Finite Group Databasebeta

← #15917573

Subgroups — #15917573

Order 3328.

1276 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718741C211yesmaximal, characteristic, complemented
2C2×#11718670C211yesmaximal, characteristic, complemented
3#13120002C211yesmaximal, characteristic, complemented
4#13116022C212yesmaximal, complemented
5#13116015C212yesmaximal, complemented
6#13115785C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13115029C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114661C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41—21no—
13C13×#547—24no—
14C13×#547—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×#121C2212yes—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C2×#88124C2211yescharacteristic
23#11718883—21no—
24C2×#88072C2212yes—
25C2×#88072C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27#11718873C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718741—24no—
32#11718670—24no—
33#11718643—21no—
34C2×#88048C2212yes—
35C2×#88048C2211yescharacteristic
36C2×#88047C2212yes—
37C2×#88047C2211yescharacteristic
38#11718606—22no—
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C2×C13×#41—28no—
46C2×C13×#41—48no—
47C22×Q8×C13—21no—
48C22×D4×C13—22no—
49C22×D4×C13D411yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—22no—
52C23×C4×C13—21no—
53C23×C4×C13C2312yes—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8D414yes—
56C13×#123—216no—
57C13×C22⋊Q8—28no—
58C13×#121—24no—
59C13×#121—24no—
60C4×D4×C13—22no—
61C4×D4×C13—22no—
62C4×D4×C13—22no—
63C4×D4×C13D414yes—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2312yes—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4D412yes—
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—22no—
76C2×C22⋊Dic13—22no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2312yes—
80C2×#6101—21no—
81C2×#6101—21no—
82C2×C4×Dic13—21no—
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2312yes—
86#88124—22no—
87#88124—22no—
88#88072—22no—
89#88072—22no—
90#88072—24no—
91#88071—21no—
92#88071—22no—
93#88071—22no—
94C22⋊#1055—24no—
95C22⋊#1055—24no—
96#88048—22no—
97#88048—24no—
98#88047—22no—
99#88047—24no—
100C4⋊#1055—22no—
101#88043—22no—
102#25709—131nomaximal, Sylow
103C24×C13—21no—
104C24×C13C2×D412yes—
105C13×#41—432no—
106C2×Q8×C13—24no—
107C2×Q8×C13—44no—
108C2×D4×C13—24no—
109C2×D4×C13—28no—
110C2×D4×C13—22no—
111C2×D4×C13—21no—
112C2×D4×C13—22no—
113C2×D4×C13—22no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C2×D4×C13C2×D412yes—
117C22×C4×C13—28no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—24no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—44no—
128C22×C4×C13—44no—
129C22×C4×C13—44no—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C13×C4⋊C4—28no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4C2×D412yes—
143C13×C4⋊C4C2×D414yes—
144C13×C22⋊C4—28no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—24no—
147C42×C13C2×D412yes—
148C42×C13C2×D412yes—
149C22⋊Dic13—44no—
150C22⋊Dic13—82no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13—21no—
154C4⋊Dic13—21no—
155C4⋊Dic13—22no—
156C4⋊Dic13—22no—
157#6101—42no—
158#6101—42no—
159C4×Dic13—81no—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#1055—21no—
163C2×#1055—21no—
164C2×#1055—22no—
165C2×#1055—22no—
166C2×#1055#4114yescomplemented
167C2×#547D1311yescharacteristic
168C2×#501—131no—
169C2×#478—131no—
170#2562—131no—
171#2034—132no—
172#2033—132no—
173#1987—131no—
174#1955—131no—
175#1853—132no—
176#1852—132no—
177#1762—131no—
178C23×C13—22no—
179C23×C13—22no—
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—22no—
183C23×C13—22no—
184C23×C13—22no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—41no—
188C23×C13—41no—
189C23×C13AGL(1,ℤ/8)14yes—
190C23×C13C22×D411yescharacteristic
191Q8×C13—48no—
192D4×C13—28no—
193D4×C13—22no—
194D4×C13—22no—
195D4×C13—416no—
196D4×C13—42no—
197C2×C4×C13—22no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—48no—
206C2×C4×C13—416no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13#12012yes—
215C2×C4×C13#12012yes—
216C2×C4×C13C22×D411yescharacteristic
217C2×C4×C13C22×D411yescharacteristic
218C2×C4×C13C2×#4112yes—
219C2×C4×C132−1+412yes—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—41no—
227C2×Dic13—41no—
228#1055—24no—
229#1055—41no—
230#1055—41no—
231C22×#41—21no—
232#547—24no—
233#547—24no—
234C2×C4⋊Q8C2×D1311yescharacteristic
235C2×#125—131no—
236C2×#123—22no—
237C2×C22⋊Q8—21no—
238C2×#121C2×D1312yes—
239C2×C4×D4C2×D1311yescharacteristic
240C2×C4×D4C2×D1311yescharacteristic
241C22×C4⋊C4C2×D1312yes—
242#501—264no—
243#478—264no—
244C2×#107—131no—
245C2×#107—132no—
246C2×#106—131no—
247C2×#106—132no—
248C2×C4⋊C8—131no—
249C2×#102—131no—
250C2×#102—131no—
251C2×#102—132no—
252C2×C22⋊C8—132no—
253C2×C22⋊C8—132no—
254C2×#97—131no—
255#400—261no—
256#394—261no—
257#388—262no—
258#380—132no—
259#380—132no—
260C4×C4⋊C4—131no—
261#340—132no—
262#340—132no—
263#340—132no—
264C22×C13—24no—
265C22×C13—24no—
266C22×C13—24no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13—42no—
273C22×C13—42no—
274C22×C13—82no—
275C22×C13—82no—
276C22×C13C2×#12011yescharacteristic
277C22×C13#54712yes—
278C22×C13C2×AGL(1,ℤ/8)12yes—
279C22×C13#57711yescharacteristic
280C22×C13#57811yescharacteristic
281C4×C13—22no—
282C4×C13—22no—
283C4×C13—42no—
284C4×C13—42no—
285C4×C13—44no—
286C4×C13#53211yescharacteristic
287C4×C13#53611yescharacteristic
288C4×C13#54812yes—
289Dic13—82no—
290Dic13—81no—
291Dic13—81no—
292C2×#41—28no—
293C2×#41—48no—
294C22×Q8—21no—
295C22×D4—22no—
296C22×D4C22⋊D1311yescharacteristic
297C22×D4C22×D1311yescharacteristic
298C23×C4—22no—
299C23×C4—21no—
300C23×C4C22×D1312yes—
301C22×C8—132no—
302C22×C8—131no—
303C22×C8—131no—
304C4⋊Q8—22no—
305C4⋊Q8C22⋊D1314yes—
306#125—262no—
307#125—262no—
308#123—216no—
309C22⋊Q8—28no—
310#121—24no—
311#121—24no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4C22⋊D1314yes—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—131no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—132no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4—261no—
325C2×C4⋊C4C22⋊D1311yescharacteristic
326C2×C4⋊C4C22×D1311yescharacteristic
327C2×C4⋊C4C22×D1312yes—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—262no—
331C2×C22⋊C4—262no—
332C2×C22⋊C4C22⋊D1312yes—
333C2×C42—261no—
334C2×C42C22×D1311yescharacteristic
335#107—262no—
336#107—264no—
337#106—262no—
338#106—264no—
339C4⋊C8—262no—
340#102—264no—
341#102—262no—
342#102—262no—
343C22⋊C8—264no—
344C22⋊C8—264no—
345#97—262no—
346#95—261no—
347#95—262no—
348#95—262no—
349C2×C13—44no—
350C2×C13—82no—
351C2×C13#243211yescharacteristic
352C2×C13#300311yescharacteristic
353C2×C13#301311yescharacteristic
354C2×C13#334312yes—
355C2×C13#334512yes—
356C24—21no—
357C24C2×C22⋊D1312yes—
358#41—432no—
359C2×Q8—24no—
360C2×Q8—44no—
361C2×D4—24no—
362C2×D4—28no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4C2×C22⋊D1312yes—
370C22×C4—28no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—262no—
384C22×C4—261no—
385C22×C4—261no—
386C22×C4C2×C22⋊D1312yes—
387C22×C4C2×C22⋊D1311yescharacteristic
388C22×C4C2×C22⋊D1311yescharacteristic
389C22×C4C23×D1311yescharacteristic
390C2×C8—134no—
391C2×C8—262no—
392C2×C8—262no—
393C2×C8—262no—
394C2×C8—262no—
395C2×C8—261no—
396C2×C8—261no—
397C4⋊C4—28no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—262no—
403C4⋊C4—262no—
404C4⋊C4—261no—
405C4⋊C4—261no—
406C4⋊C4—261no—
407C4⋊C4—261no—
408C4⋊C4—522no—
409C4⋊C4—522no—
410C4⋊C4C2×C22⋊D1312yes—
411C4⋊C4C2×C22⋊D1314yes—
412C22⋊C4—28no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—524no—
416C22⋊C4—1042no—
417C42—1041no—
418C42C2×C22⋊D1312yes—
419C42C2×C22⋊D1312yes—
420C13#2570911yescharacteristic, complemented, Sylow
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23#8818614yes—
433C23C22×C22⋊D1311yescharacteristic
434Q8—48no—
435D4—28no—
436D4—22no—
437D4—22no—
438D4—416no—
439D4—42no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—48no—
449C2×C4—416no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—522no—
458C2×C4—522no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—521no—
464C2×C4—521no—
465C2×C4#8820712yes—
466C2×C4#8820712yes—
467C2×C4#41×D1312yes—
468C2×C4#8825712yes—
469C2×C4C22×C22⋊D1311yescharacteristic
470C2×C4C22×C22⋊D1311yescharacteristic
471C8—264no—
472C8—521no—
473C8—521no—
474C22—24no—
475C22—24no—
476C22—24no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—82no—
485C22—82no—
486C22C2×#8818612yes—
487C22#1171952912yes—
488C22#1171954211yescharacteristic
489C22#1171954311yescharacteristic
490C22C2×#8820711yescharacteristic
491C4—22no—
492C4—22no—
493C4—42no—
494C4—44no—
495C4—42no—
496C4—1041no—
497C4—1042no—
498C4—1041no—
499C4#1171953011yescharacteristic
500C4#1171953612yes—
501C4#1171953711yescharacteristic
502C2—44no—
503C2—82no—
504C2#1311846011yescharacteristic
505C2#1312406311yescharacteristic
506C2#1312415111yescharacteristic
507C2#1312727012yes—
508C2#1312730612yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#25709
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
2. C2×#11718670C2semidirect
3. #13120002C2semidirect
4. #13116022C2semidirect
5. #13116015C2semidirect
6. #13115785C2semidirect
7. #13115635C2semidirect
8. #13115029C2semidirect
9. #13115024C2semidirect
10. #13114661C2semidirect
166. C2×#1055#41semidirect
420. C13#25709semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
C2×#117186702
#131200022
#131160222
#131160152
#131157852
#131156352
#131150292
#131150242
#131146612
C2×C13×#5472
#2570913