Finite Group Databasebeta

← #14566388

Subgroups — #14566388

Order 2432.

484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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×#10597370C211yesmaximal, characteristic
2#11926448C212yesmaximal, complemented
3#11926438C212yesmaximal
4#11926432C212yesmaximal
5#11926427C212yesmaximal, complemented
6#11926426C212yesmaximal, complemented
7#11926395C212yesmaximal, complemented
8C4×C22⋊Dic19C211yesmaximal, characteristic
9C19×#381C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×C22⋊C4×C19C2211yescharacteristic
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊Dic19C2212yes—
15C2×C22⋊Dic19C2212yes—
16C2×C4⋊Dic19C2211yescharacteristic
17#10597370C418yescomplemented
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×C4×Dic19C2212yes—
22C2×C4×Dic19C2211yescharacteristic
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2212yes—
25C19×#95C2212yes—
26C19×#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19—41no—
34C22×C4×C19—41no—
35C22×C4×C19C2×C414yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×Dic38—41no—
45C2×Dic38—41no—
46C2×Dic38C2×C414yes—
47C22⋊C4×C19—41no—
48C22⋊C4×C19—41no—
49C22⋊Dic19—24no—
50C22⋊Dic19C2×C418yes—
51C4⋊Dic19C2×C414yes—
52Dic19⋊C4—24no—
53Dic19⋊C4—42no—
54Dic19⋊C4C2×C418yes—
55C4×Dic19—24no—
56C4×Dic19—41no—
57C4×Dic19—42no—
58C4×Dic19—41no—
59C23×C19—22no—
60C23×C19—21no—
61C23×C19—21no—
62C23×C19—22no—
63C23×C19C22×C412yes—
64C23×C19C2411yescharacteristic
65C2×C4×C19—21no—
66C2×C4×C19—21no—
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—22no—
74C2×C4×C19—22no—
75C2×C4×C19—44no—
76C2×C4×C19C22×C412yes—
77C2×C4×C19C22×C412yes—
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—22no—
87C2×Dic19C22×C414yes—
88C2×Dic19C22×C414yes—
89C2×Dic19#4114yes—
90Dic38—44no—
91#2332—191nomaximal, Sylow
92C22×C19—22no—
93C22×C19—22no—
94C22×C19—22no—
95C22×C19—42no—
96C22×C19—42no—
97C22×C19C23×C411yescharacteristic
98C22×C19C2×#4112yes—
99C22×C19H(5,𝔽2)11yescharacteristic
100C22×C19H(5,𝔽2)11yescharacteristic
101C22×C192−1+412yes—
102C4×C19—22no—
103C4×C19—22no—
104C4×C19—42no—
105C4×C19—42no—
106Dic19—24no—
107Dic19—24no—
108Dic19—24no—
109Dic19—42no—
110C2×C22⋊Q8—191no—
111#391—192no—
112#388—192no—
113#388—192no—
114#387—192no—
115#387—192no—
116#381D1911yescharacteristic
117C4×C4⋊C4—192no—
118C4×C22⋊C4—191no—
119C2×C19—42no—
120C2×C19C4×#4111yescharacteristic
121C2×C19#51811yescharacteristic
122C2×C19#51911yescharacteristic
123C2×C19#53912yes—
124C2×C19#54212yes—
125C22×Q8—191no—
126C23×C4C2×D1911yescharacteristic
127C22⋊Q8—198no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—191no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C22⋊C4—192no—
133C2×C22⋊C4—192no—
134C2×C22⋊C4C2×D1911yescharacteristic
135C2×C22⋊C4C2×D1911yescharacteristic
136C2×C42—192no—
137C2×C42—191no—
138C2×C42—191no—
139C2×C42—192no—
140#95—192no—
141#95—192no—
142#95—192no—
143#95—192no—
144#95—192no—
145#95C2×D1912yes—
146#95C2×D1912yes—
147C19#233211yescharacteristic, complemented, Sylow
148C24C22×D1911yescharacteristic
149C2×Q8—194no—
150C2×Q8—761no—
151C2×Q8—761no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—192no—
155C22×C4—192no—
156C22×C4—192no—
157C22×C4—192no—
158C22×C4C4×D1914yes—
159C22×C4C22×D1912yes—
160C22×C4C22×D1912yes—
161C22×C4C22×D1911yescharacteristic
162C22×C4C22×D1911yescharacteristic
163C4⋊C4—198no—
164C4⋊C4—194no—
165C4⋊C4—384no—
166C4⋊C4—762no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—198no—
170C22⋊C4—384no—
171C42—384no—
172C42—761no—
173C42—761no—
174C42—762no—
175C23—21no—
176C23—21no—
177C23—22no—
178C23—22no—
179C23C2×C4×D1912yes—
180C23C23×D1911yescharacteristic
181Q8—764no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—194no—
194C2×C4—194no—
195C2×C4—194no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4C2×C4×D1912yes—
206C2×C4C2×C4×D1912yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D1911yescharacteristic
213C22#1059743011yescharacteristic
214C22#1059743011yescharacteristic
215C22#41×D1912yes—
216C22#1059743612yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—42no—
221C4—384no—
222C4—384no—
223C4—384no—
224C4—762no—
225C2—42no—
226C2#1192701211yescharacteristic
227C2#1192701711yescharacteristic
228C2#1192702111yescharacteristic
229C2#1192713712yes—
230C2#1192716212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#381C2
socle, cosocleC23×C19C24
prime radicalC24×C19C23
hypercenter#381D19
hypocenterC19#2332
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #11926448C2semidirect
5. #11926427C2semidirect
6. #11926426C2semidirect
7. #11926395C2semidirect
17. #10597370C4semidirect
147. C19#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264482
#119264382
#119264322
#119264272
#119264262
#119263952
C4×C22⋊Dic192
C19×#3812
#233219