Finite Group Databasebeta

← #13115741

Subgroups — #13115741

Order 1664.

296 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×C13×SD16C211yesmaximal, characteristic
2C2×#88076C211yesmaximal, characteristic, complemented
3#11718886C211yesmaximal, characteristic, complemented
4C2×#88073C211yesmaximal, characteristic
5#11718876C211yesmaximal, characteristic
6C2×#88059C211yesmaximal, characteristic, complemented
7#11718762C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2211yescharacteristic
9C22×D4×C13C2211yescharacteristic
10C2×C13×SD16—21no—
11C2×C13×SD16—21no—
12C2×C13×SD16—22no—
13C2×C13×SD16C414yescomplemented
14C22×C8×C13C2211yescharacteristic
15#88180C2211yescharacteristic
16C2×#6099C2211yescharacteristic
17C2×#6099C2211yescharacteristic
18C2×#6099C2211yescharacteristic
19#88076—22no—
20#88075—22no—
21#88073—22no—
22#88072—22no—
23#88059—22no—
24#88055—21no—
25C8×Dic13—21no—
26C24×C13—21no—
27C2×Q8×C13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—21no—
30C2×Q8×C13—21no—
31C2×Q8×C13—21no—
32C2×Q8×C13C2×C412yes—
33C2×D4×C13—21no—
34C2×D4×C13—21no—
35C2×D4×C13—21no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2×C412yes—
39C22×C4×C13—21no—
40C22×C4×C13C2311yescharacteristic
41C13×SD16—24no—
42C13×SD16—24no—
43C2×C8×C13C2×C412yes—
44C2×C8×C13D411yescharacteristic
45C2×C8×C13D411yescharacteristic
46C2×C8×C13D412yes—
47C22⋊Dic13—21no—
48C4⋊Dic13D412yes—
49C4×Dic13—21no—
50#6099—21no—
51#6099—21no—
52#6099—21no—
53#6099—21no—
54#6099—21no—
55#6099D412yes—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055—21no—
59#1977—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—41no—
62C23×C13—41no—
63C23×C13—82no—
64C23×C13#4111yescharacteristic
65Q8×C13—22no—
66Q8×C13—22no—
67Q8×C13—41no—
68Q8×C13—41no—
69D4×C13—22no—
70D4×C13—22no—
71D4×C13—41no—
72D4×C13—41no—
73C2×C4×C13—22no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13C22×C411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13#4111yescharacteristic
82C2×Dic13—22no—
83C8×C13C22⋊C412yes—
84C8×C13C22⋊C412yes—
85#1055—22no—
86#1055—41no—
87#1055—41no—
88C22×SD16D1311yescharacteristic
89C2×#108—131no—
90#419—131no—
91#418—131no—
92C2×#101—131no—
93C2×#100—131no—
94#405—131no—
95C22×C13—22no—
96C22×C13—42no—
97C22×C13—82no—
98C22×C13—82no—
99C22×C13—82no—
100C22×C13C4×D411yescharacteristic
101C22×C13#12111yescharacteristic
102C22×C13#12411yescharacteristic
103C4×C13—42no—
104C4×C13C2×C22⋊C411yescharacteristic
105C4×C13C4×D411yescharacteristic
106C4×C13#12111yescharacteristic
107C4×C13#12711yescharacteristic
108Dic13—42no—
109C22×Q8C2×D1311yescharacteristic
110C22×D4C2×D1311yescharacteristic
111C2×SD16—21no—
112C2×SD16—21no—
113C2×SD16—22no—
114C2×SD16Dic1314yescomplemented
115C2×M16—131no—
116C2×M16—131no—
117C2×M16—131no—
118C22×C8C2×D1311yescharacteristic
119#117—131no—
120#108—262no—
121#103—262no—
122#102—262no—
123#101—262no—
124#100—262no—
125#97—261no—
126C4×C8—261no—
127C2×C13—21no—
128C2×C13—21no—
129C2×C13—82no—
130C2×C13#39011yescharacteristic
131C2×C13#47112yes—
132C24—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8C2×Dic1312yes—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C2×Dic1312yes—
145C22×C4—21no—
146C22×C4C22×D1311yescharacteristic
147SD16—24no—
148SD16—24no—
149M16—132no—
150M16—261no—
151M16—261no—
152M16—261no—
153M16—261no—
154M16—261no—
155C2×C8—261no—
156C2×C8—261no—
157C2×C8—261no—
158C2×C8C2×Dic1312yes—
159C2×C8C22⋊D1311yescharacteristic
160C2×C8C22⋊D1311yescharacteristic
161C2×C8C22⋊D1312yes—
162C4⋊C4—132no—
163C22⋊C4—261no—
164C42—261no—
165C13#197711yescharacteristic, complemented, Sylow
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#612911yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—262no—
183C2×C4D4×D1311yescharacteristic
184C2×C4D4×D1311yescharacteristic
185C2×C4#612911yescharacteristic
186C2×C4C22×Dic1311yescharacteristic
187C2×C4C2×C22⋊D1311yescharacteristic
188C2×C4C2×C22⋊D1311yescharacteristic
189C8—262no—
190C8—521no—
191C8—521no—
192C8C22⋊Dic1312yes—
193C8C22⋊Dic1312yes—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22D4×Dic1311yescharacteristic
200C22#8819011yescharacteristic
201C22#8819211yescharacteristic
202C4—42no—
203C4—522no—
204C4D4×Dic1311yescharacteristic
205C4#8819211yescharacteristic
206C4#8819411yescharacteristic
207C4C2×C22⋊Dic1311yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1171883812yes—
212C2#1171888211yescharacteristic
subgroupG/H
centerC22#88192
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC22×C13×SD16C2
socleC22×C13#121
prime radicalC22×D4×C13C22
cosocleC22×C4×C13C23
hypercenterC22×SD16D13
hypocenterC13#1977
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#88076C2semidirect
3. #11718886C2semidirect
6. C2×#88059C2semidirect
7. #11718762C2semidirect
13. C2×C13×SD16C4semidirect
114. C2×SD16Dic13semidirect
165. C13#1977semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD162
C2×#880762
#117188862
C2×#880732
#117188762
C2×#880592
#117187622
#197713