Finite Group Databasebeta

← #18069901

Subgroups — #18069901

Order 4864.

342 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 47 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#14561569C211yesmaximal, characteristic, complemented
2#14561461C211yesmaximal, characteristic, complemented
3C19×#1793C211yesmaximal, characteristic
4#11926299—21no—
5#11926270—21no—
6C2×C19×2−1+4C411yescharacteristic
7C2×C19×#104—21no—
8C19×#417—21no—
9C2×C19×#101C411yescharacteristic
10C19×#391C2211yescharacteristic
11C19×2−1+4—21no—
12C19×2−1+4—41no—
13C19×2−1+4—42no—
14C19×2−1+4C812yescomplemented
15C2×#41×C19—21no—
16C2×#41×C19—41no—
17C2×#41×C19—41no—
18C22×Q8×C19—41no—
19C22×Q8×C19C2×C411yescharacteristic
20C2×M16×C19—21no—
21C2×C4⋊C4×C19D411yescharacteristic
22C2×C42×C19D411yescharacteristic
23C22×C19⋊C8—41no—
24C19×#104—42no—
25C19×#103—41no—
26C19×#102—41no—
27C19×#101—41no—
28C19×#95—41no—
29C22⋊(C19⋊C8)—41no—
30#41×C19—22no—
31#41×C19—22no—
32#41×C19—41no—
33#41×C19—42no—
34#41×C19—42no—
35#41×C19—42no—
36#41×C19—42no—
37#41×C19—44no—
38#41×C19—42no—
39#41×C19—42no—
40#41×C19—41no—
41C2×Q8×C19—21no—
42C2×Q8×C19—21no—
43C2×Q8×C19—41no—
44C2×Q8×C19—41no—
45C2×Q8×C19—42no—
46C2×Q8×C19—42no—
47C2×Q8×C19—44no—
48C2×Q8×C19—41no—
49C2×Q8×C19C2×C811yescharacteristic
50C2×Q8×C19M1611yescharacteristic
51C2×D4×C19—21no—
52C2×D4×C19—41no—
53C2×D4×C19—41no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19—42no—
59C22×C4×C19C22⋊C411yescharacteristic
60M16×C19—41no—
61M16×C19—41no—
62C2×C8×C19—41no—
63C4⋊C4×C19—41no—
64C42×C19—41no—
65C2×C19⋊C8—42no—
66C2×C19⋊C8—81no—
67C2×C19⋊C8—81no—
68C2×C19⋊C8—81no—
69#7345—191nomaximal, Sylow
70C23×C19—41no—
71C23×C19#9911yescharacteristic
72Q8×C19—22no—
73Q8×C19—41no—
74Q8×C19—41no—
75Q8×C19—42no—
76Q8×C19—41no—
77Q8×C19—42no—
78Q8×C19—42no—
79D4×C19—22no—
80D4×C19—41no—
81D4×C19—42no—
82D4×C19—42no—
83D4×C19—42no—
84D4×C19—42no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19—41no—
94C2×C4×C19—44no—
95C2×C4×C19—44no—
96C2×C4×C19—41no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—81no—
102C2×C4×C19C22⋊C811yescharacteristic
103C2×C4×C19#10011yescharacteristic
104C8×C19—81no—
105C19⋊C8—82no—
106C19⋊C8—161no—
107#1793D1911yescharacteristic
108#1319—191no—
109#1272—191no—
110C22×C19—21no—
111C22×C19—21no—
112C22×C19—42no—
113C22×C19—81no—
114C22×C19—81no—
115C22×C19#32311yescharacteristic
116C22×C19AΣL(1,𝔽16)11yescharacteristic
117C22×C19AΣL(1,𝔽16)11yescharacteristic
118C4×C19—21no—
119C4×C19—21no—
120C4×C19—41no—
121C4×C19—41no—
122C4×C19—41no—
123C4×C19—41no—
124C4×C19—42no—
125C4×C19—81no—
126C2×2−1+4Dic1911yescharacteristic
127C2×#104—21no—
128#417—21no—
129C2×#101Dic1911yescharacteristic
130#391C2×D1911yescharacteristic
131#336—381no—
132#324—381no—
133C2×C19—21no—
134C2×C19—21no—
135C2×C19—82no—
136C2×C19#131611yescharacteristic
137C2×C19#140411yescharacteristic
138C2×C19#140511yescharacteristic
1392−1+4—21no—
1402−1+4—41no—
1412−1+4—42no—
1422−1+4C19⋊C812yescomplemented
143C2×#41—21no—
144C2×#41—41no—
145C2×#41—41no—
146C22×Q8—41no—
147C22×Q8C2×Dic1911yescharacteristic
148C2×M16—21no—
149C22×C8—761no—
150C2×C4⋊C4C22⋊D1911yescharacteristic
151C2×C42C22⋊D1911yescharacteristic
152#104—42no—
153#103—41no—
154#102—41no—
155#101—41no—
156C22⋊C8—761no—
157#95—41no—
158C19#734511yescharacteristic, complemented, Sylow
159#41—22no—
160#41—22no—
161#41—41no—
162#41—42no—
163#41—42no—
164#41—42no—
165#41—42no—
166#41—44no—
167#41—42no—
168#41—42no—
169#41—41no—
170C2×Q8—21no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—44no—
177C2×Q8—41no—
178C2×Q8C2×C19⋊C811yescharacteristic
179C2×Q8#6452011yescharacteristic
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4C22⋊Dic1911yescharacteristic
189M16—41no—
190M16—41no—
191C2×C8—41no—
192C2×C8—762no—
193C2×C8—1521no—
194C2×C8—1521no—
195C2×C8—1521no—
196C4⋊C4—41no—
197C42—41no—
198C23—41no—
199C23#1059729111yescharacteristic
200Q8—22no—
201Q8—41no—
202Q8—41no—
203Q8—42no—
204Q8—41no—
205Q8—42no—
206Q8—42no—
207D4—22no—
208D4—41no—
209D4—42no—
210D4—42no—
211D4—42no—
212D4—42no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4C22⋊(C19⋊C8)11yescharacteristic
231C2×C4#1059729011yescharacteristic
232C8—81no—
233C8—3041no—
234C8—1522no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—81no—
239C22—81no—
240C22#1192626811yescharacteristic
241C22#1192633111yescharacteristic
242C22#1192633111yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—42no—
250C4—81no—
251C2—21no—
252C2—21no—
253C2—82no—
254C2#1456156311yescharacteristic
255C2#1456178611yescharacteristic
256C2#1456178911yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×Q8×C19C2×C8
Frattini#391C2×D19
FittingC19×#1793C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC2×C19×2−1+4C4
cosocleC19×#391C22
hypercenter#1793D19
hypocenterC19#7345
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1793

Complements

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

NH ≅ G/Ntype
1. #14561569C2semidirect
2. #14561461C2semidirect
14. C19×2−1+4C8semidirect
142. 2−1+4C19⋊C8semidirect
158. C19#7345semidirect

Maximal subgroups

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

subgroupindex
#145615692
#145614612
C19×#17932
#734519