Finite Group Databasebeta

← #14574642

Subgroups — #14574642

Order 2432.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#11927094C211yesmaximal, characteristic
2#11926936C212yesmaximal, complemented
3#11926906C212yesmaximal, complemented
4#11926754C212yesmaximal, complemented
5#11926744C212yesmaximal, complemented
6#11926704C214yesmaximal, complemented
7#11926601C211yesmaximal, characteristic, complemented
8C19×#533C211yesmaximal, characteristic, complemented
9C2×#64541C2212yes—
10C19×C4⋊Q8C2211yescharacteristic
11C19×C4⋊Q8C2211yescharacteristic
12C19×#125—21no—
13C19×C22⋊Q8—21no—
14C19×C22⋊Q8C2212yes—
15C4×Q8×C19—21no—
16C4×Q8×C19C2212yes—
17C19×#117—21no—
18C2×C42×C19C2211yescharacteristic
19C2×#64528C2214yes—
20C2×#64527C2214yes—
21#10597376—21no—
22#10597376—21no—
23#10597321C2212yes—
24#10597320C2211yescharacteristic
25C4×D76—21no—
26C4×D76—21no—
27#10597315C2211yescharacteristic
28C22⋊(C19⋊C8)C2212yes—
29#10597267C2214yes—
30#10597266C2214yes—
31C4⋊(C19⋊C8)C2212yes—
32#10597260C2212yes—
33C2×Q8×C19—21no—
34C2×Q8×C19C2312yes—
35C22×C4×C19D411yescharacteristic
36C22×C4×C19D411yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C2×C22⋊D19—22no—
39#64541—44no—
40C2×D76—21no—
41C2×D76—21no—
42C2×D76C2312yes—
43C2×C4×D19—22no—
44C2×Dic38C2312yes—
45C4⋊C4×C19—21no—
46C4⋊C4×C19—21no—
47C4⋊C4×C19—21no—
48C4⋊C4×C19—22no—
49C4⋊C4×C19—22no—
50C4⋊C4×C19C2312yes—
51C22⋊C4×C19—22no—
52C42×C19—22no—
53C42×C19D411yescharacteristic
54C42×C19D411yescharacteristic
55C42×C19C2311yescharacteristic
56C42×C19C2311yescharacteristic
57#64528—44no—
58#64527—44no—
59(C2×D19)⋊C4—22no—
60(C2×D19)⋊C4—22no—
61C4⋊Dic19—21no—
62C4⋊Dic19—21no—
63C2×C19⋊C8C2314yes—
64C23×C19C2×D411yescharacteristic
65C22×D19—22no—
66Q8×C19—22no—
67Q8×C19—22no—
68Q8×C19—42no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—41no—
74C2×C4×C19C2×D411yescharacteristic
75C2×C4×C19C2×D411yescharacteristic
76C2×C4×C19C2×D411yescharacteristic
77C2×C4×C19C2×D411yescharacteristic
78C2×C4×C19C2×D411yescharacteristic
79C2×C4×C19C2411yescharacteristic
80C22⋊D19—44no—
81C2×Dic19—22no—
82D76—24no—
83D76—42no—
84D76—42no—
85C4×D19—44no—
86Dic38—24no—
87C19⋊C8—24no—
88#3216—191nomaximal, Sylow
89C22×C19—21no—
90C22×C19—21no—
91C22×C19—21no—
92C22×C19C22×D411yescharacteristic
93C2×D19—42no—
94C2×D19—42no—
95C2×D19—42no—
96C4×C19—21no—
97C4×C19—21no—
98C4×C19—21no—
99C4×C19—21no—
100C4×C19—42no—
101C4×C19—42no—
102C4×C19#13712yes—
103C4×C19H(5,𝔽2)12yes—
104Dic19—42no—
105#533D1911yescharacteristic, complemented
106#532—191no—
107#497—192no—
108#489—192no—
109#462—192no—
110#460—192no—
111#452—194no—
112#432—191no—
113C2×C19—41no—
114C2×C19#53511yescharacteristic
115C2×C19C2×#13711yescharacteristic
116C2×C19#57511yescharacteristic
117D19—82no—
118C2×#41—192no—
119C2×Q16—194no—
120C2×SD16—194no—
121C4⋊Q8—191no—
122C4⋊Q8C2×D1911yescharacteristic
123C4⋊Q8C2×D1911yescharacteristic
124#127—191no—
125#125—21no—
126#124—192no—
127C22⋊Q8—21no—
128C22⋊Q8C2×D1912yes—
129#121—381no—
130#121—381no—
131C4×Q8—21no—
132C4×Q8C2×D1912yes—
133C4×D4—381no—
134C4×D4—381no—
135#117—21no—
136C2×C42C2×D1911yescharacteristic
137C4⋊C8—192no—
138#103—194no—
139#102—194no—
140C22⋊C8—192no—
141#97—192no—
142C19#321611yescharacteristic, complemented, Sylow
143#41—764no—
144C2×Q8—21no—
145C2×Q8—192no—
146C2×Q8C22×D1912yes—
147C2×D4—192no—
148C2×D4—382no—
149C2×D4—381no—
150C2×D4—381no—
151C22×C4—382no—
152C22×C4C22⋊D1911yescharacteristic
153C22×C4C22⋊D1911yescharacteristic
154C22×C4C22×D1911yescharacteristic
155Q16—764no—
156SD16—764no—
157C2×C8—194no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—381no—
164C4⋊C4—381no—
165C4⋊C4C22×D1912yes—
166C22⋊C4—22no—
167C22⋊C4—382no—
168C22⋊C4—382no—
169C42—22no—
170C42C22⋊D1911yescharacteristic
171C42C22⋊D1911yescharacteristic
172C42C22×D1911yescharacteristic
173C42C22×D1911yescharacteristic
174C23—382no—
175C23C2×C22⋊D1911yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—42no—
179Q8—384no—
180D4—384no—
181D4—762no—
182D4—764no—
183D4—762no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—382no—
190C2×C4—764no—
191C2×C4C2×C22⋊D1911yescharacteristic
192C2×C4C2×C22⋊D1911yescharacteristic
193C2×C4C2×C22⋊D1911yescharacteristic
194C2×C4C2×C22⋊D1911yescharacteristic
195C2×C4C2×C22⋊D1911yescharacteristic
196C2×C4C23×D1911yescharacteristic
197C8—384no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—762no—
202C22—762no—
203C22—762no—
204C22C22×C22⋊D1911yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—42no—
211C4—762no—
212C4#1059738812yes—
213C4#1059743512yes—
214C2—41no—
215C2—1522no—
216C2#1192710811yescharacteristic
217C2C2×#1059738811yescharacteristic
218C2#1192734211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#533C2
socleC22×C19C22×D4
prime radical#11927094C2
hypercenter#533D19
hypocenterC19#3216
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #11926936C2semidirect
3. #11926906C2semidirect
4. #11926754C2semidirect
5. #11926744C2semidirect
6. #11926704C2semidirect
7. #11926601C2semidirect
8. C19×#533C2semidirect
105. #533D19semidirect
142. C19#3216semidirect

Maximal subgroups

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

subgroupindex
#119270942
#119269362
#119269062
#119267542
#119267442
#119267042
#119266012
C19×#5332
#321619