Finite Group Databasebeta

← #15793973

Subgroups — #15793973

Order 3328.

1530 conjugacy classes of subgroups; only the 371 normal subgroups are shown.

normal subgroups only

This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 371 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
1C22×#88130C211yesmaximal, characteristic
2C2×#11718598C211yesmaximal, characteristic, complemented
3#13113086C216yesmaximal, complemented
4#13113078C216yesmaximal
5C2×C13×#384C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2216yes—
7C22×C42×C13C2211yescharacteristic
8C22×#6103C2213yes—
9C22×#6103C2214yes—
10C22×#6101C2213yes—
11C2×#88130—24no—
12C2×#88130—24no—
13C2×#88130C418yescomplemented
14C13×#384—24no—
15C2×#88071C2216yes—
16C2×#88071C22112yes—
17#11718598—24no—
18C24×D13C2311yescharacteristic
19C23×C4×C13C2314yes—
20C23×C4×C13C2313yes—
21C23×Dic13C2314yes—
22C23×Dic13C2313yes—
23C2×C13×C4⋊C4—212no—
24C2×C13×C4⋊C4—412no—
25C2×C42×C13C2×C414yes—
26C2×C42×C13D414yes—
27C2×C42×C13D414yes—
28C2×#6103—26no—
29C2×#6103—26no—
30C2×#6103—412no—
31C2×#6103C2×C4112yes—
32C2×#6101—26no—
33C2×#6101—26no—
34C2×#6101C2×C4112yes—
35#88130—232no—
36#88071—212no—
37#88071—412no—
38#14665—131nomaximal, Sylow
39C24×C13C2411yescharacteristic
40C23×D13—21no—
41C23×D13—21no—
42C23×D13—26no—
43C23×D13—26no—
44C23×D13C22×C412yes—
45C22×C4×C13—26no—
46C22×C4×C13—26no—
47C22×C4×C13—24no—
48C22×C4×C13—212no—
49C22×C4×C13—212no—
50C22×C4×C13C22×C416yes—
51C22×C4×C13C2×D416yes—
52C22×C4×C13C2×D416yes—
53C22×Dic13—23no—
54C22×Dic13—23no—
55C22×Dic13—26no—
56C22×Dic13—26no—
57C22×Dic13—24no—
58C22×Dic13—212no—
59C22×Dic13—212no—
60C22×Dic13C22×C416yes—
61C13×C4⋊C4—424no—
62C42×C13C22⋊C4116yescomplemented
63#6103—224no—
64#6103—416no—
65#6101—224no—
66C22×#126—131no—
67C2×#384D1311yescharacteristic, complemented
68C2×#383—131no—
69#1441—136no—
70#1439—136no—
71C23×C13C23×C411yescharacteristic
72C23×C13C22×D411yescharacteristic
73C23×C13C22×D411yescharacteristic
74C23×C13H(5,𝔽2)16yes—
75C23×C132−1+416yes—
76C22×D13—22no—
77C22×D13—212no—
78C22×D13—43no—
79C22×D13—43no—
80C22×D13—46no—
81C22×D13—44no—
82C22×D13—412no—
83C2×C4×C13—212no—
84C2×C4×C13—26no—
85C2×C4×C13—26no—
86C2×C4×C13—212no—
87C2×C4×C13—412no—
88C2×C4×C13—44no—
89C2×C4×C13—412no—
90C2×C4×C13C2×C22⋊C4112yes—
91C2×Dic13—26no—
92C2×Dic13—212no—
93C2×Dic13—43no—
94C2×Dic13—43no—
95C2×Dic13—46no—
96C2×Dic13—412no—
97C2×Dic13—44no—
98C2×Dic13—412no—
99C2×#126—138no—
100C2×#126—264no—
101C2×#126—264no—
102C22×C4⋊C4—133no—
103C22×C4⋊C4C2×D1316yes—
104C22×C22⋊C4—133no—
105C22×C22⋊C4—134no—
106C22×C42C2×D1311yescharacteristic
107#384—24no—
108#383—264no—
109C2×#95—136no—
110C2×#95—1312no—
111C22×C13C22×C22⋊C411yescharacteristic
112C22×C13#52016yes—
113C22×C13#53513yes—
114C22×C13#53613yes—
115C22×C13#53716yes—
116C22×C13#56014yes—
117C22×C13#563112yes—
118C2×D13—46no—
119C2×D13—48no—
120C2×D13—81no—
121C2×D13—83no—
122C2×D13—84no—
123C4×C13—212no—
124C4×C13—84no—
125Dic13—46no—
126Dic13—84no—
127C25—131no—
128C23×C4—133no—
129C23×C4—134no—
130C23×C4C22×D1314yes—
131C23×C4C22×D1313yes—
132#126—2632no—
133C2×C4⋊C4—212no—
134C2×C4⋊C4—412no—
135C2×C4⋊C4—1312no—
136C2×C4⋊C4—266no—
137C2×C4⋊C4—266no—
138C2×C22⋊C4—1312no—
139C2×C22⋊C4—266no—
140C2×C22⋊C4—266no—
141C2×C22⋊C4—5212no—
142C2×C42C4×D1314yes—
143C2×C42D5214yes—
144C2×C42C22⋊D1314yes—
145#95—2612no—
146#95—5212no—
147C2×C13#231113yes—
148C2×C13#238314yes—
149C2×C13#281811yescharacteristic
150C2×C13#282113yes—
151C2×C13#282314yes—
152D13—82no—
153C24—132no—
154C24—261no—
155C24—266no—
156C24—266no—
157C24—261no—
158C24C23×D1311yescharacteristic
159C22×C4—26no—
160C22×C4—26no—
161C22×C4—212no—
162C22×C4—212no—
163C22×C4—24no—
164C22×C4—136no—
165C22×C4—263no—
166C22×C4—266no—
167C22×C4—266no—
168C22×C4—263no—
169C22×C4—264no—
170C22×C4—2612no—
171C22×C4—2612no—
172C22×C4C2×C4×D1316yes—
173C22×C4C2×D5216yes—
174C22×C4C2×C22⋊D1316yes—
175C4⋊C4—424no—
176C4⋊C4—2624no—
177C22⋊C4—2624no—
178C22⋊C4—5216no—
179C42#6103116yescomplemented
180C13#1466511yescharacteristic, complemented, Sylow
181C23—2612no—
182C23—262no—
183C23—524no—
184C23—5212no—
185C23—526no—
186C23—523no—
187C23—523no—
188C23C22×C4×D1311yescharacteristic
189C23C22×D5211yescharacteristic
190C23#8825116yes—
191C23#8825416yes—
192C23C22×C22⋊D1311yescharacteristic
193C2×C4—212no—
194C2×C4—212no—
195C2×C4—26no—
196C2×C4—26no—
197C2×C4—44no—
198C2×C4—412no—
199C2×C4—412no—
200C2×C4—2612no—
201C2×C4—266no—
202C2×C4—526no—
203C2×C4—523no—
204C2×C4—523no—
205C2×C4—524no—
206C2×C4—5212no—
207C2×C4—5212no—
208C2×C4C2×#6103112yes—
209C22—528no—
210C22—526no—
211C22—1041no—
212C22—1043no—
213C22—1044no—
214C22#1171920916yes—
215C22#1171921516yes—
216C22#1171942514yes—
217C22#11719440112yes—
218C22C22×#610311yescharacteristic
219C22#1171951013yes—
220C22#1171952113yes—
221C4—212no—
222C4—84no—
223C4—526no—
224C4—1044no—
225C2—1042no—
226C2#1311742913yes—
227C2#1311802914yes—
228C2#1312287711yescharacteristic
229C2#1312289513yes—
230C2#1312291014yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#384C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#384D13
hypocenterC13#14665
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. C2×#11718598C2semidirect
3. #13113086C2semidirect
5. C2×C13×#384C2semidirect
13. C2×#88130C4semidirect
62. C42×C13C22⋊C4semidirect
67. C2×#384D13semidirect
179. C42#6103semidirect
180. C13#14665semidirect

Maximal subgroups

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

subgroupindex
C22×#881302
C2×#117185982
#131130862
#131130782
C2×C13×#3842
#1466513