Finite Group Databasebeta

← #13125757

Subgroups — #13125757

Order 1664.

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

normal subgroups only

This group has 428 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
1D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719421C211yesmaximal, characteristic
3C13×#492C211yesmaximal, characteristic, complemented
4#11718831C214yesmaximal, complemented
5#11718823C214yesmaximal, complemented
6#11718742C211yesmaximal, characteristic, complemented
7#11718737C211yesmaximal, characteristic, complemented
8#11718346C211yesmaximal, characteristic, complemented
9#11718342C211yesmaximal, characteristic, complemented
10C2×Q8×D13C2212yes—
11C2×#6129—21no—
12C2×C13×SD16C2214yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#127C2211yescharacteristic
15#88198C2212yes—
16#88192—21no—
17#88192C2212yes—
18#88190—21no—
19D4×Dic13—21no—
20D4×Dic13C2212yes—
21C2×#6105C2214yes—
22C4⋊C4×D13—21no—
23C4⋊C4×D13—21no—
24#88142—21no—
25#88142—21no—
26C42×D13C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×C8×C13C2211yescharacteristic
30#88075C2214yes—
31#88060C2212yes—
32#88056C2214yes—
33#88054C2212yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13C2312yes—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C2×C22⋊D13—22no—
40C22×Dic13—22no—
41Q8×D13—44no—
42#6129—44no—
43C2×C4×D13—22no—
44C2×C4×D13D411yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×C4×D13C2311yescharacteristic
47C2×Dic26—21no—
48C2×Dic26—22no—
49C2×Dic26C2312yes—
50C13×SD16—44no—
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56C22⋊Dic13—22no—
57#6105—44no—
58C4⋊Dic13—21no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101—22no—
64C4×Dic13D411yescharacteristic
65C4×Dic13D411yescharacteristic
66C4×Dic13C2311yescharacteristic
67C2×#1055C2312yes—
68#3206—131nomaximal, Sylow
69C23×C13—22no—
70C22×D13C2×D411yescharacteristic
71Q8×C13—24no—
72D4×C13—24no—
73D4×C13—42no—
74D4×C13—42no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2411yescharacteristic
79C22⋊D13—44no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—44no—
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C2×Dic13C2×D411yescharacteristic
86C4×D13—22no—
87C4×D13—22no—
88C4×D13—44no—
89C4×D13SD1614yescomplemented
90Dic26—24no—
91Dic26—44no—
92Dic26—42no—
93C8×C13—22no—
94#1055—22no—
95#532—131no—
96C2×C4⋊Q8—131no—
97#492—131no—
98#492D1311yescharacteristic, complemented
99#487—131no—
100#487—131no—
101#461—134no—
102#448—134no—
103#431—131no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13C22×D411yescharacteristic
108C2×D13—21no—
109C2×D13—21no—
110C2×D13C2×SD1612yes—
111C4×C13—42no—
112C4×C13C2×SD1612yes—
113C4×C13#13712yes—
114C4×C13H(5,𝔽2)12yes—
115Dic13—21no—
116Dic13—21no—
117Dic13—42no—
118Dic13—42no—
119Dic13C2×SD1612yes—
120C2×#41—261no—
121C22×Q8—132no—
122C2×SD16—134no—
123C2×SD16C2×D1314yes—
124C4⋊Q8—132no—
125C4⋊Q8—131no—
126C4⋊Q8—131no—
127C4⋊Q8—261no—
128C4⋊Q8—261no—
129C4⋊Q8C2×D1311yescharacteristic
130#127C2×D1311yescharacteristic
131#124—261no—
132#121—132no—
133#121—261no—
134C4×D4—132no—
135C4×D4—261no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—261no—
138C2×C42—131no—
139C4⋊C8—132no—
140#103—134no—
141#103—134no—
142C22⋊C8—132no—
143C4×C8—131no—
144C4×C8C2×D1311yescharacteristic
145C2×C13—82no—
146C2×C13#53511yescharacteristic
147C2×C13C22×SD1611yescharacteristic
148C2×C13C2×#13711yescharacteristic
149D13—22no—
150#41—524no—
151C2×Q8—132no—
152C2×Q8—262no—
153C2×Q8—261no—
154C2×Q8—524no—
155C2×Q8C22×D1312yes—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—262no—
159C2×D4C22×D1312yes—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—262no—
164C22×C4—262no—
165SD16—44no—
166SD16—524no—
167C2×C8—132no—
168C2×C8C22×D1312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C42—131no—
180C42—131no—
181C42—131no—
182C42C22×D1311yescharacteristic
183C13#320611yescharacteristic, complemented, Sylow
184C23—22no—
185C23—131no—
186Q8—24no—
187Q8—264no—
188Q8—524no—
189Q8—522no—
190D4—24no—
191D4—42no—
192D4—42no—
193D4—524no—
194C2×C4—22no—
195C2×C4—131no—
196C2×C4—134no—
197C2×C4—131no—
198C2×C4—131no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—524no—
204C2×C4—524no—
205C2×C4D4×D1311yescharacteristic
206C2×C4D4×D1311yescharacteristic
207C2×C4C23×D1311yescharacteristic
208C8—22no—
209C8—262no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—132no—
214C22—261no—
215C22—261no—
216C22C2×D4×D1311yescharacteristic
217C4—42no—
218C4—132no—
219C4—261no—
220C4—261no—
221C4—522no—
222C4—522no—
223C4SD16×D1312yes—
224C4#8816912yes—
225C4#8825112yes—
226C2—82no—
227C2—262no—
228C2#1171942011yescharacteristic
229C2C2×SD16×D1311yescharacteristic
230C2C2×#8816911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#492C2
socleC22×C13C22×D4
prime radical#11719421C2
hypercenter#492D13
hypocenterC13#3206
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D13×C4⋊Q8C2semidirect
3. C13×#492C2semidirect
4. #11718831C2semidirect
5. #11718823C2semidirect
6. #11718742C2semidirect
7. #11718737C2semidirect
8. #11718346C2semidirect
9. #11718342C2semidirect
89. C4×D13SD16semidirect
98. #492D13semidirect
183. C13#3206semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117194212
C13×#4922
#117188312
#117188232
#117187422
#117187372
#117183462
#117183422
#320613