Finite Group Databasebeta

← #14568632

Subgroups — #14568632

Order 2432.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597390C211yesmaximal, characteristic, complemented
2C2×#10597393C211yesmaximal, characteristic
3C2×#10597321C211yesmaximal, characteristic
4C2×#10597339C211yesmaximal, characteristic
5#11926473C214yesmaximal, complemented
6#11926449C211yesmaximal, characteristic, complemented
7#11926403C214yesmaximal, complemented
8C4×Dic19⋊C4C211yesmaximal, characteristic, complemented
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×C4×D19C2212yes—
13C22×Dic38C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C42×C19C2211yescharacteristic
16#10597393—24no—
17#10597390—24no—
18C2×(C2×D19)⋊C4C2214yes—
19C2×(C2×D19)⋊C4C2214yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25C2×C4×Dic19C2211yescharacteristic
26#10597339—24no—
27#10597321—24no—
28C19×#95C2214yes—
29C19⋊#95C2212yes—
30C19⋊#95C2214yes—
31C23×D19C2312yes—
32C2×Q8×C19—22no—
33C2×Q8×C19—22no—
34C2×Q8×C19—22no—
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2311yescharacteristic
42C22×Dic19C2311yescharacteristic
43C2×D76—22no—
44C2×D76—22no—
45C2×D76D414yes—
46C2×C4×D19—24no—
47C2×C4×D19—28no—
48C2×Dic38—22no—
49C2×Dic38—22no—
50C2×Dic38—22no—
51C4⋊C4×C19—22no—
52C42×C19—22no—
53(C2×D19)⋊C4—28no—
54(C2×D19)⋊C4—28no—
55(C2×D19)⋊C4—24no—
56Dic19⋊C4—24no—
57Dic19⋊C4—24no—
58Dic19⋊C4—24no—
59C4×Dic19—22no—
60C4×Dic19D414yes—
61C23×C19C2411yescharacteristic
62C22×D19—22no—
63C22×D19—24no—
64C22×D19—22no—
65C22×D19—24no—
66C22×D19C2×D414yes—
67Q8×C19—44no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—24no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19C2×D412yes—
77C2×C4×C19C2×D412yes—
78C2×C4×C19#4112yes—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19C2×D412yes—
87C2×Dic19C2×D412yes—
88C2×Dic19#4114yes—
89D76—28no—
90C4×D19—48no—
91Dic38—44no—
92#2547—191nomaximal, Sylow
93C22×C19C22×D411yescharacteristic
94C22×C19C22×D411yescharacteristic
95C22×C19C2×#4111yescharacteristic
96C22×C19C2×#4112yes—
97C22×C192−1+412yes—
98C2×D19—24no—
99C2×D19—28no—
100C2×D19—42no—
101C2×D19—42no—
102C2×D19—44no—
103C4×C19—42no—
104C4×C19—42no—
105C4×C19—42no—
106C4×C19#12114yes—
107Dic19—22no—
108Dic19—42no—
109Dic19—42no—
110Dic19#12414yescomplemented
111C2×C4⋊Q8—191no—
112C2×#124—191no—
113C2×#124—191no—
114C2×C4×D4—191no—
115#397—194no—
116#391—191no—
117#391D1911yescharacteristic, complemented
118#380—194no—
119C4×C4⋊C4—191no—
120C2×C19C2×#12111yescharacteristic
121C2×C19C2×#12411yescharacteristic
122C2×C19#53611yescharacteristic
123C2×C19#54712yes—
124C2×C19#55612yes—
125D19—44no—
126C22×Q8—191no—
127C22×Q8C2×D1911yescharacteristic
128C22×D4—191no—
129C23×C4—192no—
130C4⋊Q8—384no—
131#124—384no—
132#124—384no—
133C4×D4—384no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4—192no—
136C2×C4⋊C4—192no—
137C2×C4⋊C4C2×D1911yescharacteristic
138C2×C22⋊C4—192no—
139C2×C22⋊C4—194no—
140C2×C22⋊C4—194no—
141C2×C42—191no—
142C2×C42—191no—
143C2×C42C2×D1911yescharacteristic
144#95—192no—
145#95—194no—
146#95C2×D1914yes—
147C19#254711yescharacteristic, complemented, Sylow
148C24—192no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—382no—
153C2×Q8—382no—
154C2×Q8—382no—
155C2×D4—194no—
156C2×D4—382no—
157C2×D4—382no—
158C22×C4—191no—
159C22×C4—191no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4—384no—
163C22×C4—388no—
164C22×C4C22×D1912yes—
165C22×C4C22×D1912yes—
166C22×C4C22×D1912yes—
167C22×C4C22×D1911yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—384no—
170C4⋊C4—384no—
171C4⋊C4—384no—
172C22⋊C4—384no—
173C22⋊C4—388no—
174C22⋊C4—388no—
175C42—22no—
176C42—194no—
177C42—382no—
178C23—194no—
179C23—382no—
180C23—382no—
181C23—384no—
182C23—384no—
183C23C23×D1911yescharacteristic
184Q8—44no—
185Q8—764no—
186D4—388no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—192no—
196C2×C4—194no—
197C2×C4—192no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—768no—
206C2×C4#6454112yes—
207C2×C4D4×D1912yes—
208C2×C4D4×D1912yes—
209C22—388no—
210C22—384no—
211C22—762no—
212C22—762no—
213C22—764no—
214C22C2×#6454111yescharacteristic
215C22C2×D4×D1911yescharacteristic
216C22C2×D4×D1911yescharacteristic
217C22#1059743312yes—
218C22#41×D1912yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—194no—
223C4—382no—
224C4—762no—
225C4—762no—
226C4#1059733014yes—
227C2—764no—
228C2C2×#1059733011yescharacteristic
229C2#124×D1911yescharacteristic
230C2#1192711911yescharacteristic
231C2#1192719612yes—
232C2#1192726612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC22×D76C22
hypercenter#391D19
hypocenterC19#2547
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#10597390C2semidirect
5. #11926473C2semidirect
6. #11926449C2semidirect
7. #11926403C2semidirect
8. C4×Dic19⋊C4C2semidirect
9. C19×#391C2semidirect
110. Dic19#124semidirect
117. #391D19semidirect
147. C19#2547semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
C2×#105973932
C2×#105973212
C2×#105973392
#119264732
#119264492
#119264032
C4×Dic19⋊C42
C19×#3912
#254719