Finite Group Databasebeta

← #28406478

Subgroups — #28406478

Order 14464.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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#20299566C211yesmaximal, characteristic
2#20299540C211yesmaximal, characteristic
3#20299471C214yesmaximal, complemented
4C2×C4⋊C4×D113C211yesmaximal, characteristic
5C2×#14268655C2212yes—
6C2×C4⋊#90673C2212yes—
7C2×C22⋊#90673—21no—
8#16813679—21no—
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11C22×C4×D113—21no—
12C22×C4×D113C2211yescharacteristic
13C2×C4⋊Dic113C411yescharacteristic, complemented
14C2×#14268626—21no—
15C4⋊C4×D113—21no—
16C4⋊C4×D113—21no—
17C4⋊C4×D113C412yescomplemented
18C4⋊C4×D113C2212yes—
19C2×C4⋊C4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268655—24no—
22C2×#11744753—22no—
23C4⋊#90673—24no—
24C22⋊#90673—42no—
25C23×D113D411yescharacteristic
26C22×Dic113—21no—
27C22×Dic113D411yescharacteristic
28C2×C4×D113—24no—
29C2×C4×D113—22no—
30C2×C4×D113—22no—
31C2×C4×D113—44no—
32C2×C4×D113C2×C411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113C2311yescharacteristic
36C4⋊Dic113—21no—
37C4⋊Dic113C2×C412yes—
38#14268626—22no—
39#14268626—22no—
40C22×C4×C113—21no—
41C22×C4×C113C2×C411yescharacteristic
42C4⋊C4×C113—21no—
43C4⋊C4×C113C2×C412yes—
44C23×C113C22⋊C411yescharacteristic
45C22×D113—22no—
46C22×D113—22no—
47C22×D113C22⋊C411yescharacteristic
48C22×D113SD1612yes—
49C22×D113Q1612yes—
50C22×D113C2×D411yescharacteristic
51C2×#90673—42no—
52C2×#90673—42no—
53C2×#90673—42no—
54C2×C4×C113—22no—
55C2×C4×C113—22no—
56C2×C4×C113—42no—
57C2×C4×C113C22⋊C411yescharacteristic
58C2×C4×C113C22×C411yescharacteristic
59C2×Dic113—22no—
60C2×Dic113—22no—
61C2×Dic113—42no—
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C2×D411yescharacteristic
64C4×D113—22no—
65C4×D113—22no—
66C4×D113—22no—
67C4×D113—44no—
68C4×D113—44no—
69C4×D113#4114yes—
70#11744753—42no—
71C22×C113—21no—
72C22×C113—21no—
73C22×C113#10312yes—
74C22×C113C2×C22⋊C411yescharacteristic
75C2×D113—21no—
76C2×D113—21no—
77C2×D113—24no—
78C2×D113—24no—
79C2×D113#10312yes—
80C2×D113#12312yes—
81C2×D113C2×SD1611yescharacteristic
82C2×D113C2×Q1611yescharacteristic
83C2×D113AGL(1,ℤ/8)12yes—
84#90673—82no—
85C4×C113—21no—
86C4×C113—42no—
87C4×C113#11712yes—
88Dic113—21no—
89Dic113—42no—
90Dic113#12312yes—
91C2×C113—22no—
92C2×C113#38111yescharacteristic
93C2×C113C2×#10311yescharacteristic
94C2×C113#41811yescharacteristic
95D113—22no—
96D113#48112yes—
97D113#48412yes—
98#1824—1131nomaximal, Sylow
99C113#182411yescharacteristic, complemented, Sylow
100C22×C4⋊C4—1131no—
101C2×C22⋊C8—1131no—
102#380—1131no—
103#340—1134no—
104C23×C4—1131no—
105C23×C4—2261no—
106C22×C8—1132no—
107C2×C4⋊C4—1131no—
108C2×C4⋊C4—1132no—
109C2×C4⋊C4—1132no—
110C2×C4⋊C4—1132no—
111C2×C4⋊C4—2261no—
112C2×C4⋊C4—2261no—
113C2×C4⋊C4—2261no—
114C2×C4⋊C4#9067311yescharacteristic, complemented
115C2×C22⋊C4—2261no—
116C22⋊C8—2261no—
117C22⋊C8—2261no—
118#95—2261no—
119C24—1131no—
120C22×C4—21no—
121C22×C4—1131no—
122C22×C4—1131no—
123C22×C4—1131no—
124C22×C4—1131no—
125C22×C4—1131no—
126C22×C4—4524no—
127C22×C4—2264no—
128C22×C4—2262no—
129C22×C4—2262no—
130C22×C4—2262no—
131C22×C4—2261no—
132C22×C4C2×#9067311yescharacteristic
133C2×C8—2262no—
134C2×C8—2264no—
135C4⋊C4—21no—
136C4⋊C4—1132no—
137C4⋊C4—2262no—
138C4⋊C4—2262no—
139C4⋊C4—2264no—
140C4⋊C4—2261no—
141C4⋊C4C2×#9067312yes—
142C22⋊C4—4522no—
143C23—1131no—
144C23—1132no—
145C23—1132no—
146C23—1131no—
147C23—2262no—
148C23—2262no—
149C23C22⋊#9067311yescharacteristic
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—1131no—
154C2×C4—1134no—
155C2×C4—1131no—
156C2×C4—4524no—
157C2×C4—4524no—
158C2×C4—4522no—
159C2×C4—4522no—
160C2×C4—4522no—
161C2×C4—4522no—
162C2×C4—2262no—
163C2×C4—2262no—
164C2×C4—2262no—
165C2×C4—2262no—
166C2×C4—2262no—
167C2×C4C22⋊#9067311yescharacteristic
168C2×C4C22×#9067311yescharacteristic
169C8—4522no—
170C22—21no—
171C22—21no—
172C22—1132no—
173C22—1131no—
174C22—1131no—
175C22—1132no—
176C22—1132no—
177C22—2264no—
178C22—2264no—
179C22—2261no—
180C22—2261no—
181C22#1681368512yes—
182C22C2×C22⋊#9067311yescharacteristic
183C4—21no—
184C4—42no—
185C4—1132no—
186C4—9042no—
187C4—4522no—
188C4—2261no—
189C4#1681370112yes—
190C2—22no—
191C2—1132no—
192C2—1132no—
193C2—2262no—
194C2#2029954111yescharacteristic
195C2C2×#1681368511yescharacteristic
196C2#2029959011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×C4⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1824
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20299471C2semidirect
13. C2×C4⋊Dic113C4semidirect
17. C4⋊C4×D113C4semidirect
19. C2×C4⋊C4×C113C4semidirect
99. C113#1824semidirect
114. C2×C4⋊C4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995402
#202994712
C2×C4⋊C4×D1132
#1824113