Finite Group Databasebeta

← #15776266

Subgroups — #15776266

Order 3328.

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

normal subgroups only

This group has 310 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, complemented
2#13116389C211yesmaximal, characteristic
3#13112824C212yesmaximal, complemented
4#13112774C211yesmaximal, characteristic
5C13×#3202C211yesmaximal, characteristic
6C13×#536—21no—
7C13×#485—22no—
8C13×#470C2212yes—
9C13×#467—21no—
10C13×#451—22no—
11C13×#408C2211yescharacteristic
12#11718897—21no—
13#11718786C2211yescharacteristic
14#11718763—21no—
15#11718157—22no—
16#11718149C2211yescharacteristic
17#11718145C2212yes—
18#11718079—22no—
19C2×C13×#41D411yescharacteristic
20C22×Q8×C13—21no—
21C2×C13×Q16—21no—
22C2×C13×Q16D412yes—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13D411yescharacteristic
25C13×C4⋊Q8—41no—
26C13×#124—41no—
27C13×#123—41no—
28C13×#123—41no—
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C13×#117—21no—
32#88180—21no—
33C2×#6099—21no—
34C13×#107—21no—
35C13×#106D412yes—
36C13×#103—22no—
37C13×#103—22no—
38C13×C22⋊C8—22no—
39#88077—42no—
40#88059—22no—
41#88054—42no—
42#88052—22no—
43#12302—131nomaximal, Sylow
44C13×#41—41no—
45C13×#41—41no—
46C2×Q8×C13—22no—
47C2×Q8×C13—41no—
48C2×Q8×C13—81no—
49C2×Q8×C13—81no—
50C2×Q8×C13SD1611yescharacteristic
51C2×D4×C13—21no—
52C2×D4×C13SD1611yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—41no—
55C22×C4×C13C2×D411yescharacteristic
56C13×Q16—42no—
57C13×Q16—81no—
58C13×M16—41no—
59C2×C8×C13—21no—
60C2×C8×C13—41no—
61C2×C8×C13C2×D412yes—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C22⋊C4—41no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C42×C13—41no—
69C22⋊Dic13—41no—
70C4⋊Dic13—41no—
71C4×Dic13—22no—
72#6099—41no—
73#6099—41no—
74C2×#1055—41no—
75#6090—42no—
76#3202D1311yescharacteristic
77#2239—132no—
78#2098—131no—
79#1340—132no—
80#1321—131no—
81C23×C13—21no—
82C23×C13AGL(1,ℤ/8)11yescharacteristic
83Q8×C13—41no—
84Q8×C13—42no—
85Q8×C13—42no—
86Q8×C13—82no—
87D4×C13—41no—
88D4×C13—81no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—82no—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13C2×SD1611yescharacteristic
99C2×Dic13—42no—
100C8×C13—22no—
101C8×C13—41no—
102#1055—81no—
103#536—21no—
104#485—22no—
105#470C2×D1312yes—
106#467—21no—
107#451—22no—
108#430—131no—
109#424—261no—
110#421—261no—
111#408C2×D1311yescharacteristic
112#365—262no—
113#362—262no—
114#349—132no—
115H(3,ℤ/4)—131no—
116C22×C13—21no—
117C22×C13—41no—
118C22×C13—42no—
119C22×C13—41no—
120C22×C13#45011yescharacteristic
121C4×C13—21no—
122C4×C13—41no—
123C4×C13—82no—
124C4×C13—82no—
125C4×C13#45311yescharacteristic
126C4×C13#45811yescharacteristic
127Dic13—82no—
128C2×#41C22⋊D1311yescharacteristic
129C22×Q8—21no—
130C2×Q16—21no—
131C2×Q16C22⋊D1312yes—
132C2×M16—261no—
133C2×M16C22×D1311yescharacteristic
134C22×C8C22⋊D1311yescharacteristic
135C4⋊Q8—41no—
136#124—41no—
137#123—41no—
138#123—41no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141#117—21no—
142#117—261no—
143M32—262no—
144#108—262no—
145#107—21no—
146#106C22⋊D1312yes—
147C4⋊C8—522no—
148#104—522no—
149#103—22no—
150#103—22no—
151C22⋊C8—22no—
152C2×C13—21no—
153C2×C13—41no—
154C2×C13—81no—
155C2×C13#161311yescharacteristic
156#41—41no—
157#41—41no—
158C2×Q8—22no—
159C2×Q8—41no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8#610511yescharacteristic
163C2×D4—21no—
164C2×D4#610511yescharacteristic
165C22×C4—21no—
166C22×C4—41no—
167C22×C4C2×C22⋊D1311yescharacteristic
168Q16—42no—
169Q16—81no—
170M16—41no—
171M16—521no—
172M16—521no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—521no—
176C2×C8C2×C22⋊D1312yes—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—521no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—521no—
185C42—41no—
186C42—262no—
187C16—522no—
188C13#1230211yescharacteristic, complemented, Sylow
189C23—21no—
190C23#8818611yescharacteristic
191Q8—41no—
192Q8—42no—
193Q8—42no—
194Q8—82no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—82no—
205C2×C4—522no—
206C2×C4C2×#610511yescharacteristic
207C2×C4#8820711yescharacteristic
208C8—22no—
209C8—41no—
210C8—1041no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1171887911yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—1042no—
221C4#1171890211yescharacteristic
222C4#1171890411yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1311385611yescharacteristic
subgroupG/H
centerC2#13113856
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
FittingC13×#3202C2
socleC2×C13#1613
prime radicalC2×C13×#41D4
hypercenter#3202D13
hypocenterC13#12302
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3202

Complements

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

NH ≅ G/Ntype
1. #13117053C2semidirect
3. #13112824C2semidirect
188. C13#12302semidirect

Maximal subgroups

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

subgroupindex
#131170532
#131163892
#131128242
#131127742
C13×#32022
#1230213