Finite Group Databasebeta

← #28389894

Subgroups — #28389894

Order 14464.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#20299342C211yesmaximal, characteristic
2#20299007C211yesmaximal, characteristic, complemented
3#20298992C211yesmaximal, characteristic, complemented
4#20298957C211yesmaximal, characteristic, complemented
5#20298339C211yesmaximal, characteristic, complemented
6#20298337C211yesmaximal, characteristic, complemented
7#329×C113C211yesmaximal, characteristic, complemented
8C2×Dic452—21no—
9C2×#14268636—21no—
10#16813622C2211yescharacteristic
11#16813614C2211yescharacteristic
12#16813610C2211yescharacteristic
13#16813606—21no—
14#16813604—21no—
15#16813599—21no—
16#16813598—21no—
17#16813595—21no—
18#16813594—21no—
19#16813556—21no—
20#16813554—21no—
21#16813546—21no—
22#16813543—21no—
23#16813533C2211yescharacteristic
24#124×C113C2211yescharacteristic
25#97×C113C2211yescharacteristic
26#97×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226D411yescharacteristic
29C2×D452D411yescharacteristic
30C2×C22⋊D113—21no—
31C2×C22⋊D113—21no—
32C22×Dic113—21no—
33C2×C4×D113—21no—
34Dic452—42no—
35#14268636—42no—
36C2×#11744751—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113—21no—
40C4⋊Dic113D411yescharacteristic
41C4⋊Dic113D411yescharacteristic
42#14268626—21no—
43#14268626—21no—
44#14268626—21no—
45C22⋊Dic113—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49C2×Q8×C113D411yescharacteristic
50C2×D4×C113D411yescharacteristic
51C2×C8×C113—21no—
52C2×C8×C113—21no—
53C22⋊C4×C113—21no—
54C22⋊C4×C113—21no—
55C42×C113C2311yescharacteristic
56C23×C113—21no—
57C22×D113—21no—
58Q8×C113—41no—
59D4×C113—41no—
60C2×C4×C113—21no—
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C22⋊D113—81no—
65C22⋊D113—81no—
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—41no—
70C2×Dic113—81no—
71D452—41no—
72C4×D113—81no—
73Dic226—41no—
74Dic226—41no—
75Dic226—41no—
76C8×C113—22no—
77C8×C113—22no—
78#11744751—41no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113—41no—
82C22×C113#12011yescharacteristic
83C2×D113—41no—
84C2×D113—41no—
85C2×D113—41no—
86C4×C113—21no—
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—41no—
90Dic113—41no—
91Dic113—41no—
92Dic113—41no—
93Dic113—81no—
94C2×C113—81no—
95C2×C113#45311yescharacteristic
96C2×C113#45511yescharacteristic
97C2×C113#45611yescharacteristic
98D113—81no—
99#1661—1131nomaximal, Sylow
100C113#166111yescharacteristic, complemented, Sylow
101#562—1131no—
102#501—1131no—
103#497—1131no—
104#489—1131no—
105#330—1131no—
106#329—1131no—
107#329D11311yescharacteristic, complemented
108C2×Q16—2261no—
109C2×SD16—2261no—
110C4⋊Q8—1131no—
111#125—1131no—
112#124—1131no—
113#124C2×D11311yescharacteristic
114#123—2261no—
115#123—2261no—
116C22⋊Q8—2261no—
117C22⋊Q8—2261no—
118#121—2261no—
119#121—2261no—
120#107—2261no—
121#106—2261no—
122#103—2261no—
123#102—2261no—
124#97—1131no—
125#97C2×D11311yescharacteristic
126#97C2×D11311yescharacteristic
127C2×Q8—1131no—
128C2×Q8—2261no—
129C2×Q8D45211yescharacteristic
130C2×D4—1131no—
131C2×D4—2261no—
132C2×D4—2261no—
133C2×D4D45211yescharacteristic
134C22×C4—2261no—
135C22×C4—2261no—
136Q16—4522no—
137SD16—4522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2261no—
141C4⋊C4—1131no—
142C4⋊C4—1131no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—2261no—
152C22⋊C4—2261no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C42C22×D11311yescharacteristic
156C23—21no—
157C23—2261no—
158Q8—41no—
159Q8—4521no—
160Q8—4521no—
161Q8—4521no—
162D4—41no—
163D4—9041no—
164D4—9041no—
165D4—4521no—
166C2×C4—21no—
167C2×C4—9041no—
168C2×C4—9041no—
169C2×C4—4521no—
170C2×C4—2261no—
171C2×C4—2261no—
172C2×C4—2261no—
173C2×C4D4×D11311yescharacteristic
174C2×C4D4×D11311yescharacteristic
175C2×C4C2×D45211yescharacteristic
176C8—22no—
177C8—22no—
178C8—4521no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—4521no—
183C22—4521no—
184C22—4521no—
185C22#1681359211yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—9041no—
191C4—4521no—
192C4—4521no—
193C4—4521no—
194C2—81no—
195C2—9041no—
196C2#2029876711yescharacteristic
197C2#2029877811yescharacteristic
198C2#2029878211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#329×C113C2
socleC22×C113#120
prime radical#20299342C2
hypercenter#329D113
hypocenterC113#1661
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20299007C2semidirect
3. #20298992C2semidirect
4. #20298957C2semidirect
5. #20298339C2semidirect
6. #20298337C2semidirect
7. #329×C113C2semidirect
100. C113#1661semidirect
107. #329D113semidirect

Maximal subgroups

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

subgroupindex
#202993422
#202990072
#202989922
#202989572
#202983392
#202983372
#329×C1132
#1661113