Finite Group Databasebeta

← #14565010

Subgroups — #14565010

Order 2432.

284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10597265C211yesmaximal, characteristic, complemented
2C2×Dic19⋊C8C211yesmaximal, characteristic, complemented
3C2×#10597278C211yesmaximal, characteristic
4C2×#10597266C211yesmaximal, characteristic
5#11926445C211yesmaximal, characteristic
6#11926440C211yesmaximal, characteristic, complemented
7C19×#340C211yesmaximal, characteristic, complemented
8C22×D76C2211yescharacteristic
9C22×C8×C19C2211yescharacteristic
10C2×C4⋊C4×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×(C2×D19)⋊C4—21no—
13C2×(C2×D19)⋊C4—21no—
14C2×C4⋊Dic19C2211yescharacteristic
15C2×Dic19⋊C4—21no—
16C2×C4×Dic19C2211yescharacteristic
17C22×C19⋊C8C2211yescharacteristic
18C19⋊#95—21no—
19#10597278—22no—
20Dic19⋊C8—22no—
21#10597266—22no—
22#10597265—22no—
23C23×D19—21no—
24C22×C4×C19—21no—
25C22×C4×C19—21no—
26C22×C4×C19C2311yescharacteristic
27C22×Dic19—21no—
28C22×Dic19D411yescharacteristic
29C22×Dic19D411yescharacteristic
30C2×D76—21no—
31C2×D76—21no—
32C2×D76—21no—
33C2×D76—21no—
34C2×D76—21no—
35C2×D76Q812yes—
36C2×C8×C19—21no—
37C2×C8×C19—21no—
38C2×C8×C19—21no—
39C4⋊C4×C19—21no—
40C4⋊C4×C19—21no—
41C4⋊C4×C19—21no—
42C4⋊C4×C19—21no—
43(C2×D19)⋊C4—42no—
44(C2×D19)⋊C4—42no—
45C4⋊Dic19—21no—
46C4⋊Dic19D412yes—
47Dic19⋊C4—42no—
48C4×Dic19—21no—
49C4×Dic19—21no—
50C2×C19⋊C8—21no—
51C2×C19⋊C8—21no—
52C2×C19⋊C8D412yes—
53C23×C19C2×D411yescharacteristic
54C22×D19—22no—
55C22×D19—41no—
56C22×D19—41no—
57C22×D19—41no—
58C22×D19—41no—
59C22×D19—41no—
60C22×D19—41no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—41no—
67C2×C4×C19C2×D411yescharacteristic
68C2×C4×C19C2×D411yescharacteristic
69C2×C4×C19C2×Q811yescharacteristic
70C2×C4×C19#4111yescharacteristic
71C2×C4×C19#4111yescharacteristic
72C2×C4×C19#4111yescharacteristic
73C2×Dic19—21no—
74C2×Dic19—21no—
75C2×Dic19—21no—
76C2×Dic19—22no—
77C2×Dic19—21no—
78C2×Dic19—21no—
79C2×Dic19—41no—
80C2×Dic19—41no—
81C2×Dic19SD1612yes—
82D76—22no—
83D76—22no—
84D76—41no—
85D76—41no—
86C8×C19—41no—
87C19⋊C8—22no—
88#2065—191nomaximal, Sylow
89C22×C19#12111yescharacteristic
90C22×C19#12111yescharacteristic
91C22×C19C22⋊Q811yescharacteristic
92C22×C19C2×SD1611yescharacteristic
93C22×C19#13511yescharacteristic
94C22×C19AGL(1,ℤ/8)11yescharacteristic
95C22×C19AGL(1,ℤ/8)11yescharacteristic
96C2×D19—42no—
97C2×D19—42no—
98C2×D19—42no—
99C2×D19—81no—
100C2×D19—81no—
101C2×D19—81no—
102C2×D19—81no—
103C4×C19—81no—
104C4×C19—81no—
105C4×C19#12111yescharacteristic
106C4×C19C22⋊Q811yescharacteristic
107C4×C19C22⋊Q811yescharacteristic
108C4×C19#12611yescharacteristic
109Dic19—22no—
110Dic19—42no—
111Dic19—41no—
112C2×#106—191no—
113C2×C4⋊C8—191no—
114C2×#102—191no—
115C2×#102—191no—
116#390—191no—
117#389—191no—
118#340D1911yescharacteristic, complemented
119C2×C19#39611yescharacteristic
120C2×C19#46011yescharacteristic
121C2×C19#46311yescharacteristic
122C2×C19#46511yescharacteristic
123C2×C19#46911yescharacteristic
124C2×C19#47611yescharacteristic
125C2×C19#47811yescharacteristic
126D19—82no—
127C22×D4—191no—
128C22×C8—191no—
129C22×C8C2×D1911yescharacteristic
130C2×C4⋊C4—191no—
131C2×C4⋊C4—381no—
132C2×C4⋊C4C2×D1911yescharacteristic
133C2×C4⋊C4C2×D1911yescharacteristic
134C2×C22⋊C4—381no—
135C2×C22⋊C4—381no—
136C2×C42—191no—
137#106—382no—
138C4⋊C8—382no—
139#102—382no—
140#102—382no—
141#95—381no—
142C19#206511yescharacteristic, complemented, Sylow
143C24—381no—
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—191no—
153C22×C4—191no—
154C22×C4—381no—
155C22×C4C22×D1911yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—192no—
160C2×C8—381no—
161C2×C8—381no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—192no—
167C4⋊C4—381no—
168C4⋊C4—762no—
169C22⋊C4—762no—
170C22⋊C4—762no—
171C42—381no—
172C42—381no—
173C23—382no—
174C23—761no—
175C23—761no—
176C23—761no—
177C23—761no—
178C23—761no—
179C23—761no—
180C23D4×D1911yescharacteristic
181D4—382no—
182D4—382no—
183D4—761no—
184D4—761no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—192no—
192C2×C4—381no—
193C2×C4—381no—
194C2×C4—381no—
195C2×C4—382no—
196C2×C4—381no—
197C2×C4—381no—
198C2×C4—761no—
199C2×C4—761no—
200C2×C4#6454111yescharacteristic
201C2×C4#6454111yescharacteristic
202C2×C4#6454111yescharacteristic
203C2×C4D4×D1911yescharacteristic
204C2×C4D4×D1911yescharacteristic
205C2×C4Q8×D1911yescharacteristic
206C8—41no—
207C8—382no—
208C22—762no—
209C22—762no—
210C22—762no—
211C22—1521no—
212C22—1521no—
213C22—1521no—
214C22—1521no—
215C22#1059733011yescharacteristic
216C22#1059733011yescharacteristic
217C22#1059734211yescharacteristic
218C22#1059735711yescharacteristic
219C22SD16×D1911yescharacteristic
220C22#1059736011yescharacteristic
221C22#1059736511yescharacteristic
222C4—81no—
223C4—81no—
224C4—382no—
225C4—761no—
226C4—762no—
227C4#1059732211yescharacteristic
228C4#1059733011yescharacteristic
229C4#1059734211yescharacteristic
230C4#1059734211yescharacteristic
231C2—1522no—
232C2#1192646811yescharacteristic
233C2#1192674311yescharacteristic
234C2#1192676211yescharacteristic
235C2#1192677611yescharacteristic
236C2#1192679611yescharacteristic
237C2#1192683311yescharacteristic
238C2#1192684711yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#340C2
socleC23×C19C2×D4
prime radicalC22×D76C22
hypercenter#340D19
hypocenterC19#2065
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#10597265C2semidirect
2. C2×Dic19⋊C8C2semidirect
6. #11926440C2semidirect
7. C19×#340C2semidirect
118. #340D19semidirect
142. C19#2065semidirect

Maximal subgroups

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

subgroupindex
C2×#105972652
C2×Dic19⋊C82
C2×#105972782
C2×#105972662
#119264452
#119264402
C19×#3402
#206519