Finite Group Databasebeta

← #18080164

Subgroups — #18080164

Order 4864.

434 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 103 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#14566741C211yesmaximal, characteristic
2#14562262C211yesmaximal, characteristic
3#14562147C212yesmaximal
4#14561529C212yesmaximal
5C19×#3166C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926430—22no—
8#11926430—22no—
9C4⋊C4×Dic19—22no—
10#11926390C2212yes—
11#11926286—22no—
12#11926281—22no—
13#11926281—22no—
14C19×#533C2211yescharacteristic
15C2×C19×#125C2211yescharacteristic
16C19×#501C414yescomplemented
17C19×#499—22no—
18C19×#428—22no—
19C4×M16×C19C2211yescharacteristic
20C2×M16×C19—21no—
21C19×C4⋊Q8C2×C412yes—
22C19×#125—21no—
23C19×#125—22no—
24C19×#125C2×C412yes—
25C19×#125D412yes—
26C19×C22⋊Q8—22no—
27C4×Q8×C19—22no—
28C19×#117—21no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19D412yes—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—22no—
33C2×C4×Dic19—22no—
34C2×C4×Dic19—22no—
35C19×#107—24no—
36C19×#106—24no—
37C19×#97C2×C412yes—
38C4×C8×C19—21no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41C19⋊#95—22no—
42C19⋊#95D412yes—
43C19⋊#95D412yes—
44C22⋊(C19⋊C8)—22no—
45C4⋊(C19⋊C8)—22no—
46#10597260—22no—
47C2×Q8×C19—22no—
48C22×C4×C19—22no—
49C22×C4×C19C2×D412yes—
50C22×C4×C19C2×D411yescharacteristic
51C22×Dic19—22no—
52C22×Dic19—22no—
53M16×C19—24no—
54C2×C8×C19—22no—
55C4⋊C4×C19—24no—
56C4⋊C4×C19—24no—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—22no—
60C4⋊C4×C19—42no—
61C4⋊C4×C19C22⋊C414yes—
62C22⋊C4×C19—41no—
63C42×C19—41no—
64C42×C19C22×C411yescharacteristic
65C42×C19C2×D411yescharacteristic
66C42×C19#4112yes—
67C4⋊Dic19—44no—
68C4×Dic19—44no—
69C4×Dic19—44no—
70C2×C19⋊C8—42no—
71#9440—191nomaximal, Sylow
72C23×C19#12011yescharacteristic
73Q8×C19—82no—
74C2×C4×C19—22no—
75C2×C4×C19—24no—
76C2×C4×C19—42no—
77C2×C4×C19—42no—
78C2×C4×C19—42no—
79C2×C4×C19—42no—
80C2×C4×C19C2×C22⋊C411yescharacteristic
81C2×C4×C19C4×D412yes—
82C2×C4×C19#12112yes—
83C2×C4×C19#12311yescharacteristic
84C2×Dic19—24no—
85C2×Dic19—42no—
86C2×Dic19—42no—
87C2×Dic19—42no—
88C2×Dic19—42no—
89C2×Dic19—42no—
90C8×C19—24no—
91C19⋊C8—82no—
92#3166D1911yescharacteristic
93#2371—191no—
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—82no—
106Dic19—44no—
107Dic19—82no—
108#533C2×D1911yescharacteristic
109C2×#125C2×D1911yescharacteristic
110#501Dic1914yescomplemented
111#499—22no—
112#432—192no—
113#428—22no—
114C4×M16C2×D1911yescharacteristic
115#387—382no—
116#387—382no—
117C4×C4⋊C4—382no—
118#376—192no—
119#330—382no—
120#328—382no—
121#328—382no—
122C2×C19—22no—
123C2×C19#188611yescharacteristic
124C2×C19#190612yes—
125C2×M16—21no—
126C4⋊Q8C2×Dic1912yes—
127#125—22no—
128#125—21no—
129#125C2×Dic1912yes—
130#125C22⋊D1912yes—
131C22⋊Q8—22no—
132C4×Q8—22no—
133#117—21no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—382no—
136C2×C4⋊C4C22⋊D1912yes—
137C2×C42—382no—
138C2×C42—382no—
139C2×C42C22×D1911yescharacteristic
140#107—24no—
141#106—24no—
142C4⋊C8—382no—
143C22⋊C8—382no—
144#97—382no—
145#97C2×Dic1912yes—
146C4×C8—21no—
147#95—192no—
148#95—192no—
149#95—382no—
150#95—382no—
151#95—382no—
152C19#944011yescharacteristic, complemented, Sylow
153C2×Q8—22no—
154C22×C4—22no—
155C22×C4—382no—
156C22×C4—382no—
157C22×C4D4×D1912yes—
158C22×C4C2×C22⋊D1911yescharacteristic
159M16—24no—
160C2×C8—22no—
161C2×C8—762no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—24no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—42no—
168C4⋊C4—764no—
169C4⋊C4C22⋊Dic1914yes—
170C22⋊C4—41no—
171C42—41no—
172C42—764no—
173C42—764no—
174C42#6454312yes—
175C42C22×Dic1911yescharacteristic
176C42C2×C22⋊D1911yescharacteristic
177C23#1059738311yescharacteristic
178Q8—82no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—384no—
186C2×C4—762no—
187C2×C4—762no—
188C2×C4—762no—
189C2×C4—762no—
190C2×C4—762no—
191C2×C4D4×Dic1912yes—
192C2×C4#1059738111yescharacteristic
193C2×C4#1059738512yes—
194C2×C4C2×C22⋊Dic1911yescharacteristic
195C8—24no—
196C8—1522no—
197C22—22no—
198C22#1192642411yescharacteristic
199C22#1192672612yes—
200C4—22no—
201C4—22no—
202C4—21no—
203C4—21no—
204C4—44no—
205C4—82no—
206C4—764no—
207C4—1522no—
208C2—22no—
209C2#1456402911yescharacteristic
210C2#1456413812yes—
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3166C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#3166D19
hypocenterC19#9440
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
16. C19×#501C4semidirect
110. #501Dic19semidirect
152. C19#9440semidirect

Maximal subgroups

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

subgroupindex
#145667412
#145622622
#145621472
#145615292
C19×#31662
#944019