Finite Group Databasebeta

← #16791479

Subgroups — #16791479

Order 3328.

184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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#13131237C211yesmaximal, characteristic, complemented
2#13131235C211yesmaximal, characteristic, complemented
3#13129999C211yesmaximal, characteristic, complemented
4#13129988C211yesmaximal, characteristic, complemented
5#13129987C211yesmaximal, characteristic, complemented
6#13129942C211yesmaximal, characteristic, complemented
7#13117144C211yesmaximal, characteristic
8#11719111—21no—
9#11719103—21no—
10#11718580C2211yescharacteristic
11#11718573C2211yescharacteristic
12#11718281—21no—
13#11718277—21no—
14#11718223C2211yescharacteristic
15#11718223C2211yescharacteristic
16C16×#261C2211yescharacteristic
17D13⋊C32C2211yescharacteristic
18C13×SD64C411yescharacteristic, complemented
19#11718114C411yescharacteristic, complemented
20#11718111C411yescharacteristic, complemented
21#11718041C411yescharacteristic, complemented
22D13×C32C2211yescharacteristic
23#88240—41no—
24#88238—41no—
25#88173—21no—
26#88166—21no—
27#88118—41no—
28#88116—41no—
29#88104—21no—
30#88104—21no—
31C8×#261D411yescharacteristic
32D13⋊C16D411yescharacteristic
33C13×Q32C2×C411yescharacteristic
34C13×D16C2×C411yescharacteristic
35#88068—21no—
36#88067—21no—
37Dic104C2×C411yescharacteristic
38D208C2×C411yescharacteristic
39C16×D13C2311yescharacteristic
40#88036—21no—
41C13×C32C2×C411yescharacteristic
42#88034C2×C411yescharacteristic
43#13656—131nomaximal, Sylow
44#6131—41no—
45#6129—41no—
46#6122—81no—
47C2×#1057—81no—
48C4×#261D811yescharacteristic
49#6118—41no—
50#6118—41no—
51#6118—81no—
52D13⋊C8—81no—
53D13⋊C8D811yescharacteristic
54C13×Q16—21no—
55C13×D8—21no—
56#6106—41no—
57#6105—41no—
58Dic52—21no—
59D104—21no—
60C8×D13C2×D411yescharacteristic
61#6092—21no—
62C13×C16C22×C411yescharacteristic
63#6090#4111yescharacteristic
64#2262—131no—
65#2178—131no—
66#2178—131no—
67#1425—131no—
68#1417—131no—
69#1417—131no—
70#1397—131no—
71C2×#261—21no—
72Q8×C13—41no—
73D4×C13—41no—
74C22⋊D13—81no—
75C2×Dic13—81no—
76D52—41no—
77D52—81no—
78C4×D13—81no—
79C4×D13C2×D811yescharacteristic
80Dic26—41no—
81#1057—81no—
82#1057—81no—
83#1057D1611yescharacteristic
84#1057D1611yescharacteristic
85C8×C13C4×D411yescharacteristic
86#1055#13511yescharacteristic
87#508—131no—
88#508—131no—
89#443—261no—
90#443—261no—
91Q64—131no—
92SD64—131no—
93SD64#26111yescharacteristic, complemented
94D32—131no—
95C2×C32—131no—
96C2×C32—131no—
97#368—131no—
98#368—131no—
99#359—261no—
100#359—261no—
101C4×C16—131no—
102C22×C13—81no—
103C2×D13—81no—
104C2×D13#50811yescharacteristic
105#261—41no—
106C4×C13—81no—
107C4×C13C4×D811yescharacteristic
108Dic13—81no—
109Dic13C2×D1611yescharacteristic
110#135—261no—
111#135—261no—
112#131—521no—
113#131—521no—
114Q32—131no—
115Q32C2×#26111yescharacteristic
116SD32—261no—
117SD32—261no—
118D16—131no—
119D16C2×#26111yescharacteristic
120C2×C16—131no—
121C2×C16—131no—
122#108—261no—
123#108—261no—
124#104—521no—
125#104—521no—
126C4×C8—131no—
127C32—131no—
128C32—261no—
129C32C2×#26111yescharacteristic
130C2×C13—161no—
131C2×C13C4×D1611yescharacteristic
132D13—21no—
133D13—161no—
134#41—521no—
135#41—521no—
136Q16—21no—
137Q16—261no—
138SD16—521no—
139SD16—521no—
140D8—21no—
141D8—261no—
142M16—521no—
143M16—521no—
144M16—1041no—
145M16—1041no—
146C2×C8—131no—
147C2×C8—131no—
148C2×C8—1041no—
149C2×C8—1041no—
150C42—131no—
151C16—131no—
152C16—261no—
153C16C22×#26111yescharacteristic
154C13#1365611yescharacteristic, complemented, Sylow
155Q8—41no—
156Q8—521no—
157D4—41no—
158D4—521no—
159D4—1041no—
160D4—1041no—
161C2×C4—131no—
162C2×C4—261no—
163C2×C4—1041no—
164C2×C4—1041no—
165C8—131no—
166C8—131no—
167C8—131no—
168C8—1041no—
169C8—1041no—
170C8D4×#26111yescharacteristic
171C22—81no—
172C22—131no—
173C22—1041no—
174C4—81no—
175C4—131no—
176C4—521no—
177C4—1041no—
178C4D8×#26111yescharacteristic
179C2—161no—
180C2—261no—
181C2—2081no—
182C2D16×#26111yescharacteristic
subgroupG/H
centerC2D16×#261
commutatorC13×C16C22×C4
FrattiniC16C22×#261
FittingC13×SD64C4
socleC2×C13C4×D16
prime radical#13117144C2
cosocleC16×D13C23
hypercenterSD64#261
hypocenterC13#13656
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
1. #13131237C2semidirect
2. #13131235C2semidirect
3. #13129999C2semidirect
4. #13129988C2semidirect
5. #13129987C2semidirect
6. #13129942C2semidirect
18. C13×SD64C4semidirect
19. #11718114C4semidirect
20. #11718111C4semidirect
21. #11718041C4semidirect
93. SD64#261semidirect
154. C13#13656semidirect

Maximal subgroups

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

subgroupindex
#131312372
#131312352
#131299992
#131299882
#131299872
#131299422
#131171442
#1365613