—22no—
61C22×D19—22no—
62C22×D19—22no—
63C22×D19—22no—
64C22×D19—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×C4×C19—22no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19#4112yes—
77C2×C4×C19#4114yes—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19#4114yes—
87D76—44no—
88#2593—191nomaximal, Sylow
89C22×C19C2×#4111yescharacteristic
90C22×C19C2×#4112yes—
91C22×C19C2×#4112yes—
92C22×C19H(5,𝔽2)11yescharacteristic
93C22×C19H(5,𝔽2)11yescharacteristic
94C2×D19—42no—
95C2×D19—42no—
96C2×D19—42no—
97C2×D19—42no—
98C2×D19—42no—
99C2×D19—42no—
100C2×D19—42no—
101C4×C19—24no—
102C4×C19—22no—
103C4×C19—42no—
104C4×C19—41no—
105C4×C19—41no—
106Dic19—24no—
107Dic19—42no—
108Dic19—42no—
109#400—191no—
110#398D1911yescharacteristic, complemented
111#394—192no—
112#390—191no—
113#388—192no—
114#388—192no—
115#388—192no—
116#388—192no—
117C4×C4⋊C4—192no—
118C2×C19#52912yes—
119C2×C19#53811yescharacteristic
120C2×C19#55312yes—
121C2×C19#55511yescharacteristic
122C2×C19#55911yescharacteristic
123D19—82no—
124C22×D4—191no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—191no—
127C2×C4⋊C4C2×D1912yes—
128C2×C4⋊C4C2×D1911yescharacteristic
129C2×C4⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4—192no—
131C2×C22⋊C4—192no—
132C2×C22⋊C4—192no—
133C2×C22⋊C4—192no—
134C2×C22⋊C4—192no—
135C2×C22⋊C4—192no—
136C2×C42—192no—
137C2×C42—191no—
138C2×C42—192no—
139#95—192no—
140#95—192no—
141#95—192no—
142#95—191no—
143#95C2×D1911yescharacteristic
144#95C2×D1912yes—
145C19#259311yescharacteristic, complemented, Sylow
146C24—192no—
147C2×D4—382no—
148C2×D4—761no—
149C2×D4—761no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4C22×D1911yescharacteristic
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1912yes—
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C4⋊C4—24no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—384no—
162C4⋊C4—761no—
163C22⋊C4—384no—
164C22⋊C4—384no—
165C22⋊C4—384no—
166C22⋊C4—384no—
167C22⋊C4—762no—
168C22⋊C4—762no—
169C42—384no—
170C42—761no—
171C42—762no—
172C23—382no—
173C23—382no—
174C23—382no—
175C23—382no—
176C23—382no—
177C23—382no—
178C23—382no—
179C23C23×D1911yescharacteristic
180D4—764no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—194no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4#6454312yes—
202C2×C4#6454514yes—
203C22—762no—
204C22—762no—
205C22—762no—
206C22—762no—
207C22—762no—
208C22—762no—
209C22—762no—
210C22C2×#6454311yescharacteristic
211C22#1059743011yescharacteristic
212C22C2×#6454512yes—
213C22#41×D1912yes—
214C22#1059743511yescharacteristic
215C4—24no—
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—384no—
221C4—762no—
222C4—762no—
223C2—1522no—
224C2#1192708012yes—
225C2#1192713111yescharacteristic
226C2#1192724712yes—
227C2#1192726011yescharacteristic
228C2#1192727811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#398C2
prime radicalC22×D76C22
hypercenter#398D19
hypocenterC19#2593
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #11926483C2semidirect
4. #11926436C2semidirect
5. #11926436C2semidirect
6. #11926436C2semidirect
7. #11926434C2semidirect
8. C4⋊C4×Dic19C2semidirect
9. C19×#398C2semidirect
110. #398D19semidirect
145. C19#2593semidirect

Maximal subgroups

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

subgroupindex
#119264832
#119264612
#119264452
#119264362
#119264342
C4⋊C4×Dic192
C19×#3982
#259319