Finite Group Databasebeta

← #28391112

Subgroups — #28391112

Order 14464.

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

normal subgroups only

This group has 314 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#20299076C211yesmaximal, characteristic, complemented
2#20298615C212yesmaximal
3C2×#16813541C211yesmaximal, characteristic, complemented
4#20298354C212yesmaximal, complemented
5#536×C113C211yesmaximal, characteristic
6C2×#14268631C2212yes—
7Q8×Dic113—24no—
8#16813581—22no—
9#16813581C2212yes—
10#16813549—24no—
11#16813541—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—22no—
20#14268631—22no—
21C2×#11744751—22no—
22C4⋊Dic113—24no—
23C4⋊Dic113—22no—
24C22⋊Dic113—22no—
25C4×Dic113—24no—
26C4×Dic113D414yes—
27#41×C113—22no—
28#41×C113—22no—
29C2×Q8×C113—22no—
30C2×Q8×C113—22no—
31C2×Q8×C113C2×C411yescharacteristic
32C2×Q8×C113C2×C412yes—
33C2×Q8×C113D412yes—
34C2×D4×C113—21no—
35C2×D4×C113C2×C411yescharacteristic
36C22×C4×C113—21no—
37C22×C4×C113D412yes—
38C22×C4×C113C2311yescharacteristic
39C4⋊C4×C113—24no—
40C4⋊C4×C113—21no—
41C22⋊C4×C113—21no—
42C22⋊C4×C113—24no—
43C42×C113C2×C412yes—
44C23×C113—21no—
45C23×C113C2×D411yescharacteristic
46Q8×C113—24no—
47Q8×C113—24no—
48Q8×C113—22no—
49D4×C113—22no—
50D4×C113—41no—
51D4×C113—41no—
52C2×C4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—22no—
55C2×C4×C113—21no—
56C2×C4×C113—42no—
57C2×C4×C113C22⋊C414yes—
58C2×C4×C113C22×C411yescharacteristic
59C2×C4×C113C2×D412yes—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113#4112yes—
62C2×Dic113—24no—
63#11744751—42no—
64C22×C113—41no—
65C22×C113—42no—
66C22×C113—41no—
67C22×C113C2×C22⋊C411yescharacteristic
68C22×C113#12011yescharacteristic
69C22×C113#12311yescharacteristic
70C4×C113—24no—
71C4×C113—42no—
72C4×C113—41no—
73C4×C113C4×D412yes—
74C4×C113#12112yes—
75Dic113—44no—
76C2×C113—21no—
77C2×C113—21no—
78C2×C113—21no—
79C2×C113—81no—
80C2×C113#38611yescharacteristic
81#1912—1131nomaximal, Sylow
82C113#191211yescharacteristic, complemented, Sylow
83#536D11311yescharacteristic
84#519—1131no—
85#421—1132no—
86C2×#101—1131no—
87H(3,ℤ/4)—1132no—
88C2×#41C2×D11311yescharacteristic
89C22×Q8C2×D11311yescharacteristic
90C2×M16—1132no—
91C4⋊Q8Dic11312yescomplemented
92#124Dic11312yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95C4×Q8—2264no—
96#117—1132no—
97#117—2262no—
98#117C2×D11311yescharacteristic
99#104—2264no—
100#101—2262no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic11311yescharacteristic
106C2×Q8C2×Dic11312yes—
107C2×Q8C22⋊D11312yes—
108C2×D4—21no—
109C2×D4C2×Dic11311yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D11312yes—
112C22×C4C22×D11311yescharacteristic
113M16—2262no—
114M16—2262no—
115C2×C8—2262no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—2264no—
119C4⋊C4—2262no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—2262no—
123C42—1134no—
124C42—2264no—
125C42C2×Dic11312yes—
126C23—21no—
127C23C2×C22⋊D11311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—2264no—
140C2×C4C22⋊Dic11314yes—
141C2×C4C22×Dic11311yescharacteristic
142C2×C4D4×D11312yes—
143C2×C4C2×C22⋊D11311yescharacteristic
144C2×C4#1426864612yes—
145C8—4522no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22C2×C22⋊Dic11311yescharacteristic
150C22#1681359011yescharacteristic
151C22#1681360311yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—4524no—
156C4D4×Dic11312yes—
157C4#1681359412yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#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#1912
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
1. #20299076C2semidirect
3. C2×#16813541C2semidirect
4. #20298354C2semidirect
14. C4⋊Q8×C113C4semidirect
15. #124×C113C4semidirect
82. C113#1912semidirect
91. C4⋊Q8Dic113semidirect
92. #124Dic113semidirect

Maximal subgroups

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

subgroupindex
#202990762
#202986152
C2×#168135412
#202983542
#536×C1132
#1912113