Finite Group Databasebeta

← #16788902

Subgroups — #16788902

Order 3328.

204 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 66 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#13131228C211yesmaximal, characteristic, complemented
2#13131226C211yesmaximal, characteristic, complemented
3#13129864C211yesmaximal, characteristic, complemented
4#13129801C211yesmaximal, characteristic, complemented
5#13129800C211yesmaximal, characteristic, complemented
6#13129752C211yesmaximal, characteristic, complemented
7#13116719C211yesmaximal, characteristic
8#11719162—21no—
9#11719096—21no—
10#11718857C2211yescharacteristic
11#11718855C411yescharacteristic
12#11718556C2211yescharacteristic
13#11718304—21no—
14#11718270—21no—
15#11718261C2211yescharacteristic
16#11718261C2211yescharacteristic
17#11718258C2211yescharacteristic
18#11718251C2211yescharacteristic
19C13×#359C411yescharacteristic
20#11718102C411yescharacteristic
21#11718094C2211yescharacteristic
22#11718085C411yescharacteristic
23C13×#135C2×C411yescharacteristic
24#88202—21no—
25#88161—21no—
26#88158C2×C411yescharacteristic
27C4×#1057—21no—
28#88106—21no—
29#88106—21no—
30#88106—41no—
31C2×#6092—41no—
32C2×#6092D411yescharacteristic
33C2×#6092D411yescharacteristic
34#88098—41no—
35D13⋊C16—41no—
36C2×C13×C16C2×C411yescharacteristic
37C13×#108C2×C411yescharacteristic
38#88077—21no—
39#88069C811yescharacteristic, complemented
40#88068C811yescharacteristic, complemented
41#88067C811yescharacteristic, complemented
42#88066C811yescharacteristic, complemented
43#88065—21no—
44#88059C2×C411yescharacteristic
45C8×Dic13C2311yescharacteristic
46C2×#6090C2×C411yescharacteristic
47#12068—131nomaximal, Sylow
48C13×#41—21no—
49#6127—21no—
50C2×#1057—41no—
51C13×Q16C2×C811yescharacteristic
52C13×SD16—21no—
53C13×D8C2×C811yescharacteristic
54C13×M16—21no—
55C2×C8×C13C22×C411yescharacteristic
56C4×Dic13#4111yescharacteristic
57#6099—21no—
58#6099—41no—
59C2×#1055—41no—
60C2×#1055C2×D411yescharacteristic
61Dic52C2×C811yescharacteristic
62D104C2×C811yescharacteristic
63#6095—21no—
64#6094—41no—
65C8×D13—41no—
66#6092—21no—
67#6092—21no—
68#6092—41no—
69#6092—41no—
70C13×C16—21no—
71#6090C2×C811yescharacteristic
72#6090C2×C811yescharacteristic
73#2179—131no—
74#2171—131no—
75#2171—131no—
76#1369—131no—
77#1336—131no—
78#1336—131no—
79#1313—131no—
80Q8×C13—21no—
81D4×C13—21no—
82D4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13C4×D411yescharacteristic
85C22⋊D13—41no—
86C2×Dic13—21no—
87D52—21no—
88C4×D13—41no—
89Dic26—21no—
90#1057—81no—
91C8×C13—41no—
92C8×C13C22×C811yescharacteristic
93C8×C13#13111yescharacteristic
94#1055—41no—
95#1055AGL(1,ℤ/8)11yescharacteristic
96#1055AGL(1,ℤ/8)11yescharacteristic
97#508—131no—
98#504—261no—
99#504—261no—
100#443—131no—
101#443—131no—
102#368—131no—
103#364—131no—
104#364—131no—
105#359—131no—
106#359#26111yescharacteristic
107#350—261no—
108#350—261no—
109#346—131no—
110#346—131no—
111#322—131no—
112C22×C13—41no—
113C22×C13#44411yescharacteristic
114C2×D13—41no—
115C4×C13—41no—
116C4×C13C8×D411yescharacteristic
117C4×C13#44211yescharacteristic
118Dic13—41no—
119Dic13—41no—
120#135—131no—
121#135C2×#26111yescharacteristic
122#131—261no—
123#131—261no—
124Q32—131no—
125SD32—131no—
126SD32—131no—
127D16—131no—
128M32—261no—
129M32—261no—
130M32—521no—
131M32—521no—
132C2×C16—131no—
133C2×C16—131no—
134C2×C16—131no—
135C2×C16—521no—
136C2×C16—521no—
137C2×C16C2×#26111yescharacteristic
138#108—131no—
139#108C2×#26111yescharacteristic
140#104—261no—
141#104—261no—
142C4×C8—131no—
143C4×C8—261no—
144C2×C13—21no—
145C2×C13—81no—
146C2×C13#158011yescharacteristic
147D13—81no—
148#41—21no—
149#41—261no—
150Q16—131no—
151Q16D13⋊C811yescharacteristic
152SD16—21no—
153SD16—261no—
154D8—131no—
155D8D13⋊C811yescharacteristic
156M16—21no—
157M16—261no—
158M16—521no—
159M16—521no—
160C2×C8—131no—
161C2×C8—521no—
162C2×C8—521no—
163C2×C8—521no—
164C2×C8C22×#26111yescharacteristic
165C42—131no—
166C16—21no—
167C16—131no—
168C16—131no—
169C16—261no—
170C16—261no—
171C16—521no—
172C16—521no—
173C13#1206811yescharacteristic, complemented, Sylow
174Q8—21no—
175Q8—261no—
176D4—21no—
177D4—41no—
178D4—261no—
179D4—521no—
180C2×C4—41no—
181C2×C4—261no—
182C2×C4—521no—
183C2×C4D4×#26111yescharacteristic
184C8—41no—
185C8—131no—
186C8—131no—
187C8—521no—
188C8—1041no—
189C8C2×D13⋊C811yescharacteristic
190C8#8823811yescharacteristic
191C22—41no—
192C22—521no—
193C22#1171910811yescharacteristic
194C4—41no—
195C4—521no—
196C4—521no—
197C4#1171906311yescharacteristic
198C4#1171910211yescharacteristic
199C2—21no—
200C2—81no—
201C2—1041no—
202C2#1313043311yescharacteristic
subgroupG/H
centerC4#11719102
commutatorC8×C13C22×C8
FrattiniC2×C8C22×#261
FittingC13×#359C4
socleC2×C13#1580
prime radical#11718855C4
cosocleC8×Dic13C23
hypercenter#359#261
hypocenterC13#12068
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
1. #13131228C2semidirect
2. #13131226C2semidirect
3. #13129864C2semidirect
4. #13129801C2semidirect
5. #13129800C2semidirect
6. #13129752C2semidirect
39. #88069C8semidirect
40. #88068C8semidirect
41. #88067C8semidirect
42. #88066C8semidirect
173. C13#12068semidirect

Maximal subgroups

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

subgroupindex
#131312282
#131312262
#131298642
#131298012
#131298002
#131297522
#131167192
#1206813