Finite Group Databasebeta

← #15777146

Subgroups — #15777146

Order 3328.

230 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117088C211yesmaximal, characteristic, complemented
2#13116667C211yesmaximal, characteristic
3#13114202C211yesmaximal, characteristic
4#13114198C211yesmaximal, characteristic
5#13112909C211yesmaximal, characteristic, complemented
6#13112886C211yesmaximal, characteristic, complemented
7C13×#1362C211yesmaximal, characteristic, complemented
8C13×#494C2211yescharacteristic
9C2×#88069—21no—
10C2×#88069—21no—
11#11718748—21no—
12C2×#88038—21no—
13#11718507—21no—
14#11718360C2211yescharacteristic
15C8×D52C2211yescharacteristic
16C13×C4⋊C16C2211yescharacteristic
17C13×#335C2211yescharacteristic
18#11718139—21no—
19#11718099—21no—
20#11718078—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×Dic52—21no—
27C2×Dic52—21no—
28C2×C8×D13—21no—
29C4×D52D411yescharacteristic
30#88123—21no—
31C2×C13×C16—21no—
32C13×C4⋊C8—21no—
33C4×C8×C13C2311yescharacteristic
34#88069—42no—
35#88069—42no—
36#88061—41no—
37#88060—21no—
38#88058—41no—
39C2×#6090D411yescharacteristic
40C2×#6090D411yescharacteristic
41#88049—41no—
42#88047—41no—
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45#88038—42no—
46#12434—131nomaximal, Sylow
47C2×Q8×C13—41no—
48C2×D52D811yescharacteristic
49C2×C4×D13—21no—
50C2×Dic26—41no—
51C13×Q16—41no—
52C13×Q16—41no—
53C13×Q16—81no—
54C2×C8×C13—41no—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C42×C13C2×D411yescharacteristic
60#6103—21no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C4⋊Dic13D811yescharacteristic
64C2×#1055—21no—
65C2×#1055—41no—
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69C8×D13—41no—
70C8×D13—41no—
71C13×C16—41no—
72#6090—21no—
73#6090D812yes—
74#2247—131no—
75#2169—131no—
76#1669—131no—
77#1669—131no—
78#1372—131no—
79#1362—131no—
80#1362D1311yescharacteristic, complemented
81C22×D13—21no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13#13511yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—81no—
90D52—21no—
91D52—21no—
92C4×D13—41no—
93C4×D13—41no—
94Dic26—81no—
95Dic26—81no—
96C8×C13—21no—
97C8×C13—81no—
98C8×C13C2×D811yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100#1055—41no—
101#1055—81no—
102C2×Q32—261no—
103C2×Q32—261no—
104C2×M32—261no—
105#494—131no—
106#494C2×D1311yescharacteristic
107#474—261no—
108#474—261no—
109C8×D4—131no—
110C4⋊C16C2×D1311yescharacteristic
111C22⋊C16—261no—
112C4×C16—131no—
113#335—131no—
114#335C2×D1311yescharacteristic
115#332—261no—
116#332—261no—
117C22×C13#46611yescharacteristic
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—41no—
121C4×C13—21no—
122C4×C13—161no—
123C4×C13#45911yescharacteristic
124C4×C13#47211yescharacteristic
125C4×C13#51011yescharacteristic
126C4×C13#51011yescharacteristic
127Dic13—41no—
128Dic13—161no—
129C2×Q16—21no—
130C2×Q16—21no—
131C2×Q16—261no—
132C2×Q16—261no—
133C22×C8—261no—
134C4⋊Q8—21no—
135C4⋊Q8—261no—
136C4×D4—131no—
137Q32—522no—
138Q32—522no—
139M32—522no—
140C2×C16—21no—
141C2×C16—131no—
142C2×C16—131no—
143#107—521no—
144#107—521no—
145C4⋊C8—21no—
146C4⋊C8—131no—
147C4⋊C8—261no—
148#102—521no—
149#102—521no—
150C22⋊C8—261no—
151C4×C8C22×D1311yescharacteristic
152C2×C13#166711yescharacteristic
153C2×C13#221911yescharacteristic
154C2×C13#222211yescharacteristic
155D13—81no—
156C2×Q8—41no—
157C2×Q8—521no—
158C2×D4—131no—
159C22×C4—261no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163Q16—521no—
164Q16—521no—
165Q16—1041no—
166C2×C8—41no—
167C2×C8—261no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8—521no—
171C2×C8#612711yescharacteristic
172C2×C8D4×D1311yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—131no—
176C4⋊C4—521no—
177C4⋊C4—521no—
178C22⋊C4—261no—
179C42D4×D1311yescharacteristic
180C16—41no—
181C16—132no—
182C16—261no—
183C13#1243411yescharacteristic, complemented, Sylow
184C23—261no—
185Q8—81no—
186Q8—81no—
187Q8—1041no—
188Q8—1041no—
189D4—261no—
190D4—261no—
191C2×C4—81no—
192C2×C4—261no—
193C2×C4—521no—
194C2×C4—521no—
195C2×C4—1041no—
196C2×C4#8813811yescharacteristic
197C2×C4D8×D1311yescharacteristic
198C2×C4#8817011yescharacteristic
199C8—21no—
200C8—81no—
201C8—521no—
202C8—1041no—
203C8D8×D1311yescharacteristic
204C8#8816811yescharacteristic
205C22—521no—
206C22—521no—
207C22—521no—
208C22#1171843611yescharacteristic
209C4—21no—
210C4—161no—
211C4—521no—
212C4—2081no—
213C4#1171841011yescharacteristic
214C4#1171844711yescharacteristic
215C4#1171857611yescharacteristic
216C4#1171857911yescharacteristic
217C2—1041no—
218C2#1311419011yescharacteristic
219C2#1311694311yescharacteristic
220C2#1311696011yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socleC22×C13#466
prime radicalC2×D52D8
hypercenter#1362D13
hypocenterC13#12434
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13117088C2semidirect
5. #13112909C2semidirect
6. #13112886C2semidirect
7. C13×#1362C2semidirect
80. #1362D13semidirect
183. C13#12434semidirect

Maximal subgroups

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

subgroupindex
#131170882
#131166672
#131142022
#131141982
#131129092
#131128862
C13×#13622
#1243413