Finite Group Databasebeta

← #28402229

Subgroups — #28402229

Order 14464.

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

normal subgroups only

This group has 476 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
1C2×#16813651C212yesmaximal, complemented
2#20299256C212yesmaximal, complemented
3#20298841C212yesmaximal, complemented
4#20298817C212yesmaximal, complemented
5#20298752C212yesmaximal, complemented
6#20298740C212yesmaximal, complemented
7C4×Dic452C211yesmaximal, characteristic, complemented
8#20298677C211yesmaximal, characteristic, complemented
9#495×C113C211yesmaximal, characteristic, complemented
10C2×#14268646C2212yes—
11C2×Q8×D113C2212yes—
12#16813651—28no—
13C2×Dic452C2211yescharacteristic
14C2×#14268637C2212yes—
15C2×#14268635C2212yes—
16C2×#14268630C2212yes—
17#16813608—22no—
18#16813599—22no—
19#16813598C2212yes—
20#16813595—22no—
21#16813593C2212yes—
22C4×Dic226C2212yes—
23C4×D452C2211yescharacteristic
24#16813582—22no—
25#16813556C2211yescharacteristic
26C4⋊#11744751C2211yescharacteristic
27#16813547C2212yes—
28#16813546C2212yes—
29#16813543C2212yes—
30#16813534C2212yes—
31C2×Q16×C113C2211yescharacteristic
32C2×SD16×C113C2212yes—
33C2×D8×C113C2211yescharacteristic
34#124×C113C2212yes—
35C4×C8×C113C2211yescharacteristic
36#14268646—24no—
37#14268646—42no—
38C2×Dic226—22no—
39C2×Dic226C2312yes—
40Q8×D113—24no—
41Q8×D113—42no—
42C2×D452D411yescharacteristic
43C2×C22⋊D113—22no—
44C2×C22⋊D113—22no—
45C22×Dic113—22no—
46C2×C4×D113—22no—
47C2×C4×D113C2312yes—
48Dic452D414yescomplemented
49#14268637—24no—
50#14268635—24no—
51#14268630—24no—
52C2×#11744751C2312yes—
53C4⋊Dic113D411yescharacteristic
54C4⋊Dic113C2312yes—
55#14268626—22no—
56#14268626—22no—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624D412yes—
60C4×Dic113—22no—
61C2×Q8×C113C2312yes—
62C2×D4×C113C2312yes—
63Q16×C113—41no—
64SD16×C113—24no—
65D8×C113—41no—
66C2×C8×C113C2311yescharacteristic
67C2×C8×C113C2311yescharacteristic
68C22⋊C4×C113—22no—
69C22⋊C4×C113—22no—
70C42×C113C2311yescharacteristic
71C23×C113—22no—
72C22×D113C2×D412yes—
73Q8×C113—22no—
74Q8×C113—22no—
75D4×C113—22no—
76D4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2411yescharacteristic
81C22⋊D113—44no—
82C22⋊D113—44no—
83C2×Dic113—22no—
84C2×Dic113—22no—
85C2×Dic113—44no—
86C2×Dic113C2×D412yes—
87D452—41no—
88C4×D113—22no—
89C4×D113—22no—
90C4×D113—44no—
91Dic226—22no—
92Dic226—44no—
93Dic226C2×D414yes—
94C8×C113—21no—
95C8×C113C2×D412yes—
96#11744751—22no—
97C22×C113—42no—
98C22×C113—42no—
99C22×C113—42no—
100C22×C113C22×D411yescharacteristic
101C2×D113—22no—
102C2×D113—22no—
103C2×D113—22no—
104C4×C113—21no—
105C4×C113—21no—
106C4×C113—42no—
107C4×C113C22×D411yescharacteristic
108C4×C113H(5,𝔽2)11yescharacteristic
109Dic113—24no—
110Dic113—22no—
111Dic113—42no—
112C2×C113—82no—
113C2×C113D4211yescharacteristic
114C2×C113#57511yescharacteristic
115C2×C113#57811yescharacteristic
116D113—42no—
117#3277—1131nomaximal, Sylow
118C113#327711yescharacteristic, complemented, Sylow
119C2×#137—1132no—
120#548—1132no—
121#495D11311yescharacteristic, complemented
122#468—1132no—
123#464—1132no—
124#451—1132no—
125#449—1132no—
126C4×Q16—1131no—
127#436—1131no—
128C2×#41—1132no—
129C22×Q8—1132no—
130#137—2268no—
131C2×Q16—1132no—
132C2×Q16—1131no—
133C2×Q16C2×D11311yescharacteristic
134C2×SD16—1132no—
135C2×SD16C2×D11312yes—
136C2×D8C2×D11311yescharacteristic
137C2×M16—1132no—
138#124—2262no—
139#124C2×D11312yes—
140C22⋊Q8—1132no—
141C22⋊Q8—2262no—
142#121—1132no—
143#121—2262no—
144C4×Q8—1132no—
145C4×D4—1131no—
146C4×D4—2262no—
147#107—1131no—
148C4⋊C8—1131no—
149#103—1132no—
150#103—1132no—
151#102—1132no—
152C22⋊C8—1132no—
153C4×C8C2×D11311yescharacteristic
154#41—4522no—
155#41—2264no—
156C2×Q8—1132no—
157C2×Q8—4522no—
158C2×Q8—2262no—
159C2×Q8—2264no—
160C2×Q8C22×D11312yes—
161C2×D4—1131no—
162C2×D4—2262no—
163C2×D4—2262no—
164C2×D4C22×D11312yes—
165C22×C4—1132no—
166C22×C4—2262no—
167C22×C4—2262no—
168Q16—41no—
169Q16—1134no—
170Q16—2264no—
171SD16—24no—
172SD16—2264no—
173D8—41no—
174M16—2264no—
175C2×C8—1132no—
176C2×C8C22×D11311yescharacteristic
177C2×C8C22×D11311yescharacteristic
178C4⋊C4—1131no—
179C4⋊C4—1132no—
180C4⋊C4—2262no—
181C4⋊C4—2262no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—1132no—
185C22⋊C4—2262no—
186C22⋊C4—2262no—
187C42—2262no—
188C42C22×D11311yescharacteristic
189C23—22no—
190C23—1132no—
191Q8—22no—
192Q8—22no—
193Q8—1134no—
194Q8—4524no—
195Q8—2262no—
196D4—22no—
197D4—22no—
198D4—4521no—
199D4—4524no—
200D4—4524no—
201C2×C4—22no—
202C2×C4—1132no—
203C2×C4—4524no—
204C2×C4—4524no—
205C2×C4—2262no—
206C2×C4—2262no—
207C2×C4—2262no—
208C2×C4—2262no—
209C2×C4D4×D11311yescharacteristic
210C2×C4D4×D11311yescharacteristic
211C2×C4C23×D11311yescharacteristic
212C8—21no—
213C8—2262no—
214C8D4×D11312yes—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—2262no—
219C22—2262no—
220C22—2262no—
221C22C2×D4×D11311yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—4522no—
226C4—2262no—
227C4—2264no—
228C4C2×D4×D11311yescharacteristic
229C4#1681366711yescharacteristic
230C2—82no—
231C2—4522no—
232C2#2029923311yescharacteristic
233C2#2029939511yescharacteristic
234C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#495×C113C2
socleC22×C113C22×D4
hypercenter#495D113
hypocenterC113#3277
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. #20299256C2semidirect
3. #20298841C2semidirect
4. #20298817C2semidirect
5. #20298752C2semidirect
6. #20298740C2semidirect
7. C4×Dic452C2semidirect
8. #20298677C2semidirect
9. #495×C113C2semidirect
48. Dic452D4semidirect
118. C113#3277semidirect
121. #495D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
#202992562
#202988412
#202988172
#202987522
#202987402
C4×Dic4522
#202986772
#495×C1132
#3277113