Finite Group Databasebeta

← #13130846

Subgroups — #13130846

Order 1664.

386 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 68 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#11719623C211yesmaximal, characteristic
2D13×#123C211yesmaximal, characteristic
3D13⋊#99C211yesmaximal, characteristic
4#11719135C212yesmaximal, complemented
5#11718238C212yesmaximal, complemented
6C2×D4×D13C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×C22⋊#261C2212yes—
10C2×C22⋊#261C2212yes—
11D4×#261—24no—
12#88237—21no—
13C13×#123C411yescharacteristic, complemented
14#88189C411yescharacteristic, complemented
15#88183C411yescharacteristic, complemented
16#88148—21no—
17C4⋊C4×D13—21no—
18#88140C411yescharacteristic, complemented
19#88137—21no—
20C22⋊C4×D13—21no—
21C22⋊C4×D13C2211yescharacteristic
22#88119—21no—
23(C2×#261)⋊C4—24no—
24#88107—21no—
25C23×D13D411yescharacteristic
26C23×D13C2311yescharacteristic
27C22×#261—22no—
28C22×#261—22no—
29C22×#261D414yes—
30C2×D4×C13C2×C411yescharacteristic
31C22×C4×C13C2×C411yescharacteristic, complemented
32C2×C22⋊D13C2×C411yescharacteristic
33C2×C22⋊D13D411yescharacteristic
34C22×Dic13C2×C411yescharacteristic, complemented
35D4×D13—22no—
36D4×D13—22no—
37C2×D52D411yescharacteristic
38C2×C4×D13—22no—
39C2×C4×D13—21no—
40C2×C4×D13—21no—
41C2×C4×D13—21no—
42C2×C4×D13—22no—
43C2×C4×D13D411yescharacteristic
44C22⋊#261—22no—
45C22⋊#261—22no—
46C22⋊#261—22no—
47C22⋊#261—22no—
48C22⋊#261—22no—
49C4⋊#261—22no—
50C4×#261—22no—
51C13×C4⋊C4—21no—
52C13×C22⋊C4—21no—
53C13×C22⋊C4C2×C411yescharacteristic, complemented
54C22⋊Dic13—21no—
55C22⋊Dic13C2×C411yescharacteristic, complemented
56#6103—21no—
57#6103—21no—
58#6103—21no—
59C4⋊Dic13—21no—
60#6101—21no—
61#6101—21no—
62#1890—131nomaximal, Sylow
63C23×C13C22⋊C411yescharacteristic
64C23×C13C22×C411yescharacteristic
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—42no—
68C22×D13—42no—
69C22×D13C22⋊C411yescharacteristic
70C22×D13C2×D412yes—
71C22×D13C2×D411yescharacteristic
72C22×D13C2×D411yescharacteristic
73C22×D13#4112yes—
74C2×#261—24no—
75C2×#261—44no—
76C2×#261—44no—
77C2×#261—42no—
78C2×#261—82no—
79D4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13C22⋊C411yescharacteristic
84C22⋊D13—22no—
85C22⋊D13—22no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13C22⋊C411yescharacteristic
90D52—22no—
91C4×D13—21no—
92C4×D13—21no—
93C4×D13—42no—
94C4×D13—41no—
95C4×D13—42no—
96C4×D13—41no—
97C2×#123—131no—
98#518—131no—
99C2×#99—131no—
100#381—132no—
101#342—132no—
102C22×C13—21no—
103C22×C13—41no—
104C22×C13—41no—
105C22×C13C2×C22⋊C411yescharacteristic
106C22×C13C4×D412yes—
107C2×D13—22no—
108C2×D13—24no—
109C2×D13—21no—
110C2×D13—41no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—41no—
114C2×D13—81no—
115C2×D13#12011yescharacteristic
116C2×D13#12112yes—
117C2×D13#12311yescharacteristic
118#261—44no—
119#261—82no—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—41no—
123Dic13—21no—
124Dic13—41no—
125Dic13—41no—
126C22×D4—131no—
127C23×C4—131no—
128#123—131no—
129#123—131no—
130#123—131no—
131#123—261no—
132#123—261no—
133#123#26111yescharacteristic, complemented
134C4×D4—264no—
135#117—261no—
136C2×C4⋊C4—261no—
137C2×C22⋊C4—131no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—261no—
141C2×C22⋊C4—261no—
142#99—261no—
143#99—261no—
144#95—264no—
145C2×C13—21no—
146C2×C13—22no—
147C2×C13—41no—
148C2×C13#38611yescharacteristic
149D13—22no—
150D13—21no—
151D13—41no—
152D13#45812yes—
153C24—131no—
154C24—131no—
155C2×D4—131no—
156C2×D4—131no—
157C2×D4—131no—
158C2×D4—262no—
159C2×D4—262no—
160C2×D4C2×#26111yescharacteristic
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—134no—
164C22×C4—262no—
165C22×C4—261no—
166C22×C4—261no—
167C22×C4—261no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4—262no—
171C22×C4C2×#26111yescharacteristic, complemented
172C4⋊C4—21no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—262no—
176C4⋊C4—261no—
177C22⋊C4—21no—
178C22⋊C4—131no—
179C22⋊C4—261no—
180C22⋊C4—261no—
181C22⋊C4—261no—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C22⋊C4—261no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4C2×#26111yescharacteristic, complemented
189C42—262no—
190C13#189011yescharacteristic, complemented, Sylow
191C23—132no—
192C23—131no—
193C23—132no—
194C23—131no—
195C23—131no—
196C23—261no—
197C23—261no—
198C23—522no—
199C23—522no—
200C23C22⋊#26111yescharacteristic
201C23C22×#26111yescharacteristic
202D4—22no—
203D4—262no—
204D4—262no—
205D4—262no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—131no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—264no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—521no—
217C2×C4—522no—
218C2×C4—521no—
219C2×C4—522no—
220C2×C4—524no—
221C2×C4—522no—
222C2×C4—524no—
223C2×C4—1042no—
224C2×C4C22⋊#26111yescharacteristic
225C22—21no—
226C22—41no—
227C22—41no—
228C22—131no—
229C22—132no—
230C22—131no—
231C22—264no—
232C22—262no—
233C22—261no—
234C22—521no—
235C22—522no—
236C22—521no—
237C22—522no—
238C22—1041no—
239C22D4×#26112yes—
240C22C2×C22⋊#26111yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—261no—
245C4—521no—
246C4—524no—
247C4—521no—
248C4—1042no—
249C2—21no—
250C2—22no—
251C2—41no—
252C2—132no—
253C2—262no—
254C2—261no—
255C2—521no—
256C2#1171915011yescharacteristic
subgroupG/H
centerC2#11719150
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#123C4
socleC2×C13#386
prime radicalC2×D4×D13C22
cosocleC23×D13C23
hypercenter#123#261
hypocenterC13#1890
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11719135C2semidirect
5. #11718238C2semidirect
13. C13×#123C4semidirect
14. #88189C4semidirect
15. #88183C4semidirect
18. #88140C4semidirect
31. C22×C4×C13C2×C4semidirect
34. C22×Dic13C2×C4semidirect
53. C13×C22⋊C4C2×C4semidirect
55. C22⋊Dic13C2×C4semidirect
133. #123#261semidirect
171. C22×C4C2×#261semidirect
188. C22⋊C4C2×#261semidirect
190. C13#1890semidirect

Maximal subgroups

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

subgroupindex
#117196232
D13×#1232
D13⋊#992
#117191352
#117182382
#189013