Finite Group Databasebeta

← #18070133

Subgroups — #18070133

Order 4864.

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

normal subgroups only

This group has 206 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#14561762C211yesmaximal, characteristic
2#14561461C211yesmaximal, characteristic
3C19×#2028C211yesmaximal, characteristic
4C2×#10597293—21no—
5#11926299—21no—
6C19×#544C411yescharacteristic
7C19×#419—21no—
8C19×#391C2211yescharacteristic
9C19×#343C411yescharacteristic
10C19×#339—21no—
11C22×Q8×C19D411yescharacteristic
12C2×M16×C19—21no—
13C19×C4⋊Q8—41no—
14C19×#125—41no—
15C19×C22⋊Q8—41no—
16C19×#117—21no—
17C2×C4⋊C4×C19C2×C411yescharacteristic
18C2×C42×C19D411yescharacteristic
19C2×#64520—41no—
20C22×C19⋊C8—41no—
21C19×#103—41no—
22C19×#103—41no—
23C19×#95—41no—
24#10597293—22no—
25#10597293—41no—
26C2×Q8×C19—21no—
27C2×Q8×C19—41no—
28C2×Q8×C19—41no—
29C2×Q8×C19—41no—
30C2×Q8×C19SD1611yescharacteristic
31C2×Q8×C19Q1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19—21no—
35C22×C4×C19C22⋊C411yescharacteristic
36M16×C19—41no—
37M16×C19—41no—
38C2×C8×C19—41no—
39C4⋊C4×C19—21no—
40C4⋊C4×C19—21no—
41C4⋊C4×C19—41no—
42C4⋊C4×C19—41no—
43C4⋊C4×C19—42no—
44C22⋊C4×C19—41no—
45C42×C19—41no—
46C42×C19—41no—
47#64520—42no—
48#64520—81no—
49C2×C19⋊C8—42no—
50C2×C19⋊C8—81no—
51C2×C19⋊C8—81no—
52C2×C19⋊C8—81no—
53#7431—191nomaximal, Sylow
54C23×C19#9911yescharacteristic
55Q8×C19—41no—
56Q8×C19—41no—
57Q8×C19—81no—
58Q8×C19—161no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—21no—
63C2×C4×C19—21no—
64C2×C4×C19—21no—
65C2×C4×C19—41no—
66C2×C4×C19—41no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19—41no—
72C2×C4×C19—81no—
73C2×C4×C19#10311yescharacteristic
74C2×C4×C19#10411yescharacteristic
75C8×C19—81no—
76C19⋊C8—82no—
77C19⋊C8—82no—
78#2028D1911yescharacteristic
79#1394—191no—
80#1272—191no—
81C22×C19—21no—
82C22×C19—21no—
83C22×C19#32811yescharacteristic
84C22×C19AΣL(1,𝔽16)11yescharacteristic
85C22×C19#35411yescharacteristic
86C4×C19—21no—
87C4×C19—21no—
88C4×C19—41no—
89C4×C19—41no—
90C4×C19—41no—
91C4×C19—41no—
92C4×C19—81no—
93C4×C19—81no—
94C4×C19—81no—
95#544Dic1911yescharacteristic
96#419—21no—
97C2×#101—381no—
98#391C2×D1911yescharacteristic
99#343Dic1911yescharacteristic
100#339—21no—
101#336—381no—
102C2×C19—21no—
103C2×C19—21no—
104C2×C19#135111yescharacteristic
105C2×C19#140311yescharacteristic
106C2×C19#140511yescharacteristic
107C22×Q8C22⋊D1911yescharacteristic
108C2×M16—21no—
109C2×M16—761no—
110C22×C8—761no—
111C4⋊Q8—41no—
112#125—41no—
113C22⋊Q8—41no—
114#117—21no—
115C2×C4⋊C4C2×Dic1911yescharacteristic
116C2×C42C22⋊D1911yescharacteristic
117#103—41no—
118#103—41no—
119#101—382no—
120#101—761no—
121#95—41no—
122C19#743111yescharacteristic, complemented, Sylow
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—41no—
127C2×Q8#6452711yescharacteristic
128C2×Q8#6452811yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4C22⋊Dic1911yescharacteristic
133M16—41no—
134M16—41no—
135M16—762no—
136M16—1521no—
137C2×C8—41no—
138C2×C8—762no—
139C2×C8—1521no—
140C2×C8—1521no—
141C2×C8—1521no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—42no—
147C22⋊C4—41no—
148C42—41no—
149C42—41no—
150C23#1059729111yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—161no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—81no—
169C2×C4#1059729211yescharacteristic
170C2×C4#1059729411yescharacteristic
171C8—81no—
172C8—1522no—
173C8—1522no—
174C22—21no—
175C22—21no—
176C22#1192628111yescharacteristic
177C22#1192633111yescharacteristic
178C22#1192633911yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—81no—
187C4—81no—
188C2—21no—
189C2—21no—
190C2#1456165611yescharacteristic
191C2#1456178311yescharacteristic
192C2#1456178911yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×C4⋊C4×C19C2×C4
Frattini#391C2×D19
FittingC19×#2028C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC19×#391C22
hypercenter#2028D19
hypocenterC19#7431
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #2028

Complements

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

NH ≅ G/Ntype
122. C19#7431semidirect

Maximal subgroups

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

subgroupindex
#145617622
#145614612
C19×#20282
#743119