Finite Group Databasebeta

← #28309606

Subgroups — #28309606

Order 13568.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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#20291090C211yesmaximal, characteristic
2#20290937C211yesmaximal, characteristic
3#20289720C214yesmaximal, complemented
4#20285371C211yesmaximal, characteristic
5D53⋊M32—21no—
6#16811545—21no—
7#16811520—21no—
8#16811516—21no—
9#16811515C2212yes—
10#16811515C2212yes—
11#16811234C412yes—
12#16811025C411yescharacteristic
13#16810991C2212yes—
14#16810878—21no—
15#16810861—21no—
16#16810730—21no—
17Q16×Dic53—21no—
18#16810577C2211yescharacteristic
19C53×#494C411yescharacteristic
20#13133292—22no—
21#13133291—22no—
22#13133291—22no—
23D53⋊C16—22no—
24C2×#11719912D411yescharacteristic
25C2×C8×D53D411yescharacteristic
26#13133212—42no—
27#13133209C2×C412yes—
28#13133207—42no—
29#13133193—22no—
30Q8×Dic53—22no—
31#13133174C2×C411yescharacteristic
32#13133151—21no—
33#13133149—21no—
34#13133141—22no—
35#13133141—22no—
36#13133128C2311yescharacteristic
37#13133127D411yescharacteristic
38C8×Dic53D411yescharacteristic
39C2×Q16×C53—21no—
40C2×Q16×C53—21no—
41C4⋊Q8×C53C2×C412yes—
42C4×C8×C53C2×C411yescharacteristic
43C2×Q8×C53—22no—
44C2×C4×D53C22⋊C411yescharacteristic
45Q16×C53—42no—
46Q16×C53—41no—
47Q16×C53—41no—
48C2×C8×C53C22⋊C411yescharacteristic
49C2×C8×C53C22⋊C411yescharacteristic
50C4⋊C4×C53—42no—
51C42×C53C22×C411yescharacteristic
52#11719921—21no—
53#11719921—42no—
54C4⋊Dic53—22no—
55C4⋊Dic53—42no—
56#11719919—21no—
57#11719919—42no—
58#11719919—42no—
59C4×Dic53—42no—
60C4×Dic53C22⋊C411yescharacteristic
61C2×#88322C2×D411yescharacteristic
62C2×#88322C2×D411yescharacteristic
63#11719912—41no—
64C8×D53—21no—
65C8×D53—21no—
66#11719910—24no—
67#11719910—42no—
68C22×D53#10011yescharacteristic
69Q8×C53—42no—
70Q8×C53—42no—
71C2×C4×C53—21no—
72C2×C4×C53—42no—
73C2×C4×C53C2×C22⋊C411yescharacteristic
74C2×Dic53—21no—
75C2×Dic53—42no—
76C2×Dic53#10011yescharacteristic
77C4×D53—21no—
78C4×D53—21no—
79C8×C53—21no—
80C8×C53#10411yescharacteristic
81C8×C53#10411yescharacteristic
82#88322—21no—
83#88322—21no—
84#11914—531nomaximal, Sylow
85C22×C53C2×#10011yescharacteristic
86C2×D53—21no—
87C2×D53—41no—
88C4×C53—41no—
89C4×C53—82no—
90C4×C53C2×#10411yescharacteristic
91C4×C53#42111yescharacteristic
92Dic53—21no—
93Dic53—41no—
94Dic53—82no—
95#3177—531no—
96#2166—531no—
97#2110—531no—
98#1356—534no—
99C2×C53—21no—
100C2×C53#153011yescharacteristic
101D53—41no—
102#541—532no—
103C2×M32—1061no—
104#499—531no—
105#494#615711yescharacteristic
106#491—532no—
107#470—1061no—
108#467—1061no—
109#441—1061no—
110C4×Q16—1061no—
111#405—531no—
112#364—1061no—
113#349—1061no—
114#347—532no—
115#347—532no—
116#347—1061no—
117C53#1191411yescharacteristic, complemented, Sylow
118C2×Q16—21no—
119C2×Q16—21no—
120C2×M16—531no—
121C22×C8—531no—
122C4⋊Q8C2×#615712yes—
123#126—2122no—
124#125—532no—
125#125—2122no—
126C22⋊Q8—1062no—
127C4×Q8—1062no—
128#117—531no—
129M32—1062no—
130M32—1062no—
131M32—1062no—
132C2×C16—1062no—
133#107—1061no—
134#106—1061no—
135#103—1062no—
136#103—1062no—
137#97—531no—
138#97—531no—
139C4×C8—531no—
140C4×C8C2×#615711yescharacteristic
141C2×Q8—22no—
142C22×C4—531no—
143Q16—42no—
144Q16—41no—
145Q16—41no—
146M16—2121no—
147C2×C8—531no—
148C2×C8—531no—
149C2×C8—1061no—
150C2×C8—1061no—
151C2×C8C22⋊#615711yescharacteristic
152C2×C8C22⋊#615711yescharacteristic
153C4⋊C4—42no—
154C4⋊C4—1061no—
155C4⋊C4—1062no—
156C4⋊C4—2122no—
157C4⋊C4—2122no—
158C4⋊C4—2122no—
159C22⋊C4—1061no—
160C22⋊C4—2122no—
161C42—531no—
162C42—2122no—
163C42C22×#615711yescharacteristic
164C16—1064no—
165C16—2122no—
166C23—531no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—531no—
172C2×C4—1061no—
173C2×C4—1061no—
174C2×C4—1061no—
175C2×C4—2122no—
176C2×C4C2×C22⋊#615711yescharacteristic
177C8—21no—
178C8—1061no—
179C8—1061no—
180C8#1313328111yescharacteristic
181C8#1313328111yescharacteristic
182C22—1061no—
183C22—2121no—
184C22D53⋊#10011yescharacteristic
185C4—41no—
186C4—82no—
187C4—1061no—
188C4—4242no—
189C4—2121no—
190C4C2×#1313328111yescharacteristic
191C4#1681162111yescharacteristic
192C2—21no—
193C2—2121no—
194C2#2029018511yescharacteristic
subgroupG/H
centerC2#20290185
commutatorC42×C53C22×C4
FrattiniC42C22×#6157
FittingC53×#494C4
socleC2×C53#1530
prime radicalC22×D53#100
cosocle#13133128C23
hypercenter#494#6157
hypocenterC53#11914
LCSG ▷ C42×C53 ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #20289720C2semidirect
117. C53#11914semidirect

Maximal subgroups

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

subgroupindex
#202910902
#202909372
#202897202
#202853712
#1191453