Finite Group Databasebeta

← #14564676

Subgroups — #14564676

Order 2432.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597378C212yesmaximal, complemented
2#11927125C211yesmaximal, characteristic, complemented
3C2×#10597262C212yesmaximal, complemented
4#11926313C211yesmaximal, characteristic, complemented
5C19×#390C211yesmaximal, characteristic, complemented
6C22×D4×C19C2211yescharacteristic
7C2×#64541C2212yes—
8C2×C4⋊C4×C19C2211yescharacteristic
9C2×C22⋊C4×C19—22no—
10C2×C42×C19C2211yescharacteristic
11C2×#64526—22no—
12#10597378—24no—
13#10597378—24no—
14C2×#64525—22no—
15#10597376—22no—
16C2×#64520C2212yes—
17#10597343—22no—
18#10597341—22no—
19#10597262—24no—
20C24×C19—21no—
21C2×D4×C19—22no—
22C2×D4×C19—22no—
23C2×D4×C19—21no—
24C2×D4×C19D412yescomplemented
25C22×C4×C19—21no—
26C22×C4×C19D412yes—
27C22×C4×C19C2311yescharacteristic
28C2×C22⋊D19—22no—
29#64541—22no—
30#64541—22no—
31#64541—22no—
32#64541—22no—
33C2×D76—22no—
34C2×D76D412yes—
35C2×C4×D19—22no—
36C2×Dic38D412yes—
37C4⋊C4×C19—22no—
38C22⋊C4×C19—44no—
39C42×C19—22no—
40#64526—28no—
41#64525—28no—
42(C2×D19)⋊C4—24no—
43C4⋊Dic19—22no—
44#64520—22no—
45#64520D414yescomplemented
46C2×C19⋊C8—22no—
47C23×C19—22no—
48C23×C19—42no—
49C23×C19—42no—
50C23×C19—41no—
51C23×C19—41no—
52C23×C19C2×D411yescharacteristic
53C22×D19—22no—
54D4×C19—24no—
55D4×C19—42no—
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—41no—
59C2×C4×C19—41no—
60C2×C4×C19—42no—
61C2×C4×C19C2×D411yescharacteristic
62C2×C4×C19C2×D412yes—
63C2×C4×C19C2×D412yes—
64C2×C4×C19#4111yescharacteristic
65C22⋊D19—42no—
66C22⋊D19—42no—
67C2×Dic19—22no—
68D76—22no—
69D76—22no—
70D76—82no—
71C4×D19—42no—
72C4×D19—42no—
73Dic38—22no—
74Dic38—22no—
75C19⋊C8—24no—
76#2006—191nomaximal, Sylow
77C22×C19—21no—
78C22×C19—21no—
79C22×C19—44no—
80C22×C19—42no—
81C22×C19—82no—
82C22×C19—81no—
83C22×C19—81no—
84C22×C19#12011yescharacteristic
85C22×C19#12111yescharacteristic
86C22×C19#12711yescharacteristic
87C2×D19—42no—
88C2×D19—42no—
89C2×D19—42no—
90C4×C19—42no—
91C4×C19—42no—
92C4×C19#12012yes—
93C4×C19#12112yes—
94Dic19—42no—
95C2×AGL(1,ℤ/8)—192no—
96#537—191no—
97C2×#104—192no—
98#390D1911yescharacteristic, complemented
99#343—191no—
100C2×C19—21no—
101C2×C19—21no—
102C2×C19—82no—
103C2×C19#39211yescharacteristic
104C2×C19#45311yescharacteristic
105C2×C19#45411yescharacteristic
106D19—82no—
107C2×#41—192no—
108C22×D4C2×D1911yescharacteristic
109AGL(1,ℤ/8)—384no—
110AGL(1,ℤ/8)—384no—
111C2×SD16—382no—
112C2×D8—382no—
113C2×M16—192no—
114C22⋊Q8—382no—
115#121—382no—
116#121—382no—
117C2×C4⋊C4C2×D1911yescharacteristic
118C2×C22⋊C4—22no—
119C2×C42C2×D1911yescharacteristic
120#104—384no—
121C19#200611yescharacteristic, complemented, Sylow
122C24—21no—
123#41—382no—
124#41—382no—
125#41—382no—
126#41—382no—
127C2×Q8—192no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—192no—
132C2×D4—382no—
133C2×D4—382no—
134C2×D4D7612yescomplemented
135C22×C4—21no—
136C22×C4—382no—
137C22×C4C22⋊D1912yes—
138C22×C4C22×D1911yescharacteristic
139SD16—388no—
140D8—388no—
141M16—194no—
142M16—382no—
143C2×C8—382no—
144C4⋊C4—22no—
145C4⋊C4—382no—
146C22⋊C4—44no—
147C22⋊C4—384no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—382no—
155C23C2×C22⋊D1911yescharacteristic
156Q8—382no—
157Q8—382no—
158D4—24no—
159D4—42no—
160D4—382no—
161D4—382no—
162D4—762no—
163D4—762no—
164D4—1522no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—382no—
171C2×C4—762no—
172C2×C4—762no—
173C2×C4C2×D7611yescharacteristic
174C2×C4#6454111yescharacteristic
175C2×C4D4×D1912yes—
176C2×C4D4×D1912yes—
177C8—384no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—762no—
186C22—762no—
187C22—762no—
188C22#1059737611yescharacteristic
189C22#1059738311yescharacteristic
190C22#1059738611yescharacteristic
191C4—42no—
192C4—42no—
193C4—762no—
194C4#1059732812yes—
195C4#1059733012yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—1522no—
200C2#1192645311yescharacteristic
201C2#1192671111yescharacteristic
202C2#1192671611yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#390C2
socleC22×C19#120
hypercenter#390D19
hypocenterC19#2006
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#10597378C2semidirect
2. #11927125C2semidirect
3. C2×#10597262C2semidirect
4. #11926313C2semidirect
5. C19×#390C2semidirect
24. C2×D4×C19D4semidirect
45. #64520D4semidirect
98. #390D19semidirect
121. C19#2006semidirect
134. C2×D4D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973782
#119271252
C2×#105972622
#119263132
C19×#3902
#200619