Finite Group Databasebeta

← #18070090

Subgroups — #18070090

Order 4864.

228 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564859C211yesmaximal, characteristic
2#14561581C211yesmaximal, characteristic, complemented
3C19×#1296C211yesmaximal, characteristic, complemented
4#11927125C411yescharacteristic
5C2×#10597262—21no—
6#11926543—21no—
7#11926313C411yescharacteristic
8#11926270—21no—
9C2×C19×C4⋊C8—21no—
10C19×#384C2211yescharacteristic
11C2×#64541—21no—
12C22×C8×C19—41no—
13C2×C4⋊C4×C19—41no—
14C2×C4⋊C4×C19C2×C411yescharacteristic
15C2×C4⋊C4×C19D411yescharacteristic
16C2×C42×C19D411yescharacteristic
17#10597376—41no—
18C2×#64520—21no—
19#10597343—41no—
20#10597341—41no—
21C19×C4⋊C8—22no—
22C19×C4⋊C8—41no—
23C22⋊(C19⋊C8)—41no—
24#10597267—41no—
25#10597266—41no—
26#10597262—41no—
27#10597262—41no—
28C22×C4×C19—21no—
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19C22⋊C411yescharacteristic
32C2×C22⋊D19—41no—
33#64541—41no—
34#64541—41no—
35#64541—41no—
36#64541—41no—
37C2×D76—21no—
38C2×D76—41no—
39C2×C4×D19—41no—
40C2×Dic38—21no—
41C2×C8×C19—42no—
42C2×C8×C19—81no—
43C2×C8×C19—81no—
44C4⋊C4×C19—41no—
45C4⋊C4×C19—41no—
46C4⋊C4×C19—81no—
47C4⋊C4×C19—81no—
48C42×C19—21no—
49C42×C19D811yescharacteristic
50C42×C19SD1611yescharacteristic
51(C2×D19)⋊C4—42no—
52C4⋊Dic19—41no—
53#64520—41no—
54#64520—41no—
55C2×C19⋊C8—41no—
56C2×C19⋊C8—81no—
57#7417—191nomaximal, Sylow
58C23×C19#9911yescharacteristic
59C22×D19—41no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—21no—
63C2×C4×C19—21no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—81no—
71C2×C4×C19—81no—
72C2×C4×C19#10211yescharacteristic
73C2×C4×C19#10411yescharacteristic
74C22⋊D19—81no—
75C22⋊D19—81no—
76C2×Dic19—41no—
77D76—41no—
78D76—41no—
79D76—161no—
80C4×D19—81no—
81C4×D19—81no—
82Dic38—41no—
83Dic38—41no—
84C8×C19—82no—
85C19⋊C8—81no—
86C19⋊C8—161no—
87#2039—191no—
88#1325—191no—
89#1296D1911yescharacteristic, complemented
90C22×C19—21no—
91C22×C19—21no—
92C22×C19#32711yescharacteristic
93C22×C19AΣL(1,𝔽16)11yescharacteristic
94C22×C19#35511yescharacteristic
95C2×D19—81no—
96C2×D19—81no—
97C2×D19—81no—
98C4×C19—21no—
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—21no—
102C4×C19—21no—
103C4×C19—21no—
104C4×C19—81no—
105C4×C19—81no—
106Dic19—81no—
107#537—191no—
108C2×C4⋊C8—21no—
109C2×#104—381no—
110#417—381no—
111#384C2×D1911yescharacteristic
112#343—191no—
113#324—381no—
114C2×C19—21no—
115C2×C19—21no—
116C2×C19#134511yescharacteristic
117C2×C19#140211yescharacteristic
118C2×C19#140511yescharacteristic
119D19—161no—
120C2×#41—381no—
121C2×M16—381no—
122C22×C8—41no—
123C22⋊Q8—761no—
124#121—761no—
125#121—761no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4C4×D1911yescharacteristic
128C2×C4⋊C4D7611yescharacteristic
129C2×C42C22⋊D1911yescharacteristic
130C4⋊C8—22no—
131C4⋊C8—41no—
132#104—761no—
133#104—761no—
134#103—761no—
135#102—761no—
136C22⋊C8—761no—
137C19#741711yescharacteristic, complemented, Sylow
138#41—761no—
139#41—761no—
140#41—761no—
141#41—761no—
142C2×Q8—381no—
143C2×D4—381no—
144C2×D4—761no—
145C2×D4—761no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—761no—
150C22×C4(C2×D19)⋊C411yescharacteristic
151M16—761no—
152M16—761no—
153C2×C8—42no—
154C2×C8—81no—
155C2×C8—81no—
156C2×C8—761no—
157C2×C8—1521no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—81no—
161C4⋊C4—81no—
162C4⋊C4—761no—
163C22⋊C4—762no—
164C42—21no—
165C42#6452511yescharacteristic
166C42#6452711yescharacteristic
167C23—761no—
168C23#1059726311yescharacteristic
169Q8—761no—
170Q8—761no—
171D4—3041no—
172D4—761no—
173D4—761no—
174D4—1521no—
175D4—1521no—
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—81no—
187C2×C4—81no—
188C2×C4—761no—
189C2×C4—1521no—
190C2×C4—1521no—
191C2×C4#1059726211yescharacteristic
192C2×C4#1059726611yescharacteristic
193C8—82no—
194C8—3041no—
195C8—1521no—
196C22—21no—
197C22—21no—
198C22—1521no—
199C22—1521no—
200C22—1521no—
201C22#1192627711yescharacteristic
202C22#1192633211yescharacteristic
203C22#1192634011yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—21no—
210C4—81no—
211C4—81no—
212C4—1521no—
213C2—21no—
214C2—21no—
215C2—3041no—
216C2#1456163711yescharacteristic
217C2#1456178111yescharacteristic
218C2#1456179011yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×C4⋊C4×C19C2×C4
Frattini#384C2×D19
FittingC19×#1296C2
socleC22×C19AΣL(1,𝔽16)
prime radical#11927125C4
cosocleC19×#384C22
hypercenter#1296D19
hypocenterC19#7417
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #14561581C2semidirect
3. C19×#1296C2semidirect
89. #1296D19semidirect
137. C19#7417semidirect

Maximal subgroups

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

subgroupindex
#145648592
#145615812
C19×#12962
#741719