Finite Group Databasebeta

← #14564679

Subgroups — #14564679

Order 2432.

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

normal subgroups only

This group has 406 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
1C2×#10597354C212yesmaximal, complemented
2#11927125C211yesmaximal, characteristic, complemented
3C2×#10597282C212yesmaximal, complemented
4#11926445C211yesmaximal, characteristic, complemented
5C19×#343C211yesmaximal, characteristic, complemented
6C2×#64541C2212yes—
7C22×D76C2211yescharacteristic
8C2×M16×C19C2212yes—
9C2×C4⋊C4×C19C2211yescharacteristic
10#10597376—22no—
11C2×(C2×D19)⋊C4—22no—
12C2×C4×Dic19C2211yescharacteristic
13#10597354—24no—
14#10597354—24no—
15C2×D152—22no—
16C2×#64516—22no—
17#10597343—22no—
18#10597341—22no—
19#10597282—24no—
20C23×D19—21no—
21C22×C4×C19D412yes—
22C22×C4×C19C2311yescharacteristic
23C2×C22⋊D19—22no—
24C22×Dic19—21no—
25#64541—22no—
26#64541—22no—
27#64541—22no—
28#64541—22no—
29C2×D76—22no—
30C2×D76—22no—
31C2×D76—21no—
32C2×D76—22no—
33C2×D76D412yes—
34C2×D76D412yescomplemented
35C2×C4×D19—22no—
36C2×Dic38D412yes—
37M16×C19—22no—
38M16×C19D414yescomplemented
39C2×C8×C19—22no—
40C4⋊C4×C19—22no—
41(C2×D19)⋊C4—24no—
42(C2×D19)⋊C4—44no—
43C4⋊Dic19—22no—
44C4×Dic19—22no—
45D152—28no—
46#64516—28no—
47C23×C19C2×D411yescharacteristic
48C22×D19—22no—
49C22×D19—22no—
50C22×D19—42no—
51C22×D19—42no—
52C22×D19—41no—
53C22×D19—41no—
54C2×C4×C19—22no—
55C2×C4×C19—42no—
56C2×C4×C19C2×D412yes—
57C2×C4×C19C2×D411yescharacteristic
58C2×C4×C19C2×D412yes—
59C2×C4×C19#4111yescharacteristic
60C22⋊D19—42no—
61C22⋊D19—42no—
62C2×Dic19—22no—
63C2×Dic19—22no—
64C2×Dic19—41no—
65C2×Dic19—41no—
66D76—24no—
67D76—22no—
68D76—22no—
69D76—42no—
70D76—82no—
71C4×D19—42no—
72C4×D19—42no—
73Dic38—22no—
74Dic38—22no—
75C8×C19—24no—
76#2006—191nomaximal, Sylow
77C22×C19—21no—
78C22×C19—21no—
79C22×C19#12011yescharacteristic
80C22×C19#12111yescharacteristic
81C22×C19#12711yescharacteristic
82C2×D19—44no—
83C2×D19—42no—
84C2×D19—42no—
85C2×D19—42no—
86C2×D19—42no—
87C2×D19—82no—
88C2×D19—81no—
89C2×D19—81no—
90C4×C19—42no—
91C4×C19#12012yes—
92C4×C19#12112yes—
93Dic19—42no—
94Dic19—42no—
95C2×AGL(1,ℤ/8)—192no—
96#537—191no—
97C2×#104—192no—
98#390—191no—
99#343D1911yescharacteristic, complemented
100C2×C19—21no—
101C2×C19—21no—
102C2×C19#39211yescharacteristic
103C2×C19#45311yescharacteristic
104C2×C19#45411yescharacteristic
105D19—82no—
106D19—82no—
107C2×#41—192no—
108C22×D4—191no—
109AGL(1,ℤ/8)—384no—
110AGL(1,ℤ/8)—384no—
111C2×SD16—382no—
112C2×D8—382no—
113C2×M16C2×D1912yes—
114C22⋊Q8—382no—
115#121—382no—
116#121—382no—
117C2×C4⋊C4C2×D1911yescharacteristic
118C2×C22⋊C4—382no—
119C2×C42—191no—
120#104—384no—
121C19#200611yescharacteristic, complemented, Sylow
122C24—381no—
123#41—382no—
124#41—382no—
125#41—382no—
126#41—382no—
127C2×Q8—192no—
128C2×D4—192no—
129C2×D4—192no—
130C2×D4—382no—
131C2×D4—382no—
132C2×D4—382no—
133C2×D4—382no—
134C2×D4—381no—
135C22×C4—381no—
136C22×C4—382no—
137C22×C4D7612yes—
138C22×C4C22×D1911yescharacteristic
139SD16—388no—
140D8—388no—
141M16—22no—
142M16D7614yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—382no—
146C22⋊C4—384no—
147C22⋊C4—764no—
148C42—382no—
149C23—382no—
150C23—382no—
151C23—762no—
152C23—762no—
153C23—761no—
154C23—761no—
155C23C2×D7611yescharacteristic
156Q8—382no—
157Q8—382no—
158D4—382no—
159D4—384no—
160D4—382no—
161D4—762no—
162D4—762no—
163D4—762no—
164D4—1522no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—382no—
168C2×C4—382no—
169C2×C4—761no—
170C2×C4—761no—
171C2×C4—762no—
172C2×C4—762no—
173C2×C4C2×D7612yes—
174C2×C4D4×D1911yescharacteristic
175C2×C4D4×D1912yes—
176C2×C4#6454511yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—764no—
181C22—762no—
182C22—762no—
183C22—762no—
184C22—762no—
185C22—1522no—
186C22—1521no—
187C22—1521no—
188C22#1059732011yescharacteristic
189C22#1059732811yescharacteristic
190C22#1059734111yescharacteristic
191C4—42no—
192C4—762no—
193C4—762no—
194C4#1059732812yes—
195C4#1059734112yes—
196C2—21no—
197C2—21no—
198C2—1522no—
199C2—1522no—
200C2#1192645411yescharacteristic
201C2#1192671411yescharacteristic
202C2#1192671911yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#343C2
socleC22×C19#120
hypercenter#343D19
hypocenterC19#2006
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#10597354C2semidirect
2. #11927125C2semidirect
3. C2×#10597282C2semidirect
4. #11926445C2semidirect
5. C19×#343C2semidirect
34. C2×D76D4semidirect
38. M16×C19D4semidirect
99. #343D19semidirect
121. C19#2006semidirect
142. M16D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973542
#119271252
C2×#105972822
#119264452
C19×#3432
#200619