Finite Group Databasebeta

← #15875070

Subgroups — #15875070

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic
2#13117300C211yesmaximal, characteristic
3#13115794C211yesmaximal, characteristic, complemented
4#13115602C211yesmaximal, characteristic, complemented
5#13115576C211yesmaximal, characteristic, complemented
6#13115571C211yesmaximal, characteristic, complemented
7#13115532C211yesmaximal, characteristic
8#13115532C211yesmaximal, characteristic
9#13115463C211yesmaximal, characteristic
10#13115456C211yesmaximal, characteristic
11#13115414C211yesmaximal, characteristic, complemented
12#13115407C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic
14#13114689C211yesmaximal, characteristic, complemented
15C4×C13×#125C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×#88126—21no—
19C13×#389C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C13×#387—21no—
22C13×#387—21no—
23C13×#382C2211yescharacteristic
24C4×C13×C4⋊C4—21no—
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C43×C13C2211yescharacteristic
29#11718727C418yescomplemented
30C2×#88049C2211yescharacteristic
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718601—21no—
39#11718601—21no—
40#11718600C2211yescharacteristic
41#11718600C2211yescharacteristic
42C4×#6103—21no—
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718589C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C13×#125—22no—
63C13×#125C2×C414yes—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13D411yescharacteristic
75C2×C42×C13D411yescharacteristic
76C2×C42×C13D411yescharacteristic
77C2×C42×C13D411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C4×D52—22no—
97C4×D52C2×C414yes—
98#88126—44no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88049—41no—
109#88049—41no—
110#88049C2×C414yes—
111#88049C2×C414yes—
112#88048—41no—
113#88048C2×C414yes—
114#88047—41no—
115#88047C2×C414yes—
116C4⋊#1055—22no—
117C4⋊#1055C2×C414yes—
118#88043—41no—
119#88043—41no—
120#22120—131nomaximal, Sylow
121C23×D13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52C22×C412yes—
142C2×C4×D13—24no—
143C2×C4×D13—42no—
144C2×C4×D13—42no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—42no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4C22×C412yes—
156C13×C4⋊C4C22×C412yes—
157C42×C13—22no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—41no—
163C42×C13—41no—
164C42×C13—41no—
165C42×C13—42no—
166C42×C13—42no—
167C42×C13C22×C412yes—
168C42×C13#4112yes—
169#6103—24no—
170#6103—42no—
171#6103—42no—
172#6103—42no—
173#6103—42no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13C22×C412yes—
180#6101—42no—
181#6101—42no—
182C4×Dic13—42no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055C22×C412yes—
194C2×#1055C22×C412yes—
195C2×#478—131no—
196C4×#125D1311yescharacteristic, complemented
197#2293—131no—
198#1989—131no—
199#1949—131no—
200#1944—131no—
201#1943—131no—
202#1936—131no—
203#1936—131no—
204#1926—131no—
205#1925—131no—
206#1919—131no—
207#1918—131no—
208#1804—131no—
209#1767—131no—
210C23×C13C22×D411yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C4×D412yes—
247C2×C4×C13AGL(1,ℤ/8)12yes—
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13H(5,𝔽2)11yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×C4×C132−1+411yescharacteristic
253C2×C4×C132−1+411yescharacteristic
254C2×Dic13—22no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263D52—22no—
264D52—22no—
265D52—41no—
266D52—41no—
267C4×D13—48no—
268#1055—22no—
269#1055—22no—
270#1055—41no—
271#1055—41no—
272C2×#125C2×D1311yescharacteristic
273C2×C4×D4—131no—
274C2×#117—261no—
275#478—138no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×C4⋊C8—131no—
281C2×C4⋊C8—131no—
282C2×#102—131no—
283C2×#102—131no—
284C2×#102—131no—
285C2×#102—131no—
286C2×#97—131no—
287C2×#97—131no—
288#390—131no—
289#390—131no—
290#389—131no—
291#389—131no—
292#389C2×D1311yescharacteristic
293#389C2×D1311yescharacteristic
294#388—261no—
295#388—261no—
296#387—21no—
297#387—21no—
298#382C2×D1311yescharacteristic
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C4⋊C4C2×D1311yescharacteristic
304C4×C22⋊C4—261no—
305C43C2×D1311yescharacteristic
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#336—131no—
315#336—131no—
316C22×C13C2×C4×D411yescharacteristic
317C22×C13#53611yescharacteristic
318C22×C13#53711yescharacteristic
319C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C13#57511yescharacteristic
321C22×C13#57511yescharacteristic
322C22×C13#57511yescharacteristic
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—81no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C4×C13—22no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—42no—
334C4×C13—42no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13#51911yescharacteristic
341C4×C13#52011yescharacteristic
342C4×C13#54111yescharacteristic
343C4×C13#54211yescharacteristic
344Dic13—42no—
345Dic13—81no—
346Dic13—81no—
347C22×D4—131no—
348C23×C4—261no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353#125—22no—
354#125C4×D1314yes—
355C4×D4—134no—
356C4×D4—262no—
357#117—524no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—261no—
379C2×C42C22⋊D1311yescharacteristic
380C2×C42C22⋊D1311yescharacteristic
381C2×C42C22⋊D1311yescharacteristic
382C2×C42C22⋊D1311yescharacteristic
383C2×C42C22×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386#107—134no—
387#107—521no—
388#106—134no—
389#106—521no—
390C4⋊C8—134no—
391C4⋊C8—262no—
392#102—134no—
393#102—134no—
394#102—521no—
395#102—521no—
396#97—521no—
397#97—521no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—261no—
405#95—261no—
406#95—261no—
407C2×C13#232311yescharacteristic
408C2×C13#294311yescharacteristic
409C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
410C2×C13#323411yescharacteristic
411C2×C13#324011yescharacteristic
412C2×C13#325111yescharacteristic
413C2×C13#325611yescharacteristic
414D13—82no—
415C24—261no—
416C2×D4—132no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—261no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—522no—
431C22×C4—522no—
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—132no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4C2×C4×D1312yes—
470C4⋊C4C2×C4×D1312yes—
471C22⋊C4—264no—
472C22⋊C4—522no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C22⋊C4—522no—
476C42—22no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—42no—
485C42—42no—
486C42—522no—
487C42C2×C4×D1312yes—
488C42#612712yes—
489C13#2212011yescharacteristic, complemented, Sylow
490C23—262no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23C22×C22⋊D1311yescharacteristic
498D4—262no—
499D4—262no—
500D4—521no—
501D4—521no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—262no—
530C2×C4—528no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4C4×C22⋊D1312yes—
540C2×C4C4×C22⋊D1312yes—
541C2×C4#8820312yes—
542C2×C4C22×C4×D1311yescharacteristic
543C2×C4C2×#612711yescharacteristic
544C2×C4#8825411yescharacteristic
545C2×C4#8825411yescharacteristic
546C2×C4#8825611yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—262no—
549C8—262no—
550C8—521no—
551C8—521no—
552C22—522no—
553C22—522no—
554C22—522no—
555C22—1041no—
556C22—1041no—
557C22—1041no—
558C22—1041no—
559C22C2×C4×C22⋊D1311yescharacteristic
560C22#1171952111yescharacteristic
561C22C2×#8820311yescharacteristic
562C22#1171952711yescharacteristic
563C22#1171952711yescharacteristic
564C22#1171952711yescharacteristic
565C22#1171953811yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—42no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—522no—
577C4—1041no—
578C4—1041no—
579C4#1171927711yescharacteristic
580C4#1171927911yescharacteristic
581C4#1171928711yescharacteristic
582C4#1171928811yescharacteristic
583C2—1042no—
584C2#1311751211yescharacteristic
585C2#1312363411yescharacteristic
586C2C4×#8820311yescharacteristic
587C2#1312602611yescharacteristic
588C2#1312607611yescharacteristic
589C2#1312619811yescharacteristic
590C2#1312623211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#125C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#125D13
hypocenterC13#22120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
3. #13115794C2semidirect
4. #13115602C2semidirect
5. #13115576C2semidirect
6. #13115571C2semidirect
11. #13115414C2semidirect
12. #13115407C2semidirect
14. #13114689C2semidirect
15. C4×C13×#125C2semidirect
29. #11718727C4semidirect
196. C4×#125D13semidirect
489. C13#22120semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
#131173002
#131157942
#131156022
#131155762
#131155712
#131155322
#131154632
#131154562
#131154142
#131154072
#131148432
#131146892
C4×C13×#1252
#2212013