Finite Group Databasebeta

← #14562651

Subgroups — #14562651

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#11926875C211yesmaximal, characteristic, complemented
3#11926858C211yesmaximal, characteristic, complemented
4#11926469C211yesmaximal, characteristic, complemented
5#11926282C211yesmaximal, characteristic, complemented
6#11926279C211yesmaximal, characteristic, complemented
7C19×#323C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×C19C2211yescharacteristic
9#10597399—21no—
10C2×C22⋊Dic19—21no—
11#10597376C2211yescharacteristic
12C4×C22⋊D19—21no—
13C2×C4⋊Dic19C2211yescharacteristic
14#10597370C2211yescharacteristic
15#10597331—21no—
16#10597330—21no—
17#10597329—21no—
18#10597325—21no—
19C19×C22⋊C8C2211yescharacteristic
20C19×C22⋊C8C2211yescharacteristic
21C19⋊#95—21no—
22C19⋊#95C2211yescharacteristic
23#10597278—21no—
24#10597275—21no—
25#10597274—21no—
26#10597273—21no—
27C24×C19D411yescharacteristic
28C22×C4×C19D411yescharacteristic
29C22×C4×C19C2311yescharacteristic
30C2×C22⋊D19—21no—
31C2×C22⋊D19—21no—
32C2×C22⋊D19—21no—
33C22×Dic19—21no—
34C22×Dic19—21no—
35C2×D76D411yescharacteristic
36C2×C4×D19—21no—
37C2×Dic38D411yescharacteristic
38C2×C8×C19—21no—
39C2×C8×C19—21no—
40C22⋊C4×C19—21no—
41C22⋊C4×C19—21no—
42C22⋊Dic19—21no—
43C22⋊Dic19—21no—
44C22⋊Dic19—21no—
45C22⋊Dic19—42no—
46(C2×D19)⋊C4—21no—
47(C2×D19)⋊C4—21no—
48C4⋊Dic19—21no—
49C4⋊Dic19—21no—
50C4⋊Dic19D411yescharacteristic
51C4⋊Dic19D411yescharacteristic
52Dic19⋊C4—21no—
53Dic19⋊C4—21no—
54C4×Dic19—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×C19C2×D411yescharacteristic
66C2×C4×C19C2×D411yescharacteristic
67C22⋊D19—41no—
68C22⋊D19—41no—
69C22⋊D19—81no—
70C22⋊D19—81no—
71C2×Dic19—21no—
72C2×Dic19—21no—
73C2×Dic19—21no—
74C2×Dic19—41no—
75C2×Dic19—41no—
76C2×Dic19—41no—
77C2×Dic19—41no—
78C2×Dic19—41no—
79C2×Dic19—41no—
80D76—41no—
81C4×D19—81no—
82Dic38—41no—
83C8×C19—41no—
84C8×C19—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—
102Dic19—41no—
103Dic19—41no—
104Dic19—41no—
105Dic19—81no—
106Dic19—81no—
107#538—191no—
108#483—191no—
109#480—191no—
110#397—191no—
111#328—191no—
112#327—191no—
113#323D1911yescharacteristic, complemented
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⋊C4—191no—
130C2×C22⋊C4—381no—
131C2×C22⋊C4C2×D1911yescharacteristic
132#107—381no—
133#106—381no—
134#103—381no—
135#102—381no—
136C22⋊C8C2×D1911yescharacteristic
137C22⋊C8C2×D1911yescharacteristic
138#95—191no—
139#95—381no—
140C19#161211yescharacteristic, complemented, Sylow
141C24D7611yescharacteristic
142C2×Q8—191no—
143C2×D4—191no—
144C2×D4—381no—
145C2×D4—381no—
146C2×D4—381no—
147C22×C4—381no—
148C22×C4—381no—
149C22×C4—381no—
150C22×C4D7611yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—191no—
155C4⋊C4—191no—
156C4⋊C4—381no—
157C4⋊C4—381no—
158C4⋊C4—381no—
159C4⋊C4—381no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—381no—
163C22⋊C4—381no—
164C22⋊C4—381no—
165C22⋊C4—381no—
166C22⋊C4—381no—
167C22⋊C4—762no—
168C42—381no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—381no—
175C23C2×D7611yescharacteristic
176Q8—761no—
177D4—761no—
178D4—761no—
179D4—761no—
180D4—1521no—
181D4—1521no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—381no—
186C2×C4—381no—
187C2×C4—381no—
188C2×C4—761no—
189C2×C4—761no—
190C2×C4—761no—
191C2×C4—761no—
192C2×C4—761no—
193C2×C4—761no—
194C2×C4—1521no—
195C2×C4D4×D1911yescharacteristic
196C2×C4D4×D1911yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—761no—
207C22—761no—
208C22—761no—
209C22#1059732811yescharacteristic
210C22#1059735011yescharacteristic
211C22#1059735411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—761no—
216C4—761no—
217C4—761no—
218C4—1521no—
219C4—1521no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1521no—
224C2#1192669111yescharacteristic
225C2#1192672411yescharacteristic
226C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#323C2
socleC22×C19#120
prime radical#11927132C2
hypercenter#323D19
hypocenterC19#1612
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11926875C2semidirect
3. #11926858C2semidirect
4. #11926469C2semidirect
5. #11926282C2semidirect
6. #11926279C2semidirect
7. C19×#323C2semidirect
113. #323D19semidirect
140. C19#1612semidirect

Maximal subgroups

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

subgroupindex
#119271322
#119268752
#119268582
#119264692
#119262822
#119262792
C19×#3232
#161219