Finite Group Databasebeta

← #15846053

Subgroups — #15846053

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126153C212yesmaximal
2#13125350C211yesmaximal, characteristic, complemented
3#13123549C211yesmaximal, characteristic
4#13114336C214yesmaximal, complemented
5#13114236C212yesmaximal, complemented
6#13114226C212yesmaximal, complemented
7#13113524C212yesmaximal, complemented
8C2×C13×#335C211yesmaximal, characteristic, complemented
9C2×#88155—21no—
10#11719182C2211yescharacteristic
11#11719175C2212yes—
12C2×C13×C4⋊C8C2212yes—
13C2×C4×C8×C13C2211yescharacteristic
14#11718775—24no—
15#11718771—21no—
16#11718767—21no—
17#11718767—21no—
18#11718585C2211yescharacteristic
19#11718512—22no—
20#11718509—22no—
21#11718503C2214yes—
22#11718502C2214yes—
23#11718349—21no—
24#11718349C2212yes—
25C8×D52—21no—
26C8×D52C2212yes—
27#11718344—21no—
28#11718344—21no—
29#11718343C2211yescharacteristic
30#11718343C2211yescharacteristic
31#11718341C2212yes—
32C13×#335C2212yes—
33C13×#335C2212yes—
34#11718074C2214yes—
35#11718073C2214yes—
36C2×#6127—21no—
37C22×C8×C13—22no—
38C22×C8×C13D411yescharacteristic
39C22×C8×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41#88184—21no—
42#88184D412yes—
43#88180—22no—
44#88178—22no—
45#88178—22no—
46C2×#6099—21no—
47C2×#6095—24no—
48#88155—44no—
49C2×#6094—22no—
50C2×C8×D13—22no—
51#88129—21no—
52#88128D411yescharacteristic
53C4×D52—21no—
54C4×D52C2312yes—
55#88124—22no—
56#88123D411yescharacteristic
57#88123C2312yes—
58#88123C2312yes—
59C4×Dic26—22no—
60C4×Dic26—22no—
61C13×C4⋊C8—22no—
62C13×C4⋊C8C2314yes—
63C4×C8×C13D411yescharacteristic
64C4×C8×C13D411yescharacteristic
65C4×C8×C13C2311yescharacteristic
66C4×C8×C13C2311yescharacteristic
67#88061—24no—
68#88060—22no—
69#88060—22no—
70#88058—21no—
71#88058—21no—
72#88058—21no—
73#88058—21no—
74#88057—22no—
75#88057—22no—
76#88057—24no—
77#88056—24no—
78C4⋊#1055—21no—
79C4⋊#1055C2312yes—
80#19195—131nomaximal, Sylow
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C2×C22⋊D13—22no—
85#6127—42no—
86#6127—42no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52C2×D412yes—
90C2×C4×D13—22no—
91C2×Dic26—21no—
92C2×Dic26—22no—
93C2×Dic26—22no—
94C2×C8×C13—22no—
95C2×C8×C13—24no—
96C2×C8×C13—82no—
97C2×C8×C13SD1614yescomplemented
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C42×C13C2411yescharacteristic
106C22⋊Dic13—42no—
107#6103—22no—
108#6103—22no—
109C4⋊Dic13—21no—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113C4⋊Dic13—22no—
114C4⋊Dic13C2×D412yes—
115#6101—42no—
116#6101—42no—
117C4×Dic13—42no—
118#6099—42no—
119C2×#1055—22no—
120#6095—84no—
121#6094—44no—
122C8×D13—44no—
123#3246—132no—
124#3160—131no—
125#2931—131no—
126#1691—134no—
127#1675—132no—
128#1673—132no—
129C2×#335D1311yescharacteristic, complemented
130#1550—132no—
131C23×C13#12111yescharacteristic
132C22×D13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—41no—
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13C2×SD1612yes—
140C2×C4×C13#13712yes—
141C2×C4×C13C22×D411yescharacteristic
142C2×C4×C13C22×D411yescharacteristic
143C2×C4×C13C2×#4111yescharacteristic
144C22⋊D13—44no—
145C2×Dic13—22no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148D52—22no—
149D52—22no—
150D52—42no—
151D52—42no—
152C4×D13—42no—
153C4×D13—42no—
154Dic26—42no—
155Dic26—42no—
156Dic26—42no—
157Dic26—82no—
158C8×C13—21no—
159C8×C13—21no—
160C8×C13—44no—
161C8×C13C2×SD1612yes—
162C8×C13C2×SD1612yes—
163#1055—42no—
164C2×#131—261no—
165#533—132no—
166#532—131no—
167#500—131no—
168#500—131no—
169#499—261no—
170#499—261no—
171#498—132no—
172#476—134no—
173#475—262no—
174#465—264no—
175#461—134no—
176#460—262no—
177#436—132no—
178#436—261no—
179C8×D4—132no—
180C8×D4—261no—
181#427—261no—
182#427—261no—
183#423—131no—
184C2×C4⋊C8C2×D1312yes—
185#408—261no—
186C2×C4×C8C2×D1311yescharacteristic
187#335C2×D1312yes—
188#335C2×D1312yes—
189#333—134no—
190#332—134no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#46112yes—
194C22×C13C2×#12111yescharacteristic
195C2×D13—42no—
196C2×D13—42no—
197C2×D13—42no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13#46112yes—
202C4×C13C22×SD1611yescharacteristic
203C4×C13C2×#13711yescharacteristic
204C4×C13#57611yescharacteristic
205C4×C13#57811yescharacteristic
206Dic13—42no—
207Dic13—82no—
208Dic13—82no—
209C2×#41—261no—
210C2×SD16—264no—
211#131—524no—
212C2×M16—261no—
213C2×M16—262no—
214C22×C8—22no—
215C22×C8—262no—
216C22×C8D5211yescharacteristic
217C22×C8D5211yescharacteristic
218C4⋊Q8—131no—
219C4⋊Q8—132no—
220C4⋊Q8—132no—
221#127—131no—
222#125—262no—
223#124—261no—
224C22⋊Q8—262no—
225C22⋊Q8—262no—
226#121—132no—
227#121—261no—
228C4×Q8—262no—
229C4×Q8—262no—
230C4×D4—132no—
231C4×D4—261no—
232#117—262no—
233C2×C42C22×D1311yescharacteristic
234#107—261no—
235#107—261no—
236#107—261no—
237#107—261no—
238#106—264no—
239#106—262no—
240#106—262no—
241C4⋊C8—22no—
242C4⋊C8—132no—
243C4⋊C8—261no—
244C4⋊C8C22×D1314yes—
245#103—264no—
246#102—264no—
247C22⋊C8—262no—
248C22⋊C8—262no—
249C4×C8D5211yescharacteristic
250C4×C8D5211yescharacteristic
251C4×C8C22×D1311yescharacteristic
252C4×C8C22×D1311yescharacteristic
253C2×C13—22no—
254C2×C13C2×#46111yescharacteristic
255C2×C13#306111yescharacteristic
256C2×C13#306711yescharacteristic
257D13—82no—
258#41—522no—
259#41—522no—
260C2×Q8—261no—
261C2×Q8—262no—
262C2×Q8—262no—
263C2×D4—132no—
264C2×D4—262no—
265C2×D4—261no—
266C2×D4—261no—
267C22×C4—262no—
268C22×C4C2×D5211yescharacteristic
269C22×C4D4×D1311yescharacteristic
270C22×C4#613111yescharacteristic
271SD16—1044no—
272M16—522no—
273M16—524no—
274C2×C8—22no—
275C2×C8—24no—
276C2×C8—82no—
277C2×C8—262no—
278C2×C8—524no—
279C2×C8#609514yescomplemented
280C2×C8C2×D5211yescharacteristic
281C2×C8C2×D5211yescharacteristic
282C2×C8C2×D5211yescharacteristic
283C2×C8C2×D5211yescharacteristic
284C4⋊C4—132no—
285C4⋊C4—261no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4—522no—
291C4⋊C4—522no—
292C22⋊C4—262no—
293C22⋊C4—262no—
294C22⋊C4—522no—
295C42—522no—
296C42C2×D5211yescharacteristic
297C42D4×D1311yescharacteristic
298C42#613111yescharacteristic
299C42C23×D1311yescharacteristic
300C13#1919511yescharacteristic, complemented, Sylow
301C23—262no—
302C23#8814911yescharacteristic
303Q8—522no—
304Q8—522no—
305Q8—522no—
306Q8—1042no—
307D4—262no—
308D4—262no—
309D4—522no—
310D4—524no—
311D4—522no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—262no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4#8814911yescharacteristic
321C2×C4#8814911yescharacteristic
322C2×C4#8814911yescharacteristic
323C2×C4C2×#609512yes—
324C2×C4#8816312yes—
325C2×C4C22×D5211yescharacteristic
326C2×C4C2×D4×D1311yescharacteristic
327C2×C4C2×#613111yescharacteristic
328C8—21no—
329C8—21no—
330C8—44no—
331C8—522no—
332C8C2×#609512yes—
333C8C2×#609512yes—
334C22—21no—
335C22—21no—
336C22—522no—
337C22—522no—
338C22—522no—
339C22#1171850212yes—
340C22C2×#8814911yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—522no—
345C4—1042no—
346C4—1042no—
347C4#1171850212yes—
348C4C22×#609511yescharacteristic
349C4C2×#8816311yescharacteristic
350C4#1171946211yescharacteristic
351C4#1171947111yescharacteristic
352C2—22no—
353C2—1042no—
354C2C2×#1171850211yescharacteristic
355C2#1312450811yescharacteristic
356C2#1312455711yescharacteristic
subgroupG/H
centerC22C2×#88149
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#335C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenterC2×#335D13
hypocenterC13#19195
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #13125350C2semidirect
4. #13114336C2semidirect
5. #13114236C2semidirect
6. #13114226C2semidirect
7. #13113524C2semidirect
8. C2×C13×#335C2semidirect
97. C2×C8×C13SD16semidirect
129. C2×#335D13semidirect
279. C2×C8#6095semidirect
300. C13#19195semidirect

Maximal subgroups

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

subgroupindex
#131261532
#131253502
#131235492
#131143362
#131142362
#131142262
#131135242
C2×C13×#3352
#1919513