Finite Group Databasebeta

← #15898979

Subgroups — #15898979

Order 3328.

1378 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C2×#11718420C212yesmaximal, complemented
3#121×Dic13C211yesmaximal, characteristic
4#13116163C212yesmaximal, complemented
5#13115970C212yesmaximal, complemented
6#13115786C212yesmaximal, complemented
7#13115154C211yesmaximal, characteristic
8#13115026C211yesmaximal, characteristic, complemented
9#13115024C211yesmaximal, characteristic, complemented
10#13114814C211yesmaximal, characteristic, complemented
11C13×#1874C211yesmaximal, characteristic
12C23×Dic26—21no—
13C2×C13×#121C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×D4×Dic13—21no—
16C2×D4×Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101—21no—
19C22×C4×Dic13C2211yescharacteristic
20C2×#88142—21no—
21C2×#88142—21no—
22C2×#88142—28no—
23C2×#88142C2212yes—
24C2×#88142C2212yes—
25C2×C13×#102C2212yes—
26C2×C13×C22⋊C8C2211yescharacteristic
27#11718882C2211yescharacteristic
28#11718881—21no—
29C2×#88072C2212yes—
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88058C2212yes—
33C2×#88054C2212yes—
34#11718646C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C2×#88047C2212yes—
37#11718612—21no—
38C22⋊C4×Dic13—21no—
39#11718420—28no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718142C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×D4×C13—21no—
46C22×D4×C13C2311yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13C2311yescharacteristic
49C23×Dic13—21no—
50C23×Dic13—21no—
51C23×Dic13D411yescharacteristic
52C23×Dic13D411yescharacteristic
53C22×Dic26—28no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26—44no—
57C22×Dic26—44no—
58C22×C8×C13C2312yes—
59C13×#121—22no—
60C13×#121Q814yescomplemented
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4C2312yes—
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C22⋊C4—21no—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—21no—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70D4×Dic13—24no—
71D4×Dic13—44no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—24no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2312yes—
78C2×#6101—28no—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D411yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C22×#1055C2312yes—
88#88142—28no—
89#88142—28no—
90#88142—24no—
91#88142—24no—
92#88142—24no—
93#88142D418yescomplemented
94C13×#102—24no—
95C13×C22⋊C8—22no—
96#88072—24no—
97#88071—21no—
98#88071—21no—
99#88071—21no—
100C22⋊#1055—22no—
101#88058—24no—
102#88054—24no—
103#88047—24no—
104#24298—131nomaximal, Sylow
105C24×C13—21no—
106C24×C13C2×D411yescharacteristic
107C2×D4×C13—24no—
108C2×D4×C13—22no—
109C2×D4×C13—21no—
110C2×D4×C13—22no—
111C2×D4×C13—42no—
112C2×D4×C13—42no—
113C2×D4×C13C2×Q812yescomplemented
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—42no—
120C22×C4×C13—42no—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×Q812yes—
123C22×C4×C13#4112yes—
124C22×C4×C13C2411yescharacteristic
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—24no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—42no—
135C22×Dic13—42no—
136C22×Dic13—42no—
137C22×Dic13—42no—
138C22×Dic13—42no—
139C22×Dic13D814yes—
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C2×Dic26—28no—
145C2×Dic26—28no—
146C2×Dic26—44no—
147C2×Dic26—432no—
148C2×Dic26—44no—
149C2×Dic26—44no—
150C2×Dic26—44no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4C2×D414yes—
158C13×C4⋊C4C2×Q812yescomplemented
159C13×C22⋊C4—24no—
160C22⋊Dic13—42no—
161C22⋊Dic13—42no—
162C22⋊Dic13—42no—
163C22⋊Dic13—42no—
164C4⋊Dic13—24no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168C4⋊Dic13—42no—
169C4⋊Dic13C2×D414yes—
170#6101—28no—
171#6101—28no—
172C4×Dic13—22no—
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—42no—
176C4×Dic13C2×D414yes—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C22×C4⋊Q8—131no—
181C2×#474—132no—
182C4×#121—131no—
183#2057—132no—
184#2023—132no—
185#1988—132no—
186#1874—131no—
187#1874D1311yescharacteristic
188#1852—131no—
189#1852—131no—
190#1797—131no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—22no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13C22⋊Q812yes—
203C23×C13C2×D812yes—
204C23×C13#13712yes—
205C23×C13C22×D411yescharacteristic
206D4×C13—24no—
207D4×C13—48no—
208D4×C13—42no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—48no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13C22⋊Q812yes—
221C2×C4×C13C22×D412yes—
222C2×C4×C13C22×Q811yescharacteristic
223C2×C4×C13C2×#4111yescharacteristic
224C2×C4×C132−1+412yes—
225C2×Dic13—28no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—21no—
229C2×Dic13—21no—
230C2×Dic13—21no—
231C2×Dic13—21no—
232C2×Dic13—28no—
233C2×Dic13—24no—
234C2×Dic13—48no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—84no—
244C2×Dic13#12012yes—
245C2×Dic13#12012yes—
246C2×Dic13C2×D812yes—
247C2×Dic13C2×D812yes—
248C2×Dic13AGL(1,ℤ/8)12yes—
249C2×Dic13#13712yes—
250Dic26—416no—
251Dic26—416no—
252C8×C13—42no—
253#1055—42no—
254C23×Q8—261no—
255C2×C4⋊Q8—132no—
256C2×C4⋊Q8—132no—
257C2×C4⋊Q8—261no—
258C2×C4⋊Q8—261no—
259C2×C4⋊Q8—268no—
260C2×#121C2×D1311yescharacteristic
261C2×C4×D4—131no—
262C2×C4×D4—261no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—261no—
265C22×C4⋊C4C2×D1311yescharacteristic
266C22×C42—131no—
267#474—268no—
268C2×#107—132no—
269C2×#107—132no—
270C2×C4⋊C8—132no—
271C2×#102—132no—
272C2×#102C2×D1312yes—
273C2×C22⋊C8—131no—
274C2×C22⋊C8C2×D1311yescharacteristic
275#390—131no—
276#389—131no—
277#388—261no—
278#386—261no—
279#380—131no—
280C4×C4⋊C4—131no—
281C4×C22⋊C4—261no—
282#340—132no—
283#340—132no—
284#340—132no—
285#340C2×D1312yes—
286#336—132no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—81no—
297C22×C13—81no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13#47414yescomplemented
301C22×C13C2×#12011yescharacteristic
302C22×C13C2×C22⋊Q811yescharacteristic
303C22×C13#53611yescharacteristic
304C22×C13C22×D811yescharacteristic
305C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C13C2×#13711yescharacteristic
307C22×C13C2×#13711yescharacteristic
308C4×C13—22no—
309C4×C13—44no—
310C4×C13—42no—
311C4×C13#54812yes—
312C4×C13D4×Q812yes—
313Dic13—22no—
314Dic13—22no—
315Dic13—22no—
316Dic13—44no—
317Dic13—81no—
318Dic13—81no—
319Dic13#44714yes—
320C22×Q8—262no—
321C22×Q8—262no—
322C22×Q8—268no—
323C22×Q8—524no—
324C22×Q8—524no—
325C22×D4—21no—
326C22×D4C22×D1311yescharacteristic
327C23×C4—21no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4—261no—
331C23×C4—261no—
332C23×C4C22×D1311yescharacteristic
333C22×C8—132no—
334C22×C8C22×D1312yes—
335C4⋊Q8—138no—
336C4⋊Q8—264no—
337C4⋊Q8—264no—
338C4⋊Q8—268no—
339C4⋊Q8—268no—
340C4⋊Q8—264no—
341#121—22no—
342#121Dic2614yescomplemented
343C4×D4—264no—
344C4×D4—524no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—131no—
349C2×C4⋊C4—131no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—262no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—268no—
354C2×C4⋊C4—261no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4C22×D1311yescharacteristic
357C2×C4⋊C4C22×D1312yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—261no—
360C2×C22⋊C4—261no—
361C2×C22⋊C4—261no—
362C2×C22⋊C4—261no—
363C2×C42—131no—
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—264no—
368C2×C42—261no—
369#107—264no—
370#107—264no—
371C4⋊C8—264no—
372#102—24no—
373#102—264no—
374C22⋊C8—22no—
375C22⋊C8—262no—
376#95—261no—
377#95—261no—
378#95—261no—
379C2×C13—24no—
380C2×C13—82no—
381C2×C13#240911yescharacteristic
382C2×C13C2×#44711yescharacteristic
383C2×C13#300411yescharacteristic
384C2×C13C2×#47411yescharacteristic
385C2×C13#307911yescharacteristic
386C2×C13#322611yescharacteristic
387C2×C13#323911yescharacteristic
388C24—21no—
389C24D4×D1311yescharacteristic
390C2×Q8—268no—
391C2×Q8—268no—
392C2×Q8—524no—
393C2×Q8—524no—
394C2×Q8—524no—
395C2×Q8—5232no—
396C2×Q8—524no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4C2×Dic2612yescomplemented
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—131no—
412C22×C4—134no—
413C22×C4—131no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—264no—
422C22×C4—262no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—522no—
426C22×C4—522no—
427C22×C4—522no—
428C22×C4—522no—
429C22×C4—522no—
430C22×C4C2×Dic2612yes—
431C22×C4D4×D1311yescharacteristic
432C22×C4#612912yes—
433C22×C4C23×D1311yescharacteristic
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—134no—
444C4⋊C4—268no—
445C4⋊C4—268no—
446C4⋊C4—264no—
447C4⋊C4—262no—
448C4⋊C4—262no—
449C4⋊C4—262no—
450C4⋊C4—522no—
451C4⋊C4C2×Dic2612yescomplemented
452C4⋊C4D4×D1314yes—
453C22⋊C4—24no—
454C22⋊C4—522no—
455C22⋊C4—522no—
456C22⋊C4—522no—
457C22⋊C4—522no—
458C42—134no—
459C42—262no—
460C42—262no—
461C42—262no—
462C42—522no—
463C13#2429811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#8813212yes—
476C23D8×D1312yes—
477C23#8816912yes—
478C23C2×D4×D1311yescharacteristic
479Q8—5216no—
480Q8—5216no—
481D4—24no—
482D4—48no—
483D4—42no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—48no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—132no—
496C2×C4—132no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—268no—
502C2×C4—268no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—264no—
510C2×C4—528no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—1044no—
520C2×C4#8813212yes—
521C2×C4C22×Dic2611yescharacteristic
522C2×C4C2×D4×D1312yes—
523C2×C4C2×#612911yescharacteristic
524C2×C4#8825712yes—
525C8—42no—
526C8—522no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22#1171842014yescomplemented
541C22C2×#8813211yescharacteristic
542C22D13×#12011yescharacteristic
543C22#1171935311yescharacteristic
544C22C2×D8×D1311yescharacteristic
545C22C2×#8816911yescharacteristic
546C22D13×AGL(1,ℤ/8)11yescharacteristic
547C22D13×#13711yescharacteristic
548C4—22no—
549C4—44no—
550C4—42no—
551C4—134no—
552C4—262no—
553C4—262no—
554C4—262no—
555C4—524no—
556C4—1041no—
557C4—1041no—
558C4D4×Dic2612yes—
559C4#1171930312yes—
560C2—24no—
561C2—82no—
562C2#1311819811yescharacteristic
563C2D13×#44711yescharacteristic
564C2#1312406711yescharacteristic
565C2C2×#1171842011yescharacteristic
566C2#1312464711yescharacteristic
567C2#1312595511yescharacteristic
568C2#1312606411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1874C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#1874D13
hypocenterC13#24298
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
2. C2×#11718420C2semidirect
4. #13116163C2semidirect
5. #13115970C2semidirect
6. #13115786C2semidirect
8. #13115026C2semidirect
9. #13115024C2semidirect
10. #13114814C2semidirect
60. C13×#121Q8semidirect
93. #88142D4semidirect
113. C2×D4×C13C2×Q8semidirect
158. C13×C4⋊C4C2×Q8semidirect
300. C22×C13#474semidirect
342. #121Dic26semidirect
403. C2×D4C2×Dic26semidirect
451. C4⋊C4C2×Dic26semidirect
463. C13#24298semidirect
540. C22#11718420semidirect

Maximal subgroups

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

subgroupindex
C22×#881422
C2×#117184202
#121×Dic132
#131161632
#131159702
#131157862
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