Finite Group Databasebeta

← #15920670

Subgroups — #15920670

Order 3328.

758 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
1#13118560C211yesmaximal, characteristic
2#13117703C211yesmaximal, characteristic
3#13116405C211yesmaximal, characteristic, complemented
4#13116334C211yesmaximal, characteristic, complemented
5#13116329C211yesmaximal, characteristic, complemented
6#13116175C211yesmaximal, characteristic, complemented
7#13115791C211yesmaximal, characteristic, complemented
8#13115606C211yesmaximal, characteristic, complemented
9#13115429C211yesmaximal, characteristic, complemented
10#13115415C211yesmaximal, characteristic, complemented
11#13115026C211yesmaximal, characteristic
12#13114923C211yesmaximal, characteristic
13#13114861C211yesmaximal, characteristic
14C2×#11718143C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88131—21no—
20C2×#88124C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C4×C13×C22⋊C4C2211yescharacteristic
25#11718873C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31#11718607—21no—
32#11718604—21no—
33#11718603—21no—
34#11718597C2211yescharacteristic
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37#11718589C2211yescharacteristic
38#11718589C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718321—21no—
42#11718318—21no—
43#11718314—21no—
44#11718314—21no—
45C13×#336C2211yescharacteristic
46C13×#336C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C22×C8×C13—22no—
63C22×C8×C13—22no—
64C22×C8×C13—41no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—41no—
80C2×C4⋊Dic13Q814yes—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97#88131—44no—
98#88124—22no—
99#88124—41no—
100C13×C4⋊C8—22no—
101C13×C4⋊C8—41no—
102C13×C22⋊C8—22no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88058—22no—
116#88058—41no—
117#88057—22no—
118#88057—41no—
119#25998—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×Q812yes—
131C22×C4×C13#4112yes—
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—24no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—42no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—81no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—44no—
159C2×C8×C13#4112yes—
160C13×C22⋊C4—22no—
161C13×C22⋊C4—22no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C22⋊Dic13—42no—
167C22⋊Dic13—42no—
168C4⋊Dic13—24no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—42no—
183C4⋊Dic13C2×Q812yes—
184C4⋊Dic13C2×Q812yes—
185C4⋊Dic13#4112yes—
186#6101—42no—
187#6101—42no—
188#6101—42no—
189#6101—42no—
190#6101—81no—
191#6101—81no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194#2442—131no—
195#2344—131no—
196#2101—131no—
197#2088—131no—
198#2087—131no—
199#2059—131no—
200#1989—131no—
201#1949—131no—
202#1921—131no—
203#1919—131no—
204#1852—131no—
205#1850D1311yescharacteristic
206#1823—131no—
207#1807—131no—
208C2×#340—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C22⋊Q812yes—
214C23×C13#13512yes—
215C23×C13AGL(1,ℤ/8)12yes—
216C23×C13C22×D411yescharacteristic
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
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×C13C22⋊Q812yes—
236C2×C4×C13C22×Q811yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—48no—
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×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—84no—
268C8×C13—22no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13—41no—
272C23×C8C2×D1311yescharacteristic
273C2×#125—131no—
274C2×#117—261no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C2×#107—131no—
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×C4⋊C8C2×D1311yescharacteristic
282C2×C4⋊C8C2×D1311yescharacteristic
283C2×C22⋊C8C2×D1311yescharacteristic
284#400—261no—
285#398—261no—
286#389—131no—
287#389—131no—
288#389—131no—
289#389—131no—
290#387—261no—
291#387—261no—
292#385—261no—
293#382—131no—
294#381—261no—
295#380—131no—
296#380—131no—
297#380—261no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C22⋊C4C2×D1311yescharacteristic
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#336C2×D1311yescharacteristic
314#336C2×D1311yescharacteristic
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13#47814yes—
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13#54611yescharacteristic
324C22×C13#54711yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57811yescharacteristic
329C4×C13—22no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13#53311yescharacteristic
335C4×C13#54411yescharacteristic
336C4×C13#55111yescharacteristic
337C4×C13#55211yescharacteristic
338Dic13—42no—
339Dic13—42no—
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344Dic13—81no—
345Dic13—81no—
346C23×C4—261no—
347C23×C4—261no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—41no—
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356#125—262no—
357#125—521no—
358#117—524no—
359C2×C4⋊C4—134no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—262no—
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⋊C4—261no—
378C2×C4⋊C4—521no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4D5211yescharacteristic
382C2×C22⋊C4D5211yescharacteristic
383C2×C42—261no—
384C2×C42—261no—
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#107—262no—
388#107—521no—
389#106—262no—
390#106—521no—
391C4⋊C8—22no—
392C4⋊C8—41no—
393C22⋊C8—22no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95D5211yescharacteristic
405#95D5211yescharacteristic
406C2×C13—24no—
407C2×C13#243811yescharacteristic
408C2×C13C2×#47811yescharacteristic
409C2×C13#308211yescharacteristic
410C2×C13#330011yescharacteristic
411C2×C13#330611yescharacteristic
412C2×C13#333711yescharacteristic
413C2×C13#334311yescharacteristic
414C24C2×D5211yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—264no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—522no—
429C22×C4—522no—
430C22×C4—522no—
431C22×C4—522no—
432C22×C4—1041no—
433C22×C4C2×D5211yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4C2×D5211yescharacteristic
436C22×C4C2×D5211yescharacteristic
437C22×C4C2×D5211yescharacteristic
438C22×C4#612912yes—
439C22×C4Q8×D1312yes—
440C22×C4C23×D1311yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—44no—
453C2×C8#612912yes—
454C4⋊C4—132no—
455C4⋊C4—132no—
456C4⋊C4—132no—
457C4⋊C4—264no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—522no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C4⋊C4—522no—
475C4⋊C4—522no—
476C4⋊C4—1041no—
477C4⋊C4—1041no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—522no—
487C42—522no—
488C13#2599811yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23#8815112yes—
494C23#8815812yes—
495C23#8816212yes—
496C23C22×D5211yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—528no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
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×C4—521no—
540C2×C4—1044no—
541C2×C4#8815112yes—
542C2×C4C2×#612911yescharacteristic
543C2×C4C2×#612911yescharacteristic
544C2×C4#8825111yescharacteristic
545C2×C4C2×Q8×D1311yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—22no—
549C8—41no—
550C8—41no—
551C8—41no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22#1171850814yes—
559C22C2×#8815111yescharacteristic
560C22#1171925911yescharacteristic
561C22#1171926011yescharacteristic
562C22C2×#8815811yescharacteristic
563C22C2×#8816211yescharacteristic
564C22#1171945611yescharacteristic
565C22#1171945811yescharacteristic
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—522no—
572C4—522no—
573C4—522no—
574C4—1041no—
575C4—1041no—
576C4—1041no—
577C4—1041no—
578C4—1041no—
579C4#1171929211yescharacteristic
580C4#1171932711yescharacteristic
581C4#1171932811yescharacteristic
582C4#1171935511yescharacteristic
583C2—24no—
584C2#1311851011yescharacteristic
585C2C2×#1171850811yescharacteristic
586C2#1312467911yescharacteristic
587C2#1312672511yescharacteristic
588C2#1312679911yescharacteristic
589C2#1312721711yescharacteristic
590C2#1312727811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#25998
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13116405C2semidirect
4. #13116334C2semidirect
5. #13116329C2semidirect
6. #13116175C2semidirect
7. #13115791C2semidirect
8. #13115606C2semidirect
9. #13115429C2semidirect
10. #13115415C2semidirect
488. C13#25998semidirect

Maximal subgroups

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

subgroupindex
#131185602
#131177032
#131164052
#131163342
#131163292
#131161752
#131157912
#131156062
#131154292
#131154152
#131150262
#131149232
#131148612
C2×#117181432
C13×#18502
#2599813