Finite Group Databasebeta

← #13125973

Subgroups — #13125973

Order 1664.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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, complemented
2#11719430C211yesmaximal, characteristic
3C13×#498C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718739C211yesmaximal, characteristic, complemented
6#11718532C214yesmaximal, complemented
7#11718527C214yesmaximal, complemented
8#11718355C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6131—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13#88201—21no—
14#88200—21no—
15Q8×Dic13—21no—
16#88151—21no—
17#88149—21no—
18#88149C2212yes—
19#88147—21no—
20#88147C2212yes—
21#88146C2212yes—
22#88144C2212yes—
23#88141—21no—
24#88128C2211yescharacteristic
25C42×D13C2211yescharacteristic
26#88123C2211yescharacteristic
27C13×#106C2214yes—
28C4×C8×C13C2211yescharacteristic
29#88061C2214yes—
30#88060C2212yes—
31#88054C2212yes—
32#88049C2214yes—
33#88047C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13—21no—
37#6131—44no—
38C2×D52—22no—
39C2×D52—21no—
40C2×D52—21no—
41C2×D52C2312yes—
42C2×C4×D13—22no—
43C2×C4×D13D411yescharacteristic
44C2×C4×D13D411yescharacteristic
45C2×C4×D13C2311yescharacteristic
46C2×Dic26—21no—
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2312yes—
52C42×C13C2311yescharacteristic
53#6103—22no—
54#6103—22no—
55#6103—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—22no—
58C4⋊Dic13C2312yes—
59#6101—22no—
60C4×Dic13—22no—
61C4×Dic13D411yescharacteristic
62C4×Dic13D411yescharacteristic
63C4×Dic13C2311yescharacteristic
64C2×#1055C2312yes—
65#3228—131nomaximal, Sylow
66C22×D13—22no—
67C22×D13C2×D411yescharacteristic
68Q8×C13—42no—
69Q8×C13—42no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2411yescharacteristic
75C2×Dic13—22no—
76C2×Dic13C2×D411yescharacteristic
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79D52—24no—
80D52—44no—
81D52—42no—
82D52—42no—
83C4×D13—22no—
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—44no—
87Dic26—42no—
88C8×C13—22no—
89#1055—22no—
90#533—131no—
91#532—131no—
92#500—131no—
93#498D1311yescharacteristic, complemented
94#486—131no—
95#486—131no—
96#482—134no—
97#478—134no—
98#431—131no—
99C22×C13C22×D411yescharacteristic
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C4×C13—42no—
107C4×C13—42no—
108C4×C13#13512yes—
109C4×C13AGL(1,ℤ/8)12yes—
110C4×C132−1+412yes—
111Dic13—21no—
112Dic13—21no—
113Dic13—21no—
114Dic13—42no—
115C2×#41—261no—
116C4⋊Q8—131no—
117C4⋊Q8C2×D1311yescharacteristic
118C4⋊Q8C2×D1311yescharacteristic
119#127—131no—
120#125—132no—
121#124—261no—
122C22⋊Q8—261no—
123C22⋊Q8—261no—
124#121—132no—
125#121—261no—
126C4×Q8—261no—
127C4×Q8—261no—
128C4×D4—132no—
129C4×D4—261no—
130#117—132no—
131C2×C42—131no—
132#107—134no—
133#106C2×D1314yes—
134C4⋊C8—132no—
135#102—134no—
136#102—134no—
137C22⋊C8—132no—
138C4×C8—131no—
139C4×C8C2×D1311yescharacteristic
140C2×C13#53611yescharacteristic
141C2×C13C2×#13511yescharacteristic
142C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
143D13—41no—
144D13—82no—
145#41—524no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—261no—
149C2×D4—132no—
150C2×D4—262no—
151C2×D4—261no—
152C2×D4—261no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—262no—
157C2×C8—132no—
158C2×C8C22×D1312yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—132no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—261no—
165C4⋊C4C22×D1312yes—
166C4⋊C4C22×D1312yes—
167C22⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—131no—
171C42—131no—
172C42—131no—
173C42—262no—
174C42C22×D1311yescharacteristic
175C13#322811yescharacteristic, complemented, Sylow
176C23—131no—
177C23—262no—
178Q8—42no—
179Q8—42no—
180Q8—522no—
181D4—264no—
182D4—524no—
183D4—522no—
184D4—522no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—524no—
195C2×C4D4×D1311yescharacteristic
196C2×C4D4×D1311yescharacteristic
197C2×C4C23×D1311yescharacteristic
198C8—22no—
199C8—262no—
200C22—261no—
201C22—261no—
202C22—261no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22C2×D4×D1311yescharacteristic
207C4—42no—
208C4—42no—
209C4—261no—
210C4—261no—
211C4—261no—
212C4—522no—
213C4#8816812yes—
214C4#8817012yes—
215C4#8825412yes—
216C2—521no—
217C2—1042no—
218C2#1171942911yescharacteristic
219C2C2×#8816811yescharacteristic
220C2C2×#8817011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#498C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#498D13
hypocenterC13#3228
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#498C2semidirect
4. #11718749C2semidirect
5. #11718739C2semidirect
6. #11718532C2semidirect
7. #11718527C2semidirect
8. #11718355C2semidirect
9. #11718346C2semidirect
93. #498D13semidirect
175. C13#3228semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117194302
C13×#4982
#117187492
#117187392
#117185322
#117185272
#117183552
#117183462
#322813