Finite Group Databasebeta

← #14574437

Subgroups — #14574437

Order 2432.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597376C211yesmaximal, characteristic
2#11926877C212yesmaximal, complemented
3#11926857C212yesmaximal, complemented
4#11926792C214yesmaximal, complemented
5#11926694C212yesmaximal, complemented
6#11926683C212yesmaximal, complemented
7#11926508C211yesmaximal, characteristic, complemented
8C2×C19×C22⋊Q8C211yesmaximal, characteristic, complemented
9C22×Q8×C19C2211yescharacteristic, complemented
10C23×C4×C19C2211yescharacteristic
11C22×C22⋊D19—21no—
12C22×D76C2211yescharacteristic
13C19×C22⋊Q8—21no—
14C19×C22⋊Q8—21no—
15C19×C22⋊Q8C2212yes—
16C19×C22⋊Q8C2212yescomplemented
17C2×C4⋊C4×C19—21no—
18C2×C4⋊C4×C19C2211yescharacteristic, complemented
19C2×C22⋊C4×C19—21no—
20C2×#64527C2214yescomplemented
21#10597376—21no—
22#10597376—21no—
23#10597376C2212yes—
24#10597376C2212yes—
25C2×(C2×D19)⋊C4—21no—
26C2×C4⋊Dic19C2211yescharacteristic
27C2×#64520C2212yescomplemented
28#10597292C2214yescomplemented
29C22⋊(C19⋊C8)C2212yes—
30C22⋊(C19⋊C8)C2212yescomplemented
31#10597266C2214yescomplemented
32#10597264C2214yescomplemented
33C24×C19D411yescharacteristic
34C23×D19—21no—
35C2×Q8×C19—21no—
36C2×Q8×C19—42no—
37C2×Q8×C19C2312yes—
38C22×C4×C19—21no—
39C22×C4×C19—21no—
40C22×C4×C19—42no—
41C22×C4×C19D411yescharacteristic
42C22×C4×C19D411yescharacteristic
43C22×C4×C19D411yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2311yescharacteristic
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C2×C22⋊D19—44no—
50C22×Dic19—21no—
51C2×D76—21no—
52C2×D76—42no—
53C2×D76C2312yes—
54C4⋊C4×C19—22no—
55C4⋊C4×C19—22no—
56C4⋊C4×C19—21no—
57C4⋊C4×C19C2312yes—
58C22⋊C4×C19—22no—
59C22⋊C4×C19—22no—
60#64527—44no—
61(C2×D19)⋊C4—22no—
62(C2×D19)⋊C4—22no—
63C4⋊Dic19—21no—
64C4⋊Dic19C2312yes—
65#64520—42no—
66C2×C19⋊C8C2314yes—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—41no—
70C23×C19C2×D411yescharacteristic
71C23×C19C2×D411yescharacteristic
72C23×C19C2×D411yescharacteristic
73C22×D19—22no—
74C22×D19—42no—
75C22×D19—42no—
76C22×D19—42no—
77Q8×C19—24no—
78Q8×C19—42no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—41no—
87C2×C4×C19—42no—
88C2×C4×C19—42no—
89C2×C4×C19C2×D411yescharacteristic
90C2×C4×C19C2×D411yescharacteristic
91C2×C4×C19C2×D411yescharacteristic
92C2×C4×C19C2411yescharacteristic
93C22⋊D19—44no—
94C22⋊D19—44no—
95C2×Dic19—22no—
96C2×Dic19—42no—
97D76—24no—
98D76—42no—
99C19⋊C8—24no—
100#3193—191nomaximal, Sylow
101C22×C19—21no—
102C22×C19—21no—
103C22×C19—21no—
104C22×C19—21no—
105C22×C19—21no—
106C22×C19—21no—
107C22×C19—21no—
108C22×C19—44no—
109C22×C19AGL(1,ℤ/8)12yes—
110C22×C19#13712yes—
111C22×C19C22×D411yescharacteristic
112C2×D19—42no—
113C2×D19—42no—
114C2×D19—42no—
115C2×D19—84no—
116C4×C19—21no—
117C4×C19—21no—
118C4×C19—21no—
119C4×C19—42no—
120C4×C19—42no—
121C4×C19H(5,𝔽2)12yes—
122Dic19—42no—
123C2×C22⋊Q8D1911yescharacteristic, complemented
124C2×#121—191no—
125#484—192no—
126#480—192no—
127#468—194no—
128#450—192no—
129#448—192no—
130#407—191no—
131C2×C19—22no—
132C2×C19—22no—
133C2×C19—41no—
134C2×C19#53411yescharacteristic
135C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C19C2×#13711yescharacteristic
137D19—82no—
138C22×Q8C2×D1911yescharacteristic, complemented
139C22×D4—191no—
140C22×D4—381no—
141C23×C4C2×D1911yescharacteristic
142C2×SD16—194no—
143C2×M16—192no—
144C22⋊Q8—21no—
145C22⋊Q8—21no—
146C22⋊Q8C2×D1912yes—
147C22⋊Q8C2×D1912yescomplemented
148#121—192no—
149#121—192no—
150#121—381no—
151#121—381no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—191no—
154C2×C4⋊C4C2×D1911yescharacteristic, complemented
155C2×C22⋊C4—21no—
156C2×C22⋊C4—381no—
157#107—194no—
158#103—194no—
159#102—194no—
160C22⋊C8—192no—
161C22⋊C8—192no—
162C19#319311yescharacteristic, complemented, Sylow
163C24—381no—
164C24C22⋊D1911yescharacteristic
165C2×Q8—21no—
166C2×Q8—42no—
167C2×Q8C22×D1912yes—
168C2×D4—192no—
169C2×D4—382no—
170C2×D4—382no—
171C2×D4—381no—
172C2×D4—762no—
173C2×D4—764no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—42no—
177C22×C4—381no—
178C22×C4C22⋊D1911yescharacteristic
179C22×C4C22⋊D1911yescharacteristic
180C22×C4C22⋊D1911yescharacteristic
181C22×C4C22×D1911yescharacteristic
182C22×C4C22×D1911yescharacteristic
183C22×C4C22×D1911yescharacteristic
184SD16—764no—
185M16—762no—
186C2×C8—194no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—192no—
191C4⋊C4—381no—
192C4⋊C4C22×D1912yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—382no—
196C22⋊C4—382no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—382no—
201C23—762no—
202C23—762no—
203C23—762no—
204C23C2×C22⋊D1911yescharacteristic
205C23C2×C22⋊D1911yescharacteristic
206C23C2×C22⋊D1911yescharacteristic
207Q8—24no—
208Q8—42no—
209D4—384no—
210D4—762no—
211D4—764no—
212D4—764no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—382no—
224C2×C4—762no—
225C2×C4C2×C22⋊D1911yescharacteristic
226C2×C4C2×C22⋊D1911yescharacteristic
227C2×C4C2×C22⋊D1911yescharacteristic
228C2×C4C23×D1911yescharacteristic
229C8—384no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—44no—
238C22—762no—
239C22—762no—
240C22—762no—
241C22—1524no—
242C22#1059738812yes—
243C22#1059739512yes—
244C22C22×C22⋊D1911yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—762no—
251C4#1059743012yes—
252C2—22no—
253C2—22no—
254C2—41no—
255C2—1522no—
256C2#1192710311yescharacteristic
257C2C2×#1059739511yescharacteristic
258C2C2×#1059738811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×C22⋊Q8C2
socleC22×C19C22×D4
prime radicalC2×#10597376C2
hypercenterC2×C22⋊Q8D19
hypocenterC19#3193
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11926877C2semidirect
3. #11926857C2semidirect
4. #11926792C2semidirect
5. #11926694C2semidirect
6. #11926683C2semidirect
7. #11926508C2semidirect
8. C2×C19×C22⋊Q8C2semidirect
9. C22×Q8×C19C22semidirect
16. C19×C22⋊Q8C22semidirect
18. C2×C4⋊C4×C19C22semidirect
20. C2×#64527C22semidirect
27. C2×#64520C22semidirect
28. #10597292C22semidirect
30. C22⋊(C19⋊C8)C22semidirect
31. #10597266C22semidirect
32. #10597264C22semidirect
123. C2×C22⋊Q8D19semidirect
138. C22×Q8C2×D19semidirect
147. C22⋊Q8C2×D19semidirect
154. C2×C4⋊C4C2×D19semidirect
162. C19#3193semidirect

Maximal subgroups

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

subgroupindex
C2×#105973762
#119268772
#119268572
#119267922
#119266942
#119266832
#119265082
C2×C19×C22⋊Q82
#319319