Finite Group Databasebeta

← #15767375

Subgroups — #15767375

Order 3328.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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#13115594C212yesmaximal
2#13114992C211yesmaximal, characteristic
3#13112719C211yesmaximal, characteristic
4#13112677C212yesmaximal
5C13×#2571C211yesmaximal, characteristic
6C13×#400—22no—
7C13×#389—22no—
8C13×#384C2211yescharacteristic
9C13×#382—22no—
10C4×C13×C4⋊C4C2212yes—
11C2×#88048—22no—
12C2×#88047—22no—
13#11718596C2211yescharacteristic
14C2×C4⋊#1055C2212yes—
15C2×C4×#1055C2211yescharacteristic
16#11718121—22no—
17C2×C13×C4⋊C4—22no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4D412yes—
20C2×C13×C4⋊C4D412yes—
21C2×C13×C4⋊C4D412yes—
22C2×C42×C13—22no—
23C2×C42×C13C2311yescharacteristic
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13—21no—
26C22×#1055—21no—
27C22×#1055—22no—
28C13×#95—22no—
29C13×#95—24no—
30C13×#95—22no—
31#88048—44no—
32#88047—44no—
33C4⋊#1055—22no—
34C4⋊#1055Q814yes—
35C4×#1055—21no—
36C4×#1055Q812yes—
37#10577—131nomaximal, Sylow
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13C2×D412yes—
43C22×Dic13—41no—
44C13×C4⋊C4—22no—
45C13×C4⋊C4—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—42no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—82no—
52C42×C13—42no—
53C42×C13—42no—
54C42×C13C2×Q811yescharacteristic
55C42×C13C2×Q812yes—
56C42×C13#4111yescharacteristic
57C4⋊Dic13—42no—
58C4⋊Dic13—42no—
59C4⋊Dic13—42no—
60C2×#1055—22no—
61C2×#1055—22no—
62C2×#1055—22no—
63C2×#1055—24no—
64C2×#1055—42no—
65C2×#1055—42no—
66#2571D1311yescharacteristic
67#1947—132no—
68#1844—131no—
69#1296—131no—
70#1279—132no—
71C23×C13#12011yescharacteristic
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—44no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13C22⋊Q811yescharacteristic
83C2×C4×C13C22⋊Q812yes—
84C2×C4×C13C4⋊Q811yescharacteristic
85C2×C4×C13C4⋊Q812yes—
86C2×C4×C13#13512yes—
87C2×C4×C13#13512yes—
88C2×C4×C13AGL(1,ℤ/8)12yes—
89C2×C4×C13#13712yes—
90C2×Dic13—82no—
91C2×Dic13—81no—
92#1055—24no—
93#1055—44no—
94C2×#107—262no—
95C2×#106—262no—
96C2×C4⋊C8—132no—
97C2×C4×C8—131no—
98#400—22no—
99#389—22no—
100#384—131no—
101#384C2×D1311yescharacteristic
102#382—22no—
103C4×C4⋊C4C2×D1312yes—
104#340—262no—
105C22×C13#39511yescharacteristic
106C22×C13#44912yes—
107C22×C13#45212yes—
108C22×C13#45311yescharacteristic
109C22×C13#45611yescharacteristic
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—82no—
113C4×C13—82no—
114C4×C13—82no—
115C4×C13#47812yes—
116C4×C13#47912yes—
117C4×C13#49912yes—
118C4×C13#50112yes—
119Dic13—161no—
120C22×C8—261no—
121C22×C8—262no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—262no—
125C2×C4⋊C4—261no—
126C2×C4⋊C4C22⋊D1312yes—
127C2×C4⋊C4C22⋊D1312yes—
128C2×C4⋊C4C22⋊D1312yes—
129C2×C42—22no—
130C2×C42C22×D1311yescharacteristic
131#107—524no—
132#106—524no—
133C4⋊C8—134no—
134C4⋊C8—262no—
135C4×C8—132no—
136C4×C8—261no—
137#95—22no—
138#95—24no—
139#95—22no—
140C2×C13#162411yescharacteristic
141C2×C13#163011yescharacteristic
142C2×C13#165212yes—
143C2×C13#205912yes—
144C2×C13#206011yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—521no—
149C22×C4C2×C22⋊D1311yescharacteristic
150C22×C4C2×C22⋊D1312yes—
151C2×C8—262no—
152C2×C8—262no—
153C2×C8—262no—
154C2×C8—264no—
155C2×C8—522no—
156C2×C8—522no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—82no—
165C4⋊C4—522no—
166C4⋊C4—522no—
167C4⋊C4—522no—
168C42—42no—
169C42—42no—
170C42Q8×D1311yescharacteristic
171C42Q8×D1312yes—
172C42#613111yescharacteristic
173C13#1057711yescharacteristic, complemented, Sylow
174C23#8820711yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—1042no—
186C2×C4—1041no—
187C2×C4#8819811yescharacteristic
188C2×C4#8819812yes—
189C2×C4#8820011yescharacteristic
190C2×C4#8820012yes—
191C2×C4#8820312yes—
192C2×C4#8820412yes—
193C2×C4#8820412yes—
194C2×C4#8820512yes—
195C8—264no—
196C8—524no—
197C22#1171889011yescharacteristic
198C22#1171889912yes—
199C22#1171890012yes—
200C22#1171890211yescharacteristic
201C22#1171890711yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—2081no—
208C4#1171872412yes—
209C4#1171872512yes—
210C4#1171872612yes—
211C4#1171872712yes—
212C2#1311391911yescharacteristic
213C2#1311395711yescharacteristic
214C2#1311410612yes—
215C2#1311617112yes—
216C2#1311617811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2571C2
socle, prime radicalC23×C13#120
hypercenter#2571D13
hypocenterC13#10577
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
173. C13#10577semidirect

Maximal subgroups

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

subgroupindex
#131155942
#131149922
#131127192
#131126772
C13×#25712
#1057713