Finite Group Databasebeta

← #14565014

Subgroups — #14565014

Order 2432.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10597274C211yesmaximal, characteristic
2C2×Dic19⋊C8C211yesmaximal, characteristic
3C2×#10597292C211yesmaximal, characteristic
4#11926451C211yesmaximal, characteristic
5#11926440C211yesmaximal, characteristic
6#11926306C211yesmaximal, characteristic
7C2×C19×#103C211yesmaximal, characteristic
8C22×Q8×C19C2211yescharacteristic
9C22×C8×C19C2211yescharacteristic
10C2×C4⋊C4×C19C2211yescharacteristic
11C2×C4⋊Dic19C2211yescharacteristic
12C2×C4⋊Dic19C2211yescharacteristic
13C2×Dic19⋊C4—21no—
14C2×C4×Dic19C2211yescharacteristic
15C22×C19⋊C8C2211yescharacteristic
16C19×#103—22no—
17#10597292—22no—
18C19⋊#95—21no—
19C19⋊#95—21no—
20C19⋊#95—21no—
21#10597274—22no—
22Dic19⋊C8—22no—
23C2×Q8×C19—21no—
24C2×Q8×C19—21no—
25C2×Q8×C19—21no—
26C2×Q8×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19Q812yes—
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19C2311yescharacteristic
32C22×Dic19—21no—
33C22×Dic19—21no—
34C22×Dic19D411yescharacteristic
35C22×Dic19D411yescharacteristic
36C2×C8×C19—21no—
37C2×C8×C19—21no—
38C2×C8×C19D412yes—
39C4⋊C4×C19—21no—
40C4⋊C4×C19—21no—
41C4⋊Dic19—21no—
42C4⋊Dic19—21no—
43C4⋊Dic19—21no—
44C4⋊Dic19D412yes—
45Dic19⋊C4—42no—
46C4×Dic19—21no—
47C4×Dic19—21no—
48C2×C19⋊C8—21no—
49C2×C19⋊C8—21no—
50C2×C19⋊C8—21no—
51C23×C19C2×D411yescharacteristic
52Q8×C19—22no—
53Q8×C19—22no—
54Q8×C19—41no—
55Q8×C19—41no—
56C2×C4×C19—22no—
57C2×C4×C19—41no—
58C2×C4×C19—41no—
59C2×C4×C19—41no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19C2×D411yescharacteristic
63C2×C4×C19C2×D411yescharacteristic
64C2×C4×C19C2×Q811yescharacteristic
65C2×C4×C19#4111yescharacteristic
66C2×C4×C19#4111yescharacteristic
67C2×C4×C19#4111yescharacteristic
68C2×Dic19—21no—
69C2×Dic19—21no—
70C2×Dic19—21no—
71C2×Dic19—22no—
72C2×Dic19—21no—
73C2×Dic19—21no—
74C2×Dic19—41no—
75C2×Dic19—41no—
76C2×Dic19—41no—
77C2×Dic19—41no—
78C2×Dic19—41no—
79C2×Dic19SD1612yes—
80C8×C19—22no—
81C19⋊C8—41no—
82#2066—191nomaximal, Sylow
83C22×C19#12111yescharacteristic
84C22×C19#12111yescharacteristic
85C22×C19C22⋊Q811yescharacteristic
86C22×C19C2×SD1611yescharacteristic
87C22×C19#13511yescharacteristic
88C22×C19#13711yescharacteristic
89C22×C19#13711yescharacteristic
90C4×C19—42no—
91C4×C19—81no—
92C4×C19#12111yescharacteristic
93C4×C19C22⋊Q811yescharacteristic
94C4×C19C22⋊Q811yescharacteristic
95C4×C19#12611yescharacteristic
96Dic19—22no—
97Dic19—42no—
98Dic19—41no—
99Dic19—81no—
100C2×#106—191no—
101C2×C4⋊C8—191no—
102C2×#103—191no—
103C2×#103D1911yescharacteristic
104#391—191no—
105#389—191no—
106#340—191no—
107C2×C19#39611yescharacteristic
108C2×C19#46111yescharacteristic
109C2×C19#46411yescharacteristic
110C2×C19#46511yescharacteristic
111C2×C19#47011yescharacteristic
112C2×C19#47511yescharacteristic
113C2×C19#47911yescharacteristic
114C22×Q8C2×D1911yescharacteristic
115C22×C8—191no—
116C22×C8C2×D1911yescharacteristic
117C2×C4⋊C4—191no—
118C2×C4⋊C4—191no—
119C2×C4⋊C4—381no—
120C2×C4⋊C4C2×D1911yescharacteristic
121C2×C42—191no—
122#106—382no—
123C4⋊C8—382no—
124#103—22no—
125#103—382no—
126#95—381no—
127#95—381no—
128#95—381no—
129C19#206611yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic3812yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—191no—
139C22×C4—191no—
140C22×C4—381no—
141C22×C4—381no—
142C22×C4C22×D1911yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—381no—
146C2×C8—381no—
147C2×C8—381no—
148C2×C8C22⋊D1912yes—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—192no—
152C4⋊C4—381no—
153C4⋊C4—381no—
154C4⋊C4—381no—
155C4⋊C4—762no—
156C42—381no—
157C42—381no—
158C23D4×D1911yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—192no—
170C2×C4—381no—
171C2×C4—381no—
172C2×C4—381no—
173C2×C4—382no—
174C2×C4—381no—
175C2×C4—381no—
176C2×C4—761no—
177C2×C4—761no—
178C2×C4—761no—
179C2×C4—761no—
180C2×C4—761no—
181C2×C4C2×Dic3811yescharacteristic
182C2×C4#6454111yescharacteristic
183C2×C4D4×D1911yescharacteristic
184C2×C4#6454311yescharacteristic
185C2×C4#6454311yescharacteristic
186C2×C4C2×C22⋊D1911yescharacteristic
187C8—22no—
188C8—761no—
189C22#1059732411yescharacteristic
190C22#1059733011yescharacteristic
191C22SD16×D1911yescharacteristic
192C22#1059736211yescharacteristic
193C22#1059736411yescharacteristic
194C22#1059736411yescharacteristic
195C22#1059738411yescharacteristic
196C4—42no—
197C4—81no—
198C4—382no—
199C4—761no—
200C4—762no—
201C4—1521no—
202C4#1059732411yescharacteristic
203C4#1059732511yescharacteristic
204C4#1059737011yescharacteristic
205C4#1059738511yescharacteristic
206C2#1192646711yescharacteristic
207C2#1192674811yescharacteristic
208C2#1192676911yescharacteristic
209C2#1192677011yescharacteristic
210C2#1192679911yescharacteristic
211C2#1192682711yescharacteristic
212C2#1192684911yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC2×C19×#103C2
socle, prime radicalC23×C19C2×D4
hypercenterC2×#103D19
hypocenterC19#2066
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
129. C19#2066semidirect

Maximal subgroups

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

subgroupindex
C2×#105972742
C2×Dic19⋊C82
C2×#105972922
#119264512
#119264402
#119263062
C2×C19×#1032
#206619