Finite Group Databasebeta

← #15917639

Subgroups — #15917639

Order 3328.

1038 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
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718681C211yesmaximal, characteristic, complemented
3#13120009C211yesmaximal, characteristic
4#13116036C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic
8#13115035C212yesmaximal, complemented
9#13115029C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic
12C13×#552—24no—
13C13×#552—24no—
14C2×C13×#126—21no—
15C2×C13×#125—21no—
16C2×C13×#125C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C13×#117—21no—
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28#11718882—21no—
29#11718873C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2212yes—
33#11718726—24no—
34#11718681—24no—
35#11718638—21no—
36C2×#88048C2212yes—
37C2×#88048C2212yes—
38C2×#88047C2212yes—
39#11718608—21no—
40#11718608—21no—
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×Dic26—21no—
53C13×#126—28no—
54C13×#125—28no—
55C13×#125—22no—
56C13×#125D414yes—
57C13×#123—28no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13D414yes—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C13×#117—28no—
67C13×#117—22no—
68C13×#117—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2312yes—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97#88123—22no—
98#88123—22no—
99#88075—24no—
100#88075—24no—
101#88071—21no—
102#88071—22no—
103#88071—22no—
104C22⋊#1055—24no—
105C22⋊#1055—24no—
106#88048—24no—
107#88048—24no—
108#88047—24no—
109C4⋊#1055—22no—
110#88043—22no—
111#25715—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C24×C13C2×D411yescharacteristic
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13C2×D412yes—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—41no—
121C22×C4×C13—24no—
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—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C22×Dic13—22no—
143C2×Dic26—42no—
144C2×Dic26—82no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4C2×D412yes—
156C13×C4⋊C4C2×D412yes—
157C13×C4⋊C4C2×D412yes—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—22no—
162C13×C22⋊C4—22no—
163C42×C13—24no—
164C42×C13—24no—
165C42×C13C2×D412yes—
166C42×C13C2×D412yes—
167C22⋊Dic13—82no—
168C22⋊Dic13—82no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—42no—
174C4×Dic13—42no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055#4114yes—
181C2×#552D1311yescharacteristic
182C2×#501—131no—
183C2×#475—131no—
184#2563—131no—
185#2036—132no—
186#2035—132no—
187#1989—131no—
188#1955—131no—
189#1854—132no—
190#1853—132no—
191#1763—131no—
192C23×C13—21no—
193C23×C13—22no—
194C23×C13—21no—
195C23×C13—22no—
196C23×C13—21no—
197C23×C13—22no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13#13712yes—
202C23×C13C22×D411yescharacteristic
203Q8×C13—22no—
204Q8×C13—22no—
205Q8×C13—42no—
206D4×C13—44no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—22no—
210C2×C4×C13—21no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—48no—
219C2×C4×C13—42no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13#12012yes—
232C2×C4×C13#12012yes—
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4112yes—
236C2×C4×C132−1+412yes—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243Dic26—84no—
244#1055—24no—
245#1055—42no—
246#552—24no—
247#552—24no—
248C2×C4⋊Q8—131no—
249C2×#126—21no—
250C2×#125—21no—
251C2×#125C2×D1311yescharacteristic
252C2×#123—21no—
253C2×C22⋊Q8C2×D1311yescharacteristic
254C2×C22⋊Q8C2×D1311yescharacteristic
255C2×C4×Q8C2×D1311yescharacteristic
256C2×C4×D4C2×D1311yescharacteristic
257C2×#117—21no—
258C2×#117C2×D1311yescharacteristic
259C22×C4⋊C4C2×D1311yescharacteristic
260#501—264no—
261#475—264no—
262C2×#107—132no—
263C2×#106—132no—
264C2×#106—132no—
265C2×C4⋊C8—131no—
266C2×#103—132no—
267C2×#103—132no—
268C2×C22⋊C8—132no—
269C2×C22⋊C8—132no—
270C2×#97—131no—
271#393—261no—
272#393—261no—
273#390—261no—
274#382—261no—
275#380—132no—
276#380—132no—
277C4×C4⋊C4—131no—
278#340—132no—
279#340—132no—
280#340—132no—
281C22×C13—24no—
282C22×C13—22no—
283C22×C13—42no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13C2×#12011yescharacteristic
292C22×C13#54712yes—
293C22×C13C2×#13711yescharacteristic
294C22×C13#57511yescharacteristic
295C22×C13#57712yes—
296C4×C13—22no—
297C4×C13—22no—
298C4×C13—41no—
299C4×C13—41no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13#53211yescharacteristic
305C4×C13#53611yescharacteristic
306C4×C13#54812yes—
307Dic13—82no—
308Dic13—82no—
309C22×Q8—261no—
310C22×Q8C22×D1311yescharacteristic
311C22×D4C22⋊D1311yescharacteristic
312C23×C4—21no—
313C23×C4C22×D1311yescharacteristic
314C23×C4C22×D1311yescharacteristic
315C22×C8—132no—
316C22×C8—132no—
317C4⋊Q8—262no—
318C4⋊Q8—262no—
319#126—28no—
320#125—28no—
321#125—22no—
322#125C22⋊D1314yes—
323#123—28no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C4×Q8—22no—
329C4×Q8C22⋊D1314yes—
330C4×D4—22no—
331C4×D4—22no—
332#117—28no—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—132no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4—261no—
346C2×C4⋊C4C22⋊D1311yescharacteristic
347C2×C4⋊C4C22×D1311yescharacteristic
348C2×C4⋊C4C22×D1311yescharacteristic
349C2×C4⋊C4C22×D1311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—262no—
354C2×C22⋊C4—262no—
355C2×C22⋊C4C22⋊D1311yescharacteristic
356C2×C22⋊C4C22⋊D1311yescharacteristic
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—261no—
360C2×C42C22×D1311yescharacteristic
361#107—264no—
362#106—264no—
363#106—264no—
364C4⋊C8—262no—
365#103—264no—
366#103—264no—
367C22⋊C8—264no—
368C22⋊C8—264no—
369#97—262no—
370#95—261no—
371#95—262no—
372#95—262no—
373C2×C13—42no—
374C2×C13—81no—
375C2×C13#243211yescharacteristic
376C2×C13#300711yescharacteristic
377C2×C13#301011yescharacteristic
378C2×C13#334412yes—
379C2×C13#334812yes—
380C24C2×C22⋊D1311yescharacteristic
381C24C2×C22⋊D1311yescharacteristic
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—522no—
386C2×Q8—1042no—
387C2×Q8C2×C22⋊D1312yes—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—41no—
391C22×C4—24no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4C2×C22⋊D1311yescharacteristic
409C22×C4C2×C22⋊D1311yescharacteristic
410C22×C4C2×C22⋊D1311yescharacteristic
411C22×C4C2×C22⋊D1311yescharacteristic
412C22×C4C23×D1311yescharacteristic
413C2×C8—134no—
414C2×C8—262no—
415C2×C8—262no—
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—262no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—262no—
430C4⋊C4—262no—
431C4⋊C4—262no—
432C4⋊C4—262no—
433C4⋊C4—522no—
434C4⋊C4C2×C22⋊D1312yes—
435C4⋊C4C2×C22⋊D1312yes—
436C4⋊C4C2×C22⋊D1312yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—1042no—
443C22⋊C4—1042no—
444C42—24no—
445C42—24no—
446C42—522no—
447C42C2×C22⋊D1312yes—
448C42C2×C22⋊D1312yes—
449C13#2571511yescharacteristic, complemented, Sylow
450C23—21no—
451C23—22no—
452C23—22no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—22no—
457C23—22no—
458C23—21no—
459C23#8820512yes—
460C23C22×C22⋊D1311yescharacteristic
461Q8—22no—
462Q8—22no—
463Q8—42no—
464Q8—1044no—
465D4—44no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—48no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—522no—
491C2×C4—522no—
492C2×C4—522no—
493C2×C4—522no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4#8820712yes—
497C2×C4#8820712yes—
498C2×C4#41×D1312yes—
499C2×C4#8825712yes—
500C2×C4C22×C22⋊D1311yescharacteristic
501C2×C4C22×C22⋊D1311yescharacteristic
502C8—264no—
503C8—522no—
504C22—22no—
505C22—24no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—42no—
513C22—41no—
514C22#1171952711yescharacteristic
515C22C2×#8820511yescharacteristic
516C22#1171952912yes—
517C22#1171954212yes—
518C22C2×#8820711yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—41no—
525C4—41no—
526C4—42no—
527C4—1042no—
528C4—1042no—
529C4#1171953011yescharacteristic
530C4#1171953612yes—
531C4#1171953711yescharacteristic
532C2—42no—
533C2—81no—
534C2#1311846011yescharacteristic
535C2#1312409611yescharacteristic
536C2#1312412211yescharacteristic
537C2#1312729112yes—
538C2#1312734512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#25715
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718681C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115794C2semidirect
8. #13115035C2semidirect
9. #13115029C2semidirect
10. #13114666C2semidirect
449. C13#25715semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117186812
#131200092
#131160362
#131160292
#131157942
#131156352
#131150352
#131150292
#131146662
C2×C13×#5522
#2571513