Finite Group Databasebeta

← #15793975

Subgroups — #15793975

Order 3328.

1530 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 411 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
1C2×#11718596C211yesmaximal, characteristic, complemented
2C2×#11718598C211yesmaximal, characteristic, complemented
3#13113089C216yesmaximal, complemented
4#13113081C216yesmaximal
5C22×C13×#126C211yesmaximal, characteristic
6C2×C13×#126—24no—
7C2×C13×#126—24no—
8C2×C13×#126C418yescomplemented
9C22×C13×C4⋊C4C2213yes—
10C22×C13×C22⋊C4C2213yes—
11C22×C42×C13C2211yescharacteristic
12C22×C22⋊Dic13C2214yes—
13C22×C4⋊Dic13C2216yes—
14C2×#88071C2216yes—
15C2×#88071C22112yes—
16#11718598—24no—
17#11718596—24no—
18C25×C13C2311yescharacteristic
19C23×C4×C13C2313yes—
20C23×C4×C13C2313yes—
21C23×Dic13C2314yes—
22C23×Dic13C2314yes—
23C13×#126—232no—
24C2×C13×C4⋊C4—26no—
25C2×C13×C4⋊C4—26no—
26C2×C13×C4⋊C4C2×C4112yes—
27C2×C13×C22⋊C4—26no—
28C2×C13×C22⋊C4—26no—
29C2×C13×C22⋊C4C2×C4112yes—
30C2×C42×C13C2×C414yes—
31C2×C42×C13D414yes—
32C2×C42×C13D414yes—
33C2×C22⋊Dic13—412no—
34C2×C4⋊Dic13—212no—
35C2×C4⋊Dic13—412no—
36#88071—212no—
37#88071—412no—
38#14665—131nomaximal, Sylow
39C24×C13—21no—
40C24×C13—21no—
41C24×C13—26no—
42C24×C13—26no—
43C24×C13C22×C412yes—
44C24×C13C2411yescharacteristic
45C22×C4×C13—26no—
46C22×C4×C13—26no—
47C22×C4×C13—23no—
48C22×C4×C13—23no—
49C22×C4×C13—26no—
50C22×C4×C13—26no—
51C22×C4×C13C22×C416yes—
52C22×C4×C13C22×C416yes—
53C22×C4×C13C2×D416yes—
54C22×C4×C13C2×D416yes—
55C22×Dic13—24no—
56C22×Dic13—24no—
57C22×Dic13—212no—
58C22×Dic13—212no—
59C22×Dic13—212no—
60C22×Dic13—212no—
61C13×C4⋊C4—224no—
62C13×C22⋊C4—224no—
63C42×C13C22⋊C4116yescomplemented
64C22⋊Dic13—416no—
65C4⋊Dic13—424no—
66C22×#126D1311yescharacteristic
67C2×#384—131no—
68C2×#383—131no—
69#1441—136no—
70#1439—136no—
71C23×C13—22no—
72C23×C13—212no—
73C23×C13—43no—
74C23×C13—43no—
75C23×C13—46no—
76C23×C13—44no—
77C23×C13—412no—
78C23×C13C23×C411yescharacteristic
79C23×C13C22×D411yescharacteristic
80C23×C13C22×D411yescharacteristic
81C23×C13H(5,𝔽2)16yes—
82C23×C132−1+416yes—
83C2×C4×C13—212no—
84C2×C4×C13—26no—
85C2×C4×C13—26no—
86C2×C4×C13—212no—
87C2×C4×C13—26no—
88C2×C4×C13—212no—
89C2×C4×C13—43no—
90C2×C4×C13—43no—
91C2×C4×C13—46no—
92C2×C4×C13C2×C22⋊C4112yes—
93C2×Dic13—412no—
94C2×Dic13—412no—
95C2×Dic13—44no—
96C2×Dic13—44no—
97C2×Dic13—412no—
98C2×Dic13—412no—
99C2×#126—24no—
100C2×#126—24no—
101C2×#126Dic1318yescomplemented
102C22×C4⋊C4—136no—
103C22×C4⋊C4C2×D1313yes—
104C22×C22⋊C4—134no—
105C22×C22⋊C4C2×D1313yes—
106C22×C42C2×D1311yescharacteristic
107#384—264no—
108#383—264no—
109C2×#95—136no—
110C2×#95—1312no—
111C22×C13—46no—
112C22×C13—48no—
113C22×C13—81no—
114C22×C13—83no—
115C22×C13—84no—
116C22×C13C22×C22⋊C411yescharacteristic
117C22×C13#52016yes—
118C22×C13#53513yes—
119C22×C13#53613yes—
120C22×C13#53716yes—
121C22×C13#56014yes—
122C22×C13#563112yes—
123C4×C13—212no—
124C4×C13—46no—
125Dic13—84no—
126Dic13—84no—
127C25C22×D1311yescharacteristic
128C23×C4—134no—
129C23×C4—134no—
130C23×C4C22×D1313yes—
131C23×C4C22×D1313yes—
132#126—232no—
133C2×C4⋊C4—26no—
134C2×C4⋊C4—26no—
135C2×C4⋊C4—2612no—
136C2×C4⋊C4—5212no—
137C2×C4⋊C4C2×Dic13112yes—
138C2×C22⋊C4—26no—
139C2×C22⋊C4—26no—
140C2×C22⋊C4—5212no—
141C2×C22⋊C4C2×Dic13112yes—
142C2×C42C2×Dic1314yes—
143C2×C42C22⋊D1314yes—
144C2×C42C22⋊D1314yes—
145#95—2612no—
146#95—5212no—
147C2×C13—82no—
148C2×C13#231113yes—
149C2×C13#238314yes—
150C2×C13#281811yescharacteristic
151C2×C13#282113yes—
152C2×C13#282314yes—
153C24—26no—
154C24—26no—
155C24—21no—
156C24—21no—
157C24C22×Dic1312yes—
158C24C23×D1311yescharacteristic
159C22×C4—26no—
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—26no—
163C22×C4—23no—
164C22×C4—23no—
165C22×C4—2612no—
166C22×C4—2612no—
167C22×C4—2612no—
168C22×C4—2612no—
169C22×C4—264no—
170C22×C4—264no—
171C22×C4C22×Dic1316yes—
172C22×C4C22×Dic1316yes—
173C22×C4C2×C22⋊D1316yes—
174C22×C4C2×C22⋊D1316yes—
175C4⋊C4—224no—
176C4⋊C4—5224no—
177C22⋊C4—224no—
178C22⋊C4—5216no—
179C42C22⋊Dic13116yescomplemented
180C13#1466511yescharacteristic, complemented, Sylow
181C23—212no—
182C23—22no—
183C23—43no—
184C23—43no—
185C23—46no—
186C23—44no—
187C23—412no—
188C23#8825616yes—
189C23#8825716yes—
190C23C23×Dic1311yescharacteristic
191C23C22×C22⋊D1311yescharacteristic
192C23C22×C22⋊D1311yescharacteristic
193C2×C4—26no—
194C2×C4—212no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—43no—
200C2×C4—43no—
201C2×C4—46no—
202C2×C4—5212no—
203C2×C4—5212no—
204C2×C4—524no—
205C2×C4—524no—
206C2×C4—5212no—
207C2×C4—5212no—
208C2×C4C2×C22⋊Dic13112yes—
209C22—48no—
210C22—46no—
211C22—81no—
212C22—83no—
213C22—84no—
214C22#1171941614yes—
215C22#11719417112yes—
216C22#1171953013yes—
217C22#1171953216yes—
218C22#1171953513yes—
219C22#1171953816yes—
220C22C22×C22⋊Dic1311yescharacteristic
221C4—212no—
222C4—46no—
223C4—1044no—
224C4—1044no—
225C2—82no—
226C2#1311742813yes—
227C2#1311802814yes—
228C2#1312287611yescharacteristic
229C2#1312289413yes—
230C2#1312290814yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×#126C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×#126D13
hypocenterC13#14665
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C2×#11718596C2semidirect
2. C2×#11718598C2semidirect
3. #13113089C2semidirect
8. C2×C13×#126C4semidirect
63. C42×C13C22⋊C4semidirect
101. C2×#126Dic13semidirect
179. C42C22⋊Dic13semidirect
180. C13#14665semidirect

Maximal subgroups

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

subgroupindex
C2×#117185962
C2×#117185982
#131130892
#131130812
C22×C13×#1262
#1466513