Finite Group Databasebeta

← #18070087

Subgroups — #18070087

Order 4864.

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

normal subgroups only

This group has 224 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#14564864C211yesmaximal, characteristic
2#14561579C211yesmaximal, characteristic, complemented
3C19×#1295C211yesmaximal, characteristic, complemented
4#11927125C411yescharacteristic
5C2×#10597262—21no—
6#11926543—21no—
7#11926313C411yescharacteristic
8#11926270—21no—
9C2×C19×#97—21no—
10C19×#382C2211yescharacteristic
11C2×#64541—21no—
12C22×C8×C19—41no—
13C2×C4⋊C4×C19C2×C411yescharacteristic
14C2×C4⋊C4×C19D411yescharacteristic
15C2×C42×C19D411yescharacteristic
16#10597376—41no—
17C2×#64520—21no—
18#10597343—41no—
19#10597341—41no—
20C19×#97—22no—
21C19×#97—41no—
22C19×#95—41no—
23C22⋊(C19⋊C8)—41no—
24#10597267—41no—
25#10597266—41no—
26#10597262—41no—
27#10597262—41no—
28C22×C4×C19—21no—
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19C22⋊C411yescharacteristic
32C2×C22⋊D19—41no—
33#64541—41no—
34#64541—41no—
35#64541—41no—
36#64541—41no—
37C2×D76—21no—
38C2×D76—41no—
39C2×C4×D19—41no—
40C2×Dic38—21no—
41C2×C8×C19—42no—
42C2×C8×C19—42no—
43C2×C8×C19—42no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—41no—
46C42×C19—21no—
47C42×C19D811yescharacteristic
48C42×C19SD1611yescharacteristic
49(C2×D19)⋊C4—42no—
50C4⋊Dic19—41no—
51#64520—41no—
52#64520—41no—
53C2×C19⋊C8—41no—
54C2×C19⋊C8—81no—
55#7416—191nomaximal, Sylow
56C23×C19#9911yescharacteristic
57C22×D19—41no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—41no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—81no—
67C2×C4×C19—81no—
68C2×C4×C19#10211yescharacteristic
69C2×C4×C19#10411yescharacteristic
70C22⋊D19—81no—
71C22⋊D19—81no—
72C2×Dic19—41no—
73D76—41no—
74D76—41no—
75D76—161no—
76C4×D19—81no—
77C4×D19—81no—
78Dic38—41no—
79Dic38—41no—
80C8×C19—44no—
81C19⋊C8—81no—
82C19⋊C8—161no—
83#2040—191no—
84#1324—191no—
85#1295D1911yescharacteristic, complemented
86C22×C19—21no—
87C22×C19—21no—
88C22×C19#32711yescharacteristic
89C22×C19AΣL(1,𝔽16)11yescharacteristic
90C22×C19#35511yescharacteristic
91C2×D19—81no—
92C2×D19—81no—
93C2×D19—81no—
94C4×C19—21no—
95C4×C19—21no—
96C4×C19—41no—
97C4×C19—41no—
98C4×C19—81no—
99C4×C19—81no—
100Dic19—81no—
101#537—191no—
102C2×#104—381no—
103#417—381no—
104C2×#97—21no—
105#382C2×D1911yescharacteristic
106#343—191no—
107#324—381no—
108C2×C19—21no—
109C2×C19—21no—
110C2×C19#134511yescharacteristic
111C2×C19#140311yescharacteristic
112C2×C19#140411yescharacteristic
113D19—161no—
114C2×#41—381no—
115C2×M16—381no—
116C22×C8—41no—
117C22⋊Q8—761no—
118#121—761no—
119#121—761no—
120C2×C4⋊C4C4×D1911yescharacteristic
121C2×C4⋊C4D7611yescharacteristic
122C2×C42C22⋊D1911yescharacteristic
123#104—761no—
124#104—761no—
125#103—761no—
126#102—761no—
127C22⋊C8—761no—
128#97—22no—
129#97—41no—
130#95—41no—
131C19#741611yescharacteristic, complemented, Sylow
132#41—761no—
133#41—761no—
134#41—761no—
135#41—761no—
136C2×Q8—381no—
137C2×D4—381no—
138C2×D4—761no—
139C2×D4—761no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—761no—
144C22×C4(C2×D19)⋊C411yescharacteristic
145M16—761no—
146M16—761no—
147C2×C8—42no—
148C2×C8—42no—
149C2×C8—42no—
150C2×C8—761no—
151C2×C8—1521no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—761no—
155C22⋊C4—762no—
156C42—21no—
157C42#6452511yescharacteristic
158C42#6452711yescharacteristic
159C23—761no—
160C23#1059726311yescharacteristic
161Q8—761no—
162Q8—761no—
163D4—3041no—
164D4—761no—
165D4—761no—
166D4—1521no—
167D4—1521no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—761no—
179C2×C4—1521no—
180C2×C4—1521no—
181C2×C4#1059726211yescharacteristic
182C2×C4#1059726611yescharacteristic
183C8—44no—
184C8—3041no—
185C8—1521no—
186C22—21no—
187C22—21no—
188C22—1521no—
189C22—1521no—
190C22—1521no—
191C22#1192627711yescharacteristic
192C22#1192633211yescharacteristic
193C22#1192634011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—81no—
200C4—1521no—
201C2—21no—
202C2—21no—
203C2—3041no—
204C2#1456163711yescharacteristic
205C2#1456178411yescharacteristic
206C2#1456178711yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×C4⋊C4×C19C2×C4
Frattini#382C2×D19
FittingC19×#1295C2
socleC22×C19AΣL(1,𝔽16)
prime radical#11927125C4
cosocleC19×#382C22
hypercenter#1295D19
hypocenterC19#7416
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #14561579C2semidirect
3. C19×#1295C2semidirect
85. #1295D19semidirect
131. C19#7416semidirect

Maximal subgroups

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

subgroupindex
#145648642
#145615792
C19×#12952
#741619