Finite Group Databasebeta

← #16016367

Subgroups — #16016367

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×#11718378C211yesmaximal, characteristic, complemented
3#13116732C214yesmaximal, complemented
4#13116725C214yesmaximal, complemented
5#13116608C211yesmaximal, characteristic, complemented
6#13116585C211yesmaximal, characteristic, complemented
7#13116571C211yesmaximal, characteristic, complemented
8C2×#11718058C211yesmaximal, characteristic, complemented
9C13×#2943C211yesmaximal, characteristic, complemented
10C2×C13×#135C2211yescharacteristic
11C4×C13×#41—21no—
12C2×#88158C2211yescharacteristic
13C2×#88155—21no—
14C13×#442C2212yescomplemented
15C13×#441C2212yescomplemented
16C13×#440—22no—
17C13×#427C2211yescharacteristic
18C13×#416—21no—
19C2×C13×#97C2211yescharacteristic
20#11718856C412yescomplemented
21#11718855C414yescomplemented
22#11718854C412yescomplemented
23#11718840C2212yes—
24#11718808C2212yes—
25C2×#88059C2211yescharacteristic
26C2×#88052C2211yescharacteristic
27C2×#88052C2211yescharacteristic
28C2×#88045—21no—
29#11718378—22no—
30#11718378C2214yes—
31#11718157C2212yescomplemented
32#11718155C2212yescomplemented
33#11718080C2214yes—
34#11718079C2214yescomplemented
35#11718058C2214yescomplemented
36C2×C13×#41—21no—
37C2×#6127—21no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135C2×C412yes—
41C13×#135C2×C412yes—
42C2×C13×Q16C2311yescharacteristic
43C2×C13×SD16—21no—
44C2×C13×D8C2311yescharacteristic
45C22×C8×C13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C4×Q8×C13—22no—
48C4×D4×C13—22no—
49C4×D4×C13—42no—
50C13×#117—21no—
51C13×#117—41no—
52C2×C42×C13—41no—
53C2×C42×C13D411yescharacteristic
54C2×#6099—21no—
55C2×Dic52C2×C411yescharacteristic, complemented
56#88158—21no—
57#88158—21no—
58#88158C2×C412yescomplemented
59#88158C2312yes—
60C2×D104C2×C411yescharacteristic, complemented
61C2×#6095—21no—
62#88155—24no—
63#88155—42no—
64C2×#6094—41no—
65C2×C8×D13—41no—
66C13×#107—21no—
67C13×#106C2312yes—
68C13×#103—22no—
69C13×#102—22no—
70C13×#97D412yes—
71C13×#97C2312yes—
72#88069C2×C414yescomplemented
73#88068C2×C414yescomplemented
74#88067C2×C414yescomplemented
75#88066C2×C414yescomplemented
76#88059—21no—
77#88059C2312yes—
78#88052—21no—
79#88052C2×C412yescomplemented
80#88052C2312yes—
81#88052C2312yes—
82C2×#6090—21no—
83C2×#6090C2×C412yescomplemented
84#88045—24no—
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—21no—
94C22×C4×C13—42no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C2×C22⋊D13—41no—
98#6127—22no—
99#6127—22no—
100#6127—41no—
101#6127—41no—
102C2×D52—21no—
103C2×C4×D13—41no—
104C2×Dic26—21no—
105C13×Q16—21no—
106C13×Q16C22×C412yes—
107C13×SD16—22no—
108C13×SD16—22no—
109C13×D8—21no—
110C13×D8C22×C412yes—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13C22×C411yescharacteristic
114C2×C8×C13C22×C411yescharacteristic
115C2×C8×C13C2×D412yes—
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13#4111yescharacteristic
118C2×C8×C13#4111yescharacteristic
119C2×C8×C13C2411yescharacteristic
120C13×C4⋊C4—22no—
121C13×C4⋊C4—42no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—41no—
124C42×C13—21no—
125C42×C13—42no—
126C42×C13—41no—
127C42×C13C2×D412yes—
128#6099—22no—
129#6099—41no—
130C2×#1055—41no—
131Dic52—21no—
132Dic52C22×C412yes—
133D104—21no—
134D104C22×C412yes—
135#6095—22no—
136#6095—22no—
137#6094—44no—
138C8×D13—44no—
139#6090—22no—
140#6090C22×C414yes—
141#3414—131no—
142C2×#444—131no—
143#2943D1311yescharacteristic, complemented
144AGL(1,ℤ/16)—134no—
145#2180—134no—
146#2155—131no—
147#2148—131no—
148#2145—131no—
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—22no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—81no—
165C2×C4×C13—84no—
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13C4×D411yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13C22×D411yescharacteristic
172C22⋊D13—42no—
173C22⋊D13—42no—
174C2×Dic13—41no—
175D52—22no—
176D52—41no—
177C4×D13—42no—
178C4×D13—42no—
179Dic26—22no—
180Dic26—41no—
181C8×C13—22no—
182C8×C13C4×D411yescharacteristic
183C8×C13C4×D411yescharacteristic
184C8×C13C23×C411yescharacteristic
185C8×C13C2×#4111yescharacteristic
186#1055—42no—
187C2×#135—131no—
188C2×#135C2×D1311yescharacteristic
189C2×#131—261no—
190C4×#41—21no—
191#510—132no—
192#510—132no—
193#509—132no—
194#509—132no—
195#508—134no—
196C2×M32—131no—
197C2×M32—131no—
198#444—134no—
199#444—262no—
200#442C2×D1312yescomplemented
201#441C2×D1312yescomplemented
202#440—22no—
203C2×#108—131no—
204#427C2×D1311yescharacteristic
205C2×#104—261no—
206#416—21no—
207C2×#97C2×D1311yescharacteristic
208#365—134no—
209#362—132no—
210#361—132no—
211#360—134no—
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—42no—
223C4×C13—82no—
224C4×C13#44211yescharacteristic
225C4×C13#44211yescharacteristic
226C4×C13C2×C4×D411yescharacteristic
227C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
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×D1312yes—
238#135C4×D1312yes—
239C2×Q16—131no—
240C2×Q16C22×D1311yescharacteristic
241C2×SD16—21no—
242C2×SD16—261no—
243C2×D8—131no—
244C2×D8C22×D1311yescharacteristic
245#131—264no—
246#131—522no—
247C2×M16—261no—
248C2×M16—521no—
249C22×C8—521no—
250C22×C8C22⋊D1311yescharacteristic
251C22×C8C22×D1311yescharacteristic
252C4×Q8—22no—
253C4×D4—22no—
254C4×D4—42no—
255#117—21no—
256#117—41no—
257C2×C42—41no—
258C2×C42C22⋊D1311yescharacteristic
259Q32—134no—
260SD32—134no—
261SD32—134no—
262D16—134no—
263M32—132no—
264M32—132no—
265M32—132no—
266M32—261no—
267C2×C16—132no—
268C2×C16—261no—
269#108—132no—
270#108—261no—
271#107—21no—
272#106C22×D1312yes—
273#104—264no—
274#103—22no—
275#102—22no—
276#97C22⋊D1312yes—
277#97C22×D1312yes—
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—21no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—521no—
302C22×C4C2×C22⋊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—21no—
319C2×C8—21no—
320C2×C8—524no—
321C2×C8—521no—
322C2×C8C2×C4×D1311yescharacteristic
323C2×C8C2×C4×D1311yescharacteristic
324C2×C8#612711yescharacteristic
325C2×C8#612711yescharacteristic
326C2×C8C2×C22⋊D1312yes—
327C2×C8C2×C22⋊D1311yescharacteristic
328C2×C8C23×D1311yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C42—21no—
334C42—42no—
335C42—41no—
336C42C2×C22⋊D1312yes—
337C16—134no—
338C16—262no—
339C13#3346811yescharacteristic, complemented, Sylow
340C23—41no—
341C23—521no—
342C23#8818611yescharacteristic
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—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—84no—
362C2×C4—521no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4C4×C22⋊D1311yescharacteristic
366C2×C4C4×C22⋊D1311yescharacteristic
367C2×C4#8818611yescharacteristic
368C2×C4#8820311yescharacteristic
369C2×C4#8820311yescharacteristic
370C2×C4C22×C22⋊D1311yescharacteristic
371C8—22no—
372C8—522no—
373C8C4×C22⋊D1311yescharacteristic
374C8C4×C22⋊D1311yescharacteristic
375C8C22×C4×D1311yescharacteristic
376C8C2×#612711yescharacteristic
377C22—41no—
378C22—42no—
379C22—82no—
380C22—522no—
381C22—1042no—
382C22#1171867511yescharacteristic
383C22#1171867511yescharacteristic
384C22C2×#8818611yescharacteristic
385C4—42no—
386C4—42no—
387C4—82no—
388C4—522no—
389C4#1171867511yescharacteristic
390C4#1171867511yescharacteristic
391C4C2×C4×C22⋊D1311yescharacteristic
392C4C2×#8820311yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—1042no—
398C2C2×#1171867511yescharacteristic
subgroupG/H
centerC4#11718675
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2943C2
socleC2×C13C2×#442
prime radical#13127970C2
cosocleC2×C8×C13C24
hypercenter#2943D13
hypocenterC13#33468
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C2×#11718378C2semidirect
3. #13116732C2semidirect
4. #13116725C2semidirect
5. #13116608C2semidirect
6. #13116585C2semidirect
7. #13116571C2semidirect
8. C2×#11718058C2semidirect
9. C13×#2943C2semidirect
14. C13×#442C22semidirect
15. C13×#441C22semidirect
20. #11718856C4semidirect
21. #11718855C4semidirect
22. #11718854C4semidirect
31. #11718157C22semidirect
32. #11718155C22semidirect
34. #11718079C22semidirect
35. #11718058C22semidirect
55. C2×Dic52C2×C4semidirect
58. #88158C2×C4semidirect
60. C2×D104C2×C4semidirect
72. #88069C2×C4semidirect
73. #88068C2×C4semidirect
74. #88067C2×C4semidirect
75. #88066C2×C4semidirect
79. #88052C2×C4semidirect
83. C2×#6090C2×C4semidirect
143. #2943D13semidirect
200. #442C2×D13semidirect
201. #441C2×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×#117183782
#131167322
#131167252
#131166082
#131165852
#131165712
C2×#117180582
C13×#29432
#3346813