Finite Group Databasebeta

← #16015955

Subgroups — #16015955

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×M32C211yesmaximal, characteristic
2C2×#11718541C211yesmaximal, characteristic
3D13×#427C211yesmaximal, characteristic
4#13116625C211yesmaximal, characteristic, complemented
5#13116624C211yesmaximal, characteristic, complemented
6#13116623C212yesmaximal, complemented
7#13116622C211yesmaximal, characteristic, complemented
8#13116621C212yesmaximal, complemented
9#13116619C212yesmaximal, complemented
10#13116617C212yesmaximal, complemented
11C13×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D13C2211yescharacteristic
13D13×#117—21no—
14C2×#88146—21no—
15C2×C13×M32C2211yescharacteristic
16C13×#427C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18#11718767C2211yescharacteristic
19C2×#88058C2211yescharacteristic
20C2×#88052C2211yescharacteristic
21#11718659—21no—
22C2×#88048—21no—
23D13×M32C418yescomplemented
24C2×#88038C2212yes—
25C2×C16×D13C2212yes—
26#11718541—21no—
27#11718541—21no—
28#11718541C2211yescharacteristic
29#11718541C2211yescharacteristic
30#11718541C2212yes—
31#11718541C2212yes—
32D13×#107C2211yescharacteristic
33D13×#107C2211yescharacteristic
34#11718521—21no—
35D13×#106—21no—
36C13×#367C2212yescomplemented
37C13×#366C2212yescomplemented
38#11718097C2212yescomplemented
39#11718096C2212yescomplemented
40#11718082C2212yescomplemented
41#11718082C2212yescomplemented
42#11718081C2212yescomplemented
43#11718081C2212yescomplemented
44C22×C4×D13D411yescharacteristic
45C22×C8×C13C2311yescharacteristic
46C13×#117—21no—
47C2×C13×C4⋊C4—21no—
48C2×#6103—41no—
49#88180—21no—
50C2×C4⋊Dic13—21no—
51C2×C4×Dic13—41no—
52C22×#1055D411yescharacteristic
53C2×C8×D13C2×C414yes—
54C2×C8×D13D411yescharacteristic
55C2×C8×D13D411yescharacteristic
56C2×C8×D13Q814yes—
57C2×C8×D13C2311yescharacteristic
58C2×C8×D13C2311yescharacteristic
59#88146—22no—
60#88146—22no—
61#88146—21no—
62#88146—21no—
63#88146—41no—
64#88146—41no—
65C4⋊C4×D13—21no—
66C4⋊C4×D13—21no—
67C22⋊C4×D13—41no—
68#88131—41no—
69#88126—41no—
70C42×D13—41no—
71C13×M32C2×C414yescomplemented
72C2×C13×C16C2312yes—
73C13×#107—21no—
74C13×#107C2312yes—
75C13×#107C2311yescharacteristic
76C13×#107C2311yescharacteristic
77C13×#106—21no—
78#88058—21no—
79#88058C2312yes—
80#88058C2311yescharacteristic
81#88058C2311yescharacteristic
82#88057—21no—
83#88052C2×C414yescomplemented
84C2×#6090C2312yes—
85#88048—21no—
86#88048—21no—
87#88048—22no—
88#88048—22no—
89#88047—21no—
90#88047—21no—
91#88038C2×C418yescomplemented
92C16×D13C2×C418yescomplemented
93#33409—131nomaximal, Sylow
94C23×D13D811yescharacteristic
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×Dic13—41no—
98C22×Dic13D811yescharacteristic
99C2×C4×D13—41no—
100C2×C4×D13—41no—
101C2×C4×D13C4⋊C414yes—
102C2×C4×D13D811yescharacteristic
103C2×C4×D13D811yescharacteristic
104C2×C4×D13Q1614yes—
105C2×C4×D13C2×D411yescharacteristic
106C2×C4×D13C2×D411yescharacteristic
107C2×C8×C13C22×C412yes—
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×Q812yes—
110C2×C8×C13C2411yescharacteristic
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—41no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117C22⋊Dic13—41no—
118#6103—41no—
119#6103—41no—
120#6103—42no—
121#6103—42no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—22no—
125C4⋊Dic13—41no—
126#6101—41no—
127#6101—41no—
128C4×Dic13—41no—
129C4×Dic13—41no—
130C4×Dic13—41no—
131C4×Dic13—42no—
132C4×Dic13—42no—
133C2×#1055C4⋊C414yes—
134C2×#1055C2×D411yescharacteristic
135C2×#1055C2×D411yescharacteristic
136C8×D13C4⋊C414yes—
137C8×D13C4⋊C414yes—
138C8×D13C22×C412yes—
139C8×D13C22×C412yes—
140C8×D13C2×Q812yes—
141C8×D13C2×Q812yes—
142C13×C16C22×C414yes—
143#6090C22×C414yes—
144C22×M32—131no—
145C2×#427—131no—
146C2×#427—131no—
147#2159—131no—
148#2159—131no—
149#2159—131no—
150#2159—132no—
151#2159—132no—
152#2159D1311yescharacteristic, complemented
153#2158—132no—
154#2158—132no—
155C23×C13C2×D811yescharacteristic
156C22×D13—41no—
157C22×D13—41no—
158C22×D13#10714yes—
159C22×D13C2×D811yescharacteristic
160C22×D13C2×D811yescharacteristic
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—82no—
165C2×C4×C13C2×C4⋊C412yes—
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×Q1612yes—
168C2×C4×C13C22×D411yescharacteristic
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—42no—
172C2×Dic13—82no—
173C2×Dic13#10714yes—
174C2×Dic13C2×D811yescharacteristic
175C2×Dic13C2×D811yescharacteristic
176C4×D13—82no—
177C4×D13—82no—
178C4×D13#10714yes—
179C4×D13#10714yes—
180C4×D13C2×C4⋊C412yes—
181C4×D13C2×C4⋊C412yes—
182C4×D13C2×Q1612yes—
183C4×D13C2×Q1612yes—
184C8×C13C2×C4⋊C412yes—
185C8×C13C23×C411yescharacteristic
186C8×C13C22×Q811yescharacteristic
187#1055C2×C4⋊C412yes—
188#1055C2×C4⋊C412yes—
189C23×C8—131no—
190C2×#117—261no—
191C2×#117—261no—
192C2×M32—131no—
193C2×M32—138no—
194C2×M32—132no—
195C2×M32C2×D1311yescharacteristic
196C22×C16—132no—
197#427—131no—
198#427—131no—
199#427—132no—
200#427—131no—
201#427—132no—
202#427—261no—
203#427—261no—
204#427—261no—
205#427—261no—
206#427C2×D1311yescharacteristic
207C2×#107—131no—
208C2×#107—131no—
209C2×#107—131no—
210C2×#107C2×D1311yescharacteristic
211C2×#106—261no—
212C2×#106—261no—
213#367—132no—
214#367—132no—
215#367—132no—
216#367C2×D1312yescomplemented
217#366—132no—
218#366—132no—
219#366—132no—
220#366C2×D1312yescomplemented
221C22×C13—21no—
222C22×C13—21no—
223C22×C13C2×#10712yes—
224C22×C13C22×D811yescharacteristic
225C2×D13—21no—
226C2×D13—21no—
227C2×D13—21no—
228C2×D13—21no—
229C2×D13—44no—
230C2×D13C2×#10712yes—
231C2×D13C2×#10712yes—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—82no—
235C4×C13C2×#10712yes—
236C4×C13C22×C4⋊C411yescharacteristic
237C4×C13C22×Q1611yescharacteristic
238Dic13—81no—
239Dic13—81no—
240Dic13—82no—
241Dic13C2×#10712yes—
242Dic13C2×#10712yes—
243C23×C4—131no—
244C22×C8—131no—
245C22×C8—134no—
246C22×C8—131no—
247C22×C8—131no—
248C22×C8—134no—
249C22×C8—131no—
250C22×C8—131no—
251C22×C8C22×D1311yescharacteristic
252#117—21no—
253#117—261no—
254#117—261no—
255#117—262no—
256#117—262no—
257#117—261no—
258#117—521no—
259#117—521no—
260#117—521no—
261#117—521no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4—261no—
266C2×C22⋊C4—521no—
267C2×C22⋊C4—521no—
268C2×C42—521no—
269C2×C42—521no—
270M32—134no—
271M32—138no—
272M32C4×D1314yescomplemented
273C2×C16—132no—
274C2×C16—138no—
275C2×C16C22×D1312yes—
276#107—21no—
277#107—131no—
278#107—132no—
279#107—131no—
280#107—261no—
281#107—261no—
282#107—261no—
283#107C22×D1311yescharacteristic
284#107C22×D1312yes—
285#107C22×D1311yescharacteristic
286#106—21no—
287#106—261no—
288#106—261no—
289#106—262no—
290#106—262no—
291#106—261no—
292C2×C13—22no—
293C2×C13C22×#10711yescharacteristic
294C2×C13#341411yescharacteristic
295C2×C13#341411yescharacteristic
296D13—22no—
297D13—22no—
298C24—131no—
299C22×C4—41no—
300C22×C4—131no—
301C22×C4—134no—
302C22×C4—131no—
303C22×C4—131no—
304C22×C4—134no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4D4×D1311yescharacteristic
311C2×C8—134no—
312C2×C8—131no—
313C2×C8—131no—
314C2×C8—134no—
315C2×C8—134no—
316C2×C8—132no—
317C2×C8—132no—
318C2×C8—132no—
319C2×C8—132no—
320C2×C8C2×C4×D1312yes—
321C2×C8D4×D1311yescharacteristic
322C2×C8Q8×D1312yes—
323C2×C8C23×D1311yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—262no—
329C4⋊C4—261no—
330C4⋊C4—261no—
331C4⋊C4—521no—
332C4⋊C4—521no—
333C4⋊C4—521no—
334C22⋊C4—41no—
335C22⋊C4—521no—
336C22⋊C4—521no—
337C22⋊C4—522no—
338C22⋊C4—522no—
339C22⋊C4—521no—
340C42—41no—
341C42—521no—
342C42—521no—
343C42—522no—
344C42—522no—
345C42—521no—
346C16—134no—
347C16C2×C4×D1314yes—
348C13#3340911yescharacteristic, complemented, Sylow
349C23—131no—
350C23—131no—
351C23—134no—
352C23—521no—
353C23—521no—
354C23D8×D1311yescharacteristic
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—131no—
360C2×C4—131no—
361C2×C4—134no—
362C2×C4—132no—
363C2×C4—132no—
364C2×C4—132no—
365C2×C4—132no—
366C2×C4—134no—
367C2×C4—134no—
368C2×C4—521no—
369C2×C4—522no—
370C2×C4—521no—
371C2×C4—1042no—
372C2×C4—1042no—
373C2×C4—1042no—
374C2×C4C4⋊C4×D1312yes—
375C2×C4D8×D1311yescharacteristic
376C2×C4Q16×D1312yes—
377C2×C4C2×D4×D1311yescharacteristic
378C8—132no—
379C8—132no—
380C8C4⋊C4×D1312yes—
381C8C22×C4×D1311yescharacteristic
382C8C2×Q8×D1311yescharacteristic
383C22—21no—
384C22—21no—
385C22—132no—
386C22—132no—
387C22—261no—
388C22—261no—
389C22—261no—
390C22—261no—
391C22—524no—
392C22D13×#10712yes—
393C22C2×D8×D1311yescharacteristic
394C4—82no—
395C4—81no—
396C4—81no—
397C4—132no—
398C4—132no—
399C4—1041no—
400C4—1041no—
401C4—1042no—
402C4D13×#10712yes—
403C4C2×C4⋊C4×D1311yescharacteristic
404C4C2×Q16×D1311yescharacteristic
405C2—22no—
406C2—262no—
407C2—262no—
408C2C2×D13×#10711yescharacteristic
409C2#1312796811yescharacteristic
410C2#1312797111yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2159C2
socleC22×C13C22×D8
prime radicalC23×D13D8
cosocleC2×C8×C13C24
hypercenter#2159D13
hypocenterC13#33409
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #13116625C2semidirect
5. #13116624C2semidirect
6. #13116623C2semidirect
7. #13116622C2semidirect
8. #13116621C2semidirect
9. #13116619C2semidirect
10. #13116617C2semidirect
11. C13×#2159C2semidirect
23. D13×M32C4semidirect
36. C13×#367C22semidirect
37. C13×#366C22semidirect
38. #11718097C22semidirect
39. #11718096C22semidirect
40. #11718082C22semidirect
41. #11718082C22semidirect
42. #11718081C22semidirect
43. #11718081C22semidirect
71. C13×M32C2×C4semidirect
83. #88052C2×C4semidirect
91. #88038C2×C4semidirect
92. C16×D13C2×C4semidirect
152. #2159D13semidirect
216. #367C2×D13semidirect
220. #366C2×D13semidirect
272. M32C4×D13semidirect
348. C13#33409semidirect

Maximal subgroups

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

subgroupindex
C2×D13×M322
C2×#117185412
D13×#4272
#131166252
#131166242
#131166232
#131166222
#131166212
#131166192
#131166172
C13×#21592
#3340913