Finite Group Databasebeta

← #15776261

Subgroups — #15776261

Order 3328.

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

normal subgroups only

This group has 342 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#13117048C212yesmaximal, complemented
2#13116389C211yesmaximal, characteristic, complemented
3#13112821C212yesmaximal, complemented
4#13112774C211yesmaximal, characteristic, complemented
5C13×#3199C211yesmaximal, characteristic
6C13×#535—21no—
7C13×#482—22no—
8C13×#469C2212yes—
9C13×#466—21no—
10C13×#447—22no—
11C13×#408C2211yescharacteristic
12#11718897—21no—
13#11718786C2211yescharacteristic, complemented
14#11718763—21no—
15#11718155—22no—
16#11718149C2211yescharacteristic, complemented
17#11718145C2212yescomplemented
18#11718079—22no—
19C2×C13×#41D411yescharacteristic
20C22×D4×C13—21no—
21C2×C13×D8—21no—
22C2×C13×D8D412yes—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13D411yescharacteristic
25C13×#127—41no—
26C13×#124—41no—
27C13×#121—22no—
28C13×#121—22no—
29C13×#120—41no—
30C13×#120—41no—
31C13×#117—21no—
32#88180—21no—
33C2×#6099—21no—
34C13×#107—21no—
35C13×#106D412yes—
36C13×#102—22no—
37C13×#102—22no—
38C13×C22⋊C8—22no—
39#88077—42no—
40#88059—22no—
41#88054—42no—
42#88052—22no—
43#12301—131nomaximal, Sylow
44C24×C13—41no—
45C13×#41—41no—
46C13×#41—41no—
47C2×Q8×C13SD1611yescharacteristic
48C2×D4×C13—21no—
49C2×D4×C13—22no—
50C2×D4×C13—41no—
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—81no—
54C2×D4×C13—81no—
55C2×D4×C13SD1611yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13C2×D411yescharacteristic
58C13×D8—42no—
59C13×D8—81no—
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D412yes—
64C13×C4⋊C4—22no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—41no—
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#3199D1311yescharacteristic
77#2238—132no—
78#2098—131no—
79#1339—132no—
80#1321—131no—
81C23×C13—21no—
82C23×C13—42no—
83C23×C13—82no—
84C23×C13—162no—
85C23×C13AGL(1,ℤ/8)11yescharacteristic
86Q8×C13—41no—
87D4×C13—41no—
88D4×C13—42no—
89D4×C13—42no—
90D4×C13—81no—
91D4×C13—82no—
92D4×C13—162no—
93D4×C13—162no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13#12011yescharacteristic
101C2×C4×C13C2×SD1611yescharacteristic
102C2×Dic13—42no—
103C8×C13—22no—
104C8×C13—41no—
105#1055—81no—
106#535—21no—
107#482—22no—
108#469C2×D1312yes—
109#466—21no—
110#447—22no—
111#430—131no—
112#424—261no—
113#421—261no—
114#408C2×D1311yescharacteristic
115#365—262no—
116#361—262no—
117#349—132no—
118H(3,ℤ/4)—131no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13—42no—
122C22×C13—41no—
123C22×C13—82no—
124C22×C13—82no—
125C22×C13—82no—
126C22×C13—164no—
127C22×C13#45011yescharacteristic
128C4×C13—21no—
129C4×C13—41no—
130C4×C13—82no—
131C4×C13#45311yescharacteristic
132C4×C13#45811yescharacteristic
133Dic13—82no—
134C2×#41C22⋊D1311yescharacteristic
135C22×D4—21no—
136C2×D8—21no—
137C2×D8C22⋊D1312yes—
138C2×M16—261no—
139C2×M16C22×D1311yescharacteristic
140C22×C8C22⋊D1311yescharacteristic
141#127—41no—
142#124—41no—
143#121—22no—
144#121—22no—
145#120—41no—
146#120—41no—
147#117—21no—
148#117—261no—
149M32—262no—
150#108—262no—
151#107—21no—
152#106C22⋊D1312yes—
153C4⋊C8—522no—
154#104—522no—
155#102—22no—
156#102—22no—
157C22⋊C8—22no—
158C2×C13—21no—
159C2×C13—41no—
160C2×C13—81no—
161C2×C13—162no—
162C2×C13#161311yescharacteristic
163C24—41no—
164#41—41no—
165#41—41no—
166C2×Q8#610511yescharacteristic
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—41no—
170C2×D4—42no—
171C2×D4—42no—
172C2×D4—81no—
173C2×D4—81no—
174C2×D4#610511yescharacteristic
175C22×C4—21no—
176C22×C4C2×C22⋊D1311yescharacteristic
177D8—42no—
178D8—81no—
179M16—41no—
180M16—521no—
181M16—521no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—521no—
185C2×C8C2×C22⋊D1312yes—
186C4⋊C4—22no—
187C4⋊C4—521no—
188C22⋊C4—42no—
189C22⋊C4—41no—
190C22⋊C4—42no—
191C22⋊C4—521no—
192C42—41no—
193C42—262no—
194C16—522no—
195C13#1230111yescharacteristic, complemented, Sylow
196C23—21no—
197C23—42no—
198C23—82no—
199C23—162no—
200C23#8818611yescharacteristic
201Q8—41no—
202D4—41no—
203D4—42no—
204D4—42no—
205D4—81no—
206D4—82no—
207D4—162no—
208D4—162no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—522no—
216C2×C4C2×#610511yescharacteristic
217C2×C4#8820711yescharacteristic
218C8—22no—
219C8—41no—
220C8—1041no—
221C22—21no—
222C22—41no—
223C22—42no—
224C22—41no—
225C22—82no—
226C22—82no—
227C22—82no—
228C22—164no—
229C22#1171887911yescharacteristic
230C4—21no—
231C4—41no—
232C4—82no—
233C4—1042no—
234C4#1171890211yescharacteristic
235C4#1171890411yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—162no—
240C2#1311385611yescharacteristic
subgroupG/H
centerC2#13113856
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
Fitting, prime radicalC13×#3199C2
socleC2×C13#1613
hypercenter#3199D13
hypocenterC13#12301
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3199

Complements

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

NH ≅ G/Ntype
1. #13117048C2semidirect
2. #13116389C2semidirect
3. #13112821C2semidirect
4. #13112774C2semidirect
13. #11718786C22semidirect
16. #11718149C22semidirect
17. #11718145C22semidirect
195. C13#12301semidirect

Maximal subgroups

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

subgroupindex
#131170482
#131163892
#131128212
#131127742
C13×#31992
#1230113