Finite Group Databasebeta

← #14571990

Subgroups — #14571990

Order 2432.

752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597386C211yesmaximal, characteristic
3C2×#10597393C211yesmaximal, characteristic, complemented
4C2×#10597321C211yesmaximal, characteristic, complemented
5C2×#10597382C211yesmaximal, characteristic, complemented
6#11926444C218yesmaximal, complemented
7C42×Dic19C211yesmaximal, characteristic, complemented
8C2×C19×#124C211yesmaximal, characteristic, complemented
9C22×Q8×C19C2211yescharacteristic
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19C2214yes—
12C22×D76C2211yescharacteristic
13C22×Dic38C2211yescharacteristic
14C19×#124—24no—
15C2×C22⋊C4×C19C2214yes—
16C2×C42×C19C2211yescharacteristic
17C2×C22⋊Dic19C2214yes—
18#10597393—24no—
19#10597390—24no—
20#10597386—24no—
21#10597382—24no—
22C2×(C2×D19)⋊C4C2214yes—
23C2×(C2×D19)⋊C4C2214yes—
24C2×Dic19⋊C4C2214yes—
25C2×C4×Dic19C2214yes—
26C2×C4×Dic19C2211yescharacteristic
27C2×C4×Dic19C2211yescharacteristic
28#10597321—24no—
29C24×C19C2312yes—
30C23×D19C2312yes—
31C2×Q8×C19—22no—
32C2×Q8×C19—22no—
33C2×Q8×C19—22no—
34C2×D4×C19—22no—
35C2×D4×C19—22no—
36C2×D4×C19—22no—
37C22×C4×C19C2312yes—
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C2×C22⋊D19—28no—
41C2×C22⋊D19—216no—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C2×D76—22no—
46C2×D76—22no—
47C2×D76—22no—
48C2×Dic38—22no—
49C2×Dic38—22no—
50C2×Dic38—22no—
51C22⋊C4×C19—28no—
52C42×C19D414yescomplemented
53C22⋊Dic19—28no—
54(C2×D19)⋊C4—28no—
55(C2×D19)⋊C4—28no—
56Dic19⋊C4—28no—
57C4×Dic19—28no—
58C4×Dic19D414yes—
59C4×Dic19D414yescomplemented
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—28no—
64C23×C19C2411yescharacteristic
65C22×D19—22no—
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—28no—
69Q8×C19—44no—
70D4×C19—44no—
71C2×C4×C19—24no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19C2×D412yes—
76C2×C4×C19C2×D412yes—
77C2×C4×C19C2×D414yes—
78C2×C4×C19C2×D412yes—
79C22⋊D19—416no—
80C2×Dic19—24no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19C2×D414yes—
85C2×Dic19C2×D414yes—
86C2×Dic19#4118yes—
87D76—44no—
88Dic38—44no—
89#2858—191nomaximal, Sylow
90C22×C19—44no—
91C22×C19—42no—
92C22×C19—44no—
93C22×C19—44no—
94C22×C19C22×D411yescharacteristic
95C22×C19C22×D411yescharacteristic
96C22×C19C22×D411yescharacteristic
97C22×C19C2×#4114yes—
98C2×D19—44no—
99C2×D19—42no—
100C2×D19—44no—
101C2×D19—44no—
102C4×C19—24no—
103C4×C19—42no—
104C4×C19#12714yes—
105Dic19—24no—
106Dic19—42no—
107Dic19#12418yescomplemented
108C2×C4⋊Q8—191no—
109C2×#127—191no—
110C2×#124—191no—
111C2×#124—191no—
112C2×#124—191no—
113C2×#124D1911yescharacteristic, complemented
114#390—198no—
115C43—191no—
116C2×C19—82no—
117C2×C19C2×#12412yes—
118C2×C19C2×#12711yescharacteristic
119C2×C19#53212yes—
120C2×C19#53212yes—
121D19—82no—
122C22×Q8—191no—
123C22×Q8C2×D1911yescharacteristic
124C22×D4—194no—
125C22×D4—191no—
126C22×D4C2×D1911yescharacteristic
127C4⋊Q8—384no—
128#127—384no—
129#124—24no—
130#124—384no—
131#124—384no—
132#124—384no—
133C2×C4⋊C4—194no—
134C2×C22⋊C4—194no—
135C2×C22⋊C4—194no—
136C2×C22⋊C4—194no—
137C2×C22⋊C4C2×D1914yes—
138C2×C42—191no—
139C2×C42—191no—
140C2×C42—194no—
141C2×C42C2×D1911yescharacteristic
142C19#285811yescharacteristic, complemented, Sylow
143C24—192no—
144C24C22×D1912yes—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—382no—
149C2×Q8—382no—
150C2×Q8—382no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—388no—
155C2×D4—3816no—
156C2×D4—382no—
157C2×D4—382no—
158C2×D4—382no—
159C22×C4—192no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4C22×D1912yes—
163C22×C4C22×D1912yes—
164C22×C4C22×D1911yescharacteristic
165C4⋊C4—388no—
166C22⋊C4—28no—
167C22⋊C4—388no—
168C22⋊C4—388no—
169C22⋊C4—388no—
170C42—194no—
171C42—194no—
172C42—388no—
173C42C22⋊D1914yescomplemented
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—382no—
179C23—382no—
180C23—388no—
181C23—382no—
182C23C23×D1911yescharacteristic
183Q8—44no—
184Q8—764no—
185D4—44no—
186D4—7616no—
187D4—764no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—194no—
193C2×C4—198no—
194C2×C4—194no—
195C2×C4—384no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4D4×D1912yes—
200C2×C4D4×D1912yes—
201C2×C4C2×C22⋊D1914yes—
202C2×C4C2×C22⋊D1912yes—
203C22—44no—
204C22—42no—
205C22—44no—
206C22—44no—
207C22—764no—
208C22—762no—
209C22—764no—
210C22—764no—
211C22C2×D4×D1911yescharacteristic
212C22C2×D4×D1911yescharacteristic
213C22#41×D1914yes—
214C22C22×C22⋊D1911yescharacteristic
215C4—24no—
216C4—42no—
217C4—198no—
218C4—384no—
219C4—762no—
220C4#1059738614yes—
221C2—82no—
222C2—1522no—
223C2#124×D1912yes—
224C2C2×#1059738611yescharacteristic
225C2#1192709012yes—
226C2#1192709312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#124C2
prime radicalC2×#10597386C2
hypercenterC2×#124D19
hypocenterC19#2858
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10597390C2semidirect
3. C2×#10597393C2semidirect
4. C2×#10597321C2semidirect
5. C2×#10597382C2semidirect
6. #11926444C2semidirect
7. C42×Dic19C2semidirect
8. C2×C19×#124C2semidirect
52. C42×C19D4semidirect
59. C4×Dic19D4semidirect
107. Dic19#124semidirect
113. C2×#124D19semidirect
142. C19#2858semidirect
173. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
C2×#105973862
C2×#105973932
C2×#105973212
C2×#105973822
#119264442
C42×Dic192
C2×C19×#1242
#285819