Finite Group Databasebeta

← #15890416

Subgroups — #15890416

Order 3328.

1558 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718625C211yesmaximal, characteristic, complemented
2C2×#11718886C211yesmaximal, characteristic, complemented
3C2×#11718886C211yesmaximal, characteristic, complemented
4C2×#11718868C211yesmaximal, characteristic
5#13117219C211yesmaximal, characteristic
6#13116036C214yesmaximal, complemented
7#13116029C214yesmaximal, complemented
8#13114555C211yesmaximal, characteristic, complemented
9C22×C13×C22⋊Q8C211yesmaximal, characteristic
10C23×Q8×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C2×C13×C22⋊Q8—24no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×C22⋊Q8—24no—
15C2×C13×C22⋊Q8C2214yes—
16C22×C13×C4⋊C4—21no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4—21no—
19C2×#88180C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23#11718908—21no—
24#11718886—24no—
25#11718886—24no—
26C2×#88075C2212yescomplemented
27C2×#88075C2214yescomplemented
28C2×#88075C2212yescomplemented
29#11718873C2212yes—
30#11718873C2212yes—
31#11718872—21no—
32C4×C22⋊Dic13—22no—
33#11718868—24no—
34C2×C22⋊#1055C2214yes—
35#11718625—24no—
36C2×#88048C2212yescomplemented
37C2×#88047C2212yescomplemented
38#11718121C2214yescomplemented
39C25×C13D411yescharacteristic
40C22×Q8×C13—22no—
41C22×Q8×C13—21no—
42C22×Q8×C13—22no—
43C22×Q8×C13—22no—
44C22×Q8×C13—22no—
45C22×Q8×C13—22no—
46C22×Q8×C13D414yes—
47C22×Q8×C13C2312yes—
48C23×C4×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D412yes—
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C13×C22⋊Q8—216no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—28no—
63C2×C13×C4⋊C4—28no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4D414yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C22⋊C4—28no—
70C2×C13×C22⋊C4—24no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—22no—
74C2×C22⋊Dic13—22no—
75#88180—22no—
76#88180—22no—
77#88180—22no—
78#88180—22no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2312yes—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×#6099—22no—
85C2×#6099—22no—
86C2×#6099—22no—
87C2×#6099—22no—
88C2×#6099—22no—
89C2×#6099D414yes—
90C22×#1055C2312yes—
91C22×#1055C2312yes—
92#88075—24no—
93#88075—24no—
94#88075—28no—
95#88071—22no—
96#88071—22no—
97C22⋊#1055—28no—
98#88048—24no—
99#88047—24no—
100#23481—131nomaximal, Sylow
101C24×C13—22no—
102C24×C13—24no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—42no—
106C24×C13C2×D412yes—
107C24×C13C2×D411yescharacteristic
108C2×Q8×C13—24no—
109C2×Q8×C13—22no—
110C2×Q8×C13—28no—
111C2×Q8×C13—28no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13—42no—
117C2×Q8×C13—44no—
118C2×Q8×C13—42no—
119C2×Q8×C13—44no—
120C2×Q8×C13C2×D414yes—
121C22×C4×C13—24no—
122C22×C4×C13—24no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—24no—
129C22×C4×C13—24no—
130C22×C4×C13—24no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—44no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13—44no—
141C22×C4×C13—44no—
142C22×C4×C13—44no—
143C22×C4×C13—44no—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13#4112yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C13×C4⋊C4—216no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4C2×D414yes—
160C13×C22⋊C4—216no—
161C22⋊Dic13—44no—
162C22⋊Dic13—42no—
163C22⋊Dic13—42no—
164C22⋊Dic13—44no—
165C4⋊Dic13—22no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—22no—
171C4×Dic13—42no—
172C4×Dic13—42no—
173#6099—28no—
174#6099—44no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055C2×D414yes—
181C22×C22⋊Q8D1311yescharacteristic
182C2×#428—131no—
183C2×#419—131no—
184C2×#419—131no—
185C2×#407—131no—
186#2280—131no—
187#2036—134no—
188#2035—134no—
189#1736—131no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—28no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—48no—
200C23×C13—48no—
201C23×C13—44no—
202C23×C13—44no—
203C23×C13#12012yes—
204C23×C13#12112yes—
205C23×C13#12312yes—
206C23×C13#13714yes—
207C23×C13C22×D411yescharacteristic
208Q8×C13—24no—
209Q8×C13—24no—
210Q8×C13—42no—
211Q8×C13—42no—
212Q8×C13—48no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—48no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—44no—
222C2×C4×C13—44no—
223C2×C4×C13—48no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—48no—
229C2×C4×C13#12012yes—
230C2×C4×C13#12114yes—
231C2×C4×C13#12114yes—
232C2×C4×C13#12112yes—
233C2×C4×C13#12314yes—
234C2×C4×C13#12312yes—
235C2×C4×C13#12414yes—
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249#1055—24no—
250#1055—42no—
251C23×Q8C2×D1311yescharacteristic
252C24×C4C2×D1311yescharacteristic
253C22×M16—131no—
254C22×M16—131no—
255C2×C22⋊Q8—24no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—24no—
258C2×C22⋊Q8C2×D1314yes—
259C2×#117—131no—
260C2×#117—131no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4C2×D1311yescharacteristic
263C22×C22⋊C4—21no—
264#428—264no—
265C2×#107—132no—
266C2×#106—132no—
267#419—264no—
268#419—264no—
269C2×#103—132no—
270C2×#103—134no—
271C2×#103—132no—
272#407—264no—
273C2×C22⋊C8—134no—
274#381—261no—
275#380—132no—
276#380—132no—
277#379—261no—
278C4×C22⋊C4—262no—
279#340—134no—
280C22×C13—24no—
281C22×C13—22no—
282C22×C13—22no—
283C22×C13—24no—
284C22×C13—24no—
285C22×C13—24no—
286C22×C13—24no—
287C22×C13—416no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13#39414yes—
293C22×C13C2×#12011yescharacteristic
294C22×C13C2×#12111yescharacteristic
295C22×C13C2×#12311yescharacteristic
296C22×C13C2×#13712yes—
297C22×C13#57512yes—
298C4×C13—42no—
299C4×C13—44no—
300C4×C13—44no—
301C4×C13#39414yes—
302C4×C13C2×#12111yescharacteristic
303C4×C13C2×#12111yescharacteristic
304C4×C13C2×#12311yescharacteristic
305C4×C13C2×#12411yescharacteristic
306Dic13—81no—
307Dic13—81no—
308Dic13—82no—
309C25C22⋊D1311yescharacteristic
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8C22⋊D1314yes—
317C22×Q8C22×D1312yes—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4C22⋊D1311yescharacteristic
327C23×C4C22⋊D1312yes—
328C23×C4C22×D1312yes—
329C23×C4C22×D1311yescharacteristic
330C2×M16—134no—
331C2×M16—262no—
332C2×M16—262no—
333C2×M16—262no—
334C2×M16—262no—
335C2×M16—262no—
336C22×C8—132no—
337C22×C8—132no—
338C22⋊Q8—216no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341#117—262no—
342#117—262no—
343#117—262no—
344#117—262no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—132no—
350C2×C4⋊C4—131no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4C22⋊D1314yes—
353C2×C4⋊C4C22×D1312yes—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—261no—
357C2×C22⋊C4—261no—
358C2×C22⋊C4—262no—
359C2×C22⋊C4—262no—
360C2×C42—261no—
361C2×C42—261no—
362#107—264no—
363#106—264no—
364#103—268no—
365#103—264no—
366#103—264no—
367C22⋊C8—268no—
368#95—262no—
369#95—262no—
370C2×C13—24no—
371C2×C13—44no—
372C2×C13C2×#39411yescharacteristic
373C2×C13#300411yescharacteristic
374C2×C13#300511yescharacteristic
375C2×C13#305612yes—
376C2×C13#309512yes—
377C24—24no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—42no—
382C24C2×C22⋊D1312yes—
383C24C2×C22⋊D1311yescharacteristic
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—42no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—42no—
396C2×Q8C2×C22⋊D1314yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—44no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—262no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4D4×D1312yes—
424C22×C4#612912yes—
425C22×C4#612912yes—
426C22×C4#612912yes—
427C22×C4C2×C22⋊D1312yes—
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1312yes—
430C22×C4C2×C22⋊D1312yes—
431C22×C4C23×D1311yescharacteristic
432M16—268no—
433M16—524no—
434C2×C8—134no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C4⋊C4—216no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—262no—
444C4⋊C4—262no—
445C4⋊C4—261no—
446C4⋊C4—261no—
447C4⋊C4—261no—
448C4⋊C4—261no—
449C4⋊C4C2×C22⋊D1314yes—
450C22⋊C4—216no—
451C22⋊C4—524no—
452C22⋊C4—522no—
453C22⋊C4—524no—
454C22⋊C4—522no—
455C42—522no—
456C42—522no—
457C13#2348111yescharacteristic, complemented, Sylow
458C23—22no—
459C23—22no—
460C23—28no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—48no—
468C23—48no—
469C23—44no—
470C23—44no—
471C23#8818912yes—
472C23#8819312yes—
473C23#8819614yes—
474C23#8820712yes—
475C23C22×C22⋊D1311yescharacteristic
476Q8—24no—
477Q8—24no—
478Q8—42no—
479Q8—42no—
480Q8—48no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—48no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—48no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—521no—
503C2×C4—521no—
504C2×C4#8818914yes—
505C2×C4#8818912yes—
506C2×C4#8819014yes—
507C2×C4#8819214yes—
508C2×C4#8819314yes—
509C2×C4#8819312yes—
510C2×C4#8820712yes—
511C2×C4C2×D4×D1311yescharacteristic
512C2×C4C2×#612911yescharacteristic
513C2×C4C2×#612911yescharacteristic
514C2×C4C2×#612911yescharacteristic
515C2×C4C22×C22⋊D1311yescharacteristic
516C2×C4C22×C22⋊D1311yescharacteristic
517C8—264no—
518C8—522no—
519C22—24no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—24no—
525C22—24no—
526C22—416no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22#1171888314yes—
532C22C2×#8818911yescharacteristic
533C22C2×#8819311yescharacteristic
534C22C2×#8819612yes—
535C22#1171952712yes—
536C22C2×#8820711yescharacteristic
537C4—42no—
538C4—44no—
539C4—44no—
540C4—1042no—
541C4—1041no—
542C4—1041no—
543C4#1171888314yes—
544C4C2×#8818911yescharacteristic
545C4C2×#8819011yescharacteristic
546C4C2×#8819211yescharacteristic
547C4C2×#8819311yescharacteristic
548C2—24no—
549C2—44no—
550C2C2×#1171888311yescharacteristic
551C2#1312407011yescharacteristic
552C2#1312407811yescharacteristic
553C2#1312446212yes—
554C2#1312478012yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊Q8C2
socleC23×C13C22×D4
prime radicalC25×C13D4
hypercenterC22×C22⋊Q8D13
hypocenterC13#23481
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718625C2semidirect
2. C2×#11718886C2semidirect
3. C2×#11718886C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13114555C2semidirect
26. C2×#88075C22semidirect
27. C2×#88075C22semidirect
28. C2×#88075C22semidirect
36. C2×#88048C22semidirect
37. C2×#88047C22semidirect
38. #11718121C22semidirect
457. C13#23481semidirect

Maximal subgroups

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

subgroupindex
C2×#117186252
C2×#117188862
C2×#117188682
#131172192
#131160362
#131160292
#131145552
C22×C13×C22⋊Q82
#2348113