Finite Group Databasebeta

← #18069969

Subgroups — #18069969

Order 4864.

202 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 43 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#14563849C211yesmaximal, characteristic
2#14561569C211yesmaximal, characteristic
3C19×#1272C211yesmaximal, characteristic
4#11927022C411yescharacteristic
5#11926584—21no—
6C2×#10597293C411yescharacteristic
7#11926304—21no—
8#11926270—21no—
9C19×#391C2211yescharacteristic
10C19×#336—21no—
11C22×Q8×C19C2×C411yescharacteristic
12C22×C8×C19—41no—
13C2×C4⋊C4×C19D411yescharacteristic
14C2×C42×C19D411yescharacteristic
15Q8×Dic19—41no—
16Q8×Dic19—41no—
17#10597372—21no—
18#10597372—41no—
19C2×#64520—21no—
20C19×#95—41no—
21#10597293—21no—
22#10597293C812yescomplemented
23C22⋊(C19⋊C8)—41no—
24#10597265—41no—
25#10597264—41no—
26C2×Q8×C19—21no—
27C2×Q8×C19—41no—
28C2×Q8×C19—41no—
29C2×Q8×C19C2×C811yescharacteristic
30C2×Q8×C19M1611yescharacteristic
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19C22⋊C411yescharacteristic
35C2×C8×C19—42no—
36C2×C8×C19—81no—
37C2×C8×C19—81no—
38C4⋊C4×C19—41no—
39C42×C19—41no—
40C22⋊Dic19—41no—
41C4⋊Dic19—21no—
42C4⋊Dic19—21no—
43C4⋊Dic19—41no—
44C4⋊Dic19—41no—
45C4×Dic19—41no—
46C4×Dic19—42no—
47#64520—22no—
48#64520—41no—
49C2×C19⋊C8—41no—
50C2×C19⋊C8—81no—
51#7376—191nomaximal, Sylow
52C23×C19#9911yescharacteristic
53Q8×C19—41no—
54Q8×C19—41no—
55Q8×C19—42no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
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—41no—
67C2×C4×C19—81no—
68C2×C4×C19C22⋊C811yescharacteristic
69C2×C4×C19#10111yescharacteristic
70C2×Dic19—41no—
71C2×Dic19—41no—
72C8×C19—82no—
73C19⋊C8—42no—
74C19⋊C8—161no—
75#1857—191no—
76#1319—191no—
77#1272D1911yescharacteristic
78C22×C19—21no—
79C22×C19—21no—
80C22×C19#32411yescharacteristic
81C22×C19AΣL(1,𝔽16)11yescharacteristic
82C22×C19#35211yescharacteristic
83C4×C19—21no—
84C4×C19—21no—
85C4×C19—41no—
86C4×C19—41no—
87C4×C19—41no—
88C4×C19—41no—
89C4×C19—81no—
90Dic19—81no—
91Dic19—81no—
92#519—191no—
93#428—381no—
94C2×#101—191no—
95#391C2×D1911yescharacteristic
96#339—381no—
97#336—21no—
98#324—381no—
99C2×C19—21no—
100C2×C19—21no—
101C2×C19#132611yescharacteristic
102C2×C19#140411yescharacteristic
103C2×C19#140511yescharacteristic
104C22×Q8C4×D1911yescharacteristic
105C2×M16—381no—
106C22×C8—41no—
107C4×Q8—761no—
108C4×Q8—761no—
109#117—381no—
110#117—761no—
111C2×C4⋊C4D7611yescharacteristic
112C2×C42C22⋊D1911yescharacteristic
113#107—761no—
114#106—761no—
115#101—192no—
116#101—381no—
117C22⋊C8—761no—
118#95—41no—
119C19#737611yescharacteristic, complemented, Sylow
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C8×D1911yescharacteristic
124C2×Q8#6451511yescharacteristic
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4(C2×D19)⋊C411yescharacteristic
129M16—382no—
130M16—761no—
131C2×C8—42no—
132C2×C8—81no—
133C2×C8—81no—
134C2×C8—761no—
135C2×C8—1521no—
136C4⋊C4—41no—
137C4⋊C4—381no—
138C4⋊C4—381no—
139C4⋊C4—761no—
140C4⋊C4—761no—
141C22⋊C4—761no—
142C42—41no—
143C42—761no—
144C42—762no—
145C23#1059726311yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—761no—
162C2×C4—761no—
163C2×C4(C2×D19)⋊C811yescharacteristic
164C2×C4#1059728111yescharacteristic
165C8—82no—
166C8—3041no—
167C8—762no—
168C22—21no—
169C22—21no—
170C22#1192626911yescharacteristic
171C22#1192633211yescharacteristic
172C22#1192633311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—1521no—
181C4—1521no—
182C2—21no—
183C2—21no—
184C2#1456158411yescharacteristic
185C2#1456178711yescharacteristic
186C2#1456179011yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×Q8×C19C2×C8
Frattini#391C2×D19
FittingC19×#1272C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC19×#391C22
hypercenter#1272D19
hypocenterC19#7376
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
22. #10597293C8semidirect
119. C19#7376semidirect

Maximal subgroups

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

subgroupindex
#145638492
#145615692
C19×#12722
#737619