Finite Group Databasebeta

← #18070091

Subgroups — #18070091

Order 4864.

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

normal subgroups only

This group has 228 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#14561581C211yesmaximal, characteristic, complemented
2#14561518C211yesmaximal, characteristic, complemented
3C19×#2039C211yesmaximal, characteristic
4C2×C4⋊(C19⋊C8)—21no—
5#11926270—21no—
6C19×#537C411yescharacteristic
7C2×C19×#104—21no—
8C19×#417—21no—
9C19×#384C2211yescharacteristic
10C19×#343C411yescharacteristic
11C2×#41×C19—21no—
12C2×M16×C19—21no—
13C19×C22⋊Q8—41no—
14C19×#121—41no—
15C19×#121—41no—
16C2×C4⋊C4×C19—41no—
17C2×C4⋊C4×C19C2×C411yescharacteristic
18C2×C4⋊C4×C19D411yescharacteristic
19C2×C42×C19D411yescharacteristic
20C22×C19⋊C8—41no—
21C19×#104—41no—
22C19×#104—41no—
23C19×#103—41no—
24C19×#102—41no—
25C22⋊(C19⋊C8)—41no—
26C4⋊(C19⋊C8)—22no—
27C4⋊(C19⋊C8)—41no—
28#41×C19—41no—
29#41×C19—41no—
30#41×C19—41no—
31#41×C19—41no—
32C2×Q8×C19—21no—
33C2×D4×C19—21no—
34C2×D4×C19—41no—
35C2×D4×C19—41no—
36C22×C4×C19—21no—
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—41no—
40C22×C4×C19C22⋊C411yescharacteristic
41M16×C19—41no—
42M16×C19—41no—
43C2×C8×C19—41no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—41no—
46C4⋊C4×C19—41no—
47C4⋊C4×C19—81no—
48C4⋊C4×C19—81no—
49C22⋊C4×C19—42no—
50C42×C19—21no—
51C42×C19D811yescharacteristic
52C42×C19SD1611yescharacteristic
53C2×C19⋊C8—42no—
54C2×C19⋊C8—81no—
55C2×C19⋊C8—81no—
56C2×C19⋊C8—81no—
57#7417—191nomaximal, Sylow
58C23×C19—41no—
59C23×C19#9911yescharacteristic
60Q8×C19—41no—
61Q8×C19—41no—
62D4×C19—41no—
63D4×C19—41no—
64D4×C19—81no—
65D4×C19—81no—
66D4×C19—161no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—41no—
76C2×C4×C19—41no—
77C2×C4×C19—41no—
78C2×C4×C19—81no—
79C2×C4×C19—81no—
80C2×C4×C19—81no—
81C2×C4×C19—81no—
82C2×C4×C19#10211yescharacteristic
83C2×C4×C19#10411yescharacteristic
84C8×C19—81no—
85C19⋊C8—82no—
86C19⋊C8—161no—
87#2039D1911yescharacteristic
88#1325—191no—
89#1296—191no—
90C22×C19—21no—
91C22×C19—21no—
92C22×C19—81no—
93C22×C19—81no—
94C22×C19—81no—
95C22×C19#32711yescharacteristic
96C22×C19AΣL(1,𝔽16)11yescharacteristic
97C22×C19#35511yescharacteristic
98C4×C19—21no—
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—21no—
102C4×C19—21no—
103C4×C19—21no—
104C4×C19—81no—
105C4×C19—81no—
106C4×C19—81no—
107#537Dic1911yescharacteristic
108C2×C4⋊C8—381no—
109C2×#104—21no—
110#417—21no—
111#384C2×D1911yescharacteristic
112#343Dic1911yescharacteristic
113#324—381no—
114C2×C19—21no—
115C2×C19—21no—
116C2×C19—161no—
117C2×C19#134511yescharacteristic
118C2×C19#140211yescharacteristic
119C2×C19#140511yescharacteristic
120C2×#41—21no—
121C2×M16—21no—
122C22×C8—761no—
123C22⋊Q8—41no—
124#121—41no—
125#121—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4C2×Dic1911yescharacteristic
128C2×C4⋊C4C22⋊D1911yescharacteristic
129C2×C42C22⋊D1911yescharacteristic
130C4⋊C8—382no—
131C4⋊C8—761no—
132#104—41no—
133#104—41no—
134#103—41no—
135#102—41no—
136C22⋊C8—761no—
137C19#741711yescharacteristic, complemented, Sylow
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142C2×Q8—21no—
143C2×D4—21no—
144C2×D4—41no—
145C2×D4—41no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4C22⋊Dic1911yescharacteristic
151M16—41no—
152M16—41no—
153C2×C8—41no—
154C2×C8—762no—
155C2×C8—1521no—
156C2×C8—1521no—
157C2×C8—1521no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—81no—
162C4⋊C4—81no—
163C22⋊C4—42no—
164C42—21no—
165C42#6452511yescharacteristic
166C42#6452611yescharacteristic
167C23—41no—
168C23#1059729111yescharacteristic
169Q8—41no—
170Q8—41no—
171D4—41no—
172D4—41no—
173D4—81no—
174D4—81no—
175D4—161no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#1059728911yescharacteristic
192C2×C4#1059729411yescharacteristic
193C8—81no—
194C8—3041no—
195C8—1522no—
196C22—21no—
197C22—21no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22#1192627811yescharacteristic
202C22#1192633111yescharacteristic
203C22#1192634111yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—21no—
210C4—81no—
211C4—81no—
212C4—81no—
213C2—21no—
214C2—21no—
215C2—161no—
216C2#1456163811yescharacteristic
217C2#1456178011yescharacteristic
218C2#1456178911yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×C4⋊C4×C19C2×C4
Frattini#384C2×D19
FittingC19×#2039C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC19×#537C4
cosocleC19×#384C22
hypercenter#2039D19
hypocenterC19#7417
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #14561581C2semidirect
2. #14561518C2semidirect
137. C19#7417semidirect

Maximal subgroups

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

subgroupindex
#145615812
#145615182
C19×#20392
#741719