Finite Group Databasebeta

← #14571693

Subgroups — #14571693

Order 2432.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597315C211yesmaximal, characteristic, complemented
2#11926483C212yesmaximal, complemented
3#11926480C212yesmaximal
4#11926474C212yesmaximal, complemented
5#11926469C212yesmaximal
6#11926464C212yesmaximal, complemented
7#11926456C212yesmaximal
8#11926412C211yesmaximal, characteristic, complemented
9C2×C19×#126C211yesmaximal, characteristic
10C22×Dic38C2212yes—
11C19×#126—24no—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C42×C19C2211yescharacteristic
19C2×C22⋊Dic19C2214yes—
20C2×C4⋊Dic19C2212yes—
21C2×C4⋊Dic19C2212yes—
22C2×Dic19⋊C4C2214yes—
23#10597315—24no—
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2214yes—
28C19⋊#95C2214yes—
29C24×C19C2311yescharacteristic
30C22×C4×C19C2311yescharacteristic
31C22×C4×C19C2311yescharacteristic
32C22×C4×C19C2311yescharacteristic
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×Dic19C2314yes—
37C22×Dic19C2314yes—
38C2×Dic38—24no—
39C2×Dic38—44no—
40C4⋊C4×C19—22no—
41C4⋊C4×C19—22no—
42C4⋊C4×C19—22no—
43C22⋊C4×C19—22no—
44C22⋊C4×C19—22no—
45C22⋊C4×C19—22no—
46C42×C19D414yes—
47C22⋊Dic19—44no—
48C4⋊Dic19—24no—
49C4⋊Dic19—24no—
50Dic19⋊C4—44no—
51C23×C19—21no—
52C23×C19—22no—
53C23×C19—22no—
54C23×C19—22no—
55C23×C19C2411yescharacteristic
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—22no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19C2×D412yes—
66C2×C4×C19C2×D412yes—
67C2×C4×C19C2×D412yes—
68C2×Dic19—24no—
69C2×Dic19—24no—
70C2×Dic19—24no—
71C2×Dic19—24no—
72C2×Dic19—24no—
73C2×Dic19—24no—
74Dic38—48no—
75#2821—191nomaximal, Sylow
76C22×C19—41no—
77C22×C19—41no—
78C22×C19—41no—
79C22×C19—44no—
80C22×C19C22×D411yescharacteristic
81C22×C19H(5,𝔽2)12yes—
82C22×C192−1+412yes—
83C22×C192−1+412yes—
84C4×C19—22no—
85C4×C19—22no—
86C4×C19—22no—
87C4×C19—41no—
88C4×C19—41no—
89C4×C19—41no—
90Dic19—44no—
91Dic19—44no—
92C2×C4⋊Q8—191no—
93C2×#126D1911yescharacteristic
94#400—192no—
95#399—192no—
96#398—192no—
97#397—192no—
98#395—192no—
99#393—192no—
100#383—191no—
101C2×C19—81no—
102C2×C19#53511yescharacteristic
103C2×C19#53611yescharacteristic
104C2×C19#53611yescharacteristic
105C2×C19#56314yes—
106C22×Q8—192no—
107C4⋊Q8—384no—
108#126—24no—
109C2×C4⋊C4—192no—
110C2×C4⋊C4—192no—
111C2×C4⋊C4—194no—
112C2×C4⋊C4C2×D1911yescharacteristic
113C2×C4⋊C4C2×D1911yescharacteristic
114C2×C4⋊C4C2×D1911yescharacteristic
115C2×C22⋊C4—194no—
116C2×C22⋊C4C2×D1911yescharacteristic
117C2×C22⋊C4C2×D1911yescharacteristic
118C2×C22⋊C4C2×D1911yescharacteristic
119C2×C42C2×D1911yescharacteristic
120#95—192no—
121#95—192no—
122#95—192no—
123#95—194no—
124#95—194no—
125C19#282111yescharacteristic, complemented, Sylow
126C24C22×D1911yescharacteristic
127C2×Q8—384no—
128C2×Q8—764no—
129C22×C4—194no—
130C22×C4—194no—
131C22×C4C22×D1911yescharacteristic
132C22×C4C22×D1911yescharacteristic
133C22×C4C22×D1911yescharacteristic
134C22×C4C22×D1911yescharacteristic
135C22×C4C22×D1911yescharacteristic
136C22×C4C22×D1911yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4—384no—
141C4⋊C4—384no—
142C4⋊C4—764no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—764no—
147C42C22⋊D1914yes—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—21no—
152C23C23×D1911yescharacteristic
153Q8—768no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—384no—
164C2×C4—384no—
165C2×C4—384no—
166C2×C4—384no—
167C2×C4—384no—
168C2×C4—384no—
169C2×C4C2×C22⋊D1912yes—
170C2×C4C2×C22⋊D1912yes—
171C2×C4C2×C22⋊D1912yes—
172C22—44no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1059743512yes—
177C22#1059743612yes—
178C22#1059743612yes—
179C22C22×C22⋊D1911yescharacteristic
180C4—22no—
181C4—22no—
182C4—22no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4—764no—
187C4—764no—
188C2—81no—
189C2#1192710811yescharacteristic
190C2#1192711511yescharacteristic
191C2#1192711511yescharacteristic
192C2#1192729614yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#126C2
prime radicalC24×C19C23
hypercenterC2×#126D19
hypocenterC19#2821
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10597315C2semidirect
2. #11926483C2semidirect
4. #11926474C2semidirect
6. #11926464C2semidirect
8. #11926412C2semidirect
125. C19#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#105973152
#119264832
#119264802
#119264742
#119264692
#119264642
#119264562
#119264122
C2×C19×#1262
#282119