Finite Group Databasebeta

← #28389659

Subgroups — #28389659

Order 14464.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299313C211yesmaximal, characteristic, complemented
2#20298971C211yesmaximal, characteristic, complemented
3#20298794C211yesmaximal, characteristic, complemented
4#20298793C211yesmaximal, characteristic, complemented
5#20298346C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—22no—
9C2×D904—21no—
10C2×#14268632—21no—
11#16813622C2211yescharacteristic
12#16813619C2211yescharacteristic
13#16813608—22no—
14#16813596—21no—
15#16813593—21no—
16C4×D452C2211yescharacteristic
17#16813581—21no—
18#16813580—21no—
19C4⋊#11744751C2211yescharacteristic
20#16813544—21no—
21#16813542—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D412yes—
26C2×D452—21no—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452D411yescharacteristic
30C2×C22⋊D113—22no—
31C2×C4×D113—21no—
32#14268636—44no—
33D904—42no—
34#14268632—42no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113D411yescharacteristic
39C22⋊Dic113—22no—
40#14268624—22no—
41#14268624—21no—
42C4×Dic113—22no—
43C2×D4×C113D411yescharacteristic
44C22×C4×C113—21no—
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C22×D113—21no—
52C22×D113—41no—
53D4×C113—21no—
54D4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C22⋊D113—82no—
62C2×Dic113—21no—
63C2×Dic113—22no—
64D452—21no—
65D452—21no—
66D452—42no—
67D452—41no—
68D452—41no—
69D452—41no—
70D452—41no—
71C4×D113—41no—
72C4×D113—41no—
73Dic226—42no—
74C8×C113—22no—
75C8×C113—41no—
76#11744751—41no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113#12011yescharacteristic
81C2×D113—41no—
82C2×D113—41no—
83C2×D113—41no—
84C2×D113—81no—
85C2×D113—81no—
86C2×D113—81no—
87C4×C113—21no—
88C4×C113—41no—
89C4×C113#13511yescharacteristic
90C4×C113#13511yescharacteristic
91C4×C113AGL(1,ℤ/8)11yescharacteristic
92C4×C113AGL(1,ℤ/8)11yescharacteristic
93Dic113—41no—
94Dic113—42no—
95C2×C113—81no—
96C2×C113#44911yescharacteristic
97C2×C113#44911yescharacteristic
98C2×C113#45311yescharacteristic
99D113—81no—
100D113—161no—
101#1624—1131nomaximal, Sylow
102C113#162411yescharacteristic, complemented, Sylow
103#555—1131no—
104#492—1131no—
105#459—1131no—
106#459—1131no—
107#333—1131no—
108D4⋊C8—1131no—
109D4⋊C8D11311yescharacteristic, complemented
110C2×SD16—2262no—
111C2×D8—2261no—
112C2×D8—2261no—
113C4⋊Q8—1131no—
114#127—1131no—
115#124—2262no—
116#121—2261no—
117#121—2261no—
118C4×D4—1131no—
119C4×D4C2×D11311yescharacteristic
120#117—2261no—
121#117—2261no—
122C4⋊C8—1131no—
123C4⋊C8C2×D11311yescharacteristic
124#102—2261no—
125#102—2261no—
126C4×C8C2×D11311yescharacteristic
127C2×Q8—1132no—
128C2×D4—1131no—
129C2×D4—2262no—
130C2×D4—2261no—
131C2×D4—2261no—
132C2×D4—2261no—
133C2×D4D45211yescharacteristic
134C22×C4—21no—
135C22×C4—2261no—
136SD16—4524no—
137D8—4522no—
138D8—4522no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—2261no—
142C4⋊C4—1131no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4D45211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—2262no—
148C22⋊C4—2262no—
149C22⋊C4—2261no—
150C42—2262no—
151C42C22×D11311yescharacteristic
152C23—21no—
153C23—4521no—
154C23—2261no—
155Q8—4522no—
156D4—21no—
157D4—21no—
158D4—9042no—
159D4—4522no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163D4—4521no—
164D4—2261no—
165D4—2261no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—2261no—
172C2×C4—2262no—
173C2×C4D4×D11311yescharacteristic
174C2×C4D4×D11311yescharacteristic
175C2×C4C2×D45211yescharacteristic
176C8—22no—
177C8—41no—
178C8—4521no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—9041no—
183C22—9041no—
184C22—9041no—
185C22—4521no—
186C22—4521no—
187C22—4521no—
188C22#1681359211yescharacteristic
189C4—21no—
190C4—41no—
191C4—4522no—
192C4—4521no—
193C4#1681364311yescharacteristic
194C4#1681364411yescharacteristic
195C4#1681364611yescharacteristic
196C4#1681365011yescharacteristic
197C2—81no—
198C2—18081no—
199C2—9041no—
200C2#2029874411yescharacteristic
201C2#2029874511yescharacteristic
202C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
hypercenterD4⋊C8D113
hypocenterC113#1624
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #20299313C2semidirect
2. #20298971C2semidirect
3. #20298794C2semidirect
4. #20298793C2semidirect
5. #20298346C2semidirect
6. #20298327C2semidirect
7. D4⋊C8×C113C2semidirect
102. C113#1624semidirect
109. D4⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202989712
#202987942
#202987932
#202983462
#202983272
D4⋊C8×C1132
#1624113