Finite Group Databasebeta

← #13130823

Subgroups — #13130823

Order 1664.

456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×C4⋊#261C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic
3C2×#88115C212yesmaximal, complemented
4D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
5#11718246C212yesmaximal, complemented
6C23×#261—21no—
7C2×D4×D13—21no—
8C2×D4×D13C2211yescharacteristic
9C22×C4×D13C2211yescharacteristic
10C2×C4⋊#261—21no—
11C2×C4⋊#261—24no—
12C2×C4⋊#261C2212yes—
13C2×D13⋊C8C2212yes—
14C13×#121C411yescharacteristic, complemented
15#88193—21no—
16#88192C411yescharacteristic, complemented
17#88184C411yescharacteristic, complemented
18#88149C411yescharacteristic, complemented
19C4⋊C4×D13C2211yescharacteristic
20#88138—21no—
21C22⋊C4×D13—21no—
22C22⋊#1057—21no—
23#88115—24no—
24#88111—21no—
25C23×D13—21no—
26C23×D13D411yescharacteristic
27C22×#261—24no—
28C22×#261—22no—
29C22×#261—42no—
30C22×#261—42no—
31C2×D4×C13—21no—
32C2×D4×C13C2×C411yescharacteristic, complemented
33C22×C4×C13C2×C411yescharacteristic
34C2×C22⋊D13—21no—
35C2×C22⋊D13—21no—
36C2×C22⋊D13—21no—
37C22×Dic13D411yescharacteristic
38D4×D13—22no—
39D4×D13—22no—
40D4×D13—42no—
41D4×D13—42no—
42C2×D52—21no—
43C2×D52C2×C411yescharacteristic, complemented
44C2×C4×D13—22no—
45C2×C4×D13—22no—
46C2×C4×D13—21no—
47C2×C4×D13C2×C411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13D411yescharacteristic
50C2×C4×D13C2311yescharacteristic
51C2×#1057—22no—
52C4⋊#261—24no—
53C4⋊#261—22no—
54C4⋊#261D414yescomplemented
55D13⋊C8—22no—
56D13⋊C8—22no—
57C13×C4⋊C4C2×C411yescharacteristic, complemented
58C13×C22⋊C4—21no—
59C22⋊Dic13—21no—
60#6103—21no—
61#6103—21no—
62C4⋊Dic13C2×C411yescharacteristic, complemented
63#6101—21no—
64#1874—131nomaximal, Sylow
65C23×C13—21no—
66C23×C13C22⋊C411yescharacteristic
67C22×D13—21no—
68C22×D13—21no—
69C22×D13—21no—
70C22×D13—21no—
71C22×D13—21no—
72C22×D13—41no—
73C22×D13—41no—
74C22×D13—41no—
75C22×D13—41no—
76C22×D13—41no—
77C22×D13—41no—
78C22×D13C22⋊C411yescharacteristic
79C22×D13D812yes—
80C22×D13SD1612yes—
81C22×D13C2×D411yescharacteristic
82C2×#261—24no—
83C2×#261—48no—
84C2×#261—42no—
85C2×#261—42no—
86D4×C13—22no—
87D4×C13—42no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13C22⋊C411yescharacteristic
91C2×C4×C13C22×C411yescharacteristic
92C22⋊D13—42no—
93C22⋊D13—42no—
94C22⋊D13—42no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13C22⋊C411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99D52—22no—
100D52—42no—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—22no—
104C4×D13—22no—
105C4×D13—41no—
106C4×D13—41no—
107C4×D13C2×D412yes—
108C4×D13#4112yes—
109#1057—42no—
110C2×#121—131no—
111C22×C4⋊C4—131no—
112C2×#102—132no—
113C2×C22⋊C8—131no—
114#340—132no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13#10212yescomplemented
121C22×C13C2×C22⋊C411yescharacteristic
122C2×D13—21no—
123C2×D13—21no—
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—81no—
132C2×D13—81no—
133C2×D13—81no—
134C2×D13—81no—
135C2×D13#10212yescomplemented
136C2×D13#12011yescharacteristic
137C2×D13#12311yescharacteristic
138C2×D13C2×D811yescharacteristic
139C2×D13C2×SD1611yescharacteristic
140C2×D13AGL(1,ℤ/8)11yescharacteristic
141C2×D13#13711yescharacteristic
142#261—44no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13C4×D412yes—
146Dic13—21no—
147Dic13—41no—
148Dic13#12112yes—
149C22×D4—131no—
150C22×D4—261no—
151C23×C4—131no—
152C23×C4—261no—
153C22×C8—132no—
154#121—131no—
155#121—131no—
156#121—131no—
157#121—261no—
158#121—261no—
159#121#26111yescharacteristic, complemented
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—264no—
163C2×C4⋊C4—261no—
164C2×C22⋊C4—261no—
165#102—264no—
166C22⋊C8—261no—
167C22⋊C8—261no—
168C2×C13—22no—
169C2×C13—81no—
170C2×C13#38611yescharacteristic
171C2×C13C2×#10211yescharacteristic
172C2×C13#41711yescharacteristic
173D13—22no—
174D13—81no—
175D13#44711yescharacteristic
176D13#44811yescharacteristic
177D13#48011yescharacteristic
178D13#48111yescharacteristic
179C24—131no—
180C24—261no—
181C2×D4—21no—
182C2×D4—131no—
183C2×D4—261no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—261no—
187C2×D4—261no—
188C2×D4—261no—
189C2×D4—522no—
190C2×D4—522no—
191C2×D4C2×#26111yescharacteristic, complemented
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—262no—
198C22×C4—262no—
199C22×C4—261no—
200C22×C4—262no—
201C22×C4—264no—
202C22×C4—522no—
203C22×C4—522no—
204C22×C4C2×#26111yescharacteristic
205C2×C8—262no—
206C2×C8—262no—
207C2×C8—262no—
208C4⋊C4—134no—
209C4⋊C4—131no—
210C4⋊C4—261no—
211C4⋊C4—262no—
212C4⋊C4—264no—
213C4⋊C4C2×#26111yescharacteristic, complemented
214C22⋊C4—21no—
215C22⋊C4—261no—
216C22⋊C4—261no—
217C22⋊C4—261no—
218C13#187411yescharacteristic, complemented, Sylow
219C23—21no—
220C23—131no—
221C23—132no—
222C23—132no—
223C23—131no—
224C23—261no—
225C23—261no—
226C23—261no—
227C23—261no—
228C23—261no—
229C23—521no—
230C23—521no—
231C23—521no—
232C23—521no—
233C23—521no—
234C23—521no—
235C23C22⋊#26111yescharacteristic
236D4—22no—
237D4—42no—
238D4—262no—
239D4—522no—
240D4—522no—
241D4—522no—
242D4—522no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—131no—
246C2×C4—132no—
247C2×C4—132no—
248C2×C4—131no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—264no—
255C2×C4—261no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—528no—
261C2×C4C22⋊#26111yescharacteristic
262C2×C4C22×#26111yescharacteristic
263C8—522no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—131no—
270C22—131no—
271C22—131no—
272C22—131no—
273C22—131no—
274C22—131no—
275C22—132no—
276C22—262no—
277C22—262no—
278C22—262no—
279C22—262no—
280C22—261no—
281C22—261no—
282C22—521no—
283C22—521no—
284C22—521no—
285C22—1041no—
286C22—1041no—
287C22—1041no—
288C22—1041no—
289C22#8811512yescomplemented
290C22C2×C22⋊#26111yescharacteristic
291C4—21no—
292C4—41no—
293C4—132no—
294C4—261no—
295C4—524no—
296C4—521no—
297C4D4×#26112yes—
298C2—22no—
299C2—81no—
300C2—131no—
301C2—131no—
302C2—131no—
303C2—131no—
304C2—262no—
305C2—1041no—
306C2C2×#8811511yescharacteristic
307C2#1171915011yescharacteristic
308C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radicalD13×#121C2
cosocleC2×C4×D13C23
hypercenter#121#261
hypocenterC13#1874
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊#261C2semidirect
3. C2×#88115C2semidirect
4. D13⋊(C22⋊C8)C2semidirect
5. #11718246C2semidirect
14. C13×#121C4semidirect
16. #88192C4semidirect
17. #88184C4semidirect
18. #88149C4semidirect
32. C2×D4×C13C2×C4semidirect
43. C2×D52C2×C4semidirect
54. C4⋊#261D4semidirect
57. C13×C4⋊C4C2×C4semidirect
62. C4⋊Dic13C2×C4semidirect
120. C22×C13#102semidirect
135. C2×D13#102semidirect
159. #121#261semidirect
191. C2×D4C2×#261semidirect
213. C4⋊C4C2×#261semidirect
218. C13#1874semidirect
289. C22#88115semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#2612
D13×#1212
C2×#881152
D13⋊(C22⋊C8)2
#117182462
#187413