Finite Group Databasebeta

← #13125617

Subgroups — #13125617

Order 1664.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2#11719496C211yesmaximal, characteristic
3#11718889C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5C2×C22⋊#1055C211yesmaximal, characteristic, complemented
6#11718712C212yesmaximal, complemented
7#11718709C212yesmaximal, complemented
8#11718708C212yesmaximal, complemented
9#11718706C212yesmaximal, complemented
10#11718632C211yesmaximal, characteristic, complemented
11#11718628C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C13×C22⋊Q8—21no—
16C13×C22⋊Q8—21no—
17C13×C22⋊Q8C2212yes—
18C13×C22⋊Q8C2212yes—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4—21no—
22#88207—21no—
23C2×#6107C2212yescomplemented
24C2×#6106C2212yescomplemented
25#88184C2211yescharacteristic
26#88184C2211yescharacteristic
27#88183—21no—
28C4×C22⋊D13—21no—
29C4×C22⋊D13—21no—
30#88180C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C22×#1055C2212yes—
34#88075C2212yescomplemented
35#88075C2212yescomplemented
36C22⋊#1055C2212yes—
37C22⋊#1055C2211yescharacteristic
38C22⋊#1055C2211yescharacteristic
39#88050C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13D411yescharacteristic
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2312yes—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—42no—
50C22×C4×C13D411yescharacteristic
51C22×C4×C13D411yescharacteristic
52C22×C4×C13D411yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C2×C22⋊D13—21no—
57C2×C22⋊D13—21no—
58C2×C22⋊D13—21no—
59#6127—42no—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×Dic26C2311yescharacteristic
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2312yes—
67C13×C22⋊C4—22no—
68C13×C22⋊C4—22no—
69C22⋊Dic13—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72#6107—42no—
73#6106—42no—
74#6103—21no—
75#6103—21no—
76C4⋊Dic13C2311yescharacteristic
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79#6101—21no—
80C4×Dic13—21no—
81C2×#1055—42no—
82C2×#1055C2312yes—
83C2×#1055C2312yes—
84#3190—131nomaximal, Sylow
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—41no—
88C23×C13C2×D411yescharacteristic
89C23×C13C2×D411yescharacteristic
90C23×C13C2×D411yescharacteristic
91C22×D13—21no—
92Q8×C13—22no—
93Q8×C13—22no—
94Q8×C13—42no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2411yescharacteristic
109C22⋊D13—42no—
110C22⋊D13—42no—
111C22⋊D13—42no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115D52—22no—
116C4×D13—42no—
117Dic26—22no—
118#1055—22no—
119#1055—22no—
120#525—131no—
121C2×C22⋊Q8D1311yescharacteristic, complemented
122#485—132no—
123#483—131no—
124#480—131no—
125#467—132no—
126#465—132no—
127#452—132no—
128#451—131no—
129#448—131no—
130C2×C22⋊C8—131no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—44no—
139C22×C13#13512yes—
140C22×C13#13712yes—
141C22×C13C22×D411yescharacteristic
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—41no—
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—42no—
149C4×C13—42no—
150C4×C13H(5,𝔽2)12yes—
151Dic13—41no—
152Dic13—41no—
153Dic13—41no—
154C2×#41—131no—
155C22×Q8C2×D1311yescharacteristic
156C23×C4C2×D1311yescharacteristic
157C2×Q16—132no—
158C2×SD16—132no—
159C22×C8—132no—
160#123—261no—
161C22⋊Q8—21no—
162C22⋊Q8—21no—
163C22⋊Q8—131no—
164C22⋊Q8—131no—
165C22⋊Q8C2×D1312yes—
166C22⋊Q8C2×D1312yes—
167#121—131no—
168#121—131no—
169#120—261no—
170C4×D4—261no—
171C4×D4—261no—
172#117—131no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×D1311yescharacteristic
175C2×C22⋊C4—21no—
176#107—132no—
177#106—132no—
178#103—132no—
179#103—132no—
180#103—132no—
181#102—132no—
182C22⋊C8—131no—
183C22⋊C8—131no—
184C22⋊C8—132no—
185C2×C13—22no—
186C2×C13—22no—
187C2×C13—41no—
188C2×C13#53411yescharacteristic
189C2×C13C2×#13511yescharacteristic
190C2×C13C2×#13711yescharacteristic
191D13—81no—
192C24C22⋊D1311yescharacteristic
193#41—522no—
194C2×Q8—21no—
195C2×Q8—42no—
196C2×Q8—131no—
197C2×Q8C22×D1312yes—
198C2×D4—131no—
199C2×D4—261no—
200C2×D4—261no—
201C2×D4—261no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—261no—
206C22×C4C22⋊D1311yescharacteristic
207C22×C4C22⋊D1311yescharacteristic
208C22×C4C22⋊D1311yescharacteristic
209C22×C4C22×D1311yescharacteristic
210C22×C4C22×D1311yescharacteristic
211C22×C4C22×D1311yescharacteristic
212Q16—522no—
213SD16—522no—
214C2×C8—132no—
215C2×C8—132no—
216C2×C8—522no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—21no—
220C4⋊C4—131no—
221C4⋊C4—131no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4C22×D1312yes—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C22⋊C4—261no—
228C22⋊C4—261no—
229C22⋊C4—261no—
230C22⋊C4—261no—
231C22⋊C4—261no—
232C42—261no—
233C13#319011yescharacteristic, complemented, Sylow
234C23—22no—
235C23—22no—
236C23—41no—
237C23—261no—
238C23C2×C22⋊D1311yescharacteristic
239C23C2×C22⋊D1311yescharacteristic
240C23C2×C22⋊D1311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—262no—
245D4—262no—
246D4—522no—
247D4—522no—
248D4—522no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—522no—
263C2×C4C2×C22⋊D1311yescharacteristic
264C2×C4C2×C22⋊D1311yescharacteristic
265C2×C4C2×C22⋊D1311yescharacteristic
266C2×C4C23×D1311yescharacteristic
267C8—262no—
268C8—262no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—521no—
278C22—521no—
279C22—521no—
280C22#8819612yes—
281C22#8820412yes—
282C22C22×C22⋊D1311yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—521no—
289C4—521no—
290C4—521no—
291C4#8825112yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—1041no—
296C2#1171950911yescharacteristic
297C2C2×#8819611yescharacteristic
298C2C2×#8820411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊Q8C2
socleC22×C13C22×D4
prime radical#11719496C2
hypercenterC2×C22⋊Q8D13
hypocenterC13#3190
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
3. #11718889C2semidirect
4. #11718888C2semidirect
5. C2×C22⋊#1055C2semidirect
6. #11718712C2semidirect
7. #11718709C2semidirect
8. #11718708C2semidirect
9. #11718706C2semidirect
10. #11718632C2semidirect
11. #11718628C2semidirect
23. C2×#6107C22semidirect
24. C2×#6106C22semidirect
34. #88075C22semidirect
35. #88075C22semidirect
39. #88050C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
121. C2×C22⋊Q8D13semidirect
233. C13#3190semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
#117194962
#117188892
#117188882
C2×C22⋊#10552
#117187122
#117187092
#117187082
#117187062
#117186322
#117186282
#319013