Finite Group Databasebeta

← #15891492

Subgroups — #15891492

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718785C211yesmaximal, characteristic, complemented
2#13123400C211yesmaximal, characteristic, complemented
3#13123353C211yesmaximal, characteristic
4C2×#11718627C211yesmaximal, characteristic
5C2×#11718793C211yesmaximal, characteristic
6#13116200C214yesmaximal, complemented
7#13116193C214yesmaximal, complemented
8C2×#11718122C211yesmaximal, characteristic, complemented
9C2×C13×#428C211yesmaximal, characteristic, complemented
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C22×#6099C2211yescharacteristic
17C13×#428—22no—
18C13×#428C2214yes—
19C2×C13×#107—21no—
20C2×C13×#106—21no—
21C2×#88064C2212yes—
22#11718793—24no—
23C2×#88063C2212yes—
24#11718785—24no—
25C2×#88062C2214yes—
26#11718665C2212yes—
27#11718663—22no—
28#11718662C2212yes—
29#11718660—22no—
30#11718660C2214yes—
31C2×#88050C2212yes—
32#11718627—21no—
33#11718627—21no—
34#11718627—22no—
35#11718627—22no—
36C2×#88049C2212yes—
37#11718585—22no—
38#11718122C2214yes—
39C23×C4×C13—21no—
40C23×C4×C13C2311yescharacteristic
41C22×C22⋊D13—21no—
42C2×#6127—22no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127—22no—
48C2×#6127—22no—
49C2×#6127Q814yes—
50C22×D52C2311yescharacteristic
51C22×C4×D13—21no—
52C22×Dic26C2311yescharacteristic
53C2×C13×M16—21no—
54C2×C13×M16—22no—
55C2×C13×M16D414yes—
56C2×C13×M16C2312yes—
57C22×C8×C13—21no—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117D412yes—
61C13×#117C2312yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×#6099—22no—
73C2×#6099—22no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—22no—
77C2×#6099—22no—
78C2×#6099—22no—
79C2×#6099—22no—
80C2×#6099D412yes—
81C2×#6099D412yes—
82C2×#6099C2312yes—
83C2×#6099C2312yes—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055C2312yes—
87C13×#107—24no—
88C13×#106—24no—
89#88064—24no—
90#88063—24no—
91#88062—28no—
92#88050—22no—
93#88050—22no—
94#88050—24no—
95#88049—22no—
96#88049—22no—
97#88049—24no—
98C4⋊#1055—28no—
99#23604—131nomaximal, Sylow
100C24×C13#4111yescharacteristic
101C23×D13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—82no—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×Q812yes—
114C22×C4×C13#4112yes—
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4112yes—
117C22×C4×C13C2411yescharacteristic
118C2×C22⋊D13—24no—
119C2×C22⋊D13—41no—
120C2×C22⋊D13—41no—
121C2×C22⋊D13—42no—
122C22×Dic13—21no—
123#6127—24no—
124#6127—24no—
125#6127—24no—
126#6127—24no—
127#6127—42no—
128#6127—42no—
129#6127—42no—
130#6127—42no—
131C2×D52—21no—
132C2×D52—21no—
133C2×D52—21no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52C2×Q812yes—
137C2×C4×D13—24no—
138C2×C4×D13—41no—
139C2×C4×D13—41no—
140C2×C4×D13—42no—
141C2×Dic26—21no—
142C2×Dic26—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26C2×Q812yes—
147C13×M16—24no—
148C13×M16—22no—
149C13×M16C2×D414yes—
150C2×C8×C13—24no—
151C2×C8×C13—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C22⋊C4—22no—
161C13×C22⋊C4—22no—
162C42×C13—22no—
163C42×C13—22no—
164#6099—24no—
165#6099—24no—
166#6099—22no—
167#6099—22no—
168#6099—22no—
169#6099—22no—
170#6099—42no—
171#6099—42no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—42no—
177C2×#1055—42no—
178C2×#1055C2×D414yes—
179C2×#430—131no—
180C2×#428D1311yescharacteristic, complemented
181#2905—131no—
182#2896—131no—
183C2×#417—131no—
184C2×#413—131no—
185#2064—134no—
186#2063—134no—
187C2×#343—131no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13#12111yescharacteristic
191C23×C13#12111yescharacteristic
192C23×C13C22⋊Q812yes—
193C23×C13#12612yes—
194C23×C13C2×#4111yescharacteristic
195C22×D13—22no—
196C22×D13—41no—
197C22×D13—41no—
198C22×D13—81no—
199C22×D13—81no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—42no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13—82no—
206C2×C4×C13—82no—
207C2×C4×C13—82no—
208C2×C4×C13#12112yes—
209C2×C4×C13#12112yes—
210C2×C4×C13#12112yes—
211C2×C4×C13#12112yes—
212C2×C4×C13#12111yescharacteristic
213C2×C4×C13#12111yescharacteristic
214C2×C4×C13C22⋊Q812yes—
215C2×C4×C13C22⋊Q812yes—
216C2×C4×C13C22⋊Q812yes—
217C2×C4×C13C22⋊Q812yes—
218C2×C4×C13C22⋊Q812yes—
219C2×C4×C13#12612yes—
220C2×C4×C13C22×D411yescharacteristic
221C2×C4×C13C22×D411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×Q811yescharacteristic
224C2×C4×C13C2×#4111yescharacteristic
225C2×C4×C13C2×#4111yescharacteristic
226C22⋊D13—44no—
227C22⋊D13—44no—
228C2×Dic13—22no—
229C2×Dic13—41no—
230C2×Dic13—41no—
231D52—22no—
232D52—22no—
233D52—41no—
234D52—41no—
235C4×D13—44no—
236C4×D13—44no—
237Dic26—22no—
238Dic26—22no—
239Dic26—41no—
240Dic26—41no—
241C8×C13—24no—
242#1055—24no—
243#1055—42no—
244#1055—42no—
245C22×#41—131no—
246C22×M16—131no—
247C22×M16—131no—
248C22×M16—131no—
249C22×M16C2×D1311yescharacteristic
250C2×#117C2×D1311yescharacteristic
251C22×C4⋊C4C2×D1311yescharacteristic
252#430—264no—
253C2×#108—134no—
254#428—22no—
255#428C2×D1314yes—
256C2×#107—21no—
257C2×#106—21no—
258#424—134no—
259#424—262no—
260#423—262no—
261#419—132no—
262#418—132no—
263#417—262no—
264#417—262no—
265#417—261no—
266#417—261no—
267#416—262no—
268C2×#103—132no—
269C2×#102—132no—
270#413—264no—
271C2×#101—132no—
272C2×#100—132no—
273#343—134no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13#39612yes—
283C22×C13#39612yes—
284C22×C13C2×#12111yescharacteristic
285C22×C13C2×C22⋊Q811yescharacteristic
286C22×C13C2×#12611yescharacteristic
287C2×D13—42no—
288C2×D13—82no—
289C2×D13—81no—
290C2×D13—81no—
291C2×D13—82no—
292C4×C13—42no—
293C4×C13—42no—
294C4×C13—82no—
295C4×C13#39612yes—
296C4×C13#39612yes—
297C4×C13C2×#12111yescharacteristic
298C4×C13C2×#12111yescharacteristic
299C4×C13C2×C22⋊Q811yescharacteristic
300C4×C13C2×C22⋊Q811yescharacteristic
301Dic13—42no—
302C2×#41—134no—
303C2×#41—262no—
304C2×#41—262no—
305C2×#41—261no—
306C2×#41—261no—
307C2×#41—262no—
308C2×#41—261no—
309C2×#41—261no—
310C22×Q8—131no—
311C22×D4—131no—
312C22×D4—261no—
313C23×C4—21no—
314C23×C4—261no—
315C23×C4C22×D1311yescharacteristic
316C2×M16—22no—
317C2×M16—21no—
318C2×M16—132no—
319C2×M16—132no—
320C2×M16—132no—
321C2×M16—132no—
322C2×M16—262no—
323C2×M16—262no—
324C2×M16—261no—
325C2×M16—261no—
326C2×M16—262no—
327C2×M16—262no—
328C2×M16—262no—
329C2×M16—262no—
330C2×M16D5214yes—
331C2×M16C22×D1312yes—
332C22×C8—21no—
333C22×C8—132no—
334C22×C8—261no—
335C22×C8—261no—
336#117—21no—
337#117—21no—
338#117C22⋊D1312yes—
339#117C22×D1312yes—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C22⋊D1311yescharacteristic
346C2×C4⋊C4C22⋊D1311yescharacteristic
347C2×C4⋊C4C22×D1312yes—
348C2×C22⋊C4—21no—
349C2×C42—21no—
350#108—268no—
351#107—24no—
352#106—24no—
353C4⋊C8—268no—
354#103—264no—
355#103—262no—
356#103—262no—
357#102—264no—
358#102—262no—
359#102—262no—
360#101—264no—
361#100—264no—
362C2×C13—21no—
363C2×C13—21no—
364C2×C13—22no—
365C2×C13—22no—
366C2×C13C2×#39611yescharacteristic
367C2×C13#306811yescharacteristic
368C2×C13#306911yescharacteristic
369D13—82no—
370C24—261no—
371C24#612911yescharacteristic
372#41—264no—
373#41—264no—
374#41—264no—
375#41—264no—
376#41—522no—
377#41—522no—
378#41—522no—
379#41—522no—
380C2×Q8—132no—
381C2×Q8—261no—
382C2×Q8—261no—
383C2×Q8—261no—
384C2×Q8—261no—
385C2×Q8—261no—
386C2×D4—132no—
387C2×D4—264no—
388C2×D4—261no—
389C2×D4—261no—
390C2×D4—261no—
391C2×D4—261no—
392C2×D4—261no—
393C2×D4—522no—
394C2×D4—521no—
395C2×D4—521no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—82no—
402C22×C4—261no—
403C22×C4—264no—
404C22×C4—522no—
405C22×C4—521no—
406C22×C4—521no—
407C22×C4C2×D5212yes—
408C22×C4#612712yes—
409C22×C4D4×D1311yescharacteristic
410C22×C4D4×D1311yescharacteristic
411C22×C4#612911yescharacteristic
412C22×C4Q8×D1312yes—
413C22×C4#613112yes—
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C23×D1311yescharacteristic
417M16—24no—
418M16—22no—
419M16—264no—
420M16—264no—
421M16—262no—
422M16—262no—
423M16—262no—
424M16—262no—
425M16—522no—
426M16—522no—
427M16C2×D5214yes—
428C2×C8—24no—
429C2×C8—22no—
430C2×C8—134no—
431C2×C8—262no—
432C2×C8—262no—
433C2×C8—262no—
434C2×C8—262no—
435C2×C8—522no—
436C2×C8—522no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4C2×C22⋊D1312yes—
444C4⋊C4C2×C22⋊D1312yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C13#2360411yescharacteristic, complemented, Sylow
450C23—41no—
451C23—41no—
452C23—262no—
453C23—521no—
454C23—521no—
455C23—1041no—
456C23—1041no—
457C23#8815112yes—
458C23#8815212yes—
459C23#8819311yescharacteristic
460C23#8819311yescharacteristic
461C23C2×#612911yescharacteristic
462Q8—262no—
463Q8—262no—
464Q8—521no—
465Q8—521no—
466D4—262no—
467D4—262no—
468D4—524no—
469D4—524no—
470D4—521no—
471D4—521no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—262no—
481C2×C4—521no—
482C2×C4—521no—
483C2×C4—524no—
484C2×C4—524no—
485C2×C4#8814912yes—
486C2×C4#8814912yes—
487C2×C4#8815012yes—
488C2×C4#8815012yes—
489C2×C4#8815112yes—
490C2×C4#8815212yes—
491C2×C4#8818412yes—
492C2×C4#8818412yes—
493C2×C4#8819311yescharacteristic
494C2×C4#8819311yescharacteristic
495C2×C4#8820012yes—
496C2×C4#8820012yes—
497C2×C4C22×D5211yescharacteristic
498C2×C4C2×#612711yescharacteristic
499C2×C4C2×D4×D1311yescharacteristic
500C2×C4C2×Q8×D1311yescharacteristic
501C2×C4C2×#613111yescharacteristic
502C2×C4C22×C22⋊D1311yescharacteristic
503C8—24no—
504C8—264no—
505C8—522no—
506C8—522no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—522no—
516C22—1042no—
517C22—1042no—
518C22—1041no—
519C22—1041no—
520C22#1171865512yes—
521C22#1171865512yes—
522C22C2×#8815111yescharacteristic
523C22C2×#8815211yescharacteristic
524C22C2×#8819311yescharacteristic
525C4—42no—
526C4—42no—
527C4—82no—
528C4—522no—
529C4#1171865512yes—
530C4#1171865512yes—
531C4C2×#8814911yescharacteristic
532C4C2×#8815011yescharacteristic
533C4C2×#8818411yescharacteristic
534C4C2×#8820011yescharacteristic
535C2—21no—
536C2—21no—
537C2—22no—
538C2—22no—
539C2—1042no—
540C2C2×#1171865511yescharacteristic
541C2#1312456111yescharacteristic
542C2#1312457011yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#428C2
socleC22×C13C2×#121
prime radicalC22×#6127C22
hypercenterC2×#428D13
hypocenterC13#23604
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#11718785C2semidirect
2. #13123400C2semidirect
6. #13116200C2semidirect
7. #13116193C2semidirect
8. C2×#11718122C2semidirect
9. C2×C13×#428C2semidirect
180. C2×#428D13semidirect
449. C13#23604semidirect

Maximal subgroups

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

subgroupindex
C2×#117187852
#131234002
#131233532
C2×#117186272
C2×#117187932
#131162002
#131161932
C2×#117181222
C2×C13×#4282
#2360413