Finite Group Databasebeta

← #16016365

Subgroups — #16016365

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#13127970C211yesmaximal, characteristic
2C2×#11718858C211yesmaximal, characteristic, complemented
3#13123636C211yesmaximal, characteristic, complemented
4#13116731C214yesmaximal, complemented
5#13116724C214yesmaximal, complemented
6#13116608C211yesmaximal, characteristic, complemented
7#13116586C211yesmaximal, characteristic, complemented
8C2×#11718104C211yesmaximal, characteristic, complemented
9C13×#2145C211yesmaximal, characteristic, complemented
10C2×C13×#135C2211yescharacteristic
11C2×#88202—21no—
12C2×#88158C2211yescharacteristic
13#11719227—21no—
14C2×C13×M32C2211yescharacteristic
15C13×#427C2211yescharacteristic
16C2×#88077—21no—
17#11718858—22no—
18#11718858C2214yes—
19#11718856C2212yes—
20#11718855C414yescomplemented
21#11718854C2212yes—
22#11718840C412yescomplemented
23#11718808C412yescomplemented
24C2×#88059C2211yescharacteristic
25C2×#88055C2211yescharacteristic
26C2×#88052C2211yescharacteristic
27#11718663—21no—
28#11718550—22no—
29#11718530C2212yescomplemented
30#11718514C2212yescomplemented
31C13×#360C2214yes—
32#11718109C2212yescomplemented
33#11718108C2212yescomplemented
34#11718104C2214yescomplemented
35#11718079C2214yescomplemented
36C2×C13×#41—21no—
37C2×#6127—21no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135C2×C412yescomplemented
41C13×#135C2312yes—
42C2×C13×Q16C2×C411yescharacteristic, complemented
43C2×C13×SD16—21no—
44C2×C13×D8C2×C411yescharacteristic, complemented
45C22×C8×C13C2311yescharacteristic
46C13×#117—21no—
47#88202—24no—
48#88202—42no—
49C2×C4×Dic13D411yescharacteristic
50C2×#6099—21no—
51C2×#6099—41no—
52C22×#1055—41no—
53C22×#1055D411yescharacteristic
54C2×Dic52C2311yescharacteristic
55#88158—21no—
56#88158—21no—
57#88158C2×C412yes—
58#88158C2×C412yes—
59C2×D104C2311yescharacteristic
60C2×#6095—21no—
61#88147—22no—
62#88141—22no—
63#88135—42no—
64#88126—41no—
65C42×D13—41no—
66C13×M32—21no—
67C13×M32C2312yes—
68C2×C13×C16—21no—
69C13×#107—21no—
70C13×#106C2312yes—
71#88077—24no—
72#88069C2×C414yescomplemented
73#88068C2×C414yescomplemented
74#88067C2×C414yescomplemented
75#88066C2×C414yescomplemented
76#88059—21no—
77#88059C2312yes—
78#88055D412yes—
79#88055C2312yes—
80#88052C2×C412yescomplemented
81#88052C2312yes—
82C2×#6090C2×C412yescomplemented
83#88050—22no—
84#88049—22no—
85#33468—131nomaximal, Sylow
86C13×#41—22no—
87C13×#41—22no—
88C13×#41—41no—
89C13×#41—41no—
90C2×Q8×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C2×D411yescharacteristic
95C2×C22⋊D13—41no—
96C22×Dic13—21no—
97#6127—22no—
98#6127—22no—
99#6127—41no—
100#6127—41no—
101C2×D52—21no—
102C2×C4×D13—41no—
103C2×C4×D13—42no—
104C2×Dic26—21no—
105C13×Q16—21no—
106C13×Q16C22×C412yes—
107C13×SD16—22no—
108C13×SD16—22no—
109C13×D8—21no—
110C13×D8C22×C412yes—
111C2×C8×C13C22×C411yescharacteristic
112C2×C8×C13C22×C411yescharacteristic
113C2×C8×C13C2×D411yescharacteristic
114C2×C8×C13#4111yescharacteristic
115C2×C8×C13#4111yescharacteristic
116C2×C8×C13C2411yescharacteristic
117C13×C4⋊C4—22no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120#6103—42no—
121#6101—42no—
122C4×Dic13—21no—
123C4×Dic13—42no—
124C4×Dic13C2×D412yes—
125#6099—22no—
126#6099—44no—
127#6099—41no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—44no—
131C2×#1055—41no—
132C2×#1055C2×D412yes—
133Dic52—21no—
134Dic52C22×C412yes—
135D104—21no—
136D104C22×C412yes—
137#6095—22no—
138#6095—22no—
139C13×C16—22no—
140#6090C22×C414yes—
141#3414—131no—
142C2×#444—131no—
143#2943—131no—
144AGL(1,ℤ/16)—134no—
145#2180—134no—
146#2155—131no—
147#2148—131no—
148#2145D1311yescharacteristic, complemented
149C2×#347—131no—
150C23×C13—41no—
151C23×C13AGL(1,ℤ/8)11yescharacteristic
152C22×D13—41no—
153Q8×C13—22no—
154Q8×C13—41no—
155D4×C13—22no—
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13C4×D411yescharacteristic
164C2×C4×C13C4×D411yescharacteristic
165C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C22⋊D13—42no—
170C22⋊D13—42no—
171C2×Dic13—22no—
172C2×Dic13—41no—
173C2×Dic13—81no—
174D52—22no—
175D52—41no—
176C4×D13—42no—
177C4×D13—42no—
178C4×D13—84no—
179Dic26—22no—
180Dic26—41no—
181C8×C13C4×D411yescharacteristic
182C8×C13C4×D411yescharacteristic
183C8×C13C23×C411yescharacteristic
184C8×C13C2×#4111yescharacteristic
185#1055—22no—
186#1055—42no—
187C2×#135—131no—
188C2×#135C2×D1311yescharacteristic
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×#108—131no—
204#427C2×D1311yescharacteristic
205C2×#104—261no—
206#416—261no—
207C2×#97—131no—
208#365—134no—
209#362—132no—
210#361—132no—
211#360C2×D1314yes—
212#347—134no—
213C22×C13—41no—
214C22×C13—42no—
215C22×C13—82no—
216C22×C13#44211yescharacteristic
217C22×C13#44211yescharacteristic
218C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
219C2×D13—42no—
220C2×D13—82no—
221C4×C13—42no—
222C4×C13—82no—
223C4×C13#44211yescharacteristic
224C4×C13#44211yescharacteristic
225C4×C13C2×C4×D411yescharacteristic
226C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
227Dic13—42no—
228Dic13—42no—
229C2×#41—21no—
230C2×#41—261no—
231#135—21no—
232#135—21no—
233#135—132no—
234#135—132no—
235#135—261no—
236#135—261no—
237#135C4×D1312yescomplemented
238#135C22×D1312yes—
239C2×Q16—131no—
240C2×Q16C4×D1311yescharacteristic, complemented
241C2×SD16—21no—
242C2×SD16—261no—
243C2×D8—131no—
244C2×D8C4×D1311yescharacteristic, complemented
245#131—264no—
246#131—522no—
247C2×M16—261no—
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—21no—
264M32—132no—
265M32—132no—
266M32C22×D1312yes—
267C2×C16—21no—
268C2×C16—132no—
269#108—132no—
270#108—261no—
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×C13—82no—
282C2×C13C2×#44211yescharacteristic
283D13—82no—
284#41—22no—
285#41—22no—
286#41—41no—
287#41—41no—
288#41—262no—
289#41—262no—
290#41—521no—
291#41—521no—
292C2×Q8—21no—
293C2×Q8—261no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—261no—
297C2×D4—521no—
298C22×C4—41no—
299C22×C4—261no—
300C22×C4—522no—
301C22×C4—521no—
302C22×C4D4×D1311yescharacteristic
303Q16—21no—
304Q16—132no—
305Q16—261no—
306Q16C2×C4×D1312yes—
307SD16—22no—
308SD16—22no—
309SD16—262no—
310SD16—262no—
311D8—21no—
312D8—132no—
313D8—261no—
314D8C2×C4×D1312yes—
315M16—262no—
316M16—524no—
317M16—521no—
318C2×C8—132no—
319C2×C8—261no—
320C2×C8—261no—
321C2×C8—524no—
322C2×C8—521no—
323C2×C8C2×C4×D1311yescharacteristic
324C2×C8C2×C4×D1311yescharacteristic
325C2×C8D4×D1311yescharacteristic
326C2×C8#612911yescharacteristic
327C2×C8#612911yescharacteristic
328C2×C8C23×D1311yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—522no—
331C22⋊C4—41no—
332C22⋊C4—522no—
333C42—41no—
334C42—132no—
335C42—261no—
336C42—522no—
337C16—22no—
338C16—134no—
339C13#3346811yescharacteristic, complemented, Sylow
340C23—41no—
341C23—521no—
342C23#8816511yescharacteristic
343Q8—22no—
344Q8—41no—
345Q8—262no—
346Q8—521no—
347D4—22no—
348D4—42no—
349D4—42no—
350D4—41no—
351D4—262no—
352D4—522no—
353D4—522no—
354D4—521no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—262no—
360C2×C4—521no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—1044no—
364C2×C4—1041no—
365C2×C4#8813511yescharacteristic
366C2×C4#8813511yescharacteristic
367C2×C4#8816511yescharacteristic
368C2×C4#8816811yescharacteristic
369C2×C4#8816811yescharacteristic
370C2×C4C2×D4×D1311yescharacteristic
371C8—262no—
372C8—522no—
373C8#8813511yescharacteristic
374C8#8813511yescharacteristic
375C8C22×C4×D1311yescharacteristic
376C8C2×#612911yescharacteristic
377C22—41no—
378C22—42no—
379C22—82no—
380C22—522no—
381C22—1042no—
382C22#1171844611yescharacteristic
383C22#1171844611yescharacteristic
384C22C2×#8816511yescharacteristic
385C4—42no—
386C4—82no—
387C4—522no—
388C4—522no—
389C4#1171844611yescharacteristic
390C4#1171844611yescharacteristic
391C4C2×#8813511yescharacteristic
392C4C2×#8816811yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—1042no—
398C2C2×#1171844611yescharacteristic
subgroupG/H
centerC4#11718446
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2145C2
socleC2×C13C2×#442
prime radical#13127970C2
cosocleC2×C8×C13C24
hypercenter#2145D13
hypocenterC13#33468
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
2. C2×#11718858C2semidirect
3. #13123636C2semidirect
4. #13116731C2semidirect
5. #13116724C2semidirect
6. #13116608C2semidirect
7. #13116586C2semidirect
8. C2×#11718104C2semidirect
9. C13×#2145C2semidirect
20. #11718855C4semidirect
22. #11718840C4semidirect
23. #11718808C4semidirect
29. #11718530C22semidirect
30. #11718514C22semidirect
32. #11718109C22semidirect
33. #11718108C22semidirect
34. #11718104C22semidirect
35. #11718079C22semidirect
40. C13×#135C2×C4semidirect
42. C2×C13×Q16C2×C4semidirect
44. C2×C13×D8C2×C4semidirect
72. #88069C2×C4semidirect
73. #88068C2×C4semidirect
74. #88067C2×C4semidirect
75. #88066C2×C4semidirect
80. #88052C2×C4semidirect
82. C2×#6090C2×C4semidirect
148. #2145D13semidirect
237. #135C4×D13semidirect
240. C2×Q16C4×D13semidirect
244. C2×D8C4×D13semidirect
339. C13#33468semidirect

Maximal subgroups

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

subgroupindex
#131279702
C2×#117188582
#131236362
#131167312
#131167242
#131166082
#131165862
C2×#117181042
C13×#21452
#3346813