Finite Group Databasebeta

← #18086682

Subgroups — #18086682

Order 4864.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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#14575016C211yesmaximal, characteristic
2#14562355C212yesmaximal, complemented
3#14562245C212yesmaximal, complemented
4#14561546C211yesmaximal, characteristic, complemented
5C19×#1838C211yesmaximal, characteristic, complemented
6#11927094C2212yes—
7#11926835—22no—
8#11926797—22no—
9#11926740—22no—
10#11926601C2212yes—
11#11926289—22no—
12#11926287—22no—
13#11926283—24no—
14C19×#423C2211yescharacteristic
15C19×#423C2211yescharacteristic
16C2×C19×#97C2211yescharacteristic
17C19×#341—22no—
18C2×#64541—22no—
19C2×M16×C19—21no—
20C2×M16×C19D412yes—
21C22×C8×C19—21no—
22C2×C42×C19C2311yescharacteristic
23#10597376—22no—
24#10597376—22no—
25C2×D152—22no—
26#10597321—22no—
27#10597320D412yes—
28C4×D76—22no—
29C4×D76—22no—
30#10597315D412yes—
31C19×C4⋊C8—22no—
32C19×C4⋊C8—22no—
33C19×#97—21no—
34C19×#97D412yes—
35C22⋊(C19⋊C8)—22no—
36#10597278—24no—
37#10597274—22no—
38C4⋊(C19⋊C8)—22no—
39#10597260—22no—
40C22×C4×C19C2×D411yescharacteristic
41C22×C4×C19#4112yes—
42C2×C22⋊D19—42no—
43#64541—84no—
44C2×D76—22no—
45C2×D76—22no—
46C2×D76—22no—
47C2×C4×D19—42no—
48C2×Dic38—22no—
49M16×C19—42no—
50M16×C19—42no—
51C2×C8×C19—22no—
52C2×C8×C19—22no—
53C2×C8×C19—41no—
54C2×C8×C19—41no—
55C2×C8×C19—41no—
56C42×C19C2×D411yescharacteristic
57C42×C19C2×D412yes—
58C42×C19#4111yescharacteristic
59(C2×D19)⋊C4—42no—
60(C2×D19)⋊C4—42no—
61C4⋊Dic19—22no—
62C4⋊Dic19—22no—
63C2×C19⋊C8—42no—
64D152—82no—
65#10525—191nomaximal, Sylow
66C23×C19#12411yescharacteristic
67C22×D19—42no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—42no—
71C2×C4×C19#12011yescharacteristic
72C2×C4×C19#12111yescharacteristic
73C2×C4×C19#12112yes—
74C2×C4×C19#12312yes—
75C22⋊D19—84no—
76C2×Dic19—42no—
77D76—42no—
78D76—42no—
79D76—82no—
80D76—82no—
81C4×D19—84no—
82Dic38—82no—
83C8×C19—42no—
84C8×C19—42no—
85C8×C19—81no—
86C19⋊C8—82no—
87#3253—191no—
88#1838D1911yescharacteristic, complemented
89#1557—192no—
90#1530—192no—
91#1307—191no—
92C22×C19—22no—
93C22×C19—21no—
94C22×C19#39411yescharacteristic
95C2×D19—82no—
96C2×D19—82no—
97C2×D19—82no—
98C4×C19—22no—
99C4×C19—22no—
100C4×C19—21no—
101C4×C19#45411yescharacteristic
102C4×C19#45511yescharacteristic
103Dic19—82no—
104#532—192no—
105#476—382no—
106#469—382no—
107#459—382no—
108#432—192no—
109#423C2×D1911yescharacteristic
110#423C2×D1911yescharacteristic
111C2×#97C2×D1911yescharacteristic
112#341—22no—
113#332—382no—
114#331—382no—
115#329—384no—
116C2×C19—41no—
117C2×C19#204011yescharacteristic
118C2×C19#204812yes—
119D19—162no—
120C2×#41—382no—
121C2×D8—382no—
122C2×M16—21no—
123C2×M16C22⋊D1912yes—
124C22×C8—21no—
125C4⋊Q8—192no—
126#127—192no—
127#124—382no—
128#121—382no—
129#121—382no—
130C4×D4—382no—
131C4×D4—382no—
132C2×C42C22×D1911yescharacteristic
133#106—382no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—382no—
137#102—384no—
138C22⋊C8—382no—
139#97—21no—
140#97—382no—
141#97D7612yes—
142C19#1052511yescharacteristic, complemented, Sylow
143#41—1524no—
144C2×Q8—382no—
145C2×D4—382no—
146C2×D4—382no—
147C2×D4—382no—
148C2×D4—762no—
149C22×C4—762no—
150C22×C4#6454512yes—
151C22×C4C2×C22⋊D1911yescharacteristic
152D8—1522no—
153M16—42no—
154M16—42no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—762no—
161C4⋊C4—382no—
162C4⋊C4—382no—
163C22⋊C4—762no—
164C22⋊C4—762no—
165C42C2×D7611yescharacteristic
166C42#6454111yescharacteristic
167C42D4×D1912yes—
168C23—762no—
169C23#1059739311yescharacteristic
170Q8—1522no—
171D4—762no—
172D4—762no—
173D4—1522no—
174D4—1522no—
175D4—1524no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—762no—
180C2×C4—1524no—
181C2×C4#1059734012yes—
182C2×C4#1059734112yes—
183C2×C4#1059737611yescharacteristic
184C2×C4#1059738311yescharacteristic
185C8—42no—
186C8—42no—
187C8—81no—
188C8—1522no—
189C22—21no—
190C22—22no—
191C22—1522no—
192C22—1522no—
193C22—1522no—
194C22#1192646111yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—1522no—
199C4#1192671611yescharacteristic
200C4#1192672111yescharacteristic
201C2—41no—
202C2—3042no—
203C2#1456486411yescharacteristic
204C2#1456491012yes—
subgroupG/H
centerC22#11926461
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1838C2
socleC22×C19#394
prime radical#14575016C2
hypercenter#1838D19
hypocenterC19#10525
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #14562355C2semidirect
3. #14562245C2semidirect
4. #14561546C2semidirect
5. C19×#1838C2semidirect
88. #1838D19semidirect
142. C19#10525semidirect

Maximal subgroups

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

subgroupindex
#145750162
#145623552
#145622452
#145615462
C19×#18382
#1052519