Finite Group Databasebeta

← #15875031

Subgroups — #15875031

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718551C211yesmaximal, characteristic
2C4×#88142C211yesmaximal, characteristic, complemented
3#13117294C211yesmaximal, characteristic
4#13115786C211yesmaximal, characteristic, complemented
5#13115598C211yesmaximal, characteristic, complemented
6#13115575C211yesmaximal, characteristic, complemented
7#13115573C211yesmaximal, characteristic, complemented
8#13115534C211yesmaximal, characteristic
9#13115531C211yesmaximal, characteristic
10#13115464C211yesmaximal, characteristic
11#13115463C211yesmaximal, characteristic
12#13115425C211yesmaximal, characteristic, complemented
13#13114835C211yesmaximal, characteristic
14#13114688C211yesmaximal, characteristic, complemented
15C13×#1921C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88146—21no—
18C2×#88142C2211yescharacteristic
19C2×C4×Dic26—21no—
20C2×C13×#107C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C2×#88061C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88057C2211yescharacteristic
26C2×#88055C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30#11718651—21no—
31#11718649C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718646C2211yescharacteristic
34#11718637C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36#11718634C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718600C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×#6101—21no—
44C42×Dic13C2211yescharacteristic
45#11718551C418yescomplemented
46#11718331—21no—
47#11718327—21no—
48#11718308—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#336C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×Dic26—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13D411yescharacteristic
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96#88147—22no—
97#88147C2×C414yes—
98#88146—44no—
99#88142—22no—
100#88142C2×C414yes—
101C4×Dic26—44no—
102C13×#107C2×C414yes—
103C13×#95—21no—
104C13×#95—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88061—41no—
111#88061C2×C414yes—
112#88057—41no—
113#88055—41no—
114#88055—41no—
115#88054—22no—
116#88054C2×C414yes—
117#88049—41no—
118#88049C2×C414yes—
119#88048—41no—
120#88047C2×C414yes—
121#22116—131nomaximal, Sylow
122C23×D13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2411yescharacteristic
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C22×C412yes—
143C2×C4×D13—24no—
144C2×C4×D13—42no—
145C2×C4×D13—42no—
146C2×Dic26—24no—
147C2×Dic26—42no—
148C2×Dic26—42no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13C22×C412yes—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4C22×C412yes—
163C13×C4⋊C4C22×C412yes—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—42no—
167#6103—24no—
168#6103—42no—
169#6103—42no—
170#6103—42no—
171#6103—42no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—42no—
178C4⋊Dic13—42no—
179C4⋊Dic13C22×C412yes—
180#6101—24no—
181#6101—42no—
182#6101—42no—
183#6101—42no—
184C4×Dic13—22no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13—41no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13C22×C412yes—
193C4×Dic13#4112yes—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#474—131no—
201C4×C4⋊Q8—131no—
202#2293—131no—
203#1988—131no—
204#1948—131no—
205#1943—131no—
206#1943—131no—
207#1936—131no—
208#1936—131no—
209#1926—131no—
210#1926—131no—
211#1921—131no—
212#1921D1311yescharacteristic, complemented
213#1802—131no—
214#1767—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13#13712yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13H(5,𝔽2)11yescharacteristic
244C2×C4×C132−1+411yescharacteristic
245C2×C4×C132−1+411yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—22no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13C4×D412yes—
265C2×Dic13C4×D412yes—
266C2×Dic13AGL(1,ℤ/8)12yes—
267C2×Dic13AGL(1,ℤ/8)12yes—
268D52—22no—
269D52—22no—
270D52—41no—
271D52—41no—
272C4×D13—48no—
273Dic26—48no—
274C8×C13—22no—
275C8×C13—41no—
276#1055—22no—
277#1055—41no—
278C2×C4⋊Q8—131no—
279C2×C4×Q8—261no—
280C2×C4×D4—131no—
281C2×#117—261no—
282#474—138no—
283C2×#107—131no—
284C2×#107C2×D1311yescharacteristic
285C2×#106—131no—
286C2×#106—131no—
287C2×C4⋊C8—131no—
288C2×C4⋊C8—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#97—131no—
294C2×#97—131no—
295#391—261no—
296#390—131no—
297#390—131no—
298#389—131no—
299#389—131no—
300#389—131no—
301#389—261no—
302#389C2×D1311yescharacteristic
303#388—261no—
304#388—261no—
305#384—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—261no—
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C22⋊C4—261no—
311C43—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340C2×D1311yescharacteristic
318#340C2×D1311yescharacteristic
319#340C2×D1311yescharacteristic
320#336—131no—
321#336C2×D1311yescharacteristic
322C22×C13C2×C4×D411yescharacteristic
323C22×C13#53611yescharacteristic
324C22×C13#53711yescharacteristic
325C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13C2×#13711yescharacteristic
328C22×C13#57511yescharacteristic
329C2×D13—42no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—81no—
336C4×C13—22no—
337C4×C13—42no—
338C4×C13—42no—
339C4×C13—41no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13#51911yescharacteristic
343C4×C13#52011yescharacteristic
344C4×C13#54111yescharacteristic
345C4×C13#54211yescharacteristic
346Dic13—22no—
347Dic13—42no—
348Dic13—41no—
349Dic13—41no—
350Dic13—81no—
351Dic13—81no—
352Dic13#44214yes—
353C22×Q8—261no—
354C22×D4—131no—
355C23×C4—261no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8C22×D1311yescharacteristic
359C22×C8C22×D1311yescharacteristic
360C4⋊Q8—134no—
361C4⋊Q8—262no—
362C4×Q8—524no—
363C4×D4—134no—
364C4×D4—262no—
365#117—524no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—21no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395#107—134no—
396#107C4×D1314yes—
397#106—521no—
398#106—521no—
399C4⋊C8—134no—
400C4⋊C8—262no—
401#102—134no—
402#102—134no—
403#102—521no—
404#102—521no—
405#97—521no—
406#97—521no—
407#95—21no—
408#95—21no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414C2×C13#232311yescharacteristic
415C2×C13C2×#44211yescharacteristic
416C2×C13C4×#13711yescharacteristic
417C2×C13#323511yescharacteristic
418C2×C13#323911yescharacteristic
419C2×C13#325111yescharacteristic
420C2×C13#325411yescharacteristic
421D13—82no—
422C24—261no—
423C2×Q8—264no—
424C2×Q8—522no—
425C2×Q8—522no—
426C2×D4—132no—
427C2×D4—261no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4D4×D1311yescharacteristic
447C22×C4D4×D1311yescharacteristic
448C22×C4C23×D1311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—132no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8C2×C4×D1312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—132no—
469C4⋊C4—264no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4—522no—
480C4⋊C4C2×C4×D1312yes—
481C4⋊C4C2×C4×D1312yes—
482C22⋊C4—264no—
483C22⋊C4—522no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C22⋊C4—522no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—132no—
491C42—132no—
492C42—262no—
493C42—262no—
494C42—262no—
495C42—261no—
496C42—261no—
497C42—521no—
498C42—522no—
499C42—522no—
500C13#2211611yescharacteristic, complemented, Sylow
501C23—262no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23—521no—
507C23—521no—
508C23C2×D4×D1311yescharacteristic
509Q8—528no—
510D4—262no—
511D4—262no—
512D4—521no—
513D4—521no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
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—41no—
530C2×C4—41no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—262no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—528no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4#8817212yes—
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4#8825411yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825611yescharacteristic
558C2×C4#8825711yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—22no—
561C8—41no—
562C8—262no—
563C8—521no—
564C22—522no—
565C22—522no—
566C22—522no—
567C22—1041no—
568C22—1041no—
569C22—1041no—
570C22—1041no—
571C22C4×D4×D1311yescharacteristic
572C22#1171933411yescharacteristic
573C22#1171935311yescharacteristic
574C22C2×#8817211yescharacteristic
575C22#1171947311yescharacteristic
576C22D13×AGL(1,ℤ/8)11yescharacteristic
577C22D13×AGL(1,ℤ/8)11yescharacteristic
578C4—22no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—134no—
585C4—262no—
586C4—522no—
587C4—521no—
588C4—521no—
589C4—1041no—
590C4—1041no—
591C4#1171922811yescharacteristic
592C4#1171927711yescharacteristic
593C4#1171940111yescharacteristic
594C4#1171941511yescharacteristic
595C2—1042no—
596C2#1311751711yescharacteristic
597C2D13×#44211yescharacteristic
598C2C4×#8817211yescharacteristic
599C2#1312603111yescharacteristic
600C2#1312606911yescharacteristic
601C2#1312619711yescharacteristic
602C2#1312622211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1921C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1921D13
hypocenterC13#22116
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
2. C4×#88142C2semidirect
4. #13115786C2semidirect
5. #13115598C2semidirect
6. #13115575C2semidirect
7. #13115573C2semidirect
12. #13115425C2semidirect
14. #13114688C2semidirect
15. C13×#1921C2semidirect
45. #11718551C4semidirect
212. #1921D13semidirect
500. C13#22116semidirect

Maximal subgroups

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

subgroupindex
C2×#117185512
C4×#881422
#131172942
#131157862
#131155982
#131155752
#131155732
#131155342
#131155312
#131154642
#131154632
#131154252
#131148352
#131146882
C13×#19212
#2211613