Finite Group Databasebeta

← #13115409

Subgroups — #13115409

Order 1664.

230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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×#107C211yesmaximal, characteristic
2#11718646C211yesmaximal, characteristic
3C4⋊C4×Dic13C211yesmaximal, characteristic
4#11718143C211yesmaximal, characteristic
5#11718142C211yesmaximal, characteristic
6#11718121C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic
8C22×C8×C13C2211yescharacteristic
9C2×C13×C4⋊C4C2211yescharacteristic
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic13—21no—
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4×Dic13—21no—
15C2×C4×Dic13C2211yescharacteristic
16C22×#1055C2211yescharacteristic
17C13×#107C414yescomplemented
18#88071—21no—
19#88071—21no—
20C22×C4×C13—21no—
21C22×C4×C13—21no—
22C22×C4×C13C2311yescharacteristic
23C22×Dic13—21no—
24C22×Dic13—21no—
25C22×Dic13D411yescharacteristic
26C22×Dic13D411yescharacteristic
27C2×C8×C13—21no—
28C2×C8×C13—21no—
29C2×C8×C13C2×C412yes—
30C13×C4⋊C4—21no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4C2×C412yes—
33C13×C4⋊C4C2×C412yes—
34C4⋊Dic13—21no—
35C4⋊Dic13—21no—
36C4⋊Dic13—21no—
37C4⋊Dic13—42no—
38C4⋊Dic13Q812yes—
39C4×Dic13—21no—
40C4×Dic13—21no—
41C4×Dic13—42no—
42C2×#1055—21no—
43C2×#1055—21no—
44C2×#1055—21no—
45#1918—131nomaximal, Sylow
46C23×C13C2×D411yescharacteristic
47C2×C4×C13—22no—
48C2×C4×C13—22no—
49C2×C4×C13—41no—
50C2×C4×C13—41no—
51C2×C4×C13—41no—
52C2×C4×C13—41no—
53C2×C4×C13C22×C411yescharacteristic
54C2×C4×C13C2×Q811yescharacteristic
55C2×C4×C13#4111yescharacteristic
56C2×C4×C13#4111yescharacteristic
57C2×C4×C13#4111yescharacteristic
58C2×C4×C13#4111yescharacteristic
59C2×Dic13—21no—
60C2×Dic13—21no—
61C2×Dic13—22no—
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13—21no—
65C2×Dic13—41no—
66C2×Dic13—41no—
67C2×Dic13—41no—
68C2×Dic13—41no—
69C2×Dic13—41no—
70C2×Dic13D812yes—
71C8×C13—22no—
72#1055—41no—
73C2×#107D1311yescharacteristic
74#389—131no—
75C4×C4⋊C4—131no—
76#340—131no—
77#340—131no—
78#340—131no—
79#336—131no—
80C22×C13C4×D411yescharacteristic
81C22×C13C22⋊Q811yescharacteristic
82C22×C13#12311yescharacteristic
83C22×C13C2×D811yescharacteristic
84C22×C13#13511yescharacteristic
85C22×C13#13711yescharacteristic
86C22×C13#13711yescharacteristic
87C4×C13—42no—
88C4×C13—42no—
89C4×C13#11711yescharacteristic
90C4×C13C4×Q811yescharacteristic
91C4×C13#12511yescharacteristic
92C4×C13#12611yescharacteristic
93Dic13—22no—
94Dic13—42no—
95Dic13—41no—
96Dic13—81no—
97C22×C8—131no—
98C22×C8C2×D1311yescharacteristic
99C2×C4⋊C4—131no—
100C2×C4⋊C4—131no—
101C2×C4⋊C4—261no—
102C2×C4⋊C4C2×D1311yescharacteristic
103C2×C4⋊C4C2×D1311yescharacteristic
104C2×C42—131no—
105C2×C42—261no—
106#107Dic1314yescomplemented
107#95—261no—
108#95—261no—
109C2×C13#38711yescharacteristic
110C2×C13C4×D811yescharacteristic
111C2×C13#44111yescharacteristic
112C2×C13#47411yescharacteristic
113C2×C13#47911yescharacteristic
114C2×C13#48011yescharacteristic
115C2×C13#48511yescharacteristic
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—131no—
119C22×C4—131no—
120C22×C4—261no—
121C22×C4—261no—
122C22×C4C22×D1311yescharacteristic
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—261no—
126C2×C8—261no—
127C2×C8—261no—
128C2×C8C2×Dic1312yes—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—132no—
132C4⋊C4—261no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4—522no—
136C4⋊C4C2×Dic1312yes—
137C4⋊C4C2×Dic1312yes—
138C42—261no—
139C42—261no—
140C42—522no—
141C13#191811yescharacteristic, complemented, Sylow
142C23D4×D1311yescharacteristic
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—132no—
150C2×C4—261no—
151C2×C4—261no—
152C2×C4—261no—
153C2×C4—262no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—521no—
157C2×C4—521no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4—521no—
161C2×C4#612711yescharacteristic
162C2×C4#612711yescharacteristic
163C2×C4#612911yescharacteristic
164C2×C4Q8×D1311yescharacteristic
165C2×C4#613111yescharacteristic
166C2×C4C22×Dic1311yescharacteristic
167C8—22no—
168C8—521no—
169C22#8814811yescharacteristic
170C22#8815011yescharacteristic
171C22D8×D1311yescharacteristic
172C22#8816611yescharacteristic
173C22#8817211yescharacteristic
174C22#8817211yescharacteristic
175C22D4×Dic1311yescharacteristic
176C4—42no—
177C4—42no—
178C4—262no—
179C4—521no—
180C4—522no—
181C4—1041no—
182C4#8814311yescharacteristic
183C4#8815211yescharacteristic
184C4#8818011yescharacteristic
185C4Q8×Dic1311yescharacteristic
186C2#1171853811yescharacteristic
187C2#1171854311yescharacteristic
188C2#1171854911yescharacteristic
189C2#1171855111yescharacteristic
190C2#1171864211yescharacteristic
191C2D8×Dic1311yescharacteristic
192C2#1171884511yescharacteristic
subgroupG/H
centerC23D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×#107C2
socle, prime radicalC23×C13C2×D4
cosocleC22×C4×C13C23
hypercenterC2×#107D13
hypocenterC13#1918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
17. C13×#107C4semidirect
106. #107Dic13semidirect
141. C13#1918semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1072
#117186462
C4⋊C4×Dic132
#117181432
#117181422
#117181212
#191813