Finite Group Databasebeta

← #14568618

Subgroups — #14568618

Order 2432.

576 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10597333C211yesmaximal, characteristic, complemented
5#11926468C214yesmaximal, complemented
6#11926445C211yesmaximal, characteristic
7#11926433C214yesmaximal, complemented
8C4×Dic19⋊C4C211yesmaximal, characteristic, complemented
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15#10597393—24no—
16#10597390—24no—
17C2×(C2×D19)⋊C4C2214yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2214yes—
21C2×Dic19⋊C4C2214yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25C2×C4×Dic19C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597333—24no—
28#10597321—24no—
29C19×#95C2214yes—
30C19⋊#95C2212yes—
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×Dic19C2311yescharacteristic
41C22×Dic19C2311yescharacteristic
42C22×Dic19C2312yes—
43C2×D76—22no—
44C2×D76—22no—
45C2×D76—22no—
46C2×Dic38—22no—
47C2×Dic38—22no—
48C2×Dic38D414yes—
49C4⋊C4×C19—22no—
50C42×C19—22no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—24no—
53(C2×D19)⋊C4—28no—
54(C2×D19)⋊C4—28no—
55Dic19⋊C4—28no—
56Dic19⋊C4—24no—
57Dic19⋊C4—24no—
58C4×Dic19—22no—
59C4×Dic19—24no—
60C4×Dic19D414yes—
61C23×C19C2411yescharacteristic
62C22×D19—22no—
63C22×D19—22no—
64C22×D19—24no—
65C22×D19—22no—
66C22×D19—24no—
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×Dic19C2×D412yes—
86C2×Dic19C2×D412yes—
87C2×Dic19C2×D414yes—
88C2×Dic19#4114yes—
89D76—44no—
90Dic38—28no—
91#2545—191nomaximal, Sylow
92C22×C19C22×D411yescharacteristic
93C22×C19C22×D411yescharacteristic
94C22×C19C2×#4111yescharacteristic
95C22×C19C2×#4112yes—
96C22×C192−1+412yes—
97C2×D19—42no—
98C2×D19—42no—
99C2×D19—42no—
100C2×D19—44no—
101C2×D19—44no—
102C4×C19—42no—
103C4×C19—42no—
104C4×C19—42no—
105C4×C19#12114yes—
106Dic19—24no—
107Dic19—22no—
108Dic19—22no—
109Dic19—24no—
110C2×C4⋊Q8—191no—
111C2×#124—191no—
112C2×#124—191no—
113C2×C4×Q8—191no—
114#396—194no—
115#391D1911yescharacteristic, complemented
116#390—191no—
117#388—194no—
118C4×C4⋊C4—191no—
119C2×C19C2×#12111yescharacteristic
120C2×C19#53211yescharacteristic
121C2×C19#53611yescharacteristic
122C2×C19#54812yes—
123C2×C19#55612yes—
124D19—82no—
125C22×Q8—191no—
126C22×Q8C2×D1911yescharacteristic
127C22×D4—191no—
128C4⋊Q8—384no—
129#124—384no—
130#124—384no—
131C4×Q8—384no—
132C2×C4⋊C4—192no—
133C2×C4⋊C4—194no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4C2×D1911yescharacteristic
136C2×C22⋊C4—192no—
137C2×C22⋊C4—194no—
138C2×C22⋊C4—192no—
139C2×C22⋊C4—194no—
140C2×C42—191no—
141C2×C42—192no—
142C2×C42—191no—
143C2×C42C2×D1911yescharacteristic
144#95—192no—
145#95C2×D1914yes—
146C19#254511yescharacteristic, complemented, Sylow
147C24—192no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—194no—
152C2×Q8—382no—
153C2×Q8—382no—
154C2×D4—382no—
155C2×D4—382no—
156C2×D4—382no—
157C22×C4—191no—
158C22×C4—192no—
159C22×C4—191no—
160C22×C4—192no—
161C22×C4C22×D1912yes—
162C22×C4C22×D1912yes—
163C22×C4C22×D1912yes—
164C22×C4C22×D1911yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—388no—
169C22⋊C4—388no—
170C22⋊C4—388no—
171C22⋊C4—384no—
172C22⋊C4—384no—
173C42—22no—
174C42—194no—
175C42—384no—
176C42—382no—
177C23—382no—
178C23—382no—
179C23—382no—
180C23—384no—
181C23—384no—
182C23C23×D1911yescharacteristic
183Q8—44no—
184Q8—388no—
185D4—764no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—192no—
195C2×C4—192no—
196C2×C4—194no—
197C2×C4—194no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4#6454112yes—
205C2×C4D4×D1912yes—
206C2×C4D4×D1912yes—
207C22—762no—
208C22—762no—
209C22—764no—
210C22—764no—
211C22—762no—
212C22C2×#6454111yescharacteristic
213C22C2×D4×D1911yescharacteristic
214C22C2×D4×D1911yescharacteristic
215C22#1059743312yes—
216C22#41×D1912yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—382no—
221C4—382no—
222C4—384no—
223C4—384no—
224C4#1059733014yes—
225C2—1522no—
226C2C2×#1059733011yescharacteristic
227C2#1192709311yescharacteristic
228C2#1192711911yescharacteristic
229C2#1192720412yes—
230C2#1192726612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC22×D76C22
hypercenter#391D19
hypocenterC19#2545
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#10597390C2semidirect
4. C2×#10597333C2semidirect
5. #11926468C2semidirect
7. #11926433C2semidirect
8. C4×Dic19⋊C4C2semidirect
9. C19×#391C2semidirect
115. #391D19semidirect
146. C19#2545semidirect

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×#105973332
#119264682
#119264452
#119264332
C4×Dic19⋊C42
C19×#3912
#254519