Finite Group Databasebeta

← #18075938

Subgroups — #18075938

Order 4864.

554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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#14563397C212yesmaximal
2#14561516C214yesmaximal, complemented
3C2×C19×#382C211yesmaximal, characteristic
4C2×C22⋊(C19⋊C8)—22no—
5C2×#10597260C2214yes—
6#11926299—22no—
7C22×C4⋊C4×C19C411yescharacteristic
8C22×C4⋊C4×C19C411yescharacteristic
9C22×C42×C19C2211yescharacteristic
10C19×#382—22no—
11C19×#382C412yes—
12C19×#382C2212yes—
13C2×C19×#95—22no—
14C23×C4×C19—21no—
15C23×C4×C19—21no—
16C23×C4×C19C2×C411yescharacteristic
17C23×C4×C19D412yes—
18C2×C4⋊C4×C19—21no—
19C2×C4⋊C4×C19—21no—
20C2×C4⋊C4×C19—42no—
21C2×C4⋊C4×C19—42no—
22C2×C4⋊C4×C19C2×C412yes—
23C2×C4⋊C4×C19C2×C412yes—
24C2×C42×C19—24no—
25C2×C42×C19C2×C411yescharacteristic
26C2×C42×C19D412yes—
27C2×C42×C19C2311yescharacteristic
28C22×C19⋊C8—24no—
29C19×#95—24no—
30C19×#95—24no—
31C22⋊(C19⋊C8)—28no—
32#10597260—28no—
33C24×C19C22⋊C411yescharacteristic
34C22×C4×C19—22no—
35C22×C4×C19—22no—
36C22×C4×C19—22no—
37C22×C4×C19—24no—
38C22×C4×C19—24no—
39C22×C4×C19—22no—
40C22×C4×C19—22no—
41C22×C4×C19—42no—
42C22×C4×C19—44no—
43C22×C4×C19—42no—
44C22×C4×C19—42no—
45C22×C4×C19—44no—
46C22×C4×C19C22⋊C412yes—
47C22×C4×C19C22⋊C411yescharacteristic
48C22×C4×C19C22×C411yescharacteristic
49C22×C4×C19C2×D412yes—
50C4⋊C4×C19—42no—
51C4⋊C4×C19—42no—
52C4⋊C4×C19—42no—
53C4⋊C4×C19—42no—
54C42×C19—22no—
55C42×C19—24no—
56C42×C19#4114yes—
57C2×C19⋊C8—28no—
58C2×C19⋊C8—44no—
59C2×C19⋊C8—44no—
60#8718—191nomaximal, Sylow
61C23×C19—21no—
62C23×C19—21no—
63C23×C19—22no—
64C23×C19#10012yes—
65C23×C19#10414yes—
66C23×C19C2×C22⋊C411yescharacteristic
67C2×C4×C19—28no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—48no—
78C2×C4×C19—42no—
79C2×C4×C19—42no—
80C2×C4×C19—44no—
81C2×C4×C19—44no—
82C2×C4×C19—84no—
83C2×C4×C19—84no—
84C2×C4×C19#10112yes—
85C2×C4×C19#11712yes—
86C2×C4×C19#12314yes—
87C19⋊C8—48no—
88C2×#382D1911yescharacteristic
89#1749—192no—
90#1295—194no—
91C22×C19—22no—
92C22×C19—24no—
93C22×C19—24no—
94C22×C19—22no—
95C22×C19#32914yes—
96C22×C19#38111yescharacteristic
97C22×C19C2×#10011yescharacteristic
98C22×C19C2×#10111yescharacteristic
99C22×C19C2×#10412yes—
100C22×C19#42112yes—
101C4×C19—22no—
102C4×C19—22no—
103C4×C19—24no—
104C4×C19—42no—
105C4×C19—82no—
106C4×C19—82no—
107C22×C4⋊C4Dic1911yescharacteristic
108C22×C4⋊C4Dic1911yescharacteristic
109C22×C42C2×D1911yescharacteristic
110C2×C22⋊C8—382no—
111C2×#97—194no—
112#382—22no—
113#382Dic1912yes—
114#382C2×D1912yes—
115C2×#95—22no—
116#336—382no—
117C2×C19—24no—
118C2×C19C2×#32911yescharacteristic
119C2×C19#152812yes—
120C2×C19#153311yescharacteristic
121C2×C19#182111yescharacteristic
122C2×C19#182612yes—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4C2×Dic1911yescharacteristic
126C23×C4C22⋊D1912yes—
127C22×C8—384no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4C2×Dic1912yes—
133C2×C4⋊C4C2×Dic1912yes—
134C2×C42—24no—
135C2×C42C2×Dic1911yescharacteristic
136C2×C42C22⋊D1912yes—
137C2×C42C22×D1911yescharacteristic
138C22⋊C8—388no—
139#97—388no—
140#95—24no—
141#95—24no—
142C19#871811yescharacteristic, complemented, Sylow
143C24C22⋊Dic1911yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—24no—
148C22×C4—24no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—44no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—44no—
156C22×C4C22⋊Dic1912yes—
157C22×C4C22⋊Dic1911yescharacteristic
158C22×C4C22×Dic1911yescharacteristic
159C22×C4C2×C22⋊D1912yes—
160C2×C8—388no—
161C2×C8—764no—
162C2×C8—764no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C42—22no—
168C42—24no—
169C42#6454114yes—
170C23—22no—
171C23—21no—
172C23—21no—
173C23#1059729012yes—
174C23#1059729414yes—
175C23C2×C22⋊Dic1911yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—44no—
188C2×C4—44no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—84no—
192C2×C4—84no—
193C2×C4#1059729312yes—
194C2×C4#1059737212yes—
195C2×C4#1059737514yes—
196C8—768no—
197C22—22no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22#1192628414yes—
202C22#1192640711yescharacteristic
203C22C2×#1059729011yescharacteristic
204C22C2×#1059729311yescharacteristic
205C22C2×#1059729412yes—
206C22#1192656112yes—
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—24no—
214C2C2×#1192628411yescharacteristic
215C2#1456223712yes—
216C2#1456225911yescharacteristic
217C2#1456371511yescharacteristic
218C2#1456373412yes—
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#382C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#382D19
hypocenterC19#8718
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #14561516C2semidirect
142. C19#8718semidirect

Maximal subgroups

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

subgroupindex
#145633972
#145615162
C2×C19×#3822
#871819