Finite Group Databasebeta

← #13125785

Subgroups — #13125785

Order 1664.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719433C211yesmaximal, characteristic
2D13×C4⋊Q8C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718753C211yesmaximal, characteristic, complemented
6#11718469C214yesmaximal
7#11718454C214yesmaximal, complemented
8#11718360C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic
10C2×Q8×D13C2212yes—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13#88200—21no—
14Q8×Dic13—21no—
15#88198C2212yes—
16C2×#6107C2214yes—
17C2×Dic52C2214yes—
18#88151C2212yes—
19#88146—21no—
20C4⋊C4×D13—21no—
21C4⋊C4×D13—21no—
22#88144—21no—
23#88142—21no—
24#88142—21no—
25#88141C2212yes—
26C42×D13C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#103C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88060C2212yes—
32#88054C2212yes—
33#88050C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13C2312yes—
37Q8×D13—44no—
38C2×C4×D13—22no—
39C2×C4×D13D411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13C2311yescharacteristic
42C2×Dic26—22no—
43C2×Dic26C2312yes—
44C2×Dic26C2312yes—
45C2×C8×C13C2312yes—
46C13×C4⋊C4—21no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51#6107—44no—
52#6103—22no—
53C4⋊Dic13—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13—21no—
57C4⋊Dic13—22no—
58#6101—22no—
59#6101—22no—
60#6101—22no—
61C4×Dic13—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66Dic52—44no—
67#3209—131nomaximal, Sylow
68C22×D13C2×D411yescharacteristic
69Q8×C13—24no—
70Q8×C13—42no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2411yescharacteristic
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81C4×D13—22no—
82C4×D13—22no—
83C4×D13—44no—
84C4×D13Q1614yescomplemented
85Dic26—24no—
86Dic26—24no—
87Dic26—44no—
88C8×C13—22no—
89#1055—22no—
90#533—131no—
91C2×C4⋊Q8—131no—
92#494—131no—
93#494—131no—
94#487—131no—
95#487D1311yescharacteristic, complemented
96#462—134no—
97#451—134no—
98#431—131no—
99C22×C13C22×D411yescharacteristic
100C2×D13—21no—
101C2×D13—21no—
102C2×D13C2×Q1612yes—
103C4×C13—42no—
104C4×C13—42no—
105C4×C13C2×Q1612yes—
106C4×C13#13712yes—
107C4×C13H(5,𝔽2)12yes—
108Dic13—21no—
109Dic13—21no—
110Dic13—42no—
111Dic13—42no—
112Dic13C2×Q1612yes—
113C22×Q8—132no—
114C2×Q16—134no—
115C2×Q16—134no—
116C4⋊Q8—132no—
117C4⋊Q8—131no—
118C4⋊Q8—131no—
119C4⋊Q8—261no—
120C4⋊Q8—261no—
121C4⋊Q8C2×D1311yescharacteristic
122C4⋊Q8C2×D1311yescharacteristic
123#125—261no—
124C22⋊Q8—132no—
125C22⋊Q8—261no—
126C4×Q8—132no—
127C4×Q8—261no—
128#117—261no—
129C2×C4⋊C4—261no—
130C2×C4⋊C4—261no—
131C2×C42—131no—
132C4⋊C8—132no—
133#103—134no—
134#103C2×D1314yes—
135C22⋊C8—132no—
136C4×C8—131no—
137C4×C8C2×D1311yescharacteristic
138C2×C13#53511yescharacteristic
139C2×C13C22×Q1611yescharacteristic
140C2×C13C2×#13711yescharacteristic
141D13—22no—
142C2×Q8—21no—
143C2×Q8—132no—
144C2×Q8—132no—
145C2×Q8—262no—
146C2×Q8—524no—
147C2×Q8C22×D1312yes—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—262no—
152Q16—524no—
153Q16—524no—
154C2×C8—132no—
155C2×C8C22×D1312yes—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—262no—
160C4⋊C4—262no—
161C4⋊C4—262no—
162C4⋊C4—262no—
163C4⋊C4—261no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C4⋊C4C22×D1312yes—
168C22⋊C4—262no—
169C42—131no—
170C42—131no—
171C42—131no—
172C42—262no—
173C42C22×D1311yescharacteristic
174C13#320911yescharacteristic, complemented, Sylow
175C23—131no—
176Q8—24no—
177Q8—42no—
178Q8—264no—
179Q8—264no—
180Q8—524no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—131no—
184C2×C4—134no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—524no—
192C2×C4D4×D1311yescharacteristic
193C2×C4D4×D1311yescharacteristic
194C2×C4C23×D1311yescharacteristic
195C8—22no—
196C8—262no—
197C22—132no—
198C22—261no—
199C22—261no—
200C22C2×D4×D1311yescharacteristic
201C4—42no—
202C4—42no—
203C4—132no—
204C4—261no—
205C4—261no—
206C4—522no—
207C4—522no—
208C4#8816912yes—
209C4Q16×D1312yes—
210C4#8825612yes—
211C2—262no—
212C2#1171937911yescharacteristic
213C2C2×#8816911yescharacteristic
214C2C2×Q16×D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#487D13
hypocenterC13#3209
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C13×#487C2semidirect
4. #11718754C2semidirect
5. #11718753C2semidirect
7. #11718454C2semidirect
8. #11718360C2semidirect
84. C4×D13Q16semidirect
95. #487D13semidirect
174. C13#3209semidirect

Maximal subgroups

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

subgroupindex
#117194332
D13×C4⋊Q82
C13×#4872
#117187542
#117187532
#117184692
#117184542
#117183602
#117183462
#320913