Finite Group Databasebeta

← #13125663

Subgroups — #13125663

Order 1664.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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×#88200C211yesmaximal, characteristic, complemented
2#11719311C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic, complemented
4#11718889C211yesmaximal, characteristic, complemented
5#11718835C212yesmaximal, complemented
6#11718834C212yesmaximal, complemented
7#11718695C211yesmaximal, characteristic, complemented
8#11718477C212yesmaximal, complemented
9#11718475C212yesmaximal, complemented
10#11718387C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×#6129C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×SD16C2212yescomplemented
16C13×#121C2211yescharacteristic
17#88200—21no—
18#88200—21no—
19#88200C2212yes—
20#88200C2212yes—
21C2×#6107C2212yescomplemented
22#88192C2211yescharacteristic
23#88191—21no—
24D4×Dic13—21no—
25C2×#6103—21no—
26C2×C4⋊Dic13C2211yescharacteristic
27#88178C2211yescharacteristic
28C2×#6101—21no—
29C2×#6094C2212yes—
30#88151C2211yescharacteristic
31#88146C2211yescharacteristic
32#88137—21no—
33#88135—21no—
34C13×#103C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36#88075C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88060C2212yes—
40#88058C2212yescomplemented
41#88056C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2312yes—
47C2×D4×C13—21no—
48C2×D4×C13C2311yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56#6129—42no—
57C2×C4×D13—42no—
58C2×C4×D13D411yescharacteristic
59C2×C4×D13D411yescharacteristic
60C2×C4×D13C2311yescharacteristic
61C2×C4×D13C2311yescharacteristic
62C2×Dic26C2311yescharacteristic
63C13×SD16—42no—
64C2×C8×C13C2312yes—
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C22⋊Dic13—21no—
68C22⋊Dic13—21no—
69#6107—42no—
70#6103—21no—
71#6103—21no—
72#6103—22no—
73#6103—22no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2312yes—
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79#6101—22no—
80#6101—22no—
81C4×Dic13—21no—
82C2×#1055C2312yes—
83#6094—42no—
84#3196—131nomaximal, Sylow
85C23×C13—21no—
86C23×C13C2×D411yescharacteristic
87C22×D13—22no—
88C22×D13—41no—
89C22×D13—41no—
90C22×D13C2×D411yescharacteristic
91C22×D13C2×D411yescharacteristic
92Q8×C13—22no—
93Q8×C13—22no—
94Q8×C13—42no—
95D4×C13—22no—
96D4×C13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—42no—
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2411yescharacteristic
103C22⋊D13—42no—
104C22⋊D13—42no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13C2×D411yescharacteristic
112C2×Dic13C2×D411yescharacteristic
113C4×D13—22no—
114C4×D13—22no—
115C4×D13—41no—
116C4×D13—41no—
117Dic26—22no—
118C8×C13—22no—
119#1055—22no—
120#525—131no—
121C2×C22⋊Q8—131no—
122#485—132no—
123#484—131no—
124#481—131no—
125#470—132no—
126#468—132no—
127#452—132no—
128#451—131no—
129#448D1311yescharacteristic, complemented
130#407—131no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13#13712yes—
137C22×C13C22×D411yescharacteristic
138C2×D13—21no—
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—21no—
144C2×D13—44no—
145C4×C13—21no—
146C4×C13—42no—
147C4×C13—41no—
148C4×C13H(5,𝔽2)12yes—
149Dic13—21no—
150Dic13—21no—
151Dic13—41no—
152Dic13—42no—
153Dic13—41no—
154C2×#41—131no—
155C22×Q8C2×D1311yescharacteristic
156C23×C4—131no—
157C2×Q16—132no—
158C2×SD16C2×D1312yescomplemented
159C2×M16—132no—
160#123—261no—
161C22⋊Q8—132no—
162C22⋊Q8—132no—
163C22⋊Q8—131no—
164C22⋊Q8—131no—
165C22⋊Q8—261no—
166C22⋊Q8—261no—
167#121—131no—
168#121C2×D1311yescharacteristic
169#120—261no—
170C4×D4—261no—
171C4×D4—261no—
172#117—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C22⋊C4—261no—
176#107—132no—
177#106—132no—
178#103—132no—
179#103—132no—
180#103C2×D1312yescomplemented
181#102—132no—
182C22⋊C8—131no—
183C22⋊C8—132no—
184C22⋊C8C2×D1311yescharacteristic
185C2×C13—22no—
186C2×C13—81no—
187C2×C13#53411yescharacteristic
188C2×C13C2×#13711yescharacteristic
189C2×C13#57511yescharacteristic
190D13—41no—
191D13—41no—
192C24—131no—
193#41—522no—
194C2×Q8—21no—
195C2×Q8—42no—
196C2×Q8—131no—
197C2×Q8C22×D1312yes—
198C2×D4—21no—
199C2×D4—261no—
200C2×D4—261no—
201C2×D4C22×D1311yescharacteristic
202C22×C4—21no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—522no—
211C22×C4C22×D1311yescharacteristic
212Q16—522no—
213SD16—42no—
214M16—522no—
215C2×C8—132no—
216C2×C8C22×D1312yes—
217C4⋊C4—132no—
218C4⋊C4—131no—
219C4⋊C4—262no—
220C4⋊C4—262no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C22⋊C4—261no—
230C22⋊C4—261no—
231C22⋊C4—261no—
232C42—261no—
233C13#319611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—131no—
236C23—131no—
237C23—262no—
238C23—521no—
239C23—521no—
240C23D4×D1311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—262no—
245D4—22no—
246D4—42no—
247D4—522no—
248D4—522no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—131no—
254C2×C4—131no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—261no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4D4×D1311yescharacteristic
266C2×C4C23×D1311yescharacteristic
267C8—22no—
268C8—262no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—261no—
275C22—261no—
276C22—261no—
277C22—261no—
278C22—261no—
279C22—261no—
280C22—524no—
281C22#8816912yes—
282C22C2×D4×D1311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—261no—
287C4—261no—
288C4—522no—
289C4—521no—
290C4—521no—
291C4#8825112yes—
292C2—22no—
293C2—81no—
294C2—521no—
295C2—521no—
296C2#1171929411yescharacteristic
297C2C2×#8816911yescharacteristic
298C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radical#11719311C2
hypercenter#448D13
hypocenterC13#3196
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#448C2semidirect
4. #11718889C2semidirect
5. #11718835C2semidirect
6. #11718834C2semidirect
7. #11718695C2semidirect
8. #11718477C2semidirect
9. #11718475C2semidirect
10. #11718387C2semidirect
11. #11718383C2semidirect
15. C2×C13×SD16C22semidirect
21. C2×#6107C22semidirect
34. C13×#103C22semidirect
36. #88075C22semidirect
37. #88072C22semidirect
40. #88058C22semidirect
41. #88056C22semidirect
42. #88048C22semidirect
129. #448D13semidirect
158. C2×SD16C2×D13semidirect
180. #103C2×D13semidirect
233. C13#3196semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
#117193112
C13×#4482
#117188892
#117188352
#117188342
#117186952
#117184772
#117184752
#117183872
#117183832
#319613