Finite Group Databasebeta

← #14570604

Subgroups — #14570604

Order 2432.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597392C212yesmaximal, complemented
2#11926484C212yesmaximal, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926471C212yesmaximal, complemented
5#11926461C211yesmaximal, characteristic
6#11926435C212yesmaximal, complemented
7#11926422C212yesmaximal
8#11926418C212yesmaximal, complemented
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×C4×D19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15#10597392—28no—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C19×#95C2212yes—
26C19×#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2211yescharacteristic
32C23×D19C2312yes—
33C2×Q8×C19—41no—
34C2×Q8×C19—41no—
35C2×Q8×C19D414yescomplemented
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×D76—24no—
45C2×D76—41no—
46C2×C4×D19—24no—
47C2×C4×D19—42no—
48C2×C4×D19—42no—
49C4⋊C4×C19—41no—
50C42×C19—41no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—24no—
53(C2×D19)⋊C4—24no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4—42no—
56C4⋊Dic19—24no—
57C4⋊Dic19—41no—
58Dic19⋊C4—24no—
59Dic19⋊C4—24no—
60C23×C19C2411yescharacteristic
61C22×D19—22no—
62C22×D19—22no—
63C22×D19—22no—
64C22×D19—22no—
65C22×D19—22no—
66C22×D19—22no—
67C22×D19#4114yes—
68Q8×C19—44no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19C2×D412yes—
81C2×C4×C19C2×D414yes—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91D76—44no—
92C4×D19—48no—
93#2728—191nomaximal, Sylow
94C22×C19C22×D411yescharacteristic
95C22×C19C2×#4112yes—
96C22×C19H(5,𝔽2)11yescharacteristic
97C22×C19H(5,𝔽2)11yescharacteristic
98C22×C192−1+412yes—
99C2×D19—24no—
100C2×D19—24no—
101C2×D19—24no—
102C2×D19—42no—
103C2×D19—42no—
104C2×D19—42no—
105C2×D19—42no—
106C4×C19—24no—
107C4×C19—22no—
108C4×C19—42no—
109C4×C19—41no—
110C4×C19—41no—
111Dic19—42no—
112Dic19—42no—
113Dic19—42no—
114C2×C22⋊Q8—192no—
115#400—192no—
116#398—191no—
117#397—192no—
118#394—191no—
119#391D1911yescharacteristic, complemented
120#388—192no—
121#386—192no—
122#385—192no—
123C2×C19#53411yescharacteristic
124C2×C19#53912yes—
125C2×C19#54812yes—
126C2×C19#55111yescharacteristic
127C2×C19#56311yescharacteristic
128D19—44no—
129C22×Q8C2×D1911yescharacteristic
130C22×D4—191no—
131C23×C4—192no—
132C22⋊Q8—388no—
133C2×C4⋊C4—192no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4—192no—
136C2×C4⋊C4—191no—
137C2×C4⋊C4C2×D1911yescharacteristic
138C2×C22⋊C4—192no—
139C2×C22⋊C4—192no—
140C2×C22⋊C4—192no—
141C2×C22⋊C4—192no—
142C2×C22⋊C4—192no—
143C2×C42C2×D1911yescharacteristic
144#95—192no—
145#95—192no—
146#95—192no—
147#95—191no—
148#95—191no—
149#95C2×D1912yes—
150#95C2×D1912yes—
151C19#272811yescharacteristic, complemented, Sylow
152C24—192no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8D7614yescomplemented
156C2×D4—384no—
157C2×D4—761no—
158C22×C4—192no—
159C22×C4—192no—
160C22×C4—192no—
161C22×C4—384no—
162C22×C4—762no—
163C22×C4—762no—
164C22×C4C22×D1911yescharacteristic
165C22×C4C22×D1912yes—
166C22×C4C22×D1911yescharacteristic
167C22×C4C22×D1912yes—
168C22×C4C22×D1911yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—384no—
171C4⋊C4—384no—
172C4⋊C4—384no—
173C4⋊C4—761no—
174C22⋊C4—384no—
175C22⋊C4—384no—
176C22⋊C4—384no—
177C22⋊C4—384no—
178C22⋊C4—762no—
179C42—41no—
180C23—194no—
181C23—382no—
182C23—382no—
183C23—382no—
184C23—382no—
185C23—382no—
186C23—382no—
187C23C23×D1911yescharacteristic
188Q8—44no—
189D4—764no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—382no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—768no—
211C2×C4C2×D7612yes—
212C2×C4C2×D7614yes—
213C22—384no—
214C22—384no—
215C22—384no—
216C22—762no—
217C22—762no—
218C22—762no—
219C22—762no—
220C22C22×D7611yescharacteristic
221C22#1059743011yescharacteristic
222C22#1059743011yescharacteristic
223C22#1059743312yes—
224C22#41×D1912yes—
225C4—24no—
226C4—22no—
227C4—42no—
228C4—41no—
229C4—41no—
230C4—762no—
231C4—762no—
232C4—762no—
233C2—764no—
234C2#1192710611yescharacteristic
235C2#1192714012yes—
236C2#1192720612yes—
237C2#1192722411yescharacteristic
238C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC22×D76C22
hypercenter#391D19
hypocenterC19#2728
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#10597392C2semidirect
2. #11926484C2semidirect
3. #11926474C2semidirect
4. #11926471C2semidirect
6. #11926435C2semidirect
8. #11926418C2semidirect
9. C19×#391C2semidirect
35. C2×Q8×C19D4semidirect
119. #391D19semidirect
151. C19#2728semidirect
155. C2×Q8D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
#119264842
#119264742
#119264712
#119264612
#119264352
#119264222
#119264182
C19×#3912
#272819