Finite Group Databasebeta

← #13114154

Subgroups — #13114154

Order 1664.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#11719389C211yesmaximal, characteristic
2#11718721C211yesmaximal, characteristic, complemented
3#11718375C211yesmaximal, characteristic, complemented
4#11718363C211yesmaximal, characteristic, complemented
5C13×#329C211yesmaximal, characteristic, complemented
6#11718057C211yesmaximal, characteristic, complemented
7#11718056C211yesmaximal, characteristic, complemented
8C13×#124C2211yescharacteristic
9#88200—21no—
10C2×#6107—21no—
11#88193—21no—
12C2×#6105—21no—
13#88140—21no—
14#88138—21no—
15#88137—21no—
16#88132—21no—
17#88129C2211yescharacteristic
18#88124C2211yescharacteristic
19#88123C2211yescharacteristic
20C13×#97C2211yescharacteristic
21C13×#97C2211yescharacteristic
22#88061—21no—
23#88058—21no—
24#88057—21no—
25#88056—21no—
26#88043C2211yescharacteristic
27C2×Q8×C13D411yescharacteristic
28C2×D4×C13D411yescharacteristic
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C22×Dic13—21no—
32C2×D52D411yescharacteristic
33C2×C4×D13—21no—
34C2×Dic26—21no—
35C2×Dic26D411yescharacteristic
36C2×C8×C13—21no—
37C2×C8×C13—21no—
38C13×C22⋊C4—21no—
39C13×C22⋊C4—21no—
40C42×C13C2311yescharacteristic
41C22⋊Dic13—21no—
42#6107—42no—
43#6105—42no—
44#6103—21no—
45#6103—21no—
46#6103—21no—
47C4⋊Dic13—21no—
48C4⋊Dic13—21no—
49C4⋊Dic13—21no—
50C4⋊Dic13D411yescharacteristic
51C4⋊Dic13D411yescharacteristic
52#6101—21no—
53#6101—21no—
54#6101—21no—
55C2×#1055—21no—
56#1661—131nomaximal, Sylow
57C23×C13—21no—
58C22×D13—21no—
59Q8×C13—41no—
60D4×C13—41no—
61C2×C4×C13—21no—
62C2×C4×C13C2×D411yescharacteristic
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13C2×D411yescharacteristic
65C22⋊D13—81no—
66C22⋊D13—81no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—41no—
71C2×Dic13—81no—
72D52—41no—
73C4×D13—81no—
74Dic26—41no—
75Dic26—41no—
76Dic26—41no—
77C8×C13—22no—
78C8×C13—41no—
79#1055—22no—
80#562—131no—
81#501—131no—
82#497—131no—
83#489—131no—
84#330—131no—
85#329—131no—
86#329D1311yescharacteristic, complemented
87C22×C13—41no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13#12011yescharacteristic
91C2×D13—41no—
92C2×D13—41no—
93C2×D13—41no—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—21no—
97C4×C13—41no—
98Dic13—41no—
99Dic13—41no—
100Dic13—41no—
101Dic13—81no—
102C2×Q16—261no—
103C2×SD16—261no—
104C4⋊Q8—131no—
105#125—131no—
106#124—131no—
107#124C2×D1311yescharacteristic
108#123—261no—
109#123—261no—
110C22⋊Q8—261no—
111C22⋊Q8—261no—
112#121—261no—
113#121—261no—
114#107—261no—
115#106—261no—
116#103—261no—
117#102—261no—
118#97—131no—
119#97C2×D1311yescharacteristic
120#97C2×D1311yescharacteristic
121C2×C13—81no—
122C2×C13#45311yescharacteristic
123C2×C13#45511yescharacteristic
124C2×C13#45611yescharacteristic
125D13—81no—
126C2×Q8—131no—
127C2×Q8—261no—
128C2×Q8D5211yescharacteristic
129C2×D4—131no—
130C2×D4—261no—
131C2×D4—261no—
132C2×D4D5211yescharacteristic
133C22×C4—261no—
134C22×C4—261no—
135Q16—522no—
136SD16—522no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—261no—
140C4⋊C4—131no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4—261no—
145C4⋊C4—261no—
146C4⋊C4—261no—
147C4⋊C4—261no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—261no—
151C22⋊C4—261no—
152C22⋊C4—261no—
153C22⋊C4—261no—
154C42C22×D1311yescharacteristic
155C13#166111yescharacteristic, complemented, Sylow
156C23—21no—
157C23—261no—
158Q8—41no—
159Q8—521no—
160Q8—521no—
161Q8—521no—
162D4—41no—
163D4—521no—
164D4—1041no—
165D4—1041no—
166C2×C4—21no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—521no—
171C2×C4—1041no—
172C2×C4—1041no—
173C2×C4C2×D5211yescharacteristic
174C2×C4D4×D1311yescharacteristic
175C2×C4D4×D1311yescharacteristic
176C8—22no—
177C8—41no—
178C8—262no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—521no—
183C22—521no—
184C22—521no—
185C22#8813611yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—521no—
191C4—521no—
192C4—521no—
193C4—1041no—
194C2—81no—
195C2—1041no—
196C2#1171840811yescharacteristic
197C2#1171848611yescharacteristic
198C2#1171848711yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#329C2
socleC22×C13#120
prime radical#11719389C2
hypercenter#329D13
hypocenterC13#1661
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11718721C2semidirect
3. #11718375C2semidirect
4. #11718363C2semidirect
5. C13×#329C2semidirect
6. #11718057C2semidirect
7. #11718056C2semidirect
86. #329D13semidirect
155. C13#1661semidirect

Maximal subgroups

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

subgroupindex
#117193892
#117187212
#117183752
#117183632
C13×#3292
#117180572
#117180562
#166113