Finite Group Databasebeta

← #13125294

Subgroups — #13125294

Order 1664.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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×#88172C214yesmaximal, complemented
2#11719430C211yesmaximal, characteristic
3D13×C4⋊Q8C211yesmaximal, characteristic, complemented
4C13×#494C211yesmaximal, characteristic, complemented
5#11718851C214yesmaximal, complemented
6#11718753C211yesmaximal, characteristic, complemented
7#11718746C211yesmaximal, characteristic, complemented
8#11718354C211yesmaximal, characteristic, complemented
9C4×#6094C211yesmaximal, characteristic, complemented
10C2×#6131C2212yes—
11C2×Q8×D13C2212yes—
12C2×C13×Q16C2214yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88201C2212yes—
16#88198C2212yes—
17C2×#6107C2214yes—
18C2×#6106C2214yes—
19#88172—216no—
20C2×#6095C2214yes—
21C2×#6094C2212yes—
22#88149—22no—
23#88147—22no—
24C4⋊C4×D13—22no—
25#88142—22no—
26#88128C2211yescharacteristic
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×C8×C13C2211yescharacteristic
30#88055C2212yes—
31C4×#1055C2211yescharacteristic
32C2×Q8×C13C2312yes—
33C2×Q8×C13C2312yes—
34#6131—28no—
35Q8×D13—28no—
36C2×D52—22no—
37C2×D52—22no—
38C2×D52C2312yes—
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13D412yes—
42C2×C4×D13C2311yescharacteristic
43C2×Dic26—22no—
44C2×Dic26C2312yes—
45C13×Q16—28no—
46C2×C8×C13C2312yes—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C42×C13C2311yescharacteristic
50#6107—28no—
51#6106—28no—
52#6103—24no—
53C4⋊Dic13—22no—
54#6101—24no—
55C4×Dic13D412yes—
56C4×Dic13C2311yescharacteristic
57C2×#1055C2312yes—
58#6095—28no—
59#6094D418yescomplemented
60#3152—131nomaximal, Sylow
61C22×D13—22no—
62C22×D13C2×D411yescharacteristic
63Q8×C13—24no—
64Q8×C13—24no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2411yescharacteristic
69C2×Dic13—22no—
70C2×Dic13C2×D412yes—
71C2×Dic13C2×D411yescharacteristic
72D52—24no—
73D52—44no—
74D52—44no—
75C4×D13—24no—
76C4×D13—44no—
77C4×D13—44no—
78C4×D13C2×D414yes—
79Dic26—24no—
80Dic26—44no—
81C8×C13C2×D414yes—
82#1055C2×D414yes—
83C2×#137—134no—
84#532—131no—
85C2×C4⋊Q8—131no—
86#497—134no—
87#494—131no—
88#494D1311yescharacteristic, complemented
89#492—131no—
90#492—131no—
91C4×M16—131no—
92C22×C13C22×D411yescharacteristic
93C2×D13—22no—
94C2×D13—42no—
95C2×D13—44no—
96C2×D13#12712yes—
97C4×C13—42no—
98C4×C13—42no—
99C4×C13#13714yescomplemented
100C4×C13C22×D412yes—
101Dic13—22no—
102Dic13—42no—
103Dic13#12712yes—
104C2×#41—132no—
105C22×Q8—132no—
106#137—2616no—
107C2×Q16—134no—
108C2×Q16C2×D1314yes—
109C2×SD16—134no—
110C2×SD16—134no—
111C2×M16—132no—
112C4⋊Q8—132no—
113C4⋊Q8—131no—
114C4⋊Q8—262no—
115C4⋊Q8C2×D1311yescharacteristic
116C4⋊Q8C2×D1311yescharacteristic
117#127—131no—
118#124—132no—
119#121—262no—
120C4×D4—262no—
121C2×C4⋊C4—262no—
122C2×C42—131no—
123#97—132no—
124C4×C8—131no—
125C4×C8C2×D1311yescharacteristic
126C2×C13C2×#12711yescharacteristic
127C2×C13C2×#13712yes—
128D13—22no—
129D13—82no—
130#41—268no—
131C2×Q8—132no—
132C2×Q8—262no—
133C2×Q8—268no—
134C2×Q8C22×D1312yes—
135C2×Q8C22×D1312yes—
136C2×D4—132no—
137C2×D4—262no—
138C2×D4—262no—
139C22×C4—131no—
140C22×C4—132no—
141C22×C4—262no—
142C22×C4—262no—
143Q16—28no—
144Q16—268no—
145SD16—268no—
146SD16—268no—
147M16—138no—
148C2×C8—132no—
149C2×C8C22×D1312yes—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—264no—
153C4⋊C4—262no—
154C22⋊C4—264no—
155C42—132no—
156C42—131no—
157C42C22×D1311yescharacteristic
158C13#315211yescharacteristic, complemented, Sylow
159C23—131no—
160C23—262no—
161Q8—24no—
162Q8—24no—
163Q8—264no—
164Q8—524no—
165D4—264no—
166D4—524no—
167D4—524no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—131no—
171C2×C4—134no—
172C2×C4—132no—
173C2×C4—264no—
174C2×C4—262no—
175C2×C4—524no—
176C2×C4—524no—
177C2×C4D4×D1312yes—
178C2×C4C23×D1311yescharacteristic
179C8—134no—
180C8D4×D1314yes—
181C22—132no—
182C22—262no—
183C22—524no—
184C22—522no—
185C22C2×D4×D1311yescharacteristic
186C4—42no—
187C4—42no—
188C4—132no—
189C4—262no—
190C4—522no—
191C4#8817214yescomplemented
192C4C2×D4×D1312yes—
193C2—262no—
194C2—1042no—
195C2D13×#12711yescharacteristic
196C2C2×#8817212yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#494C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#494D13
hypocenterC13#3152
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C2×#88172C2semidirect
3. D13×C4⋊Q8C2semidirect
4. C13×#494C2semidirect
5. #11718851C2semidirect
6. #11718753C2semidirect
7. #11718746C2semidirect
8. #11718354C2semidirect
9. C4×#6094C2semidirect
59. #6094D4semidirect
88. #494D13semidirect
99. C4×C13#137semidirect
158. C13#3152semidirect
191. C4#88172semidirect

Maximal subgroups

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

subgroupindex
C2×#881722
#117194302
D13×C4⋊Q82
C13×#4942
#117188512
#117187532
#117187462
#117183542
C4×#60942
#315213