Finite Group Databasebeta

← #13131156

Subgroups — #13131156

Order 1664.

224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D13×#135C211yesmaximal, characteristic
2#11719092C211yesmaximal, characteristic, complemented
3C2×#88098C211yesmaximal, characteristic, complemented
4#11718279C212yesmaximal, complemented
5#11718275C212yesmaximal, complemented
6#41×D13—21no—
7#88237—21no—
8C13×#135C411yescharacteristic, complemented
9#88204—21no—
10#88173C2211yescharacteristic
11Q16×D13C411yescharacteristic, complemented
12#88170—21no—
13SD16×D13—21no—
14#88166C2211yescharacteristic
15D8×D13C411yescharacteristic, complemented
16#88158C411yescharacteristic, complemented
17C2×C8×D13C2211yescharacteristic
18C2×#6092—21no—
19#88102—21no—
20#88101C2212yescomplemented
21#88098—21no—
22#88098C2212yescomplemented
23C13×#41—21no—
24#6131—21no—
25Q8×D13—21no—
26#6129—21no—
27#6129—41no—
28D4×D13—21no—
29D4×D13—41no—
30#6127—21no—
31#6127—41no—
32C2×C4×D13—41no—
33C2×C4×D13D411yescharacteristic
34C22⋊#261—41no—
35C4⋊#261—22no—
36C4×#261—41no—
37C13×Q16C2×C411yescharacteristic
38C13×SD16—21no—
39C13×D8C2×C411yescharacteristic
40C2×C8×C13C2×C411yescharacteristic
41#6107—21no—
42#6106—21no—
43#6105—21no—
44#6104—21no—
45C2×#1055D411yescharacteristic
46Dic52C2×C411yescharacteristic
47D104C2×C411yescharacteristic
48#6095—21no—
49C8×D13C2×C411yescharacteristic
50C8×D13D411yescharacteristic
51C8×D13D411yescharacteristic
52C8×D13C2311yescharacteristic
53#6092—22no—
54#2145—131nomaximal, Sylow
55C22×D13—41no—
56C22×D13D811yescharacteristic
57C2×#261—42no—
58Q8×C13—21no—
59D4×C13—21no—
60D4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13C22⋊C411yescharacteristic
63C22⋊D13—41no—
64C22⋊D13—41no—
65C22⋊D13—41no—
66C2×Dic13—41no—
67C2×Dic13SD1611yescharacteristic
68D52—21no—
69D52—41no—
70C4×D13—41no—
71C4×D13—41no—
72C4×D13—41no—
73C4×D13C22⋊C411yescharacteristic
74C4×D13D811yescharacteristic
75C4×D13SD1611yescharacteristic
76C4×D13C2×D411yescharacteristic
77Dic26—21no—
78Dic26—41no—
79C8×C13C22⋊C411yescharacteristic
80C8×C13C22×C411yescharacteristic
81#1055C22⋊C411yescharacteristic
82#1055C2×D411yescharacteristic
83C2×#135—131no—
84C2×M32—131no—
85#427—131no—
86#360—132no—
87#360—132no—
88C22×C13—41no—
89C22×C13#10211yescharacteristic
90C2×D13—41no—
91C2×D13—41no—
92C2×D13—82no—
93C2×D13#10211yescharacteristic
94C2×D13C2×D811yescharacteristic
95#261—82no—
96C4×C13—41no—
97C4×C13#10211yescharacteristic
98C4×C13C2×C22⋊C411yescharacteristic
99Dic13—41no—
100Dic13#10211yescharacteristic
101Dic13C2×SD1611yescharacteristic
102C2×#41—261no—
103#135—131no—
104#135—131no—
105#135—131no—
106#135—261no—
107#135—261no—
108#135#26111yescharacteristic, complemented
109C2×Q16—131no—
110C2×SD16—261no—
111C2×D8—131no—
112C22×C8—131no—
113#117—261no—
114M32—132no—
115M32—261no—
116C2×C16—261no—
117#107—261no—
118#106—132no—
119C2×C13—21no—
120C2×C13—81no—
121C2×C13C2×#10211yescharacteristic
122D13—21no—
123D13—21no—
124D13—81no—
125#41—21no—
126#41—261no—
127#41—261no—
128#41—261no—
129#41—521no—
130#41—521no—
131C2×Q8—261no—
132C2×D4—261no—
133C2×D4—521no—
134C22×C4—131no—
135C22×C4—521no—
136Q16—131no—
137Q16—261no—
138Q16C2×#26111yescharacteristic
139SD16—21no—
140SD16—261no—
141SD16—261no—
142SD16—261no—
143D8—131no—
144D8—261no—
145D8C2×#26111yescharacteristic
146C2×C8—131no—
147C2×C8—131no—
148C2×C8—131no—
149C2×C8—131no—
150C2×C8—131no—
151C2×C8C2×#26111yescharacteristic
152C4⋊C4—262no—
153C22⋊C4—521no—
154C42—521no—
155C16—262no—
156C13#214511yescharacteristic, complemented, Sylow
157C23—131no—
158C23—521no—
159Q8—21no—
160Q8—261no—
161Q8—521no—
162D4—21no—
163D4—41no—
164D4—261no—
165D4—521no—
166D4—521no—
167D4—521no—
168D4—521no—
169C2×C4—41no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—522no—
180C2×C4C22⋊#26111yescharacteristic
181C8—131no—
182C8—131no—
183C8C22⋊#26111yescharacteristic
184C8C22×#26111yescharacteristic
185C22—41no—
186C22—131no—
187C22—131no—
188C22—521no—
189C22—521no—
190C22—1042no—
191C22#8811511yescharacteristic
192C4—41no—
193C4—131no—
194C4—131no—
195C4—521no—
196C4—1042no—
197C4#8811511yescharacteristic
198C4C2×C22⋊#26111yescharacteristic
199C2—21no—
200C2—81no—
201C2—261no—
202C2—261no—
203C2—1041no—
204C2C2×#8811511yescharacteristic
subgroupG/H
centerC4#88115
commutatorC8×C13C22×C4
FrattiniC8C22×#261
FittingC13×#135C4
socleC2×C13C2×#102
prime radicalD13×#135C2
cosocleC8×D13C23
hypercenter#135#261
hypocenterC13#2145
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #11719092C2semidirect
3. C2×#88098C2semidirect
4. #11718279C2semidirect
5. #11718275C2semidirect
8. C13×#135C4semidirect
11. Q16×D13C4semidirect
15. D8×D13C4semidirect
16. #88158C4semidirect
20. #88101C22semidirect
22. #88098C22semidirect
108. #135#261semidirect
156. C13#2145semidirect

Maximal subgroups

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

subgroupindex
D13×#1352
#117190922
C2×#880982
#117182792
#117182752
#214513