Finite Group Databasebeta

← #18080099

Subgroups — #18080099

Order 4864.

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

normal subgroups only

This group has 508 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#14566816C211yesmaximal, characteristic, complemented
2#14562361C211yesmaximal, characteristic, complemented
3#14562182C212yesmaximal
4#14561500C212yesmaximal, complemented
5C19×#3152C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926451—22no—
8#11926430—24no—
9#11926412C2212yes—
10#11926293—22no—
11#11926278—24no—
12C2×C19×#137—22no—
13C19×#532C2211yescharacteristic
14C2×C19×C4⋊Q8C2211yescharacteristic
15C19×#497—22no—
16C19×#494C412yescomplemented
17C19×#492C412yescomplemented
18C4×M16×C19C2211yescharacteristic
19C2×#41×C19—21no—
20C22×Q8×C19D412yes—
21C19×#137—44no—
22C19×#137—44no—
23C2×Q16×C19—24no—
24C2×SD16×C19—24no—
25C2×M16×C19—21no—
26C19×C4⋊Q8—22no—
27C19×C4⋊Q8C2×C411yescharacteristic
28C19×C4⋊Q8C2×C412yes—
29C19×C4⋊Q8D412yes—
30C19×#127C2×C411yescharacteristic
31C19×#124—21no—
32C19×#121—22no—
33C4×D4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—22no—
37C2×C4×Dic19—22no—
38C19×#97—21no—
39C4×C8×C19C2×C412yes—
40C19⋊#95—24no—
41C19⋊#95—22no—
42C19⋊#95—22no—
43C19⋊#95D414yes—
44C22⋊(C19⋊C8)—22no—
45C4⋊(C19⋊C8)—22no—
46#10597260—22no—
47#41×C19—42no—
48#41×C19—42no—
49C2×Q8×C19—22no—
50C2×Q8×C19—21no—
51C2×Q8×C19—42no—
52C2×Q8×C19—42no—
53C2×Q8×C19C22⋊C414yes—
54C2×D4×C19—21no—
55C2×D4×C19—22no—
56C2×D4×C19—41no—
57C22×C4×C19—22no—
58C22×C4×C19—41no—
59C22×C4×C19C2×D412yes—
60C22×C4×C19C2×D411yescharacteristic
61C22×Dic19—24no—
62Q16×C19—48no—
63SD16×C19—48no—
64M16×C19—24no—
65C2×C8×C19—22no—
66C4⋊C4×C19—24no—
67C4⋊C4×C19—24no—
68C4⋊C4×C19—22no—
69C22⋊C4×C19—42no—
70C42×C19C22×C411yescharacteristic
71C42×C19C2×D411yescharacteristic
72C42×C19#4112yes—
73C4⋊Dic19—82no—
74C4×Dic19—82no—
75C2×C19⋊C8—42no—
76#9429—191nomaximal, Sylow
77C23×C19—41no—
78C23×C19#12011yescharacteristic
79Q8×C19—44no—
80Q8×C19—42no—
81Q8×C19—82no—
82D4×C19—42no—
83D4×C19—82no—
84D4×C19—82no—
85C2×C4×C19—22no—
86C2×C4×C19—24no—
87C2×C4×C19—42no—
88C2×C4×C19—42no—
89C2×C4×C19—42no—
90C2×C4×C19—41no—
91C2×C4×C19—81no—
92C2×C4×C19—81no—
93C2×C4×C19C2×C22⋊C411yescharacteristic
94C2×C4×C19C4×D412yes—
95C2×C4×C19#12112yes—
96C2×C4×C19#12311yescharacteristic
97C2×Dic19—48no—
98C2×Dic19—44no—
99C8×C19—24no—
100C19⋊C8—82no—
101#3152D1911yescharacteristic
102#2381—191no—
103#1558—191no—
104#1514—192no—
105#1288—192no—
106C22×C19—22no—
107C22×C19—81no—
108C22×C19—82no—
109C22×C19#38611yescharacteristic
110C22×C19#45312yes—
111C4×C19—21no—
112C4×C19—21no—
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—44no—
116C4×C19—81no—
117Dic19—84no—
118C2×#137—22no—
119#532C2×D1911yescharacteristic
120C2×C4⋊Q8C2×D1911yescharacteristic
121#497—22no—
122#494Dic1912yescomplemented
123#492Dic1912yescomplemented
124#432—192no—
125C4×M16C2×D1911yescharacteristic
126#391—382no—
127#387—384no—
128#383—192no—
129#333—382no—
130#327—384no—
131C2×C19—22no—
132C2×C19—161no—
133C2×C19#188711yescharacteristic
134C2×C19#190512yes—
135C2×#41—21no—
136C22×Q8C22⋊D1912yes—
137#137—44no—
138#137—44no—
139C2×Q16—24no—
140C2×SD16—24no—
141C2×M16—21no—
142C4⋊Q8—22no—
143C4⋊Q8C2×Dic1911yescharacteristic
144C4⋊Q8C2×Dic1912yes—
145C4⋊Q8C22⋊D1912yes—
146#127C2×Dic1911yescharacteristic
147#124—21no—
148#121—22no—
149C4×D4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—382no—
152C2×C42—382no—
153C2×C42C22×D1911yescharacteristic
154C4⋊C8—382no—
155C22⋊C8—382no—
156#97—21no—
157#97—382no—
158C4×C8C2×Dic1912yes—
159#95—194no—
160#95—384no—
161#95—382no—
162#95—382no—
163C19#942911yescharacteristic, complemented, Sylow
164#41—42no—
165#41—42no—
166C2×Q8—22no—
167C2×Q8—21no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8C22⋊Dic1914yes—
171C2×D4—22no—
172C2×D4—21no—
173C2×D4—41no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4—384no—
177C22×C4D4×D1912yes—
178C22×C4C2×C22⋊D1911yescharacteristic
179Q16—48no—
180SD16—48no—
181M16—24no—
182C2×C8—22no—
183C2×C8—762no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—1522no—
188C22⋊C4—42no—
189C42—1522no—
190C42#6454312yes—
191C42C22×Dic1911yescharacteristic
192C42C2×C22⋊D1911yescharacteristic
193C23—41no—
194C23#1059738311yescharacteristic
195Q8—44no—
196Q8—42no—
197Q8—82no—
198D4—42no—
199D4—82no—
200D4—82no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4—768no—
210C2×C4—764no—
211C2×C4D4×Dic1912yes—
212C2×C4#1059738111yescharacteristic
213C2×C4#1059738512yes—
214C2×C4C2×C22⋊Dic1911yescharacteristic
215C8—24no—
216C8—1522no—
217C22—22no—
218C22—82no—
219C22—81no—
220C22#1192642411yescharacteristic
221C22#1192671112yes—
222C4—22no—
223C4—22no—
224C4—21no—
225C4—21no—
226C4—44no—
227C4—81no—
228C4—1524no—
229C2—22no—
230C2—161no—
231C2#1456403411yescharacteristic
232C2#1456413112yes—
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3152C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#3152D19
hypocenterC19#9429
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. #14566816C2semidirect
2. #14562361C2semidirect
4. #14561500C2semidirect
16. C19×#494C4semidirect
17. C19×#492C4semidirect
122. #494Dic19semidirect
123. #492Dic19semidirect
163. C19#9429semidirect

Maximal subgroups

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

subgroupindex
#145668162
#145623612
#145621822
#145615002
C19×#31522
#942919