Finite Group Databasebeta

← #18087049

Subgroups — #18087049

Order 4864.

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

normal subgroups only

This group has 350 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#14571910C211yesmaximal, characteristic
2#14563770C212yesmaximal
3#14561517C212yesmaximal
4#14561516C211yesmaximal, characteristic
5C19×#1836C211yesmaximal, characteristic
6C2×#10597260C2212yes—
7#11926478—22no—
8#11926477—22no—
9#11926476—22no—
10#11926410C2212yes—
11#11926306—22no—
12#11926306—22no—
13C2×C19×#97C2211yescharacteristic
14C19×#384C2211yescharacteristic
15C19×#382C2211yescharacteristic
16C19×#340—22no—
17C22×C8×C19—21no—
18C2×C4⋊C4×C19—21no—
19C2×C4⋊C4×C19—22no—
20C2×C4⋊C4×C19D412yes—
21C2×C42×C19C2311yescharacteristic
22C2×C4⋊Dic19—22no—
23C2×C4⋊Dic19D412yes—
24C2×C4⋊Dic19D412yes—
25C2×Dic19⋊C4—22no—
26C2×Dic19⋊C4—22no—
27C22×C19⋊C8—22no—
28C19×#97—21no—
29C19×#97Q812yes—
30C19×#95—22no—
31C19⋊#95—22no—
32C19⋊#95—22no—
33C19⋊#95—22no—
34#10597260—22no—
35#10597260Q814yes—
36C22×C4×C19—22no—
37C22×C4×C19—41no—
38C22×C4×C19C2×D412yes—
39C22×C4×C19C2×D411yescharacteristic
40C22×Dic19—22no—
41C22×Dic19—22no—
42C2×C8×C19—22no—
43C2×C8×C19—41no—
44C2×C8×C19—41no—
45C4⋊C4×C19—42no—
46C4⋊C4×C19—44no—
47C4⋊C4×C19—42no—
48C42×C19C2×Q811yescharacteristic
49C42×C19C2×Q812yes—
50C42×C19#4111yescharacteristic
51C4⋊Dic19—42no—
52C4⋊Dic19—42no—
53C4⋊Dic19—82no—
54Dic19⋊C4—82no—
55Dic19⋊C4—82no—
56C2×C19⋊C8—24no—
57C2×C19⋊C8—42no—
58C2×C19⋊C8—42no—
59#10586—191nomaximal, Sylow
60C23×C19#12011yescharacteristic
61C2×C4×C19—22no—
62C2×C4×C19—21no—
63C2×C4×C19—22no—
64C2×C4×C19—21no—
65C2×C4×C19—42no—
66C2×C4×C19—42no—
67C2×C4×C19—42no—
68C2×C4×C19—82no—
69C2×C4×C19—81no—
70C2×C4×C19C22⋊Q812yes—
71C2×C4×C19C22⋊Q811yescharacteristic
72C2×C4×C19C4⋊Q811yescharacteristic
73C2×C4×C19C4⋊Q812yes—
74C2×Dic19—42no—
75C2×Dic19—42no—
76C2×Dic19—42no—
77C2×Dic19—42no—
78C2×Dic19—42no—
79C2×Dic19—42no—
80C8×C19—42no—
81C19⋊C8—44no—
82#2845—191no—
83#1836—192no—
84#1836D1911yescharacteristic
85#1295—192no—
86#1295—191no—
87C22×C19#39511yescharacteristic
88C22×C19#45412yes—
89C22×C19#45411yescharacteristic
90C22×C19#45512yes—
91C22×C19#45511yescharacteristic
92C4×C19—22no—
93C4×C19—21no—
94C4×C19—22no—
95C4×C19—21no—
96C4×C19—82no—
97C4×C19—161no—
98Dic19—82no—
99Dic19—82no—
100C2×#97—192no—
101C2×#97C2×D1911yescharacteristic
102#398—382no—
103#398—382no—
104#398—382no—
105#384C2×D1911yescharacteristic
106#382—192no—
107#382C2×D1911yescharacteristic
108#340—22no—
109#340—382no—
110#340—382no—
111C2×C19#165811yescharacteristic
112C2×C19#166211yescharacteristic
113C2×C19#166212yes—
114C2×C19#206112yes—
115C2×C19#206111yescharacteristic
116C22×C8—21no—
117C22×C8—382no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—382no—
123C2×C4⋊C4—382no—
124C2×C4⋊C4—382no—
125C2×C4⋊C4C22⋊D1912yes—
126C2×C42C22×D1911yescharacteristic
127#97—21no—
128#97—194no—
129#97—382no—
130#97Dic3812yes—
131#95—22no—
132#95—382no—
133#95—382no—
134#95—382no—
135C19#1058611yescharacteristic, complemented, Sylow
136C22×C4—22no—
137C22×C4—41no—
138C22×C4—382no—
139C22×C4—382no—
140C22×C4D4×D1912yes—
141C22×C4C2×C22⋊D1911yescharacteristic
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8—384no—
146C2×C8—762no—
147C2×C8—762no—
148C4⋊C4—42no—
149C4⋊C4—44no—
150C4⋊C4—42no—
151C4⋊C4—762no—
152C4⋊C4—762no—
153C4⋊C4—1522no—
154C4⋊C4—1522no—
155C4⋊C4—1522no—
156C42C2×Dic3811yescharacteristic
157C42#6454111yescharacteristic
158C42Q8×D1912yes—
159C23#1059738311yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—82no—
168C2×C4—81no—
169C2×C4—762no—
170C2×C4—762no—
171C2×C4—762no—
172C2×C4—762no—
173C2×C4—762no—
174C2×C4—762no—
175C2×C4#1059733412yes—
176C2×C4#1059734212yes—
177C2×C4#1059737011yescharacteristic
178C2×C4#1059739011yescharacteristic
179C8—42no—
180C8—764no—
181C22#1192646411yescharacteristic
182C22#1192671512yes—
183C22#1192671611yescharacteristic
184C22#1192672012yes—
185C22#1192672111yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—161no—
192C4—1522no—
193C4—1522no—
194C2#1456293611yescharacteristic
195C2#1456295611yescharacteristic
196C2#1456295712yes—
197C2#1456498312yes—
198C2#1456498511yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1836C2
socle, prime radicalC23×C19#120
hypercenter#1836D19
hypocenterC19#10586
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
135. C19#10586semidirect

Maximal subgroups

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

subgroupindex
#145719102
#145637702
#145615172
#145615162
C19×#18362
#1058619