Finite Group Databasebeta

← #13120211

Subgroups — #13120211

Order 1664.

544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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×#88178C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic
3C4×C13×C22⋊C4C211yesmaximal, characteristic
4#11718611C212yesmaximal
5#11718611C212yesmaximal
6#11718589C214yesmaximal, complemented
7#11718322C212yesmaximal, complemented
8#11718317C212yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C23×Dic13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C42×C13C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2214yes—
18C2×C4⋊Dic13C2214yes—
19#88178—24no—
20C2×#6101—24no—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C13×#95C2212yes—
25#88071C2214yes—
26#88071C2214yes—
27C24×C13C2311yescharacteristic
28C22×C4×C13—42no—
29C22×C4×C13D414yes—
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2314yes—
33C22×Dic13—22no—
34C22×Dic13—24no—
35C22×Dic13—22no—
36C22×Dic13—42no—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×Dic26—22no—
42C2×Dic26—42no—
43C13×C22⋊C4Q818yescomplemented
44C42×C13—42no—
45C22⋊Dic13—24no—
46C4⋊Dic13—22no—
47C4⋊Dic13—28no—
48C4⋊Dic13—44no—
49#6101—24no—
50#6101—24no—
51#6101—24no—
52#2583—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—22no—
55C23×C13C2×D412yes—
56C23×C13C2×Q814yes—
57C23×C13C2411yescharacteristic
58C2×C4×C13—24no—
59C2×C4×C13—24no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—44no—
63C2×C4×C13C2×D412yes—
64C2×C4×C13C2×D412yes—
65C2×C4×C13C2×Q818yes—
66C2×Dic13—28no—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—24no—
73C2×Dic13—24no—
74C2×Dic13—24no—
75C2×Dic13—44no—
76C2×Dic13#4114yes—
77Dic26—44no—
78C2×C22⋊Q8—131no—
79C22×C4⋊C4—131no—
80#398—132no—
81#395—132no—
82#389—134no—
83#385—132no—
84#385—132no—
85C4×C22⋊C4D1311yescharacteristic
86C22×C13—22no—
87C22×C13—22no—
88C22×C13—28no—
89C22×C13C4⋊Q814yes—
90C22×C13C22×D411yescharacteristic
91C22×C13C22×Q812yes—
92C22×C13C2×#4112yes—
93C22×C13H(5,𝔽2)12yes—
94C4×C13—22no—
95C4×C13—22no—
96C4×C13—28no—
97Dic13—24no—
98Dic13—42no—
99Dic13—42no—
100Dic13—42no—
101C22×Q8—131no—
102C23×C4—131no—
103C23×C4—131no—
104C23×C4C2×D1311yescharacteristic
105C22⋊Q8—264no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—131no—
110C2×C4⋊C4—134no—
111C2×C4⋊C4—134no—
112C2×C4⋊C4—264no—
113C2×C22⋊C4—132no—
114C2×C22⋊C4C2×D1312yes—
115C2×C42C2×D1312yes—
116#95—134no—
117#95—134no—
118#95C2×D1312yes—
119C2×C13—24no—
120C2×C13#52511yescharacteristic
121C2×C13C2×C4⋊Q811yescharacteristic
122C2×C13#53411yescharacteristic
123C2×C13#55414yes—
124C24C22×D1311yescharacteristic
125C2×Q8—262no—
126C2×Q8—522no—
127C22×C4—42no—
128C22×C4—132no—
129C22×C4—132no—
130C22×C4—132no—
131C22×C4—132no—
132C22×C4—264no—
133C22×C4—262no—
134C22×C4—262no—
135C22×C4—522no—
136C22×C4D5214yes—
137C22×C4C22×D1314yes—
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1311yescharacteristic
140C4⋊C4—268no—
141C4⋊C4—264no—
142C4⋊C4—264no—
143C4⋊C4—264no—
144C4⋊C4—262no—
145C4⋊C4—524no—
146C22⋊C4—264no—
147C22⋊C4Dic2618yescomplemented
148C42—42no—
149C13#258311yescharacteristic, complemented, Sylow
150C23—22no—
151C23—22no—
152C23C2×Dic2614yes—
153C23C2×D5212yes—
154C23C23×D1311yescharacteristic
155Q8—524no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—134no—
162C2×C4—268no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—264no—
169C2×C4—264no—
170C2×C4—264no—
171C2×C4—524no—
172C2×C4C2×Dic2618yes—
173C2×C4C2×D5212yes—
174C2×C4C2×D5212yes—
175C22—22no—
176C22—22no—
177C22—28no—
178C22#8812314yes—
179C22C22×Dic2612yes—
180C22C22×D5211yescharacteristic
181C22#8825112yes—
182C22#41×D1312yes—
183C4—22no—
184C4—22no—
185C4—28no—
186C4—264no—
187C4—522no—
188C4—522no—
189C4—522no—
190C2—24no—
191C2C2×#8812311yescharacteristic
192C2#1171919811yescharacteristic
193C2#1171922911yescharacteristic
194C2#1171924414yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C22⋊C4C2
prime radicalC24×C13C23
hypercenterC4×C22⋊C4D13
hypocenterC13#2583
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #11718589C2semidirect
7. #11718322C2semidirect
8. #11718317C2semidirect
43. C13×C22⋊C4Q8semidirect
147. C22⋊C4Dic26semidirect
149. C13#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#881782
C22×#61012
C4×C13×C22⋊C42
#117186112
#117185892
#117183222
#117183172
#258313