Finite Group Databasebeta

← #15875025

Subgroups — #15875025

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×#11718420C211yesmaximal, characteristic
2#13117407C211yesmaximal, characteristic, complemented
3#13117298C211yesmaximal, characteristic
4#13115786C211yesmaximal, characteristic, complemented
5#13115598C211yesmaximal, characteristic, complemented
6#13115574C211yesmaximal, characteristic, complemented
7#13115571C211yesmaximal, characteristic, complemented
8#13115536C211yesmaximal, characteristic
9#13115466C211yesmaximal, characteristic
10#13115465C211yesmaximal, characteristic
11#13115427C211yesmaximal, characteristic, complemented
12#13115426C211yesmaximal, characteristic, complemented
13#13114834C211yesmaximal, characteristic
14#13114690C211yesmaximal, characteristic, complemented
15C13×#1936C211yesmaximal, characteristic
16C2×D4×Dic13C2211yescharacteristic
17C2×#88142C2211yescharacteristic
18C2×#88141—21no—
19C2×#88131—21no—
20C2×C13×#102C2211yescharacteristic
21C2×C13×#102C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25#11718882C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32#11718637C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36#11718634C2211yescharacteristic
37#11718633—21no—
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718606—21no—
41#11718605—21no—
42C22⋊C4×Dic13—21no—
43C42×Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718589C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718420C418yescomplemented
48#11718310—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×Dic13—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×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13C2311yescharacteristic
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75D4×Dic13—22no—
76D4×Dic13C2×C414yes—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13D411yescharacteristic
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98#88142—22no—
99#88142C2×C414yes—
100#88141—44no—
101#88131—44no—
102C13×#102—41no—
103C13×#102C2×C414yes—
104C13×#97—41no—
105C13×#95—21no—
106#88072—41no—
107#88072C2×C414yes—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88058C2×C414yes—
115#88057—41no—
116#88054—22no—
117#88054C2×C414yes—
118#88048—41no—
119#88047C2×C414yes—
120#88043—41no—
121#22116—131nomaximal, Sylow
122C24×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13C22×C412yes—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—24no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—42no—
141C22×Dic13—42no—
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
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—42no—
161C13×C4⋊C4C22×C412yes—
162C13×C22⋊C4—42no—
163C13×C22⋊C4—42no—
164C42×C13—21no—
165C42×C13—21no—
166C22⋊Dic13—24no—
167C22⋊Dic13—42no—
168C22⋊Dic13—42no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13C22×C412yes—
176C4⋊Dic13C22×C412yes—
177#6101—24no—
178#6101—42no—
179#6101—42no—
180#6101—42no—
181#6101—42no—
182#6101—42no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—41no—
189C4×Dic13—42no—
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#1936D1311yescharacteristic
209#1926—131no—
210#1926—131no—
211#1921—131no—
212#1921—131no—
213#1802—131no—
214#1767—131no—
215C23×C13—22no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13C22×D411yescharacteristic
223D4×C13—22no—
224D4×C13—22no—
225D4×C13—41no—
226D4×C13—41no—
227C2×C4×C13—22no—
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—41no—
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×C13C23×C411yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13H(5,𝔽2)11yescharacteristic
245C2×C4×C132−1+411yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—48no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13C4×D412yes—
269C2×Dic13C4×D412yes—
270C2×Dic13AGL(1,ℤ/8)12yes—
271C2×Dic13AGL(1,ℤ/8)12yes—
272C2×Dic13#13712yes—
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×#107—131no—
285C2×#106—131no—
286C2×#106—131no—
287C2×C4⋊C8—131no—
288C2×C4⋊C8—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102C2×D1311yescharacteristic
292C2×#102C2×D1311yescharacteristic
293C2×#97—131no—
294C2×#97C2×D1311yescharacteristic
295#391—261no—
296#390—131no—
297#390C2×D1311yescharacteristic
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—131no—
309C4×C4⋊C4—261no—
310C4×C22⋊C4—261no—
311C43—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340C2×D1311yescharacteristic
319#340C2×D1311yescharacteristic
320#336—131no—
321#336—131no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13C2×C4×D411yescharacteristic
330C22×C13#53611yescharacteristic
331C22×C13#53711yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C13C2×#13711yescharacteristic
335C22×C13#57511yescharacteristic
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13#51911yescharacteristic
342C4×C13#52011yescharacteristic
343C4×C13#54111yescharacteristic
344C4×C13#54211yescharacteristic
345Dic13—22no—
346Dic13—22no—
347Dic13—42no—
348Dic13—42no—
349Dic13—41no—
350Dic13—81no—
351Dic13—81no—
352Dic13#44214yes—
353C22×Q8—261no—
354C22×D4C22×D1311yescharacteristic
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—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395#107—134no—
396#107—134no—
397#106—521no—
398#106—521no—
399C4⋊C8—134no—
400C4⋊C8—262no—
401#102—41no—
402#102—134no—
403#102—521no—
404#102C4×D1314yes—
405#97—41no—
406#97—521no—
407#95—21no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414C2×C13—82no—
415C2×C13#232311yescharacteristic
416C2×C13C2×#44211yescharacteristic
417C2×C13C4×#13711yescharacteristic
418C2×C13#323511yescharacteristic
419C2×C13#323911yescharacteristic
420C2×C13#325111yescharacteristic
421C2×C13#325411yescharacteristic
422C24—21no—
423C2×Q8—264no—
424C2×Q8—522no—
425C2×Q8—522no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C2×C4×D1312yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—264no—
440C22×C4—261no—
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—42no—
467C4⋊C4—132no—
468C4⋊C4—132no—
469C4⋊C4—264no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4C2×C4×D1312yes—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—264no—
485C22⋊C4—522no—
486C22⋊C4—522no—
487C42—21no—
488C42—21no—
489C42—132no—
490C42—132no—
491C42—262no—
492C42—262no—
493C42—262no—
494C42—261no—
495C42—261no—
496C42—521no—
497C42—522no—
498C42—522no—
499C42—522no—
500C13#2211611yescharacteristic, complemented, Sylow
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D1311yescharacteristic
509Q8—528no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
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—132no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—261no—
543C2×C4—528no—
544C2×C4—521no—
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—521no—
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4#8825111yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825711yescharacteristic
558C2×C4#8825711yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—22no—
561C8—41no—
562C8—262no—
563C8—521no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C4×D4×D1311yescharacteristic
572C22#1171930211yescharacteristic
573C22#1171938011yescharacteristic
574C22D13×AGL(1,ℤ/8)11yescharacteristic
575C22D13×AGL(1,ℤ/8)11yescharacteristic
576C22#1171947811yescharacteristic
577C22D13×#13711yescharacteristic
578C4—42no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—134no—
584C4—262no—
585C4—262no—
586C4—522no—
587C4—522no—
588C4—521no—
589C4—1041no—
590C4—1041no—
591C4#1171922111yescharacteristic
592C4#1171925111yescharacteristic
593C4#1171936711yescharacteristic
594C4#1171940611yescharacteristic
595C2—82no—
596C2#1311751111yescharacteristic
597C2D13×#44211yescharacteristic
598C2#1312365811yescharacteristic
599C2#1312602911yescharacteristic
600C2#1312606211yescharacteristic
601C2#1312619111yescharacteristic
602C2#1312621811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1936C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1936D13
hypocenterC13#22116
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #13117407C2semidirect
4. #13115786C2semidirect
5. #13115598C2semidirect
6. #13115574C2semidirect
7. #13115571C2semidirect
11. #13115427C2semidirect
12. #13115426C2semidirect
14. #13114690C2semidirect
47. #11718420C4semidirect
500. C13#22116semidirect

Maximal subgroups

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

subgroupindex
C2×#117184202
#131174072
#131172982
#131157862
#131155982
#131155742
#131155712
#131155362
#131154662
#131154652
#131154272
#131154262
#131148342
#131146902
C13×#19362
#2211613