Finite Group Databasebeta

← #14574455

Subgroups — #14574455

Order 2432.

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

normal subgroups only

This group has 410 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
1C22⋊Q8×D19C212yesmaximal
2#11926876C212yesmaximal, complemented
3#11926873C212yesmaximal, complemented
4#11926802C211yesmaximal, characteristic, complemented
5#11926800C212yesmaximal, complemented
6#11926701C212yesmaximal, complemented
7#11926698C212yesmaximal, complemented
8#11926507C211yesmaximal, characteristic
9C19×#470C211yesmaximal, characteristic, complemented
10C2×Q8×D19C2212yes—
11C22×C4×D19C2211yescharacteristic
12C2×Q16×C19C2211yescharacteristic, complemented
13C2×M16×C19C2211yescharacteristic
14C19×C22⋊Q8C2212yes—
15#10597392C2212yes—
16C2×#64528C2212yescomplemented
17#10597370C2212yes—
18C2×#64520C2211yescharacteristic
19C2×Dic76C2211yescharacteristic, complemented
20#10597343C2212yes—
21#10597342—22no—
22C4⋊C4×D19—22no—
23C4⋊C4×D19C2212yes—
24C22⋊C4×D19—22no—
25#10597324—22no—
26C19×#106C2211yescharacteristic, complemented
27C19×#103C2212yescomplemented
28#10597292C2212yescomplemented
29(C2×D19)⋊C8C2212yes—
30(C2×D19)⋊C8C2212yes—
31#10597274C2211yescharacteristic, complemented
32#10597273C2212yescomplemented
33#10597267C2212yescomplemented
34#10597265C2212yescomplemented
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—
50M16×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—
65#64520—41no—
66C2×C19⋊C8C2312yes—
67Dic76—41no—
68C23×C19C2×D411yescharacteristic
69C22×D19—24no—
70C22×D19—41no—
71C22×D19C2×D412yes—
72Q8×C19—22no—
73Q8×C19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19C2×D411yescharacteristic
79C2×C4×C19C2411yescharacteristic
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—41no—
83C2×Dic19C2×D412yes—
84C4×D19—22no—
85C4×D19—22no—
86C4×D19—42no—
87C4×D19—44no—
88C4×D19—44no—
89Dic38—22no—
90Dic38—22no—
91Dic38—44no—
92C8×C19—21no—
93C8×C19—21no—
94C19⋊C8—22no—
95#3195—191nomaximal, Sylow
96C22×C19—21no—
97C22×C19—22no—
98C22×C19C22×D411yescharacteristic
99C2×D19—22no—
100C2×D19—22no—
101C2×D19—44no—
102C2×D19#13714yes—
103C4×C19—21no—
104C4×C19—42no—
105C4×C19—42no—
106C4×C19H(5,𝔽2)11yescharacteristic
107C4×C19H(5,𝔽2)11yescharacteristic
108Dic19—22no—
109Dic19—42no—
110Dic19—42no—
111C2×C22⋊Q8—192no—
112#483—192no—
113#483—192no—
114#470—191no—
115#470—192no—
116#470D1911yescharacteristic, complemented
117#451—192no—
118#451—192no—
119#407—191no—
120C2×C19—41no—
121C2×C19#53411yescharacteristic
122C2×C19C2×#13712yes—
123D19—24no—
124C22×Q8—192no—
125C23×C4—191no—
126C2×Q16—192no—
127C2×Q16—191no—
128C2×Q16C2×D1911yescharacteristic, complemented
129C2×M16—191no—
130C2×M16C2×D1911yescharacteristic
131C22⋊Q8—192no—
132C22⋊Q8—192no—
133C22⋊Q8—192no—
134C22⋊Q8—382no—
135C22⋊Q8—382no—
136C22⋊Q8C2×D1912yes—
137C2×C4⋊C4—192no—
138C2×C4⋊C4—382no—
139C2×C22⋊C4—382no—
140#106—191no—
141#106—192no—
142#106C2×D1911yescharacteristic, complemented
143#103—192no—
144#103—192no—
145#103—192no—
146#103C2×D1912yescomplemented
147C22⋊C8—192no—
148C22⋊C8—192no—
149C19#319511yescharacteristic, complemented, Sylow
150C24—191no—
151C2×Q8—192no—
152C2×Q8—382no—
153C2×Q8—762no—
154C2×Q8—762no—
155C2×Q8C22×D1912yes—
156C22×C4—191no—
157C22×C4—192no—
158C22×C4—192no—
159C22×C4—382no—
160C22×C4—382no—
161C22×C4—761no—
162C22×C4—761no—
163C22×C4C22×D1911yescharacteristic
164Q16—41no—
165Q16—761no—
166Q16—762no—
167M16—41no—
168M16—761no—
169C2×C8—192no—
170C2×C8C22×D1911yescharacteristic
171C2×C8C22×D1911yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—192no—
174C4⋊C4—382no—
175C4⋊C4—382no—
176C4⋊C4—382no—
177C4⋊C4—382no—
178C4⋊C4C22×D1912yes—
179C22⋊C4—22no—
180C22⋊C4—382no—
181C22⋊C4—382no—
182C22⋊C4—382no—
183C23—192no—
184C23—384no—
185C23—761no—
186C23D4×D1911yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—382no—
190Q8—382no—
191Q8—764no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—192no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—762no—
202C2×C4—764no—
203C2×C4—764no—
204C2×C4—761no—
205C2×C4D4×D1911yescharacteristic
206C2×C4C23×D1911yescharacteristic
207C8—21no—
208C8—21no—
209C8—382no—
210C22—22no—
211C22—21no—
212C22—194no—
213C22—382no—
214C22—382no—
215C22—764no—
216C22C2×D4×D1911yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—382no—
221C4—762no—
222C4—762no—
223C4#1059743011yescharacteristic
224C4#1059743511yescharacteristic
225C2—41no—
226C2—384no—
227C2#1192710211yescharacteristic
228C2#137×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#470C2
socleC22×C19C22×D4
prime radicalC23×D19D4
hypercenter#470D19
hypocenterC19#3195
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
2. #11926876C2semidirect
3. #11926873C2semidirect
4. #11926802C2semidirect
5. #11926800C2semidirect
6. #11926701C2semidirect
7. #11926698C2semidirect
9. C19×#470C2semidirect
12. C2×Q16×C19C22semidirect
16. C2×#64528C22semidirect
19. C2×Dic76C22semidirect
26. C19×#106C22semidirect
27. C19×#103C22semidirect
28. #10597292C22semidirect
31. #10597274C22semidirect
32. #10597273C22semidirect
33. #10597267C22semidirect
34. #10597265C22semidirect
116. #470D19semidirect
128. C2×Q16C2×D19semidirect
142. #106C2×D19semidirect
146. #103C2×D19semidirect
149. C19#3195semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D192
#119268762
#119268732
#119268022
#119268002
#119267012
#119266982
#119265072
C19×#4702
#319519