Finite Group Databasebeta

← #28400866

Subgroups — #28400866

Order 14464.

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

normal subgroups only

This group has 382 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
1#20299203C211yesmaximal, characteristic
2#20299075C211yesmaximal, characteristic, complemented
3#20298923C212yesmaximal, complemented
4#20298906C212yesmaximal, complemented
5#20298799C212yesmaximal, complemented
6#20298739C212yesmaximal, complemented
7#20298700C212yesmaximal, complemented
8C4×#14268636C212yesmaximal, complemented
9#433×C113C211yesmaximal, characteristic, complemented
10C22×Dic226C2211yescharacteristic
11C2×#14268636C2212yes—
12C2×#14268636C2212yes—
13#16813619C2211yescharacteristic
14#16813614C2211yescharacteristic
15#16813607—22no—
16#16813596C2212yes—
17#16813595—22no—
18C4×Dic226C2212yes—
19C4×Dic226C2212yes—
20#16813587—22no—
21C4×D452C2212yes—
22#16813581C2211yescharacteristic
23#16813578—22no—
24#16813556C2212yes—
25#16813554C2212yes—
26#16813547C2212yes—
27#16813547C2212yes—
28#16813544C2212yes—
29#16813544C2212yes—
30#117×C113C2211yescharacteristic
31C4⋊C8×C113C2212yes—
32C22⋊C8×C113C2212yes—
33#97×C113C2211yescharacteristic
34C4×C8×C113C2211yescharacteristic
35C2×Dic226—21no—
36C2×Dic226—24no—
37C2×Dic226C2312yes—
38C2×D452—22no—
39C2×D452C2312yes—
40C2×C22⋊D113—22no—
41C22×Dic113—21no—
42C2×C4×D113—22no—
43#14268636—24no—
44#14268636—24no—
45C4⋊Dic113C2312yes—
46C4⋊Dic113C2312yes—
47#14268626—22no—
48#14268626—22no—
49#14268626—22no—
50C22⋊Dic113—21no—
51#14268624—22no—
52#14268624—22no—
53C4×Dic113—22no—
54C4×Dic113—22no—
55C4×Dic113—21no—
56C22×C4×C113C2311yescharacteristic
57C2×C8×C113C2312yes—
58C2×C8×C113C2312yes—
59C4⋊C4×C113D412yes—
60C22⋊C4×C113D412yes—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113C2×D411yescharacteristic
64C22×D113—22no—
65C2×C4×C113—22no—
66C2×C4×C113C2×D412yes—
67C2×C4×C113C2×D412yes—
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2411yescharacteristic
70C22⋊D113—82no—
71C2×Dic113—24no—
72C2×Dic113—22no—
73C2×Dic113—22no—
74C2×Dic113—22no—
75D452—22no—
76D452—22no—
77D452—82no—
78C4×D113—82no—
79Dic226—24no—
80Dic226—22no—
81Dic226#4114yes—
82C8×C113—22no—
83C8×C113—22no—
84C22×C113—21no—
85C22×C113—22no—
86C22×C113C22×D411yescharacteristic
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—42no—
90C4×C113—21no—
91C4×C113—22no—
92C4×C113—22no—
93C4×C113C2×#4112yes—
94Dic113—24no—
95Dic113—42no—
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#519—1131no—
105#482—1132no—
106#479—1132no—
107#460—1132no—
108#448—1132no—
109#440—1132no—
110C4×SD16—1132no—
111#433D11311yescharacteristic, complemented
112C22×Q8—1131no—
113C2×SD16—1132no—
114C2×SD16—1132no—
115#127—1131no—
116#125—1131no—
117#123—2262no—
118#121—1132no—
119#121—2262no—
120C4×Q8—1132no—
121C4×Q8—1132no—
122C4×Q8—2262no—
123C4×D4—1132no—
124#117—1131no—
125#117—2262no—
126#117C2×D11311yescharacteristic
127#107—1132no—
128#106—1132no—
129C4⋊C8C2×D11312yes—
130#103—1132no—
131#103—1132no—
132#102—1132no—
133#102—1132no—
134C22⋊C8C2×D11312yes—
135#97C2×D11311yescharacteristic
136C4×C8C2×D11311yescharacteristic
137C2×Q8—1132no—
138C2×Q8—2264no—
139C2×Q8—2261no—
140C2×D4—1132no—
141C2×D4—2262no—
142C2×D4—2262no—
143C22×C4—2262no—
144C22×C4—2261no—
145C22×C4C22×D11311yescharacteristic
146SD16—2264no—
147SD16—2264no—
148C2×C8C22×D11312yes—
149C2×C8C22×D11312yes—
150C4⋊C4—1132no—
151C4⋊C4—1132no—
152C4⋊C4—2262no—
153C4⋊C4—2262no—
154C4⋊C4—2262no—
155C4⋊C4D45212yes—
156C22⋊C4—2261no—
157C22⋊C4—2262no—
158C22⋊C4—2262no—
159C22⋊C4D45212yes—
160C42—2261no—
161C42—2262no—
162C42—2262no—
163C42C22×D11311yescharacteristic
164C42C22×D11311yescharacteristic
165C23—2262no—
166C23C2×D45211yescharacteristic
167Q8—1134no—
168Q8—2264no—
169Q8—2262no—
170D4—9042no—
171D4—9042no—
172D4—2262no—
173D4—2262no—
174C2×C4—22no—
175C2×C4—9042no—
176C2×C4—2262no—
177C2×C4—2262no—
178C2×C4—2264no—
179C2×C4—2262no—
180C2×C4C2×D45212yes—
181C2×C4C2×D45212yes—
182C2×C4C2×D45211yescharacteristic
183C2×C4C23×D11311yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—4522no—
189C22—4522no—
190C22—4522no—
191C22C22×D45211yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—4522no—
196C4—4522no—
197C4—2264no—
198C4#41×D11312yes—
199C2—41no—
200C2—9042no—
201C2#2029911011yescharacteristic
202C2#2029941012yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#433×C113C2
socleC22×C113C22×D4
prime radical#20299203C2
hypercenter#433D113
hypocenterC113#3126
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20299075C2semidirect
3. #20298923C2semidirect
4. #20298906C2semidirect
5. #20298799C2semidirect
6. #20298739C2semidirect
7. #20298700C2semidirect
8. C4×#14268636C2semidirect
9. #433×C113C2semidirect
102. C113#3126semidirect
111. #433D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202990752
#202989232
#202989062
#202987992
#202987392
#202987002
C4×#142686362
#433×C1132
#3126113