Finite Group Databasebeta

← #18069860

Subgroups — #18069860

Order 4864.

374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 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#14561965C212yesmaximal
2C19×#1445C211yesmaximal, characteristic
3#11926508—22no—
4#11926270—22no—
5#11926270C414yescomplemented
6C22×C4⋊C4×C19C2211yescharacteristic
7C2×C19×#95—22no—
8C2×C19×#95C411yescharacteristic
9C2×C19×#95C411yescharacteristic
10C23×C4×C19—21no—
11C23×C4×C19—21no—
12C23×C4×C19C2×C411yescharacteristic
13C23×C4×C19D412yes—
14C2×C4⋊C4×C19—41no—
15C2×C4⋊C4×C19—41no—
16C2×C4⋊C4×C19C2×C412yes—
17C2×C4⋊C4×C19D411yescharacteristic
18C2×C4⋊C4×C19Q811yescharacteristic
19C2×#64520—42no—
20C19×#95—44no—
21C19×#95—41no—
22C19×#95—41no—
23C22⋊(C19⋊C8)—24no—
24C22⋊(C19⋊C8)—42no—
25C24×C19C22⋊C411yescharacteristic
26C22×C4×C19—21no—
27C22×C4×C19—21no—
28C22×C4×C19—22no—
29C22×C4×C19—22no—
30C22×C4×C19—22no—
31C22×C4×C19—22no—
32C22×C4×C19—42no—
33C22×C4×C19—42no—
34C22×C4×C19—42no—
35C22×C4×C19—42no—
36C22×C4×C19—42no—
37C22×C4×C19—41no—
38C22×C4×C19—41no—
39C22×C4×C19—42no—
40C22×C4×C19—42no—
41C22×C4×C19—41no—
42C22×C4×C19—41no—
43C22×C4×C19C4211yescharacteristic
44C22×C4×C19C22⋊C412yes—
45C22×C4×C19C4⋊C412yes—
46C22×C4×C19C4⋊C411yescharacteristic
47C4⋊C4×C19—42no—
48C4⋊C4×C19—41no—
49C4⋊C4×C19—41no—
50#64520—82no—
51#64520—82no—
52C2×C19⋊C8—44no—
53#7326—191nomaximal, Sylow
54C23×C19—22no—
55C23×C19—21no—
56C23×C19—21no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19#9511yescharacteristic
60C23×C19#9911yescharacteristic
61C23×C19#9911yescharacteristic
62C2×C4×C19—22no—
63C2×C4×C19—21no—
64C2×C4×C19—22no—
65C2×C4×C19—21no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—42no—
69C2×C4×C19—42no—
70C2×C4×C19—42no—
71C2×C4×C19—42no—
72C2×C4×C19—42no—
73C2×C4×C19—42no—
74C2×C4×C19—44no—
75C2×C4×C19—44no—
76C2×C4×C19—42no—
77C2×C4×C19—42no—
78C2×C4×C19—82no—
79C2×C4×C19—82no—
80C2×C4×C19—82no—
81C2×C4×C19—81no—
82C2×C4×C19—81no—
83C2×C4×C19—81no—
84C2×C4×C19—81no—
85C19⋊C8—84no—
86#1463—192no—
87#1445D1911yescharacteristic
88C22×C19—22no—
89C22×C19—22no—
90C22×C19—22no—
91C22×C19—22no—
92C22×C19—21no—
93C22×C19—21no—
94C22×C19—21no—
95C22×C19—21no—
96C22×C19—21no—
97C22×C19—21no—
98C22×C19#34211yescharacteristic
99C22×C19#34412yes—
100C22×C19#35311yescharacteristic
101C22×C19#35411yescharacteristic
102C22×C19#35511yescharacteristic
103C22×C19#35611yescharacteristic
104C4×C19—41no—
105C4×C19—41no—
106C4×C19—42no—
107C4×C19—42no—
108C4×C19—82no—
109C4×C19—82no—
110C22×C4⋊C4C2×D1911yescharacteristic
111#407—382no—
112C2×#95—22no—
113C2×#95Dic1911yescharacteristic
114C2×#95Dic1911yescharacteristic
115#324—194no—
116#324—382no—
117C2×C19—21no—
118C2×C19—21no—
119C2×C19—22no—
120C2×C19—21no—
121C2×C19—21no—
122C2×C19#130611yescharacteristic
123C2×C19#139311yescharacteristic
124C2×C19#139411yescharacteristic
125C23×C4—21no—
126C23×C4—21no—
127C23×C4C2×Dic1911yescharacteristic
128C23×C4C22⋊D1912yes—
129C2×M16—762no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4Dic3811yescharacteristic
133C2×C4⋊C4C4×D1912yes—
134C2×C4⋊C4D7611yescharacteristic
135C22⋊C8—384no—
136C22⋊C8—762no—
137#95—41no—
138#95—41no—
139#95—44no—
140C19#732611yescharacteristic, complemented, Sylow
141C24C22⋊Dic1911yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C4×Dic1911yescharacteristic
160C22×C4Dic19⋊C412yes—
161C22×C4C4⋊Dic1911yescharacteristic
162C22×C4(C2×D19)⋊C412yes—
163M16—1522no—
164M16—1522no—
165C2×C8—764no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23C19⋊#9511yescharacteristic
175C23#1059729111yescharacteristic
176C23#1059729111yescharacteristic
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C8—1524no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1192631111yescharacteristic
212C22#1192631412yes—
213C22#1192633711yescharacteristic
214C22#1192633911yescharacteristic
215C22#1192634111yescharacteristic
216C22#1192634311yescharacteristic
217C4—41no—
218C4—41no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2#1456154311yescharacteristic
229C2#1456176011yescharacteristic
230C2#1456176211yescharacteristic
subgroupG/H
centerC22#11926311
commutatorC22×C4×C19C42
FrattiniC22×C4⋊C4C2×D19
FittingC19×#1445C2
socleC22×C19#342
prime radicalC24×C19C22⋊C4
cosocleC22×C4⋊C4×C19C22
hypercenter#1445D19
hypocenterC19#7326
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
5. #11926270C4semidirect
140. C19#7326semidirect

Maximal subgroups

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

subgroupindex
#145619652
C19×#14452
#732619