Finite Group Databasebeta

← #15767712

Subgroups — #15767712

Order 3328.

310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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#13115011C211yesmaximal, characteristic
2#13113508C212yesmaximal
3#13112694C212yesmaximal
4#13112681C211yesmaximal, characteristic
5C13×#1960C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#103—21no—
8C2×C13×#103—21no—
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11C2×#88059—21no—
12C2×#88059—21no—
13#11718586C2212yes—
14#11718585C2212yes—
15#11718139—24no—
16C22×Q8×C13—21no—
17C22×C8×C13D411yescharacteristic
18C22×C8×C13D411yescharacteristic
19C13×C4⋊Q8—22no—
20C13×C4⋊Q8—21no—
21C13×C4⋊Q8D412yes—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—21no—
24C2×C42×C13C2311yescharacteristic
25C2×#6099—22no—
26C13×#103—42no—
27C13×#103—42no—
28C13×#97—22no—
29C13×#95—22no—
30C22⋊#1055—22no—
31#88059—42no—
32#88059—42no—
33C4⋊#1055—22no—
34C4⋊#1055—22no—
35C4⋊#1055—22no—
36C4×#1055—22no—
37#10632—131nomaximal, Sylow
38C2×Q8×C13—22no—
39C2×Q8×C13—41no—
40C2×Q8×C13—41no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13#4112yes—
48C2×C8×C13—21no—
49C2×C8×C13—21no—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13D812yes—
53C2×C8×C13SD1612yes—
54C13×C4⋊C4—24no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C42×C13C2×D411yescharacteristic
59C42×C13#4111yescharacteristic
60C42×C13#4112yes—
61#6099—42no—
62#6099—42no—
63C2×#1055—42no—
64C2×#1055—42no—
65#1960D1311yescharacteristic
66#1849—131no—
67#1546—132no—
68#1286—132no—
69#1281—131no—
70C23×C13#12411yescharacteristic
71Q8×C13—42no—
72Q8×C13—42no—
73Q8×C13—81no—
74Q8×C13—81no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—81no—
78C2×C4×C13—81no—
79C2×C4×C13—82no—
80C2×C4×C13—81no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13#12312yes—
83C2×C4×C13#12311yescharacteristic
84C2×C4×C13#12612yes—
85C2×C4×C13C2×D811yescharacteristic
86C2×C4×C13C2×SD1611yescharacteristic
87C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C13#13711yescharacteristic
89C8×C13—22no—
90C8×C13—22no—
91#1055—82no—
92#1055—82no—
93C2×C4⋊Q8C2×D1311yescharacteristic
94#431—132no—
95C2×#108—261no—
96C2×#108—261no—
97#423—132no—
98C2×#103—21no—
99C2×#103—21no—
100C2×#97C2×D1311yescharacteristic
101#382C2×D1311yescharacteristic
102#332—264no—
103C22×C13—22no—
104C22×C13#39711yescharacteristic
105C22×C13#48611yescharacteristic
106C22×C13#48911yescharacteristic
107C4×C13—22no—
108C4×C13—22no—
109C4×C13—82no—
110C4×C13—161no—
111C4×C13#45911yescharacteristic
112C4×C13#46111yescharacteristic
113C4×C13#48011yescharacteristic
114C4×C13#48111yescharacteristic
115C22×Q8—21no—
116C2×M16—262no—
117C22×C8C22⋊D1311yescharacteristic
118C22×C8C22⋊D1311yescharacteristic
119C4⋊Q8—21no—
120C4⋊Q8—22no—
121C4⋊Q8D5212yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—21no—
124C2×C42C22×D1311yescharacteristic
125#108—522no—
126#108—522no—
127C4⋊C8—262no—
128C4⋊C8—262no—
129C4⋊C8—262no—
130#103—42no—
131#103—42no—
132C22⋊C8—262no—
133#97—22no—
134C4×C8—262no—
135#95—22no—
136C2×C13—21no—
137C2×C13—21no—
138C2×C13#207111yescharacteristic
139C2×C13#208212yes—
140C2×Q8—22no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4#612912yes—
149C22×C4C2×C22⋊D1311yescharacteristic
150M16—522no—
151M16—522no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—522no—
157C2×C8—522no—
158C2×C8#610412yes—
159C2×C8#610512yes—
160C4⋊C4—24no—
161C4⋊C4—42no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C42C2×D5211yescharacteristic
165C42#612711yescharacteristic
166C42#612912yes—
167C13#1063211yescharacteristic, complemented, Sylow
168C23#8819011yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—81no—
172Q8—81no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4#8813312yes—
180C2×C4#8814012yes—
181C2×C4#8818411yescharacteristic
182C2×C4C2×#610411yescharacteristic
183C2×C4C2×#610511yescharacteristic
184C2×C4#8818911yescharacteristic
185C2×C4#8820311yescharacteristic
186C2×C4#8820511yescharacteristic
187C8—22no—
188C8—22no—
189C8—1042no—
190C8—1042no—
191C22—22no—
192C22#1171861411yescharacteristic
193C22#1171871611yescharacteristic
194C22#1171873111yescharacteristic
195C4—22no—
196C4—22no—
197C4—82no—
198C4—161no—
199C4#1171867611yescharacteristic
200C4#1171868011yescharacteristic
201C4#1171869411yescharacteristic
202C4#1171869511yescharacteristic
203C2—21no—
204C2—21no—
205C2#1311623911yescharacteristic
206C2#1311630012yes—
subgroupG/H
centerC22#11718614
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1960C2
socleC22×C13#397
prime radicalC23×C13#124
hypercenter#1960D13
hypocenterC13#10632
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
167. C13#10632semidirect

Maximal subgroups

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

subgroupindex
#131150112
#131135082
#131126942
#131126812
C13×#19602
#1063213