Finite Group Databasebeta

← #13130998

Subgroups — #13130998

Order 1664.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q16×D13C211yesmaximal, characteristic
2D13⋊#101C212yesmaximal
3#11719153C212yesmaximal
4D13⋊#108C211yesmaximal, characteristic
5#11719089C211yesmaximal, characteristic
6C2×Q8×D13C2212yes—
7#88237C2211yescharacteristic
8D13⋊M16C2212yes—
9D13⋊M16C2211yescharacteristic
10C2×C13×Q16C411yescharacteristic, complemented
11C2×#6107C412yescomplemented
12Q16×D13—21no—
13Q16×D13—21no—
14Q16×D13—21no—
15Q16×D13—21no—
16C2×Dic52C411yescharacteristic, complemented
17C2×C8×D13C2211yescharacteristic
18#88117—24no—
19#88113—24no—
20#88104—21no—
21#88103—21no—
22#88100—21no—
23C8×#261—21no—
24C2×Q8×C13C2×C412yes—
25Q8×D13—22no—
26Q8×D13—22no—
27Q8×D13—22no—
28Q8×D13—22no—
29C2×C4×D13—22no—
30C2×C4×D13C2311yescharacteristic
31C2×Dic26—22no—
32C2×Dic26C2×C412yes—
33C22⋊#261—21no—
34#6122—22no—
35#6122D412yes—
36C4⋊#261D412yes—
37C4×#261—21no—
38#6118—21no—
39#6118—22no—
40D13⋊C8—21no—
41D13⋊C8—22no—
42C13×Q16—21no—
43C13×Q16—21no—
44C2×C8×C13C2×C411yescharacteristic
45#6107—22no—
46#6107—22no—
47C2×#1055C2×C411yescharacteristic
48Dic52—21no—
49Dic52—21no—
50C8×D13D411yescharacteristic
51C8×D13D411yescharacteristic
52C8×D13D411yescharacteristic
53C8×D13D411yescharacteristic
54#1979—131nomaximal, Sylow
55C22×D13#4111yescharacteristic
56C2×#261—22no—
57Q8×C13—22no—
58Q8×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13C22×C411yescharacteristic
61C2×Dic13—22no—
62C2×Dic13C2×D411yescharacteristic
63C4×D13—42no—
64C4×D13—42no—
65C4×D13C2×D411yescharacteristic
66C4×D13C2×D411yescharacteristic
67C4×D13C2×D411yescharacteristic
68C4×D13#4111yescharacteristic
69Dic26—22no—
70Dic26—22no—
71Dic26—42no—
72Dic26—42no—
73#1057—22no—
74#1057—42no—
75C8×C13C22⋊C411yescharacteristic
76C8×C13C22⋊C411yescharacteristic
77#1055C22⋊C411yescharacteristic
78#1055C22⋊C411yescharacteristic
79C22×Q16—131no—
80C2×#108—131no—
81#419—132no—
82C2×#101—132no—
83#405—131no—
84C22×C13C4×D411yescharacteristic
85C2×D13—22no—
86C2×D13#12111yescharacteristic
87C2×D13#12411yescharacteristic
88#261—42no—
89C4×C13—42no—
90C4×C13C2×C22⋊C411yescharacteristic
91C4×C13C4×D411yescharacteristic
92Dic13—42no—
93Dic13#12111yescharacteristic
94Dic13#12711yescharacteristic
95C22×Q8—132no—
96C2×Q16—132no—
97C2×Q16—131no—
98C2×Q16—261no—
99C2×Q16—261no—
100C2×Q16—261no—
101C2×Q16—261no—
102C2×Q16#26111yescharacteristic, complemented
103C2×M16—131no—
104C2×M16—132no—
105C22×C8—131no—
106#117—131no—
107#108—261no—
108#108—261no—
109#103—264no—
110#101—264no—
111#97—261no—
112C4×C8—261no—
113C2×C13—21no—
114C2×C13#39011yescharacteristic
115D13—21no—
116D13#47312yes—
117C2×Q8—132no—
118C2×Q8—262no—
119C2×Q8—262no—
120C2×Q8—262no—
121C2×Q8—262no—
122C2×Q8—262no—
123C2×Q8C2×#26112yes—
124C22×C4—131no—
125C22×C4—262no—
126Q16—21no—
127Q16—21no—
128Q16—262no—
129Q16—262no—
130Q16—261no—
131Q16—261no—
132M16—132no—
133M16—261no—
134M16—262no—
135M16—262no—
136C2×C8—131no—
137C2×C8—131no—
138C2×C8—131no—
139C2×C8—131no—
140C2×C8—131no—
141C2×C8—261no—
142C2×C8—262no—
143C2×C8C2×#26111yescharacteristic
144C4⋊C4—132no—
145C22⋊C4—261no—
146C42—261no—
147C13#197911yescharacteristic, complemented, Sylow
148C23—131no—
149Q8—22no—
150Q8—22no—
151Q8—262no—
152Q8—262no—
153Q8—522no—
154Q8—522no—
155C2×C4—22no—
156C2×C4—131no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4C22×#26111yescharacteristic
166C8—131no—
167C8—131no—
168C8—262no—
169C8—522no—
170C8C22⋊#26111yescharacteristic
171C8C22⋊#26111yescharacteristic
172C22—131no—
173C22—131no—
174C22—262no—
175C22D4×#26111yescharacteristic
176C4—42no—
177C4—131no—
178C4—131no—
179C4—522no—
180C4—522no—
181C4D4×#26111yescharacteristic
182C4C2×C22⋊#26111yescharacteristic
183C2—21no—
184C2—132no—
185C2—261no—
186C2#1171915111yescharacteristic
subgroupG/H
centerC2#11719151
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×Q16C4
socleC2×C13#390
prime radicalC22×D13#41
cosocleC2×C4×D13C23
hypercenterC2×Q16#261
hypocenterC13#1979
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
10. C2×C13×Q16C4semidirect
11. C2×#6107C4semidirect
16. C2×Dic52C4semidirect
102. C2×Q16#261semidirect
147. C13#1979semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D132
D13⋊#1012
#117191532
D13⋊#1082
#117190892
#197913