Finite Group Databasebeta

← #27287586

Subgroups — #27287586

Order 13568.

386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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#20282783C211yesmaximal, characteristic
2#20275683C212yesmaximal
3C2×#16810364C212yesmaximal
4#20272596C211yesmaximal, characteristic
5C53×#1836C211yesmaximal, characteristic
6C2×#13133209C2212yes—
7C2×#13133128C2212yes—
8#16810563—22no—
9#16810555—22no—
10#16810553—22no—
11#16810385—22no—
12#16810385—22no—
13#16810364—24no—
14C2×#97×C53C2211yescharacteristic
15C53×#384C2211yescharacteristic
16C53×#382C2211yescharacteristic
17C53×#340—22no—
18C22×#88322—22no—
19#13133209—22no—
20#13133209—22no—
21#13133209—22no—
22#13133209—22no—
23C2×C4⋊Dic53—22no—
24C2×C4⋊Dic53D412yes—
25C2×C4⋊Dic53D412yes—
26C2×#11719919—22no—
27C2×#11719919—22no—
28#13133128—22no—
29#13133128—22no—
30#13133124—24no—
31#13133124—22no—
32C22×C8×C53—21no—
33C2×C4⋊C4×C53—21no—
34C2×C4⋊C4×C53—22no—
35C2×C4⋊C4×C53D412yes—
36C2×C42×C53C2311yescharacteristic
37#97×C53—21no—
38#97×C53D412yes—
39#95×C53—22no—
40C22×C4×C53—22no—
41C22×C4×C53—41no—
42C22×C4×C53C2×D412yes—
43C22×C4×C53C2×D411yescharacteristic
44C22×Dic53—22no—
45C22×Dic53—22no—
46C2×C8×C53—22no—
47C2×C8×C53—41no—
48C2×C8×C53—41no—
49C4⋊C4×C53—42no—
50C4⋊C4×C53—44no—
51C4⋊C4×C53—42no—
52C42×C53C2×D411yescharacteristic
53C42×C53#4111yescharacteristic
54C42×C53#4112yes—
55C4⋊Dic53—22no—
56C4⋊Dic53—22no—
57C4⋊Dic53—22no—
58C4⋊Dic53—22no—
59C4⋊Dic53—82no—
60#11719919—42no—
61#11719919—42no—
62#11719919—42no—
63#11719919—42no—
64C2×#88322—24no—
65C2×#88322—42no—
66C2×#88322—42no—
67C23×C53#12011yescharacteristic
68C2×C4×C53—22no—
69C2×C4×C53—21no—
70C2×C4×C53—21no—
71C2×C4×C53—22no—
72C2×C4×C53—42no—
73C2×C4×C53—42no—
74C2×C4×C53—42no—
75C2×C4×C53—82no—
76C2×C4×C53—81no—
77C2×C4×C53#12111yescharacteristic
78C2×C4×C53#12112yes—
79C2×C4×C53#12312yes—
80C2×C4×C53#12411yescharacteristic
81C2×Dic53—42no—
82C2×Dic53—42no—
83C2×Dic53—42no—
84C2×Dic53—42no—
85C2×Dic53—42no—
86C2×Dic53—42no—
87C8×C53—42no—
88#88322—44no—
89#10428—531nomaximal, Sylow
90C22×C53#39411yescharacteristic
91C22×C53#45412yes—
92C22×C53#45411yescharacteristic
93C22×C53#45511yescharacteristic
94C22×C53#45612yes—
95C4×C53—22no—
96C4×C53—22no—
97C4×C53—21no—
98C4×C53—21no—
99C4×C53—82no—
100C4×C53—161no—
101Dic53—82no—
102Dic53—82no—
103#2822—531no—
104#1992—532no—
105#1836D5311yescharacteristic
106C2×#330—532no—
107#1295—531no—
108C2×C53#165811yescharacteristic
109C2×C53#166311yescharacteristic
110C2×C53#166412yes—
111C2×C53#203812yes—
112C2×C53#204011yescharacteristic
113C2×#125—532no—
114C2×#97—532no—
115C2×#97C2×D5311yescharacteristic
116#400—1062no—
117#398—1062no—
118#398—1062no—
119#384C2×D5311yescharacteristic
120#382C2×D5311yescharacteristic
121#340—22no—
122#340—1062no—
123#340—1062no—
124#330—1064no—
125C53#1042811yescharacteristic, complemented, Sylow
126C22×C8—21no—
127C22×C8—1062no—
128#125—1062no—
129#125—1062no—
130#125—1062no—
131#125—1062no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—532no—
135C2×C4⋊C4—532no—
136C2×C4⋊C4—1062no—
137C2×C4⋊C4—1062no—
138C2×C4⋊C4—1062no—
139C2×C4⋊C4C22⋊D5312yes—
140C2×C42C22×D5311yescharacteristic
141#97—21no—
142#97—1062no—
143#97—1062no—
144#97D21212yes—
145#95—22no—
146#95—1064no—
147#95—1062no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—1062no—
151C22×C4—1062no—
152C22×C4D4×D5312yes—
153C22×C4C2×C22⋊D5311yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—1064no—
158C2×C8—2122no—
159C2×C8—2122no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—1062no—
164C4⋊C4—1062no—
165C4⋊C4—1062no—
166C4⋊C4—1062no—
167C4⋊C4—4242no—
168C4⋊C4—2122no—
169C4⋊C4—2122no—
170C4⋊C4—2122no—
171C4⋊C4—2122no—
172C42C2×D21211yescharacteristic
173C42#1171994511yescharacteristic
174C42#1171994912yes—
175C23#1313318511yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—2122no—
186C2×C4—2122no—
187C2×C4—2122no—
188C2×C4—2122no—
189C2×C4—2122no—
190C2×C4—2122no—
191C2×C4#1313319111yescharacteristic
192C2×C4#1313319212yes—
193C2×C4#1313320212yes—
194C2×C4#1313320611yescharacteristic
195C8—42no—
196C8—2124no—
197C22#1681054011yescharacteristic
198C22#1681079412yes—
199C22#1681079511yescharacteristic
200C22#1681080011yescharacteristic
201C22#1681080412yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—4242no—
209C4—4242no—
210C2#2027401611yescharacteristic
211C2#2027404111yescharacteristic
212C2#2027404812yes—
213C2#2027593412yes—
214C2#2027594411yescharacteristic
subgroupG/H
centerC23#13133185
commutator, cosocleC2×C42×C53C23
FrattiniC2×C42C22×D53
FittingC53×#1836C2
socle, prime radicalC23×C53#120
hypercenter#1836D53
hypocenterC53#10428
LCSG ▷ C2×C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
125. C53#10428semidirect

Maximal subgroups

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

subgroupindex
#202827832
#202756832
C2×#168103642
#202725962
C53×#18362
#1042853