Finite Group Databasebeta

← #14564813

Subgroups — #14564813

Order 2432.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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#11927170C211yesmaximal, characteristic, complemented
2C2×#10597263C211yesmaximal, characteristic
3C2×#10597263C211yesmaximal, characteristic
4C2×#10597263C211yesmaximal, characteristic
5#11926311C211yesmaximal, characteristic, complemented
6#11926310C211yesmaximal, characteristic, complemented
7C19×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D19C2211yescharacteristic
9C2×C22⋊C4×C19C2211yescharacteristic
10C2×C22⋊C4×C19C2211yescharacteristic
11C2×C22⋊C4×C19C2211yescharacteristic
12C2×C22⋊Dic19C2211yescharacteristic
13C2×C22⋊Dic19C2211yescharacteristic
14C2×C22⋊Dic19C2211yescharacteristic
15#10597370—22no—
16#10597324—22no—
17#10597324—22no—
18#10597263—22no—
19#10597263—22no—
20#10597263—22no—
21C24×C19C2311yescharacteristic
22C23×D19Q811yescharacteristic, complemented
23C22×C4×C19—21no—
24C22×C4×C19—21no—
25C22×C4×C19—21no—
26C2×C22⋊D19—21no—
27C2×C22⋊D19—21no—
28C2×C22⋊D19—21no—
29C2×C22⋊D19—21no—
30C2×C22⋊D19—21no—
31C2×C22⋊D19—21no—
32C22×Dic19—21no—
33C22×Dic19—21no—
34C22×Dic19—21no—
35C22×Dic19Q811yescharacteristic, complemented
36C2×Dic38—22no—
37C22⋊C4×C19—21no—
38C22⋊C4×C19—21no—
39C22⋊C4×C19—21no—
40C22⋊C4×C19—21no—
41C22⋊C4×C19—21no—
42C22⋊C4×C19D412yes—
43C22⋊Dic19—21no—
44C22⋊Dic19—21no—
45C22⋊Dic19—21no—
46C22⋊Dic19—21no—
47C22⋊Dic19D412yes—
48C22⋊Dic19D412yes—
49C4⋊Dic19—22no—
50Dic19⋊C4—24no—
51C23×C19—81no—
52C23×C19C2×D411yescharacteristic
53C23×C19C2×D411yescharacteristic
54C23×C19C2×D411yescharacteristic
55C23×C19C2×Q811yescharacteristic
56C23×C19#4111yescharacteristic
57C23×C19#4111yescharacteristic
58C23×C19#4111yescharacteristic
59C22×D19—21no—
60C22×D19—21no—
61C22×D19—21no—
62C22×D19—81no—
63C2×C4×C19—22no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—81no—
67C2×C4×C19—81no—
68C2×C4×C19—81no—
69C22⋊D19—41no—
70C22⋊D19—41no—
71C22⋊D19—41no—
72C22⋊D19—41no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—21no—
76C2×Dic19—21no—
77C2×Dic19—21no—
78C2×Dic19—41no—
79C2×Dic19—81no—
80C2×Dic19—81no—
81C2×Dic19—81no—
82Dic38—82no—
83#2032—191nomaximal, Sylow
84C22×C19—41no—
85C22×C19—41no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—41no—
89C22×C19—41no—
90C22×C19—41no—
91C22×C19#12011yescharacteristic
92C22×C19C22⋊Q811yescharacteristic
93C22×C19C22⋊Q811yescharacteristic
94C22×C19C22⋊Q811yescharacteristic
95C22×C19#12411yescharacteristic
96C22×C19#12411yescharacteristic
97C22×C19#12411yescharacteristic
98C2×D19—41no—
99C2×D19—81no—
100C2×D19—81no—
101C2×D19—81no—
102C4×C19—42no—
103C4×C19—81no—
104C4×C19—81no—
105Dic19—42no—
106Dic19—42no—
107Dic19—41no—
108Dic19—81no—
109#543—191no—
110C2×#99—191no—
111C2×#99—191no—
112C2×#99—191no—
113#342—191no—
114#342—191no—
115#342D1911yescharacteristic, complemented
116C2×C19—21no—
117C2×C19—21no—
118C2×C19—21no—
119C2×C19—21no—
120C2×C19—21no—
121C2×C19—21no—
122C2×C19—21no—
123C2×C19#39311yescharacteristic
124D19—81no—
125C22×D4—191no—
126C22⋊Q8—382no—
127C22⋊Q8—382no—
128C22⋊Q8—382no—
129C2×C22⋊C4—191no—
130C2×C22⋊C4—191no—
131C2×C22⋊C4—191no—
132C2×C22⋊C4C2×D1911yescharacteristic
133C2×C22⋊C4C2×D1911yescharacteristic
134C2×C22⋊C4C2×D1911yescharacteristic
135#99—382no—
136#99—382no—
137#99—382no—
138C19#203211yescharacteristic, complemented, Sylow
139C24—191no—
140C24C22×D1911yescharacteristic
141C2×Q8—382no—
142C2×D4—381no—
143C2×D4—381no—
144C2×D4—381no—
145C2×D4—381no—
146C2×D4—381no—
147C2×D4—381no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—191no—
152C22×C4—381no—
153C22×C4—381no—
154C22×C4—381no—
155C4⋊C4—384no—
156C4⋊C4—382no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—192no—
163C22⋊C4—192no—
164C22⋊C4—381no—
165C22⋊C4—381no—
166C22⋊C4—381no—
167C22⋊C4—381no—
168C22⋊C4D7612yes—
169C23—81no—
170C23—381no—
171C23—381no—
172C23—381no—
173C23—1521no—
174C23C2×D7611yescharacteristic
175C23#6454111yescharacteristic
176C23#6454111yescharacteristic
177C23D4×D1911yescharacteristic
178C23D4×D1911yescharacteristic
179C23#6454311yescharacteristic
180C23Q8×D1911yescharacteristic
181Q8—1522no—
182D4—761no—
183D4—761no—
184D4—761no—
185D4—761no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—381no—
195C2×C4—381no—
196C2×C4—381no—
197C2×C4—761no—
198C2×C4—1521no—
199C2×C4—1521no—
200C2×C4—1521no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—761no—
209C22—1521no—
210C22—1521no—
211C22—1521no—
212C22#1059732111yescharacteristic
213C22#1059732811yescharacteristic
214C22#1059733111yescharacteristic
215C22#1059733111yescharacteristic
216C22#1059734211yescharacteristic
217C22#1059734211yescharacteristic
218C22#1059734311yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—762no—
223C4—762no—
224C4—761no—
225C4—1521no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—1521no—
234C2#1192645711yescharacteristic
subgroupG/H
centerC2#11926457
commutator, cosocleC24×C19C23
FrattiniC24C22×D19
FittingC19×#342C2
socleC2×C19#393
prime radicalC22×C22⋊D19C22
hypercenter#342D19
hypocenterC19#2032
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #11927170C2semidirect
5. #11926311C2semidirect
6. #11926310C2semidirect
7. C19×#342C2semidirect
22. C23×D19Q8semidirect
35. C22×Dic19Q8semidirect
115. #342D19semidirect
138. C19#2032semidirect

Maximal subgroups

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

subgroupindex
#119271702
C2×#105972632
#119263112
#119263102
C19×#3422
#203219