Finite Group Databasebeta

← #18076946

Subgroups — #18076946

Order 4864.

336 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 95 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#14572741C211yesmaximal, characteristic
2#14562400C212yesmaximal
3#14562230C211yesmaximal, characteristic
4#14561528C212yesmaximal
5C19×#1995C211yesmaximal, characteristic
6#11926675—22no—
7#11926675—22no—
8#11926605—22no—
9#11926601C2212yes—
10C4×#64520C2212yes—
11#11926296—22no—
12#11926294—22no—
13#11926286C411yescharacteristic, complemented
14#11926286C412yescomplemented
15#11926286C411yescharacteristic, complemented
16C19×#533C2211yescharacteristic
17C19×#423C2211yescharacteristic
18C19×#376C2211yescharacteristic
19C19×#339—22no—
20C2×M16×C19—21no—
21C19×C4⋊Q8Q812yes—
22C19×#125C2×C411yescharacteristic
23C19×#125C2×C411yescharacteristic
24C19×C22⋊Q8—22no—
25C4×Q8×C19—22no—
26C19×#117D412yes—
27C2×C42×C19—21no—
28C2×C42×C19C2311yescharacteristic
29C2×#64520—22no—
30C19×C4⋊C8—22no—
31C19×#95—22no—
32C22⋊(C19⋊C8)—22no—
33C4⋊(C19⋊C8)—22no—
34C4⋊(C19⋊C8)—22no—
35C4⋊(C19⋊C8)D412yes—
36C4⋊(C19⋊C8)D412yes—
37#10597260—22no—
38#10597260—22no—
39#10597260C2×C412yes—
40#10597260C2×C412yes—
41C4×C19⋊C8—22no—
42C4×C19⋊C8—22no—
43C2×Q8×C19—22no—
44C22×C4×C19—41no—
45C22×C4×C19C2×D411yescharacteristic
46C22×C4×C19#4112yes—
47M16×C19—42no—
48C2×C8×C19—41no—
49C4⋊C4×C19—22no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—22no—
52C4⋊C4×C19C4⋊C412yes—
53C4⋊C4×C19C4⋊C412yes—
54C22⋊C4×C19—22no—
55C42×C19—22no—
56C42×C19—22no—
57C42×C19—41no—
58C42×C19C22×C411yescharacteristic
59C42×C19C2×D412yes—
60C42×C19C2×Q811yescharacteristic
61#64520—44no—
62C2×C19⋊C8—22no—
63C2×C19⋊C8—22no—
64C2×C19⋊C8—22no—
65C2×C19⋊C8—22no—
66#8919—191nomaximal, Sylow
67C23×C19#12311yescharacteristic
68Q8×C19—82no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—42no—
74C2×C4×C19—42no—
75C2×C4×C19—82no—
76C2×C4×C19C2×C4⋊C411yescharacteristic
77C2×C4×C19C4×D412yes—
78C2×C4×C19#12011yescharacteristic
79C2×C4×C19C22⋊Q812yes—
80C8×C19—81no—
81C19⋊C8—24no—
82C19⋊C8—42no—
83C19⋊C8—42no—
84C19⋊C8—42no—
85#2987—191no—
86#1995D1911yescharacteristic
87#1569—192no—
88#1526—191no—
89#1300—192no—
90C22×C19—21no—
91C22×C19—22no—
92C22×C19#38511yescharacteristic
93C4×C19—21no—
94C4×C19—22no—
95C4×C19—22no—
96C4×C19—42no—
97C4×C19—42no—
98C4×C19—82no—
99C4×C19#45411yescharacteristic
100C4×C19#45611yescharacteristic
101#533C2×D1911yescharacteristic
102#446—382no—
103#446—382no—
104#433—382no—
105#432—192no—
106#423C2×D1911yescharacteristic
107C4×M16—192no—
108#376C2×D1911yescharacteristic
109#339—22no—
110#335—382no—
111#334—382no—
112#330—191no—
113#330—192no—
114#330—191no—
115C2×C19—41no—
116C2×C19#185711yescharacteristic
117C2×C19#186112yes—
118C2×M16—21no—
119C2×M16—382no—
120C4⋊Q8Dic3812yes—
121#125C4×D1911yescharacteristic
122#125C4×D1911yescharacteristic
123C22⋊Q8—22no—
124C4×Q8—22no—
125#117C22⋊D1912yes—
126C2×C42—21no—
127C2×C42C22×D1911yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—192no—
130C4⋊C8—192no—
131C4⋊C8—382no—
132C4⋊C8—382no—
133C22⋊C8—382no—
134#97—192no—
135#97—192no—
136#97—382no—
137#97—382no—
138C4×C8—382no—
139C4×C8—382no—
140#95—22no—
141C19#891911yescharacteristic, complemented, Sylow
142C2×Q8—22no—
143C22×C4—41no—
144C22×C4#6454312yes—
145C22×C4C2×C22⋊D1911yescharacteristic
146M16—42no—
147M16—764no—
148C2×C8—41no—
149C2×C8—382no—
150C2×C8—382no—
151C2×C8—382no—
152C2×C8—382no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4Dic19⋊C412yes—
157C4⋊C4Dic19⋊C412yes—
158C22⋊C4—22no—
159C42—22no—
160C42—22no—
161C42—41no—
162C42C2×Dic3811yescharacteristic
163C42C2×C4×D1911yescharacteristic
164C42D4×D1912yes—
165C23#1059738111yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—82no—
174C2×C4#1059732412yes—
175C2×C4(C22⋊D19)⋊C412yes—
176C2×C4C2×Dic19⋊C411yescharacteristic
177C2×C4#1059738311yescharacteristic
178C8—81no—
179C8—384no—
180C8—762no—
181C8—762no—
182C8—762no—
183C22—21no—
184C22—22no—
185C22#1192641611yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—82no—
192C4#1192671611yescharacteristic
193C4#1192672611yescharacteristic
194C2—41no—
195C2#1456384911yescharacteristic
196C2#1456387312yes—
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1995C2
socleC22×C19#385
prime radicalC23×C19#123
cosocleC2×C42×C19C23
hypercenter#1995D19
hypocenterC19#8919
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
13. #11926286C4semidirect
14. #11926286C4semidirect
15. #11926286C4semidirect
141. C19#8919semidirect

Maximal subgroups

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

subgroupindex
#145727412
#145624002
#145622302
#145615282
C19×#19952
#891919