Finite Group Databasebeta

← #14568119

Subgroups — #14568119

Order 2432.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597392C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic
3#11926485C214yesmaximal, complemented
4#11926451C211yesmaximal, characteristic, complemented
5#11926410C211yesmaximal, characteristic, complemented
6#11926409C211yesmaximal, characteristic, complemented
7#11926406C214yesmaximal
8C4×(C2×D19)⋊C4C211yesmaximal, characteristic
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×C4×D19C2212yes—
12C22×C4×D19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15#10597392—24no—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×C4⋊Dic19C2211yescharacteristic
19C2×C4⋊Dic19C2211yescharacteristic
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×C4×Dic19C2211yescharacteristic
23C4⋊C4×D19—24no—
24C19×#95C2214yes—
25C19⋊#95C2212yes—
26C19⋊#95C2214yes—
27C19⋊#95C2214yes—
28C19⋊#95C2214yes—
29C23×D19C2311yescharacteristic
30C2×Q8×C19—22no—
31C2×Q8×C19—22no—
32C2×Q8×C19—22no—
33C22×C4×C19C2312yes—
34C22×C4×C19C2312yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2311yescharacteristic
41C2×C4×D19—22no—
42C2×C4×D19—22no—
43C2×C4×D19—24no—
44C2×C4×D19—28no—
45C2×C4×D19D414yes—
46C4⋊C4×C19—22no—
47C42×C19—22no—
48(C2×D19)⋊C4—24no—
49(C2×D19)⋊C4—24no—
50C4⋊Dic19—22no—
51C4⋊Dic19—22no—
52Dic19⋊C4—24no—
53Dic19⋊C4—24no—
54C4×Dic19—22no—
55C23×C19C2411yescharacteristic
56C22×D19—21no—
57C22×D19—21no—
58C22×D19—22no—
59C22×D19C2×D412yes—
60C22×D19#4114yes—
61Q8×C19—44no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—24no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19C2×D412yes—
71C2×C4×C19#4112yes—
72C2×C4×C19#4112yes—
73C2×Dic19—21no—
74C2×Dic19—21no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—24no—
80C2×Dic19—24no—
81C2×Dic19—22no—
82C2×Dic19C2×D412yes—
83C4×D19—28no—
84C4×D19—48no—
85#2503—191nomaximal, Sylow
86C22×C19C22×D411yescharacteristic
87C22×C19C2×#4111yescharacteristic
88C22×C19C2×#4111yescharacteristic
89C22×C19C2×#4112yes—
90C22×C192−1+412yes—
91C2×D19—22no—
92C2×D19—22no—
93C2×D19—24no—
94C2×D19—24no—
95C2×D19#12414yes—
96C4×C19—42no—
97C4×C19—42no—
98C4×C19—42no—
99C4×C19#12314yes—
100Dic19—22no—
101Dic19—42no—
102Dic19—42no—
103Dic19—42no—
104C2×C22⋊Q8—191no—
105C22×C4⋊C4—191no—
106#400—194no—
107#391—191no—
108#391D1911yescharacteristic, complemented
109#382—191no—
110#382—191no—
111#381—194no—
112C4×C22⋊C4—191no—
113C2×C19C2×#12311yescharacteristic
114C2×C19C2×#12411yescharacteristic
115C2×C19#53611yescharacteristic
116C2×C19#55212yes—
117C2×C19#55212yes—
118D19—24no—
119C22×Q8C2×D1911yescharacteristic
120C23×C4—191no—
121C23×C4—192no—
122C22⋊Q8—384no—
123C2×C4⋊C4—191no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—384no—
128C2×C4⋊C4C2×D1911yescharacteristic
129C2×C22⋊C4—192no—
130C2×C22⋊C4—192no—
131C2×C42—191no—
132C2×C42C2×D1911yescharacteristic
133#95—192no—
134#95—194no—
135#95—194no—
136#95—194no—
137#95C2×D1914yes—
138C19#250311yescharacteristic, complemented, Sylow
139C24—191no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—191no—
144C22×C4—194no—
145C22×C4—192no—
146C22×C4—192no—
147C22×C4—192no—
148C22×C4—384no—
149C22×C4—388no—
150C22×C4—382no—
151C22×C4—382no—
152C22×C4C22×D1912yes—
153C22×C4C22×D1912yes—
154C22×C4C22×D1912yes—
155C22×C4C22×D1911yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—384no—
158C4⋊C4—384no—
159C4⋊C4—382no—
160C4⋊C4—382no—
161C22⋊C4—384no—
162C22⋊C4—384no—
163C42—22no—
164C42—382no—
165C23—192no—
166C23—194no—
167C23—381no—
168C23—381no—
169C23—382no—
170C23C23×D1911yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—192no—
181C2×C4—381no—
182C2×C4—381no—
183C2×C4—388no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—384no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—384no—
191C2×C4—768no—
192C2×C4#6454112yes—
193C2×C4D4×D1912yes—
194C2×C4#6454312yes—
195C22—194no—
196C22—382no—
197C22—382no—
198C22—384no—
199C22—384no—
200C22C2×#6454111yescharacteristic
201C22C2×D4×D1911yescharacteristic
202C22C2×#6454311yescharacteristic
203C22#1059743312yes—
204C22#41×D1912yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—382no—
209C4—762no—
210C4—762no—
211C4—762no—
212C4#1059732914yes—
213C2—384no—
214C2C2×#1059732911yescharacteristic
215C2#124×D1911yescharacteristic
216C2#1192711911yescharacteristic
217C2#1192722812yes—
218C2#1192723512yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC23×D19C23
hypercenter#391D19
hypocenterC19#2503
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #11926485C2semidirect
4. #11926451C2semidirect
5. #11926410C2semidirect
6. #11926409C2semidirect
9. C19×#391C2semidirect
108. #391D19semidirect
138. C19#2503semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
C2×C4⋊C4×D192
#119264852
#119264512
#119264102
#119264092
#119264062
C4×(C2×D19)⋊C42
C19×#3912
#250319