Finite Group Databasebeta

← #14562634

Subgroups — #14562634

Order 2432.

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

normal subgroups only

This group has 216 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#11927141C211yesmaximal, characteristic
2#11926875C211yesmaximal, characteristic, complemented
3#11926858C211yesmaximal, characteristic
4#11926474C211yesmaximal, characteristic, complemented
5#11926282C211yesmaximal, characteristic, complemented
6#11926279C211yesmaximal, characteristic
7C19×#324C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C19C2211yescharacteristic
9#10597376C2211yescharacteristic
10#10597375—21no—
11C4×C22⋊D19—21no—
12C2×C4⋊Dic19C2211yescharacteristic
13#10597370C2211yescharacteristic
14C2×Dic19⋊C4—21no—
15#10597344—21no—
16#10597342—21no—
17#10597340—21no—
18#10597335—21no—
19C19×C22⋊C8C2211yescharacteristic
20C19×C22⋊C8C2211yescharacteristic
21C19⋊#95—21no—
22C19⋊#95C2211yescharacteristic
23#10597278—21no—
24#10597275—21no—
25#10597274—21no—
26#10597273—21no—
27C22×C4×C19D411yescharacteristic
28C22×C4×C19D411yescharacteristic
29C22×C4×C19C2311yescharacteristic
30C2×C22⋊D19—21no—
31C22×Dic19—21no—
32C22×Dic19—21no—
33C2×D76D411yescharacteristic
34C2×C4×D19—21no—
35C2×Dic38D411yescharacteristic
36C2×C8×C19—21no—
37C2×C8×C19—21no—
38C4⋊C4×C19—21no—
39C4⋊C4×C19—21no—
40C22⋊Dic19—21no—
41(C2×D19)⋊C4—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44(C2×D19)⋊C4—21no—
45C4⋊Dic19—21no—
46C4⋊Dic19—21no—
47C4⋊Dic19D411yescharacteristic
48C4⋊Dic19D411yescharacteristic
49Dic19⋊C4—21no—
50Dic19⋊C4—21no—
51Dic19⋊C4—21no—
52Dic19⋊C4—21no—
53Dic19⋊C4—42no—
54C4×Dic19—21no—
55C23×C19C2×D411yescharacteristic
56C22×D19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19C2×D411yescharacteristic
64C2×C4×C19C2×D411yescharacteristic
65C22⋊D19—41no—
66C22⋊D19—41no—
67C2×Dic19—22no—
68C2×Dic19—21no—
69C2×Dic19—21no—
70C2×Dic19—21no—
71C2×Dic19—41no—
72C2×Dic19—41no—
73C2×Dic19—41no—
74C2×Dic19—41no—
75C2×Dic19—41no—
76D76—41no—
77C4×D19—81no—
78Dic38—41no—
79C8×C19—41no—
80C8×C19—41no—
81#1609—191nomaximal, Sylow
82C22×C19—21no—
83C22×C19—21no—
84C22×C19#12011yescharacteristic
85C22×C19#13511yescharacteristic
86C22×C19AGL(1,ℤ/8)11yescharacteristic
87C2×D19—41no—
88C2×D19—41no—
89C2×D19—41no—
90C4×C19—21no—
91C4×C19—21no—
92C4×C19—41no—
93C4×C19—41no—
94Dic19—42no—
95Dic19—41no—
96Dic19—41no—
97Dic19—41no—
98Dic19—81no—
99#539—191no—
100#483—191no—
101#480—191no—
102#398—191no—
103#328—191no—
104#327—191no—
105#324D1911yescharacteristic, complemented
106C2×C19—21no—
107C2×C19—21no—
108C2×C19#44911yescharacteristic
109C2×C19#45611yescharacteristic
110C2×C19#45811yescharacteristic
111D19—81no—
112#126—381no—
113#125—381no—
114#123—381no—
115#123—381no—
116C22⋊Q8—191no—
117C22⋊Q8—381no—
118#121—191no—
119C4×D4—381no—
120C2×C4⋊C4—191no—
121C2×C4⋊C4—381no—
122C2×C4⋊C4C2×D1911yescharacteristic
123#107—381no—
124#106—381no—
125#103—381no—
126#102—381no—
127C22⋊C8C2×D1911yescharacteristic
128C22⋊C8C2×D1911yescharacteristic
129#95—191no—
130#95—381no—
131C19#160911yescharacteristic, complemented, Sylow
132C2×Q8—191no—
133C2×D4—191no—
134C2×D4—381no—
135C22×C4—381no—
136C22×C4—381no—
137C22×C4—381no—
138C22×C4D7611yescharacteristic
139C22×C4D7611yescharacteristic
140C22×C4C22×D1911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—191no—
146C4⋊C4—191no—
147C4⋊C4—381no—
148C4⋊C4—381no—
149C4⋊C4—381no—
150C4⋊C4—381no—
151C4⋊C4—381no—
152C4⋊C4—381no—
153C4⋊C4—762no—
154C22⋊C4—381no—
155C22⋊C4—381no—
156C22⋊C4—381no—
157C22⋊C4—381no—
158C22⋊C4—381no—
159C42—381no—
160C23—381no—
161C23C2×D7611yescharacteristic
162Q8—761no—
163D4—761no—
164D4—761no—
165D4—761no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—382no—
173C2×C4—381no—
174C2×C4—381no—
175C2×C4—381no—
176C2×C4—761no—
177C2×C4—761no—
178C2×C4—761no—
179C2×C4—761no—
180C2×C4—761no—
181C2×C4—1521no—
182C2×C4D4×D1911yescharacteristic
183C2×C4D4×D1911yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—761no—
189C22—761no—
190C22—761no—
191C22#1059732811yescharacteristic
192C22#1059735011yescharacteristic
193C22#1059735411yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—762no—
199C4—761no—
200C4—761no—
201C4—761no—
202C4—1521no—
203C2—21no—
204C2—21no—
205C2—1521no—
206C2#1192669111yescharacteristic
207C2#1192672911yescharacteristic
208C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#324C2
socleC22×C19#120
prime radical#10597376C22
hypercenter#324D19
hypocenterC19#1609
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #11926875C2semidirect
4. #11926474C2semidirect
5. #11926282C2semidirect
7. C19×#324C2semidirect
105. #324D19semidirect
131. C19#1609semidirect

Maximal subgroups

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

subgroupindex
#119271412
#119268752
#119268582
#119264742
#119262822
#119262792
C19×#3242
#160919