Finite Group Databasebeta

← #15773465

Subgroups — #15773465

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#13116652C211yesmaximal, characteristic
3#13112829C212yesmaximal
4#13112823C212yesmaximal
5C13×#1747C211yesmaximal, characteristic
6#11719223—21no—
7C13×#405—21no—
8C13×#405C2211yescharacteristic
9#11718798C2212yes—
10#11718777—21no—
11#11718377C412yescomplemented
12#11718364—21no—
13#11718360C411yescharacteristic, complemented
14C4×Dic52—21no—
15#11718344C411yescharacteristic, complemented
16C13×#338C2211yescharacteristic
17C13×H(3,ℤ/4)—21no—
18C13×H(3,ℤ/4)C2211yescharacteristic
19#11718145C2212yes—
20#11718058—21no—
21#11718055—21no—
22C2×C13×M16—21no—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13D411yescharacteristic
25C13×#117—21no—
26C13×#117D411yescharacteristic
27#88178—22no—
28C2×Dic52—21no—
29C2×Dic52C2×C412yes—
30#88143—42no—
31#88133—42no—
32#88124—21no—
33#88123—21no—
34C4×Dic26—22no—
35C13×#97—22no—
36C13×#97C2×C411yescharacteristic
37C13×#97D411yescharacteristic
38C4×C8×C13—22no—
39C4×C8×C13C2×C411yescharacteristic
40C4×C8×C13D411yescharacteristic
41#88058—21no—
42#88057C2×C412yes—
43#88056—22no—
44#88056—22no—
45#88052—22no—
46#11771—131nomaximal, Sylow
47C22×C4×C13C2×D411yescharacteristic
48C2×Dic26—22no—
49C13×M16—41no—
50C13×M16—41no—
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—21no—
54C2×C8×C13—22no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22×C411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C13×C4⋊C4—21no—
60C13×C4⋊C4—41no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—41no—
63C42×C13—22no—
64C42×C13C22⋊C411yescharacteristic
65C42×C13C22⋊C411yescharacteristic
66C22⋊Dic13—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—42no—
69#6101—42no—
70#6101—42no—
71#6101—42no—
72C4×Dic13—42no—
73Dic52—42no—
74Dic52—41no—
75Dic52—41no—
76#6090—42no—
77#3177—131no—
78#2166—131no—
79#1747D1311yescharacteristic
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×C13—42no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
90C2×Dic13—42no—
91C2×Dic13—42no—
92Dic26—42no—
93Dic26—42no—
94C8×C13—21no—
95C8×C13—21no—
96C8×C13—21no—
97C8×C13—42no—
98C8×C13#10411yescharacteristic
99C8×C13#10411yescharacteristic
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—21no—
109#405C2×D1311yescharacteristic
110#364—261no—
111#349—132no—
112#347—261no—
113#338C2×D1311yescharacteristic
114H(3,ℤ/4)—21no—
115H(3,ℤ/4)C2×D1311yescharacteristic
116C22×C13—21no—
117C22×C13—41no—
118C22×C13#41811yescharacteristic
119C4×C13—21no—
120C4×C13—41no—
121C4×C13—41no—
122C4×C13—82no—
123C4×C13#41011yescharacteristic
124C4×C13C2×#10411yescharacteristic
125Dic13—82no—
126Dic13—82no—
127C2×Q16—132no—
128C2×Q16—261no—
129C2×M16—21no—
130C2×M16C22×D1311yescharacteristic
131C22×C8C22⋊D1311yescharacteristic
132C4⋊Q8—261no—
133#126—522no—
134#125—261no—
135#125—522no—
136C22⋊Q8—262no—
137C4×Q8—262no—
138#117—21no—
139#117C22⋊D1311yescharacteristic
140M32—262no—
141#107—261no—
142#106—132no—
143#103—262no—
144#103—262no—
145#97—22no—
146#97C4×D1311yescharacteristic
147#97D5211yescharacteristic
148C4×C8—22no—
149C4×C8C4×D1311yescharacteristic
150C4×C8D5211yescharacteristic
151C2×C13—21no—
152C2×C13—41no—
153C2×C13#150511yescharacteristic
154C2×Q8—262no—
155C22×C4C2×C22⋊D1311yescharacteristic
156Q16—522no—
157Q16—521no—
158Q16—521no—
159M16—41no—
160M16—41no—
161M16—41no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—22no—
165C2×C8#610311yescharacteristic
166C2×C8#610311yescharacteristic
167C2×C8C2×C4×D1311yescharacteristic
168C2×C8C2×D5211yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—262no—
172C4⋊C4—522no—
173C4⋊C4—522no—
174C4⋊C4—522no—
175C4⋊C4—522no—
176C22⋊C4—21no—
177C22⋊C4—41no—
178C22⋊C4—522no—
179C42—22no—
180C42—522no—
181C42#610311yescharacteristic
182C42#610311yescharacteristic
183C16—522no—
184C13#1177111yescharacteristic, complemented, Sylow
185C23#8820311yescharacteristic
186Q8—522no—
187Q8—522no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—522no—
194C2×C4—522no—
195C2×C4C2×#610311yescharacteristic
196C2×C4#8820311yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—42no—
201C8#8804511yescharacteristic
202C8#8804511yescharacteristic
203C22—21no—
204C22—41no—
205C22#1171866211yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—82no—
210C4—1042no—
211C4—1042no—
212C4C2×#8804511yescharacteristic
213C4#1171866711yescharacteristic
214C2—21no—
215C2—41no—
216C2#1311334311yescharacteristic
subgroupG/H
centerC2#13113343
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1747C2
socleC2×C13#1505
prime radicalC23×C13AGL(1,ℤ/8)
cosocleC2×C13×M16C23
hypercenter#1747D13
hypocenterC13#11771
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #1747

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
#131166522
#131128292
#131128232
C13×#17472
#1177113