Finite Group Databasebeta

← #14574478

Subgroups — #14574478

Order 2432.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#11927057C212yesmaximal, complemented
2#11926883C212yesmaximal, complemented
3#11926870C212yesmaximal, complemented
4#11926797C211yesmaximal, characteristic, complemented
5#11926792C212yesmaximal, complemented
6#11926705C212yesmaximal, complemented
7#11926692C212yesmaximal, complemented
8#11926507C211yesmaximal, characteristic, complemented
9C19×#470C211yesmaximal, characteristic, complemented
10C2×#64545C2212yes—
11C22×C4×D19C2211yescharacteristic
12C2×Q16×C19C2211yescharacteristic, complemented
13C2×M16×C19C2211yescharacteristic
14C19×C22⋊Q8C2212yes—
15#10597392C2212yes—
16C2×#64527C2212yescomplemented
17#10597376C2212yes—
18C2×#64520C2211yescharacteristic
19C2×D152C2211yescharacteristic, complemented
20#10597341C2212yes—
21#10597340—22no—
22#10597339—22no—
23#10597338C2212yes—
24#10597328—22no—
25(C22⋊D19)⋊C4—22no—
26C19×#106C2211yescharacteristic, complemented
27C19×#103C2212yescomplemented
28#10597292C2212yescomplemented
29#10597278C2212yescomplemented
30(C2×D19)⋊C8C2212yes—
31(C2×D19)⋊C8C2212yes—
32#10597274C2211yescharacteristic, complemented
33#10597266C2212yescomplemented
34#10597264C2212yescomplemented
35C23×D19D411yescharacteristic
36C2×Q8×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C2×C22⋊D19—22no—
39C22×Dic19D411yescharacteristic
40#64545—42no—
41#64545—42no—
42C2×D76—22no—
43C2×D76—22no—
44C2×D76C2312yes—
45C2×C4×D19—22no—
46C2×C4×D19—41no—
47C2×C4×D19—41no—
48C2×C4×D19D412yes—
49C2×C4×D19C2312yes—
50Q16×C19—41no—
51M16×C19—41no—
52C2×C8×C19C2311yescharacteristic
53C2×C8×C19C2311yescharacteristic
54C4⋊C4×C19—22no—
55C4⋊C4×C19C2312yes—
56C22⋊C4×C19—22no—
57#64527—42no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—22no—
60(C2×D19)⋊C4—22no—
61(C2×D19)⋊C4—22no—
62C4⋊Dic19C2312yes—
63Dic19⋊C4—22no—
64C4×Dic19—22no—
65#64520—41no—
66C2×C19⋊C8C2312yes—
67D152—41no—
68C23×C19C2×D411yescharacteristic
69C22×D19—22no—
70C22×D19—41no—
71C22×D19—42no—
72C22×D19C2×D412yes—
73Q8×C19—22no—
74Q8×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19C2×D411yescharacteristic
80C2×C4×C19C2411yescharacteristic
81C22⋊D19—44no—
82C2×Dic19—22no—
83C2×Dic19—41no—
84C2×Dic19C2×D412yes—
85D76—22no—
86D76—22no—
87D76—44no—
88D76—44no—
89C4×D19—22no—
90C4×D19—22no—
91C4×D19—42no—
92C4×D19—44no—
93C8×C19—21no—
94C8×C19—21no—
95C19⋊C8—22no—
96#3197—191nomaximal, Sylow
97C22×C19—21no—
98C22×C19—22no—
99C22×C19C22×D411yescharacteristic
100C2×D19—22no—
101C2×D19—22no—
102C2×D19—22no—
103C2×D19—44no—
104C2×D19—42no—
105C2×D19—42no—
106C2×D19—42no—
107C4×C19—21no—
108C4×C19—42no—
109C4×C19—42no—
110C4×C19H(5,𝔽2)11yescharacteristic
111C4×C19H(5,𝔽2)11yescharacteristic
112Dic19—22no—
113Dic19—42no—
114#525—192no—
115#485—192no—
116#482—192no—
117#470D1911yescharacteristic, complemented
118#469—191no—
119#468—192no—
120#452—192no—
121#449—192no—
122#407—191no—
123C2×C19—41no—
124C2×C19#53411yescharacteristic
125C2×C19#57512yes—
126D19—42no—
127D19—82no—
128C2×#41—192no—
129C23×C4—191no—
130C2×Q16C2×D1911yescharacteristic, complemented
131C2×SD16—192no—
132C2×D8—191no—
133C2×M16—191no—
134C2×M16C2×D1911yescharacteristic
135#123—382no—
136C22⋊Q8—192no—
137C22⋊Q8C2×D1912yes—
138#121—192no—
139#121—192no—
140#120—382no—
141C4×D4—382no—
142C4×D4—382no—
143#117—192no—
144#107—192no—
145#106—191no—
146#106C2×D1911yescharacteristic, complemented
147#103—192no—
148#103C2×D1912yescomplemented
149#102—192no—
150#102—192no—
151C22⋊C8—192no—
152C22⋊C8—192no—
153C19#319711yescharacteristic, complemented, Sylow
154C24—191no—
155#41—762no—
156#41—762no—
157C2×Q8C22×D1912yes—
158C2×D4—192no—
159C2×D4—382no—
160C2×D4—382no—
161C2×D4—382no—
162C22×C4—191no—
163C22×C4—192no—
164C22×C4—192no—
165C22×C4—382no—
166C22×C4—761no—
167C22×C4—761no—
168C22×C4C22×D1911yescharacteristic
169Q16—41no—
170SD16—762no—
171D8—761no—
172M16—41no—
173M16—761no—
174C2×C8—192no—
175C2×C8C22×D1911yescharacteristic
176C2×C8C22×D1911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—192no—
179C4⋊C4—382no—
180C4⋊C4C22×D1912yes—
181C22⋊C4—22no—
182C22⋊C4—382no—
183C22⋊C4—382no—
184C22⋊C4—382no—
185C22⋊C4—382no—
186C42—382no—
187C23—192no—
188C23—382no—
189C23—761no—
190C23—762no—
191C23D4×D1911yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—382no—
195D4—382no—
196D4—764no—
197D4—764no—
198D4—764no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—192no—
204C2×C4—382no—
205C2×C4—382no—
206C2×C4—382no—
207C2×C4—762no—
208C2×C4—764no—
209C2×C4—761no—
210C2×C4D4×D1911yescharacteristic
211C2×C4C23×D1911yescharacteristic
212C8—21no—
213C8—21no—
214C8—382no—
215C22—22no—
216C22—21no—
217C22—382no—
218C22—382no—
219C22—382no—
220C22—764no—
221C22—762no—
222C22—762no—
223C22—762no—
224C22C2×D4×D1911yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—382no—
229C4—762no—
230C4#1059743011yescharacteristic
231C4#1059743511yescharacteristic
232C2—41no—
233C2—762no—
234C2—1522no—
235C2#1192710211yescharacteristic
236C2#1192734312yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#470C2
socleC22×C19C22×D4
hypercenter#470D19
hypocenterC19#3197
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #11927057C2semidirect
2. #11926883C2semidirect
3. #11926870C2semidirect
4. #11926797C2semidirect
5. #11926792C2semidirect
6. #11926705C2semidirect
7. #11926692C2semidirect
8. #11926507C2semidirect
9. C19×#470C2semidirect
12. C2×Q16×C19C22semidirect
16. C2×#64527C22semidirect
19. C2×D152C22semidirect
26. C19×#106C22semidirect
27. C19×#103C22semidirect
28. #10597292C22semidirect
29. #10597278C22semidirect
32. #10597274C22semidirect
33. #10597266C22semidirect
34. #10597264C22semidirect
117. #470D19semidirect
130. C2×Q16C2×D19semidirect
146. #106C2×D19semidirect
148. #103C2×D19semidirect
153. C19#3197semidirect

Maximal subgroups

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

subgroupindex
#119270572
#119268832
#119268702
#119267972
#119267922
#119267052
#119266922
#119265072
C19×#4702
#319719