Finite Group Databasebeta

← #28389685

Subgroups — #28389685

Order 14464.

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

normal subgroups only

This group has 216 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#20299322C211yesmaximal, characteristic, complemented
2#20298946C211yesmaximal, characteristic, complemented
3#20298799C211yesmaximal, characteristic, complemented
4#20298794C211yesmaximal, characteristic
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#332×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—21no—
9C2×D904—21no—
10#16813619C2211yescharacteristic
11#16813617—22no—
12#16813611—21no—
13#16813602—21no—
14Q8×Dic113—21no—
15C4×Dic226C2211yescharacteristic
16C4×D452C2211yescharacteristic
17#16813580—21no—
18#16813544—21no—
19#16813544—21no—
20#16813542—22no—
21C4×#11744751C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×D452—21no—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452D411yescharacteristic
30C2×C4×D113—21no—
31#14268636—42no—
32D904—42no—
33C2×#11744751—21no—
34C4⋊Dic113—22no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268624—22no—
39#14268624—22no—
40#14268624—21no—
41C4×Dic113—22no—
42C4×Dic113—21no—
43C2×Q8×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D412yes—
48C42×C113C2311yescharacteristic
49C22×D113—21no—
50C22×D113—41no—
51Q8×C113—41no—
52Q8×C113—41no—
53C2×C4×C113—22no—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60D452—21no—
61D452—21no—
62D452—42no—
63D452—41no—
64D452—41no—
65D452—41no—
66D452—41no—
67C4×D113—41no—
68C4×D113—41no—
69Dic226—21no—
70Dic226—21no—
71C8×C113—41no—
72C8×C113—41no—
73#11744751—41no—
74C22×C113#12011yescharacteristic
75C2×D113—41no—
76C2×D113—41no—
77C2×D113—41no—
78C2×D113—81no—
79C2×D113—81no—
80C2×D113—81no—
81C4×C113—21no—
82C4×C113—42no—
83C4×C113#13511yescharacteristic
84C4×C113#13511yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87Dic113—41no—
88Dic113—41no—
89Dic113—41no—
90C2×C113#44911yescharacteristic
91C2×C113#44911yescharacteristic
92C2×C113#45411yescharacteristic
93D113—81no—
94D113—161no—
95#1628—1131nomaximal, Sylow
96C113#162811yescharacteristic, complemented, Sylow
97#556—1131no—
98#486—1131no—
99#460—1131no—
100#459—1131no—
101#332D11311yescharacteristic, complemented
102Q8⋊C8—1131no—
103D4⋊C8—1131no—
104C2×SD16—2261no—
105C2×D8—2261no—
106C4⋊Q8C2×D11311yescharacteristic
107#127—1131no—
108#126—2262no—
109#124—2261no—
110C22⋊Q8—2261no—
111C4×Q8—1131no—
112C4×Q8—2261no—
113C4×D4—1131no—
114#117—2261no—
115C4⋊C8C2×D11311yescharacteristic
116C4⋊C8C2×D11311yescharacteristic
117#102—2261no—
118#102—2261no—
119#102—2262no—
120C4×C8—1131no—
121C2×Q8—21no—
122C2×Q8—1131no—
123C2×D4—1131no—
124C2×D4—2261no—
125C2×D4—2261no—
126C2×D4—2261no—
127C22×C4—2261no—
128SD16—4522no—
129D8—4522no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—2261no—
133C4⋊C4—21no—
134C4⋊C4—1131no—
135C4⋊C4—1131no—
136C4⋊C4—2262no—
137C4⋊C4—2261no—
138C4⋊C4D45212yes—
139C22⋊C4—2262no—
140C22⋊C4—2262no—
141C22⋊C4—2261no—
142C42—2262no—
143C42—2261no—
144C42C22×D11311yescharacteristic
145C23—4521no—
146C23—2261no—
147Q8—41no—
148Q8—41no—
149Q8—2261no—
150Q8—2261no—
151D4—4522no—
152D4—4521no—
153D4—4521no—
154D4—4521no—
155D4—4521no—
156D4—2261no—
157D4—2261no—
158C2×C4—22no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—2261no—
162C2×C4—2261no—
163C2×C4—2261no—
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C2×C4C2×D45211yescharacteristic
167C8—41no—
168C8—41no—
169C8—4521no—
170C22—9041no—
171C22—9041no—
172C22—9041no—
173C22—4521no—
174C22—4521no—
175C22—4521no—
176C22#1681359211yescharacteristic
177C4—21no—
178C4—42no—
179C4—4521no—
180C4—4521no—
181C4—4521no—
182C4#1681364311yescharacteristic
183C4#1681364511yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681364911yescharacteristic
186C2—18081no—
187C2—9041no—
188C2#2029874411yescharacteristic
189C2#2029874611yescharacteristic
190C2#2029877311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113#120
prime radical#20298794C2
hypercenter#332D113
hypocenterC113#1628
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #20299322C2semidirect
2. #20298946C2semidirect
3. #20298799C2semidirect
5. #20298328C2semidirect
6. #20298325C2semidirect
7. #332×C113C2semidirect
96. C113#1628semidirect
101. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202993222
#202989462
#202987992
#202987942
#202983282
#202983252
#332×C1132
#1628113