Finite Group Databasebeta

← #15776300

Subgroups — #15776300

Order 3328.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117053C212yesmaximal
2#13116411C211yesmaximal, characteristic
3#13112824C212yesmaximal
4#13112787C211yesmaximal, characteristic
5C13×#3255C211yesmaximal, characteristic
6C13×#533—21no—
7C13×#475—22no—
8C13×#470—21no—
9C13×#470C2212yes—
10C13×#462—22no—
11C13×#423C2211yescharacteristic
12#11718786C2211yescharacteristic
13#11718157—22no—
14#11718151—21no—
15#11718149C2211yescharacteristic
16#11718145C2212yes—
17#11718115—21no—
18#11718079—22no—
19C2×C13×Q16—21no—
20C2×C13×Q16D412yes—
21C2×C13×M16D411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8—21no—
25C13×#125—41no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—41no—
28C4×Q8×C13—22no—
29C4×Q8×C13—41no—
30C13×#117—41no—
31C2×C42×C13D411yescharacteristic
32#88180—21no—
33C2×#6099—21no—
34C13×#106—21no—
35C13×#106D412yes—
36C13×C4⋊C8—22no—
37C13×#103—22no—
38C13×#103—22no—
39#88059—22no—
40#88052—22no—
41#12308—131nomaximal, Sylow
42C2×Q8×C13—22no—
43C2×Q8×C13—41no—
44C22×C4×C13—21no—
45C22×C4×C13C2×D411yescharacteristic
46C13×Q16—42no—
47C13×Q16—81no—
48C13×M16—41no—
49C13×M16—41no—
50C2×C8×C13—21no—
51C2×C8×C13C2×D412yes—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—42no—
58C13×C22⋊C4—42no—
59C42×C13—21no—
60C42×C13—42no—
61C42×C13SD1611yescharacteristic
62C42×C13SD1611yescharacteristic
63C22⋊Dic13—41no—
64C4⋊Dic13—41no—
65C4×Dic13—41no—
66#6099—41no—
67#6099—41no—
68C2×#1055—41no—
69#6090—42no—
70#3255D1311yescharacteristic
71#2239—132no—
72#2102—131no—
73#1340—132no—
74#1327—131no—
75C23×C13AGL(1,ℤ/8)11yescharacteristic
76Q8×C13—42no—
77Q8×C13—42no—
78Q8×C13—82no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13#12011yescharacteristic
87C2×C4×C13C2×SD1611yescharacteristic
88C2×Dic13—81no—
89C8×C13—22no—
90C8×C13—41no—
91#1055—81no—
92#533—21no—
93#475—22no—
94#470—21no—
95#470C2×D1312yes—
96#462—22no—
97#430—131no—
98#423C2×D1311yescharacteristic
99#365—262no—
100#362—262no—
101#349—132no—
102#344—261no—
103#339—261no—
104H(3,ℤ/4)—131no—
105C22×C13—21no—
106C22×C13—41no—
107C22×C13#45011yescharacteristic
108C4×C13—22no—
109C4×C13—21no—
110C4×C13—41no—
111C4×C13—82no—
112C4×C13—82no—
113C4×C13#45411yescharacteristic
114C4×C13#45811yescharacteristic
115Dic13—161no—
116C2×Q16—21no—
117C2×Q16C22⋊D1312yes—
118C2×M16—261no—
119C2×M16C22⋊D1311yescharacteristic
120C2×M16C22×D1311yescharacteristic
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123#125—41no—
124C22⋊Q8—22no—
125C22⋊Q8—41no—
126C4×Q8—22no—
127C4×Q8—41no—
128#117—41no—
129#117—261no—
130C2×C42C22⋊D1311yescharacteristic
131M32—262no—
132#108—262no—
133#106—21no—
134#106C22⋊D1312yes—
135C4⋊C8—22no—
136#103—22no—
137#103—22no—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13#161611yescharacteristic
141C2×Q8—22no—
142C2×Q8—41no—
143C22×C4—21no—
144C22×C4C2×C22⋊D1311yescharacteristic
145Q16—42no—
146Q16—81no—
147M16—41no—
148M16—41no—
149M16—521no—
150M16—521no—
151C2×C8—21no—
152C2×C8—521no—
153C2×C8C2×C22⋊D1312yes—
154C4⋊C4—22no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—41no—
159C4⋊C4—42no—
160C4⋊C4—521no—
161C22⋊C4—42no—
162C22⋊C4—521no—
163C42—21no—
164C42—42no—
165C42—521no—
166C42#610511yescharacteristic
167C42#610511yescharacteristic
168C16—522no—
169C13#1230811yescharacteristic, complemented, Sylow
170C23#8818611yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—1041no—
182C2×C4C2×#610511yescharacteristic
183C2×C4#8820711yescharacteristic
184C8—22no—
185C8—41no—
186C8—1041no—
187C22—21no—
188C22—41no—
189C22#1171887911yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—2081no—
196C4#1171890411yescharacteristic
197C4#1171890611yescharacteristic
198C2—21no—
199C2—41no—
200C2#1311387311yescharacteristic
subgroupG/H
centerC2#13113873
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
FittingC13×#3255C2
socleC2×C13#1616
prime radicalC23×C13AGL(1,ℤ/8)
hypercenter#3255D13
hypocenterC13#12308
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3255

Complements

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

NH ≅ G/Ntype
169. C13#12308semidirect

Maximal subgroups

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

subgroupindex
#131170532
#131164112
#131128242
#131127872
C13×#32552
#1230813