Finite Group Databasebeta

← #18080163

Subgroups — #18080163

Order 4864.

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

normal subgroups only

This group has 434 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#14574184C211yesmaximal, characteristic
2#14562262C211yesmaximal, characteristic
3#14562146C212yesmaximal
4#14561528C212yesmaximal
5C19×#2371C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7#11926954C414yescomplemented
8#11926943—22no—
9#11926601C2212yes—
10#11926584—22no—
11C4×#64520C2211yescharacteristic
12#11926286—22no—
13#11926280—22no—
14#11926280—22no—
15C2×C19×#125C2211yescharacteristic
16C19×#387—22no—
17C19×#387—22no—
18C4×C4⋊C4×C19—22no—
19C19×#376C2212yes—
20C19×#125—22no—
21C19×#125C2×C412yes—
22C19×#125D412yes—
23C2×C4⋊C4×C19—22no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19D412yes—
26C2×C42×C19—22no—
27C2×C42×C19—22no—
28C2×C42×C19C2311yescharacteristic
29#10597372—21no—
30#10597370—22no—
31C2×#64520—21no—
32#10597316—21no—
33#10597315C2×C412yes—
34C4×Dic38—22no—
35C19×#95—22no—
36C19×#95—22no—
37C19×#95—22no—
38C19×#95D412yes—
39C19×#95D412yes—
40C22⋊(C19⋊C8)—22no—
41#10597265—24no—
42#10597264—24no—
43C4⋊(C19⋊C8)—22no—
44#10597260—22no—
45#10597260C2×C412yes—
46C4×C19⋊C8—21no—
47C22×C4×C19—22no—
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19C2×D411yescharacteristic
51C22×C4×C19C2×D412yes—
52C2×Dic38—22no—
53C4⋊C4×C19—24no—
54C4⋊C4×C19—24no—
55C4⋊C4×C19—22no—
56C4⋊C4×C19—44no—
57C4⋊C4×C19C22⋊C414yes—
58C42×C19—44no—
59C42×C19—44no—
60C42×C19C22×C411yescharacteristic
61C42×C19C2×D411yescharacteristic
62C42×C19#4112yes—
63C22⋊Dic19—41no—
64C4⋊Dic19—22no—
65C4⋊Dic19—22no—
66Dic19⋊C4—42no—
67C4×Dic19—41no—
68#64520—24no—
69C2×C19⋊C8—22no—
70C2×C19⋊C8—42no—
71#9440—191nomaximal, Sylow
72C23×C19#12011yescharacteristic
73C2×C4×C19—22no—
74C2×C4×C19—24no—
75C2×C4×C19—24no—
76C2×C4×C19—42no—
77C2×C4×C19—42no—
78C2×C4×C19—42no—
79C2×C4×C19—42no—
80C2×C4×C19—42no—
81C2×C4×C19—42no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19C2×C22⋊C411yescharacteristic
85C2×C4×C19C4×D412yes—
86C2×C4×C19#12112yes—
87C2×C4×C19#12311yescharacteristic
88C2×Dic19—42no—
89Dic38—82no—
90C19⋊C8—24no—
91C19⋊C8—82no—
92#3166—191no—
93#2371D1911yescharacteristic
94#1534—191no—
95#1506—192no—
96#1300—192no—
97C22×C19—22no—
98C22×C19#38611yescharacteristic
99C22×C19#45612yes—
100C4×C19—21no—
101C4×C19—21no—
102C4×C19—22no—
103C4×C19—22no—
104C4×C19—44no—
105C4×C19—44no—
106C4×C19—82no—
107Dic19—82no—
108#533—191no—
109C2×#125C2×D1911yescharacteristic
110#501—194no—
111#499—382no—
112#432—192no—
113#428—382no—
114C4×M16—191no—
115#387—22no—
116#387—22no—
117C4×C4⋊C4—22no—
118#376C2×D1912yes—
119#330—382no—
120#328—382no—
121#328—382no—
122C2×C19—22no—
123C2×C19#188611yescharacteristic
124C2×C19#190612yes—
125C2×M16—381no—
126C4⋊Q8—192no—
127#125—22no—
128#125—381no—
129#125C4×D1912yes—
130#125D7612yes—
131C22⋊Q8—382no—
132C4×Q8—382no—
133#117—381no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C22⋊D1912yes—
137C2×C42—22no—
138C2×C42—22no—
139C2×C42C22×D1911yescharacteristic
140#107—384no—
141#106—384no—
142C4⋊C8—382no—
143C22⋊C8—382no—
144#97—192no—
145#97—382no—
146C4×C8—381no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95C22⋊D1912yes—
151#95C22⋊D1912yes—
152C19#944011yescharacteristic, complemented, Sylow
153C2×Q8—382no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4C2×C22⋊D1911yescharacteristic
158C22×C4C2×C22⋊D1912yes—
159M16—384no—
160C2×C8—382no—
161C2×C8—762no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—44no—
166C4⋊C4—382no—
167C4⋊C4—382no—
168C4⋊C4—762no—
169C4⋊C4(C2×D19)⋊C414yes—
170C22⋊C4—761no—
171C42—44no—
172C42—44no—
173C42—761no—
174C42C2×C4×D1911yescharacteristic
175C42C2×D7611yescharacteristic
176C42#6454112yes—
177C23#1059739911yescharacteristic
178Q8—1522no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—762no—
191C2×C4C2×(C2×D19)⋊C411yescharacteristic
192C2×C4C4×C22⋊D1912yes—
193C2×C4#1059737511yescharacteristic
194C2×C4#1059737612yes—
195C8—384no—
196C8—1522no—
197C22—22no—
198C22#1192642311yescharacteristic
199C22#1192672712yes—
200C4—22no—
201C4—22no—
202C4—21no—
203C4—21no—
204C4—44no—
205C4—44no—
206C4—82no—
207C4—1522no—
208C2—22no—
209C2#1456402811yescharacteristic
210C2#1456413612yes—
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2371C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#2371D19
hypocenterC19#9440
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
7. #11926954C4semidirect
152. C19#9440semidirect

Maximal subgroups

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

subgroupindex
#145741842
#145622622
#145621462
#145615282
C19×#23712
#944019