Finite Group Databasebeta

← #14574422

Subgroups — #14574422

Order 2432.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#11927054C212yesmaximal, complemented
2#11926887C212yesmaximal, complemented
3#11926866C212yesmaximal, complemented
4#11926785C211yesmaximal, characteristic, complemented
5#11926771C212yesmaximal, complemented
6#11926707C212yesmaximal, complemented
7#11926686C212yesmaximal, complemented
8C2×(C2×D19)⋊C8C211yesmaximal, characteristic, complemented
9C19×#466C211yesmaximal, characteristic, complemented
10C2×#64543C2212yes—
11C22×C4×D19C2211yescharacteristic
12C2×D8×C19C2211yescharacteristic, complemented
13C22×C8×C19C2211yescharacteristic
14C19×#121C2212yes—
15#10597384C2212yes—
16#10597383—22no—
17D4×Dic19—22no—
18C2×#64526C2212yescomplemented
19#10597370C2212yes—
20C22×C19⋊C8C2211yescharacteristic
21C2×Dic76C2211yescharacteristic, complemented
22#10597343C2212yes—
23#10597338C2212yes—
24#10597329—22no—
25(C22⋊D19)⋊C4—22no—
26C19×#107C2211yescharacteristic, complemented
27C19×#102C2212yescomplemented
28#10597289C2212yescomplemented
29(C2×D19)⋊C8C2212yes—
30(C2×D19)⋊C8C2212yes—
31#10597275C2211yescharacteristic, complemented
32#10597273C2212yescomplemented
33#10597267C2212yescomplemented
34#10597265C2212yescomplemented
35C23×D19D411yescharacteristic
36C2×D4×C19—22no—
37C2×D4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C2×C22⋊D19—22no—
40C2×C22⋊D19—22no—
41C22×Dic19—22no—
42C22×Dic19D411yescharacteristic
43#64543—42no—
44#64543—42no—
45C2×C4×D19—41no—
46C2×C4×D19—41no—
47C2×C4×D19D412yes—
48C2×C4×D19C2312yes—
49C2×Dic38C2312yes—
50D8×C19—41no—
51C2×C8×C19—41no—
52C2×C8×C19C2311yescharacteristic
53C2×C8×C19C2311yescharacteristic
54C4⋊C4×C19C2312yes—
55C22⋊C4×C19—22no—
56C22⋊Dic19—22no—
57C22⋊Dic19—22no—
58#64526—42no—
59(C2×D19)⋊C4—22no—
60(C2×D19)⋊C4—22no—
61C4⋊Dic19—22no—
62C4⋊Dic19C2312yes—
63Dic19⋊C4—22no—
64C4×Dic19—22no—
65C2×C19⋊C8—41no—
66C2×C19⋊C8C2312yes—
67Dic76—41no—
68C23×C19—22no—
69C23×C19C2×D411yescharacteristic
70C22×D19—22no—
71C22×D19—41no—
72C22×D19—41no—
73C22×D19C2×D412yes—
74D4×C19—22no—
75D4×C19—22no—
76D4×C19—44no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19C2×D411yescharacteristic
81C2×C4×C19C2411yescharacteristic
82C22⋊D19—44no—
83C22⋊D19—44no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—41no—
87C2×Dic19—44no—
88C2×Dic19C2×D412yes—
89C4×D19—22no—
90C4×D19—22no—
91C4×D19—42no—
92Dic38—22no—
93Dic38—22no—
94C8×C19—21no—
95C8×C19—21no—
96C19⋊C8—22no—
97#3191—191nomaximal, Sylow
98C22×C19—21no—
99C22×C19—21no—
100C22×C19—42no—
101C22×C19—42no—
102C22×C19—42no—
103C22×C19#13512yes—
104C22×C19C22×D411yescharacteristic
105C2×D19—22no—
106C2×D19—22no—
107C2×D19—22no—
108C2×D19—44no—
109C4×C19—21no—
110C4×C19—42no—
111C4×C19H(5,𝔽2)11yescharacteristic
112C4×C19H(5,𝔽2)11yescharacteristic
113Dic19—22no—
114Dic19—42no—
115Dic19—42no—
116#525—192no—
117#485—192no—
118#482—192no—
119#467—191no—
120#466D1911yescharacteristic, complemented
121#465—192no—
122#452—192no—
123#449—192no—
124C2×C22⋊C8—191no—
125C2×C19—22no—
126C2×C19—82no—
127C2×C19#53411yescharacteristic
128C2×C19C2×#13511yescharacteristic
129C2×C19#57511yescharacteristic
130D19—42no—
131C2×#41—192no—
132C23×C4—191no—
133C2×Q16—191no—
134C2×SD16—192no—
135C2×D8C2×D1911yescharacteristic, complemented
136C22×C8—191no—
137C22×C8C2×D1911yescharacteristic
138#123—382no—
139C22⋊Q8—192no—
140C22⋊Q8—192no—
141#121—192no—
142#121C2×D1912yes—
143#120—382no—
144C4×D4—382no—
145C4×D4—382no—
146#117—192no—
147#107—191no—
148#107C2×D1911yescharacteristic, complemented
149#106—192no—
150#103—192no—
151#103—192no—
152#102—192no—
153#102C2×D1912yescomplemented
154C22⋊C8—192no—
155C22⋊C8—192no—
156C19#319111yescharacteristic, complemented, Sylow
157C24—191no—
158#41—762no—
159#41—762no—
160C2×Q8—192no—
161C2×D4—22no—
162C2×D4—382no—
163C2×D4—382no—
164C2×D4C22×D1912yes—
165C22×C4—191no—
166C22×C4—192no—
167C22×C4—192no—
168C22×C4—382no—
169C22×C4—761no—
170C22×C4—761no—
171C22×C4C22×D1911yescharacteristic
172Q16—761no—
173SD16—762no—
174D8—41no—
175C2×C8—41no—
176C2×C8—192no—
177C2×C8—761no—
178C2×C8C22×D1911yescharacteristic
179C2×C8C22×D1911yescharacteristic
180C4⋊C4—192no—
181C4⋊C4—382no—
182C4⋊C4—382no—
183C4⋊C4C22×D1912yes—
184C22⋊C4—22no—
185C22⋊C4—382no—
186C22⋊C4—382no—
187C22⋊C4—382no—
188C22⋊C4—382no—
189C42—382no—
190C23—22no—
191C23—192no—
192C23—382no—
193C23—761no—
194C23—761no—
195C23D4×D1911yescharacteristic
196Q8—382no—
197Q8—382no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—764no—
202D4—764no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—192no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—762no—
212C2×C4—761no—
213C2×C4—764no—
214C2×C4D4×D1911yescharacteristic
215C2×C4C23×D1911yescharacteristic
216C8—21no—
217C8—21no—
218C8—382no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—382no—
225C22—382no—
226C22—382no—
227C22—764no—
228C22#1059735812yes—
229C22C2×D4×D1911yescharacteristic
230C4—21no—
231C4—42no—
232C4—382no—
233C4—762no—
234C4—762no—
235C4#1059743011yescharacteristic
236C4#1059743511yescharacteristic
237C2—22no—
238C2—82no—
239C2—762no—
240C2#1192710211yescharacteristic
241C2C2×#1059735811yescharacteristic
242C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#466C2
socleC22×C19C22×D4
hypercenter#466D19
hypocenterC19#3191
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #11927054C2semidirect
2. #11926887C2semidirect
3. #11926866C2semidirect
4. #11926785C2semidirect
5. #11926771C2semidirect
6. #11926707C2semidirect
7. #11926686C2semidirect
8. C2×(C2×D19)⋊C8C2semidirect
9. C19×#466C2semidirect
12. C2×D8×C19C22semidirect
18. C2×#64526C22semidirect
21. C2×Dic76C22semidirect
26. C19×#107C22semidirect
27. C19×#102C22semidirect
28. #10597289C22semidirect
31. #10597275C22semidirect
32. #10597273C22semidirect
33. #10597267C22semidirect
34. #10597265C22semidirect
120. #466D19semidirect
135. C2×D8C2×D19semidirect
148. #107C2×D19semidirect
153. #102C2×D19semidirect
156. C19#3191semidirect

Maximal subgroups

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

subgroupindex
#119270542
#119268872
#119268662
#119267852
#119267712
#119267072
#119266862
C2×(C2×D19)⋊C82
C19×#4662
#319119