Finite Group Databasebeta

← #15773466

Subgroups — #15773466

Order 3328.

292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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#13116652C211yesmaximal, characteristic
2#13114591C211yesmaximal, characteristic
3#13112830C212yesmaximal
4#13112824C212yesmaximal
5C13×#3177C211yesmaximal, characteristic
6C13×#541—21no—
7C13×#499C411yescharacteristic, complemented
8C13×#494C411yescharacteristic, complemented
9C13×#491—21no—
10C13×#470C2212yes—
11C13×#467—21no—
12C13×#441C412yescomplemented
13C4×C13×Q16—21no—
14C13×#405C2211yescharacteristic
15#11718762—21no—
16#11718152C2211yescharacteristic
17#11718149C2211yescharacteristic
18#11718145C2212yes—
19#11718123—21no—
20#11718058—21no—
21#11718055—21no—
22C2×C13×Q16—21no—
23C2×C13×Q16C2×C412yes—
24C2×C13×M16C2311yescharacteristic
25C22×C8×C13D411yescharacteristic
26C13×C4⋊Q8—21no—
27C13×#126—42no—
28C13×#125—21no—
29C13×#125—42no—
30C13×C22⋊Q8—22no—
31C4×Q8×C13—22no—
32C13×#117D411yescharacteristic
33#88180—21no—
34C2×#6099—21no—
35C13×#107—21no—
36C13×#106C2×C412yes—
37C13×#103—22no—
38C13×#103—22no—
39C13×#97C2×C411yescharacteristic
40C13×#97D411yescharacteristic
41C4×C8×C13C2×C411yescharacteristic
42C4×C8×C13D411yescharacteristic
43#88055—22no—
44C8×Dic13—22no—
45#88052—22no—
46#11771—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C22×C4×C13C2×D411yescharacteristic
49C13×Q16—42no—
50C13×Q16—41no—
51C13×Q16—41no—
52C13×M16—41no—
53C2×C8×C13—21no—
54C2×C8×C13—21no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22×C411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C13×C4⋊C4—21no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C22⋊C4—21no—
66C13×C22⋊C4—42no—
67C42×C13—42no—
68C42×C13C22⋊C411yescharacteristic
69C42×C13C22⋊C411yescharacteristic
70C22⋊Dic13—41no—
71C4⋊Dic13—41no—
72C4×Dic13—22no—
73#6099—41no—
74#6099—41no—
75C2×#1055—22no—
76#6090—42no—
77#3177D1311yescharacteristic
78#2166—131no—
79#1747—131no—
80#1342—132no—
81#1340—132no—
82C23×C13AGL(1,ℤ/8)11yescharacteristic
83Q8×C13—42no—
84Q8×C13—42no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
93C2×Dic13—42no—
94C8×C13—21no—
95C8×C13—21no—
96C8×C13—21no—
97C8×C13#10411yescharacteristic
98C8×C13#10411yescharacteristic
99#1055—42no—
100#541—21no—
101#499Dic1311yescharacteristic, complemented
102#494Dic1311yescharacteristic, complemented
103#491—21no—
104#470C2×D1312yes—
105#467—21no—
106#441Dic1312yescomplemented
107C4×Q16—21no—
108#405—261no—
109#405C2×D1311yescharacteristic
110#364—261no—
111#349—132no—
112#347—261no—
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—82no—
123C4×C13—82no—
124C4×C13#41011yescharacteristic
125C4×C13C2×#10411yescharacteristic
126Dic13—82no—
127C2×Q16—21no—
128C2×Q16C2×Dic1312yes—
129C2×M16—261no—
130C2×M16C22×D1311yescharacteristic
131C22×C8C22⋊D1311yescharacteristic
132C4⋊Q8—21no—
133#126—42no—
134#125—21no—
135#125—42no—
136C22⋊Q8—22no—
137C4×Q8—22no—
138#117—261no—
139#117C22⋊D1311yescharacteristic
140M32—262no—
141#107—21no—
142#106C2×Dic1312yes—
143#103—22no—
144#103—22no—
145#97—262no—
146#97C2×Dic1311yescharacteristic
147#97C22⋊D1311yescharacteristic
148C4×C8—262no—
149C4×C8C2×Dic1311yescharacteristic
150C4×C8C22⋊D1311yescharacteristic
151C2×C13—21no—
152C2×C13—41no—
153C2×C13#150511yescharacteristic
154C2×Q8—22no—
155C22×C4C2×C22⋊D1311yescharacteristic
156Q16—42no—
157Q16—41no—
158Q16—41no—
159M16—41no—
160M16—521no—
161M16—521no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—262no—
165C2×C8C22⋊Dic1311yescharacteristic
166C2×C8C22⋊Dic1311yescharacteristic
167C2×C8C22×Dic1311yescharacteristic
168C2×C8C2×C22⋊D1311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—521no—
176C22⋊C4—21no—
177C22⋊C4—42no—
178C22⋊C4—521no—
179C42—42no—
180C42—262no—
181C42C22⋊Dic1311yescharacteristic
182C42C22⋊Dic1311yescharacteristic
183C16—522no—
184C13#1177111yescharacteristic, complemented, Sylow
185C23#8818611yescharacteristic
186Q8—42no—
187Q8—42no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—522no—
195C2×C4#8818611yescharacteristic
196C2×C4C2×C22⋊Dic1311yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—522no—
201C8#8807711yescharacteristic
202C8#8807711yescharacteristic
203C22—21no—
204C22—41no—
205C22#1171887611yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—82no—
210C4—82no—
211C4—1042no—
212C4C2×#8807711yescharacteristic
213C4#1171890111yescharacteristic
214C2—21no—
215C2—41no—
216C2#1311334411yescharacteristic
subgroupG/H
centerC2#13113344
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#3177C2
socleC2×C13#1505
prime radicalC23×C13AGL(1,ℤ/8)
cosocleC2×C13×M16C23
hypercenter#3177D13
hypocenterC13#11771
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
7. C13×#499C4semidirect
8. C13×#494C4semidirect
12. C13×#441C4semidirect
101. #499Dic13semidirect
102. #494Dic13semidirect
106. #441Dic13semidirect
184. C13#11771semidirect

Maximal subgroups

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

subgroupindex
#131166522
#131145912
#131128302
#131128242
C13×#31772
#1177113