Finite Group Databasebeta

← #14570653

Subgroups — #14570653

Order 2432.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597392C212yesmaximal, complemented
2#11926481C212yesmaximal, complemented
3#11926476C212yesmaximal, complemented
4#11926466C212yesmaximal, complemented
5#11926446C211yesmaximal, characteristic
6#11926442C211yesmaximal, characteristic, complemented
7#11926422C212yesmaximal
8#11926418C212yesmaximal, complemented
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×C4×D19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15#10597392—28no—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×C4⋊Dic19C2212yes—
23C2×C4⋊Dic19C2211yescharacteristic
24C2×C4⋊Dic19C2211yescharacteristic
25C2×C4⋊Dic19C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C19×#95C2212yes—
29C19×#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C23×D19C2312yes—
33C2×Q8×C19—41no—
34C2×Q8×C19—41no—
35C2×Q8×C19D414yescomplemented
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×D76—41no—
45C2×D76—41no—
46C2×D76Q814yescomplemented
47C2×C4×D19—24no—
48C2×C4×D19—42no—
49C2×C4×D19—42no—
50C4⋊C4×C19—41no—
51C42×C19—41no—
52(C2×D19)⋊C4—24no—
53(C2×D19)⋊C4—24no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4—42no—
56(C2×D19)⋊C4—42no—
57C4⋊Dic19—24no—
58C4⋊Dic19—22no—
59C4⋊Dic19—41no—
60C4⋊Dic19—42no—
61C4⋊Dic19—41no—
62Dic19⋊C4—24no—
63Dic19⋊C4—24no—
64C23×C19C2411yescharacteristic
65C22×D19—22no—
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19—22no—
70C22×D19—22no—
71C22×D19C2×Q814yes—
72Q8×C19—44no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19C2×D412yes—
85C2×C4×C19C2×D414yes—
86C2×C4×C19C2×Q812yes—
87C2×C4×C19#4112yes—
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—
97D76—44no—
98C4×D19—48no—
99#2732—191nomaximal, Sylow
100C22×C19C22×D411yescharacteristic
101C22×C19C22×Q811yescharacteristic
102C22×C19C2×#4111yescharacteristic
103C22×C19H(5,𝔽2)11yescharacteristic
104C22×C19H(5,𝔽2)11yescharacteristic
105C22×C19H(5,𝔽2)11yescharacteristic
106C22×C192−1+411yescharacteristic
107C2×D19—24no—
108C2×D19—24no—
109C2×D19—24no—
110C2×D19—42no—
111C2×D19—42no—
112C2×D19—42no—
113C2×D19—42no—
114C4×C19—24no—
115C4×C19—22no—
116C4×C19—22no—
117C4×C19—22no—
118C4×C19—42no—
119Dic19—42no—
120Dic19—42no—
121Dic19—42no—
122C2×C22⋊Q8—192no—
123#399—192no—
124#398—192no—
125#396—192no—
126#391D1911yescharacteristic, complemented
127#390—191no—
128#389—191no—
129#386—192no—
130#385—192no—
131C2×C19#53411yescharacteristic
132C2×C19#53911yescharacteristic
133C2×C19#54311yescharacteristic
134C2×C19D4×Q811yescharacteristic
135C2×C19#55011yescharacteristic
136C2×C19#55411yescharacteristic
137C2×C19#56211yescharacteristic
138D19—44no—
139C22×Q8C2×D1911yescharacteristic
140C22×D4—191no—
141C23×C4—192no—
142C22⋊Q8—388no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4—192no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4—191no—
147C2×C4⋊C4—191no—
148C2×C4⋊C4—191no—
149C2×C4⋊C4—192no—
150C2×C4⋊C4C2×D1911yescharacteristic
151C2×C22⋊C4—192no—
152C2×C22⋊C4—192no—
153C2×C22⋊C4—192no—
154C2×C22⋊C4—192no—
155C2×C22⋊C4—192no—
156C2×C42C2×D1911yescharacteristic
157#95—192no—
158#95—192no—
159#95C2×D1912yes—
160#95C2×D1912yes—
161C19#273211yescharacteristic, complemented, Sylow
162C24—192no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8D7614yescomplemented
166C2×D4—194no—
167C2×D4—761no—
168C2×D4—761no—
169C22×C4—192no—
170C22×C4—192no—
171C22×C4—192no—
172C22×C4—384no—
173C22×C4—762no—
174C22×C4—762no—
175C22×C4C22×D1912yes—
176C22×C4C22×D1912yes—
177C22×C4C22×D1911yescharacteristic
178C22×C4C22×D1911yescharacteristic
179C22×C4C22×D1911yescharacteristic
180C4⋊C4—41no—
181C4⋊C4—384no—
182C4⋊C4—384no—
183C4⋊C4—384no—
184C4⋊C4—382no—
185C4⋊C4—761no—
186C4⋊C4—761no—
187C4⋊C4—762no—
188C22⋊C4—384no—
189C22⋊C4—384no—
190C22⋊C4—384no—
191C22⋊C4—762no—
192C22⋊C4—762no—
193C42—41no—
194C23—194no—
195C23—382no—
196C23—382no—
197C23—382no—
198C23—382no—
199C23—382no—
200C23—382no—
201C23C23×D1911yescharacteristic
202Q8—44no—
203D4—764no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4—382no—
224C2×C4—768no—
225C2×C4C2×D7612yes—
226C2×C4C2×D7614yes—
227C2×C4Q8×D1912yes—
228C2×C4#6454512yes—
229C22—384no—
230C22—384no—
231C22—384no—
232C22—762no—
233C22—762no—
234C22—762no—
235C22—762no—
236C22C22×D7611yescharacteristic
237C22#1059743011yescharacteristic
238C22#1059743011yescharacteristic
239C22C2×Q8×D1911yescharacteristic
240C22C2×#6454511yescharacteristic
241C22#1059743511yescharacteristic
242C22#1059743611yescharacteristic
243C4—24no—
244C4—22no—
245C4—22no—
246C4—22no—
247C4—42no—
248C4—762no—
249C4—762no—
250C4—762no—
251C2—764no—
252C2#1192710611yescharacteristic
253C2#1192714311yescharacteristic
254C2#1192716911yescharacteristic
255C2Q8×D7611yescharacteristic
256C2#1192721611yescharacteristic
257C2#1192725511yescharacteristic
258C2#1192728811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC22×D76C22
hypercenter#391D19
hypocenterC19#2732
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#10597392C2semidirect
2. #11926481C2semidirect
3. #11926476C2semidirect
4. #11926466C2semidirect
6. #11926442C2semidirect
8. #11926418C2semidirect
9. C19×#391C2semidirect
35. C2×Q8×C19D4semidirect
46. C2×D76Q8semidirect
126. #391D19semidirect
161. C19#2732semidirect
165. C2×Q8D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
#119264812
#119264762
#119264662
#119264462
#119264422
#119264222
#119264182
C19×#3912
#273219