Finite Group Databasebeta

← #14564448

Subgroups — #14564448

Order 2432.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10597393C211yesmaximal, characteristic
2C2×#10597292C211yesmaximal, characteristic, complemented
3C2×#10597278C211yesmaximal, characteristic
4C2×#10597266C211yesmaximal, characteristic
5C2×#10597272C211yesmaximal, characteristic, complemented
6#11926413C211yesmaximal, characteristic, complemented
7C2×C19×#103C211yesmaximal, characteristic, complemented
8C22×Q8×C19C2211yescharacteristic
9C22×D76C2211yescharacteristic
10C22×C8×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12#10597393—22no—
13#10597393C414yescomplemented
14C2×(C2×D19)⋊C4—22no—
15C2×C4⋊Dic19C2211yescharacteristic
16C2×Dic19⋊C4—22no—
17C2×C4×Dic19C2211yescharacteristic
18C22×C19⋊C8C2211yescharacteristic
19C19×#103—22no—
20#10597292—22no—
21#10597278—22no—
22#10597272—22no—
23#10597266—22no—
24C23×D19—21no—
25C2×Q8×C19—21no—
26C2×Q8×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19—21no—
29C2×Q8×C19—21no—
30C2×Q8×C19C2×C412yes—
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19C2311yescharacteristic
34C22×Dic19—21no—
35C22×Dic19D412yes—
36C2×D76—21no—
37C2×D76—21no—
38C2×D76—21no—
39C2×D76—21no—
40C2×D76—21no—
41C2×D76C2×C412yes—
42C2×C8×C19—21no—
43C2×C8×C19—21no—
44C2×C8×C19D412yes—
45C4⋊C4×C19—21no—
46C4⋊C4×C19—21no—
47(C2×D19)⋊C4—28no—
48C4⋊Dic19—21no—
49C4⋊Dic19—21no—
50Dic19⋊C4—44no—
51C4×Dic19C2×C412yes—
52C4×Dic19D412yes—
53C2×C19⋊C8—21no—
54C2×C19⋊C8—21no—
55C2×C19⋊C8D412yes—
56C23×C19C2×D411yescharacteristic
57C22×D19—22no—
58C22×D19—41no—
59C22×D19—41no—
60C22×D19—42no—
61C22×D19—42no—
62Q8×C19—22no—
63Q8×C19—22no—
64Q8×C19—41no—
65Q8×C19—41no—
66C2×C4×C19—22no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—42no—
71C2×C4×C19C22×C411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19C2×D411yescharacteristic
74C2×C4×C19C2×D411yescharacteristic
75C2×C4×C19#4111yescharacteristic
76C2×C4×C19#4111yescharacteristic
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—41no—
80C2×Dic19—42no—
81C2×Dic19C22⋊C414yes—
82D76—22no—
83D76—22no—
84D76—41no—
85D76—41no—
86C8×C19—22no—
87C19⋊C8—22no—
88#1959—191nomaximal, Sylow
89C22×C19C2×C22⋊C411yescharacteristic
90C22×C19#12411yescharacteristic
91C22×C19#12711yescharacteristic
92C22×C19AGL(1,ℤ/8)12yes—
93C22×C19#13712yes—
94C2×D19—42no—
95C2×D19—44no—
96C2×D19—82no—
97C2×D19—81no—
98C2×D19—81no—
99C4×C19—42no—
100C4×C19—81no—
101C4×C19C4×D411yescharacteristic
102C4×C19C4×D411yescharacteristic
103C4×C19#12111yescharacteristic
104C4×C19#12111yescharacteristic
105Dic19—24no—
106Dic19—81no—
107C2×#124—191no—
108C2×#103—191no—
109C2×#103D1911yescharacteristic, complemented
110C2×#102—191no—
111C2×#102—191no—
112C2×#97—191no—
113#384—191no—
114C2×C19#39011yescharacteristic
115C2×C19#41712yes—
116C2×C19#48912yes—
117C2×C19#49611yescharacteristic
118C2×C19#49711yescharacteristic
119D19—82no—
120C22×Q8C2×D1911yescharacteristic
121C22×D4—191no—
122C22×C8—191no—
123C22×C8C2×D1911yescharacteristic
124#124—194no—
125#124—382no—
126C2×C4⋊C4—191no—
127C2×C4⋊C4—382no—
128C2×C4⋊C4C2×D1911yescharacteristic
129C2×C22⋊C4—382no—
130C2×C42—191no—
131#103—22no—
132#103—382no—
133#102—382no—
134#102—382no—
135#97—382no—
136C19#195911yescharacteristic, complemented, Sylow
137C24—381no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C4×D1912yes—
144C2×D4—192no—
145C2×D4—381no—
146C2×D4—381no—
147C2×D4—381no—
148C2×D4—381no—
149C2×D4—381no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—192no—
153C22×C4—381no—
154C22×C4C22×D1911yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—192no—
158C2×C8—381no—
159C2×C8—381no—
160C2×C8C22⋊D1912yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—381no—
164C4⋊C4—381no—
165C4⋊C4—764no—
166C22⋊C4—388no—
167C42—192no—
168C42—192no—
169C23—382no—
170C23—761no—
171C23—761no—
172C23—762no—
173C23—762no—
174C23D4×D1911yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—382no—
180D4—382no—
181D4—761no—
182D4—761no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—194no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—761no—
192C2×C4—762no—
193C2×C4C2×C4×D1911yescharacteristic
194C2×C4#6454111yescharacteristic
195C2×C4D4×D1911yescharacteristic
196C2×C4D4×D1911yescharacteristic
197C2×C4#6454311yescharacteristic
198C2×C4C2×C22⋊D1911yescharacteristic
199C8—22no—
200C8—382no—
201C22—764no—
202C22—762no—
203C22—1522no—
204C22—1521no—
205C22—1521no—
206C22C22⋊C4×D1911yescharacteristic
207C22#1059733111yescharacteristic
208C22#1059736012yes—
209C22#1059736412yes—
210C22#1059738611yescharacteristic
211C4—42no—
212C4—81no—
213C4—384no—
214C4—1521no—
215C4(C22⋊D19)⋊C411yescharacteristic
216C4#1059733011yescharacteristic
217C4C4×C22⋊D1911yescharacteristic
218C4#1059738511yescharacteristic
219C2—1522no—
220C2#1192644411yescharacteristic
221C2#1192654412yes—
222C2#1192690512yes—
223C2#1192693011yescharacteristic
224C2#1192693711yescharacteristic
subgroupG/H
centerC23D4×D19
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC2×C19×#103C2
socleC23×C19C2×D4
prime radicalC22×D76C22
cosocleC22×C4×C19C23
hypercenterC2×#103D19
hypocenterC19#1959
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#10597292C2semidirect
5. C2×#10597272C2semidirect
6. #11926413C2semidirect
7. C2×C19×#103C2semidirect
13. #10597393C4semidirect
109. C2×#103D19semidirect
136. C19#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#105973932
C2×#105972922
C2×#105972782
C2×#105972662
C2×#105972722
#119264132
C2×C19×#1032
#195919