Finite Group Databasebeta

← #14574835

Subgroups — #14574835

Order 2432.

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

normal subgroups only

This group has 366 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#11927101C211yesmaximal, characteristic, complemented
2#11927094C211yesmaximal, characteristic
3#11926953C212yesmaximal, complemented
4#11926909C212yesmaximal, complemented
5#11926869C214yesmaximal, complemented
6#11926835C212yesmaximal, complemented
7#11926825C212yesmaximal, complemented
8C19×#432C211yesmaximal, characteristic, complemented
9C2×#64541—21no—
10C2×C42×C19C2211yescharacteristic
11#10597376—21no—
12#10597376C2212yes—
13#10597372C2212yes—
14#10597370—21no—
15#10597370—21no—
16#10597321—21no—
17#10597320C2211yescharacteristic
18C4×D76—21no—
19C4×D76C2212yes—
20#10597316C2212yes—
21#10597315C2211yescharacteristic
22#10597315C2211yescharacteristic
23#10597315C2211yescharacteristic
24C4×Dic38—21no—
25C4×Dic38—21no—
26C19×C4⋊C8C2212yes—
27C19×C22⋊C8C2212yes—
28C19×#97C2212yes—
29#10597278C2214yes—
30#10597278C2214yes—
31#10597275C2214yes—
32#10597274C2214yes—
33C22×C4×C19D411yescharacteristic
34C22×C4×C19D411yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C2×C22⋊D19—22no—
37#64541—44no—
38C2×D76—21no—
39C2×D76—21no—
40C2×D76C2312yes—
41C2×C4×D19—22no—
42C2×Dic38—21no—
43C2×Dic38—21no—
44C2×Dic38—21no—
45C2×C8×C19C2314yes—
46C42×C19D411yescharacteristic
47C42×C19D411yescharacteristic
48C42×C19C2311yescharacteristic
49C42×C19C2311yescharacteristic
50C22⋊Dic19—22no—
51(C2×D19)⋊C4—22no—
52(C2×D19)⋊C4—22no—
53C4⋊Dic19—21no—
54C4⋊Dic19—21no—
55C4⋊Dic19—21no—
56C4⋊Dic19C2312yes—
57C4⋊Dic19C2312yes—
58C4⋊Dic19C2312yes—
59Dic19⋊C4—22no—
60Dic19⋊C4—22no—
61C4×Dic19—22no—
62C23×C19C2×D411yescharacteristic
63C22×D19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—41no—
67C2×C4×C19C2×D411yescharacteristic
68C2×C4×C19C2×D411yescharacteristic
69C2×C4×C19C2×D411yescharacteristic
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2411yescharacteristic
73C22⋊D19—44no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77D76—24no—
78D76—42no—
79D76—42no—
80C4×D19—44no—
81Dic38—42no—
82Dic38—42no—
83Dic38—42no—
84C8×C19—24no—
85#3235—191nomaximal, Sylow
86C22×C19—21no—
87C22×C19—21no—
88C22×C19—21no—
89C22×C19C22×D411yescharacteristic
90C2×D19—42no—
91C2×D19—42no—
92C2×D19—42no—
93C4×C19—21no—
94C4×C19—21no—
95C4×C19—21no—
96C4×C19—21no—
97C4×C19AGL(1,ℤ/8)12yes—
98C4×C192−1+412yes—
99Dic19—42no—
100Dic19—42no—
101Dic19—42no—
102#533—191no—
103#532—191no—
104#501—192no—
105#490—192no—
106#482—194no—
107#476—192no—
108#474—192no—
109#432D1911yescharacteristic, complemented
110C2×C19—41no—
111C2×C19#53611yescharacteristic
112C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
113C2×C19#57511yescharacteristic
114D19—82no—
115C2×#41—381no—
116C4⋊Q8—191no—
117C4⋊Q8—191no—
118C4⋊Q8—191no—
119#127—191no—
120#125—192no—
121#124—381no—
122C22⋊Q8—381no—
123C22⋊Q8—381no—
124#121—192no—
125#121—381no—
126C4×Q8—381no—
127C4×Q8—381no—
128C4×D4—192no—
129C4×D4—381no—
130#117—192no—
131C2×C42C2×D1911yescharacteristic
132#107—194no—
133#106—194no—
134C4⋊C8C2×D1912yes—
135#102—194no—
136#102—194no—
137C22⋊C8C2×D1912yes—
138#97C2×D1912yes—
139C19#323511yescharacteristic, complemented, Sylow
140#41—764no—
141C2×Q8—381no—
142C2×Q8—381no—
143C2×Q8—381no—
144C2×D4—192no—
145C2×D4—382no—
146C2×D4—381no—
147C2×D4—381no—
148C22×C4—382no—
149C22×C4D7611yescharacteristic
150C22×C4D7611yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C2×C8C22×D1914yes—
153C4⋊C4—192no—
154C4⋊C4—192no—
155C4⋊C4—192no—
156C4⋊C4—382no—
157C4⋊C4—382no—
158C4⋊C4—381no—
159C4⋊C4—381no—
160C4⋊C4—381no—
161C22⋊C4—382no—
162C22⋊C4—382no—
163C22⋊C4—382no—
164C42—382no—
165C42D7611yescharacteristic
166C42D7611yescharacteristic
167C42C22×D1911yescharacteristic
168C42C22×D1911yescharacteristic
169C23—382no—
170C23C2×D7611yescharacteristic
171Q8—762no—
172Q8—762no—
173Q8—762no—
174D4—384no—
175D4—762no—
176D4—762no—
177D4—764no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—764no—
185C2×C4C2×D7611yescharacteristic
186C2×C4C2×D7611yescharacteristic
187C2×C4C2×D7611yescharacteristic
188C2×C4C2×D7611yescharacteristic
189C2×C4C2×D7611yescharacteristic
190C2×C4C23×D1911yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—762no—
196C22—762no—
197C22—762no—
198C22C22×D7611yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—762no—
204C4—762no—
205C4—762no—
206C4#1059735412yes—
207C4#1059743612yes—
208C2—41no—
209C2—1522no—
210C2#1192712011yescharacteristic
211C2C2×#1059735411yescharacteristic
212C2#1192734411yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#432C2
socleC22×C19C22×D4
prime radical#11927094C2
hypercenter#432D19
hypocenterC19#3235
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #11927101C2semidirect
3. #11926953C2semidirect
4. #11926909C2semidirect
5. #11926869C2semidirect
6. #11926835C2semidirect
7. #11926825C2semidirect
8. C19×#432C2semidirect
109. #432D19semidirect
139. C19#3235semidirect

Maximal subgroups

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

subgroupindex
#119271012
#119270942
#119269532
#119269092
#119268692
#119268352
#119268252
C19×#4322
#323519