Finite Group Databasebeta

← #14574406

Subgroups — #14574406

Order 2432.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C22⋊Q8×D19C212yesmaximal
2#11926881C212yesmaximal, complemented
3#11926878C212yesmaximal, complemented
4#11926785C211yesmaximal, characteristic, complemented
5#11926783C212yesmaximal, complemented
6#11926701C212yesmaximal, complemented
7#11926698C212yesmaximal, complemented
8C2×(C2×D19)⋊C8C211yesmaximal, characteristic
9C19×#467C211yesmaximal, characteristic, complemented
10C2×Q8×D19C2212yes—
11C22×C4×D19C2211yescharacteristic
12C2×Q16×C19C2211yescharacteristic, complemented
13C22×C8×C19C2211yescharacteristic
14C19×C22⋊Q8C2212yes—
15#10597392C2212yes—
16C2×#64528C2212yescomplemented
17#10597370C2212yes—
18C22×C19⋊C8C2211yescharacteristic
19C2×Dic76C2211yescharacteristic, complemented
20#10597343C2212yes—
21#10597342—22no—
22C4⋊C4×D19—22no—
23C4⋊C4×D19C2212yes—
24C22⋊C4×D19—22no—
25#10597324—22no—
26C19×#107C2211yescharacteristic, complemented
27C19×#103C2212yescomplemented
28#10597292C2212yescomplemented
29(C2×D19)⋊C8C2212yes—
30(C2×D19)⋊C8C2212yes—
31#10597275C2211yescharacteristic, complemented
32#10597273C2212yescomplemented
33#10597267C2212yescomplemented
34#10597264C2212yescomplemented
35C23×D19D411yescharacteristic
36C2×Q8×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×Dic19D411yescharacteristic
39Q8×D19—42no—
40Q8×D19—42no—
41C2×C4×D19—22no—
42C2×C4×D19—22no—
43C2×C4×D19—41no—
44C2×C4×D19—41no—
45C2×C4×D19D412yes—
46C2×C4×D19C2312yes—
47C2×Dic38—22no—
48C2×Dic38C2312yes—
49Q16×C19—41no—
50C2×C8×C19—41no—
51C2×C8×C19C2311yescharacteristic
52C2×C8×C19C2311yescharacteristic
53C4⋊C4×C19—22no—
54C4⋊C4×C19C2312yes—
55C22⋊C4×C19—22no—
56C22⋊Dic19—22no—
57#64528—42no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—22no—
60C4⋊Dic19—22no—
61C4⋊Dic19C2312yes—
62Dic19⋊C4—22no—
63Dic19⋊C4—22no—
64Dic19⋊C4—22no—
65C2×C19⋊C8—41no—
66C2×C19⋊C8C2312yes—
67Dic76—41no—
68C23×C19C2×D411yescharacteristic
69C22×D19—41no—
70C22×D19—41no—
71C22×D19Q1614yescomplemented
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
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—41no—
84C2×Dic19C2×D412yes—
85C4×D19—22no—
86C4×D19—22no—
87C4×D19—42no—
88C4×D19—44no—
89C4×D19—44no—
90Dic38—22no—
91Dic38—22no—
92Dic38—44no—
93C8×C19—21no—
94C8×C19—21no—
95C19⋊C8—22no—
96#3189—191nomaximal, Sylow
97C22×C19—21no—
98C22×C19—21no—
99C22×C19C2×Q1612yes—
100C22×C19C22×D411yescharacteristic
101C2×D19—22no—
102C2×D19—22no—
103C2×D19—44no—
104C2×D19C2×Q1614yes—
105C4×C19—21no—
106C4×C19—42no—
107C4×C19—42no—
108C4×C19H(5,𝔽2)11yescharacteristic
109C4×C19H(5,𝔽2)11yescharacteristic
110Dic19—22no—
111Dic19—42no—
112Dic19—42no—
113C2×C22⋊Q8—192no—
114#484—192no—
115#484—192no—
116#467—191no—
117#467—192no—
118#467D1911yescharacteristic, complemented
119#451—192no—
120#451—192no—
121C2×C22⋊C8—191no—
122C2×C19—22no—
123C2×C19#53411yescharacteristic
124C2×C19C22×Q1611yescharacteristic
125C2×C19#57511yescharacteristic
126D19—24no—
127C22×Q8—192no—
128C23×C4—191no—
129C2×Q16—192no—
130C2×Q16—191no—
131C2×Q16C2×D1911yescharacteristic, complemented
132C22×C8—191no—
133C22×C8C2×D1911yescharacteristic
134C22⋊Q8—192no—
135C22⋊Q8—192no—
136C22⋊Q8—192no—
137C22⋊Q8—382no—
138C22⋊Q8—382no—
139C22⋊Q8C2×D1912yes—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—382no—
142C2×C22⋊C4—382no—
143#107—191no—
144#107—192no—
145#107C2×D1911yescharacteristic, complemented
146#103—192no—
147#103—192no—
148#103—192no—
149#103C2×D1912yescomplemented
150C22⋊C8—192no—
151C22⋊C8—192no—
152C19#318911yescharacteristic, complemented, Sylow
153C24—191no—
154C2×Q8—192no—
155C2×Q8—382no—
156C2×Q8—762no—
157C2×Q8—762no—
158C2×Q8C22×D1912yes—
159C22×C4—191no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4—382no—
163C22×C4—382no—
164C22×C4—761no—
165C22×C4—761no—
166C22×C4C22×D1911yescharacteristic
167Q16—41no—
168Q16—761no—
169Q16—762no—
170C2×C8—41no—
171C2×C8—192no—
172C2×C8—761no—
173C2×C8C22×D1911yescharacteristic
174C2×C8C22×D1911yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—192no—
177C4⋊C4—382no—
178C4⋊C4—382no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4C22×D1912yes—
182C22⋊C4—22no—
183C22⋊C4—382no—
184C22⋊C4—382no—
185C22⋊C4—382no—
186C23—192no—
187C23—194no—
188C23—761no—
189C23—761no—
190C23D4×D1911yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—382no—
194Q8—382no—
195Q8—764no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—192no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—762no—
206C2×C4—764no—
207C2×C4—764no—
208C2×C4—761no—
209C2×C4D4×D1911yescharacteristic
210C2×C4C23×D1911yescharacteristic
211C8—21no—
212C8—21no—
213C8—382no—
214C22—21no—
215C22—21no—
216C22—194no—
217C22—382no—
218C22—382no—
219C22—764no—
220C22Q16×D1912yes—
221C22C2×D4×D1911yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—382no—
226C4—762no—
227C4—762no—
228C4#1059743011yescharacteristic
229C4#1059743511yescharacteristic
230C2—22no—
231C2—384no—
232C2#1192710211yescharacteristic
233C2C2×Q16×D1911yescharacteristic
234C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#467C2
socleC22×C19C22×D4
prime radicalC23×D19D4
hypercenter#467D19
hypocenterC19#3189
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #11926881C2semidirect
3. #11926878C2semidirect
4. #11926785C2semidirect
5. #11926783C2semidirect
6. #11926701C2semidirect
7. #11926698C2semidirect
9. C19×#467C2semidirect
12. C2×Q16×C19C22semidirect
16. C2×#64528C22semidirect
19. C2×Dic76C22semidirect
26. C19×#107C22semidirect
27. C19×#103C22semidirect
28. #10597292C22semidirect
31. #10597275C22semidirect
32. #10597273C22semidirect
33. #10597267C22semidirect
34. #10597264C22semidirect
71. C22×D19Q16semidirect
118. #467D19semidirect
131. C2×Q16C2×D19semidirect
145. #107C2×D19semidirect
149. #103C2×D19semidirect
152. C19#3189semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D192
#119268812
#119268782
#119267852
#119267832
#119267012
#119266982
C2×(C2×D19)⋊C82
C19×#4672
#318919