Finite Group Databasebeta

← #18080174

Subgroups — #18080174

Order 4864.

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

normal subgroups only

This group has 456 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, complemented
2#14562262C211yesmaximal, characteristic, complemented
3#14562143C212yesmaximal
4#14561529C212yesmaximal, complemented
5C19×#3142C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926430—22no—
8#11926430—22no—
9C4⋊C4×Dic19—22no—
10#11926390C2212yes—
11#11926286—22no—
12#11926278—22no—
13#11926278—22no—
14C19×#532C2211yescharacteristic
15C2×C19×#125C2211yescharacteristic
16C19×#491C412yescomplemented
17C19×#490C412yescomplemented
18C19×#488—22no—
19C19×#417—22no—
20C4×M16×C19C2211yescharacteristic
21C2×#41×C19—21no—
22C2×M16×C19—21no—
23C19×C4⋊Q8C2×C411yescharacteristic
24C19×#127C2×C411yescharacteristic
25C19×#125—22no—
26C19×#125C2×C412yes—
27C19×#125D412yes—
28C19×#124—21no—
29C19×#121—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19D412yes—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—22no—
35C2×C4×Dic19—22no—
36C2×C4×Dic19—22no—
37C19×#103—24no—
38C19×#102—24no—
39C19×#97C2×C412yes—
40C4×C8×C19—21no—
41C19⋊#95—22no—
42C19⋊#95—22no—
43C19⋊#95—22no—
44C19⋊#95D412yes—
45C19⋊#95D412yes—
46C22⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48#10597260—22no—
49#41×C19—44no—
50C2×Q8×C19—21no—
51C2×D4×C19—21no—
52C2×D4×C19—22no—
53C2×D4×C19—41no—
54C22×C4×C19—22no—
55C22×C4×C19—41no—
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D411yescharacteristic
58C22×Dic19—22no—
59C22×Dic19—22no—
60M16×C19—42no—
61C2×C8×C19—22no—
62C4⋊C4×C19—24no—
63C4⋊C4×C19—24no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—22no—
66C4⋊C4×C19C22⋊C414yes—
67C22⋊C4×C19—42no—
68C42×C19C22×C411yescharacteristic
69C42×C19C2×D411yescharacteristic
70C42×C19#4112yes—
71C4⋊Dic19—44no—
72C4×Dic19—44no—
73C4×Dic19—44no—
74C2×C19⋊C8—42no—
75#9442—191nomaximal, Sylow
76C23×C19—41no—
77C23×C19#12011yescharacteristic
78Q8×C19—42no—
79D4×C19—42no—
80D4×C19—82no—
81D4×C19—82no—
82C2×C4×C19—22no—
83C2×C4×C19—24no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19—41no—
88C2×C4×C19—82no—
89C2×C4×C19C2×C22⋊C411yescharacteristic
90C2×C4×C19C4×D412yes—
91C2×C4×C19#12112yes—
92C2×C4×C19#12311yescharacteristic
93C2×Dic19—24no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C8×C19—42no—
100C19⋊C8—82no—
101#3142D1911yescharacteristic
102#2371—191no—
103#1534—191no—
104#1505—192no—
105#1300—192no—
106C22×C19—22no—
107C22×C19—81no—
108C22×C19—82no—
109C22×C19#38611yescharacteristic
110C22×C19#45412yes—
111C4×C19—21no—
112C4×C19—21no—
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—44no—
116C4×C19—81no—
117Dic19—44no—
118Dic19—82no—
119#532C2×D1911yescharacteristic
120C2×#125C2×D1911yescharacteristic
121#491Dic1912yescomplemented
122#490Dic1912yescomplemented
123#488—22no—
124#432—192no—
125#417—22no—
126C4×M16C2×D1911yescharacteristic
127#387—382no—
128#387—382no—
129C4×C4⋊C4—382no—
130#376—192no—
131#330—382no—
132#327—382no—
133#327—382no—
134C2×C19—22no—
135C2×C19—161no—
136C2×C19#188811yescharacteristic
137C2×C19#190612yes—
138C2×#41—21no—
139C2×M16—21no—
140C4⋊Q8C2×Dic1911yescharacteristic
141#127C2×Dic1911yescharacteristic
142#125—22no—
143#125C2×Dic1912yes—
144#125C22⋊D1912yes—
145#124—21no—
146#121—22no—
147C4×D4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—382no—
150C2×C4⋊C4C22⋊D1912yes—
151C2×C42—382no—
152C2×C42—382no—
153C2×C42C22×D1911yescharacteristic
154C4⋊C8—382no—
155#103—24no—
156#102—24no—
157C22⋊C8—382no—
158#97—382no—
159#97C2×Dic1912yes—
160C4×C8—21no—
161#95—192no—
162#95—192no—
163#95—382no—
164#95—382no—
165#95—382no—
166C19#944211yescharacteristic, complemented, Sylow
167#41—44no—
168C2×Q8—21no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—41no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4—382no—
175C22×C4—382no—
176C22×C4D4×D1912yes—
177C22×C4C2×C22⋊D1911yescharacteristic
178M16—42no—
179C2×C8—22no—
180C2×C8—762no—
181C4⋊C4—24no—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—764no—
186C4⋊C4C22⋊Dic1914yes—
187C22⋊C4—42no—
188C42—764no—
189C42—764no—
190C42#6454312yes—
191C42C22×Dic1911yescharacteristic
192C42C2×C22⋊D1911yescharacteristic
193C23—41no—
194C23#1059738311yescharacteristic
195Q8—42no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—82no—
206C2×C4—384no—
207C2×C4—762no—
208C2×C4—762no—
209C2×C4—762no—
210C2×C4—762no—
211C2×C4—762no—
212C2×C4D4×Dic1912yes—
213C2×C4#1059738111yescharacteristic
214C2×C4#1059738512yes—
215C2×C4C2×C22⋊Dic1911yescharacteristic
216C8—42no—
217C8—1522no—
218C22—22no—
219C22—82no—
220C22—81no—
221C22#1192642411yescharacteristic
222C22#1192671612yes—
223C4—22no—
224C4—22no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—81no—
229C4—764no—
230C4—1522no—
231C2—22no—
232C2—161no—
233C2#1456403911yescharacteristic
234C2#1456413812yes—
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3142C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#3142D19
hypocenterC19#9442
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. #14566741C2semidirect
2. #14562262C2semidirect
4. #14561529C2semidirect
16. C19×#491C4semidirect
17. C19×#490C4semidirect
121. #491Dic19semidirect
122. #490Dic19semidirect
166. C19#9442semidirect

Maximal subgroups

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

subgroupindex
#145667412
#145622622
#145621432
#145615292
C19×#31422
#944219