Finite Group Databasebeta

← #28391097

Subgroups — #28391097

Order 14464.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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#20299365C211yesmaximal, characteristic
2#20298607C212yesmaximal, complemented
3#20298572C211yesmaximal, characteristic
4#20298354C212yesmaximal, complemented
5#536×C113C211yesmaximal, characteristic
6#16813629—24no—
7C2×#14268631—22no—
8C2×#14268631C2212yes—
9#16813581C2212yes—
10#16813546—24no—
11#16813537—22no—
12C2×#41×C113C2211yescharacteristic
13C22×Q8×C113C2211yescharacteristic
14C4⋊Q8×C113C412yescomplemented
15#124×C113C412yescomplemented
16#123×C113—22no—
17C22⋊Q8×C113—22no—
18#117×C113C2211yescharacteristic
19#14268631—24no—
20#14268631—22no—
21#14268631—22no—
22C2×#11744751—24no—
23C2×#11744751D414yes—
24C4⋊Dic113—22no—
25C22⋊Dic113—22no—
26C4×Dic113—22no—
27#41×C113—22no—
28#41×C113—22no—
29C2×Q8×C113—21no—
30C2×Q8×C113—22no—
31C2×Q8×C113—22no—
32C2×Q8×C113C2×C412yes—
33C2×Q8×C113C2×C411yescharacteristic
34C2×D4×C113C2×C411yescharacteristic
35C2×D4×C113D412yes—
36C22×C4×C113—21no—
37C22×C4×C113D412yes—
38C22×C4×C113C2311yescharacteristic
39C4⋊C4×C113—24no—
40C4⋊C4×C113—21no—
41C22⋊C4×C113—24no—
42C22⋊C4×C113—21no—
43C42×C113C2×C412yes—
44C23×C113C22⋊C412yes—
45C23×C113C2×D411yescharacteristic
46Q8×C113—22no—
47Q8×C113—24no—
48Q8×C113—41no—
49Q8×C113—41no—
50D4×C113—24no—
51D4×C113—22no—
52C2×C4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—22no—
55C2×C4×C113—22no—
56C2×C4×C113—42no—
57C2×C4×C113C22⋊C412yes—
58C2×C4×C113C22×C411yescharacteristic
59C2×C4×C113C2×D412yes—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113#4112yes—
62C2×Dic113—42no—
63#11744751—24no—
64C22×C113—22no—
65C22×C113—41no—
66C22×C113—42no—
67C22×C113C2×C22⋊C411yescharacteristic
68C22×C113#12112yes—
69C4×C113—22no—
70C4×C113—42no—
71C4×C113—42no—
72C4×C113C4×D412yes—
73C4×C113#12011yescharacteristic
74C4×C113#12311yescharacteristic
75Dic113—82no—
76C2×C113—22no—
77C2×C113—21no—
78C2×C113—42no—
79C2×C113#38611yescharacteristic
80#1909—1131nomaximal, Sylow
81C113#190911yescharacteristic, complemented, Sylow
82#568—1131no—
83#536D11311yescharacteristic
84#419—1132no—
85#410—1131no—
86H(3,ℤ/4)—1132no—
87C2×#41C2×D11311yescharacteristic
88C22×Q8C2×D11311yescharacteristic
89#131—2264no—
90C2×M16—1132no—
91C2×M16—2262no—
92C4⋊Q8Dic11312yescomplemented
93#124Dic11312yescomplemented
94#123—22no—
95C22⋊Q8—22no—
96#117—1132no—
97#117C2×D11311yescharacteristic
98#103—2264no—
99#99—2262no—
100#41—22no—
101#41—22no—
102C2×Q8—21no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic11312yes—
106C2×Q8C2×Dic11311yescharacteristic
107C2×D4C2×Dic11311yescharacteristic
108C2×D4C22⋊D11312yes—
109C22×C4—21no—
110C22×C4C22⋊D11312yes—
111C22×C4C22×D11311yescharacteristic
112M16—2264no—
113M16—2262no—
114M16—2262no—
115C2×C8—1134no—
116C2×C8—2264no—
117C4⋊C4—24no—
118C4⋊C4—21no—
119C4⋊C4—2262no—
120C22⋊C4—24no—
121C22⋊C4—21no—
122C22⋊C4—2262no—
123C42—2262no—
124C42C2×Dic11312yes—
125C23C22⋊Dic11312yes—
126C23C2×C22⋊D11311yescharacteristic
127Q8—22no—
128Q8—24no—
129Q8—41no—
130Q8—41no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—4522no—
139C2×C4C22⋊Dic11312yes—
140C2×C4C22×Dic11311yescharacteristic
141C2×C4D4×D11312yes—
142C2×C4C2×C22⋊D11311yescharacteristic
143C2×C4#1426864612yes—
144C8—2264no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×C22⋊Dic11311yescharacteristic
149C22#1681359412yes—
150C4—22no—
151C4—42no—
152C4—42no—
153C4—9042no—
154C4D4×Dic11312yes—
155C4#1681359011yescharacteristic
156C4#1681360311yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#2029847811yescharacteristic
subgroupG/H
centerC2#20298478
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#536×C113C2
socleC2×C113#386
prime radicalC2×#41×C113C22
cosocleC22×C4×C113C23
hypercenter#536D113
hypocenterC113#1909
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20298607C2semidirect
4. #20298354C2semidirect
14. C4⋊Q8×C113C4semidirect
15. #124×C113C4semidirect
81. C113#1909semidirect
92. C4⋊Q8Dic113semidirect
93. #124Dic113semidirect

Maximal subgroups

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

subgroupindex
#202993652
#202986072
#202985722
#202983542
#536×C1132
#1909113