Finite Group Databasebeta

← #14574833

Subgroups — #14574833

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#11927094C211yesmaximal, characteristic
2#11926954C212yesmaximal, complemented
3#11926910C212yesmaximal, complemented
4#11926868C214yesmaximal, complemented
5#11926831C212yesmaximal, complemented
6#11926821C212yesmaximal, complemented
7#11926601C211yesmaximal, characteristic, complemented
8C19×#533C211yesmaximal, characteristic, complemented
9C2×#64541—21no—
10C19×C4⋊Q8C2211yescharacteristic
11C19×C4⋊Q8C2211yescharacteristic
12C19×#125C2212yes—
13C19×C22⋊Q8—21no—
14C19×C22⋊Q8—21no—
15C4×Q8×C19—21no—
16C4×Q8×C19—21no—
17C19×#117C2212yes—
18C2×C42×C19C2211yescharacteristic
19#10597376—21no—
20#10597376C2212yes—
21#10597321—21no—
22#10597320C2211yescharacteristic
23C4×D76—21no—
24C4×D76C2212yes—
25#10597315C2211yescharacteristic
26C22⋊(C19⋊C8)C2212yes—
27#10597266C2214yes—
28#10597266C2214yes—
29#10597265C2214yes—
30#10597264C2214yes—
31C4⋊(C19⋊C8)C2212yes—
32#10597260C2212yes—
33C2×Q8×C19—21no—
34C2×Q8×C19—21no—
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×Dic38—21no—
45C4⋊C4×C19—22no—
46C4⋊C4×C19—22no—
47C4⋊C4×C19—21no—
48C4⋊C4×C19—21no—
49C4⋊C4×C19C2312yes—
50C4⋊C4×C19C2312yes—
51C22⋊C4×C19—22no—
52C42×C19—22no—
53C42×C19D411yescharacteristic
54C42×C19D411yescharacteristic
55C42×C19C2311yescharacteristic
56C42×C19C2311yescharacteristic
57(C2×D19)⋊C4—22no—
58(C2×D19)⋊C4—22no—
59C4⋊Dic19—21no—
60C4⋊Dic19C2312yes—
61C2×C19⋊C8C2314yes—
62C23×C19C2×D411yescharacteristic
63C22×D19—22no—
64Q8×C19—42no—
65Q8×C19—42no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—41no—
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19C2×D411yescharacteristic
74C2×C4×C19C2×D411yescharacteristic
75C2×C4×C19C2×D411yescharacteristic
76C2×C4×C19C2411yescharacteristic
77C22⋊D19—44no—
78C2×Dic19—22no—
79D76—24no—
80D76—42no—
81D76—42no—
82C4×D19—44no—
83Dic38—42no—
84C19⋊C8—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×C19—42no—
98C4×C19—42no—
99C4×C19AGL(1,ℤ/8)12yes—
100C4×C192−1+412yes—
101Dic19—42no—
102#533D1911yescharacteristic, complemented
103#532—191no—
104#501—192no—
105#490—192no—
106#482—194no—
107#476—192no—
108#474—192no—
109#432—191no—
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⋊Q8C2×D1911yescharacteristic
118C4⋊Q8C2×D1911yescharacteristic
119#127—191no—
120#125C2×D1912yes—
121#124—381no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124#121—192no—
125#121—381no—
126C4×Q8—21no—
127C4×Q8—21no—
128C4×D4—192no—
129C4×D4—381no—
130#117C2×D1912yes—
131C2×C42C2×D1911yescharacteristic
132#107—194no—
133#106—194no—
134C4⋊C8—192no—
135#102—194no—
136#102—194no—
137C22⋊C8—192no—
138#97—192no—
139C19#323511yescharacteristic, complemented, Sylow
140#41—764no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—381no—
144C2×D4—192no—
145C2×D4—382no—
146C2×D4—381no—
147C2×D4—381no—
148C22×C4—382no—
149C22×C4C22⋊D1911yescharacteristic
150C22×C4C22⋊D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C2×C8—194no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—192no—
158C4⋊C4—381no—
159C4⋊C4C22×D1912yes—
160C4⋊C4C22×D1912yes—
161C22⋊C4—22no—
162C22⋊C4—382no—
163C22⋊C4—382no—
164C42—22no—
165C42C22⋊D1911yescharacteristic
166C42C22⋊D1911yescharacteristic
167C42C22×D1911yescharacteristic
168C42C22×D1911yescharacteristic
169C23—382no—
170C23C2×C22⋊D1911yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—762no—
174D4—384no—
175D4—762no—
176D4—762no—
177D4—764no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—382no—
184C2×C4—764no—
185C2×C4C2×C22⋊D1911yescharacteristic
186C2×C4C2×C22⋊D1911yescharacteristic
187C2×C4C2×C22⋊D1911yescharacteristic
188C2×C4C2×C22⋊D1911yescharacteristic
189C2×C4C2×C22⋊D1911yescharacteristic
190C2×C4C23×D1911yescharacteristic
191C8—384no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—762no—
196C22—762no—
197C22—762no—
198C22C22×C22⋊D1911yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—762no—
206C4#1059739512yes—
207C4#1059743312yes—
208C2—41no—
209C2—1522no—
210C2#1192711811yescharacteristic
211C2C2×#1059739511yescharacteristic
212C2#1192734211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#533C2
socleC22×C19C22×D4
prime radical#11927094C2
hypercenter#533D19
hypocenterC19#3235
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. #11926954C2semidirect
3. #11926910C2semidirect
4. #11926868C2semidirect
5. #11926831C2semidirect
6. #11926821C2semidirect
7. #11926601C2semidirect
8. C19×#533C2semidirect
102. #533D19semidirect
139. C19#3235semidirect

Maximal subgroups

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

subgroupindex
#119270942
#119269542
#119269102
#119268682
#119268312
#119268212
#119266012
C19×#5332
#323519