Finite Group Databasebeta

← #13113879

Subgroups — #13113879

Order 1664.

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

normal subgroups only

This group has 202 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#11718705C211yesmaximal, characteristic
3#11718383C211yesmaximal, characteristic
4#11718320C211yesmaximal, characteristic
5C13×#328C211yesmaximal, characteristic
6#11718061C211yesmaximal, characteristic
7#11718044C211yesmaximal, characteristic
8C13×C22⋊Q8C2211yescharacteristic
9#88198—21no—
10C2×C4⋊Dic13C2211yescharacteristic
11#88178C2211yescharacteristic
12C2×#6101C2211yescharacteristic
13#88143—21no—
14#88143—21no—
15#88142—21no—
16#88132—21no—
17#88131—21no—
18C13×C22⋊C8C2211yescharacteristic
19C13×#95C2211yescharacteristic
20#88075—21no—
21#88071—21no—
22#88071—21no—
23C22⋊#1055C2211yescharacteristic
24#88058—21no—
25#88056—21no—
26#88047—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⋊Dic13D411yescharacteristic
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—21no—
48#6101—21no—
49#6101—21no—
50#6101—21no—
51C4×Dic13—21no—
52C4×Dic13—21no—
53C2×#1055—21no—
54#1617—131nomaximal, Sylow
55C23×C13C2×D411yescharacteristic
56Q8×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13C2×D411yescharacteristic
65C2×Dic13—21no—
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—41no—
71C2×Dic13—42no—
72C2×Dic13—41no—
73C2×Dic13Q1612yes—
74Dic26—41no—
75Dic26—81no—
76C8×C13—41no—
77#1055—41no—
78#544—131no—
79#484—131no—
80#484—131no—
81#400—131no—
82#328—131no—
83#328D1311yescharacteristic
84#324—131no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13#12011yescharacteristic
88C22×C13C2×Q1611yescharacteristic
89C22×C13#13711yescharacteristic
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—41no—
93C4×C13—41no—
94C4×C13—81no—
95Dic13—22no—
96Dic13—41no—
97Dic13—41no—
98Dic13—41no—
99Dic13—81no—
100C4⋊Q8—261no—
101C4⋊Q8—261no—
102#125—261no—
103#125—261no—
104C22⋊Q8—131no—
105C22⋊Q8—261no—
106C22⋊Q8C2×D1311yescharacteristic
107#117—261no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—131no—
110#107—261no—
111#107—261no—
112#103—261no—
113#103—261no—
114C22⋊C8—131no—
115C22⋊C8C2×D1311yescharacteristic
116#95—261no—
117#95—261no—
118#95C2×D1311yescharacteristic
119C2×C13—21no—
120C2×C13—21no—
121C2×C13#45111yescharacteristic
122C2×C13#45411yescharacteristic
123C2×C13#45811yescharacteristic
124C2×Q8—131no—
125C2×Q8—261no—
126C2×Q8D5211yescharacteristic
127C22×C4—21no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—261no—
131C22×C4C22×D1311yescharacteristic
132C2×C8—21no—
133C2×C8—261no—
134C4⋊C4—21no—
135C4⋊C4—131no—
136C4⋊C4—261no—
137C4⋊C4—261no—
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⋊C4D5211yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—261no—
149C42—261no—
150C42—261no—
151C13#161711yescharacteristic, complemented, Sylow
152C23D4×D1311yescharacteristic
153Q8—41no—
154Q8—521no—
155Q8—1041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—132no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—261no—
167C2×C4—261no—
168C2×C4—521no—
169C2×C4—522no—
170C2×C4—521no—
171C2×C4C2×D5211yescharacteristic
172C2×C4D4×D1311yescharacteristic
173C8—41no—
174C8—521no—
175C22—21no—
176C22—21no—
177C22#8813611yescharacteristic
178C22#8816911yescharacteristic
179C22Q16×D1311yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—262no—
186C4—521no—
187C4—521no—
188C4—521no—
189C4—1041no—
190C2—21no—
191C2—21no—
192C2#1171840311yescharacteristic
193C2#1171846911yescharacteristic
194C2#1171848811yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#328C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#328D13
hypocenterC13#1617
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
151. C13#1617semidirect

Maximal subgroups

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

subgroupindex
#117193282
#117187052
#117183832
#117183202
C13×#3282
#117180612
#117180442
#161713