Finite Group Databasebeta

← #18086634

Subgroups — #18086634

Order 4864.

364 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 77 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#14574980C211yesmaximal, characteristic
2#14563788C211yesmaximal, characteristic
3#14562336C212yesmaximal
4#14562148C212yesmaximal
5C19×#1290C211yesmaximal, characteristic
6#11927101C2212yes—
7#11926840—22no—
8#11926785—22no—
9#11926755—22no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×Dic19⋊C8—22no—
12#11926390C2211yescharacteristic
13#11926291—22no—
14#11926289—22no—
15#11926282—24no—
16C19×#432C2212yes—
17C2×C19×C4⋊C8C2211yescharacteristic
18C22×C8×C19D412yes—
19C2×C42×C19C2311yescharacteristic
20#10597372—22no—
21#10597370—22no—
22#10597370—22no—
23C2×C4×Dic19—21no—
24C22×C19⋊C8—21no—
25C2×Dic76—22no—
26#10597316—22no—
27#10597315D412yes—
28#10597315D412yes—
29C4×Dic38—22no—
30C4×Dic38—22no—
31C19×C4⋊C8—22no—
32C19×C4⋊C8—22no—
33C19×C22⋊C8—22no—
34C19×#97—22no—
35C19⋊#95—21no—
36C19⋊#95D412yes—
37#10597275—22no—
38#10597273—24no—
39Dic19⋊C8—44no—
40C4⋊(C19⋊C8)—22no—
41C22×C4×C19C2×D411yescharacteristic
42C22×C4×C19C2×D411yescharacteristic
43C22×C4×C19#4111yescharacteristic
44C22×Dic19—22no—
45C2×Dic38—22no—
46C2×Dic38—22no—
47C2×C8×C19—22no—
48C2×C8×C19—42no—
49C2×C8×C19—42no—
50C42×C19C2×D412yes—
51C42×C19#4112yes—
52C22⋊Dic19—42no—
53C4⋊Dic19—22no—
54C4⋊Dic19—22no—
55C4⋊Dic19—22no—
56C4⋊Dic19—22no—
57Dic19⋊C4—42no—
58Dic19⋊C4—42no—
59C4×Dic19—22no—
60C4×Dic19—22no—
61C4×Dic19—42no—
62C2×C19⋊C8—42no—
63C2×C19⋊C8—41no—
64Dic76—82no—
65#10516—191nomaximal, Sylow
66C23×C19#12111yescharacteristic
67C2×C4×C19—22no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—41no—
71C2×C4×C19#12011yescharacteristic
72C2×C4×C19#12112yes—
73C2×C4×C19#12312yes—
74C2×C4×C19#12411yescharacteristic
75C2×Dic19—24no—
76C2×Dic19—42no—
77C2×Dic19—42no—
78C2×Dic19—42no—
79C2×Dic19—42no—
80Dic38—42no—
81Dic38—42no—
82Dic38—82no—
83C8×C19—42no—
84C8×C19—82no—
85C19⋊C8—81no—
86#3249—191no—
87#1843—191no—
88#1552—192no—
89#1506—192no—
90#1290D1911yescharacteristic
91C22×C19—21no—
92C22×C19—21no—
93C22×C19#39411yescharacteristic
94C22×C19#47312yes—
95C4×C19—22no—
96C4×C19—21no—
97C4×C19—22no—
98C4×C19#45311yescharacteristic
99C4×C19#45611yescharacteristic
100Dic19—44no—
101Dic19—82no—
102Dic19—82no—
103#533—192no—
104#477—382no—
105#467—382no—
106#462—382no—
107#432C2×D1912yes—
108C2×C4⋊C8—191no—
109C2×C4⋊C8—382no—
110C2×C4⋊C8C2×D1911yescharacteristic
111#376—191no—
112#332—382no—
113#332—382no—
114#328—384no—
115C2×C19—22no—
116C2×C19#203911yescharacteristic
117C2×C19#204711yescharacteristic
118C2×C19#205311yescharacteristic
119C2×Q16—382no—
120C22×C8—381no—
121C22×C8D7612yes—
122C4⋊Q8—192no—
123C4⋊Q8—192no—
124#125—382no—
125C22⋊Q8—382no—
126C22⋊Q8—382no—
127C4×Q8—382no—
128C4×Q8—382no—
129#117—382no—
130C2×C42—381no—
131C2×C42C22×D1911yescharacteristic
132#107—382no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—382no—
136C4⋊C8—764no—
137#103—384no—
138C22⋊C8—22no—
139#97—22no—
140#95—192no—
141#95—381no—
142C19#1051611yescharacteristic, complemented, Sylow
143C2×Q8—382no—
144C2×Q8—382no—
145C22×C4—382no—
146C22×C4C2×D7611yescharacteristic
147C22×C4D4×D1911yescharacteristic
148C22×C4#6454511yescharacteristic
149Q16—1522no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—762no—
154C2×C8—761no—
155C4⋊C4—382no—
156C4⋊C4—382no—
157C4⋊C4—382no—
158C4⋊C4—382no—
159C4⋊C4—762no—
160C4⋊C4—762no—
161C22⋊C4—762no—
162C42—382no—
163C42—382no—
164C42—762no—
165C42#6454112yes—
166C42D4×D1912yes—
167C23#1059734111yescharacteristic
168Q8—762no—
169Q8—762no—
170Q8—1522no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—384no—
176C2×C4—762no—
177C2×C4—762no—
178C2×C4—762no—
179C2×C4—762no—
180C2×C4#1059732111yescharacteristic
181C2×C4#1059732811yescharacteristic
182C2×C4#1059733012yes—
183C2×C4#1059734012yes—
184C8—42no—
185C8—82no—
186C8—1521no—
187C22—21no—
188C22—21no—
189C22#1192646211yescharacteristic
190C22#1192682012yes—
191C4—22no—
192C4—22no—
193C4—21no—
194C4—764no—
195C4—1522no—
196C4—1522no—
197C4#1192671411yescharacteristic
198C4#1192672911yescharacteristic
199C2—22no—
200C2#1456486011yescharacteristic
201C2#1456490411yescharacteristic
202C2#1456494211yescharacteristic
subgroupG/H
centerC22#11926462
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1290C2
socleC22×C19#394
prime radicalC23×C19#121
hypercenter#1290D19
hypocenterC19#10516
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
142. C19#10516semidirect

Maximal subgroups

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

subgroupindex
#145749802
#145637882
#145623362
#145621482
C19×#12902
#1051619