Finite Group Databasebeta

← #28406741

Subgroups — #28406741

Order 14464.

428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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, complemented
2C2×#16813684C214yesmaximal, complemented
3C4×C4⋊#90673C211yesmaximal, characteristic, complemented
4#127×D113C211yesmaximal, characteristic
5C2×#14268655C2212yes—
6C2×C4⋊#90673C2212yes—
7C2×C4×#90673—21no—
8#16813689—21no—
9C4⋊#11744753—21no—
10#16813684—28no—
11(C2×#90673)⋊C4—21no—
12C2×D4×D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15#16813619C411yescharacteristic, complemented
16#16813618—21no—
17#16813618—21no—
18#16813618C412yescomplemented
19C42×D113C2211yescharacteristic
20#127×C113C411yescharacteristic, complemented
21C22×#90673—22no—
22#14268655—24no—
23C2×#11744753—22no—
24C4⋊#90673—22no—
25C4⋊#90673D414yescomplemented
26C4×#90673—42no—
27C23×D113—22no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452C2×C412yes—
31C2×C22⋊D113—22no—
32C2×C22⋊D113—22no—
33C2×C22⋊D113—22no—
34D4×D113—24no—
35D4×D113—24no—
36D4×D113—44no—
37D4×D113—42no—
38D4×D113—42no—
39C2×C4×D113D411yescharacteristic
40C2×C4×D113D411yescharacteristic
41C2×C4×D113C2311yescharacteristic
42C4×Dic113C2×C411yescharacteristic
43C4×Dic113D411yescharacteristic
44C4×Dic113D411yescharacteristic
45C2×D4×C113—21no—
46C2×D4×C113—21no—
47C2×D4×C113C2×C412yes—
48C42×C113C2×C411yescharacteristic
49C23×C113—22no—
50C22×D113—22no—
51C22×D113—44no—
52C22×D113—42no—
53C22×D113—42no—
54C22×D113—44no—
55C22×D113C2×D411yescharacteristic
56C2×#90673—24no—
57C2×#90673—42no—
58C2×#90673—42no—
59D4×C113—24no—
60D4×C113—42no—
61D4×C113—42no—
62C2×C4×C113C22⋊C411yescharacteristic
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22×C411yescharacteristic
65C22⋊D113—44no—
66C22⋊D113—44no—
67C22⋊D113—42no—
68C22⋊D113—42no—
69C2×Dic113C22⋊C411yescharacteristic
70C2×Dic113C22⋊C411yescharacteristic
71C2×Dic113C2×D411yescharacteristic
72D452—24no—
73D452—42no—
74D452—42no—
75C4×D113—22no—
76C4×D113D812yes—
77C4×D113SD1612yes—
78C4×D113C2×D412yes—
79C4×D113#4112yes—
80#11744753—42no—
81C22×C113—42no—
82C22×C113—42no—
83C22×C113—42no—
84C22×C113C2×C22⋊C411yescharacteristic
85C2×D113—42no—
86C2×D113—42no—
87C2×D113—42no—
88C2×D113—84no—
89C2×D113—84no—
90C2×D113#12112yes—
91C2×D113C2×D811yescharacteristic
92C2×D113C2×SD1611yescharacteristic
93C2×D113AGL(1,ℤ/8)12yes—
94#90673—44no—
95C4×C113—21no—
96C4×C113#10212yescomplemented
97C4×C113C4×D412yes—
98Dic113—21no—
99Dic113#10212yescomplemented
100Dic113#12411yescharacteristic
101Dic113#12711yescharacteristic
102C2×C113—82no—
103C2×C113#39011yescharacteristic
104C2×C113C2×#10211yescharacteristic
105C2×C113#41811yescharacteristic
106D113—82no—
107D113#45912yes—
108D113#46012yes—
109#1982—1131nomaximal, Sylow
110C113#198211yescharacteristic, complemented, Sylow
111C2×#127—1131no—
112C2×C4⋊C8—1131no—
113C2×#102—1134no—
114C4×C4⋊C4—1131no—
115C22×D4—1132no—
116C22×D4—2261no—
117C22×D4—2261no—
118C22×C8—1132no—
119#127—1132no—
120#127—1131no—
121#127—2261no—
122#127—2261no—
123#127#9067311yescharacteristic, complemented
124C2×C4⋊C4—1132no—
125C2×C42—1131no—
126C2×C42—2261no—
127C4⋊C8—2261no—
128C4⋊C8—2261no—
129#102—2268no—
130#95—2261no—
131C24—2262no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—1132no—
135C2×D4—4522no—
136C2×D4—4522no—
137C2×D4—4524no—
138C2×D4—2264no—
139C2×D4—2264no—
140C2×D4—2262no—
141C2×D4—2262no—
142C2×D4—2262no—
143C2×D4—2261no—
144C2×D4—2261no—
145C2×D4C2×#9067312yes—
146C22×C4—1131no—
147C22×C4—1131no—
148C22×C4—1131no—
149C22×C4—2262no—
150C2×C8—2264no—
151C2×C8—2262no—
152C4⋊C4—1134no—
153C4⋊C4—2262no—
154C42—1131no—
155C42—1131no—
156C42—1131no—
157C42—4522no—
158C42C2×#9067311yescharacteristic
159C23—22no—
160C23—1131no—
161C23—4522no—
162C23—4522no—
163C23—4524no—
164C23—4524no—
165C23—2262no—
166D4—24no—
167D4—42no—
168D4—42no—
169D4—4522no—
170D4—4524no—
171D4—4522no—
172D4—4522no—
173D4—4524no—
174D4—4522no—
175D4—2264no—
176C2×C4—1131no—
177C2×C4—1131no—
178C2×C4—1132no—
179C2×C4—1132no—
180C2×C4—1132no—
181C2×C4—1132no—
182C2×C4—1131no—
183C2×C4—4522no—
184C2×C4—4522no—
185C2×C4—2262no—
186C2×C4—2264no—
187C2×C4C22⋊#9067311yescharacteristic
188C2×C4C22⋊#9067311yescharacteristic
189C2×C4C22×#9067311yescharacteristic
190C8—4522no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—1132no—
195C22—1131no—
196C22—1131no—
197C22—1132no—
198C22—9044no—
199C22—9044no—
200C22—4522no—
201C22—4522no—
202C22—4522no—
203C22C2×C22⋊#9067311yescharacteristic
204C4—21no—
205C4—1131no—
206C4—1131no—
207C4—1132no—
208C4—4524no—
209C4—2261no—
210C4#1681368412yescomplemented
211C4D4×#9067312yes—
212C2—82no—
213C2—1132no—
214C2—1132no—
215C2—9042no—
216C2#2029955011yescharacteristic
217C2C2×#1681368411yescharacteristic
218C2#2029959011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#127×C113C4
socleC22×C113C2×C22⋊C4
prime radical#127×D113C2
cosocleC2×C4×D113C23
hypercenter#127#90673
hypocenterC113#1982
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20299599C2semidirect
2. C2×#16813684C2semidirect
3. C4×C4⋊#90673C2semidirect
15. #16813619C4semidirect
18. #16813618C4semidirect
20. #127×C113C4semidirect
25. C4⋊#90673D4semidirect
96. C4×C113#102semidirect
99. Dic113#102semidirect
110. C113#1982semidirect
123. #127#90673semidirect
210. C4#16813684semidirect

Maximal subgroups

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

subgroupindex
#202995992
C2×#168136842
C4×C4⋊#906732
#127×D1132
#1982113