Finite Group Databasebeta

← #28312483

Subgroups — #28312483

Order 13568.

318 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 60 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#20291008C212yesmaximal
2#20289859C214yesmaximal, complemented
3#20285061C211yesmaximal, characteristic
4#16811609—22no—
5#16811534C2214yes—
6#16811532—22no—
7#16811180C411yescharacteristic
8#16811173C2211yescharacteristic
9#16810992C2212yes—
10#16810988C412yes—
11#16810983—22no—
12#16810620—22no—
13C2×#97×C53C411yescharacteristic
14D53⋊M16—42no—
15#13133278—24no—
16#13133277—42no—
17C2×#11719945D412yes—
18#13133217—21no—
19#13133217C2311yescharacteristic
20#13133214C2×C411yescharacteristic
21#13133209C2×C412yes—
22#13133205D412yes—
23#13133196—41no—
24#13133191—41no—
25C4×Dic106—41no—
26C4×D212—41no—
27#13133176—21no—
28#13133142—24no—
29#13133139—24no—
30C22×C8×C53—21no—
31C2×C42×C53C2×C411yescharacteristic
32#97×C53—21no—
33#97×C53C2×C412yes—
34C22×C4×C53—21no—
35C22×C4×C53C22⋊C411yescharacteristic
36C2×C22⋊D53—22no—
37#11719945—42no—
38#11719945—42no—
39C2×D212—41no—
40C2×D212C22⋊C412yes—
41C2×C4×D53—22no—
42C2×Dic106—41no—
43C2×Dic106C2×D412yes—
44#11719940—44no—
45#11719936—82no—
46D53⋊C8—82no—
47C2×C8×C53—22no—
48C2×C8×C53—41no—
49C2×C8×C53—41no—
50C42×C53—21no—
51C42×C53C22⋊C411yescharacteristic
52C42×C53C22×C411yescharacteristic
53C22⋊Dic53—41no—
54#11719921—42no—
55C4⋊Dic53—22no—
56C4⋊Dic53—41no—
57C4⋊Dic53—41no—
58#11719919—42no—
59C4×Dic53—41no—
60C23×C53#9911yescharacteristic
61C22×D53—22no—
62C2×C4×C53—21no—
63C2×C4×C53—21no—
64C2×C4×C53—21no—
65C2×C4×C53—21no—
66C2×C4×C53—81no—
67C2×C4×C53#9911yescharacteristic
68C2×C4×C53C2×C22⋊C411yescharacteristic
69C22⋊D53—82no—
70C2×Dic53—22no—
71C2×Dic53—42no—
72D212—42no—
73D212—82no—
74C4×D53—42no—
75C4×D53—42no—
76Dic106—42no—
77Dic106—82no—
78#88324—84no—
79C8×C53—42no—
80#13598—531nomaximal, Sylow
81C22×C53—21no—
82C22×C53—41no—
83C22×C53C2×#9911yescharacteristic
84C2×D53—42no—
85C2×D53—82no—
86C4×C53—21no—
87C4×C53—41no—
88C4×C53—41no—
89C4×C53#35411yescharacteristic
90C4×C53#35411yescharacteristic
91Dic53—42no—
92Dic53—82no—
93#3135—531no—
94#2132—532no—
95#1413—534no—
96C2×C53—21no—
97C2×C53—41no—
98C2×C53C2×#35411yescharacteristic
99D53—82no—
100#533—531no—
101#532—531no—
102#491—532no—
103#490—532no—
104#489—1062no—
105#416—1062no—
106#413—1062no—
107C2×#97#615711yescharacteristic
108#356—534no—
109#355—1062no—
110C53#1359811yescharacteristic, complemented, Sylow
111C2×#41—532no—
112C2×M16—2122no—
113C22×C8—21no—
114C4⋊Q8—531no—
115C4⋊Q8—1061no—
116#127—531no—
117#125—532no—
118#124—532no—
119C22⋊Q8—2121no—
120#121—2121no—
121C4×Q8—2121no—
122C4×D4—2121no—
123#117—1061no—
124C2×C42C2×#615711yescharacteristic
125#103—1064no—
126#102—1064no—
127#101—1064no—
128#100—2122no—
129#97—21no—
130#97C2×#615712yes—
131#41—2122no—
132#41—2122no—
133C2×Q8—532no—
134C2×Q8—2121no—
135C2×D4—532no—
136C2×D4—1062no—
137C2×D4—2121no—
138C22×C4—21no—
139C22×C4—1062no—
140C22×C4C22⋊#615711yescharacteristic
141M16—4242no—
142M16—2124no—
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8—4242no—
147C4⋊C4—1062no—
148C4⋊C4—2121no—
149C4⋊C4—2122no—
150C4⋊C4—2121no—
151C22⋊C4—2122no—
152C22⋊C4—2121no—
153C42—21no—
154C42—2121no—
155C42C22⋊#615711yescharacteristic
156C42C22×#615711yescharacteristic
157C23—1062no—
158C23#1313327611yescharacteristic
159Q8—4242no—
160Q8—2122no—
161D4—4242no—
162D4—4242no—
163D4—2122no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—1062no—
170C2×C4—2122no—
171C2×C4—2122no—
172C2×C4—2122no—
173C2×C4#1313327611yescharacteristic
174C2×C4C2×C22⋊#615711yescharacteristic
175C8—42no—
176C8—4244no—
177C22—21no—
178C22—41no—
179C22—4242no—
180C22—2122no—
181C22C2×#1313327611yescharacteristic
182C4—21no—
183C4—41no—
184C4—41no—
185C4—4242no—
186C4—2122no—
187C4#1681153011yescharacteristic
188C4#1681153011yescharacteristic
189C2—21no—
190C2—41no—
191C2—4242no—
192C2C2×#1681153011yescharacteristic
subgroupG/H
centerC4#16811530
commutatorC42×C53C22×C4
FrattiniC42C22×#6157
FittingC2×#97×C53C4
socleC2×C53C2×#354
prime radical#16811173C22
cosocle#13133217C23
hypercenterC2×#97#6157
hypocenterC53#13598
LCSG ▷ C42×C53 ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #20289859C2semidirect
110. C53#13598semidirect

Maximal subgroups

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

subgroupindex
#202910082
#202898592
#202850612
#1359853