Finite Group Databasebeta

← #18080173

Subgroups — #18080173

Order 4864.

456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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#14574038C211yesmaximal, characteristic
2#14562262C211yesmaximal, characteristic, complemented
3#14562142C212yesmaximal
4#14561528C212yesmaximal, complemented
5C19×#2371C211yesmaximal, characteristic, complemented
6#11927094C2211yescharacteristic
7#11926914C412yescomplemented
8#11926910C412yescomplemented
9#11926901—22no—
10#11926601C2212yes—
11#11926543—22no—
12C4×#64520C2211yescharacteristic
13#11926286—22no—
14#11926277—22no—
15#11926277—22no—
16C2×C19×#125C2211yescharacteristic
17C19×#387—22no—
18C19×#387—22no—
19C4×C4⋊C4×C19—22no—
20C19×#376C2212yes—
21C2×#64541—21no—
22C19×#125—22no—
23C19×#125C2×C412yes—
24C19×#125D412yes—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19D412yes—
28C2×C42×C19—22no—
29C2×C42×C19—22no—
30C2×C42×C19C2311yescharacteristic
31#10597376—22no—
32C2×#64520—21no—
33#10597321—21no—
34#10597320C2×C411yescharacteristic
35C4×D76—22no—
36#10597315C2×C411yescharacteristic
37C19×#95—22no—
38C19×#95—22no—
39C19×#95—22no—
40C19×#95D412yes—
41C19×#95D412yes—
42C22⋊(C19⋊C8)—22no—
43#10597267—24no—
44#10597266—24no—
45C4⋊(C19⋊C8)—22no—
46#10597260—22no—
47#10597260C2×C412yes—
48C4×C19⋊C8—21no—
49C22×C4×C19—22no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19C2×D411yescharacteristic
53C22×C4×C19C2×D412yes—
54C2×C22⋊D19—41no—
55#64541—44no—
56C2×D76—21no—
57C2×D76—22no—
58C2×C4×D19—41no—
59C2×Dic38—21no—
60C4⋊C4×C19—24no—
61C4⋊C4×C19—24no—
62C4⋊C4×C19—22no—
63C4⋊C4×C19—44no—
64C4⋊C4×C19C22⋊C414yes—
65C42×C19—44no—
66C42×C19—44no—
67C42×C19C22×C411yescharacteristic
68C42×C19C2×D411yescharacteristic
69C42×C19#4112yes—
70(C2×D19)⋊C4—42no—
71C4⋊Dic19—22no—
72#64520—42no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—42no—
75#9442—191nomaximal, Sylow
76C23×C19#12011yescharacteristic
77C22×D19—41no—
78C2×C4×C19—22no—
79C2×C4×C19—24no—
80C2×C4×C19—24no—
81C2×C4×C19—42no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19—42no—
88C2×C4×C19—42no—
89C2×C4×C19C2×C22⋊C411yescharacteristic
90C2×C4×C19C4×D412yes—
91C2×C4×C19#12112yes—
92C2×C4×C19#12311yescharacteristic
93C22⋊D19—82no—
94C2×Dic19—41no—
95D76—42no—
96D76—82no—
97C4×D19—82no—
98Dic38—42no—
99C19⋊C8—42no—
100C19⋊C8—82no—
101#3142—191no—
102#2371D1911yescharacteristic, complemented
103#1534—191no—
104#1505—192no—
105#1300—192no—
106C22×C19—22no—
107C22×C19#38611yescharacteristic
108C22×C19#45412yes—
109C2×D19—81no—
110C2×D19—82no—
111C4×C19—21no—
112C4×C19—21no—
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—44no—
116C4×C19—44no—
117C4×C19—82no—
118Dic19—81no—
119#532—191no—
120C2×#125C2×D1911yescharacteristic
121#491—192no—
122#490—192no—
123#488—382no—
124#432—192no—
125#417—382no—
126C4×M16—191no—
127#387—22no—
128#387—22no—
129C4×C4⋊C4—22no—
130#376C2×D1912yes—
131#330—382no—
132#327—382no—
133#327—382no—
134C2×C19—22no—
135C2×C19#188811yescharacteristic
136C2×C19#190612yes—
137D19—161no—
138C2×#41—381no—
139C2×M16—381no—
140C4⋊Q8—191no—
141#127—191no—
142#125—22no—
143#125C4×D1912yes—
144#125D7612yes—
145#124—381no—
146#121—382no—
147C4×D4—382no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4C22⋊D1912yes—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42C22×D1911yescharacteristic
154C4⋊C8—382no—
155#103—384no—
156#102—384no—
157C22⋊C8—382no—
158#97—192no—
159#97—382no—
160C4×C8—381no—
161#95—22no—
162#95—22no—
163#95—22no—
164#95C22⋊D1912yes—
165#95C22⋊D1912yes—
166C19#944211yescharacteristic, complemented, Sylow
167#41—764no—
168C2×Q8—381no—
169C2×D4—381no—
170C2×D4—382no—
171C2×D4—761no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—761no—
176C22×C4C2×C22⋊D1911yescharacteristic
177C22×C4C2×C22⋊D1912yes—
178M16—762no—
179C2×C8—382no—
180C2×C8—762no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—44no—
185C4⋊C4—382no—
186C4⋊C4(C2×D19)⋊C414yes—
187C22⋊C4—762no—
188C42—44no—
189C42—44no—
190C42C2×C4×D1911yescharacteristic
191C42C2×D7611yescharacteristic
192C42#6454112yes—
193C23—761no—
194C23#1059739911yescharacteristic
195Q8—762no—
196D4—762no—
197D4—1522no—
198D4—1522no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—761no—
211C2×C4—1522no—
212C2×C4C2×(C2×D19)⋊C411yescharacteristic
213C2×C4C4×C22⋊D1912yes—
214C2×C4#1059737511yescharacteristic
215C2×C4#1059737612yes—
216C8—762no—
217C8—1522no—
218C22—22no—
219C22—1522no—
220C22—1521no—
221C22#1192642311yescharacteristic
222C22#1192671712yes—
223C4—22no—
224C4—22no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—44no—
229C4—82no—
230C4—1521no—
231C2—22no—
232C2—3041no—
233C2#1456403811yescharacteristic
234C2#1456413612yes—
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2371C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#2371D19
hypocenterC19#9442
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #14562262C2semidirect
4. #14561528C2semidirect
5. C19×#2371C2semidirect
7. #11926914C4semidirect
8. #11926910C4semidirect
102. #2371D19semidirect
166. C19#9442semidirect

Maximal subgroups

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

subgroupindex
#145740382
#145622622
#145621422
#145615282
C19×#23712
#944219