Finite Group Databasebeta

← #28391739

Subgroups — #28391739

Order 14464.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#20299224C211yesmaximal, characteristic, complemented
2#20298453C212yesmaximal
3#20298453C211yesmaximal, characteristic
4#20298364C212yesmaximal, complemented
5#342×C113C211yesmaximal, characteristic, complemented
6C24×D113C2211yescharacteristic
7#16813601—22no—
8#16813599—24no—
9C2×C22⋊Dic113C2211yescharacteristic
10C2×C22⋊Dic113C2212yes—
11C2×#14268624—24no—
12C2×#14268624—22no—
13C2×C22⋊C4×C113C2212yes—
14C2×C22⋊C4×C113C2211yescharacteristic
15C23×D113—22no—
16C23×D113—21no—
17C23×D113—21no—
18C23×D113—22no—
19C23×D113—44no—
20C23×D113Q812yescomplemented
21C2×Dic226—22no—
22C22×Dic113—21no—
23C22×Dic113D414yes—
24C4⋊Dic113—22no—
25#14268626—24no—
26C22⋊Dic113—22no—
27C22⋊Dic113—22no—
28C22⋊Dic113—22no—
29#14268624—48no—
30#14268624—44no—
31C24×C113C2311yescharacteristic
32C22×C4×C113—22no—
33C22×C4×C113D412yes—
34C22⋊C4×C113—22no—
35C22⋊C4×C113—22no—
36C22⋊C4×C113—22no—
37C23×C113—42no—
38C23×C113C2×D412yes—
39C23×C113C2×D411yescharacteristic
40C23×C113C2×Q811yescharacteristic
41C23×C113#4111yescharacteristic
42C23×C113#4112yes—
43C22×D113—28no—
44C22×D113—24no—
45C22×D113—24no—
46C22×D113—22no—
47C22×D113—44no—
48C22×D113—44no—
49C22×D113—48no—
50C22×D113—44no—
51C22×D113—42no—
52C22×D113—41no—
53C22×D113—42no—
54C22×D113—41no—
55C2×C4×C113—22no—
56C2×C4×C113—42no—
57C2×C4×C113—44no—
58C2×C4×C113—42no—
59C2×Dic113—24no—
60C2×Dic113—44no—
61C2×Dic113—42no—
62C2×Dic113—41no—
63Dic226—82no—
64C22×C113—24no—
65C22×C113—22no—
66C22×C113—41no—
67C22×C113—41no—
68C22×C113—42no—
69C22×C113#12011yescharacteristic
70C22×C113C22⋊Q812yes—
71C22×C113C22⋊Q811yescharacteristic
72C22×C113#12412yes—
73C22×C113#12411yescharacteristic
74C2×D113—28no—
75C2×D113—24no—
76C2×D113—44no—
77C2×D113—48no—
78C2×D113—44no—
79C2×D113—42no—
80C2×D113—42no—
81C2×D113—44no—
82C4×C113—42no—
83C4×C113—82no—
84Dic113—44no—
85Dic113—81no—
86C2×C113—21no—
87C2×C113—22no—
88C2×C113—22no—
89C2×C113—21no—
90C2×C113#39311yescharacteristic
91C2×C113B(4,𝔽2)12yes—
92D113—44no—
93#2029—1131nomaximal, Sylow
94C113#202911yescharacteristic, complemented, Sylow
95#543—1131no—
96#379—1132no—
97#379—1131no—
98#342—1132no—
99#342D11311yescharacteristic, complemented
100C25—1131no—
101C22⋊Q8—2264no—
102C22⋊Q8—2262no—
103C2×C22⋊C4—1132no—
104C2×C22⋊C4—1131no—
105C2×C22⋊C4—2264no—
106C2×C22⋊C4—2262no—
107C2×C22⋊C4C2×D11312yes—
108C2×C22⋊C4C2×D11311yescharacteristic
109C24—1132no—
110C24—4524no—
111C24—2261no—
112C24—2262no—
113C24—2262no—
114C24—2261no—
115C24C22×D11311yescharacteristic
116C2×Q8—2262no—
117C22×C4—22no—
118C22×C4—1134no—
119C22×C4—2261no—
120C22×C4D45212yes—
121C4⋊C4—2264no—
122C4⋊C4—2262no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—4524no—
127C22⋊C4—4528no—
128C22⋊C4—2262no—
129C22⋊C4—2262no—
130C22⋊C4—2262no—
131C23—42no—
132C23—4524no—
133C23—4522no—
134C23—4524no—
135C23—4528no—
136C23—4524no—
137C23—4521no—
138C23—4522no—
139C23—4521no—
140C23—2268no—
141C23—2264no—
142C23—2264no—
143C23—2262no—
144C23D4×D11312yes—
145C23C2×D45211yescharacteristic
146C23Q8×D11311yescharacteristic
147C23#1426864611yescharacteristic
148C23#1426864712yes—
149Q8—9042no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—4522no—
155C2×C4—4521no—
156C2×C4—4524no—
157C2×C4—2264no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—4528no—
164C22—4524no—
165C22—4524no—
166C22—4522no—
167C22—4522no—
168C22—4524no—
169C22—2268no—
170C22—2264no—
171C22#1681359211yescharacteristic
172C22#1681360012yes—
173C22#1681360211yescharacteristic
174C22#1681360812yes—
175C22#1681361011yescharacteristic
176C4—42no—
177C4—82no—
178C4—9041no—
179C4—4524no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—4524no—
185C2#2029851111yescharacteristic
186C2#2029878612yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC24×C113C23
FrattiniC24C22×D113
Fitting#342×C113C2
socleC22×C113#120
prime radicalC24×D113C22
hypercenter#342D113
hypocenterC113#2029
LCSG ▷ C24×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #20299224C2semidirect
4. #20298364C2semidirect
5. #342×C113C2semidirect
20. C23×D113Q8semidirect
94. C113#2029semidirect
99. #342D113semidirect

Maximal subgroups

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

subgroupindex
#202992242
#202984532
#202983642
#342×C1132
#2029113