Finite Group Databasebeta

← #28391111

Subgroups — #28391111

Order 14464.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#20299172C211yesmaximal, characteristic
2#20298616C212yesmaximal
3C2×#16813541C211yesmaximal, characteristic, complemented
4#20298354C212yesmaximal, complemented
5#519×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7C2×#14268631C2212yes—
8#16813620C412yescomplemented
9#16813611C412yescomplemented
10#16813605—22no—
11#16813598—22no—
12#16813581C2211yescharacteristic
13#16813550—24no—
14#16813541—22no—
15C22×Q8×C113C2211yescharacteristic
16C4×Q8×C113—24no—
17#117×C113—22no—
18#117×C113C2212yes—
19#14268647—22no—
20#14268647—22no—
21C2×Dic226C2×C411yescharacteristic
22C2×D452C2×C411yescharacteristic
23C2×C22⋊D113—21no—
24C2×C4×D113—21no—
25#14268631—22no—
26#14268631—22no—
27C2×#11744751—22no—
28C4⋊Dic113—21no—
29#14268626—24no—
30C22⋊Dic113—21no—
31#14268624—24no—
32C4×Dic113C2×C412yes—
33C2×Q8×C113—22no—
34C2×Q8×C113—22no—
35C2×Q8×C113C2×C412yes—
36C2×Q8×C113D412yes—
37C22×C4×C113D412yes—
38C22×C4×C113C2311yescharacteristic
39C4⋊C4×C113—24no—
40C4⋊C4×C113—22no—
41C22⋊C4×C113—22no—
42C42×C113—24no—
43C42×C113D414yes—
44C23×C113C2×D411yescharacteristic
45C22×D113—21no—
46Q8×C113—24no—
47Q8×C113—24no—
48C2×C4×C113—22no—
49C2×C4×C113—22no—
50C2×C4×C113—24no—
51C2×C4×C113C22⋊C414yes—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D412yes—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113#4112yes—
56C22⋊D113—41no—
57C22⋊D113—41no—
58C2×Dic113—22no—
59C2×Dic113—21no—
60D452—22no—
61C4×D113—42no—
62Dic226—22no—
63#11744751—42no—
64C22×C113—41no—
65C22×C113C2×C22⋊C411yescharacteristic
66C22×C113#12011yescharacteristic
67C22×C113#12311yescharacteristic
68C2×D113—42no—
69C2×D113—41no—
70C4×C113—24no—
71C4×C113—44no—
72C4×C113C4×D412yes—
73C4×C113#12112yes—
74Dic113—42no—
75Dic113—41no—
76C2×C113—21no—
77C2×C113—21no—
78C2×C113—21no—
79C2×C113#38611yescharacteristic
80D113—81no—
81#1912—1131nomaximal, Sylow
82C113#191211yescharacteristic, complemented, Sylow
83#536—1131no—
84#519D11311yescharacteristic, complemented
85#421—1132no—
86C2×#101—1131no—
87H(3,ℤ/4)—1132no—
88C2×#41—1131no—
89C22×Q8C2×D11311yescharacteristic
90C2×M16—1132no—
91C4⋊Q8—1132no—
92#124—1132no—
93#123—2262no—
94C22⋊Q8—2262no—
95C4×Q8—24no—
96#117—22no—
97#117—1131no—
98#117C2×D11312yes—
99#104—2264no—
100#101—2262no—
101#41—2262no—
102#41—2262no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1131no—
106C2×Q8C4×D11312yes—
107C2×Q8D45212yes—
108C2×D4—1131no—
109C2×D4—2261no—
110C22×C4—2261no—
111C22×C4C22⋊D11312yes—
112C22×C4C22×D11311yescharacteristic
113M16—2262no—
114M16—2262no—
115C2×C8—2262no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—2264no—
119C4⋊C4—2261no—
120C22⋊C4—22no—
121C22⋊C4—2261no—
122C22⋊C4—2264no—
123C42—24no—
124C42—1132no—
125C42C22⋊D11314yes—
126C23—2261no—
127C23C2×C22⋊D11311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—2262no—
131D4—4521no—
132D4—4521no—
133D4—2262no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—4522no—
138C2×C4—2262no—
139C2×C4—2261no—
140C2×C4#1426862414yes—
141C2×C4C2×C4×D11311yescharacteristic
142C2×C4C2×C22⋊D11312yes—
143C2×C4C2×D45211yescharacteristic
144C2×C4#1426864712yes—
145C8—4522no—
146C22—41no—
147C22—4522no—
148C22—4521no—
149C22C2×#1426862411yescharacteristic
150C22#1681359111yescharacteristic
151C22#1681360511yescharacteristic
152C4—24no—
153C4—44no—
154C4—4522no—
155C4—4521no—
156C4C4×C22⋊D11312yes—
157C4#1681359612yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—9041no—
162C2#2029847711yescharacteristic
subgroupG/H
centerC2#20298477
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#519×C113C2
socleC2×C113#386
prime radicalC2×#14268647C22
cosocleC22×C4×C113C23
hypercenter#519D113
hypocenterC113#1912
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#16813541C2semidirect
4. #20298354C2semidirect
5. #519×C113C2semidirect
8. #16813620C4semidirect
9. #16813611C4semidirect
82. C113#1912semidirect
84. #519D113semidirect

Maximal subgroups

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

subgroupindex
#202991722
#202986162
C2×#168135412
#202983542
#519×C1132
#1912113