Finite Group Databasebeta

← #13120809

Subgroups — #13120809

Order 1664.

436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C13×#380C211yesmaximal, characteristic
2#11718873C211yesmaximal, characteristic
3C2×#88071C211yesmaximal, characteristic
4#11718647C212yesmaximal, complemented
5#11718645C212yesmaximal, complemented
6#11718611C212yesmaximal
7#11718607C212yesmaximal
8#11718322C212yesmaximal, complemented
9#11718321C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C13×#95C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C24×C13C2311yescharacteristic
32C22×C4×C13—41no—
33C22×C4×C13—41no—
34C22×C4×C13Q814yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13—22no—
40C22×Dic13—22no—
41C22×Dic13—41no—
42C22×Dic13—41no—
43C22×Dic13—41no—
44C22×Dic13—41no—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C13×C4⋊C4—41no—
50C13×C4⋊C4—41no—
51C13×C22⋊C4—24no—
52C22⋊Dic13—24no—
53C4⋊Dic13—41no—
54C4⋊Dic13—42no—
55C4⋊Dic13—41no—
56C4⋊Dic13—42no—
57#6101—42no—
58#6101—42no—
59#2646—131nomaximal, Sylow
60C23×C13—21no—
61C23×C13—21no—
62C23×C13—21no—
63C23×C13—21no—
64C23×C13C2×Q812yes—
65C23×C13#4112yes—
66C23×C13#4112yes—
67C23×C13C2411yescharacteristic
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—44no—
79C2×C4×C13C2×Q812yes—
80C2×C4×C13C2×Q812yes—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—44no—
94C2×Dic13—44no—
95#400—132no—
96#400—132no—
97#398—132no—
98#398—132no—
99#385—132no—
100#385—132no—
101#380—131no—
102#380D1311yescharacteristic
103C2×#95—131no—
104C22×C13—22no—
105C22×C13—22no—
106C22×C13—22no—
107C22×C13—22no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13#12514yes—
111C22×C13C22×Q811yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4111yescharacteristic
114C22×C13H(5,𝔽2)11yescharacteristic
115C22×C13H(5,𝔽2)11yescharacteristic
116C22×C13H(5,𝔽2)11yescharacteristic
117C22×C132−1+411yescharacteristic
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—42no—
121C4×C13—42no—
122Dic13—42no—
123Dic13—42no—
124Dic13—42no—
125Dic13—42no—
126C23×C4—131no—
127C23×C4—131no—
128C23×C4C2×D1311yescharacteristic
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4C2×D1311yescharacteristic
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C22⋊C4—132no—
138C2×C22⋊C4C2×D1312yes—
139#95—132no—
140#95—132no—
141#95—132no—
142#95—132no—
143#95—132no—
144#95—132no—
145#95—132no—
146#95C2×D1312yes—
147C2×C13—24no—
148C2×C13C2×#12511yescharacteristic
149C2×C13#53811yescharacteristic
150C2×C13#53811yescharacteristic
151C2×C13#53911yescharacteristic
152C2×C13#53911yescharacteristic
153C2×C13#54311yescharacteristic
154C2×C13#54411yescharacteristic
155C24C22×D1311yescharacteristic
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—262no—
163C22×C4—262no—
164C22×C4—521no—
165C22×C4—521no—
166C22×C4—521no—
167C22×C4—521no—
168C22×C4Dic2614yes—
169C22×C4C22×D1312yes—
170C22×C4C22×D1312yes—
171C22×C4C22×D1311yescharacteristic
172C22×C4C22×D1311yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—522no—
176C4⋊C4—522no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C22⋊C4—24no—
182C22⋊C4—264no—
183C13#264611yescharacteristic, complemented, Sylow
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23C2×Dic2612yes—
189C23#612912yes—
190C23#613112yes—
191C23C23×D1311yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—524no—
216C2×C4—524no—
217C2×C4C2×Dic2612yes—
218C2×C4C2×Dic2612yes—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#8814414yes—
226C22C22×Dic2611yescharacteristic
227C22C2×#612911yescharacteristic
228C22#8825111yescharacteristic
229C22#8825111yescharacteristic
230C22C2×#613111yescharacteristic
231C22#8825611yescharacteristic
232C22#8825711yescharacteristic
233C4—22no—
234C4—22no—
235C4—42no—
236C4—42no—
237C4—522no—
238C4—522no—
239C4—522no—
240C4—522no—
241C2—24no—
242C2#1171918811yescharacteristic
243C2C2×#8814411yescharacteristic
244C2#1171922411yescharacteristic
245C2#1171930711yescharacteristic
246C2#1171932211yescharacteristic
247C2#1171934911yescharacteristic
248C2#1171935011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC24×C13C23
hypercenter#380D13
hypocenterC13#2646
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
4. #11718647C2semidirect
5. #11718645C2semidirect
8. #11718322C2semidirect
9. #11718321C2semidirect
183. C13#2646semidirect

Maximal subgroups

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

subgroupindex
C13×#3802
#117188732
C2×#880712
#117186472
#117186452
#117186112
#117186072
#117183222
#117183212
#264613