Finite Group Databasebeta

← #13120036

Subgroups — #13120036

Order 1664.

548 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 165 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×C4×D52C211yesmaximal, characteristic
2C2×#88124C211yesmaximal, characteristic, complemented
3C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
4#11718655C214yesmaximal, complemented
5#11718600C211yesmaximal, characteristic
6#11718600C211yesmaximal, characteristic
7#11718597C211yesmaximal, characteristic, complemented
8#11718596C211yesmaximal, characteristic, complemented
9#11718329C214yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C2×C13×C4⋊C4C2212yes—
13C2×C42×C13C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×#6103C2212yes—
17C2×#6103C2214yes—
18C2×#6103C2214yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2214yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C4×D52—24no—
26#88124—24no—
27C13×#95C2212yes—
28#88071C2214yes—
29C23×D13C2312yes—
30C22×C4×C13C2312yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×Dic13C2312yes—
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C2×D52—22no—
39C2×D52—22no—
40C2×D52Q814yes—
41C2×C4×D13—24no—
42C2×C4×D13—44no—
43C13×C4⋊C4—24no—
44C42×C13—22no—
45C42×C13—22no—
46C42×C13D414yes—
47#6103—24no—
48#6103—28no—
49#6103—44no—
50C4⋊Dic13—22no—
51C4⋊Dic13—22no—
52C4⋊Dic13—22no—
53C4⋊Dic13—44no—
54#6101—24no—
55#6101—24no—
56#2566—131nomaximal, Sylow
57C23×C13C2411yescharacteristic
58C22×D13—22no—
59C22×D13—24no—
60C22×D13—22no—
61C22×D13—24no—
62C22×D13C2×Q814yes—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×D412yes—
73C2×C4×C13C2×Q812yes—
74C2×C4×C13#4114yes—
75C2×C4×C13#4112yes—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81C2×Dic13—24no—
82D52—28no—
83C4×D13—48no—
84C2×#125—131no—
85C2×C4×D4—131no—
86#396—134no—
87#390—131no—
88#390—131no—
89#385—134no—
90#384—131no—
91#382—131no—
92C4×C4⋊C4D1311yescharacteristic, complemented
93C22×C13C22×D411yescharacteristic
94C22×C13C22×Q811yescharacteristic
95C22×C13C2×#4112yes—
96C22×C13C2×#4111yescharacteristic
97C22×C13H(5,𝔽2)12yes—
98C2×D13—24no—
99C2×D13—28no—
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—44no—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—24no—
106C4×C13—42no—
107C4×C13C22⋊Q814yes—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111C22×D4—131no—
112C23×C4—132no—
113#125—264no—
114C4×D4—264no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—131no—
120C2×C4⋊C4—134no—
121C2×C4⋊C4C2×D1312yes—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4—134no—
125C2×C42C2×D1311yescharacteristic
126C2×C42C2×D1311yescharacteristic
127C2×C42C2×D1311yescharacteristic
128#95—134no—
129#95C2×D1312yes—
130C2×C13C2×C22⋊Q811yescharacteristic
131C2×C13#53211yescharacteristic
132C2×C13#53511yescharacteristic
133C2×C13#55312yes—
134C2×C13#55412yes—
135D13—44no—
136C24—132no—
137C2×D4—134no—
138C2×D4—262no—
139C2×D4—262no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—132no—
143C22×C4—264no—
144C22×C4—524no—
145C22×C4C22×D1312yes—
146C22×C4C22×D1311yescharacteristic
147C22×C4C22×D1311yescharacteristic
148C22×C4C22×D1312yes—
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—262no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—524no—
157C22⋊C4—264no—
158C22⋊C4—268no—
159C22⋊C4—524no—
160C42—22no—
161C42—22no—
162C42D5214yes—
163C13#256611yescharacteristic, complemented, Sylow
164C23—134no—
165C23—262no—
166C23—264no—
167C23—262no—
168C23—264no—
169C23C23×D1311yescharacteristic
170D4—268no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—264no—
182C2×C4—264no—
183C2×C4—264no—
184C2×C4—528no—
185C2×C4C2×D5212yes—
186C2×C4C2×D5212yes—
187C2×C4C2×D5212yes—
188C2×C4#612714yes—
189C2×C4#612912yes—
190C2×C4Q8×D1312yes—
191C22—264no—
192C22—268no—
193C22—522no—
194C22—522no—
195C22—524no—
196C22C22×D5211yescharacteristic
197C22C2×#612712yes—
198C22C2×#612911yescharacteristic
199C22C2×Q8×D1311yescharacteristic
200C22#8825612yes—
201C4—22no—
202C4—22no—
203C4—24no—
204C4—42no—
205C4—522no—
206C4—522no—
207C4—522no—
208C4#8815114yes—
209C2—524no—
210C2#1171918211yescharacteristic
211C2C2×#8815111yescharacteristic
212C2#1171923011yescharacteristic
213C2#1171927012yes—
214C2#1171928412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C4⋊C4C2
prime radicalC22×D52C22
hypercenterC4×C4⋊C4D13
hypocenterC13#2566
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88124C2semidirect
3. C4×C13×C4⋊C4C2semidirect
4. #11718655C2semidirect
7. #11718597C2semidirect
8. #11718596C2semidirect
9. #11718329C2semidirect
92. C4×C4⋊C4D13semidirect
163. C13#2566semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D522
C2×#881242
C4×C13×C4⋊C42
#117186552
#117186002
#117185972
#117185962
#117183292
#256613