Finite Group Databasebeta

← #16016368

Subgroups — #16016368

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127972C211yesmaximal, characteristic
2C2×#11718555C211yesmaximal, characteristic, complemented
3#13123636C211yesmaximal, characteristic, complemented
4#13116733C214yesmaximal, complemented
5#13116726C214yesmaximal, complemented
6#13116583C211yesmaximal, characteristic, complemented
7#13116571C211yesmaximal, characteristic, complemented
8C2×#11718104C211yesmaximal, characteristic, complemented
9C13×#2155C211yesmaximal, characteristic, complemented
10C2×#88161—21no—
11C2×#88158C2211yescharacteristic
12C2×#88158C2211yescharacteristic
13#11719227—21no—
14C2×C13×M32C2211yescharacteristic
15C2×C13×#108C2211yescharacteristic
16C13×#427C2211yescharacteristic
17C2×#88065—21no—
18C2×#88055C2211yescharacteristic
19C2×#88052C2211yescharacteristic
20#11718663—21no—
21#11718570C412yescomplemented
22#11718570C2212yes—
23#11718569C412yescomplemented
24#11718569C2212yes—
25#11718565C414yescomplemented
26#11718555—22no—
27#11718555C2214yes—
28#11718550—22no—
29#11718530C2212yescomplemented
30#11718514C2212yescomplemented
31C13×#365C2214yescomplemented
32#11718104C2214yescomplemented
33#11718088C2212yescomplemented
34#11718087C2212yescomplemented
35#11718080C2214yes—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×C13×M16—21no—
39C22×C8×C13C2311yescharacteristic
40C13×#117—21no—
41C2×C4×Dic13D411yescharacteristic
42C22×#1055D411yescharacteristic
43#88161—24no—
44#88161—42no—
45C2×Dic52C2×C411yescharacteristic, complemented
46C2×Dic52C2311yescharacteristic
47#88158—21no—
48#88158—21no—
49#88158—21no—
50#88158—21no—
51#88158C2×C412yes—
52#88158C2×C412yes—
53#88158C2×C412yescomplemented
54#88158C2312yes—
55C2×D104C2×C411yescharacteristic, complemented
56C2×D104C2311yescharacteristic
57C2×#6095—21no—
58C2×#6095—21no—
59C2×#6094—41no—
60C2×C8×D13—41no—
61#88147—22no—
62#88141—22no—
63#88135—42no—
64#88126—41no—
65C42×D13—41no—
66C13×M32C2×C412yescomplemented
67C13×M32C2312yes—
68C2×C13×C16C2×C412yescomplemented
69C13×#108—21no—
70C13×#108C2312yes—
71C13×#107—21no—
72C13×#106C2312yes—
73#88065—24no—
74#88055D412yes—
75#88055C2312yes—
76#88052—21no—
77#88052C2312yes—
78C2×#6090—21no—
79#88050—22no—
80#88049—22no—
81Dic104C2×C414yescomplemented
82#88040C2×C414yescomplemented
83#88040C2×C414yescomplemented
84D208C2×C414yescomplemented
85#33468—131nomaximal, Sylow
86C22×C4×C13C2×D411yescharacteristic
87C2×C22⋊D13—41no—
88C2×C22⋊D13—41no—
89C22×Dic13—21no—
90#6127—22no—
91#6127—22no—
92#6127—22no—
93#6127—22no—
94#6127—41no—
95#6127—41no—
96#6127—41no—
97#6127—41no—
98C2×D52—21no—
99C2×D52—21no—
100C2×C4×D13—41no—
101C2×C4×D13—41no—
102C2×C4×D13—42no—
103C2×Dic26—21no—
104C2×Dic26—21no—
105C13×M16—22no—
106C13×M16—41no—
107C2×C8×C13—41no—
108C2×C8×C13C22×C411yescharacteristic
109C2×C8×C13C22×C411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C2×C8×C13#4111yescharacteristic
113C2×C8×C13C2411yescharacteristic
114C13×C4⋊C4—22no—
115C13×C22⋊C4—41no—
116C42×C13—41no—
117#6103—42no—
118#6101—42no—
119C4×Dic13—21no—
120C4×Dic13—42no—
121C4×Dic13C2×D412yes—
122C2×#1055—21no—
123C2×#1055—21no—
124C2×#1055C2×D412yes—
125Dic52—21no—
126Dic52—21no—
127Dic52C22×C412yes—
128Dic52C22×C412yes—
129D104—21no—
130D104—21no—
131D104C22×C412yes—
132D104C22×C412yes—
133#6095—22no—
134#6095—22no—
135#6095—22no—
136#6095—22no—
137#6094—44no—
138C8×D13—44no—
139C13×C16C22×C414yes—
140#6090—22no—
141#3414—131no—
142C2×#444—131no—
143#2943—131no—
144AGL(1,ℤ/16)—134no—
145#2180—134no—
146#2155D1311yescharacteristic, complemented
147#2148—131no—
148#2145—131no—
149C2×#347—131no—
150C23×C13AGL(1,ℤ/8)11yescharacteristic
151C22×D13—41no—
152C22×D13—41no—
153C2×C4×C13—42no—
154C2×C4×C13C4×D411yescharacteristic
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C13C22×D411yescharacteristic
160C22⋊D13—42no—
161C22⋊D13—42no—
162C22⋊D13—42no—
163C22⋊D13—42no—
164C2×Dic13—22no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—81no—
168D52—22no—
169D52—22no—
170D52—41no—
171D52—41no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—42no—
175C4×D13—42no—
176C4×D13—84no—
177Dic26—22no—
178Dic26—22no—
179Dic26—41no—
180Dic26—41no—
181C8×C13—42no—
182C8×C13C4×D411yescharacteristic
183C8×C13C4×D411yescharacteristic
184C8×C13C23×C411yescharacteristic
185C8×C13C2×#4111yescharacteristic
186#1055—22no—
187C2×#135—131no—
188C2×#135—131no—
189C2×#131—261no—
190C4×#41—261no—
191#510—132no—
192#510—132no—
193#509—132no—
194#509—132no—
195#508—134no—
196C2×M32—131no—
197C2×M32C2×D1311yescharacteristic
198#444—134no—
199#444—262no—
200#442—132no—
201#441—132no—
202#440—262no—
203C2×#108C2×D1311yescharacteristic
204#427C2×D1311yescharacteristic
205C2×#104—261no—
206#416—261no—
207C2×#97—131no—
208#365C2×D1314yescomplemented
209#362—132no—
210#361—132no—
211#360—134no—
212#347—134no—
213C22×C13—41no—
214C22×C13#44211yescharacteristic
215C22×C13#44211yescharacteristic
216C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
217C2×D13—42no—
218C2×D13—42no—
219C2×D13—82no—
220C2×D13—82no—
221C4×C13—82no—
222C4×C13#44211yescharacteristic
223C4×C13#44211yescharacteristic
224C4×C13C2×C4×D411yescharacteristic
225C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
226Dic13—42no—
227Dic13—42no—
228Dic13—42no—
229C2×#41—261no—
230C2×#41—261no—
231#135—132no—
232#135—132no—
233#135—132no—
234#135—132no—
235#135—261no—
236#135—261no—
237#135—261no—
238#135—261no—
239C2×Q16—131no—
240C2×Q16—131no—
241C2×SD16—261no—
242C2×SD16—261no—
243C2×D8—131no—
244C2×D8—131no—
245#131—264no—
246#131—522no—
247C2×M16—21no—
248C2×M16—521no—
249C22×C8—131no—
250C22×C8—521no—
251C22×C8C22×D1311yescharacteristic
252C4×Q8—262no—
253C4×D4—262no—
254C4×D4—522no—
255#117—21no—
256#117—521no—
257C2×C42—131no—
258C2×C42—521no—
259Q32—134no—
260SD32—134no—
261SD32—134no—
262D16—134no—
263M32—132no—
264M32—261no—
265M32C4×D1312yescomplemented
266M32C22×D1312yes—
267C2×C16—261no—
268C2×C16C4×D1312yescomplemented
269#108—21no—
270#108C22×D1312yes—
271#107—21no—
272#106C22×D1312yes—
273#104—264no—
274#103—262no—
275#102—262no—
276#97—132no—
277#97—132no—
278C2×C13—21no—
279C2×C13—21no—
280C2×C13—21no—
281C2×C13C2×#44211yescharacteristic
282D13—82no—
283D13—82no—
284#41—262no—
285#41—262no—
286#41—262no—
287#41—262no—
288#41—521no—
289#41—521no—
290#41—521no—
291#41—521no—
292C2×Q8—261no—
293C2×Q8—261no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—521no—
297C2×D4—521no—
298C22×C4—261no—
299C22×C4—522no—
300C22×C4—521no—
301C22×C4—521no—
302C22×C4D4×D1311yescharacteristic
303Q16—132no—
304Q16—132no—
305Q16—261no—
306Q16—261no—
307SD16—262no—
308SD16—262no—
309SD16—262no—
310SD16—262no—
311D8—132no—
312D8—132no—
313D8—261no—
314D8—261no—
315M16—22no—
316M16—41no—
317M16—524no—
318C2×C8—41no—
319C2×C8—132no—
320C2×C8—261no—
321C2×C8—261no—
322C2×C8—524no—
323C2×C8C2×C4×D1311yescharacteristic
324C2×C8C2×C4×D1311yescharacteristic
325C2×C8D4×D1311yescharacteristic
326C2×C8#613111yescharacteristic
327C2×C8#613111yescharacteristic
328C2×C8C23×D1311yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—522no—
331C22⋊C4—41no—
332C22⋊C4—522no—
333C42—41no—
334C42—132no—
335C42—261no—
336C42—522no—
337C16—262no—
338C16C2×C4×D1314yes—
339C13#3346811yescharacteristic, complemented, Sylow
340C23—521no—
341C23—521no—
342C23#8816811yescharacteristic
343Q8—262no—
344Q8—262no—
345Q8—521no—
346Q8—521no—
347D4—262no—
348D4—262no—
349D4—522no—
350D4—522no—
351D4—522no—
352D4—522no—
353D4—521no—
354D4—521no—
355C2×C4—42no—
356C2×C4—262no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—1044no—
364C2×C4—1041no—
365C2×C4#8814711yescharacteristic
366C2×C4#8814711yescharacteristic
367C2×C4#8816811yescharacteristic
368C2×C4#8816811yescharacteristic
369C2×C4#8816811yescharacteristic
370C2×C4C2×D4×D1311yescharacteristic
371C8—42no—
372C8—262no—
373C8#8814711yescharacteristic
374C8#8814711yescharacteristic
375C8C22×C4×D1311yescharacteristic
376C8C2×#613111yescharacteristic
377C22—41no—
378C22—522no—
379C22—522no—
380C22—1042no—
381C22—1042no—
382C22#1171853011yescharacteristic
383C22#1171853011yescharacteristic
384C22C2×#8816811yescharacteristic
385C4—82no—
386C4—522no—
387C4—522no—
388C4—522no—
389C4#1171853011yescharacteristic
390C4#1171853011yescharacteristic
391C4C2×#8814711yescharacteristic
392C4C2×#8816811yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—1042no—
397C2—1042no—
398C2C2×#1171853011yescharacteristic
subgroupG/H
centerC4#11718530
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2155C2
socleC2×C13C2×#442
prime radical#13127972C2
cosocleC2×C8×C13C24
hypercenter#2155D13
hypocenterC13#33468
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
2. C2×#11718555C2semidirect
3. #13123636C2semidirect
4. #13116733C2semidirect
5. #13116726C2semidirect
6. #13116583C2semidirect
7. #13116571C2semidirect
8. C2×#11718104C2semidirect
9. C13×#2155C2semidirect
21. #11718570C4semidirect
23. #11718569C4semidirect
25. #11718565C4semidirect
29. #11718530C22semidirect
30. #11718514C22semidirect
31. C13×#365C22semidirect
32. #11718104C22semidirect
33. #11718088C22semidirect
34. #11718087C22semidirect
45. C2×Dic52C2×C4semidirect
53. #88158C2×C4semidirect
55. C2×D104C2×C4semidirect
66. C13×M32C2×C4semidirect
68. C2×C13×C16C2×C4semidirect
81. Dic104C2×C4semidirect
82. #88040C2×C4semidirect
83. #88040C2×C4semidirect
84. D208C2×C4semidirect
146. #2155D13semidirect
208. #365C2×D13semidirect
265. M32C4×D13semidirect
268. C2×C16C4×D13semidirect
339. C13#33468semidirect

Maximal subgroups

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

subgroupindex
#131279722
C2×#117185552
#131236362
#131167332
#131167262
#131165832
#131165712
C2×#117181042
C13×#21552
#3346813