Finite Group Databasebeta

← #13115528

Subgroups — #13115528

Order 1664.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×C13×#103C211yesmaximal, characteristic
2#11718891C211yesmaximal, characteristic
3C2×#88075C211yesmaximal, characteristic
4C2×#88055C211yesmaximal, characteristic
5#11718646C211yesmaximal, characteristic
6#11718143C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic
8C22×Q8×C13C2211yescharacteristic
9C22×C8×C13C2211yescharacteristic
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic13—21no—
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15C22×#1055C2211yescharacteristic
16C13×#103C414yescomplemented
17#88075—22no—
18#88071—21no—
19#88071—21no—
20#88071—21no—
21#88055—22no—
22C2×Q8×C13—21no—
23C2×Q8×C13—21no—
24C2×Q8×C13—21no—
25C2×Q8×C13—21no—
26C2×Q8×C13—21no—
27C2×Q8×C13C2×C412yes—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13C2311yescharacteristic
31C22×Dic13—21no—
32C22×Dic13—21no—
33C22×Dic13D411yescharacteristic
34C22×Dic13D411yescharacteristic
35C2×C8×C13—21no—
36C2×C8×C13—21no—
37C2×C8×C13C2×C412yes—
38C13×C4⋊C4—21no—
39C13×C4⋊C4C2×C412yes—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13—42no—
45C4×Dic13—21no—
46C4×Dic13—21no—
47C2×#1055—21no—
48C2×#1055—21no—
49C2×#1055D412yes—
50#1935—131nomaximal, Sylow
51C23×C13C2×D411yescharacteristic
52Q8×C13—22no—
53Q8×C13—22no—
54Q8×C13—41no—
55Q8×C13—41no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13C22×C411yescharacteristic
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13#4111yescharacteristic
65C2×C4×C13#4111yescharacteristic
66C2×C4×C13#4111yescharacteristic
67C2×C4×C13#4111yescharacteristic
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—41no—
75C2×Dic13—41no—
76C2×Dic13—41no—
77C2×Dic13—41no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C8×C13—22no—
81#1055—22no—
82C2×#103—131no—
83C2×#103D1311yescharacteristic
84C2×#97—131no—
85#391—131no—
86#389—131no—
87#340—131no—
88#340—131no—
89C22×C13C4×D411yescharacteristic
90C22×C13#12111yescharacteristic
91C22×C13#12411yescharacteristic
92C22×C13AGL(1,ℤ/8)11yescharacteristic
93C22×C13#13711yescharacteristic
94C22×C13#13711yescharacteristic
95C22×C13#13711yescharacteristic
96C4×C13—42no—
97C4×C13—42no—
98C4×C13#11711yescharacteristic
99C4×C13C4×D411yescharacteristic
100C4×C13#12311yescharacteristic
101C4×C13#12611yescharacteristic
102Dic13—41no—
103Dic13—41no—
104Dic13—81no—
105Dic13—81no—
106C22×Q8C2×D1311yescharacteristic
107C22×C8—131no—
108C22×C8C2×D1311yescharacteristic
109C2×C4⋊C4—131no—
110C2×C4⋊C4—131no—
111C2×C4⋊C4—261no—
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C42—131no—
114#103—262no—
115#103Dic1314yescomplemented
116#97—262no—
117#95—261no—
118#95—261no—
119#95—261no—
120C2×C13#38811yescharacteristic
121C2×C13#44011yescharacteristic
122C2×C13#44111yescharacteristic
123C2×C13#46811yescharacteristic
124C2×C13#47011yescharacteristic
125C2×C13#48911yescharacteristic
126C2×C13#49111yescharacteristic
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8C2×Dic1312yes—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—261no—
138C22×C4—261no—
139C22×C4C22×D1311yescharacteristic
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—132no—
143C2×C8—261no—
144C2×C8—261no—
145C2×C8C2×Dic1312yes—
146C4⋊C4—21no—
147C4⋊C4—261no—
148C4⋊C4—261no—
149C4⋊C4—261no—
150C4⋊C4—261no—
151C4⋊C4—522no—
152C4⋊C4C2×Dic1312yes—
153C42—261no—
154C42—261no—
155C13#193511yescharacteristic, complemented, Sylow
156C23D4×D1311yescharacteristic
157Q8—22no—
158Q8—22no—
159Q8—41no—
160Q8—41no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—261no—
172C2×C4—261no—
173C2×C4—521no—
174C2×C4—521no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4#612711yescharacteristic
180C2×C4#612711yescharacteristic
181C2×C4D4×D1311yescharacteristic
182C2×C4#612911yescharacteristic
183C2×C4#612911yescharacteristic
184C2×C4C22×Dic1311yescharacteristic
185C8—22no—
186C8—262no—
187C22#8813811yescharacteristic
188C22#8813911yescharacteristic
189C22#8816811yescharacteristic
190C22#8816911yescharacteristic
191C22#8817211yescharacteristic
192C22#8817211yescharacteristic
193C22D4×Dic1311yescharacteristic
194C4—42no—
195C4—42no—
196C4—521no—
197C4—521no—
198C4—1041no—
199C4—1041no—
200C4#8813311yescharacteristic
201C4#8813711yescharacteristic
202C4#8818011yescharacteristic
203C4D4×Dic1311yescharacteristic
204C2#1171845611yescharacteristic
205C2#1171845811yescharacteristic
206C2#1171847311yescharacteristic
207C2#1171847711yescharacteristic
208C2#1171861211yescharacteristic
209C2#1171882511yescharacteristic
210C2#1171884511yescharacteristic
subgroupG/H
centerC23D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socle, prime radicalC23×C13C2×D4
cosocleC22×C4×C13C23
hypercenterC2×#103D13
hypocenterC13#1935
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
16. C13×#103C4semidirect
115. #103Dic13semidirect
155. C13#1935semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1032
#117188912
C2×#880752
C2×#880552
#117186462
#117181432
#117181212
#193513