Finite Group Databasebeta

← #16016328

Subgroups — #16016328

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127970C211yesmaximal, characteristic
2C2×#11718857C211yesmaximal, characteristic, complemented
3C2×#11718556C211yesmaximal, characteristic, complemented
4#13116719C214yesmaximal, complemented
5#13116714C214yesmaximal, complemented
6#13116630C211yesmaximal, characteristic, complemented
7#13116565C211yesmaximal, characteristic, complemented
8M32×Dic13C211yesmaximal, characteristic, complemented
9C13×#2143C211yesmaximal, characteristic, complemented
10C2×C13×#135C2211yescharacteristic
11C2×#88202—21no—
12C2×#88161—21no—
13C2×#88158C2211yescharacteristic
14C2×C13×M32C2211yescharacteristic
15C2×C13×#108C2211yescharacteristic
16C2×#88077—21no—
17#11718857—21no—
18#11718857—21no—
19#11718857C2212yescomplemented
20#11718857C2212yescomplemented
21#11718856C412yescomplemented
22#11718855C2214yes—
23#11718854C412yescomplemented
24#11718840C412yescomplemented
25#11718808C412yescomplemented
26C2×#88065—21no—
27C2×#88059C2211yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29C2×#88052C2211yescharacteristic
30#11718556—21no—
31#11718556—21no—
32#11718556C2212yescomplemented
33#11718556C2212yescomplemented
34C13×#359C2214yescomplemented
35#11718102C2214yescomplemented
36#11718094C2212yescomplemented
37C16×Dic13C2212yescomplemented
38#11718085C2214yescomplemented
39C2×C13×#41—21no—
40C2×#6127—21no—
41C13×#135—21no—
42C13×#135—21no—
43C13×#135C2×C412yes—
44C13×#135C2312yes—
45C2×C13×Q16C2×C411yescharacteristic
46C2×C13×SD16—21no—
47C2×C13×D8C2×C411yescharacteristic
48C2×C13×M16—21no—
49C22×C8×C13C2311yescharacteristic
50#88202—22no—
51#88202—22no—
52#88202—41no—
53#88202—41no—
54C2×C4×Dic13D411yescharacteristic
55C2×#6099—21no—
56C2×#6099—41no—
57C22×#1055—41no—
58C22×#1055D411yescharacteristic
59#88161—22no—
60#88161—22no—
61#88161—41no—
62#88161—41no—
63C2×Dic52C2×C411yescharacteristic
64#88158—21no—
65#88158—21no—
66#88158C2×C412yes—
67#88158C2312yes—
68C2×D104C2×C411yescharacteristic
69C2×#6095—21no—
70C2×#6094—41no—
71C2×C8×D13—41no—
72C13×M32—21no—
73C13×M32—21no—
74C2×C13×C16C2312yes—
75C13×#108—21no—
76C13×#108C2312yes—
77#88077—22no—
78#88077—22no—
79#88069C2×C414yescomplemented
80#88068C2×C414yescomplemented
81#88067C2×C414yescomplemented
82#88066C2×C414yescomplemented
83#88065—22no—
84#88065—22no—
85#88059—21no—
86#88059C2312yes—
87C8×Dic13D411yescharacteristic
88C8×Dic13D411yescharacteristic
89C8×Dic13C2311yescharacteristic
90C8×Dic13C2311yescharacteristic
91#88052C2×C412yes—
92#88052C2×C412yes—
93C2×#6090C2312yes—
94#33463—131nomaximal, Sylow
95C13×#41—22no—
96C13×#41—22no—
97C13×#41—41no—
98C13×#41—41no—
99C2×Q8×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C2×C22⋊D13—41no—
105C22×Dic13—21no—
106#6127—22no—
107#6127—22no—
108#6127—41no—
109#6127—41no—
110C2×D52—21no—
111C2×C4×D13—41no—
112C2×Dic26—21no—
113C13×Q16—21no—
114C13×Q16C22×C412yes—
115C13×SD16—22no—
116C13×SD16—22no—
117C13×D8—21no—
118C13×D8C22×C412yes—
119C13×M16—22no—
120C13×M16—41no—
121C2×C8×C13—41no—
122C2×C8×C13C22×C411yescharacteristic
123C2×C8×C13C22×C411yescharacteristic
124C2×C8×C13C2×D411yescharacteristic
125C2×C8×C13#4111yescharacteristic
126C2×C8×C13#4111yescharacteristic
127C2×C8×C13C2411yescharacteristic
128C4×Dic13—21no—
129C4×Dic13C2×D411yescharacteristic
130C4×Dic13C2×D411yescharacteristic
131#6099—22no—
132#6099—41no—
133#6099—42no—
134#6099—42no—
135C2×#1055—41no—
136C2×#1055—42no—
137C2×#1055—42no—
138C2×#1055D811yescharacteristic
139C2×#1055D811yescharacteristic
140C2×#1055D811yescharacteristic
141C2×#1055D811yescharacteristic
142C2×#1055C2×D411yescharacteristic
143C2×#1055C2×D411yescharacteristic
144Dic52—21no—
145Dic52C22×C412yes—
146D104—21no—
147D104C22×C412yes—
148#6095—22no—
149#6095—22no—
150#6094—42no—
151#6094—42no—
152C8×D13—42no—
153C8×D13—42no—
154C13×C16—22no—
155#6090C22×C414yes—
156#3414—131no—
157C2×#443—131no—
158C2×#443—131no—
159#2179—134no—
160#2178—134no—
161#2161—131no—
162#2143—131no—
163#2143D1311yescharacteristic, complemented
164C4×M32—131no—
165C23×C13—41no—
166C23×C13#13511yescharacteristic
167C22×D13—41no—
168Q8×C13—22no—
169Q8×C13—41no—
170D4×C13—22no—
171D4×C13—42no—
172D4×C13—42no—
173D4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13C4×D411yescharacteristic
178C2×C4×C13C4×D411yescharacteristic
179C2×C4×C13C2×D811yescharacteristic
180C2×C4×C13C2×D811yescharacteristic
181C2×C4×C13#13511yescharacteristic
182C2×C4×C13C22×D411yescharacteristic
183C22⋊D13—42no—
184C22⋊D13—42no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—42no—
188C2×Dic13—41no—
189D52—22no—
190D52—41no—
191C4×D13—42no—
192C4×D13—42no—
193Dic26—22no—
194Dic26—41no—
195C8×C13—42no—
196C8×C13C4×D411yescharacteristic
197C8×C13C4×D411yescharacteristic
198C8×C13C23×C411yescharacteristic
199C8×C13C2×#4111yescharacteristic
200#1055—42no—
201#1055C2×D811yescharacteristic
202#1055C2×D811yescharacteristic
203#1055C2×D811yescharacteristic
204#1055C2×D811yescharacteristic
205C2×#135—131no—
206C2×#135C2×D1311yescharacteristic
207C2×#131—261no—
208C2×#131—261no—
209#510—132no—
210#510—132no—
211#509—132no—
212#509—132no—
213#508—134no—
214C2×M32—131no—
215C2×M32C2×D1311yescharacteristic
216#443—132no—
217#443—132no—
218#443—132no—
219#443—132no—
220#443—261no—
221#443—261no—
222#443—261no—
223#443—261no—
224C2×#108—131no—
225C2×#108C2×D1311yescharacteristic
226C2×#104—261no—
227C2×#104—261no—
228C2×C4×C8—131no—
229#368—134no—
230#359—134no—
231#359C2×D1314yescomplemented
232#346—132no—
233C4×C16—132no—
234C22×C13—41no—
235C22×C13—42no—
236C22×C13—82no—
237C22×C13C4×D811yescharacteristic
238C22×C13C4×D811yescharacteristic
239C22×C13C2×#13511yescharacteristic
240C2×D13—42no—
241C2×D13—82no—
242C4×C13—42no—
243C4×C13C4×D811yescharacteristic
244C4×C13C4×D811yescharacteristic
245C4×C13C2×C4×D411yescharacteristic
246C4×C13C22×D811yescharacteristic
247Dic13—22no—
248Dic13—41no—
249Dic13—42no—
250C2×#41—21no—
251C2×#41—261no—
252#135—21no—
253#135—21no—
254#135—132no—
255#135—132no—
256#135—261no—
257#135—261no—
258#135C4×D1312yes—
259#135C22×D1312yes—
260C2×Q16—131no—
261C2×Q16C4×D1311yescharacteristic
262C2×SD16—21no—
263C2×SD16—261no—
264C2×D8—131no—
265C2×D8C4×D1311yescharacteristic
266#131—262no—
267#131—262no—
268#131—262no—
269#131—262no—
270#131—521no—
271#131—521no—
272#131—521no—
273#131—521no—
274C2×M16—21no—
275C2×M16—261no—
276C2×M16—521no—
277C2×M16—521no—
278C22×C8—131no—
279C22×C8—521no—
280C22×C8—521no—
281C22×C8C22×D1311yescharacteristic
282C2×C42—131no—
283Q32—134no—
284SD32—134no—
285SD32—134no—
286D16—134no—
287M32—21no—
288M32—21no—
289M32—132no—
290M32—132no—
291C2×C16—132no—
292C2×C16C22×D1312yes—
293#108—21no—
294#108—132no—
295#108—261no—
296#108C22×D1312yes—
297#104—262no—
298#104—262no—
299#104—262no—
300#104—262no—
301C4×C8—131no—
302C4×C8—131no—
303C4×C8—131no—
304C4×C8—131no—
305C2×C13—21no—
306C2×C13—21no—
307C2×C13—21no—
308C2×C13—82no—
309C2×C13C2×C4×D811yescharacteristic
310D13—82no—
311#41—22no—
312#41—22no—
313#41—41no—
314#41—41no—
315#41—262no—
316#41—262no—
317#41—521no—
318#41—521no—
319C2×Q8—21no—
320C2×Q8—261no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—261no—
324C2×D4—521no—
325C22×C4—41no—
326C22×C4—261no—
327C22×C4—521no—
328C22×C4D4×D1311yescharacteristic
329Q16—21no—
330Q16—132no—
331Q16—261no—
332Q16C2×C4×D1312yes—
333SD16—22no—
334SD16—22no—
335SD16—262no—
336SD16—262no—
337D8—21no—
338D8—132no—
339D8—261no—
340D8C2×C4×D1312yes—
341M16—22no—
342M16—41no—
343M16—262no—
344M16—522no—
345M16—522no—
346M16—522no—
347M16—522no—
348M16—521no—
349C2×C8—41no—
350C2×C8—131no—
351C2×C8—131no—
352C2×C8—131no—
353C2×C8—131no—
354C2×C8—131no—
355C2×C8—131no—
356C2×C8—522no—
357C2×C8—522no—
358C2×C8—522no—
359C2×C8—522no—
360C2×C8—521no—
361C2×C8C2×C4×D1311yescharacteristic
362C2×C8C2×C4×D1311yescharacteristic
363C2×C8D4×D1311yescharacteristic
364C2×C8#612911yescharacteristic
365C2×C8#612911yescharacteristic
366C2×C8C23×D1311yescharacteristic
367C42—131no—
368C42—131no—
369C42—261no—
370C16—22no—
371C16—134no—
372C13#3346311yescharacteristic, complemented, Sylow
373C23—41no—
374C23—521no—
375C23#8817011yescharacteristic
376Q8—22no—
377Q8—41no—
378Q8—262no—
379Q8—521no—
380D4—22no—
381D4—42no—
382D4—42no—
383D4—41no—
384D4—262no—
385D4—522no—
386D4—522no—
387D4—521no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—522no—
394C2×C4—521no—
395C2×C4—522no—
396C2×C4—522no—
397C2×C4#8813511yescharacteristic
398C2×C4#8813511yescharacteristic
399C2×C4D8×D1311yescharacteristic
400C2×C4D8×D1311yescharacteristic
401C2×C4#8817011yescharacteristic
402C2×C4C2×D4×D1311yescharacteristic
403C8—42no—
404C8—131no—
405C8—131no—
406C8—131no—
407C8—131no—
408C8—522no—
409C8#8813511yescharacteristic
410C8#8813511yescharacteristic
411C8C22×C4×D1311yescharacteristic
412C8C2×#612911yescharacteristic
413C22—41no—
414C22—42no—
415C22—82no—
416C22—522no—
417C22—1042no—
418C22#1171841711yescharacteristic
419C22#1171841711yescharacteristic
420C22C2×#8817011yescharacteristic
421C4—42no—
422C4—262no—
423C4—521no—
424C4—522no—
425C4#1171841711yescharacteristic
426C4#1171841711yescharacteristic
427C4C2×#8813511yescharacteristic
428C4C2×D8×D1311yescharacteristic
429C2—21no—
430C2—21no—
431C2—21no—
432C2—82no—
433C2—1042no—
434C2C2×#1171841711yescharacteristic
subgroupG/H
centerC4C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2143C2
socleC2×C13C2×C4×D8
prime radical#13127970C2
cosocleC2×C8×C13C24
hypercenter#2143D13
hypocenterC13#33463
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

Complements

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

NH ≅ G/Ntype
2. C2×#11718857C2semidirect
3. C2×#11718556C2semidirect
4. #13116719C2semidirect
5. #13116714C2semidirect
6. #13116630C2semidirect
7. #13116565C2semidirect
8. M32×Dic13C2semidirect
9. C13×#2143C2semidirect
19. #11718857C22semidirect
20. #11718857C22semidirect
21. #11718856C4semidirect
23. #11718854C4semidirect
24. #11718840C4semidirect
25. #11718808C4semidirect
32. #11718556C22semidirect
33. #11718556C22semidirect
34. C13×#359C22semidirect
35. #11718102C22semidirect
36. #11718094C22semidirect
37. C16×Dic13C22semidirect
38. #11718085C22semidirect
79. #88069C2×C4semidirect
80. #88068C2×C4semidirect
81. #88067C2×C4semidirect
82. #88066C2×C4semidirect
163. #2143D13semidirect
231. #359C2×D13semidirect
372. C13#33463semidirect

Maximal subgroups

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

subgroupindex
#131279702
C2×#117188572
C2×#117185562
#131167192
#131167142
#131166302
#131165652
M32×Dic132
C13×#21432
#3346313