Finite Group Databasebeta

← #15896885

Subgroups — #15896885

Order 3328.

1090 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719247C211yesmaximal, characteristic
2C2×#11718681C211yesmaximal, characteristic, complemented
3C2×C4×#6107C211yesmaximal, characteristic, complemented
4#13116032C212yesmaximal, complemented
5#13115844C212yesmaximal, complemented
6#13115796C211yesmaximal, characteristic, complemented
7#13115631C211yesmaximal, characteristic
8#13115149C212yesmaximal, complemented
9#13115033C212yesmaximal, complemented
10#13114838C211yesmaximal, characteristic, complemented
11C13×#2538C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2212yes—
13C2×C4×Q8×C13C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C22×#6107C2211yescharacteristic
16C2×#88190—21no—
17C2×#88180C2212yes—
18C2×#88178C2212yes—
19#11719247—24no—
20#11719247—24no—
21C2×#88141—21no—
22C2×#88133—22no—
23C2×#88123C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25C13×#396—22no—
26C13×#390—21no—
27C13×#389—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2212yes—
30C2×#88075C2211yescharacteristic
31C2×#88075C2212yes—
32C2×C22⋊#1055C2212yes—
33C2×C22⋊#1055C2212yes—
34C4×#6107—24no—
35#11718681—24no—
36C2×#88050C2211yescharacteristic
37C2×#88050C2212yes—
38C2×#88048C2212yes—
39C2×#88047C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13C2311yescharacteristic
46C22×D4×C13D411yescharacteristic
47C23×C4×C13C2312yes—
48C22×Dic26—21no—
49C22×Dic26C2311yescharacteristic
50C13×C22⋊Q8—24no—
51C13×C22⋊Q8—42no—
52C4×Q8×C13—22no—
53C4×Q8×C13—22no—
54C4×D4×C13—22no—
55C4×D4×C13—22no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C4⋊C4C2311yescharacteristic
62C2×C13×C4⋊C4C2312yes—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4D412yes—
66C2×C42×C13—21no—
67C2×C42×C13C2311yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×#6107—22no—
71C2×#6107—22no—
72C2×#6107—22no—
73#88190—28no—
74#88180—24no—
75#88180—24no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2312yes—
79#88178—24no—
80#88178—24no—
81C2×#6101—21no—
82C2×#6101—22no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—22no—
85C22×#1055C2311yescharacteristic
86C22×#1055C2312yes—
87C22×#1055C2311yescharacteristic
88#88141—28no—
89#88133—216no—
90#88123—22no—
91#88123D414yes—
92C4×Dic26—22no—
93C4×Dic26D414yes—
94C13×#95—22no—
95#88075—24no—
96#88075—22no—
97C22⋊#1055—24no—
98C22⋊#1055—42no—
99#88050—22no—
100#88050—42no—
101#88048—24no—
102#88047—22no—
103C4⋊#1055—22no—
104C4×#1055—22no—
105#24123—131nomaximal, Sylow
106C24×C13C2×D412yes—
107C2×Q8×C13—21no—
108C2×Q8×C13—21no—
109C2×Q8×C13—21no—
110C2×Q8×C13—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13#4112yes—
113C2×D4×C13—22no—
114C2×D4×C13—22no—
115C2×D4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—22no—
132C2×Dic26—21no—
133C2×Dic26—21no—
134C2×Dic26—21no—
135C2×Dic26—21no—
136C2×Dic26—24no—
137C2×Dic26—21no—
138C2×Dic26—42no—
139C2×Dic26—42no—
140C2×Dic26C2×D412yes—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—44no—
147C13×C4⋊C4—42no—
148C13×C4⋊C4—42no—
149C13×C4⋊C4—81no—
150C13×C22⋊C4—24no—
151C13×C22⋊C4—44no—
152C13×C22⋊C4—82no—
153C42×C13—42no—
154C42×C13C2×D412yes—
155C42×C13C2×D412yes—
156C22⋊Dic13—28no—
157C22⋊Dic13—28no—
158#6107—28no—
159C4⋊Dic13—24no—
160C4⋊Dic13—21no—
161C4⋊Dic13—22no—
162C4⋊Dic13C2×D412yes—
163C4⋊Dic13C2×D414yes—
164#6101—28no—
165#6101—24no—
166C4×Dic13—28no—
167C4×Dic13—24no—
168C2×#1055—21no—
169C2×#1055—21no—
170C2×#1055—21no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—21no—
174C2×#1055—22no—
175C2×#1055—21no—
176C2×#1055#4112yes—
177C2×#556—131no—
178C2×#475—131no—
179C2×C4×Q16—131no—
180#2538D1311yescharacteristic
181#2035—132no—
182#2001—132no—
183#1990—131no—
184#1954—131no—
185#1873—132no—
186#1854—132no—
187#1803—131no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13C22×D411yescharacteristic
196Q8×C13—22no—
197Q8×C13—22no—
198Q8×C13—41no—
199Q8×C13—41no—
200D4×C13—44no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—41no—
219C2×C4×C13#12012yes—
220C2×C4×C13#12012yes—
221C2×C4×C13#13512yes—
222C2×C4×C13#13712yes—
223C2×C4×C13C22×D411yescharacteristic
224C2×C4×C13C22×D411yescharacteristic
225C2×C4×C13C2×#4111yescharacteristic
226C2×C4×C13C2×#4111yescharacteristic
227C2×C4×C13H(5,𝔽2)11yescharacteristic
228C2×C4×C132−1+411yescharacteristic
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—24no—
232C2×Dic13—41no—
233C2×Dic13—41no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238Dic26—22no—
239Dic26—22no—
240Dic26—41no—
241Dic26—41no—
242Dic26—48no—
243#1055—22no—
244#1055—41no—
245#1055—42no—
246C22×Q16—131no—
247#556—264no—
248#556—264no—
249C2×C4⋊Q8—131no—
250C2×#126—262no—
251C2×#124—261no—
252C2×C22⋊Q8—132no—
253C2×C22⋊Q8C2×D1312yes—
254C2×C4×Q8—131no—
255C2×C4×Q8—261no—
256C2×C4×Q8C2×D1311yescharacteristic
257C2×C4×D4C2×D1311yescharacteristic
258C2×#117—132no—
259#475—264no—
260C4×Q16—264no—
261C2×#107—131no—
262C2×#106—132no—
263C2×C4⋊C8—131no—
264C2×#103—132no—
265C2×#103—131no—
266C2×#103—131no—
267C2×#103—132no—
268C2×C22⋊C8—132no—
269C2×C22⋊C8—132no—
270C2×C4×C8—131no—
271#396—22no—
272#390—21no—
273#389—21no—
274#384C2×D1311yescharacteristic
275#380C2×D1312yes—
276#340—132no—
277#340—132no—
278#340—132no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13C2×#12011yescharacteristic
287C22×C13#54611yescharacteristic
288C22×C13#54711yescharacteristic
289C22×C13C2×#13511yescharacteristic
290C22×C13C2×#13711yescharacteristic
291C22×C13#57711yescharacteristic
292C22×C13#57811yescharacteristic
293C4×C13—22no—
294C4×C13—42no—
295C4×C13—42no—
296C4×C13—81no—
297C4×C13—82no—
298C4×C13#45214yes—
299C4×C13#52511yescharacteristic
300C4×C13#53711yescharacteristic
301C4×C13#54811yescharacteristic
302C4×C13#55011yescharacteristic
303Dic13—42no—
304Dic13—44no—
305Dic13—42no—
306C22×Q8—131no—
307C22×Q8—261no—
308C22×Q8C22×D1311yescharacteristic
309C22×D4C22⋊D1311yescharacteristic
310C23×C4C22×D1312yes—
311C2×Q16—262no—
312C2×Q16—262no—
313C2×Q16—262no—
314C22×C8—131no—
315C22×C8—131no—
316C22×C8—132no—
317C4⋊Q8—134no—
318C4⋊Q8—262no—
319#126—2616no—
320#124—268no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—264no—
324C22⋊Q8—264no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—134no—
328C4×Q8—268no—
329C4×Q8—262no—
330C4×D4—22no—
331C4×D4—22no—
332#117—264no—
333#117—264no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—131no—
339C2×C4⋊C4—132no—
340C2×C4⋊C4—261no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—261no—
343C2×C4⋊C4C22⋊D1311yescharacteristic
344C2×C4⋊C4C22×D1311yescharacteristic
345C2×C4⋊C4C22×D1312yes—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—262no—
349C2×C22⋊C4—262no—
350C2×C22⋊C4C22⋊D1312yes—
351C2×C42—21no—
352C2×C42—262no—
353C2×C42—261no—
354C2×C42C22×D1311yescharacteristic
355#107—262no—
356#106—264no—
357C4⋊C8—262no—
358#103—262no—
359#103—262no—
360#103—264no—
361#103—522no—
362C22⋊C8—264no—
363C22⋊C8—522no—
364C4×C8—262no—
365#95—22no—
366C2×C13—82no—
367C2×C13#240711yescharacteristic
368C2×C13C2×#45211yescharacteristic
369C2×C13#301311yescharacteristic
370C2×C13#330411yescharacteristic
371C2×C13#332811yescharacteristic
372C2×C13#334211yescharacteristic
373C2×C13#335611yescharacteristic
374C24C2×C22⋊D1312yes—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—132no—
381C2×Q8—264no—
382C2×Q8—261no—
383C2×Q8—261no—
384C2×Q8—261no—
385C2×Q8—261no—
386C2×Q8—261no—
387C2×Q8—522no—
388C2×Q8—522no—
389C2×Q8#612912yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—261no—
403C22×C4—262no—
404C22×C4—261no—
405C22×C4C2×C22⋊D1312yes—
406C22×C4C2×C22⋊D1311yescharacteristic
407C22×C4C2×C22⋊D1311yescharacteristic
408C22×C4C23×D1311yescharacteristic
409Q16—268no—
410C2×C8—132no—
411C2×C8—261no—
412C2×C8—261no—
413C2×C8—261no—
414C2×C8—262no—
415C2×C8—261no—
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—261no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—44no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—81no—
428C4⋊C4—134no—
429C4⋊C4—132no—
430C4⋊C4—268no—
431C4⋊C4—264no—
432C4⋊C4—264no—
433C4⋊C4—261no—
434C4⋊C4—262no—
435C22⋊C4—24no—
436C22⋊C4—44no—
437C22⋊C4—82no—
438C22⋊C4—268no—
439C22⋊C4—268no—
440C42—42no—
441C42—268no—
442C42—264no—
443C42D4×D1312yes—
444C42D4×D1312yes—
445C13#2412311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23C22×C22⋊D1311yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—41no—
457Q8—41no—
458Q8—262no—
459Q8—262no—
460Q8—528no—
461Q8—521no—
462Q8—521no—
463D4—44no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—262no—
483C2×C4—264no—
484C2×C4—262no—
485C2×C4—521no—
486C2×C4—522no—
487C2×C4—522no—
488C2×C4—521no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4#8819112yes—
492C2×C4#8819112yes—
493C2×C4#8819612yes—
494C2×C4#8820412yes—
495C2×C4C2×D4×D1311yescharacteristic
496C2×C4C2×D4×D1311yescharacteristic
497C2×C4C2×#612911yescharacteristic
498C2×C4#8825111yescharacteristic
499C2×C4#41×D1311yescharacteristic
500C2×C4#8825711yescharacteristic
501C8—262no—
502C8—522no—
503C8—521no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×#8819111yescharacteristic
512C22#1171951111yescharacteristic
513C22C2×#8819611yescharacteristic
514C22C2×#8820411yescharacteristic
515C22#1171952911yescharacteristic
516C22#1171954111yescharacteristic
517C22#1171954311yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—81no—
522C4—82no—
523C4—522no—
524C4—524no—
525C4—522no—
526C4#1171870814yes—
527C4#1171930311yescharacteristic
528C4#1171930411yescharacteristic
529C4#1171931111yescharacteristic
530C4#1171931311yescharacteristic
531C2—82no—
532C2#1311817711yescharacteristic
533C2C2×#1171870811yescharacteristic
534C2#1312414811yescharacteristic
535C2#1312677511yescharacteristic
536C2#1312711911yescharacteristic
537C2#1312726211yescharacteristic
538C2#1312745111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2538C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2538D13
hypocenterC13#24123
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#11718681C2semidirect
3. C2×C4×#6107C2semidirect
4. #13116032C2semidirect
5. #13115844C2semidirect
6. #13115796C2semidirect
8. #13115149C2semidirect
9. #13115033C2semidirect
10. #13114838C2semidirect
445. C13#24123semidirect

Maximal subgroups

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

subgroupindex
C2×#117192472
C2×#117186812
C2×C4×#61072
#131160322
#131158442
#131157962
#131156312
#131151492
#131150332
#131148382
C13×#25382
#2412313