Finite Group Databasebeta

← #15873497

Subgroups — #15873497

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718496C211yesmaximal, characteristic
2#13117242C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115606C211yesmaximal, characteristic, complemented
5#13115604C211yesmaximal, characteristic, complemented
6#13115602C211yesmaximal, characteristic, complemented
7#13115038C211yesmaximal, characteristic
8#13115036C211yesmaximal, characteristic
9#13115034C211yesmaximal, characteristic
10#13115032C211yesmaximal, characteristic
11#13115003C211yesmaximal, characteristic, complemented
12#13115001C211yesmaximal, characteristic, complemented
13#13114968C211yesmaximal, characteristic, complemented
14#13114968C211yesmaximal, characteristic, complemented
15C13×#1949C211yesmaximal, characteristic, complemented
16C2×#88146C2211yescharacteristic
17C2×#88146C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C13×#382C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718638C2211yescharacteristic
33#11718638C2211yescharacteristic
34#11718637C2211yescharacteristic
35#11718637C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718593—21no—
44C2×C4⋊#1055C2211yescharacteristic
45#11718496C418yescomplemented
46#11718328—21no—
47#11718328—21no—
48#11718325—21no—
49#11718312—21no—
50#11718310—21no—
51#11718310—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13D411yescharacteristic
61C22×C4×D13D411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×#6101—21no—
81C2×#6101—21no—
82C2×#6101—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91#88146—41no—
92#88146—41no—
93#88146—41no—
94#88146—41no—
95C42×D13C2×C414yes—
96C42×D13Q814yes—
97C13×#107—41no—
98C13×#106—41no—
99C13×C4⋊C8C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88060C2×C414yes—
113#88060C2×C414yes—
114#88058—41no—
115#88057—41no—
116#88055C2×C414yes—
117#88055C2×C414yes—
118#88048—41no—
119#88048—41no—
120#88047—41no—
121#88047—41no—
122C4⋊#1055C2×C414yes—
123#21989—131nomaximal, Sylow
124C23×D13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—41no—
144C2×C4×D13—41no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13C4⋊C414yes—
148C2×C4×D13C4⋊C414yes—
149C2×C4×D13C22×C412yes—
150C2×C4×D13C2×Q812yes—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C22×C412yes—
156C2×C8×C13C22×C412yes—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C42×C13—42no—
166C42×C13C22×C412yes—
167C42×C13C2×Q812yes—
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—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180#6101—42no—
181#6101—42no—
182#6101—42no—
183#6101—42no—
184C4×Dic13—42no—
185C4×Dic13—42no—
186C4×Dic13—42no—
187C4×Dic13C4⋊C414yes—
188C4×Dic13C4⋊C414yes—
189C4×Dic13C22×C412yes—
190C4×Dic13C2×Q812yes—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055C22×C412yes—
196C2×#1055C22×C412yes—
197C2×#432—131no—
198#2285—131no—
199#2283—131no—
200#1949—131no—
201#1949—131no—
202#1949—131no—
203#1949D1311yescharacteristic, complemented
204#1854—131no—
205#1854—131no—
206#1854—131no—
207#1854—131no—
208#1847—131no—
209#1847—131no—
210#1836—131no—
211#1836—131no—
212C23×C13C22×D411yescharacteristic
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13—21no—
217C22×D13—21no—
218C22×D13—21no—
219C22×D13C2×C4⋊C412yes—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
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×C13C2×C4⋊C412yes—
237C2×C4×C13C2×C4⋊C412yes—
238C2×C4×C13C23×C411yescharacteristic
239C2×C4×C13C22×Q811yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C13H(5,𝔽2)11yescharacteristic
242C2×C4×C132−1+411yescharacteristic
243C2×C4×C132−1+411yescharacteristic
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13C2×C4⋊C412yes—
263C2×Dic13C2×C4⋊C412yes—
264C2×Dic13C2×C4⋊C412yes—
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—22no—
268C4×D13—22no—
269C4×D13—44no—
270C4×D13—44no—
271C8×C13—22no—
272C8×C13—22no—
273#1055—22no—
274#1055—22no—
275C2×#117—131no—
276C2×#117—131no—
277C22×C42—131no—
278#432—138no—
279C2×#107—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#107C2×D1311yescharacteristic
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—131no—
286C2×#106C2×D1311yescharacteristic
287C2×C4⋊C8—131no—
288C2×C4⋊C8C2×D1311yescharacteristic
289C2×C22⋊C8—131no—
290C2×C22⋊C8—131no—
291C2×#97—131no—
292C2×#97—131no—
293#384—131no—
294#384—131no—
295#383—261no—
296#382—131no—
297#382—131no—
298#382—131no—
299#382C2×D1311yescharacteristic
300#381—261no—
301#380—131no—
302#380—131no—
303#380—261no—
304#380—261no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—261no—
307C4×C4⋊C4—261no—
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C22⋊C4—261no—
310#376—261no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340C2×D1311yescharacteristic
318#340C2×D1311yescharacteristic
319C22×C13C22×C4⋊C411yescharacteristic
320C22×C13#53511yescharacteristic
321C22×C13#53611yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57511yescharacteristic
324C22×C13#57511yescharacteristic
325C22×C13#57511yescharacteristic
326C2×D13—22no—
327C2×D13—22no—
328C2×D13—22no—
329C2×D13—41no—
330C2×D13—41no—
331C2×D13—41no—
332C2×D13—41no—
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13#52011yescharacteristic
340C4×C13#52011yescharacteristic
341C4×C13#54411yescharacteristic
342C4×C13#54411yescharacteristic
343Dic13—22no—
344Dic13—22no—
345Dic13—22no—
346Dic13—81no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#117—521no—
358#117—521no—
359#117—521no—
360#117—521no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—21no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—134no—
382C2×C42—134no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42C22×D1311yescharacteristic
387#107—41no—
388#107—521no—
389#107—521no—
390#107—521no—
391#106—41no—
392#106—521no—
393#106—521no—
394#106—521no—
395C4⋊C8—134no—
396C4⋊C8C4×D1314yes—
397C22⋊C8—134no—
398C22⋊C8—134no—
399#97—134no—
400#97—134no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413C2×C13#231711yescharacteristic
414C2×C13#291111yescharacteristic
415C2×C13#291111yescharacteristic
416C2×C13#321911yescharacteristic
417C2×C13#321911yescharacteristic
418C2×C13#324011yescharacteristic
419C2×C13#324011yescharacteristic
420D13—42no—
421C24—131no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—132no—
430C22×C4—132no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4—521no—
445C22×C4D4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C22×C4C23×D1311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—132no—
453C2×C8—132no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C4×D1312yes—
459C2×C8C2×C4×D1312yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—261no—
469C4⋊C4—261no—
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—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C22⋊C4—522no—
483C22⋊C4—522no—
484C42—42no—
485C42—134no—
486C42—134no—
487C42—132no—
488C42—132no—
489C42—522no—
490C42—522no—
491C42—522no—
492C42C2×C4×D1312yes—
493C42Q8×D1312yes—
494C13#2198911yescharacteristic, complemented, Sylow
495C23—132no—
496C23—261no—
497C23—261no—
498C23—261no—
499C23—261no—
500C23—261no—
501C23—261no—
502C23C2×D4×D1311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—524no—
533C2×C4—524no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4C4⋊C4×D1312yes—
547C2×C4C4⋊C4×D1312yes—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4#8825111yescharacteristic
550C2×C4C2×Q8×D1311yescharacteristic
551C2×C4#8825411yescharacteristic
552C2×C4#8825611yescharacteristic
553C2×C4#8825711yescharacteristic
554C8—22no—
555C8—22no—
556C8—262no—
557C8—262no—
558C22—262no—
559C22—262no—
560C22—262no—
561C22—521no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22C2×C4⋊C4×D1311yescharacteristic
566C22#1171931211yescharacteristic
567C22#1171933311yescharacteristic
568C22#1171947311yescharacteristic
569C22#1171947311yescharacteristic
570C22#1171947811yescharacteristic
571C22#1171948211yescharacteristic
572C4—22no—
573C4—22no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—262no—
579C4—262no—
580C4—262no—
581C4—1041no—
582C4—1041no—
583C4—1041no—
584C4—1041no—
585C4#1171925111yescharacteristic
586C4#1171927911yescharacteristic
587C4#1171939411yescharacteristic
588C4#1171943411yescharacteristic
589C2—522no—
590C2#1311745811yescharacteristic
591C2#1312342311yescharacteristic
592C2#1312342411yescharacteristic
593C2#1312587211yescharacteristic
594C2#1312587811yescharacteristic
595C2#1312607511yescharacteristic
596C2#1312608111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1949C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1949D13
hypocenterC13#21989
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13115606C2semidirect
5. #13115604C2semidirect
6. #13115602C2semidirect
11. #13115003C2semidirect
12. #13115001C2semidirect
13. #13114968C2semidirect
14. #13114968C2semidirect
15. C13×#1949C2semidirect
45. #11718496C4semidirect
203. #1949D13semidirect
494. C13#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#117184962
#131172422
#131172322
#131156062
#131156042
#131156022
#131150382
#131150362
#131150342
#131150322
#131150032
#131150012
#131149682
C13×#19492
#2198913