Finite Group Databasebeta

← #14569440

Subgroups — #14569440

Order 2432.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597370C211yesmaximal, characteristic, complemented
2#11926480C212yesmaximal, complemented
3#11926467C214yesmaximal, complemented
4#11926456C212yesmaximal, complemented
5#11926417C212yesmaximal, complemented
6#11926404C211yesmaximal, characteristic, complemented
7#11926400C212yesmaximal
8C22×C22⋊C4×C19C211yesmaximal, characteristic
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×Dic38C2211yescharacteristic, complemented
13C2×C22⋊C4×C19—24no—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2214yes—
19C2×C22⋊Dic19C2214yes—
20C2×C4⋊Dic19C2211yescharacteristic, complemented
21C2×C4⋊Dic19C2212yescomplemented
22#10597370—24no—
23C2×Dic19⋊C4C2212yescomplemented
24C2×Dic19⋊C4C2214yescomplemented
25C19⋊#95C2212yescomplemented
26C19⋊#95C2214yescomplemented
27C24×C19—22no—
28C24×C19—22no—
29C24×C19—42no—
30C24×C19—42no—
31C24×C19Q814yescomplemented
32C24×C19C2312yes—
33C24×C19C2311yescharacteristic
34C22×C4×C19—22no—
35C22×C4×C19—42no—
36C22×C4×C19—42no—
37C22×C4×C19D414yes—
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2314yes—
43C22×Dic19C2312yes—
44C2×Dic38—22no—
45C2×Dic38—42no—
46C22⋊C4×C19—24no—
47C22⋊C4×C19—24no—
48C22⋊Dic19—24no—
49C22⋊Dic19—24no—
50C22⋊Dic19—44no—
51C22⋊Dic19—44no—
52C4⋊Dic19—22no—
53C4⋊Dic19—42no—
54Dic19⋊C4—24no—
55Dic19⋊C4—44no—
56C23×C19—22no—
57C23×C19—22no—
58C23×C19—28no—
59C23×C19—22no—
60C23×C19—22no—
61C23×C19—24no—
62C23×C19—24no—
63C23×C19—48no—
64C23×C19—44no—
65C23×C19—44no—
66C23×C19—48no—
67C23×C19C2×D412yes—
68C23×C19C2×Q814yes—
69C23×C19C2×Q812yes—
70C23×C19#4112yes—
71C23×C19C2411yescharacteristic
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—24no—
76C2×C4×C19—44no—
77C2×C4×C19—44no—
78C2×C4×C19C2×D412yes—
79C2×C4×C19C2×D412yes—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—24no—
83C2×Dic19—24no—
84C2×Dic19—24no—
85C2×Dic19—24no—
86C2×Dic19—24no—
87Dic38—44no—
88#2626—191nomaximal, Sylow
89C22×C19—22no—
90C22×C19—22no—
91C22×C19—24no—
92C22×C19—24no—
93C22×C19—24no—
94C22×C19—28no—
95C22×C19—416no—
96C22×C19—42no—
97C22×C19—42no—
98C22×C19—44no—
99C22×C19C22⋊Q814yes—
100C22×C19C22×D411yescharacteristic
101C22×C19C22×Q811yescharacteristic
102C22×C19C2×#4111yescharacteristic
103C22×C19H(5,𝔽2)12yes—
104C22×C19H(5,𝔽2)12yes—
105C4×C19—22no—
106C4×C19—22no—
107C4×C19—42no—
108Dic19—42no—
109Dic19—42no—
110Dic19—44no—
111C2×C22⋊Q8—191no—
112C22×C22⋊C4D1911yescharacteristic
113#399—192no—
114#396—194no—
115#393—192no—
116#385—192no—
117#380—191no—
118#379—192no—
119C2×C19—24no—
120C2×C19—44no—
121C2×C19C2×C22⋊Q811yescharacteristic
122C2×C19#53411yescharacteristic
123C2×C19#53511yescharacteristic
124C2×C19#53812yes—
125C2×C19#54312yes—
126C25C2×D1911yescharacteristic
127C22×Q8—191no—
128C23×C4C2×D1911yescharacteristic
129C23×C4C2×D1911yescharacteristic
130C22⋊Q8—384no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4—192no—
134C2×C4⋊C4—194no—
135C2×C22⋊C4—24no—
136C2×C22⋊C4—192no—
137C2×C22⋊C4—192no—
138C2×C22⋊C4—194no—
139C2×C22⋊C4—194no—
140C2×C22⋊C4C2×D1912yes—
141C2×C22⋊C4C2×D1912yes—
142#95—192no—
143#95—194no—
144C19#262611yescharacteristic, complemented, Sylow
145C24—22no—
146C24—22no—
147C24—42no—
148C24—42no—
149C24Dic3814yescomplemented
150C24C22×D1912yes—
151C24C22×D1911yescharacteristic
152C2×Q8—382no—
153C2×Q8—762no—
154C22×C4—22no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—194no—
158C22×C4—192no—
159C22×C4—192no—
160C22×C4C22⋊D1914yes—
161C22×C4C22×D1912yes—
162C22×C4C22×D1911yescharacteristic
163C22×C4C22×D1911yescharacteristic
164C4⋊C4—384no—
165C4⋊C4—382no—
166C4⋊C4—764no—
167C4⋊C4—762no—
168C22⋊C4—24no—
169C22⋊C4—24no—
170C22⋊C4—384no—
171C22⋊C4—384no—
172C22⋊C4—764no—
173C22⋊C4—764no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—24no—
178C23—24no—
179C23—22no—
180C23—28no—
181C23—48no—
182C23—44no—
183C23—44no—
184C23—48no—
185C23C2×Dic3814yes—
186C23C2×Dic3812yes—
187C23#6454112yes—
188C23C2×C22⋊D1912yes—
189C23C23×D1911yescharacteristic
190Q8—764no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—44no—
196C2×C4—44no—
197C2×C4—384no—
198C2×C4—384no—
199C2×C4—384no—
200C2×C4—384no—
201C2×C4—384no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4C2×C22⋊D1912yes—
205C2×C4C2×C22⋊D1912yes—
206C22—22no—
207C22—22no—
208C22—24no—
209C22—24no—
210C22—24no—
211C22—28no—
212C22—416no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22#1059737014yes—
217C22C22×Dic3811yescharacteristic
218C22C2×#6454111yescharacteristic
219C22#1059743012yes—
220C22#1059743012yes—
221C22C22×C22⋊D1911yescharacteristic
222C4—22no—
223C4—22no—
224C4—42no—
225C4—762no—
226C4—762no—
227C4—764no—
228C2—24no—
229C2—44no—
230C2C2×#1059737011yescharacteristic
231C2#1192710311yescharacteristic
232C2#1192711111yescharacteristic
233C2#1192713212yes—
234C2#1192717012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
prime radicalC25×C19C22
hypercenterC22×C22⋊C4D19
hypocenterC19#2626
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10597370C2semidirect
2. #11926480C2semidirect
3. #11926467C2semidirect
4. #11926456C2semidirect
5. #11926417C2semidirect
6. #11926404C2semidirect
12. C22×Dic38C22semidirect
20. C2×C4⋊Dic19C22semidirect
21. C2×C4⋊Dic19C22semidirect
23. C2×Dic19⋊C4C22semidirect
24. C2×Dic19⋊C4C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
31. C24×C19Q8semidirect
144. C19#2626semidirect
149. C24Dic38semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264802
#119264672
#119264562
#119264172
#119264042
#119264002
C22×C22⋊C4×C192
#262619