Finite Group Databasebeta

← #18070055

Subgroups — #18070055

Order 4864.

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

normal subgroups only

This group has 252 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#14561569C211yesmaximal, characteristic
3C19×#2016C211yesmaximal, characteristic
4C2×#10597293—21no—
5#11926270—21no—
6C22×Q16×C19—21no—
7C2×C19×C4⋊Q8C411yescharacteristic
8C2×C19×#103—21no—
9C19×#391C2211yescharacteristic
10C19×#336C411yescharacteristic
11C22×Q8×C19—21no—
12C22×Q8×C19D411yescharacteristic
13C2×Q16×C19—42no—
14C2×Q16×C19—42no—
15C2×Q16×C19—41no—
16C2×Q16×C19—41no—
17C22×C8×C19—21no—
18C19×C4⋊Q8—42no—
19C2×C4⋊C4×C19—41no—
20C2×C4⋊C4×C19D411yescharacteristic
21C2×C42×C19C2×C411yescharacteristic
22C2×#64520—41no—
23C19×#103—42no—
24C19×#95—41no—
25#10597293—22no—
26#10597293—41no—
27C22⋊(C19⋊C8)—41no—
28C2×Q8×C19—21no—
29C2×Q8×C19—22no—
30C2×Q8×C19—41no—
31C2×Q8×C19—41no—
32C2×Q8×C19—41no—
33C2×Q8×C19—41no—
34C2×Q8×C19—41no—
35C2×Q8×C19—41no—
36C2×Q8×C19—41no—
37C2×Q8×C19D811yescharacteristic
38C2×Q8×C19SD1611yescharacteristic
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—21no—
42C22×C4×C19—41no—
43C22×C4×C19C22⋊C411yescharacteristic
44Q16×C19—44no—
45Q16×C19—44no—
46C2×C8×C19—22no—
47C2×C8×C19—41no—
48C2×C8×C19—41no—
49C4⋊C4×C19—41no—
50C4⋊C4×C19—42no—
51C4⋊C4×C19—42no—
52C42×C19—41no—
53#64520—42no—
54#64520—81no—
55C2×C19⋊C8—81no—
56C2×C19⋊C8—81no—
57#7405—191nomaximal, Sylow
58C23×C19#9911yescharacteristic
59Q8×C19—41no—
60Q8×C19—41no—
61Q8×C19—42no—
62Q8×C19—42no—
63Q8×C19—81no—
64Q8×C19—81no—
65Q8×C19—81no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—22no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—41no—
72C2×C4×C19—41no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19—42no—
76C2×C4×C19—41no—
77C2×C4×C19—81no—
78C2×C4×C19—81no—
79C2×C4×C19—81no—
80C2×C4×C19#10211yescharacteristic
81C2×C4×C19#10411yescharacteristic
82C8×C19—42no—
83C19⋊C8—82no—
84C19⋊C8—161no—
85#2016D1911yescharacteristic
86#1394—191no—
87#1319—191no—
88C22×C19—21no—
89C22×C19—21no—
90C22×C19#32711yescharacteristic
91C22×C19AΣL(1,𝔽16)11yescharacteristic
92C22×C19#35311yescharacteristic
93C4×C19—21no—
94C4×C19—21no—
95C4×C19—42no—
96C4×C19—41no—
97C4×C19—41no—
98C4×C19—82no—
99C4×C19—81no—
100C22×Q16—21no—
101C2×C4⋊Q8Dic1911yescharacteristic
102C2×#103—21no—
103C2×#101—381no—
104#391C2×D1911yescharacteristic
105#336Dic1911yescharacteristic
106#324—381no—
107C2×C19—21no—
108C2×C19—21no—
109C2×C19#134311yescharacteristic
110C2×C19#140711yescharacteristic
111C2×C19#141111yescharacteristic
112C22×Q8—21no—
113C22×Q8C22⋊D1911yescharacteristic
114C2×Q16—42no—
115C2×Q16—42no—
116C2×Q16—41no—
117C2×Q16—41no—
118C2×M16—761no—
119C22×C8—21no—
120C4⋊Q8—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4C22⋊D1911yescharacteristic
123C2×C42C2×Dic1911yescharacteristic
124#103—42no—
125#101—382no—
126#101—761no—
127C22⋊C8—761no—
128#95—41no—
129C19#740511yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8#6452511yescharacteristic
140C2×Q8#6452611yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4C22⋊Dic1911yescharacteristic
146Q16—44no—
147Q16—44no—
148M16—762no—
149M16—1521no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—1521no—
154C2×C8—1521no—
155C4⋊C4—41no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C42—41no—
159C23#1059729111yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—42no—
163Q8—42no—
164Q8—81no—
165Q8—81no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4#1059728911yescharacteristic
182C2×C4#1059729411yescharacteristic
183C8—42no—
184C8—3041no—
185C8—1522no—
186C22—21no—
187C22—21no—
188C22#1192627811yescharacteristic
189C22#1192633111yescharacteristic
190C22#1192633711yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—81no—
197C4—82no—
198C2—21no—
199C2—21no—
200C2#1456163211yescharacteristic
201C2#1456179511yescharacteristic
202C2#1456180411yescharacteristic
subgroupG/H
centerC22#11926337
commutatorC2×C42×C19C2×C4
Frattini#391C2×D19
FittingC19×#2016C2
socleC22×C19#353
prime radicalC23×C19#99
cosocleC19×#391C22
hypercenter#2016D19
hypocenterC19#7405
LCSG ▷ C2×C42×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #2016

Complements

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

NH ≅ G/Ntype
129. C19#7405semidirect

Maximal subgroups

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

subgroupindex
#145617622
#145615692
C19×#20162
#740519