Finite Group Databasebeta

← #15759970

Subgroups — #15759970

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123285C211yesmaximal, characteristic
2#13114776C211yesmaximal, characteristic
3#13113408C211yesmaximal, characteristic, complemented
4#13113200C211yesmaximal, characteristic, complemented
5#13112741C211yesmaximal, characteristic, complemented
6#13112723C211yesmaximal, characteristic, complemented
7C13×#3007C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137C411yescharacteristic, complemented
10C2×C13×#137C411yescharacteristic, complemented
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×#88202—21no—
13C13×#452—21no—
14C13×#452—21no—
15C13×#451—21no—
16C13×#450—21no—
17C13×#417C411yescharacteristic, complemented
18C13×#417C411yescharacteristic, complemented
19C13×#407C2211yescharacteristic
20#11718895—21no—
21#11718895—22no—
22C2×#88075—21no—
23C2×#88072—21no—
24#11718873C2211yescharacteristic
25#11718868—21no—
26#11718868C2211yescharacteristic
27C2×C22⋊#1055—21no—
28C2×C22⋊#1055C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30#11718130—21no—
31#11718130—21no—
32#11718120—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—42no—
36C2×C13×#41—42no—
37C2×C13×#41C2×C411yescharacteristic
38C2×C13×#41C2×C411yescharacteristic
39C2×C13×#41D411yescharacteristic
40C2×C13×#41D411yescharacteristic
41C22×Q8×C13C2×C411yescharacteristic
42C22×Q8×C13D411yescharacteristic
43C22×D4×C13—21no—
44C22×D4×C13D411yescharacteristic
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C13×#137—42no—
48C13×#137—42no—
49C2×C13×Q16—21no—
50C2×C13×Q16—21no—
51C2×C13×SD16—21no—
52C2×C13×SD16—21no—
53C2×C13×M16C2×C411yescharacteristic
54C2×C13×M16C2×C411yescharacteristic
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C13×C22⋊Q8—21no—
58C13×C22⋊Q8—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C22⋊C4—21no—
62C2×C22⋊Dic13—21no—
63#88202—42no—
64#88202—42no—
65C2×C4⋊Dic13—21no—
66C2×#6099—22no—
67C2×#6099—21no—
68C22×#1055—22no—
69C22×#1055—21no—
70C22×#1055—21no—
71C13×#103—21no—
72C13×#103—21no—
73C13×#102—21no—
74C13×#102—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77#88075—42no—
78#88072—42no—
79#88071—21no—
80C22⋊#1055—22no—
81C22⋊#1055—22no—
82C22⋊#1055—21no—
83C22⋊#1055—21no—
84C22⋊#1055—21no—
85C22⋊#1055—21no—
86C22⋊#1055D411yescharacteristic
87C22⋊#1055D411yescharacteristic
88C22⋊#1055D412yes—
89#9345—131nomaximal, Sylow
90C24×C13—21no—
91C24×C13#4111yescharacteristic
92C13×#41—22no—
93C13×#41—22no—
94C13×#41—22no—
95C13×#41—22no—
96C13×#41—41no—
97C13×#41—41no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—44no—
101C13×#41—44no—
102C2×Q8×C13—21no—
103C2×Q8×C13—22no—
104C2×Q8×C13—21no—
105C2×Q8×C13—21no—
106C2×Q8×C13—41no—
107C2×Q8×C13—41no—
108C2×Q8×C13—41no—
109C2×Q8×C13C22⋊C411yescharacteristic
110C2×Q8×C13C22⋊C411yescharacteristic
111C2×D4×C13—21no—
112C2×D4×C13—22no—
113C2×D4×C13—21no—
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—41no—
118C2×D4×C13—44no—
119C2×D4×C13C22⋊C411yescharacteristic
120C2×D4×C13C22⋊C411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—44no—
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C22×Dic13—41no—
138C13×Q16—42no—
139C13×Q16—42no—
140C13×SD16—42no—
141C13×SD16—42no—
142C13×M16—41no—
143C13×M16—41no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C22⋊Dic13—81no—
153C4⋊Dic13—41no—
154C4⋊Dic13—41no—
155#6099—44no—
156#6099—41no—
157#6099—41no—
158C2×#1055—21no—
159C2×#1055—22no—
160C2×#1055—21no—
161C2×#1055—44no—
162C2×#1055—41no—
163C2×#1055—41no—
164C2×#1055—41no—
165C2×#1055—41no—
166C2×#1055—41no—
167#3007D1311yescharacteristic
168#2880—131no—
169#1788—131no—
170#1520—131no—
171#1472—131no—
172#1305—131no—
173#1298—131no—
174C23×C13—21no—
175C23×C13—21no—
176C23×C13—21no—
177C23×C13—21no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—42no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—81no—
184C23×C13C4×D411yescharacteristic
185C23×C13#12111yescharacteristic
186C23×C13#12311yescharacteristic
187Q8×C13—21no—
188Q8×C13—21no—
189Q8×C13—21no—
190Q8×C13—42no—
191Q8×C13—41no—
192Q8×C13—41no—
193Q8×C13—81no—
194Q8×C13#9912yes—
195D4×C13—24no—
196D4×C13—21no—
197D4×C13—21no—
198D4×C13—21no—
199D4×C13—42no—
200D4×C13—42no—
201D4×C13—42no—
202D4×C13—42no—
203D4×C13#9912yes—
204C2×C4×C13—24no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—81no—
224C2×C4×C13C2×C22⋊C411yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13#12011yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×Dic13—81no—
229C2×Dic13—81no—
230C2×Dic13—81no—
231C8×C13—41no—
232C8×C13—41no—
233#1055—41no—
234#1055—42no—
235#1055—41no—
236#1055—81no—
237C22×#41C2×D1311yescharacteristic
238C2×#137Dic1311yescharacteristic, complemented
239C2×#137Dic1311yescharacteristic, complemented
240C2×#131—261no—
241C2×C22⋊Q8C2×D1311yescharacteristic
242#452—21no—
243#452—21no—
244#451—21no—
245#450—21no—
246#417Dic1311yescharacteristic, complemented
247#417Dic1311yescharacteristic, complemented
248C2×#103—261no—
249C2×#102—261no—
250#408—262no—
251#408—261no—
252#407—131no—
253#407—261no—
254#407C2×D1311yescharacteristic
255C2×C22⋊C8—131no—
256C2×C22⋊C8—131no—
257C2×C22⋊C8—261no—
258#380—131no—
259#328—261no—
260#328—261no—
261#324—262no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—22no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13#38611yescharacteristic
281C22×C13#47111yescharacteristic
282C22×C13#47311yescharacteristic
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—22no—
286C4×C13—21no—
287C4×C13—41no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13C2×#9911yescharacteristic
291C4×C13C2×#9911yescharacteristic
292Dic13—161no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—42no—
296C2×#41—42no—
297C2×#41C2×Dic1311yescharacteristic
298C2×#41C2×Dic1311yescharacteristic
299C2×#41C22⋊D1311yescharacteristic
300C2×#41C22⋊D1311yescharacteristic
301C22×Q8C2×Dic1311yescharacteristic
302C22×Q8C22⋊D1311yescharacteristic
303C22×D4—21no—
304C22×D4C22⋊D1311yescharacteristic
305C23×C4—21no—
306C23×C4C22×D1311yescharacteristic
307#137—42no—
308#137—42no—
309C2×Q16—21no—
310C2×Q16—21no—
311C2×SD16—21no—
312C2×SD16—21no—
313#131—522no—
314#131—522no—
315C2×M16—262no—
316C2×M16—261no—
317C2×M16C2×Dic1311yescharacteristic
318C2×M16C2×Dic1311yescharacteristic
319C22×C8—262no—
320C22×C8—261no—
321C22×C8—261no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4C2×Dic1311yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—261no—
331#103—21no—
332#103—21no—
333#103—522no—
334#102—21no—
335#102—21no—
336#102—522no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—132no—
340C22⋊C8—131no—
341C22⋊C8—131no—
342C22⋊C8—262no—
343C22⋊C8—262no—
344C22⋊C8—261no—
345C22⋊C8—261no—
346C22⋊C8—261no—
347C22⋊C8—261no—
348#95—261no—
349C2×C13—21no—
350C2×C13—21no—
351C2×C13—41no—
352C2×C13—41no—
353C2×C13—42no—
354C2×C13—81no—
355C2×C13#188111yescharacteristic
356C2×C13#189811yescharacteristic
357C2×C13#190811yescharacteristic
358C24—21no—
359C24#612911yescharacteristic
360#41—22no—
361#41—22no—
362#41—22no—
363#41—22no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—44no—
369#41—44no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8C22⋊Dic1311yescharacteristic
378C2×Q8C22⋊Dic1311yescharacteristic
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—44no—
387C2×D4C22⋊Dic1311yescharacteristic
388C2×D4C22⋊Dic1311yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—44no—
399C22×C4—521no—
400C22×C4D4×D1311yescharacteristic
401C22×C4D4×D1311yescharacteristic
402C22×C4#612911yescharacteristic
403C22×C4C22×Dic1311yescharacteristic
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406Q16—42no—
407Q16—42no—
408SD16—42no—
409SD16—42no—
410M16—41no—
411M16—41no—
412M16—524no—
413M16—521no—
414M16—521no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—261no—
418C2×C8—262no—
419C2×C8—261no—
420C2×C8—524no—
421C2×C8—521no—
422C2×C8—521no—
423C2×C8—521no—
424C2×C8—521no—
425C2×C8—521no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—1041no—
435C13#934511yescharacteristic, complemented, Sylow
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23—41no—
445C23—81no—
446C23D4×Dic1311yescharacteristic
447C23#8818911yescharacteristic
448C23#8819311yescharacteristic
449Q8—21no—
450Q8—21no—
451Q8—21no—
452Q8—42no—
453Q8—41no—
454Q8—41no—
455Q8—81no—
456Q8#8807412yes—
457D4—24no—
458D4—21no—
459D4—21no—
460D4—21no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—42no—
465D4#8807412yes—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—81no—
486C2×C4—1041no—
487C2×C4—1041no—
488C2×C4—1041no—
489C2×C4D4×Dic1311yescharacteristic
490C2×C4#8819111yescharacteristic
491C2×C4#8819311yescharacteristic
492C2×C4C2×C22⋊Dic1311yescharacteristic
493C8—41no—
494C8—41no—
495C8—521no—
496C8—522no—
497C8—521no—
498C8—1041no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—22no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22#1171886411yescharacteristic
518C22#1171886511yescharacteristic
519C22#1171888111yescharacteristic
520C4—21no—
521C4—21no—
522C4—22no—
523C4—21no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—2081no—
528C4C2×#8807411yescharacteristic
529C4C2×#8807411yescharacteristic
530C2—21no—
531C2—21no—
532C2—41no—
533C2—41no—
534C2—42no—
535C2—81no—
536C2#1311520011yescharacteristic
537C2#1311529011yescharacteristic
538C2#1311535311yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3007C2
socleC22×C13#386
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenter#3007D13
hypocenterC13#9345
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
3. #13113408C2semidirect
4. #13113200C2semidirect
5. #13112741C2semidirect
6. #13112723C2semidirect
9. C2×C13×#137C4semidirect
10. C2×C13×#137C4semidirect
17. C13×#417C4semidirect
18. C13×#417C4semidirect
238. C2×#137Dic13semidirect
239. C2×#137Dic13semidirect
246. #417Dic13semidirect
247. #417Dic13semidirect
435. C13#9345semidirect

Maximal subgroups

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

subgroupindex
#131232852
#131147762
#131134082
#131132002
#131127412
#131127232
C13×#30072
#934513