Finite Group Databasebeta

← #18070129

Subgroups — #18070129

Order 4864.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564791C211yesmaximal, characteristic
2#14561456C211yesmaximal, characteristic
3C19×#1393C211yesmaximal, characteristic
4#11927175C411yescharacteristic, complemented
5#11926549—21no—
6#11926313C411yescharacteristic, complemented
7#11926304—21no—
8#11926299—21no—
9C2×C19×#99—21no—
10C19×#390C2211yescharacteristic
11C22×D4×C19D411yescharacteristic
12C2×C4⋊C4×C19C2×C411yescharacteristic
13C2×C22⋊C4×C19—41no—
14C2×C22⋊C4×C19—41no—
15C2×C42×C19D411yescharacteristic
16#10597372—21no—
17#10597370—41no—
18C2×#64520—21no—
19C22×C19⋊C8—41no—
20#10597336—41no—
21#10597334—41no—
22C19×#99—22no—
23C19×#99—41no—
24#10597289—41no—
25#10597289—41no—
26C24×C19—21no—
27C2×D4×C19—21no—
28C2×D4×C19—41no—
29C2×D4×C19—41no—
30C2×D4×C19SD1611yescharacteristic
31C2×D4×C19Q1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19—81no—
35C22×C4×C19C22⋊C411yescharacteristic
36C2×Dic38—41no—
37C4⋊C4×C19—41no—
38C22⋊C4×C19—42no—
39C22⋊C4×C19—81no—
40C22⋊C4×C19—81no—
41C22⋊C4×C19—81no—
42C42×C19—41no—
43C22⋊Dic19—41no—
44C4⋊Dic19—21no—
45C4⋊Dic19—21no—
46C4⋊Dic19—41no—
47Dic19⋊C4—42no—
48C4×Dic19—41no—
49#64520—41no—
50#64520—41no—
51C2×C19⋊C8—41no—
52C2×C19⋊C8—42no—
53C2×C19⋊C8—81no—
54C2×C19⋊C8—81no—
55#7430—191nomaximal, Sylow
56C23×C19—21no—
57C23×C19—21no—
58C23×C19—41no—
59C23×C19—41no—
60C23×C19—81no—
61C23×C19—81no—
62C23×C19#9911yescharacteristic
63D4×C19—41no—
64D4×C19—41no—
65D4×C19—81no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—41no—
71C2×C4×C19—41no—
72C2×C4×C19—41no—
73C2×C4×C19—81no—
74C2×C4×C19—82no—
75C2×C4×C19—161no—
76C2×C4×C19—161no—
77C2×C4×C19#10311yescharacteristic
78C2×C4×C19#10411yescharacteristic
79C2×Dic19—41no—
80C2×Dic19—41no—
81Dic38—161no—
82C19⋊C8—81no—
83C19⋊C8—82no—
84#2027—191no—
85#1393D1911yescharacteristic
86#1270—191no—
87C22×C19—21no—
88C22×C19—21no—
89C22×C19—41no—
90C22×C19—41no—
91C22×C19—81no—
92C22×C19—81no—
93C22×C19—81no—
94C22×C19—81no—
95C22×C19—161no—
96C22×C19#32811yescharacteristic
97C22×C19AΣL(1,𝔽16)11yescharacteristic
98C22×C19#35411yescharacteristic
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—41no—
102C4×C19—41no—
103C4×C19—81no—
104C4×C19—162no—
105Dic19—81no—
106Dic19—81no—
107#544—191no—
108#418—381no—
109C2×#99—21no—
110#390C2×D1911yescharacteristic
111#343—191no—
112#339—381no—
113#336—381no—
114C2×C19—21no—
115C2×C19—21no—
116C2×C19—81no—
117C2×C19—81no—
118C2×C19#135111yescharacteristic
119C2×C19#140211yescharacteristic
120C2×C19#140411yescharacteristic
121C22×D4C22⋊D1911yescharacteristic
122C2×M16—381no—
123C22×C8—761no—
124C4⋊Q8—761no—
125#125—761no—
126C22⋊Q8—761no—
127#117—381no—
128C2×C4⋊C4C4×D1911yescharacteristic
129C2×C22⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C42D7611yescharacteristic
132#102—761no—
133#102—761no—
134#99—22no—
135#99—41no—
136C19#743011yescharacteristic, complemented, Sylow
137C24—21no—
138C2×Q8—761no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4#6452611yescharacteristic
143C2×D4#6452811yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—81no—
147C22×C4(C2×D19)⋊C411yescharacteristic
148M16—761no—
149M16—761no—
150C2×C8—761no—
151C2×C8—762no—
152C2×C8—1521no—
153C2×C8—1521no—
154C4⋊C4—41no—
155C4⋊C4—381no—
156C4⋊C4—381no—
157C4⋊C4—761no—
158C4⋊C4—762no—
159C22⋊C4—42no—
160C22⋊C4—81no—
161C22⋊C4—81no—
162C22⋊C4—81no—
163C22⋊C4—761no—
164C42—41no—
165C42—761no—
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23#1059726311yescharacteristic
173Q8—3041no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—82no—
186C2×C4—161no—
187C2×C4—161no—
188C2×C4—761no—
189C2×C4—761no—
190C2×C4#1059726211yescharacteristic
191C2×C4#1059726711yescharacteristic
192C8—1521no—
193C8—1522no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22#1192628011yescharacteristic
204C22#1192633011yescharacteristic
205C22#1192633811yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—162no—
212C4—1521no—
213C4—1521no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2#1456165511yescharacteristic
219C2#1456177911yescharacteristic
220C2#1456178511yescharacteristic
subgroupG/H
centerC22#11926330
commutatorC2×C4⋊C4×C19C2×C4
Frattini#390C2×D19
FittingC19×#1393C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC22×D4×C19D4
cosocleC19×#390C22
hypercenter#1393D19
hypocenterC19#7430
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
4. #11927175C4semidirect
6. #11926313C4semidirect
136. C19#7430semidirect

Maximal subgroups

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

subgroupindex
#145647912
#145614562
C19×#13932
#743019