Finite Group Databasebeta

← #18069220

Subgroups — #18069220

Order 4864.

218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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#14565058C211yesmaximal, characteristic
2#14561559C211yesmaximal, characteristic
3C19×#1289C211yesmaximal, characteristic
4C2×#10597275C411yescharacteristic, complemented
5#11926404—21no—
6C22⋊(C19⋊C16)—21no—
7#11926307—21no—
8#11926307C411yescharacteristic, complemented
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×#380—21no—
11C23×C4×C19D411yescharacteristic
12C22×C8×C19C2×C411yescharacteristic
13C22×C8×C19D411yescharacteristic
14C2×C4⋊C4×C19—41no—
15C2×C22⋊C4×C19—41no—
16C2×C22⋊Dic19—41no—
17C2×C4⋊Dic19—21no—
18C2×C4⋊Dic19—21no—
19C19×C22⋊C8—41no—
20C19×#95—22no—
21C19⋊#95—41no—
22#10597275—41no—
23C2×C19⋊C16—41no—
24C24×C19D811yescharacteristic
25C22×C4×C19—21no—
26C22×C4×C19—21no—
27C22×C4×C19—41no—
28C22×C4×C19—41no—
29C22×C4×C19—42no—
30C22×C4×C19C22⋊C411yescharacteristic
31C22×C4×C19SD1611yescharacteristic
32C22×Dic19—41no—
33C22×Dic19—41no—
34C2×C8×C19—21no—
35C2×C8×C19—21no—
36C2×C8×C19—41no—
37C2×C8×C19—41no—
38C4⋊C4×C19—81no—
39C4⋊C4×C19—81no—
40C22⋊C4×C19—81no—
41C22⋊C4×C19—81no—
42C22⋊Dic19—81no—
43C22⋊Dic19—81no—
44C4⋊Dic19—41no—
45C4⋊Dic19—41no—
46C4⋊Dic19—41no—
47C4⋊Dic19—41no—
48C19⋊C16—81no—
49#7079—191nomaximal, Sylow
50C23×C19—21no—
51C23×C19—21no—
52C23×C19—41no—
53C23×C19—41no—
54C23×C19#10211yescharacteristic
55C23×C19D1611yescharacteristic
56C23×C19SD3211yescharacteristic
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19—81no—
64C2×C4×C19—82no—
65C2×C4×C19—82no—
66C2×C4×C19—82no—
67C2×C4×C19#9911yescharacteristic
68C2×C4×C19#10411yescharacteristic
69C2×Dic19—81no—
70C2×Dic19—81no—
71C2×Dic19—81no—
72C2×Dic19—81no—
73C2×Dic19—81no—
74C2×Dic19—81no—
75C8×C19—41no—
76C8×C19—41no—
77#2075—191no—
78#1314—191no—
79#1289D1911yescharacteristic
80C22×C19—21no—
81C22×C19—21no—
82C22×C19—21no—
83C22×C19—21no—
84C22×C19—41no—
85C22×C19—41no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—81no—
89C22×C19#32711yescharacteristic
90C22×C19#35711yescharacteristic
91C22×C19#36011yescharacteristic
92C4×C19—21no—
93C4×C19—41no—
94C4×C19—162no—
95C4×C19#35211yescharacteristic
96C4×C19#35411yescharacteristic
97Dic19—161no—
98Dic19—161no—
99C2×#107—191no—
100C2×C22⋊C8C2×D1911yescharacteristic
101#380—21no—
102#380—381no—
103C22⋊C16—381no—
104#340—191no—
105#340—381no—
106C2×C19—21no—
107C2×C19—21no—
108C2×C19—41no—
109C2×C19—41no—
110C2×C19#134011yescharacteristic
111C2×C19#134411yescharacteristic
112C2×C19#134711yescharacteristic
113C23×C4C22⋊D1911yescharacteristic
114C22×C8C4×D1911yescharacteristic
115C22×C8D7611yescharacteristic
116C2×C4⋊C4—41no—
117C2×C4⋊C4—381no—
118C2×C4⋊C4—381no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—761no—
121C2×C16—761no—
122#107—761no—
123C22⋊C8—41no—
124#95—22no—
125#95—761no—
126C19#707911yescharacteristic, complemented, Sylow
127C24#6452511yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—42no—
133C22×C4—761no—
134C22×C4—761no—
135C22×C4(C2×D19)⋊C411yescharacteristic
136C22×C4#6452711yescharacteristic
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—41no—
141C4⋊C4—81no—
142C4⋊C4—81no—
143C4⋊C4—761no—
144C4⋊C4—761no—
145C4⋊C4—761no—
146C4⋊C4—761no—
147C22⋊C4—81no—
148C22⋊C4—81no—
149C22⋊C4—1521no—
150C22⋊C4—1521no—
151C16—1521no—
152C23—21no—
153C23—21no—
154C23—41no—
155C23—41no—
156C23#1059726611yescharacteristic
157C23#1059728311yescharacteristic
158C23#1059728511yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4—1521no—
170C2×C4—1521no—
171C2×C4—1521no—
172C2×C4—1521no—
173C2×C4—1521no—
174C2×C4—1521no—
175C2×C4#1059726211yescharacteristic
176C2×C4#1059726311yescharacteristic
177C8—41no—
178C8—41no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22#1192627711yescharacteristic
189C22#1192634411yescharacteristic
190C22#1192635311yescharacteristic
191C4—21no—
192C4—41no—
193C4—162no—
194C4—3041no—
195C4—3041no—
196C4#1192633311yescharacteristic
197C4#1192633811yescharacteristic
198C2—21no—
199C2—21no—
200C2—41no—
201C2—41no—
202C2#1456162211yescharacteristic
203C2#1456163411yescharacteristic
204C2#1456164311yescharacteristic
subgroupG/H
centerC22#11926277
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#1289C2
socleC22×C19#327
prime radicalC24×C19D8
cosocleC2×C19×C22⋊C8C22
hypercenter#1289D19
hypocenterC19#7079
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. C2×#10597275C4semidirect
8. #11926307C4semidirect
126. C19#7079semidirect

Maximal subgroups

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

subgroupindex
#145650582
#145615592
C19×#12892
#707919