Finite Group Databasebeta

← #15758586

Subgroups — #15758586

Order 3328.

728 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic, complemented
2#13123178C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic, complemented
4C2×#11718136C211yesmaximal, characteristic, complemented
5#13112720C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#331C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×#88192—21no—
10C2×#88192—21no—
11C2×#88192C412yes—
12C2×C42×D13C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×C4⋊C8C2211yescharacteristic
15#11718882—21no—
16#11718882—21no—
17#11718882C412yes—
18C2×#88060—21no—
19C2×#88060—21no—
20C2×C8×Dic13—21no—
21#11718596C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718494—22no—
25#11718494—22no—
26C13×#331—22no—
27#11718142—21no—
28#11718136—22no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13C2×C412yes—
32C22×C22⋊D13—22no—
33C22×C4×D13C2×C411yescharacteristic
34C22×C4×D13D411yescharacteristic
35C22×C4×D13D411yescharacteristic
36C22×C8×C13—21no—
37C22×C8×C13—21no—
38C13×#127—21no—
39C13×#127—21no—
40C13×#127—21no—
41C13×#127—21no—
42C2×C42×C13C2311yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C22⋊Dic13—22no—
45C2×C22⋊Dic13—22no—
46#88192—42no—
47#88192—42no—
48#88192—42no—
49#88192—42no—
50#88192—44no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13C2×C412yes—
54C2×C4×Dic13C2×C411yescharacteristic
55C2×C4×Dic13D411yescharacteristic
56C2×C4×Dic13D411yescharacteristic
57C22×#1055—21no—
58C22×#1055—21no—
59C42×D13—21no—
60C42×D13—21no—
61C42×D13—21no—
62C42×D13—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8D412yescomplemented
67#88060—24no—
68#88060—42no—
69C8×Dic13—24no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73C4⋊#1055D412yescomplemented
74#9134—131nomaximal, Sylow
75C24×C13—22no—
76C23×D13C22⋊C411yescharacteristic
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C22×C4×C13C22×C411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C2×C22⋊D13—44no—
97C2×C22⋊D13—44no—
98C2×C22⋊D13—44no—
99C22×Dic13—22no—
100C22×Dic13C22⋊C411yescharacteristic
101C22×Dic13C22⋊C411yescharacteristic
102C22×Dic13C22⋊C411yescharacteristic
103C2×C4×D13—21no—
104C2×C4×D13—21no—
105C2×C4×D13—21no—
106C2×C4×D13—21no—
107C2×C4×D13—21no—
108C2×C4×D13—21no—
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—21no—
112C2×C4×D13—21no—
113C2×C4×D13—21no—
114C2×C4×D13—21no—
115C2×C4×D13—22no—
116C2×C4×D13—41no—
117C2×C4×D13D812yes—
118C2×C4×D13SD1612yes—
119C2×C8×C13—22no—
120C2×C8×C13—41no—
121C2×C8×C13—41no—
122C2×C8×C13—41no—
123C2×C8×C13—41no—
124C2×C8×C13—41no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128C42×C13#4111yescharacteristic
129C22⋊Dic13—44no—
130C22⋊Dic13—44no—
131C22⋊Dic13—44no—
132C4⋊Dic13—41no—
133C4⋊Dic13—41no—
134C4⋊Dic13—41no—
135C4⋊Dic13—41no—
136C4⋊Dic13—42no—
137C4×Dic13—21no—
138C4×Dic13—21no—
139C4×Dic13—21no—
140C4×Dic13—21no—
141C4×Dic13—21no—
142C4×Dic13—21no—
143C2×#1055—22no—
144C2×#1055—41no—
145C2×#1055—41no—
146C2×#1055—41no—
147C2×#1055—41no—
148C2×#1055—41no—
149C2×#431—131no—
150#2856—131no—
151#1797—131no—
152C2×#331—131no—
153C2×#331D1311yescharacteristic, complemented
154#1296—131no—
155#1296—131no—
156C23×C13—42no—
157C23×C13—42no—
158C23×C13—42no—
159C23×C13—42no—
160C23×C13—42no—
161C23×C13—42no—
162C23×C13—42no—
163C23×C13C2×C22⋊C411yescharacteristic
164C22×D13—21no—
165C22×D13—21no—
166C22×D13—21no—
167C22×D13—21no—
168C22×D13—21no—
169C22×D13—21no—
170C22×D13#10212yes—
171D4×C13—82no—
172D4×C13—82no—
173D4×C13—81no—
174D4×C13—81no—
175D4×C13—81no—
176D4×C13—81no—
177D4×C13—81no—
178D4×C13—81no—
179D4×C13—81no—
180D4×C13—81no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13C4×D411yescharacteristic
184C2×C4×C13C4×D411yescharacteristic
185C2×C4×C13#12011yescharacteristic
186C2×C4×C13#12111yescharacteristic
187C2×C4×C13#12111yescharacteristic
188C2×C4×C13#12311yescharacteristic
189C2×C4×C13C2×D811yescharacteristic
190C2×C4×C13C2×SD1611yescharacteristic
191C2×C4×C13#13511yescharacteristic
192C2×C4×C13#13511yescharacteristic
193C2×C4×C13#13511yescharacteristic
194C2×C4×C13#13511yescharacteristic
195C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
197C22⋊D13—88no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—42no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13#10012yes—
209C2×Dic13#10212yes—
210C4×D13—22no—
211C4×D13—22no—
212C4×D13—22no—
213C4×D13—22no—
214C4×D13—42no—
215C4×D13—42no—
216C4×D13—41no—
217C4×D13—41no—
218C4×D13—41no—
219C4×D13—41no—
220C8×C13—42no—
221C8×C13—81no—
222#1055—42no—
223#1055—81no—
224C2×#127C2×D1311yescharacteristic
225C2×#121—132no—
226C2×#121—261no—
227C2×#121—261no—
228C22×C42—131no—
229#431—262no—
230#431—262no—
231C2×C4⋊C8—131no—
232C2×C4⋊C8—131no—
233C2×C4⋊C8C2×D1311yescharacteristic
234C2×C4⋊C8C2×D1311yescharacteristic
235C2×C22⋊C8—261no—
236C2×C22⋊C8—261no—
237C2×C4×C8—261no—
238#390—132no—
239#390—261no—
240#390—261no—
241#384—131no—
242#336—261no—
243#331—22no—
244#331—262no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13—82no—
250C22×C13—82no—
251C22×C13—82no—
252C22×C13#38611yescharacteristic
253C22×C13C2×#10011yescharacteristic
254C22×C13#41311yescharacteristic
255C22×C13C2×#10211yescharacteristic
256C22×C13#41611yescharacteristic
257C22×C13#41611yescharacteristic
258C22×C13#41811yescharacteristic
259C2×D13—22no—
260C2×D13—22no—
261C2×D13—22no—
262C2×D13—41no—
263C2×D13—41no—
264C2×D13—41no—
265C2×D13—41no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13#44911yescharacteristic
269C4×C13#44911yescharacteristic
270C4×C13#46511yescharacteristic
271C4×C13#46511yescharacteristic
272C4×C13#46611yescharacteristic
273C4×C13#46611yescharacteristic
274C4×C13#48211yescharacteristic
275C4×C13#48211yescharacteristic
276Dic13—22no—
277Dic13—22no—
278Dic13—41no—
279Dic13—82no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—262no—
283C22×D4C4×D1312yes—
284C23×C4—131no—
285C23×C4—131no—
286C23×C4—131no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—261no—
290C22×C8—261no—
291#127—21no—
292#127—21no—
293#127—21no—
294#127—21no—
295#121—522no—
296#121—522no—
297#121—522no—
298#121—522no—
299#121—524no—
300C2×C4⋊C4—132no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4—261no—
303C2×C22⋊C4—262no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C42—131no—
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—261no—
310C2×C42—261no—
311C2×C42—261no—
312C2×C42—261no—
313C2×C42C22×D1311yescharacteristic
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—132no—
318C4⋊C8—261no—
319C4⋊C8—261no—
320C4⋊C8—261no—
321C4⋊C8C22⋊D1312yescomplemented
322C22⋊C8—264no—
323C22⋊C8—522no—
324C4×C8—264no—
325C2×C13—162no—
326C2×C13#154011yescharacteristic
327C2×C13#154311yescharacteristic
328C2×C13#154511yescharacteristic
329C2×C13#155311yescharacteristic
330C2×C13#187511yescharacteristic
331C2×C13#189311yescharacteristic
332C2×C13#190011yescharacteristic
333D13—42no—
334C24—22no—
335C24—131no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—524no—
353C2×D4—524no—
354C2×D4—524no—
355C22×C4—131no—
356C22×C4—131no—
357C22×C4—132no—
358C22×C4—132no—
359C22×C4—131no—
360C22×C4—262no—
361C22×C4—261no—
362C22×C4—261no—
363C22×C4—261no—
364C22×C4—261no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—261no—
371C22×C4—261no—
372C22×C4—261no—
373C22×C4—262no—
374C22×C4—521no—
375C22×C4C2×C4×D1311yescharacteristic
376C22×C4D4×D1311yescharacteristic
377C22×C4D4×D1311yescharacteristic
378C2×C8—22no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—262no—
385C2×C8—521no—
386C2×C8—521no—
387C2×C8—521no—
388C2×C8—521no—
389C2×C8—521no—
390C4⋊C4—522no—
391C4⋊C4—521no—
392C4⋊C4—521no—
393C4⋊C4—521no—
394C4⋊C4—521no—
395C22⋊C4—524no—
396C22⋊C4—524no—
397C22⋊C4—524no—
398C42—261no—
399C42—261no—
400C42—261no—
401C42—261no—
402C42—261no—
403C42—261no—
404C42#612711yescharacteristic
405C42D4×D1311yescharacteristic
406C42#612911yescharacteristic
407C42C2×C22⋊D1311yescharacteristic
408C13#913411yescharacteristic, complemented, Sylow
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—132no—
417C23—261no—
418C23—261no—
419C23—261no—
420C23—261no—
421C23—261no—
422C23—261no—
423C23C22⋊C4×D1311yescharacteristic
424D4—82no—
425D4—82no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—81no—
434D4—1048no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—132no—
438C2×C4—132no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—261no—
442C2×C4—261no—
443C2×C4—262no—
444C2×C4—262no—
445C2×C4—262no—
446C2×C4—262no—
447C2×C4—261no—
448C2×C4—261no—
449C2×C4—261no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—521no—
453C2×C4—521no—
454C2×C4—521no—
455C2×C4—521no—
456C2×C4—522no—
457C2×C4—522no—
458C2×C4—522no—
459C2×C4#8813511yescharacteristic
460C2×C4#8813711yescharacteristic
461C2×C4#8813811yescharacteristic
462C2×C4D8×D1311yescharacteristic
463C2×C4#8816511yescharacteristic
464C2×C4#8816611yescharacteristic
465C2×C4#8816611yescharacteristic
466C2×C4SD16×D1311yescharacteristic
467C2×C4#8816811yescharacteristic
468C2×C4#8817011yescharacteristic
469C2×C4#8817011yescharacteristic
470C2×C4C4×C22⋊D1311yescharacteristic
471C2×C4#8819111yescharacteristic
472C2×C4#8819211yescharacteristic
473C8—42no—
474C8—81no—
475C8—522no—
476C8—1041no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—262no—
485C22—262no—
486C22—262no—
487C22—521no—
488C22—521no—
489C22—521no—
490C22—521no—
491C22D13×#10011yescharacteristic
492C22#1171840611yescharacteristic
493C22D13×#10211yescharacteristic
494C22#1171843111yescharacteristic
495C22#1171843311yescharacteristic
496C22#1171843311yescharacteristic
497C22#1171861711yescharacteristic
498C4—21no—
499C4—21no—
500C4—262no—
501C4—262no—
502C4—521no—
503C4—1042no—
504C4#1171843611yescharacteristic
505C4#1171843911yescharacteristic
506C4#1171844011yescharacteristic
507C4#1171844511yescharacteristic
508C4#1171881811yescharacteristic
509C4#1171881911yescharacteristic
510C4#1171883211yescharacteristic
511C4#1171883311yescharacteristic
512C2—162no—
513C2—522no—
514C2#1311348211yescharacteristic
515C2#1311349511yescharacteristic
516C2#1311350211yescharacteristic
517C2#1311353811yescharacteristic
518C2#1311515511yescharacteristic
519C2#1311526111yescharacteristic
520C2#1311529611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#331C2
socleC23×C13C2×C22⋊C4
prime radical#13123178C2
cosocleC2×C42×C13C23
hypercenterC2×#331D13
hypocenterC13#9134
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#11718494C2semidirect
3. #13114813C2semidirect
4. C2×#11718136C2semidirect
5. #13112720C2semidirect
6. #13112720C2semidirect
7. C2×C13×#331C2semidirect
66. C13×C4⋊C8D4semidirect
73. C4⋊#1055D4semidirect
153. C2×#331D13semidirect
321. C4⋊C8C22⋊D13semidirect
408. C13#9134semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131231782
#131148132
C2×#117181362
#131127202
C2×C13×#3312
#913413