Finite Group Databasebeta

← #14564352

Subgroups — #14564352

Order 2432.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4⋊(C19⋊C8)C211yesmaximal, characteristic
2C2×Dic19⋊C8C211yesmaximal, characteristic
3C2×Dic19⋊C8C211yesmaximal, characteristic
4C2×C8×Dic19C211yesmaximal, characteristic
5C4×Dic19⋊C4C211yesmaximal, characteristic
6#11926298C211yesmaximal, characteristic
7C19×#336C211yesmaximal, characteristic
8C22×C8×C19C2211yescharacteristic
9C22×C8×C19C2211yescharacteristic
10C2×C42×C19C2211yescharacteristic
11C2×Dic19⋊C4C411yescharacteristic
12C2×Dic19⋊C4C411yescharacteristic
13C2×C4×Dic19C2211yescharacteristic
14C2×C4×Dic19C2211yescharacteristic
15C22×C19⋊C8C2211yescharacteristic
16C22×C19⋊C8C2211yescharacteristic
17C19⋊#95C411yescharacteristic
18C19⋊#95C411yescharacteristic
19Dic19⋊C8—22no—
20Dic19⋊C8—22no—
21C8×Dic19—22no—
22C4⋊(C19⋊C8)—22no—
23C22×C4×C19C2×C411yescharacteristic
24C22×C4×C19C2×C411yescharacteristic
25C22×C4×C19C2311yescharacteristic
26C22×Dic19C2×C411yescharacteristic
27C22×Dic19C2×C411yescharacteristic
28C22×Dic19C2×C411yescharacteristic
29C22×Dic19C2×C411yescharacteristic
30C2×C8×C19—21no—
31C2×C8×C19—21no—
32C2×C8×C19—21no—
33C2×C8×C19—21no—
34C2×C8×C19—21no—
35C2×C8×C19Q812yes—
36C42×C19—21no—
37C42×C19—21no—
38Dic19⋊C4—22no—
39Dic19⋊C4C814yescomplemented
40C4×Dic19—21no—
41C4×Dic19—21no—
42C4×Dic19D412yes—
43C4×Dic19Q812yes—
44C2×C19⋊C8—21no—
45C2×C19⋊C8—21no—
46C2×C19⋊C8—21no—
47C2×C19⋊C8—21no—
48C2×C19⋊C8—21no—
49C2×C19⋊C8D412yes—
50C23×C19C22×C411yescharacteristic
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—21no—
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19C2×C812yes—
57C2×C4×C19C2×D411yescharacteristic
58C2×C4×C19C2×D411yescharacteristic
59C2×C4×C19C2×Q811yescharacteristic
60C2×C4×C19C2×Q811yescharacteristic
61C2×C4×C19#4111yescharacteristic
62C2×C4×C19#4111yescharacteristic
63C2×Dic19—21no—
64C2×Dic19—21no—
65C2×Dic19—21no—
66C2×Dic19—21no—
67C2×Dic19—21no—
68C2×Dic19—21no—
69C2×Dic19—21no—
70C2×Dic19C4⋊C412yes—
71C2×Dic19C4⋊C412yes—
72C2×Dic19C2×C812yes—
73C2×Dic19C2×C812yes—
74C2×Dic19M1612yes—
75C8×C19—22no—
76C8×C19—41no—
77C19⋊C8—22no—
78C19⋊C8—41no—
79#1939—191nomaximal, Sylow
80C22×C19C2×C4⋊C411yescharacteristic
81C22×C19C4×D411yescharacteristic
82C22×C19C4×Q811yescharacteristic
83C22×C19C22×C811yescharacteristic
84C22×C19C2×M1611yescharacteristic
85C22×C19#13111yescharacteristic
86C22×C19#13111yescharacteristic
87C4×C19—22no—
88C4×C19—41no—
89C4×C19#12111yescharacteristic
90C4×C19C22⋊Q811yescharacteristic
91C4×C19#12511yescharacteristic
92C4×C19C4⋊Q811yescharacteristic
93Dic19—22no—
94Dic19—22no—
95Dic19—41no—
96Dic19C4⋊C814yescomplemented
97C2×C4⋊C8—191no—
98C2×C4⋊C8—191no—
99C2×C4⋊C8—191no—
100C2×C4×C8—191no—
101C4×C4⋊C4—191no—
102#336—191no—
103#336D1911yescharacteristic
104C2×C19#38911yescharacteristic
105C2×C19C2×C4⋊C811yescharacteristic
106C2×C19#42411yescharacteristic
107C2×C19C8×D411yescharacteristic
108C2×C19#43611yescharacteristic
109C2×C19C8×Q811yescharacteristic
110C2×C19#44611yescharacteristic
111C22×C8—191no—
112C22×C8—191no—
113C22×C8C2×D1911yescharacteristic
114C22×C8C2×D1911yescharacteristic
115C2×C4⋊C4—191no—
116C2×C4⋊C4—191no—
117C2×C42—191no—
118C2×C42—191no—
119C2×C42C2×D1911yescharacteristic
120C4⋊C8—382no—
121C4⋊C8—382no—
122C4⋊C8—382no—
123C4×C8—382no—
124#95—191no—
125#95—191no—
126C19#193911yescharacteristic, complemented, Sylow
127C22×C4—191no—
128C22×C4—191no—
129C22×C4—191no—
130C22×C4—191no—
131C22×C4C4×D1911yescharacteristic
132C22×C4C4×D1911yescharacteristic
133C22×C4C22×D1911yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—192no—
140C2×C8—381no—
141C2×C8—381no—
142C2×C8—381no—
143C2×C8—381no—
144C2×C8—381no—
145C2×C8Dic3812yes—
146C4⋊C4—194no—
147C4⋊C4—382no—
148C42—21no—
149C42—21no—
150C42—192no—
151C42—192no—
152C42—381no—
153C42—381no—
154C23C2×C4×D1911yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—192no—
161C2×C4—192no—
162C2×C4—192no—
163C2×C4—192no—
164C2×C4—192no—
165C2×C4—381no—
166C2×C4—381no—
167C2×C4—381no—
168C2×C4—381no—
169C2×C4—381no—
170C2×C4—381no—
171C2×C4—381no—
172C2×C4C8×D1912yes—
173C2×C4C2×Dic3811yescharacteristic
174C2×C4#6454111yescharacteristic
175C2×C4D4×D1911yescharacteristic
176C2×C4D4×D1911yescharacteristic
177C2×C4#6454311yescharacteristic
178C2×C4Q8×D1911yescharacteristic
179C8—22no—
180C8—41no—
181C8—382no—
182C8—761no—
183C22C4×Dic3811yescharacteristic
184C22(C22⋊D19)⋊C411yescharacteristic
185C22C4⋊C4×D1911yescharacteristic
186C22C2×C8×D1911yescharacteristic
187C22#1059734711yescharacteristic
188C22M16×D1911yescharacteristic
189C22#1059735311yescharacteristic
190C4—22no—
191C4—41no—
192C4—194no—
193C4—382no—
194C4—382no—
195C4—761no—
196C4#1059732411yescharacteristic
197C4#1059733011yescharacteristic
198C4#1059733411yescharacteristic
199C4#1059733511yescharacteristic
200C2#1192644111yescharacteristic
201C2C4⋊C8×D1911yescharacteristic
202C2#1192656911yescharacteristic
203C2(C22⋊D19)⋊C811yescharacteristic
204C2#1192661911yescharacteristic
205C2C8×Dic3811yescharacteristic
206C2#1192667211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D19
commutatorC22×C19C22×C8
FittingC19×#336C2
socle, prime radicalC23×C19C22×C4
cosocleC22×C4×C19C23
hypercenter#336D19
hypocenterC19#1939
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
39. Dic19⋊C4C8semidirect
96. Dic19C4⋊C8semidirect
126. C19#1939semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C19⋊C8)2
C2×Dic19⋊C82
C2×C8×Dic192
C4×Dic19⋊C42
#119262982
C19×#3362
#193919