Finite Group Databasebeta

← #28406754

Subgroups — #28406754

Order 14464.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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#20299599C211yesmaximal, characteristic
2C4×C4⋊#90673C211yesmaximal, characteristic
3#20299471C212yesmaximal
4#20299471C212yesmaximal
5#125×D113C211yesmaximal, characteristic
6C2×#14268655C2212yes—
7C2×C4⋊#90673C2212yes—
8C2×C4×#90673—21no—
9#16813689—21no—
10C4⋊#11744753—21no—
11(C2×#90673)⋊C4—21no—
12#16813614C411yescharacteristic, complemented
13#16813613C411yescharacteristic, complemented
14#16813613C411yescharacteristic, complemented
15#16813612—21no—
16#16813612—21no—
17C4⋊C4×D113—21no—
18C4⋊C4×D113—21no—
19C4⋊C4×D113C2211yescharacteristic
20C4⋊C4×D113C2211yescharacteristic
21C42×D113C2211yescharacteristic
22#125×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268655—24no—
25C2×#11744753—22no—
26C4⋊#90673—22no—
27C4⋊#90673Q814yes—
28C4×#90673—42no—
29C2×C4×D113—21no—
30C2×C4×D113—21no—
31C2×C4×D113D411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113C2311yescharacteristic
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113C2×C411yescharacteristic
37C4⋊Dic113C2×C411yescharacteristic
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44C4×Dic113C2×C411yescharacteristic
45C4×Dic113D411yescharacteristic
46C4×Dic113D411yescharacteristic
47C4⋊C4×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113C2×C411yescharacteristic
50C4⋊C4×C113C2×C411yescharacteristic
51C42×C113C2×C411yescharacteristic
52C22×D113C2×D411yescharacteristic
53C2×#90673—24no—
54C2×#90673—42no—
55C2×#90673—42no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22⋊C411yescharacteristic
60C2×C4×C113C22×C411yescharacteristic
61C2×Dic113—21no—
62C2×Dic113—21no—
63C2×Dic113C22⋊C411yescharacteristic
64C2×Dic113C22⋊C411yescharacteristic
65C2×Dic113C2×D411yescharacteristic
66C4×D113—22no—
67C4×D113—21no—
68C4×D113—21no—
69C4×D113—42no—
70C4×D113—41no—
71C4×D113—41no—
72C4×D113C2×Q812yes—
73C4×D113#4112yes—
74#11744753—42no—
75C22×C113C2×C22⋊C411yescharacteristic
76C2×D113C22⋊Q812yes—
77C2×D113#13512yes—
78C2×D113AGL(1,ℤ/8)11yescharacteristic
79C2×D113#13711yescharacteristic
80#90673—44no—
81C4×C113—21no—
82C4×C113—21no—
83C4×C113—41no—
84C4×C113—41no—
85C4×C113C4×Q812yes—
86Dic113—21no—
87Dic113—21no—
88Dic113—41no—
89Dic113—41no—
90Dic113#12411yescharacteristic
91Dic113C4⋊Q811yescharacteristic
92C2×C113#39111yescharacteristic
93C2×C113#41611yescharacteristic
94C2×C113#41711yescharacteristic
95D113#47812yes—
96D113#47912yes—
97#1989—1131nomaximal, Sylow
98C113#198911yescharacteristic, complemented, Sylow
99C2×#125—1131no—
100C2×C4⋊C8—1131no—
101C4×C4⋊C4—1131no—
102#340—1132no—
103#340—1132no—
104C22×C8—1132no—
105#125—1131no—
106#125—1131no—
107#125—1131no—
108#125—2261no—
109#125—2261no—
110#125#9067311yescharacteristic, complemented
111C2×C4⋊C4—1132no—
112C2×C4⋊C4—1131no—
113C2×C4⋊C4—1131no—
114C2×C4⋊C4—2261no—
115C2×C4⋊C4—2261no—
116C2×C42—1131no—
117C2×C42—2261no—
118C4⋊C8—2261no—
119C4⋊C8—2261no—
120#95—2261no—
121C22×C4—1131no—
122C22×C4—1131no—
123C22×C4—1131no—
124C22×C4—2261no—
125C22×C4—2261no—
126C22×C4—2262no—
127C2×C8—2262no—
128C2×C8—2264no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1134no—
132C4⋊C4—1131no—
133C4⋊C4—1131no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C4⋊C4—2261no—
139C4⋊C4—2261no—
140C4⋊C4—2262no—
141C4⋊C4—2261no—
142C4⋊C4—2261no—
143C4⋊C4C2×#9067311yescharacteristic
144C4⋊C4C2×#9067311yescharacteristic
145C42—1131no—
146C42—1131no—
147C42—1131no—
148C42—4522no—
149C42C2×#9067311yescharacteristic
150C23—1131no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1131no—
154C2×C4—1132no—
155C2×C4—1132no—
156C2×C4—1131no—
157C2×C4—1131no—
158C2×C4—4522no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—4522no—
162C2×C4—4522no—
163C2×C4—2261no—
164C2×C4—2262no—
165C2×C4—2261no—
166C2×C4—2264no—
167C2×C4—2261no—
168C2×C4—2261no—
169C2×C4C22⋊#9067311yescharacteristic
170C2×C4C22⋊#9067311yescharacteristic
171C2×C4C22×#9067311yescharacteristic
172C8—4522no—
173C22—1132no—
174C22—1132no—
175C22—1131no—
176C22—1131no—
177C22C2×C22⋊#9067311yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—1131no—
183C4—1131no—
184C4—4524no—
185C4—4521no—
186C4—4521no—
187C4—2261no—
188C4—2261no—
189C4Q8×#9067312yes—
190C2—1132no—
191C2—1132no—
192C2(C2×#90673)⋊Q811yescharacteristic
193C2#2029958811yescharacteristic
194C2#2029958911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#125×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenter#125#90673
hypocenterC113#1989
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #16813614C4semidirect
13. #16813613C4semidirect
14. #16813613C4semidirect
22. #125×C113C4semidirect
98. C113#1989semidirect
110. #125#90673semidirect

Maximal subgroups

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

subgroupindex
#202995992
C4×C4⋊#906732
#202994712
#125×D1132
#1989113