Finite Group Databasebeta

← #13125609

Subgroups — #13125609

Order 1664.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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
2D13×C22⋊Q8C211yesmaximal, characteristic
3C13×#451C211yesmaximal, characteristic, complemented
4#11718889C211yesmaximal, characteristic, complemented
5#11718849C212yesmaximal, complemented
6#11718847C212yesmaximal, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718474C212yesmaximal, complemented
9#11718470C212yesmaximal, complemented
10D13×C22⋊C8C211yesmaximal, characteristic
11#11718383C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×Q8×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×Q16C2212yescomplemented
16C13×C22⋊Q8C2211yescharacteristic
17#88200—21no—
18#88200—21no—
19#88200C2212yes—
20#88200C2212yes—
21#88200C2211yescharacteristic
22C2×#6107C2212yescomplemented
23C2×#6103—21no—
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26C2×#6101—21no—
27C2×C8×D13C2212yes—
28#88151C2211yescharacteristic
29#88150—21no—
30C4⋊C4×D13—21no—
31C4⋊C4×D13C2211yescharacteristic
32C22⋊C4×D13—21no—
33#88132—21no—
34C13×#103C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36#88075C2212yescomplemented
37#88075C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88060C2212yes—
40#88058C2212yescomplemented
41#88056C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2311yescharacteristic
47C2×Q8×C13C2312yes—
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13D411yescharacteristic
52Q8×D13—42no—
53C2×C4×D13—21no—
54C2×C4×D13—21no—
55C2×C4×D13—42no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×C4×D13C2311yescharacteristic
60C2×Dic26—21no—
61C2×Dic26C2311yescharacteristic
62C13×Q16—42no—
63C2×C8×C13C2312yes—
64C13×C4⋊C4—21no—
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C22⋊Dic13—21no—
68#6107—42no—
69#6103—21no—
70#6103—21no—
71#6103—22no—
72#6103—22no—
73C4⋊Dic13—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13C2311yescharacteristic
76C4⋊Dic13C2312yes—
77#6101—21no—
78#6101—21no—
79#6101—21no—
80#6101—22no—
81#6101—22no—
82C2×#1055C2312yes—
83C8×D13—42no—
84#3189—131nomaximal, Sylow
85C23×C13C2×D411yescharacteristic
86C22×D13—41no—
87C22×D13—41no—
88C22×D13Q1614yescomplemented
89C22×D13C2×D411yescharacteristic
90C22×D13C2×D411yescharacteristic
91Q8×C13—22no—
92Q8×C13—22no—
93Q8×C13—22no—
94Q8×C13—42no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C4×D13—22no—
110C4×D13—22no—
111C4×D13—41no—
112C4×D13—41no—
113C4×D13—42no—
114C4×D13—42no—
115Dic26—22no—
116Dic26—42no—
117C8×C13—22no—
118#1055—22no—
119C2×C22⋊Q8—131no—
120C2×C22⋊Q8—131no—
121#484—131no—
122#484—132no—
123#484—131no—
124#467—132no—
125#467—132no—
126#451—131no—
127#451—132no—
128#451D1311yescharacteristic, complemented
129C2×C22⋊C8—131no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13C2×Q1612yes—
133C22×C13C22×D411yescharacteristic
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—21no—
138C2×D13—44no—
139C2×D13C2×Q1612yes—
140C2×D13C2×Q1612yes—
141C4×C13—21no—
142C4×C13—41no—
143C4×C13—42no—
144C4×C13—41no—
145C4×C13H(5,𝔽2)12yes—
146Dic13—21no—
147Dic13—21no—
148Dic13—41no—
149Dic13—41no—
150Dic13—42no—
151C22×Q8—131no—
152C22×Q8C2×D1311yescharacteristic
153C23×C4—131no—
154C2×Q16—132no—
155C2×Q16C2×D1312yescomplemented
156C22×C8—132no—
157C22⋊Q8—132no—
158C22⋊Q8—131no—
159C22⋊Q8—132no—
160C22⋊Q8—131no—
161C22⋊Q8—131no—
162C22⋊Q8—261no—
163C22⋊Q8—261no—
164C22⋊Q8—261no—
165C22⋊Q8—261no—
166C22⋊Q8C2×D1311yescharacteristic
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C22⋊C4—261no—
172C2×C22⋊C4—261no—
173#107—132no—
174#107—132no—
175#103—132no—
176#103—132no—
177#103—132no—
178#103C2×D1312yescomplemented
179C22⋊C8—131no—
180C22⋊C8—132no—
181C22⋊C8C2×D1311yescharacteristic
182C2×C13—22no—
183C2×C13#53411yescharacteristic
184C2×C13C22×Q1611yescharacteristic
185C2×C13#57511yescharacteristic
186D13—22no—
187D13—22no—
188C24—131no—
189C2×Q8—21no—
190C2×Q8—42no—
191C2×Q8—131no—
192C2×Q8—261no—
193C2×Q8—522no—
194C2×Q8C22×D1311yescharacteristic
195C2×Q8C22×D1312yes—
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4—522no—
206C22×C4C22×D1311yescharacteristic
207Q16—42no—
208Q16—522no—
209C2×C8—132no—
210C2×C8—522no—
211C2×C8C22×D1312yes—
212C4⋊C4—21no—
213C4⋊C4—131no—
214C4⋊C4—132no—
215C4⋊C4—261no—
216C4⋊C4—261no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4—261no—
220C4⋊C4—261no—
221C4⋊C4—261no—
222C4⋊C4C22×D1311yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C13#318911yescharacteristic, complemented, Sylow
230C23—131no—
231C23—131no—
232C23—134no—
233C23—521no—
234C23—521no—
235C23D4×D1311yescharacteristic
236Q8—22no—
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—262no—
241Q8—522no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—131no—
248C2×C4—131no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—522no—
260C2×C4D4×D1311yescharacteristic
261C2×C4C23×D1311yescharacteristic
262C8—22no—
263C8—262no—
264C22—21no—
265C22—21no—
266C22—132no—
267C22—132no—
268C22—261no—
269C22—261no—
270C22—261no—
271C22—261no—
272C22—524no—
273C22Q16×D1312yes—
274C22C2×D4×D1311yescharacteristic
275C4—21no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—261no—
280C4—261no—
281C4—521no—
282C4—522no—
283C4—521no—
284C4#8825112yes—
285C2—22no—
286C2—262no—
287C2—262no—
288C2#1171929411yescharacteristic
289C2C2×Q16×D1311yescharacteristic
290C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radicalC23×D13D4
hypercenter#451D13
hypocenterC13#3189
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C13×#451C2semidirect
4. #11718889C2semidirect
5. #11718849C2semidirect
6. #11718847C2semidirect
7. #11718705C2semidirect
8. #11718474C2semidirect
9. #11718470C2semidirect
11. #11718383C2semidirect
15. C2×C13×Q16C22semidirect
22. C2×#6107C22semidirect
34. C13×#103C22semidirect
36. #88075C22semidirect
37. #88075C22semidirect
40. #88058C22semidirect
41. #88056C22semidirect
42. #88047C22semidirect
88. C22×D13Q16semidirect
128. #451D13semidirect
155. C2×Q16C2×D13semidirect
178. #103C2×D13semidirect
229. C13#3189semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
D13×C22⋊Q82
C13×#4512
#117188892
#117188492
#117188472
#117187052
#117184742
#117184702
D13×C22⋊C82
#117183832
#318913