Finite Group Databasebeta

← #18070317

Subgroups — #18070317

Order 4864.

348 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 63 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×#11926337C212yesmaximal
2C19×#1957C211yesmaximal, characteristic
3C2×#10597291—22no—
4#11926337—22no—
5#11926337C414yescomplemented
6C2×C19×#127C2211yescharacteristic
7C2×C19×#102—22no—
8C2×C4×C8×C19C411yescharacteristic, complemented
9C19×#384C411yescharacteristic, complemented
10C22×D4×C19—41no—
11C22×D4×C19D412yes—
12C22×C8×C19—21no—
13C19×#127—41no—
14C19×#127C2×C412yes—
15C19×#127D411yescharacteristic
16C19×#127Q811yescharacteristic
17C2×C4⋊C4×C19—21no—
18C2×C4⋊C4×C19—41no—
19C2×C42×C19C2×C411yescharacteristic
20C2×C22⋊Dic19—42no—
21C19×#102—44no—
22C4×C8×C19—41no—
23#10597291—24no—
24#10597291—42no—
25C24×C19—22no—
26C2×D4×C19—22no—
27C2×D4×C19—42no—
28C2×D4×C19—42no—
29C2×D4×C19—42no—
30C2×D4×C19—41no—
31C2×D4×C19—41no—
32C2×D4×C19—82no—
33C2×D4×C19—82no—
34C2×D4×C19C22⋊C412yes—
35C2×D4×C19C4⋊C412yes—
36C22×C4×C19—21no—
37C22×C4×C19—41no—
38C22×C4×C19C22⋊C411yescharacteristic
39C22×Dic19—82no—
40C2×C8×C19—22no—
41C2×C8×C19—41no—
42C2×C8×C19—41no—
43C4⋊C4×C19—42no—
44C4⋊C4×C19—82no—
45C42×C19—21no—
46C42×C19C4211yescharacteristic
47C42×C19C4⋊C411yescharacteristic
48C22⋊Dic19—44no—
49C22⋊Dic19—82no—
50#7498—191nomaximal, Sylow
51C23×C19—22no—
52C23×C19—22no—
53C23×C19—42no—
54C23×C19—42no—
55C23×C19—82no—
56C23×C19—82no—
57C23×C19#9911yescharacteristic
58D4×C19—42no—
59D4×C19—42no—
60D4×C19—82no—
61D4×C19—84no—
62D4×C19—82no—
63D4×C19—82no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—82no—
71C2×C4×C19—81no—
72C2×C4×C19#9511yescharacteristic
73C2×C4×C19#9911yescharacteristic
74C2×Dic19—84no—
75C2×Dic19—162no—
76C2×Dic19—162no—
77C8×C19—42no—
78C2×#353—192no—
79#1957D1911yescharacteristic
80C22×C19—21no—
81C22×C19—21no—
82C22×C19—42no—
83C22×C19—42no—
84C22×C19—82no—
85C22×C19—82no—
86C22×C19—82no—
87C22×C19—82no—
88C22×C19—162no—
89C22×C19#34211yescharacteristic
90C22×C19#35311yescharacteristic
91C22×C19#35411yescharacteristic
92C4×C19—22no—
93C4×C19—22no—
94C4×C19—21no—
95C4×C19—21no—
96C4×C19—161no—
97Dic19—164no—
98C2×#127C2×D1911yescharacteristic
99C2×#102—22no—
100C2×#99—382no—
101C2×C4×C8Dic1911yescharacteristic, complemented
102#384Dic1911yescharacteristic, complemented
103#353—194no—
104#353—382no—
105C2×C19—21no—
106C2×C19—21no—
107C2×C19—82no—
108C2×C19—82no—
109C2×C19#139311yescharacteristic
110C2×C19#140811yescharacteristic
111C2×C19#140911yescharacteristic
112C22×D4—41no—
113C22×D4C22⋊D1912yes—
114C22×C8—21no—
115#127—41no—
116#127Dic3811yescharacteristic
117#127C4×D1912yes—
118#127D7611yescharacteristic
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C22⋊C4—762no—
122C2×C42C2×Dic1911yescharacteristic
123#102—44no—
124#99—384no—
125#99—762no—
126C4×C8—41no—
127C19#749811yescharacteristic, complemented, Sylow
128C24—22no—
129C2×D4—22no—
130C2×D4—42no—
131C2×D4—42no—
132C2×D4—41no—
133C2×D4—42no—
134C2×D4—41no—
135C2×D4—82no—
136C2×D4—82no—
137C2×D4Dic19⋊C412yes—
138C2×D4(C2×D19)⋊C412yes—
139C22×C4—21no—
140C22×C4—41no—
141C22×C4—1522no—
142C22×C4C22⋊Dic1911yescharacteristic
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C4⋊C4—42no—
147C4⋊C4—82no—
148C22⋊C4—764no—
149C22⋊C4—1522no—
150C42—21no—
151C42C4×Dic1911yescharacteristic
152C42C4⋊Dic1911yescharacteristic
153C23—22no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23—82no—
158C23—82no—
159C23#1059729111yescharacteristic
160D4—42no—
161D4—42no—
162D4—82no—
163D4—82no—
164D4—84no—
165D4—82no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—3042no—
175C2×C4—3042no—
176C2×C4—1524no—
177C2×C4C19⋊#9511yescharacteristic
178C2×C4#1059729111yescharacteristic
179C8—42no—
180C22—21no—
181C22—21no—
182C22—42no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22—82no—
188C22—162no—
189C22#1192631111yescharacteristic
190C22#1192633711yescharacteristic
191C22#1192633911yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—161no—
197C4—3044no—
198C2—21no—
199C2—21no—
200C2—82no—
201C2—82no—
202C2#1456176011yescharacteristic
203C2#1456179811yescharacteristic
204C2#1456180011yescharacteristic
subgroupG/H
centerC22#11926337
commutatorC42×C19C42
FrattiniC2×#127C2×D19
FittingC19×#1957C2
socleC22×C19#353
prime radical, cosocleC2×C19×#127C22
hypercenter#1957D19
hypocenterC19#7498
LCSG ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ #1957

Complements

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

NH ≅ G/Ntype
5. #11926337C4semidirect
8. C2×C4×C8×C19C4semidirect
9. C19×#384C4semidirect
101. C2×C4×C8Dic19semidirect
102. #384Dic19semidirect
127. C19#7498semidirect

Maximal subgroups

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

subgroupindex
C2×#119263372
C19×#19572
#749819