Finite Group Databasebeta

← #18069568

Subgroups — #18069568

Order 4864.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#14563712C211yesmaximal, characteristic
2#14563401C211yesmaximal, characteristic
3C19×#1464C211yesmaximal, characteristic
4C2×C22⋊(C19⋊C8)—21no—
5C2×#10597260C411yescharacteristic, complemented
6C2×C4×C19⋊C8C411yescharacteristic, complemented
7#11926407—21no—
8#11926311—21no—
9#11926311C412yes—
10#11926299—21no—
11C2×C19×#117C2211yescharacteristic
12C19×#432—21no—
13C19×#324C412yescomplemented
14C19×#323—21no—
15C23×C4×C19D411yescharacteristic
16C19×#117—41no—
17C19×#117—41no—
18C2×C4⋊C4×C19C2×C411yescharacteristic
19C2×C4⋊C4×C19Q811yescharacteristic
20C2×C22⋊C4×C19C2×C411yescharacteristic
21C2×C22⋊C4×C19D411yescharacteristic
22C2×C42×C19C2×C411yescharacteristic
23C2×C42×C19D411yescharacteristic
24C2×C22⋊Dic19—22no—
25C22×C19⋊C8—21no—
26C22×C19⋊C8—21no—
27C19×C4⋊C8—41no—
28C19×C22⋊C8—22no—
29C19×#97—41no—
30C19⋊#95—41no—
31C19⋊#95—41no—
32C22⋊(C19⋊C8)—24no—
33#10597260—41no—
34C4×C19⋊C8—41no—
35C24×C19C22⋊C411yescharacteristic
36C22×C4×C19—22no—
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—41no—
40C22×C4×C19C4211yescharacteristic
41C22×C4×C19C22⋊C411yescharacteristic
42C22×C4×C19C22⋊C411yescharacteristic
43C22×C4×C19C4⋊C411yescharacteristic
44C22×C4×C19C4⋊C411yescharacteristic
45C22×C4×C19C4⋊C411yescharacteristic
46C22×Dic19—42no—
47C2×C8×C19—42no—
48C4⋊C4×C19—41no—
49C4⋊C4×C19—41no—
50C22⋊C4×C19—41no—
51C22⋊C4×C19—41no—
52C42×C19—21no—
53C42×C19—21no—
54C42×C19—21no—
55C42×C19—21no—
56C22⋊Dic19—42no—
57C22⋊Dic19—42no—
58C2×C19⋊C8—22no—
59C2×C19⋊C8—22no—
60C2×C19⋊C8—41no—
61C2×C19⋊C8—41no—
62C2×C19⋊C8—41no—
63C2×C19⋊C8—41no—
64#7214—191nomaximal, Sylow
65C23×C19—21no—
66C23×C19—21no—
67C23×C19—41no—
68C23×C19—41no—
69C23×C19#9511yescharacteristic
70C23×C19#10412yes—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—42no—
81C2×C4×C19—42no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19#9911yescharacteristic
87C2×C4×C19#9911yescharacteristic
88C2×Dic19—82no—
89C2×Dic19—82no—
90C2×Dic19—82no—
91C8×C19—82no—
92C19⋊C8—42no—
93C19⋊C8—42no—
94#1820—191no—
95#1750—191no—
96#1464D1911yescharacteristic
97C22×C19—21no—
98C22×C19—21no—
99C22×C19—22no—
100C22×C19—42no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—81no—
104C22×C19H(3,ℤ/4)11yescharacteristic
105C22×C19#33911yescharacteristic
106C22×C19#34211yescharacteristic
107C4×C19—21no—
108C4×C19—21no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—41no—
112C4×C19—41no—
113C4×C19—41no—
114Dic19—162no—
115C2×#117C2×D1911yescharacteristic
116#432—21no—
117C2×C22⋊C8—381no—
118C2×#97—191no—
119C2×C4×C8—191no—
120#381—381no—
121#342—192no—
122#342—381no—
123#336—381no—
124#324Dic1912yescomplemented
125#323—21no—
126C2×C19—21no—
127C2×C19—21no—
128C2×C19—42no—
129C2×C19#128411yescharacteristic
130C2×C19#139111yescharacteristic
131C2×C19#139511yescharacteristic
132C23×C4D7611yescharacteristic
133C22×C8—381no—
134C22×C8—381no—
135#117—41no—
136#117—41no—
137C2×C4⋊C4Dic3811yescharacteristic
138C2×C4⋊C4C2×Dic1911yescharacteristic
139C2×C22⋊C4—382no—
140C2×C22⋊C4C4×D1911yescharacteristic
141C2×C22⋊C4C22⋊D1911yescharacteristic
142C2×C42C4×D1911yescharacteristic
143C2×C42C22⋊D1911yescharacteristic
144C4⋊C8—41no—
145C22⋊C8—22no—
146C22⋊C8—384no—
147#97—41no—
148#97—761no—
149C4×C8—761no—
150#95—761no—
151#95—761no—
152C19#721411yescharacteristic, complemented, Sylow
153C24(C2×D19)⋊C411yescharacteristic
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—762no—
159C22×C4C4×Dic1911yescharacteristic
160C22×C4Dic19⋊C411yescharacteristic
161C22×C4Dic19⋊C411yescharacteristic
162C22×C4C4⋊Dic1911yescharacteristic
163C22×C4(C2×D19)⋊C411yescharacteristic
164C22×C4C22⋊Dic1911yescharacteristic
165C2×C8—42no—
166C2×C8—382no—
167C2×C8—382no—
168C2×C8—761no—
169C2×C8—761no—
170C2×C8—761no—
171C2×C8—761no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C22⋊C4—41no—
175C22⋊C4—41no—
176C22⋊C4—762no—
177C22⋊C4—762no—
178C42—21no—
179C42—21no—
180C42—21no—
181C42—21no—
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23#1059728212yes—
187C23C19⋊#9511yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1522no—
204C2×C4—1522no—
205C2×C4—1522no—
206C2×C4#1059726311yescharacteristic
207C2×C4#1059726311yescharacteristic
208C8—82no—
209C8—762no—
210C8—762no—
211C22—21no—
212C22—21no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22#1192630111yescharacteristic
219C22#1192630511yescharacteristic
220C22#1192631011yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—3042no—
229C2—21no—
230C2—21no—
231C2—42no—
232C2#1456148911yescharacteristic
233C2#1456175511yescharacteristic
234C2#1456176511yescharacteristic
subgroupG/H
centerC22#11926310
commutatorC22×C4×C19C42
FrattiniC2×#117C2×D19
FittingC19×#1464C2
socleC22×C19#342
prime radicalC24×C19C22⋊C4
cosocleC2×C19×#117C22
hypercenter#1464D19
hypocenterC19#7214
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
5. C2×#10597260C4semidirect
6. C2×C4×C19⋊C8C4semidirect
13. C19×#324C4semidirect
124. #324Dic19semidirect
152. C19#7214semidirect

Maximal subgroups

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

subgroupindex
#145637122
#145634012
C19×#14642
#721419