Finite Group Databasebeta

← #14564540

Subgroups — #14564540

Order 2432.

296 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10597276C211yesmaximal, characteristic, complemented
2#11926553C211yesmaximal, characteristic, complemented
3#11926549C211yesmaximal, characteristic
4C2×#10597293C211yesmaximal, characteristic, complemented
5C2×#10597290C211yesmaximal, characteristic
6#11926499C211yesmaximal, characteristic, complemented
7C22×SD16×C19C211yesmaximal, characteristic
8C22×Q8×C19C2211yescharacteristic
9C22×D4×C19C2211yescharacteristic
10C2×SD16×C19—21no—
11C2×SD16×C19—21no—
12C2×SD16×C19—22no—
13C2×SD16×C19C414yescomplemented
14C22×C8×C19C2211yescharacteristic
15#10597372C2211yescharacteristic
16C2×#64520C2211yescharacteristic
17C2×#64520C2211yescharacteristic
18C2×#64520C2211yescharacteristic
19#10597293—22no—
20#10597292—22no—
21#10597290—22no—
22#10597289—22no—
23#10597276—22no—
24#10597272—21no—
25C8×Dic19—21no—
26C24×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19—21no—
29C2×Q8×C19—21no—
30C2×Q8×C19—21no—
31C2×Q8×C19—21no—
32C2×Q8×C19C2×C412yes—
33C2×D4×C19—21no—
34C2×D4×C19—21no—
35C2×D4×C19—21no—
36C2×D4×C19—21no—
37C2×D4×C19—21no—
38C2×D4×C19C2×C412yes—
39C22×C4×C19—21no—
40C22×C4×C19C2311yescharacteristic
41SD16×C19—24no—
42SD16×C19—24no—
43C2×C8×C19C2×C412yes—
44C2×C8×C19D411yescharacteristic
45C2×C8×C19D411yescharacteristic
46C2×C8×C19D412yes—
47C22⋊Dic19—21no—
48C4⋊Dic19D412yes—
49C4×Dic19—21no—
50#64520—21no—
51#64520—21no—
52#64520—21no—
53#64520—21no—
54#64520—21no—
55#64520D412yes—
56C2×C19⋊C8—21no—
57C2×C19⋊C8—21no—
58C2×C19⋊C8—21no—
59C23×C19—22no—
60C23×C19—41no—
61C23×C19—41no—
62C23×C19—82no—
63C23×C19#4111yescharacteristic
64Q8×C19—22no—
65Q8×C19—22no—
66Q8×C19—41no—
67Q8×C19—41no—
68D4×C19—22no—
69D4×C19—22no—
70D4×C19—41no—
71D4×C19—41no—
72C2×C4×C19—22no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19C22×C411yescharacteristic
76C2×C4×C19C2×D411yescharacteristic
77C2×C4×C19C2×D411yescharacteristic
78C2×C4×C19C2×D411yescharacteristic
79C2×C4×C19C2×D411yescharacteristic
80C2×C4×C19#4111yescharacteristic
81C2×Dic19—22no—
82C8×C19C22⋊C412yes—
83C8×C19C22⋊C412yes—
84C19⋊C8—22no—
85C19⋊C8—41no—
86C19⋊C8—41no—
87#1977—191nomaximal, Sylow
88C22×C19—22no—
89C22×C19—42no—
90C22×C19—82no—
91C22×C19—82no—
92C22×C19—82no—
93C22×C19C4×D411yescharacteristic
94C22×C19#12111yescharacteristic
95C22×C19#12411yescharacteristic
96C4×C19—42no—
97C4×C19C2×C22⋊C411yescharacteristic
98C4×C19C4×D411yescharacteristic
99C4×C19#12111yescharacteristic
100C4×C19#12711yescharacteristic
101Dic19—42no—
102C22×SD16D1911yescharacteristic
103C2×#108—191no—
104#419—191no—
105#418—191no—
106C2×#101—191no—
107C2×#100—191no—
108#405—191no—
109C2×C19—21no—
110C2×C19—21no—
111C2×C19—82no—
112C2×C19#39011yescharacteristic
113C2×C19#47112yes—
114C22×Q8C2×D1911yescharacteristic
115C22×D4C2×D1911yescharacteristic
116C2×SD16—21no—
117C2×SD16—21no—
118C2×SD16—22no—
119C2×SD16Dic1914yescomplemented
120C2×M16—191no—
121C2×M16—191no—
122C2×M16—191no—
123C22×C8C2×D1911yescharacteristic
124#117—191no—
125#108—382no—
126#103—382no—
127#102—382no—
128#101—382no—
129#100—382no—
130#97—381no—
131C4×C8—381no—
132C19#197711yescharacteristic, complemented, Sylow
133C24—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C2×Dic1912yes—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C2×Dic1912yes—
146C22×C4—21no—
147C22×C4C22×D1911yescharacteristic
148SD16—24no—
149SD16—24no—
150M16—192no—
151M16—381no—
152M16—381no—
153M16—381no—
154M16—381no—
155M16—381no—
156C2×C8—381no—
157C2×C8—381no—
158C2×C8—381no—
159C2×C8C2×Dic1912yes—
160C2×C8C22⋊D1911yescharacteristic
161C2×C8C22⋊D1911yescharacteristic
162C2×C8C22⋊D1912yes—
163C4⋊C4—192no—
164C22⋊C4—381no—
165C42—381no—
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#6454311yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—382no—
183C2×C4D4×D1911yescharacteristic
184C2×C4D4×D1911yescharacteristic
185C2×C4#6454311yescharacteristic
186C2×C4C22×Dic1911yescharacteristic
187C2×C4C2×C22⋊D1911yescharacteristic
188C2×C4C2×C22⋊D1911yescharacteristic
189C8—382no—
190C8—761no—
191C8—761no—
192C8C22⋊Dic1912yes—
193C8C22⋊Dic1912yes—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22D4×Dic1911yescharacteristic
200C22#1059738211yescharacteristic
201C22#1059738411yescharacteristic
202C4—42no—
203C4—762no—
204C4D4×Dic1911yescharacteristic
205C4#1059738411yescharacteristic
206C4#1059738611yescharacteristic
207C4C2×C22⋊Dic1911yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1192644711yescharacteristic
212C2#1192680412yes—
subgroupG/H
centerC22#10597384
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC22×SD16×C19C2
socleC22×C19#121
prime radicalC22×D4×C19C22
cosocleC22×C4×C19C23
hypercenterC22×SD16D19
hypocenterC19#1977
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10597276C2semidirect
2. #11926553C2semidirect
4. C2×#10597293C2semidirect
6. #11926499C2semidirect
13. C2×SD16×C19C4semidirect
119. C2×SD16Dic19semidirect
132. C19#1977semidirect

Maximal subgroups

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

subgroupindex
C2×#105972762
#119265532
#119265492
C2×#105972932
C2×#105972902
#119264992
C22×SD16×C192
#197719