Finite Group Databasebeta

← #16795252

Subgroups — #16795252

Order 3328.

714 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131754C211yesmaximal, characteristic, complemented
2#13131752C211yesmaximal, characteristic, complemented
3#13130428C212yesmaximal, complemented
4SD16⋊#1057C212yesmaximal, complemented
5#13130423C212yesmaximal, complemented
6#13130416C212yesmaximal, complemented
7D13⋊#335C211yesmaximal, characteristic, complemented
8#13130134C211yesmaximal, characteristic, complemented
9#13130132C211yesmaximal, characteristic, complemented
10#13130040C211yesmaximal, characteristic, complemented
11C4×#88170C211yesmaximal, characteristic
12C2×#88170C411yescharacteristic
13C4×#6131C2211yescharacteristic
14C4×#6129C2211yescharacteristic
15Q8×#1057C2212yes—
16D4×#1057C2212yes—
17#11719125—21no—
18C2×#88112—21no—
19#11719074C2212yes—
20#11719073—22no—
21#11719073C2212yes—
22#11719063—22no—
23D13⋊(C4⋊C8)—21no—
24D13⋊(C4⋊C8)C2211yescharacteristic
25D13⋊(C4⋊C8)C2211yescharacteristic
26#11719049—21no—
27#11719049C2211yescharacteristic
28#11719049C2211yescharacteristic
29C4×C13×SD16C411yescharacteristic
30SD16×Dic13C2211yescharacteristic
31C4×#6107C411yescharacteristic
32C4×#6104C411yescharacteristic
33#11718521C411yescharacteristic
34#11718513C2211yescharacteristic
35#11718465C411yescharacteristic
36#11718451C2211yescharacteristic
37#11718433C411yescharacteristic
38#11718417C2211yescharacteristic
39C4×#6095C411yescharacteristic
40C4×C8×D13C2211yescharacteristic
41Q8⋊#1057C2212yes—
42D4⋊#1057C2212yes—
43#11718256C2212yes—
44#11718254C2212yes—
45#11718251C2212yes—
46C8×#1057C2212yes—
47#11718244C2212yes—
48#11718243C2212yes—
49C2×#6131C2×C411yescharacteristic
50C2×#6129C2×C411yescharacteristic
51C22×#1057—22no—
52C2×D13⋊C8—21no—
53C2×D13⋊C8—21no—
54C2×D13⋊C8—22no—
55C2×C13×SD16C2×C411yescharacteristic
56C4×Q8×C13C2×C411yescharacteristic
57C4×D4×C13C2×C411yescharacteristic
58Q8×Dic13C2311yescharacteristic
59C2×#6107C2×C411yescharacteristic
60D4×Dic13C2311yescharacteristic
61C2×#6104C2×C411yescharacteristic
62C4×C22⋊D13—21no—
63C2×C4×Dic13—21no—
64#88170C818yescomplemented
65C2×#6095C2×C411yescharacteristic
66C2×C8×D13C2×C411yescharacteristic
67C2×C8×D13C2×C411yescharacteristic
68#88147—21no—
69#88147C2311yescharacteristic
70#88146—21no—
71#88146C2×C411yescharacteristic
72#88146C2×C411yescharacteristic
73#88141C2311yescharacteristic
74#88135—21no—
75#88131—21no—
76C4×D52—21no—
77C4×D52C2×C411yescharacteristic
78C42×D13—21no—
79C42×D13C2311yescharacteristic
80C4×Dic26C2×C411yescharacteristic
81C22⋊#1057—22no—
82#88112—22no—
83#88112—21no—
84#88112—21no—
85#88112—21no—
86#88112D411yescharacteristic
87#88112D411yescharacteristic
88#88111—21no—
89#88111—22no—
90#88111D412yes—
91C4⋊#1057—22no—
92C4⋊#1057C2312yes—
93C4⋊#1057C2312yes—
94C4×#1057—22no—
95C4×#1057—22no—
96C4×#1057C2312yes—
97C4×#1057C2312yes—
98C13×#106C2×C411yescharacteristic
99C13×#103C2×C411yescharacteristic
100C13×#102C2×C411yescharacteristic
101C4×C8×C13C2×C411yescharacteristic
102#88075C2×C411yescharacteristic
103#88072C2×C411yescharacteristic
104#88061C2×C411yescharacteristic
105#88057C2×C411yescharacteristic
106#88056C2×C411yescharacteristic
107C8×Dic13C2311yescharacteristic
108C8×Dic13C2311yescharacteristic
109#88050C2×C411yescharacteristic
110#88049C2×C411yescharacteristic
111#88047C2×C411yescharacteristic
112#88047C2×C411yescharacteristic
113C4×#1055C2×C411yescharacteristic
114#17857—131nomaximal, Sylow
115C2×Q8×C13C22×C411yescharacteristic
116C2×D4×C13C22×C411yescharacteristic
117C22×C4×C13—21no—
118C2×C22⋊D13—21no—
119C22×Dic13—21no—
120C22×Dic13—21no—
121#6131—22no—
122#6131C2×C814yescomplemented
123#6129—22no—
124#6129C2×C814yescomplemented
125C2×D52—21no—
126C2×D52C22×C411yescharacteristic
127C2×C4×D13—21no—
128C2×C4×D13—21no—
129C2×C4×D13—21no—
130C2×C4×D13C22×C411yescharacteristic
131C2×C4×D13C2×D411yescharacteristic
132C2×C4×D13#4111yescharacteristic
133C2×Dic26C22×C411yescharacteristic
134C2×#1057—22no—
135C2×#1057—22no—
136C2×#1057—22no—
137C2×#1057—82no—
138C2×#1057C2×D412yes—
139C2×#1057C2×D412yes—
140D13⋊C8—82no—
141D13⋊C8—81no—
142D13⋊C8—81no—
143C13×SD16C2×C814yescomplemented
144C2×C8×C13C22×C411yescharacteristic
145C2×C8×C13C22×C411yescharacteristic
146C13×C4⋊C4—21no—
147C13×C4⋊C4C22×C411yescharacteristic
148C13×C4⋊C4C22×C411yescharacteristic
149C13×C22⋊C4—21no—
150C42×C13—21no—
151C42×C13C22×C411yescharacteristic
152C22⋊Dic13—21no—
153#6107C2×C814yescomplemented
154#6104C2×C814yescomplemented
155#6103—21no—
156#6103—21no—
157#6103—21no—
158#6103—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13C22×C411yescharacteristic
161C4⋊Dic13C22×C411yescharacteristic
162#6101—21no—
163#6101—21no—
164C4×Dic13—21no—
165C4×Dic13—21no—
166C4×Dic13—21no—
167C4×Dic13—21no—
168C4×Dic13—21no—
169C4×Dic13C2×D411yescharacteristic
170C4×Dic13#4111yescharacteristic
171C4×Dic13C2411yescharacteristic
172C2×#1055C22×C411yescharacteristic
173C2×#1055C22×C411yescharacteristic
174#6095C2×C814yescomplemented
175C8×D13—22no—
176C8×D13C2×C814yescomplemented
177#2988—131no—
178#2988—131no—
179C4×#135—131no—
180SD16⋊C8—132no—
181SD16⋊C8—132no—
182C8×Q16—132no—
183C8×D8—132no—
184C2×#335—131no—
185#1477—131no—
186#1477—131no—
187#1450—131no—
188C23×C13—21no—
189C22×D13—21no—
190C22×D13C4×D411yescharacteristic
191Q8×C13—21no—
192Q8×C13C22×C812yes—
193D4×C13—21no—
194D4×C13C22×C812yes—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—81no—
199C2×C4×C13C4×D411yescharacteristic
200C2×C4×C13C4×D411yescharacteristic
201C2×C4×C13C23×C411yescharacteristic
202C22⋊D13—24no—
203C2×Dic13—21no—
204C2×Dic13—24no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13C4×D411yescharacteristic
210C2×Dic13C22×D411yescharacteristic
211C2×Dic13C2×#4111yescharacteristic
212D52—24no—
213D52—21no—
214D52C22×C812yes—
215C4×D13—21no—
216C4×D13—21no—
217C4×D13—24no—
218C4×D13—41no—
219C4×D13—41no—
220C4×D13—41no—
221C4×D13—81no—
222C4×D13C22×C812yes—
223C4×D13#13112yes—
224Dic26—21no—
225Dic26C22×C812yes—
226#1057—22no—
227#1057—22no—
228#1057—42no—
229#1057—42no—
230#1057—42no—
231C8×C13—21no—
232C8×C13C22×C812yes—
233#1055—21no—
234#1055C22×C812yes—
235C2×#135—131no—
236C4×#41—131no—
237C4×#41—131no—
238C8×Q8—132no—
239C8×Q8—132no—
240C4×Q16—131no—
241C4×Q16—131no—
242C4×SD16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16#26111yescharacteristic
246C4×D8—131no—
247C4×D8—131no—
248C8×D4—132no—
249C8×D4—132no—
250C8×D4—262no—
251C8×D4—262no—
252#431—131no—
253#431—131no—
254#431—261no—
255#431—261no—
256#427—131no—
257C2×C4⋊C8—131no—
258C2×C4⋊C8—131no—
259C2×C4⋊C8—261no—
260C2×C4⋊C8—261no—
261#416—131no—
262#416—131no—
263C2×C4×C8—131no—
264#335—132no—
265#335—132no—
266Q8⋊C8—132no—
267Q8⋊C8—132no—
268D4⋊C8—132no—
269D4⋊C8—132no—
270#322—132no—
271C82—132no—
272C22×C13—22no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13C2×C4×D411yescharacteristic
276C2×D13—21no—
277C2×D13—21no—
278C2×D13—22no—
279C2×D13—41no—
280C2×D13—41no—
281C2×D13C8×D412yes—
282C4×C13—22no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—41no—
286C4×C13—41no—
287C4×C13C23×C811yescharacteristic
288C4×C13C2×#13111yescharacteristic
289Dic13—22no—
290Dic13—21no—
291Dic13—41no—
292Dic13—41no—
293Dic13C8×D412yes—
294Dic13#57611yescharacteristic
295Dic13#57811yescharacteristic
296C2×#41—131no—
297C2×#41—131no—
298#135—138no—
299C2×Q16—131no—
300C2×SD16—131no—
301C2×SD16C2×#26111yescharacteristic
302C2×D8—131no—
303C22×C8—131no—
304C22×C8—131no—
305C22×C8—262no—
306C22×C8—262no—
307C22×C8—261no—
308C22×C8—261no—
309C4×Q8—131no—
310C4×Q8—131no—
311C4×Q8—131no—
312C4×Q8C2×#26111yescharacteristic
313C4×D4—131no—
314C4×D4—131no—
315C4×D4—131no—
316C4×D4—261no—
317C4×D4—261no—
318C4×D4—261no—
319C4×D4—261no—
320C4×D4C2×#26111yescharacteristic
321#117—131no—
322#117—131no—
323#117—261no—
324#117—261no—
325C2×C42—131no—
326C2×C42—261no—
327C2×C42—261no—
328#107—131no—
329#107—131no—
330#106—131no—
331#106C2×#26111yescharacteristic
332C4⋊C8—131no—
333C4⋊C8—131no—
334C4⋊C8—132no—
335C4⋊C8—132no—
336C4⋊C8—261no—
337C4⋊C8—261no—
338C4⋊C8—261no—
339C4⋊C8—262no—
340C4⋊C8—262no—
341#103—131no—
342#103—131no—
343#103—131no—
344#103C2×#26111yescharacteristic
345#102—131no—
346#102—131no—
347#102—131no—
348#102C2×#26111yescharacteristic
349C22⋊C8—132no—
350C22⋊C8—262no—
351C22⋊C8—262no—
352C22⋊C8—261no—
353C4×C8—132no—
354C4×C8—131no—
355C4×C8—131no—
356C4×C8—132no—
357C4×C8—131no—
358C4×C8—262no—
359C4×C8—262no—
360C4×C8C2×#26111yescharacteristic
361C2×C13—42no—
362C2×C13C2×C8×D411yescharacteristic
363C2×C13#295111yescharacteristic
364C2×C13#295711yescharacteristic
365D13—22no—
366D13—42no—
367#41—134no—
368#41—134no—
369#41—262no—
370#41—262no—
371C2×Q8—131no—
372C2×Q8C22×#26111yescharacteristic
373C2×D4—131no—
374C2×D4—261no—
375C2×D4—261no—
376C2×D4C22×#26111yescharacteristic
377C22×C4—21no—
378C22×C4—131no—
379C22×C4—131no—
380C22×C4—131no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4—261no—
385C22×C4—261no—
386Q16—134no—
387SD16—134no—
388SD16D13⋊C814yescomplemented
389D8—134no—
390C2×C8—131no—
391C2×C8—134no—
392C2×C8—132no—
393C2×C8—132no—
394C2×C8—131no—
395C2×C8—262no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—1042no—
400C2×C8—1042no—
401C2×C8—1041no—
402C2×C8—1041no—
403C2×C8C22×#26111yescharacteristic
404C2×C8C22×#26111yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—131no—
407C4⋊C4—131no—
408C4⋊C4—261no—
409C4⋊C4—261no—
410C4⋊C4—261no—
411C4⋊C4C22×#26111yescharacteristic
412C4⋊C4C22×#26111yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—261no—
415C22⋊C4—261no—
416C22⋊C4—261no—
417C22⋊C4—261no—
418C22⋊C4—261no—
419C42—21no—
420C42—131no—
421C42—131no—
422C42—131no—
423C42—261no—
424C42—261no—
425C42—261no—
426C42—261no—
427C42—261no—
428C42C22×#26111yescharacteristic
429C13#1785711yescharacteristic, complemented, Sylow
430C23—21no—
431C23—131no—
432C23—261no—
433Q8—21no—
434Q8—132no—
435Q8—261no—
436Q8C2×D13⋊C812yes—
437D4—21no—
438D4—132no—
439D4—264no—
440D4—264no—
441D4—261no—
442D4C2×D13⋊C812yes—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—81no—
447C2×C4—131no—
448C2×C4—131no—
449C2×C4—132no—
450C2×C4—132no—
451C2×C4—131no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—264no—
455C2×C4—264no—
456C2×C4—261no—
457C2×C4—261no—
458C2×C4—261no—
459C2×C4—521no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—521no—
464C2×C4—1041no—
465C2×C4D4×#26111yescharacteristic
466C2×C4D4×#26111yescharacteristic
467C2×C4C23×#26111yescharacteristic
468C8—21no—
469C8—132no—
470C8—262no—
471C8—262no—
472C8—261no—
473C8—522no—
474C8—522no—
475C8—522no—
476C8C2×D13⋊C812yes—
477C22—22no—
478C22—41no—
479C22—41no—
480C22—132no—
481C22—261no—
482C22—261no—
483C22—262no—
484C22—521no—
485C22—521no—
486C22C2×D4×#26111yescharacteristic
487C4—22no—
488C4—21no—
489C4—21no—
490C4—41no—
491C4—41no—
492C4—132no—
493C4—131no—
494C4—131no—
495C4—262no—
496C4—261no—
497C4—521no—
498C4—521no—
499C4C22×D13⋊C811yescharacteristic
500C4D13⋊#13111yescharacteristic
501C2—42no—
502C2—262no—
503C2—522no—
504C2D4×D13⋊C811yescharacteristic
505C2#1313159811yescharacteristic
506C2#1313161411yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC4×C13×SD16C4
socleC22×C13C2×C4×D4
prime radicalC2×#88170C4
cosocleC4×Dic13C24
hypercenterC4×SD16#261
hypocenterC13#17857
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #13131754C2semidirect
2. #13131752C2semidirect
3. #13130428C2semidirect
4. SD16⋊#1057C2semidirect
5. #13130423C2semidirect
6. #13130416C2semidirect
7. D13⋊#335C2semidirect
8. #13130134C2semidirect
9. #13130132C2semidirect
10. #13130040C2semidirect
64. #88170C8semidirect
122. #6131C2×C8semidirect
124. #6129C2×C8semidirect
143. C13×SD16C2×C8semidirect
153. #6107C2×C8semidirect
154. #6104C2×C8semidirect
174. #6095C2×C8semidirect
176. C8×D13C2×C8semidirect
388. SD16D13⋊C8semidirect
429. C13#17857semidirect

Maximal subgroups

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

subgroupindex
#131317542
#131317522
#131304282
SD16⋊#10572
#131304232
#131304162
D13⋊#3352
#131301342
#131301322
#131300402
C4×#881702
#1785713