Finite Group Databasebeta

← #13113845

Subgroups — #13113845

Order 1664.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#11719328C211yesmaximal, characteristic
2#11718704C211yesmaximal, characteristic
3#11718382C211yesmaximal, characteristic
4#11718322C211yesmaximal, characteristic
5C13×#328C211yesmaximal, characteristic
6#11718061C211yesmaximal, characteristic
7#11718044C211yesmaximal, characteristic
8C13×C22⋊Q8C2211yescharacteristic
9#88198—21no—
10C2×C4⋊Dic13—21no—
11C2×C4⋊Dic13C2211yescharacteristic
12#88178C2211yescharacteristic
13C2×#6101C2211yescharacteristic
14#88143—21no—
15#88143—21no—
16#88142—21no—
17#88132—21no—
18#88131—21no—
19C13×C22⋊C8C2211yescharacteristic
20C13×#95C2211yescharacteristic
21#88075—21no—
22#88071—21no—
23C22⋊#1055C2211yescharacteristic
24#88057—21no—
25#88056—21no—
26#88048—21no—
27C2×Q8×C13D411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13C2311yescharacteristic
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32C22×Dic13D411yescharacteristic
33C2×Dic26—21no—
34C2×Dic26D411yescharacteristic
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4D411yescharacteristic
38C13×C22⋊C4—21no—
39C22⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—42no—
44C4⋊Dic13D411yescharacteristic
45#6101—21no—
46#6101—21no—
47#6101—21no—
48#6101—21no—
49#6101—21no—
50#6101—21no—
51#6101—21no—
52C4×Dic13—21no—
53C4×Dic13—21no—
54C2×#1055—21no—
55#1611—131nomaximal, Sylow
56C23×C13C2×D411yescharacteristic
57Q8×C13—41no—
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13C2×D411yescharacteristic
65C2×C4×C13C2×D411yescharacteristic
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13—41no—
72C2×Dic13—41no—
73C2×Dic13—41no—
74C2×Dic13—41no—
75C2×Dic13SD1612yes—
76Dic26—41no—
77Dic26—81no—
78C8×C13—41no—
79#1055—41no—
80#544—131no—
81#483—131no—
82#483—131no—
83#398—131no—
84#328—131no—
85#328D1311yescharacteristic
86#324—131no—
87C22×C13—21no—
88C22×C13—21no—
89C22×C13#12011yescharacteristic
90C22×C13C2×SD1611yescharacteristic
91C22×C13#13711yescharacteristic
92C4×C13—21no—
93C4×C13—21no—
94C4×C13—42no—
95C4×C13—41no—
96C4×C13—41no—
97Dic13—22no—
98Dic13—41no—
99Dic13—41no—
100Dic13—41no—
101Dic13—81no—
102C4⋊Q8—261no—
103C4⋊Q8—261no—
104#125—261no—
105#125—261no—
106C22⋊Q8—131no—
107C22⋊Q8—261no—
108C22⋊Q8C2×D1311yescharacteristic
109#117—261no—
110C2×C4⋊C4—131no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4—261no—
113#106—261no—
114#106—261no—
115#103—261no—
116#103—261no—
117C22⋊C8—131no—
118C22⋊C8C2×D1311yescharacteristic
119#95—261no—
120#95C2×D1311yescharacteristic
121C2×C13—21no—
122C2×C13—21no—
123C2×C13#44811yescharacteristic
124C2×C13#45611yescharacteristic
125C2×C13#45811yescharacteristic
126C2×Q8—131no—
127C2×Q8—261no—
128C2×Q8D5211yescharacteristic
129C22×C4—21no—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—261no—
133C22×C4C22×D1311yescharacteristic
134C2×C8—21no—
135C2×C8—261no—
136C4⋊C4—21no—
137C4⋊C4—131no—
138C4⋊C4—261no—
139C4⋊C4—261no—
140C4⋊C4—261no—
141C4⋊C4—261no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4—261no—
145C4⋊C4—261no—
146C4⋊C4—261no—
147C4⋊C4—261no—
148C4⋊C4—522no—
149C4⋊C4D5211yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—261no—
152C42—261no—
153C42—261no—
154C13#161111yescharacteristic, complemented, Sylow
155C23D4×D1311yescharacteristic
156Q8—41no—
157Q8—521no—
158Q8—1041no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—132no—
166C2×C4—261no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—521no—
172C2×C4—521no—
173C2×C4—521no—
174C2×C4—521no—
175C2×C4C2×D5211yescharacteristic
176C2×C4D4×D1311yescharacteristic
177C8—41no—
178C8—521no—
179C22—21no—
180C22—21no—
181C22#8813611yescharacteristic
182C22SD16×D1311yescharacteristic
183C22#8817211yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—262no—
190C4—521no—
191C4—521no—
192C4—521no—
193C4—1041no—
194C2—21no—
195C2—21no—
196C2#1171840311yescharacteristic
197C2#1171846711yescharacteristic
198C2#1171848711yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#328C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#328D13
hypocenterC13#1611
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
154. C13#1611semidirect

Maximal subgroups

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

subgroupindex
#117193282
#117187042
#117183822
#117183222
C13×#3282
#117180612
#117180442
#161113