Finite Group Databasebeta

← #28400865

Subgroups — #28400865

Order 14464.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299203C211yesmaximal, characteristic
2#20298922C212yesmaximal, complemented
3#20298905C212yesmaximal, complemented
4#20298798C212yesmaximal, complemented
5#20298737C212yesmaximal, complemented
6#20298696C212yesmaximal, complemented
7C4×#14268634C212yesmaximal, complemented
8#20298659C211yesmaximal, characteristic, complemented
9#519×C113C211yesmaximal, characteristic, complemented
10C2×#14268634C2212yes—
11C2×#14268634C2212yes—
12#16813619C2211yescharacteristic
13#16813614C2211yescharacteristic
14#16813607—22no—
15#16813596C2212yes—
16#16813595—22no—
17C4×D452C2212yes—
18#16813555C2212yes—
19#16813553C2212yes—
20C4⋊#11744751C2212yes—
21#16813546C2212yes—
22#16813546C2212yes—
23#16813542C2212yes—
24#16813542C2212yes—
25C22⋊#11744751C2212yes—
26#16813533C2211yescharacteristic
27C4×#11744751C2211yescharacteristic
28C22×Q8×C113C2211yescharacteristic
29C4×Q8×C113—22no—
30C4×Q8×C113C2212yes—
31C4×Q8×C113C2212yes—
32#117×C113—22no—
33#117×C113C2211yescharacteristic
34#117×C113C2211yescharacteristic
35C2×D452—22no—
36C2×D452C2312yes—
37C2×C22⋊D113—22no—
38C2×C4×D113—22no—
39#14268634—24no—
40#14268634—24no—
41C2×#11744751C2312yes—
42C2×#11744751C2312yes—
43C4⋊Dic113C2312yes—
44#14268626—22no—
45#14268624—22no—
46#14268624—22no—
47C2×Q8×C113—24no—
48C2×Q8×C113—21no—
49C2×Q8×C113C2312yes—
50C22×C4×C113—21no—
51C22×C4×C113C2311yescharacteristic
52C4⋊C4×C113—22no—
53C4⋊C4×C113—22no—
54C4⋊C4×C113D412yes—
55C4⋊C4×C113C2312yes—
56C22⋊C4×C113—21no—
57C22⋊C4×C113D412yes—
58C42×C113—22no—
59C42×C113—22no—
60C42×C113—21no—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113C2×D411yescharacteristic
64C22×D113—22no—
65Q8×C113—24no—
66Q8×C113—22no—
67Q8×C113#4114yes—
68C2×C4×C113—24no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D412yes—
73C2×C4×C113C2×D412yes—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C22⋊D113—82no—
77C2×Dic113—22no—
78D452—22no—
79D452—22no—
80D452—82no—
81C4×D113—82no—
82#11744751—22no—
83#11744751—22no—
84C22×C113—21no—
85C22×C113—22no—
86C22×C113C22×D411yescharacteristic
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—42no—
90C4×C113—24no—
91C4×C113—21no—
92C4×C113—22no—
93C4×C113—22no—
94C4×C113—42no—
95C4×C113C2×#4112yes—
96Dic113—42no—
97C2×C113—41no—
98C2×C113#52511yescharacteristic
99C2×C113#57712yes—
100D113—82no—
101#3126—1131nomaximal, Sylow
102C113#312611yescharacteristic, complemented, Sylow
103#540—1131no—
104#519D11311yescharacteristic, complemented
105#482—1132no—
106#479—1132no—
107#460—1132no—
108#448—1132no—
109#440—1132no—
110C4×SD16—1132no—
111#433—1131no—
112C22×Q8C2×D11311yescharacteristic
113C2×SD16—1132no—
114C2×SD16—1132no—
115#127—1131no—
116#125—1131no—
117#123—2262no—
118#121—1132no—
119#121—2262no—
120C4×Q8—22no—
121C4×Q8C2×D11312yes—
122C4×Q8C2×D11312yes—
123C4×D4—1132no—
124#117—22no—
125#117C2×D11311yescharacteristic
126#117C2×D11311yescharacteristic
127#107—1132no—
128#106—1132no—
129C4⋊C8—1132no—
130#103—1132no—
131#103—1132no—
132#102—1132no—
133#102—1132no—
134C22⋊C8—1132no—
135#97—1131no—
136C4×C8—1131no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D11312yes—
140C2×D4—1132no—
141C2×D4—2262no—
142C2×D4—2262no—
143C22×C4—21no—
144C22×C4—2262no—
145C22×C4C22×D11311yescharacteristic
146SD16—2264no—
147SD16—2264no—
148C2×C8—1132no—
149C2×C8—1132no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—1132no—
153C4⋊C4—2262no—
154C4⋊C4C22⋊D11312yes—
155C4⋊C4C22×D11312yes—
156C22⋊C4—21no—
157C22⋊C4—2262no—
158C22⋊C4—2262no—
159C22⋊C4C22⋊D11312yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D11311yescharacteristic
164C42C22×D11311yescharacteristic
165C23—2262no—
166C23C2×C22⋊D11311yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1426864714yes—
170D4—9042no—
171D4—9042no—
172D4—2262no—
173D4—2262no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—9042no—
179C2×C4—2262no—
180C2×C4C2×C22⋊D11312yes—
181C2×C4C2×C22⋊D11312yes—
182C2×C4C2×C22⋊D11311yescharacteristic
183C2×C4C23×D11311yescharacteristic
184C8—2262no—
185C8—2262no—
186C22—21no—
187C22—22no—
188C22—4522no—
189C22—4522no—
190C22—4522no—
191C22C22×C22⋊D11311yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—4522no—
198C4C2×#1426864712yes—
199C2—41no—
200C2—9042no—
201C2#2029910911yescharacteristic
202C2#2029940612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#519×C113C2
socleC22×C113C22×D4
prime radical#20299203C2
hypercenter#519D113
hypocenterC113#3126
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #20298922C2semidirect
3. #20298905C2semidirect
4. #20298798C2semidirect
5. #20298737C2semidirect
6. #20298696C2semidirect
7. C4×#14268634C2semidirect
8. #20298659C2semidirect
9. #519×C113C2semidirect
102. C113#3126semidirect
104. #519D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202989222
#202989052
#202987982
#202987372
#202986962
C4×#142686342
#202986592
#519×C1132
#3126113