Finite Group Databasebeta

← #14570643

Subgroups — #14570643

Order 2432.

492 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 137 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
2#11926467C212yesmaximal, complemented
3#11926458C212yesmaximal
4#11926456C212yesmaximal, complemented
5#11926451C211yesmaximal, characteristic, complemented
6#11926438C212yesmaximal, complemented
7#11926432C212yesmaximal, complemented
8#11926428C212yesmaximal, complemented
9C2×C19×#124C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C22×D4×C19C2211yescharacteristic
12C22×Dic38C2211yescharacteristic
13C19×#124—24no—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C42×C19C2211yescharacteristic
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21#10597390—24no—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27C2×C4×Dic19C2211yescharacteristic
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2212yes—
33C24×C19C2312yes—
34C2×Q8×C19—41no—
35C2×Q8×C19—41no—
36C2×Q8×C19D414yes—
37C2×D4×C19—22no—
38C2×D4×C19—41no—
39C2×D4×C19—41no—
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22×Dic19C2312yes—
48C2×Dic38—22no—
49C2×Dic38—41no—
50C2×Dic38—41no—
51C22⋊C4×C19—24no—
52C22⋊C4×C19—24no—
53C42×C19—22no—
54C22⋊Dic19—24no—
55C22⋊Dic19—24no—
56C22⋊Dic19—42no—
57C22⋊Dic19—42no—
58C4⋊Dic19—41no—
59Dic19⋊C4—24no—
60Dic19⋊C4—24no—
61Dic19⋊C4—24no—
62C4×Dic19—22no—
63C4×Dic19—41no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19C2411yescharacteristic
72Q8×C19—44no—
73D4×C19—44no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19C2×D412yes—
84C2×C4×C19C2×D412yes—
85C2×C4×C19C2×D412yes—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19#4114yes—
98Dic38—44no—
99#2731—191nomaximal, Sylow
100C22×C19—42no—
101C22×C19—42no—
102C22×C19—42no—
103C22×C19—42no—
104C22×C19—42no—
105C22×C19—42no—
106C22×C19—42no—
107C22×C19C22×D411yescharacteristic
108C22×C19C2×#4112yes—
109C22×C19H(5,𝔽2)11yescharacteristic
110C22×C19H(5,𝔽2)11yescharacteristic
111C22×C192−1+412yes—
112C4×C19—22no—
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—42no—
116Dic19—24no—
117Dic19—42no—
118Dic19—42no—
119Dic19—42no—
120C2×C4⋊Q8—191no—
121C2×#124D1911yescharacteristic
122#396—192no—
123#394—192no—
124#393—192no—
125#391—191no—
126#388—192no—
127#388—192no—
128#387—192no—
129C2×C19—82no—
130C2×C19#53411yescharacteristic
131C2×C19#54212yes—
132C2×C19#54812yes—
133C2×C19#55511yescharacteristic
134C2×C19#56311yescharacteristic
135C22×Q8—191no—
136C22×Q8C2×D1911yescharacteristic
137C22×D4C2×D1911yescharacteristic
138C4⋊Q8—384no—
139#124—24no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—191no—
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—192no—
147C2×C22⋊C4—192no—
148C2×C22⋊C4C2×D1912yes—
149C2×C22⋊C4C2×D1912yes—
150C2×C42—191no—
151C2×C42—191no—
152C2×C42C2×D1911yescharacteristic
153#95—192no—
154#95—192no—
155#95—192no—
156#95—192no—
157#95—192no—
158C19#273111yescharacteristic, complemented, Sylow
159C24C22×D1912yes—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—382no—
163C2×Q8—761no—
164C2×Q8—761no—
165C2×Q8C22⋊D1914yes—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C22×C4—192no—
170C22×C4—192no—
171C22×C4—192no—
172C22×C4—192no—
173C22×C4C22×D1912yes—
174C22×C4C22×D1911yescharacteristic
175C22×C4C22×D1911yescharacteristic
176C22×C4C22×D1911yescharacteristic
177C4⋊C4—384no—
178C4⋊C4—384no—
179C4⋊C4—384no—
180C4⋊C4—761no—
181C22⋊C4—24no—
182C22⋊C4—24no—
183C22⋊C4—384no—
184C22⋊C4—384no—
185C22⋊C4—762no—
186C22⋊C4—762no—
187C42—22no—
188C42—382no—
189C42—761no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23C23×D1911yescharacteristic
198Q8—44no—
199Q8—764no—
200D4—44no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—194no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4—382no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4C2×C22⋊D1912yes—
223C2×C4C2×C22⋊D1912yes—
224C2×C4C2×C22⋊D1912yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22#1059743011yescharacteristic
233C22#1059743011yescharacteristic
234C22#41×D1912yes—
235C22#1059743612yes—
236C22C22×C22⋊D1911yescharacteristic
237C4—22no—
238C4—22no—
239C4—22no—
240C4—42no—
241C4—384no—
242C4—762no—
243C4—762no—
244C4—762no—
245C2—82no—
246C2#1192710311yescharacteristic
247C2#1192715812yes—
248C2#1192720112yes—
249C2#1192725611yescharacteristic
250C2#1192729411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#124C2
prime radicalC22×D4×C19C22
hypercenterC2×#124D19
hypocenterC19#2731
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
2. #11926467C2semidirect
4. #11926456C2semidirect
5. #11926451C2semidirect
6. #11926438C2semidirect
7. #11926432C2semidirect
8. #11926428C2semidirect
158. C19#2731semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
#119264672
#119264582
#119264562
#119264512
#119264382
#119264322
#119264282
C2×C19×#1242
#273119