Finite Group Databasebeta

← #15773468

Subgroups — #15773468

Order 3328.

292 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 75 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#13125495C211yesmaximal, characteristic
2#13114591C211yesmaximal, characteristic
3#13112831C212yesmaximal
4#13112825C212yesmaximal
5C13×#2166C211yesmaximal, characteristic
6#11719223—21no—
7C13×#405C2211yescharacteristic
8#11718798C2212yes—
9#11718777—21no—
10#11718762—21no—
11#11718377C412yescomplemented
12#11718364—21no—
13#11718360C411yescharacteristic, complemented
14C4×Dic52—21no—
15#11718344C411yescharacteristic, complemented
16C13×#364—21no—
17C13×#349C2212yes—
18C13×#347—21no—
19#11718152C2211yescharacteristic
20#11718149C2211yescharacteristic
21#11718123—21no—
22C2×C13×M16C2311yescharacteristic
23C22×C8×C13D411yescharacteristic
24C13×#117D411yescharacteristic
25#88180—21no—
26#88178—22no—
27C2×#6099—21no—
28C2×Dic52—21no—
29C2×Dic52C2×C412yes—
30#88143—42no—
31#88133—42no—
32#88124—21no—
33#88123—21no—
34C4×Dic26—22no—
35C13×M32—22no—
36C13×#97C2×C411yescharacteristic
37C13×#97D411yescharacteristic
38C4×C8×C13C2×C411yescharacteristic
39C4×C8×C13D411yescharacteristic
40#88058—21no—
41#88057C2×C412yes—
42#88056—22no—
43#88056—22no—
44#88055—22no—
45C8×Dic13—22no—
46#11771—131nomaximal, Sylow
47C22×C4×C13C2×D411yescharacteristic
48C2×Dic26—22no—
49C13×M16—41no—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13C22⋊C411yescharacteristic
53C2×C8×C13C22⋊C411yescharacteristic
54C2×C8×C13C22×C411yescharacteristic
55C2×C8×C13C2×D411yescharacteristic
56C13×C4⋊C4—21no—
57C13×C22⋊C4—21no—
58C42×C13C22⋊C411yescharacteristic
59C42×C13C22⋊C411yescharacteristic
60C22⋊Dic13—42no—
61C22⋊Dic13—41no—
62C4⋊Dic13—22no—
63C4⋊Dic13—42no—
64C4⋊Dic13—41no—
65#6101—42no—
66#6101—42no—
67#6101—42no—
68C4×Dic13—22no—
69C4×Dic13—42no—
70#6099—41no—
71#6099—41no—
72C2×#1055—22no—
73Dic52—42no—
74Dic52—41no—
75Dic52—41no—
76C13×C16—42no—
77#3177—131no—
78#2166D1311yescharacteristic
79#1747—131no—
80#1342—132no—
81#1340—132no—
82C23×C13AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
89C2×Dic13—42no—
90C2×Dic13—42no—
91C2×Dic13—42no—
92Dic26—42no—
93Dic26—42no—
94C8×C13—21no—
95C8×C13—21no—
96C8×C13—21no—
97C8×C13#10411yescharacteristic
98C8×C13#10411yescharacteristic
99#1055—42no—
100#541—261no—
101#499—131no—
102#494—131no—
103#491—261no—
104#470—132no—
105#467—261no—
106#441—132no—
107C4×Q16—261no—
108#405—261no—
109#405C2×D1311yescharacteristic
110#364—21no—
111#349C2×D1312yes—
112#347—21no—
113#338—131no—
114H(3,ℤ/4)—131no—
115H(3,ℤ/4)—261no—
116C22×C13—21no—
117C22×C13—41no—
118C22×C13#41811yescharacteristic
119C4×C13—21no—
120C4×C13—41no—
121C4×C13—41no—
122C4×C13#41011yescharacteristic
123C4×C13C2×#10411yescharacteristic
124Dic13—82no—
125Dic13—82no—
126Dic13—82no—
127C2×Q16—132no—
128C2×Q16—261no—
129C2×M16—261no—
130C2×M16C22×D1311yescharacteristic
131C22×C8D5211yescharacteristic
132C4⋊Q8—261no—
133#126—522no—
134#125—261no—
135#125—522no—
136C22⋊Q8—262no—
137C4×Q8—262no—
138#117—261no—
139#117D5211yescharacteristic
140M32—22no—
141#107—261no—
142#106—132no—
143#103—262no—
144#103—262no—
145#97—262no—
146#97C4×D1311yescharacteristic
147#97C22⋊D1311yescharacteristic
148C4×C8—262no—
149C4×C8C4×D1311yescharacteristic
150C4×C8C22⋊D1311yescharacteristic
151C2×C13—21no—
152C2×C13—41no—
153C2×C13#150511yescharacteristic
154C2×Q8—262no—
155C22×C4C2×D5211yescharacteristic
156Q16—522no—
157Q16—521no—
158Q16—521no—
159M16—41no—
160M16—521no—
161M16—521no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—262no—
165C2×C8#610311yescharacteristic
166C2×C8#610311yescharacteristic
167C2×C8C2×C4×D1311yescharacteristic
168C2×C8C2×C22⋊D1311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—262no—
171C4⋊C4—521no—
172C4⋊C4—522no—
173C4⋊C4—522no—
174C4⋊C4—522no—
175C4⋊C4—522no—
176C22⋊C4—21no—
177C22⋊C4—521no—
178C22⋊C4—522no—
179C42—262no—
180C42—522no—
181C42#610311yescharacteristic
182C42#610311yescharacteristic
183C16—42no—
184C13#1177111yescharacteristic, complemented, Sylow
185C23#8816211yescharacteristic
186Q8—522no—
187Q8—522no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4—522no—
195C2×C4#8816211yescharacteristic
196C2×C4C2×#610311yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—522no—
201C8#8806511yescharacteristic
202C8#8806511yescharacteristic
203C22—21no—
204C22—41no—
205C22#1171879211yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—1042no—
210C4—1042no—
211C4—1042no—
212C4#1171866711yescharacteristic
213C4C2×#8806511yescharacteristic
214C2—21no—
215C2—41no—
216C2#1311334511yescharacteristic
subgroupG/H
centerC2#13113345
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2166C2
socleC2×C13#1505
prime radicalC23×C13AGL(1,ℤ/8)
cosocleC2×C13×M16C23
hypercenter#2166D13
hypocenterC13#11771
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
11. #11718377C4semidirect
13. #11718360C4semidirect
15. #11718344C4semidirect
184. C13#11771semidirect

Maximal subgroups

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

subgroupindex
#131254952
#131145912
#131128312
#131128252
C13×#21662
#1177113