Finite Group Databasebeta

← #14568112

Subgroups — #14568112

Order 2432.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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#11926478C214yesmaximal, complemented
4#11926451C211yesmaximal, characteristic, complemented
5#11926418C214yesmaximal
6#11926414C211yesmaximal, characteristic, complemented
7#11926413C211yesmaximal, characteristic, complemented
8C4×(C2×D19)⋊C4C211yesmaximal, characteristic
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×C4×D19C2211yescharacteristic
12C22×C4×D19C2212yes—
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×C4⋊Dic19C2214yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2214yes—
24C2×C4×Dic19C2211yescharacteristic
25C4⋊C4×D19—24no—
26C19×#95C2214yes—
27C19⋊#95C2212yes—
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×Dic19C2311yescharacteristic
40C22×Dic19C2312yes—
41C2×C4×D19—22no—
42C2×C4×D19—22no—
43C2×C4×D19—24no—
44C2×C4×D19—44no—
45C2×C4×D19D414yes—
46C4⋊C4×C19—22no—
47C42×C19—22no—
48(C2×D19)⋊C4—24no—
49(C2×D19)⋊C4Q818yescomplemented
50C4⋊Dic19—22no—
51C4⋊Dic19—22no—
52C4⋊Dic19—44no—
53Dic19⋊C4—24no—
54Dic19⋊C4—24no—
55Dic19⋊C4—44no—
56C4×Dic19—22no—
57C23×C19C2411yescharacteristic
58C22×D19—21no—
59C22×D19—21no—
60C22×D19—22no—
61C22×D19C2×D412yes—
62C22×D19C2×Q814yes—
63Q8×C19—44no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—24no—
71C2×C4×C19C2×D412yes—
72C2×C4×C19C2×Q814yes—
73C2×C4×C19#4112yes—
74C2×C4×C19#4112yes—
75C2×Dic19—22no—
76C2×Dic19—21no—
77C2×Dic19—21no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—24no—
82C2×Dic19—24no—
83C2×Dic19C2×D412yes—
84C2×Dic19C2×Q814yes—
85C4×D19—28no—
86C4×D19—48no—
87#2502—191nomaximal, Sylow
88C22×C19C22×D411yescharacteristic
89C22×C19C22×Q812yes—
90C22×C19C2×#4111yescharacteristic
91C22×C19C2×#4111yescharacteristic
92C22×C19H(5,𝔽2)12yes—
93C2×D19—22no—
94C2×D19—22no—
95C2×D19—24no—
96C2×D19—24no—
97C2×D19C4⋊Q814yes—
98C4×C19—24no—
99C4×C19—42no—
100C4×C19—42no—
101C4×C19#12314yes—
102Dic19—22no—
103Dic19—24no—
104Dic19—42no—
105Dic19—42no—
106C2×C22⋊Q8—191no—
107C22×C4⋊C4—191no—
108#398—194no—
109#391—191no—
110#391D1911yescharacteristic, complemented
111#385—194no—
112#384—191no—
113#384—191no—
114C4×C22⋊C4—191no—
115C2×C19C2×#12311yescharacteristic
116C2×C19C2×C4⋊Q811yescharacteristic
117C2×C19#53511yescharacteristic
118C2×C19#55412yes—
119C2×C19#55412yes—
120D19—24no—
121C22×Q8C2×D1911yescharacteristic
122C23×C4—191no—
123C23×C4—192no—
124C22⋊Q8—384no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—191no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—194no—
130C2×C4⋊C4—194no—
131C2×C4⋊C4—384no—
132C2×C4⋊C4C2×D1911yescharacteristic
133C2×C22⋊C4—192no—
134C2×C22⋊C4—192no—
135C2×C42—191no—
136C2×C42C2×D1911yescharacteristic
137#95—192no—
138#95—194no—
139#95C2×D1914yes—
140C19#250211yescharacteristic, complemented, Sylow
141C24—191no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—192no—
146C22×C4—191no—
147C22×C4—194no—
148C22×C4—192no—
149C22×C4—192no—
150C22×C4—384no—
151C22×C4—382no—
152C22×C4—382no—
153C22×C4—764no—
154C22×C4C22×D1912yes—
155C22×C4C22×D1912yes—
156C22×C4C22×D1912yes—
157C22×C4C22×D1911yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—384no—
160C4⋊C4—384no—
161C4⋊C4—382no—
162C4⋊C4—382no—
163C4⋊C4—764no—
164C4⋊C4—764no—
165C22⋊C4—198no—
166C22⋊C4—384no—
167C42—22no—
168C42—382no—
169C23—192no—
170C23—194no—
171C23—381no—
172C23—381no—
173C23—382no—
174C23C23×D1911yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—192no—
184C2×C4—194no—
185C2×C4—382no—
186C2×C4—381no—
187C2×C4—381no—
188C2×C4—382no—
189C2×C4—388no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—384no—
193C2×C4—384no—
194C2×C4—768no—
195C2×C4#6454112yes—
196C2×C4D4×D1912yes—
197C2×C4#6454312yes—
198C2×C4Q8×D1914yes—
199C22—194no—
200C22—382no—
201C22—382no—
202C22—384no—
203C22—384no—
204C22C2×#6454111yescharacteristic
205C22C2×D4×D1911yescharacteristic
206C22C2×#6454311yescharacteristic
207C22C2×Q8×D1912yes—
208C22#1059743512yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—382no—
213C4—384no—
214C4—762no—
215C4—762no—
216C4#1059732914yes—
217C2—384no—
218C2C2×#1059732911yescharacteristic
219C2C4⋊Q8×D1911yescharacteristic
220C2#1192711211yescharacteristic
221C2#1192725212yes—
222C2#1192725412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC23×D19C23
hypercenter#391D19
hypocenterC19#2502
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #11926478C2semidirect
4. #11926451C2semidirect
6. #11926414C2semidirect
7. #11926413C2semidirect
9. C19×#391C2semidirect
49. (C2×D19)⋊C4Q8semidirect
110. #391D19semidirect
140. C19#2502semidirect

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
#119264782
#119264512
#119264182
#119264142
#119264132
C4×(C2×D19)⋊C42
C19×#3912
#250219