Finite Group Databasebeta

← #13127203

Subgroups — #13127203

Order 1664.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719399C212yesmaximal
2C13×#499C211yesmaximal, characteristic, complemented
3#11718724C212yesmaximal, complemented
4#11718548C211yesmaximal, characteristic, complemented
5#11718548C211yesmaximal, characteristic, complemented
6#11718541C211yesmaximal, characteristic, complemented
7D13×#107C211yesmaximal, characteristic, complemented
8#11718528C212yesmaximal, complemented
9#11718523C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic
12C13×#125C2212yes—
13C2×Dic52C2211yescharacteristic
14C2×C8×D13C2211yescharacteristic
15C2×C8×D13C2211yescharacteristic
16#88152—22no—
17#88151C2212yes—
18#88151C2212yes—
19#88148—22no—
20#88146—22no—
21#88146C2212yes—
22C4⋊C4×D13C2212yes—
23#88144—22no—
24C4×D52C2211yescharacteristic
25C4×Dic26C2212yes—
26C13×#107C2211yescharacteristic
27C13×#107C2211yescharacteristic
28C13×#106C2212yes—
29C4×C8×C13C2211yescharacteristic
30#88060C2211yescharacteristic
31#88060C2211yescharacteristic
32#88058C2211yescharacteristic
33#88056C2212yes—
34#88050C2212yes—
35#88050C2212yes—
36#88048C2212yes—
37#88047C2212yes—
38C4⋊#1055C2211yescharacteristic
39C2×D52D411yescharacteristic
40C2×C4×D13—22no—
41C2×C4×D13C2311yescharacteristic
42C2×C4×D13C2311yescharacteristic
43C2×Dic26C2312yes—
44C2×C8×C13C2311yescharacteristic
45C2×C8×C13C2311yescharacteristic
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4C2312yes—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51#6103—22no—
52#6103—22no—
53#6103—22no—
54#6103D411yescharacteristic
55#6103D411yescharacteristic
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13D411yescharacteristic
59C4⋊Dic13C2312yes—
60#6101—22no—
61#6101—22no—
62C4×Dic13—22no—
63C4×Dic13—22no—
64C2×#1055C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66Dic52—22no—
67C8×D13—22no—
68C8×D13—22no—
69#3336—131nomaximal, Sylow
70C22×D13C2×D411yescharacteristic
71C22×D13C2×D411yescharacteristic
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2411yescharacteristic
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—22no—
82C4×D13—21no—
83C4×D13—21no—
84C4×D13—21no—
85C4×D13—21no—
86C4×D13—44no—
87Dic26—22no—
88Dic26—22no—
89C8×C13—21no—
90C8×C13#4112yes—
91#1055—21no—
92#1055—21no—
93#552—132no—
94#499D1311yescharacteristic, complemented
95#485—132no—
96#483—132no—
97#479—132no—
98#467—131no—
99#467—131no—
100C4×Q16—131no—
101C8×D4—131no—
102#427—131no—
103C2×#107—131no—
104C22×C13C22×D411yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C2×D13—21no—
109C2×D13—21no—
110C2×D13#13512yes—
111C4×C13—21no—
112C4×C13—21no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13C2×#4111yescharacteristic
116C4×C132−1+411yescharacteristic
117Dic13—21no—
118Dic13—21no—
119Dic13—42no—
120Dic13—42no—
121C2×Q16—131no—
122C22×C8—131no—
123C22×C8—131no—
124#126—262no—
125#125—262no—
126#125C2×D1312yes—
127#123—262no—
128C22⋊Q8—132no—
129C22⋊Q8—132no—
130C4×Q8—132no—
131C4×D4—131no—
132#117—132no—
133#117—262no—
134C2×C4⋊C4—132no—
135#107—131no—
136#107—132no—
137#107C2×D1311yescharacteristic
138#107C2×D1311yescharacteristic
139#106—132no—
140#106C2×D1312yes—
141C4⋊C8—131no—
142#103—132no—
143#103—132no—
144#103—132no—
145C22⋊C8—131no—
146C22⋊C8—131no—
147C4×C8C2×D1311yescharacteristic
148C2×C13#54711yescharacteristic
149C2×C13C2×#13511yescharacteristic
150C2×C13#57811yescharacteristic
151D13—22no—
152D13—41no—
153C2×Q8—132no—
154C2×D4—131no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—262no—
158Q16—262no—
159C2×C8—131no—
160C2×C8—131no—
161C2×C8—262no—
162C2×C8—262no—
163C2×C8C22×D1311yescharacteristic
164C2×C8C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—131no—
168C4⋊C4—132no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4C22×D1312yes—
174C4⋊C4C22×D1312yes—
175C22⋊C4—131no—
176C22⋊C4—131no—
177C22⋊C4—262no—
178C22⋊C4—262no—
179C22⋊C4—262no—
180C42—262no—
181C42—262no—
182C42C22×D1311yescharacteristic
183C13#333611yescharacteristic, complemented, Sylow
184C23—131no—
185C23—131no—
186Q8—262no—
187Q8—262no—
188D4—262no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—524no—
200C2×C4D4×D1311yescharacteristic
201C2×C4D4×D1311yescharacteristic
202C2×C4C23×D1311yescharacteristic
203C8—21no—
204C8—261no—
205C8—261no—
206C8#613112yes—
207C22—132no—
208C22—261no—
209C22—261no—
210C22—261no—
211C22—261no—
212C22—261no—
213C22C2×D4×D1311yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—261no—
219C4—261no—
220C4—522no—
221C4—522no—
222C4C2×#613111yescharacteristic
223C4#8825411yescharacteristic
224C2—262no—
225C2—521no—
226C2#1171943111yescharacteristic
227C2D13×#13511yescharacteristic
228C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#499C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#499D13
hypocenterC13#3336
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. C13×#499C2semidirect
3. #11718724C2semidirect
4. #11718548C2semidirect
5. #11718548C2semidirect
6. #11718541C2semidirect
7. D13×#107C2semidirect
8. #11718528C2semidirect
9. #11718523C2semidirect
10. C4×Dic52C2semidirect
94. #499D13semidirect
183. C13#3336semidirect

Maximal subgroups

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

subgroupindex
#117193992
C13×#4992
#117187242
#117185482
#117185412
D13×#1072
#117185282
#117185232
C4×Dic522
C8×D522
#333613