Finite Group Databasebeta

← #15919424

Subgroups — #15919424

Order 3328.

1292 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718743C211yesmaximal, characteristic, complemented
2C2×#11718670C211yesmaximal, characteristic, complemented
3#13120002C211yesmaximal, characteristic, complemented
4#13116036C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115760C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13114776C212yesmaximal, complemented
9#13114776C212yesmaximal, complemented
10#13114661C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41C2212yes—
13C13×#547—24no—
14C13×#547—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22C2×#88124C2211yescharacteristic
23C2×#88075C2212yes—
24C2×#88075C2212yes—
25C2×#88075C2212yes—
26C2×#88075C2212yes—
27#11718883—21no—
28C2×#88072C2212yes—
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718873C2212yes—
32#11718873C2212yes—
33C2×C22⋊#1055C2212yes—
34C2×C22⋊#1055C2212yes—
35#11718743—24no—
36#11718670—24no—
37#11718643—21no—
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718606—22no—
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45C2×C13×#41—24no—
46C2×C13×#41—24no—
47C2×C13×#41—24no—
48C2×C13×#41—24no—
49C2×C13×#41—42no—
50C2×C13×#41—42no—
51C22×Q8×C13C2312yes—
52C22×D4×C13—22no—
53C22×D4×C13D411yescharacteristic
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13—22no—
57C23×C4×C13C2312yes—
58C13×C4⋊Q8—22no—
59C13×C4⋊Q8D414yes—
60C13×#123—216no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—24no—
63C13×#121—28no—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13D414yes—
68C2×C13×C4⋊C4—28no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D412yes—
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—22no—
79C2×C22⋊Dic13—22no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2312yes—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C22×#1055C2312yes—
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89#88124—22no—
90#88124—22no—
91#88075—24no—
92#88075—24no—
93#88075—42no—
94#88075—42no—
95#88072—22no—
96#88072—22no—
97#88072—24no—
98#88071—21no—
99#88071—22no—
100#88071—22no—
101C22⋊#1055—42no—
102C22⋊#1055—42no—
103#88048—22no—
104#88047—22no—
105C4⋊#1055—22no—
106#88043—22no—
107#25892—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13C2×D412yes—
110C13×#41—48no—
111C13×#41—48no—
112C13×#41—48no—
113C13×#41—48no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13C2×D414yes—
120C2×D4×C13—28no—
121C2×D4×C13—22no—
122C2×D4×C13—21no—
123C2×D4×C13—22no—
124C2×D4×C13—42no—
125C2×D4×C13—44no—
126C2×D4×C13—44no—
127C2×D4×C13C2×D412yes—
128C2×D4×C13#4114yes—
129C22×C4×C13—28no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13—44no—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C13×C4⋊C4—28no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4C2×D412yes—
155C13×C22⋊C4—28no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C42×C13C2×D412yes—
159C42×C13C2×D412yes—
160C22⋊Dic13—44no—
161C22⋊Dic13—82no—
162C4⋊Dic13—21no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168#6101—42no—
169#6101—42no—
170C4×Dic13—81no—
171C2×#1055—21no—
172C2×#1055—21no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#547D1311yescharacteristic
179C2×#491—131no—
180C2×#478—131no—
181#2562—131no—
182#2036—132no—
183#2035—132no—
184#1981—131no—
185#1955—131no—
186#1788—132no—
187#1788—132no—
188#1762—131no—
189C23×C13—22no—
190C23×C13—24no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—42no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13C22×D411yescharacteristic
202Q8×C13—24no—
203Q8×C13—24no—
204Q8×C13—42no—
205Q8×C13—42no—
206D4×C13—22no—
207D4×C13—24no—
208D4×C13—44no—
209D4×C13—416no—
210D4×C13#12414yes—
211C2×C4×C13—22no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—48no—
220C2×C4×C13—416no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13#12012yes—
229C2×C4×C13#12012yes—
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C22×D411yescharacteristic
232C2×C4×C13C2×#4112yes—
233C2×C4×C13H(5,𝔽2)12yes—
234C2×Dic13—41no—
235C2×Dic13—41no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242#1055—41no—
243#1055—41no—
244#1055—42no—
245C22×#41C2×D1312yes—
246#547—24no—
247#547—24no—
248C2×C4⋊Q8C2×D1311yescharacteristic
249C2×#125—131no—
250C2×#123—22no—
251C2×C22⋊Q8C2×D1312yes—
252C2×#121—21no—
253C2×C4×D4C2×D1311yescharacteristic
254C2×C4×D4C2×D1311yescharacteristic
255C22×C4⋊C4—21no—
256#491—264no—
257#478—264no—
258C2×#107—131no—
259C2×#106—131no—
260C2×C4⋊C8—131no—
261C2×#103—132no—
262C2×#103—132no—
263C2×#103—132no—
264C2×#103—132no—
265C2×#102—131no—
266C2×#102—131no—
267C2×#102—132no—
268C2×C22⋊C8—132no—
269C2×C22⋊C8—132no—
270C2×#97—131no—
271#400—261no—
272#394—261no—
273#388—262no—
274#380—132no—
275#380—132no—
276C4×C4⋊C4—131no—
277#340—132no—
278C22×C13—24no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—44no—
282C22×C13—44no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13C2×#12011yescharacteristic
291C22×C13#54612yes—
292C22×C13#57512yes—
293C22×C13#57711yescharacteristic
294C22×C13#57811yescharacteristic
295C4×C13—22no—
296C4×C13—22no—
297C4×C13—42no—
298C4×C13—44no—
299C4×C13—42no—
300C4×C13C2×#12411yescharacteristic
301C4×C13#53511yescharacteristic
302C4×C13#54612yes—
303Dic13—81no—
304Dic13—81no—
305Dic13—82no—
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—24no—
309C2×#41—24no—
310C2×#41—42no—
311C2×#41—42no—
312C22×Q8C22×D1312yes—
313C22×D4—22no—
314C22×D4C22⋊D1311yescharacteristic
315C22×D4C22×D1311yescharacteristic
316C23×C4—21no—
317C23×C4—22no—
318C23×C4C22×D1312yes—
319C22×C8—132no—
320C22×C8—131no—
321C22×C8—131no—
322C4⋊Q8—22no—
323C4⋊Q8C22⋊D1314yes—
324#125—262no—
325#125—262no—
326#123—216no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329#121—28no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4C22⋊D1314yes—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—131no—
339C2×C4⋊C4—131no—
340C2×C4⋊C4—132no—
341C2×C4⋊C4—261no—
342C2×C4⋊C4—261no—
343C2×C4⋊C4C22⋊D1311yescharacteristic
344C2×C4⋊C4C22×D1311yescharacteristic
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—262no—
348C2×C22⋊C4—262no—
349C2×C22⋊C4C22⋊D1312yes—
350C2×C42—261no—
351C2×C42C22×D1311yescharacteristic
352#107—262no—
353#106—262no—
354C4⋊C8—262no—
355#103—264no—
356#103—264no—
357#103—522no—
358#103—522no—
359#102—264no—
360#102—262no—
361#102—262no—
362C22⋊C8—522no—
363C22⋊C8—522no—
364#97—262no—
365#95—261no—
366#95—262no—
367#95—262no—
368C2×C13—44no—
369C2×C13—82no—
370C2×C13#243511yescharacteristic
371C2×C13#300511yescharacteristic
372C2×C13#301311yescharacteristic
373C2×C13#330712yes—
374C2×C13#331512yes—
375C24—21no—
376C24C2×C22⋊D1312yes—
377#41—48no—
378#41—48no—
379#41—48no—
380#41—48no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8C2×C22⋊D1314yes—
387C2×D4—28no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4#612914yes—
395C2×D4C2×C22⋊D1312yes—
396C22×C4—28no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—262no—
410C22×C4—261no—
411C22×C4—261no—
412C22×C4C2×C22⋊D1312yes—
413C22×C4C2×C22⋊D1311yescharacteristic
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C23×D1311yescharacteristic
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—262no—
419C2×C8—262no—
420C2×C8—262no—
421C2×C8—261no—
422C2×C8—261no—
423C4⋊C4—28no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—262no—
429C4⋊C4—262no—
430C4⋊C4—261no—
431C4⋊C4—261no—
432C4⋊C4—261no—
433C4⋊C4—261no—
434C4⋊C4—522no—
435C4⋊C4—522no—
436C4⋊C4C2×C22⋊D1312yes—
437C22⋊C4—28no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—524no—
441C22⋊C4—1042no—
442C42—1041no—
443C42C2×C22⋊D1312yes—
444C42C2×C22⋊D1312yes—
445C13#2589211yescharacteristic, complemented, Sylow
446C23—24no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23C22×C22⋊D1311yescharacteristic
459Q8—24no—
460Q8—24no—
461Q8—42no—
462Q8—42no—
463D4—22no—
464D4—24no—
465D4—44no—
466D4—416no—
467D4#8819014yes—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—48no—
477C2×C4—416no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—522no—
486C2×C4—522no—
487C2×C4—522no—
488C2×C4—522no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—521no—
492C2×C4—521no—
493C2×C4#8820712yes—
494C2×C4#8820712yes—
495C2×C4C2×#612912yes—
496C2×C4#8825112yes—
497C2×C4C22×C22⋊D1311yescharacteristic
498C2×C4C22×C22⋊D1311yescharacteristic
499C8—521no—
500C8—521no—
501C8—522no—
502C22—24no—
503C22—44no—
504C22—42no—
505C22—44no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22#1171951112yes—
515C22#1171952712yes—
516C22#1171954211yescharacteristic
517C22#1171954311yescharacteristic
518C22C2×#8820711yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—1041no—
525C4—1042no—
526C4—1041no—
527C4C2×#8819011yescharacteristic
528C4#1171951011yescharacteristic
529C4#1171951112yes—
530C2—44no—
531C2—82no—
532C2#1311848311yescharacteristic
533C2#1312407811yescharacteristic
534C2#1312415111yescharacteristic
535C2#1312681212yes—
536C2#1312693212yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#25892
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718743C2semidirect
2. C2×#11718670C2semidirect
3. #13120002C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115760C2semidirect
7. #13115635C2semidirect
8. #13114776C2semidirect
9. #13114776C2semidirect
10. #13114661C2semidirect
445. C13#25892semidirect

Maximal subgroups

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

subgroupindex
C2×#117187432
C2×#117186702
#131200022
#131160362
#131160292
#131157602
#131156352
#131147762
#131146612
C2×C13×#5472
#2589213