Finite Group Databasebeta

← #13126189

Subgroups — #13126189

Order 1664.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719329C212yesmaximal, complemented
2C13×#467C211yesmaximal, characteristic, complemented
3#11718846C212yesmaximal, complemented
4#11718776C211yesmaximal, characteristic
5C2×#88054C211yesmaximal, characteristic, complemented
6#11718709C212yesmaximal, complemented
7#11718552C212yesmaximal, complemented
8#11718480C212yesmaximal, complemented
9#11718457C212yesmaximal, complemented
10C2×C13×Q16C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C13×C22⋊Q8C2212yes—
13#88201C2212yes—
14Q8×Dic13C2212yes—
15C2×#6106C2212yes—
16#88184C2212yes—
17C2×C4×Dic13C2211yescharacteristic
18C22×#1055C2211yescharacteristic
19C2×D104C2211yescharacteristic
20#88152—22no—
21#88147C2212yes—
22#88146—22no—
23#88144C2212yes—
24#88140—22no—
25#88135—22no—
26C13×#107C2211yescharacteristic
27C13×#103C2212yes—
28#88075C2212yes—
29#88061C2212yes—
30#88058C2211yescharacteristic
31#88054C2212yes—
32#88054C2212yes—
33#88049C2212yes—
34#88048C2212yes—
35C2×Q8×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C2×C22⋊D13—22no—
38C22×Dic13D411yescharacteristic
39C22×Dic13D411yescharacteristic
40C2×D52C2312yes—
41C2×C4×D13—22no—
42C13×Q16—41no—
43C2×C8×C13—41no—
44C2×C8×C13C2311yescharacteristic
45C2×C8×C13C2311yescharacteristic
46C13×C4⋊C4—22no—
47C13×C4⋊C4C2312yes—
48C13×C22⋊C4—22no—
49#6106—42no—
50#6103—22no—
51#6103—22no—
52#6103—22no—
53#6103—22no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13C2312yes—
57#6101—22no—
58C4×Dic13—22no—
59C4×Dic13D412yes—
60C4×Dic13C2312yes—
61C2×#1055—41no—
62C2×#1055C2312yes—
63D104—41no—
64#3250—131nomaximal, Sylow
65C23×C13C2×D411yescharacteristic
66C22×D13—22no—
67Q8×C13—22no—
68Q8×C13—22no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2411yescharacteristic
75C22⋊D13—44no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—41no—
79C2×Dic13C2×D412yes—
80C2×Dic13C2×D412yes—
81D52—22no—
82D52—22no—
83C4×D13—44no—
84C8×C13—21no—
85C8×C13—21no—
86#1055—22no—
87#529—132no—
88#479—132no—
89#478—132no—
90#467D1311yescharacteristic, complemented
91#466—131no—
92#465—132no—
93#464—132no—
94#463—132no—
95C2×C4⋊C8—131no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13#13512yes—
99C22×C13C22×D411yescharacteristic
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—42no—
103C4×C13—21no—
104C4×C13—42no—
105C4×C13—42no—
106C4×C13H(5,𝔽2)11yescharacteristic
107C4×C132−1+411yescharacteristic
108Dic13—22no—
109Dic13—22no—
110Dic13—42no—
111C2×Q16C2×D1311yescharacteristic
112C2×SD16—132no—
113C2×D8—131no—
114C22×C8—131no—
115C22×C8C2×D1311yescharacteristic
116#126—262no—
117#125—132no—
118#124—132no—
119#123—262no—
120C22⋊Q8C2×D1312yes—
121#121—132no—
122C4×Q8—132no—
123C4×D4—132no—
124C4×D4—262no—
125#117—262no—
126C2×C42—131no—
127#107—131no—
128#107C2×D1311yescharacteristic
129#106—132no—
130C4⋊C8—132no—
131C4⋊C8—132no—
132#103—132no—
133#103C2×D1312yes—
134#102—132no—
135#102—132no—
136C2×C13—22no—
137C2×C13#53711yescharacteristic
138C2×C13C2×#13511yescharacteristic
139C2×C13#57511yescharacteristic
140D13—82no—
141C2×Q8C22×D1312yes—
142C2×D4—132no—
143C2×D4—262no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—262no—
147C22×C4C22×D1311yescharacteristic
148Q16—41no—
149SD16—522no—
150D8—521no—
151C2×C8—41no—
152C2×C8—132no—
153C2×C8—521no—
154C2×C8C22×D1311yescharacteristic
155C2×C8C22×D1311yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—132no—
158C4⋊C4—262no—
159C4⋊C4—262no—
160C4⋊C4—262no—
161C4⋊C4C22×D1312yes—
162C22⋊C4—22no—
163C22⋊C4—262no—
164C22⋊C4—262no—
165C22⋊C4—262no—
166C22⋊C4—262no—
167C42—132no—
168C42—132no—
169C42—262no—
170C13#325011yescharacteristic, complemented, Sylow
171C23—262no—
172C23D4×D1311yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—262no—
176D4—262no—
177D4—524no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—132no—
183C2×C4—132no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—524no—
187C2×C4—521no—
188C2×C4D4×D1311yescharacteristic
189C2×C4C23×D1311yescharacteristic
190C8—21no—
191C8—21no—
192C8—262no—
193C22—21no—
194C22—21no—
195C22—522no—
196C22—522no—
197C22—522no—
198C22#8817312yes—
199C22C2×D4×D1311yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—262no—
204C4—262no—
205C4—522no—
206C4#8825111yescharacteristic
207C4#8825711yescharacteristic
208C2—22no—
209C2—1042no—
210C2#1171930211yescharacteristic
211C2C2×#8817311yescharacteristic
212C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#467C2
socleC22×C13C22×D4
prime radical#11718776C2
hypercenter#467D13
hypocenterC13#3250
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #11719329C2semidirect
2. C13×#467C2semidirect
3. #11718846C2semidirect
5. C2×#88054C2semidirect
6. #11718709C2semidirect
7. #11718552C2semidirect
8. #11718480C2semidirect
9. #11718457C2semidirect
90. #467D13semidirect
170. C13#3250semidirect

Maximal subgroups

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

subgroupindex
#117193292
C13×#4672
#117188462
#117187762
C2×#880542
#117187092
#117185522
#117184802
#117184572
#325013