Finite Group Databasebeta

← D13×#2255 #16018412

Subgroups — D13×#2255 #16018412

Order 3328.

518 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#500C211yesmaximal, characteristic
2D13×#499C211yesmaximal, characteristic
3#13117123C211yesmaximal, characteristic, complemented
4#13117122C211yesmaximal, characteristic, complemented
5#13117121C212yesmaximal, complemented
6#13117120C212yesmaximal, complemented
7#13117119C211yesmaximal, characteristic, complemented
8D13×#367C212yesmaximal
9D13×#366C212yesmaximal
10D13×#346C211yesmaximal, characteristic
11C13×#2255C211yesmaximal, characteristic, complemented
12D13×C4⋊Q8—21no—
13D13×#125—21no—
14C13×#500C2211yescharacteristic
15C13×#499C2211yescharacteristic
16#11718739—21no—
17#11718725—21no—
18C2×C16×D13C2212yes—
19D13×#107—21no—
20D13×#107C2211yescharacteristic
21D13×#107C2212yes—
22D13×#107C2211yescharacteristic
23#11718539C2211yescharacteristic
24#11718539C2211yescharacteristic
25#11718535—21no—
26#11718535C2212yes—
27D13×#106—21no—
28#11718519—21no—
29C4×C8×D13C2211yescharacteristic
30#11718344C2211yescharacteristic
31#11718343C2211yescharacteristic
32C13×#367C2212yes—
33C13×#366C2212yes—
34C13×#346C2211yescharacteristic
35#11718097C2212yes—
36#11718096C2212yes—
37#11718094C2212yes—
38#11718082C2212yes—
39#11718082C2212yes—
40#11718081C2212yes—
41#11718081C2212yes—
42#11718053C2211yescharacteristic
43C2×Q8×D13—41no—
44C13×C4⋊Q8—21no—
45C13×#125—21no—
46#88198—41no—
47C2×C8×D13D411yescharacteristic
48C2×C8×D13C2311yescharacteristic
49C4⋊C4×D13—22no—
50C4⋊C4×D13—21no—
51C4⋊C4×D13—21no—
52C4⋊C4×D13—41no—
53C4⋊C4×D13—41no—
54C4⋊C4×D13—41no—
55#88144—21no—
56#88144—21no—
57#88143—41no—
58#88143—41no—
59#88142—22no—
60#88142—41no—
61C42×D13D411yescharacteristic
62#88124—21no—
63#88123—21no—
64C2×C13×C16C2312yes—
65C13×#107—21no—
66C13×#107C2311yescharacteristic
67C13×#107C2312yes—
68C13×#107C2311yescharacteristic
69C13×#106—21no—
70C4×C8×C13C2311yescharacteristic
71#88058—21no—
72#88058C2312yes—
73#88058C2311yescharacteristic
74#88058C2311yescharacteristic
75#88057—21no—
76C8×Dic13D411yescharacteristic
77C8×Dic13C2311yescharacteristic
78C2×#6090C2312yes—
79#88048—21no—
80#88048—21no—
81#88047—21no—
82#88047—21no—
83#88047—22no—
84#88047—22no—
85C4×#1055D411yescharacteristic
86C16×D13Q818yescomplemented
87C2×#2255—131nomaximal, Sylow
88C2×Q8×C13—41no—
89Q8×D13—84no—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—42no—
93C2×C4×D13D811yescharacteristic
94C2×C4×D13D811yescharacteristic
95C2×C4×D13C2×D411yescharacteristic
96C2×Dic26—41no—
97C2×Dic26—42no—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2411yescharacteristic
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C42×C13C2×D411yescharacteristic
107C4⋊Dic13—22no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113#6101—41no—
114#6101—41no—
115#6101—42no—
116#6101—42no—
117#6101—41no—
118#6101—41no—
119#6101—41no—
120#6101—41no—
121C4×Dic13D811yescharacteristic
122C4×Dic13D811yescharacteristic
123C4×Dic13C2×D411yescharacteristic
124C2×#1055C2×D411yescharacteristic
125C2×#1055C2×D411yescharacteristic
126C8×D13Q1614yes—
127C8×D13C2×Q814yes—
128C13×C16C2×Q814yescomplemented
129#6090C2×Q814yescomplemented
130C2×#500—131no—
131C2×#499—131no—
132#2255—131no—
133#2255—131no—
134#2255—132no—
135#2255—132no—
136#2255—131no—
137#2255D1311yescharacteristic, direct product factor
138C2×#367—132no—
139C2×#366—132no—
140C2×#346—131no—
141C22×D13C2×D811yescharacteristic
142Q8×C13—82no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13C2×D811yescharacteristic
147C2×C4×C13C2×D811yescharacteristic
148C2×C4×C13C22×D411yescharacteristic
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—42no—
152C2×Dic13C2×D811yescharacteristic
153C2×Dic13C2×D811yescharacteristic
154C2×Dic13C2×D811yescharacteristic
155C4×D13—22no—
156C4×D13—22no—
157C4×D13—82no—
158C4×D13—84no—
159C4×D13—82no—
160C4×D13C4⋊Q812yes—
161C4×D13C2×Q1612yes—
162Dic26—84no—
163Dic26—82no—
164C8×C13C2×Q1612yes—
165C8×C13C22×Q812yes—
166#1055C4⋊Q812yes—
167#1055C2×Q1612yes—
168C2×C4⋊Q8—261no—
169C2×#125—261no—
170C22×C16—132no—
171#500—132no—
172#500—131no—
173#500—261no—
174#500—261no—
175#500C2×D1311yescharacteristic
176#499—131no—
177#499—131no—
178#499—131no—
179#499—261no—
180#499—261no—
181#499C2×D1311yescharacteristic
182C2×#107—131no—
183C2×#107—131no—
184C2×#107—132no—
185C2×#107—261no—
186C2×#106—261no—
187C2×C4×C8—131no—
188#367—132no—
189#367—132no—
190#367—132no—
191#367C2×D1312yes—
192#366—132no—
193#366—132no—
194#366—132no—
195#366C2×D1312yes—
196#346—132no—
197#346—131no—
198#346C2×D1311yescharacteristic
199C22×C13C22×D811yescharacteristic
200C2×D13#50012yes—
201C2×D13#50912yes—
202C2×D13#51012yes—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—82no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13C2×C4⋊Q811yescharacteristic
209C4×C13C22×Q1611yescharacteristic
210Dic13—21no—
211Dic13—21no—
212Dic13—82no—
213Dic13—81no—
214Dic13—81no—
215Dic13#50012yes—
216C22×Q8—521no—
217C22×C8—131no—
218C22×C8—131no—
219C4⋊Q8—21no—
220C4⋊Q8—262no—
221C4⋊Q8—261no—
222C4⋊Q8—521no—
223C4⋊Q8—521no—
224#125—21no—
225#125—261no—
226#125—261no—
227#125—261no—
228#125—521no—
229#125—521no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—521no—
234C2×C4⋊C4—521no—
235C2×C4⋊C4—521no—
236C2×C42—131no—
237C2×C16—132no—
238C2×C16—138no—
239C2×C16C22×D1312yes—
240#107—21no—
241#107—131no—
242#107—132no—
243#107—131no—
244#107—261no—
245#107—261no—
246#107—262no—
247#107—262no—
248#107—261no—
249#107C22×D1311yescharacteristic
250#107C22×D1312yes—
251#107C22×D1311yescharacteristic
252#106—21no—
253#106—261no—
254#106—261no—
255#106—261no—
256C4×C8—131no—
257C4×C8—131no—
258C4×C8—131no—
259C4×C8C22×D1311yescharacteristic
260C2×C13C2×#50011yescharacteristic
261C2×C13C2×#50911yescharacteristic
262C2×C13C2×#51011yescharacteristic
263D13#225514yesdirect product factor
264C2×Q8—41no—
265C2×Q8—522no—
266C2×Q8—521no—
267C2×Q8—1044no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—522no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8—134no—
277C2×C8—134no—
278C2×C8D4×D1311yescharacteristic
279C2×C8C23×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—261no—
287C4⋊C4—261no—
288C4⋊C4—262no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—522no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4—521no—
295C4⋊C4—521no—
296C4⋊C4—522no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—521no—
300C42—131no—
301C42—131no—
302C42—131no—
303C42D4×D1311yescharacteristic
304C16—134no—
305C16Q8×D1314yescomplemented
306C13C2×#225511yescharacteristic, complemented, Sylow
307C23—131no—
308Q8—82no—
309Q8—1042no—
310Q8—1044no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—131no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—131no—
318C2×C4—131no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—522no—
324C2×C4—1042no—
325C2×C4—1042no—
326C2×C4—1044no—
327C2×C4D8×D1311yescharacteristic
328C2×C4D8×D1311yescharacteristic
329C2×C4C2×D4×D1311yescharacteristic
330C8—132no—
331C8—132no—
332C8Q16×D1312yes—
333C8C2×Q8×D1312yes—
334C22—132no—
335C22—132no—
336C22—132no—
337C22C2×D8×D1311yescharacteristic
338C4—21no—
339C4—21no—
340C4—81no—
341C4—82no—
342C4—81no—
343C4—132no—
344C4—261no—
345C4—261no—
346C4—1041no—
347C4—1042no—
348C4—1041no—
349C4D13×C4⋊Q811yescharacteristic
350C4C2×Q16×D1311yescharacteristic
351C2—134no—
352C2D13×#50011yescharacteristic
353C2D13×#50911yescharacteristic
354C2D13×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2255C2
socleC22×C13C22×D8
prime radicalC22×D13C2×D8
hypercenter#2255D13
hypocenterC13C2×#2255
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13117123C2semidirect
4. #13117122C2semidirect
5. #13117121C2semidirect
6. #13117120C2semidirect
7. #13117119C2semidirect
11. C13×#2255C2semidirect
86. C16×D13Q8semidirect
128. C13×C16C2×Q8semidirect
129. #6090C2×Q8semidirect
137. #2255D13direct (N × H)
263. D13#2255direct (N × H)
305. C16Q8×D13semidirect
306. C13C2×#2255semidirect

Maximal subgroups

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

subgroupindex
D13×#5002
D13×#4992
#131171232
#131171222
#131171212
#131171202
#131171192
D13×#3672
D13×#3662
D13×#3462
C13×#22552
C2×#225513