Finite Group Databasebeta

← #14562647

Subgroups — #14562647

Order 2432.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#11927132C211yesmaximal, characteristic
2#11926874C211yesmaximal, characteristic, complemented
3#11926857C211yesmaximal, characteristic, complemented
4#11926280C211yesmaximal, characteristic, complemented
5#11926277C211yesmaximal, characteristic, complemented
6#11926268C211yesmaximal, characteristic, complemented
7C19×#397C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C19C2211yescharacteristic
9C2×C22⋊C4×C19—21no—
10C2×C22⋊C4×C19C2211yescharacteristic
11#10597399—21no—
12#10597376C2211yescharacteristic
13C4×C22⋊D19—21no—
14#10597370C2211yescharacteristic
15#10597331—21no—
16#10597330—21no—
17#10597329—21no—
18#10597325—21no—
19C19×#95—21no—
20C19×#95C2211yescharacteristic
21C22⋊(C19⋊C8)C2211yescharacteristic
22C22⋊(C19⋊C8)C2211yescharacteristic
23#10597267—21no—
24#10597266—21no—
25#10597265—21no—
26#10597264—21no—
27C24×C19D411yescharacteristic
28C22×C4×C19—21no—
29C22×C4×C19—21no—
30C22×C4×C19D411yescharacteristic
31C22×C4×C19C2311yescharacteristic
32C2×C22⋊D19—21no—
33C2×C22⋊D19—21no—
34C2×C22⋊D19—21no—
35C2×D76D411yescharacteristic
36C2×C4×D19—21no—
37C2×Dic38D411yescharacteristic
38C4⋊C4×C19—21no—
39C4⋊C4×C19—21no—
40C22⋊C4×C19—21no—
41C22⋊C4×C19—21no—
42C22⋊C4×C19—42no—
43C22⋊Dic19—21no—
44C22⋊Dic19—21no—
45C22⋊Dic19—21no—
46(C2×D19)⋊C4—21no—
47(C2×D19)⋊C4—21no—
48C4⋊Dic19D411yescharacteristic
49C4⋊Dic19D411yescharacteristic
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52C4×Dic19—21no—
53C2×C19⋊C8—21no—
54C2×C19⋊C8—21no—
55C23×C19—21no—
56C23×C19—21no—
57C23×C19—21no—
58C23×C19—41no—
59C23×C19—41no—
60C23×C19C2×D411yescharacteristic
61C22×D19—21no—
62C2×C4×C19—21no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—41no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C22⋊D19—41no—
74C22⋊D19—41no—
75C22⋊D19—81no—
76C22⋊D19—81no—
77C2×Dic19—21no—
78C2×Dic19—21no—
79C2×Dic19—21no—
80D76—41no—
81C4×D19—81no—
82Dic38—41no—
83C19⋊C8—41no—
84C19⋊C8—41no—
85#1612—191nomaximal, Sylow
86C22×C19—21no—
87C22×C19—21no—
88C22×C19—42no—
89C22×C19—41no—
90C22×C19—41no—
91C22×C19—41no—
92C22×C19—81no—
93C22×C19#12011yescharacteristic
94C22×C19#13511yescharacteristic
95C22×C19AGL(1,ℤ/8)11yescharacteristic
96C2×D19—41no—
97C2×D19—41no—
98C2×D19—41no—
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—41no—
102C4×C19—81no—
103C4×C19—81no—
104Dic19—41no—
105Dic19—41no—
106Dic19—41no—
107#538—191no—
108#483—191no—
109#480—191no—
110#397D1911yescharacteristic, complemented
111#328—191no—
112#327—191no—
113#323—191no—
114C2×C19—21no—
115C2×C19—21no—
116C2×C19—81no—
117C2×C19#44911yescharacteristic
118C2×C19#45511yescharacteristic
119C2×C19#45811yescharacteristic
120D19—81no—
121#126—381no—
122#124—381no—
123#123—381no—
124C22⋊Q8—191no—
125#121—191no—
126#121—381no—
127#120—381no—
128C4×D4—381no—
129C2×C4⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4C2×D1911yescharacteristic
132#107—381no—
133#106—381no—
134#103—381no—
135#102—381no—
136C22⋊C8—191no—
137C22⋊C8—191no—
138#95—21no—
139#95C2×D1911yescharacteristic
140C19#161211yescharacteristic, complemented, Sylow
141C24C22⋊D1911yescharacteristic
142C2×Q8—191no—
143C2×D4—191no—
144C2×D4—381no—
145C2×D4—381no—
146C2×D4—381no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—381no—
150C22×C4C22⋊D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C2×C8—381no—
153C2×C8—381no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—191no—
157C4⋊C4—191no—
158C4⋊C4—381no—
159C4⋊C4—381no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—381no—
164C22⋊C4—381no—
165C22⋊C4—381no—
166C22⋊C4—381no—
167C22⋊C4—381no—
168C42—381no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—381no—
175C23C2×C22⋊D1911yescharacteristic
176Q8—761no—
177D4—761no—
178D4—761no—
179D4—761no—
180D4—1521no—
181D4—1521no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—381no—
192C2×C4—381no—
193C2×C4—381no—
194C2×C4—1521no—
195C2×C4D4×D1911yescharacteristic
196C2×C4D4×D1911yescharacteristic
197C8—761no—
198C8—761no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—761no—
207C22—761no—
208C22—761no—
209C22#1059737811yescharacteristic
210C22#1059738311yescharacteristic
211C22#1059739611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—761no—
218C4—761no—
219C4—761no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1521no—
224C2#1192668711yescharacteristic
225C2#1192672111yescharacteristic
226C2#1192673311yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#397C2
socleC22×C19#120
prime radical#11927132C2
hypercenter#397D19
hypocenterC19#1612
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11926874C2semidirect
3. #11926857C2semidirect
4. #11926280C2semidirect
5. #11926277C2semidirect
6. #11926268C2semidirect
7. C19×#397C2semidirect
110. #397D19semidirect
140. C19#1612semidirect

Maximal subgroups

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

subgroupindex
#119271322
#119268742
#119268572
#119262802
#119262772
#119262682
C19×#3972
#161219