Finite Group Databasebeta

← #14568126

Subgroups — #14568126

Order 2432.

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

normal subgroups only

This group has 596 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×#10597384C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
3#11926472C214yesmaximal, complemented
4#11926447C211yesmaximal, characteristic, complemented
5#11926420C214yesmaximal, complemented
6#11926410C211yesmaximal, characteristic, complemented
7#11926409C211yesmaximal, characteristic, complemented
8C4×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
9C19×#390C211yesmaximal, characteristic, complemented
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×C4×D19C2211yescharacteristic
13C22×C4×D19C2212yes—
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C22⋊C4×C19C2214yes—
16C2×C42×C19C2211yescharacteristic
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2214yes—
19#10597384—24no—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25C4⋊C4×D19—24no—
26C19⋊#95C2212yes—
27C19⋊#95C2214yes—
28C19⋊#95C2214yes—
29C24×C19C2312yes—
30C23×D19C2311yescharacteristic
31C2×D4×C19—22no—
32C2×D4×C19—22no—
33C2×D4×C19—22no—
34C22×C4×C19C2312yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C2×C22⋊D19—24no—
38C2×C22⋊D19—28no—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2311yescharacteristic
43C2×C4×D19—22no—
44C2×C4×D19—22no—
45C2×C4×D19—24no—
46C2×C4×D19—44no—
47C2×C4×D19D414yes—
48C4⋊C4×C19—22no—
49C22⋊C4×C19—44no—
50C42×C19—22no—
51C22⋊Dic19—24no—
52C22⋊Dic19—44no—
53(C2×D19)⋊C4—24no—
54C4⋊Dic19—22no—
55C4⋊Dic19—22no—
56Dic19⋊C4—24no—
57C4×Dic19—22no—
58C23×C19—22no—
59C23×C19—24no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—24no—
63C23×C19C2411yescharacteristic
64C22×D19—21no—
65C22×D19—21no—
66C22×D19—22no—
67C22×D19C2×D412yes—
68C22×D19#4114yes—
69D4×C19—44no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—24no—
75C2×C4×C19C2×D412yes—
76C2×C4×C19#4112yes—
77C2×C4×C19#4112yes—
78C22⋊D19—48no—
79C2×Dic19—21no—
80C2×Dic19—21no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—24no—
86C2×Dic19—22no—
87C2×Dic19—24no—
88C2×Dic19C2×D412yes—
89C4×D19—28no—
90C4×D19—48no—
91#2504—191nomaximal, Sylow
92C22×C19—42no—
93C22×C19—42no—
94C22×C19—42no—
95C22×C19—44no—
96C22×C19—44no—
97C22×C19C22×D411yescharacteristic
98C22×C19C2×#4111yescharacteristic
99C22×C19C2×#4111yescharacteristic
100C22×C19C2×#4112yes—
101C22×C19H(5,𝔽2)12yes—
102C2×D19—22no—
103C2×D19—22no—
104C2×D19—24no—
105C2×D19—24no—
106C2×D19#12414yes—
107C4×C19—42no—
108C4×C19—42no—
109C4×C19#12314yes—
110Dic19—22no—
111Dic19—42no—
112Dic19—42no—
113Dic19—42no—
114C2×#121—191no—
115C22×C4⋊C4—191no—
116#397—194no—
117#390—191no—
118#390D1911yescharacteristic, complemented
119#386—194no—
120#382—191no—
121#382—191no—
122C4×C22⋊C4—191no—
123C2×C19—82no—
124C2×C19C2×#12311yescharacteristic
125C2×C19C2×#12411yescharacteristic
126C2×C19#53511yescharacteristic
127C2×C19#55312yes—
128C2×C19#55312yes—
129D19—24no—
130C22×D4—192no—
131C22×D4C2×D1911yescharacteristic
132C23×C4—191no—
133C23×C4—192no—
134#121—384no—
135C2×C4⋊C4—191no—
136C2×C4⋊C4—192no—
137C2×C4⋊C4—191no—
138C2×C4⋊C4—384no—
139C2×C4⋊C4C2×D1911yescharacteristic
140C2×C22⋊C4—192no—
141C2×C22⋊C4—192no—
142C2×C22⋊C4—194no—
143C2×C22⋊C4C2×D1914yes—
144C2×C42—191no—
145C2×C42C2×D1911yescharacteristic
146#95—192no—
147#95—194no—
148#95—194no—
149C19#250411yescharacteristic, complemented, Sylow
150C24—191no—
151C24C22×D1912yes—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—384no—
156C2×D4—388no—
157C22×C4—191no—
158C22×C4—194no—
159C22×C4—192no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4—384no—
163C22×C4—382no—
164C22×C4—382no—
165C22×C4—764no—
166C22×C4C22×D1912yes—
167C22×C4C22×D1912yes—
168C22×C4C22×D1911yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—384no—
171C4⋊C4—382no—
172C4⋊C4—382no—
173C22⋊C4—44no—
174C22⋊C4—384no—
175C22⋊C4—384no—
176C22⋊C4—764no—
177C42—22no—
178C42—382no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—24no—
184C23—192no—
185C23—194no—
186C23—381no—
187C23—381no—
188C23—382no—
189C23C23×D1911yescharacteristic
190D4—44no—
191D4—768no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—192no—
198C2×C4—381no—
199C2×C4—381no—
200C2×C4—388no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—384no—
206C2×C4—382no—
207C2×C4—384no—
208C2×C4—768no—
209C2×C4#6454112yes—
210C2×C4D4×D1912yes—
211C2×C4#6454312yes—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22—44no—
217C22—194no—
218C22—382no—
219C22—382no—
220C22—384no—
221C22—384no—
222C22C2×#6454111yescharacteristic
223C22C2×D4×D1911yescharacteristic
224C22C2×#6454311yescharacteristic
225C22#1059743012yes—
226C22#41×D1912yes—
227C4—42no—
228C4—42no—
229C4—382no—
230C4—762no—
231C4—762no—
232C4—762no—
233C4#1059732914yes—
234C2—82no—
235C2—384no—
236C2C2×#1059732911yescharacteristic
237C2#124×D1911yescharacteristic
238C2#1192710711yescharacteristic
239C2#1192724112yes—
240C2#1192724412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#390C2
prime radicalC2×#10597384C2
hypercenter#390D19
hypocenterC19#2504
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D19C2semidirect
3. #11926472C2semidirect
4. #11926447C2semidirect
5. #11926420C2semidirect
6. #11926410C2semidirect
7. #11926409C2semidirect
8. C4×(C2×D19)⋊C4C2semidirect
9. C19×#390C2semidirect
118. #390D19semidirect
149. C19#2504semidirect

Maximal subgroups

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

subgroupindex
C2×#105973842
C2×C4⋊C4×D192
#119264722
#119264472
#119264202
#119264102
#119264092
C4×(C2×D19)⋊C42
C19×#3902
#250419