Finite Group Databasebeta

← #14562686

Subgroups — #14562686

Order 2432.

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

normal subgroups only

This group has 240 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#11927134C211yesmaximal, characteristic
2#11926877C211yesmaximal, characteristic, complemented
3#11926863C211yesmaximal, characteristic, complemented
4#11926481C211yesmaximal, characteristic, complemented
5#11926277C211yesmaximal, characteristic, complemented
6#11926267C211yesmaximal, characteristic, complemented
7C19×#328C211yesmaximal, characteristic, complemented
8C19×C22⋊Q8C2211yescharacteristic
9#10597393—21no—
10#10597376C2211yescharacteristic
11C2×(C2×D19)⋊C4—21no—
12C2×(C2×D19)⋊C4C2211yescharacteristic
13C2×C4⋊Dic19—21no—
14C2×C4⋊Dic19C2211yescharacteristic
15#10597344—21no—
16#10597341—21no—
17#10597340—21no—
18#10597328—21no—
19(C22⋊D19)⋊C4—21no—
20C19×C22⋊C8C2211yescharacteristic
21C19×#95C2211yescharacteristic
22#10597292—21no—
23C22⋊(C19⋊C8)C2211yescharacteristic
24#10597278—21no—
25#10597274—21no—
26#10597264—21no—
27C23×D19D411yescharacteristic
28C2×Q8×C19D411yescharacteristic
29C22×C4×C19—21no—
30C22×C4×C19C2311yescharacteristic
31C2×C22⋊D19—21no—
32C22×Dic19—21no—
33C22×Dic19D411yescharacteristic
34C2×D76—21no—
35C2×D76—21no—
36C2×D76D411yescharacteristic
37C2×C4×D19—21no—
38C2×C8×C19—21no—
39C4⋊C4×C19—21no—
40C4⋊C4×C19D411yescharacteristic
41C22⋊C4×C19—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44(C2×D19)⋊C4—21no—
45(C2×D19)⋊C4—21no—
46(C2×D19)⋊C4—21no—
47(C2×D19)⋊C4—21no—
48(C2×D19)⋊C4—42no—
49C4⋊Dic19—21no—
50C4⋊Dic19—21no—
51C4⋊Dic19—42no—
52C4⋊Dic19D411yescharacteristic
53Dic19⋊C4—21no—
54C4×Dic19—21no—
55C2×C19⋊C8—21no—
56C23×C19C2×D411yescharacteristic
57C22×D19—21no—
58C22×D19—21no—
59C22×D19—21no—
60C22×D19—21no—
61C22×D19—41no—
62C22×D19—41no—
63Q8×C19—41no—
64C2×C4×C19—22no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C22⋊D19—41no—
73C22⋊D19—41no—
74C2×Dic19—21no—
75C2×Dic19—21no—
76C2×Dic19—41no—
77C2×Dic19—41no—
78C2×Dic19—41no—
79C2×Dic19—41no—
80D76—41no—
81D76—81no—
82D76—81no—
83C4×D19—81no—
84C8×C19—41no—
85C19⋊C8—41no—
86#1618—191nomaximal, Sylow
87C22×C19—21no—
88C22×C19—21no—
89C22×C19#12011yescharacteristic
90C22×C19#13511yescharacteristic
91C22×C19#13711yescharacteristic
92C2×D19—42no—
93C2×D19—41no—
94C2×D19—41no—
95C2×D19—41no—
96C2×D19—41no—
97C2×D19—41no—
98C2×D19—41no—
99C2×D19—81no—
100C4×C19—21no—
101C4×C19—21no—
102C4×C19—42no—
103C4×C19—41no—
104C4×C19—41no—
105Dic19—41no—
106Dic19—41no—
107Dic19—81no—
108#538—191no—
109#484—191no—
110#481—191no—
111#399—191no—
112#328D1911yescharacteristic, complemented
113#327—191no—
114#323—191no—
115C2×C19—21no—
116C2×C19—21no—
117C2×C19#45211yescharacteristic
118C2×C19#45311yescharacteristic
119C2×C19#45811yescharacteristic
120D19—81no—
121D19—81no—
122#126—381no—
123#124—381no—
124#123—381no—
125C22⋊Q8C2×D1911yescharacteristic
126#121—191no—
127#121—381no—
128#120—381no—
129C4×D4—381no—
130C2×C4⋊C4—191no—
131C2×C4⋊C4—381no—
132C2×C22⋊C4—191no—
133C2×C22⋊C4—381no—
134#107—381no—
135#106—381no—
136#103—381no—
137#102—381no—
138C22⋊C8—191no—
139C22⋊C8C2×D1911yescharacteristic
140#95C2×D1911yescharacteristic
141C19#161811yescharacteristic, complemented, Sylow
142C24—191no—
143C2×Q8D7611yescharacteristic
144C2×D4—191no—
145C2×D4—381no—
146C2×D4—381no—
147C2×D4—381no—
148C22×C4—21no—
149C22×C4—191no—
150C22×C4—381no—
151C22×C4—381no—
152C22×C4C22×D1911yescharacteristic
153C2×C8—21no—
154C2×C8—381no—
155C4⋊C4—21no—
156C4⋊C4—191no—
157C4⋊C4—381no—
158C4⋊C4—381no—
159C4⋊C4—381no—
160C4⋊C4—762no—
161C4⋊C4D7611yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—381no—
164C22⋊C4—381no—
165C22⋊C4—381no—
166C22⋊C4—381no—
167C22⋊C4—381no—
168C22⋊C4—381no—
169C22⋊C4—762no—
170C42—381no—
171C23—381no—
172C23—381no—
173C23—381no—
174C23—381no—
175C23—761no—
176C23—761no—
177C23D4×D1911yescharacteristic
178Q8—41no—
179D4—761no—
180D4—761no—
181D4—761no—
182D4—1521no—
183D4—1521no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—381no—
191C2×C4—381no—
192C2×C4—761no—
193C2×C4—761no—
194C2×C4—761no—
195C2×C4—761no—
196C2×C4—1521no—
197C2×C4C2×D7611yescharacteristic
198C2×C4D4×D1911yescharacteristic
199C8—41no—
200C8—761no—
201C22—21no—
202C22—21no—
203C22—762no—
204C22—761no—
205C22—761no—
206C22—761no—
207C22—761no—
208C22—761no—
209C22—761no—
210C22—1521no—
211C22#1059732811yescharacteristic
212C22#1059736211yescharacteristic
213C22#1059736411yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—761no—
220C4—761no—
221C4—1521no—
222C2—21no—
223C2—21no—
224C2—1521no—
225C2—1521no—
226C2#1192670911yescharacteristic
227C2#1192671311yescharacteristic
228C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#328C2
socleC22×C19#120
prime radical#11927134C2
hypercenter#328D19
hypocenterC19#1618
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #11926877C2semidirect
3. #11926863C2semidirect
4. #11926481C2semidirect
5. #11926277C2semidirect
6. #11926267C2semidirect
7. C19×#328C2semidirect
112. #328D19semidirect
141. C19#1618semidirect

Maximal subgroups

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

subgroupindex
#119271342
#119268772
#119268632
#119264812
#119262772
#119262672
C19×#3282
#161819