Finite Group Databasebeta

← #15776244

Subgroups — #15776244

Order 3328.

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

normal subgroups only

This group has 376 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#13116352C211yesmaximal, characteristic, complemented
3#13112827C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic, complemented
5C13×#3192C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C13×#481—22no—
8C13×#469—21no—
9C13×#469C2212yes—
10C13×#447—22no—
11C13×#407C2211yescharacteristic
12#11718868—21no—
13#11718786C2211yescharacteristic, complemented
14#11718785—21no—
15#11718155—22no—
16#11718152C2211yescharacteristic, complemented
17#11718145C2212yescomplemented
18#11718079—22no—
19C22×D4×C13—21no—
20C22×D4×C13—41no—
21C23×C4×C13D411yescharacteristic
22C2×C13×D8—21no—
23C2×C13×D8D412yes—
24C2×C13×M16D411yescharacteristic
25C2×C13×M16C2311yescharacteristic
26C13×#121—22no—
27C13×#121—22no—
28C13×#121—41no—
29C13×#121—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C22⋊C4—41no—
32C2×#6099—21no—
33C2×#6099—21no—
34C13×#106—21no—
35C13×#106D412yes—
36C13×#102—22no—
37C13×#102—22no—
38C13×C22⋊C8—22no—
39C22⋊#1055—42no—
40#88062—42no—
41#88059—22no—
42#88052—22no—
43#12298—131nomaximal, Sylow
44C24×C13—41no—
45C24×C13SD1611yescharacteristic
46C2×D4×C13—22no—
47C2×D4×C13—41no—
48C2×D4×C13—42no—
49C2×D4×C13—42no—
50C2×D4×C13—81no—
51C2×D4×C13—81no—
52C2×D4×C13—84no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13SD1611yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C13×D8—42no—
61C13×D8—81no—
62C13×M16—41no—
63C13×M16—41no—
64C2×C8×C13—21no—
65C2×C8×C13C2×D412yes—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—42no—
69C13×C22⋊C4—42no—
70#6099—41no—
71#6099—41no—
72#6099—41no—
73#6099—41no—
74C2×#1055—22no—
75C2×#1055—41no—
76#6090—42no—
77#3192D1311yescharacteristic
78#2238—132no—
79#2091—131no—
80#1341—132no—
81#1320—131no—
82C23×C13—21no—
83C23×C13—41no—
84C23×C13—42no—
85C23×C13—42no—
86C23×C13—82no—
87C23×C13—82no—
88C23×C13—82no—
89C23×C13C2×SD1611yescharacteristic
90D4×C13—42no—
91D4×C13—42no—
92D4×C13—82no—
93D4×C13—84no—
94D4×C13—84no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—81no—
103C2×C4×C13—82no—
104C2×C4×C13#12011yescharacteristic
105C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
106C8×C13—22no—
107C8×C13—41no—
108#1055—42no—
109#1055—81no—
110C2×#121—21no—
111#481—22no—
112#469—21no—
113#469C2×D1312yes—
114#447—22no—
115#430—131no—
116#430—261no—
117#407—261no—
118#407C2×D1311yescharacteristic
119#365—262no—
120#361—262no—
121#349—132no—
122#338—131no—
123C22×C13—22no—
124C22×C13—21no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—42no—
128C22×C13—41no—
129C22×C13—82no—
130C22×C13—82no—
131C22×C13—81no—
132C22×C13—82no—
133C22×C13—164no—
134C22×C13#45011yescharacteristic
135C4×C13—21no—
136C4×C13—41no—
137C4×C13—82no—
138C4×C13#45311yescharacteristic
139C4×C13#45811yescharacteristic
140C22×D4—21no—
141C22×D4—41no—
142C23×C4C22⋊D1311yescharacteristic
143C2×D8—21no—
144C2×D8C22⋊D1312yes—
145C2×M16—261no—
146C2×M16—261no—
147C2×M16C22⋊D1311yescharacteristic
148C2×M16C22×D1311yescharacteristic
149#121—22no—
150#121—22no—
151#121—41no—
152#121—41no—
153C2×C4⋊C4—21no—
154C2×C22⋊C4—41no—
155M32—262no—
156#108—262no—
157#108—522no—
158#106—21no—
159#106C22⋊D1312yes—
160#102—22no—
161#102—22no—
162C22⋊C8—22no—
163C22⋊C8—522no—
164C2×C13—21no—
165C2×C13—41no—
166C2×C13—42no—
167C2×C13—162no—
168C2×C13#161311yescharacteristic
169C24—41no—
170C24#610511yescharacteristic
171C2×D4—22no—
172C2×D4—41no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—81no—
176C2×D4—81no—
177C2×D4—84no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4#610511yescharacteristic
184C22×C4C2×C22⋊D1311yescharacteristic
185D8—42no—
186D8—81no—
187M16—41no—
188M16—41no—
189M16—521no—
190M16—521no—
191M16—521no—
192M16—521no—
193C2×C8—21no—
194C2×C8—262no—
195C2×C8—521no—
196C2×C8C2×C22⋊D1312yes—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C16—522no—
202C13#1229811yescharacteristic, complemented, Sylow
203C23—21no—
204C23—41no—
205C23—42no—
206C23—42no—
207C23—82no—
208C23—82no—
209C23—82no—
210C23C2×#610511yescharacteristic
211D4—42no—
212D4—42no—
213D4—82no—
214D4—84no—
215D4—84no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—82no—
225C2×C4#8818611yescharacteristic
226C2×C4#8820711yescharacteristic
227C8—22no—
228C8—41no—
229C8—522no—
230C8—1041no—
231C22—22no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22—41no—
237C22—82no—
238C22—82no—
239C22—81no—
240C22—82no—
241C22—164no—
242C22#1171887911yescharacteristic
243C4—21no—
244C4—41no—
245C4—82no—
246C4#1171890211yescharacteristic
247C4#1171890411yescharacteristic
248C2—21no—
249C2—42no—
250C2—41no—
251C2—162no—
252C2#1311385611yescharacteristic
subgroupG/H
centerC2#13113856
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
Fitting, prime radicalC13×#3192C2
socleC2×C13#1613
hypercenter#3192D13
hypocenterC13#12298
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. #13117048C2semidirect
2. #13116352C2semidirect
3. #13112827C2semidirect
4. #13112772C2semidirect
13. #11718786C22semidirect
16. #11718152C22semidirect
17. #11718145C22semidirect
202. C13#12298semidirect

Maximal subgroups

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

subgroupindex
#131170482
#131163522
#131128272
#131127722
C13×#31922
#1229813