Finite Group Databasebeta

← #15896763

Subgroups — #15896763

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718704C211yesmaximal, characteristic, complemented
2C2×#11718656C211yesmaximal, characteristic, complemented
3#13119153C211yesmaximal, characteristic
4#13116171C212yesmaximal, complemented
5#13116036C212yesmaximal, complemented
6#13115270C211yesmaximal, characteristic, complemented
7#13115134C211yesmaximal, characteristic
8#13115104C212yesmaximal, complemented
9#13115029C212yesmaximal, complemented
10#13114931C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic
12C13×#552—24no—
13C13×#552—24no—
14C2×C13×#126—21no—
15C2×C13×#125—21no—
16C2×C13×#125C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C13×#117—21no—
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6099C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29#11718881—21no—
30#11718873C2211yescharacteristic
31#11718873C2212yes—
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yes—
34#11718704—24no—
35#11718656—24no—
36#11718647—21no—
37C2×#88048C2212yes—
38C2×#88048C2212yes—
39C2×#88047C2212yes—
40#11718610—21no—
41#11718607—21no—
42#11718589C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13—21no—
53C13×#126—28no—
54C13×#125—28no—
55C13×#125—22no—
56C13×#125—22no—
57C13×#123—28no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8D414yes—
62C4×Q8×C13—22no—
63C4×Q8×C13—22no—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C13×#117—28no—
67C13×#117—22no—
68C13×#117D414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2312yes—
95C2×C4⋊Dic13C2312yes—
96C2×#6101—22no—
97C2×#6099—22no—
98C2×#6099—24no—
99C22×#1055C2312yes—
100C22×#1055C2312yes—
101#88075—24no—
102#88075—24no—
103#88071—22no—
104#88071—22no—
105#88071—21no—
106C22⋊#1055—22no—
107C22⋊#1055—24no—
108#88048—24no—
109#88048—24no—
110#88047—24no—
111#24111—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C24×C13C2×D411yescharacteristic
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13C2×D412yes—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—41no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—24no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—42no—
144C22×Dic13—82no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4C2×D412yes—
156C13×C4⋊C4C2×D412yes—
157C13×C4⋊C4C2×D412yes—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—22no—
162C13×C22⋊C4—22no—
163C42×C13—24no—
164C42×C13—24no—
165C42×C13—21no—
166C42×C13—21no—
167C22⋊Dic13—42no—
168C22⋊Dic13—82no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—42no—
174#6101—82no—
175#6099—28no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055#4114yes—
182C2×#552D1311yescharacteristic
183C2×#483—131no—
184C2×#428—131no—
185#2487—131no—
186#2059—132no—
187#2036—132no—
188#1894—131no—
189#1870—131no—
190#1865—132no—
191#1853—132no—
192#1825—131no—
193C23×C13—21no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13#12012yes—
202C23×C13#13712yes—
203C23×C13C22×D411yescharacteristic
204Q8×C13—24no—
205Q8×C13—41no—
206Q8×C13—41no—
207D4×C13—44no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—24no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—48no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13#12012yes—
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4112yes—
237C2×C4×C132−1+412yes—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—84no—
245#1055—24no—
246#1055—42no—
247C22×M16—131no—
248#552—24no—
249#552—24no—
250C2×#126—21no—
251C2×#125—21no—
252C2×#125C2×D1311yescharacteristic
253C2×#123—21no—
254C2×C22⋊Q8C2×D1311yescharacteristic
255C2×C22⋊Q8C2×D1311yescharacteristic
256C2×C4×Q8C2×D1311yescharacteristic
257C2×C4×D4C2×D1311yescharacteristic
258C2×#117—21no—
259C2×#117C2×D1311yescharacteristic
260C22×C4⋊C4—131no—
261C22×C4⋊C4C2×D1311yescharacteristic
262#483—264no—
263#428—264no—
264C2×#107—132no—
265C2×#106—132no—
266C2×#106—132no—
267C2×#103—132no—
268C2×#103—132no—
269C2×C22⋊C8—131no—
270C2×C22⋊C8—132no—
271#400—261no—
272#399—261no—
273#389—132no—
274#386—261no—
275#385—261no—
276#380—131no—
277#380—132no—
278#340—132no—
279#340—132no—
280#340—132no—
281#336—132no—
282C22×C13—24no—
283C22×C13—22no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13C2×#12011yescharacteristic
293C22×C13#54712yes—
294C22×C13C2×#13711yescharacteristic
295C22×C13#57511yescharacteristic
296C22×C13#57712yes—
297C4×C13—22no—
298C4×C13—41no—
299C4×C13—42no—
300C4×C13—41no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—41no—
304C4×C13—42no—
305C4×C13#52511yescharacteristic
306C4×C13#53611yescharacteristic
307C4×C13#54712yes—
308Dic13—82no—
309Dic13—82no—
310C22×Q8C22×D1311yescharacteristic
311C22×D4C22⋊D1311yescharacteristic
312C23×C4—21no—
313C23×C4—261no—
314C23×C4C22×D1311yescharacteristic
315C23×C4C22×D1311yescharacteristic
316C2×M16—264no—
317C2×M16—262no—
318C22×C8—132no—
319C22×C8—132no—
320#126—28no—
321#125—28no—
322#125—22no—
323#125—22no—
324#123—28no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8C22⋊D1314yes—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×D4—22no—
332C4×D4—22no—
333#117—28no—
334#117—22no—
335#117C22⋊D1314yes—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4—132no—
346C2×C4⋊C4—262no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4—262no—
350C2×C4⋊C4C22⋊D1311yescharacteristic
351C2×C4⋊C4C22×D1311yescharacteristic
352C2×C4⋊C4C22×D1311yescharacteristic
353C2×C4⋊C4C22×D1311yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—261no—
358C2×C22⋊C4—262no—
359C2×C22⋊C4C22⋊D1311yescharacteristic
360C2×C22⋊C4C22⋊D1311yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C22×D1311yescharacteristic
364#107—264no—
365#106—264no—
366#106—264no—
367#103—264no—
368#103—264no—
369C22⋊C8—264no—
370C22⋊C8—262no—
371#95—262no—
372#95—261no—
373#95—262no—
374C2×C13—42no—
375C2×C13—42no—
376C2×C13#240611yescharacteristic
377C2×C13#300711yescharacteristic
378C2×C13#301011yescharacteristic
379C2×C13#334412yes—
380C2×C13#335112yes—
381C24C2×C22⋊D1311yescharacteristic
382C24C2×C22⋊D1311yescharacteristic
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8C2×C22⋊D1312yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—262no—
404C22×C4—262no—
405C22×C4—522no—
406C22×C4—1042no—
407C22×C4C2×C22⋊D1311yescharacteristic
408C22×C4C2×C22⋊D1311yescharacteristic
409C22×C4C2×C22⋊D1311yescharacteristic
410C22×C4C2×C22⋊D1311yescharacteristic
411C22×C4C2×C22⋊D1312yes—
412C22×C4C2×C22⋊D1312yes—
413C22×C4C23×D1311yescharacteristic
414M16—268no—
415C2×C8—134no—
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—262no—
419C2×C8—262no—
420C2×C8—262no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—262no—
432C4⋊C4—262no—
433C4⋊C4—262no—
434C4⋊C4—262no—
435C4⋊C4—522no—
436C4⋊C4—1042no—
437C4⋊C4C2×C22⋊D1312yes—
438C4⋊C4C2×C22⋊D1312yes—
439C4⋊C4C2×C22⋊D1312yes—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—522no—
446C22⋊C4—1042no—
447C42—24no—
448C42—24no—
449C42—21no—
450C42—21no—
451C13#2411111yescharacteristic, complemented, Sylow
452C23—21no—
453C23—21no—
454C23—21no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—21no—
460C23#8820512yes—
461C23#8820712yes—
462C23C22×C22⋊D1311yescharacteristic
463Q8—24no—
464Q8—41no—
465Q8—41no—
466D4—44no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—48no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—522no—
493C2×C4—522no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—1044no—
499C2×C4#8820712yes—
500C2×C4#41×D1312yes—
501C2×C4#8825712yes—
502C2×C4C22×C22⋊D1311yescharacteristic
503C2×C4C22×C22⋊D1311yescharacteristic
504C8—264no—
505C8—522no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—24no—
510C22—22no—
511C22—41no—
512C22—42no—
513C22—41no—
514C22—42no—
515C22—42no—
516C22#1171952711yescharacteristic
517C22C2×#8820511yescharacteristic
518C22#1171952912yes—
519C22#1171954212yes—
520C22C2×#8820711yescharacteristic
521C4—22no—
522C4—41no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—1042no—
530C4—1042no—
531C4#1171952912yes—
532C4#1171953011yescharacteristic
533C4#1171953311yescharacteristic
534C2—42no—
535C2—42no—
536C2#1311816711yescharacteristic
537C2#1312409611yescharacteristic
538C2#1312412211yescharacteristic
539C2#1312729112yes—
540C2#1312739612yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#24111
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718704C2semidirect
2. C2×#11718656C2semidirect
4. #13116171C2semidirect
5. #13116036C2semidirect
6. #13115270C2semidirect
8. #13115104C2semidirect
9. #13115029C2semidirect
10. #13114931C2semidirect
451. C13#24111semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186562
#131191532
#131161712
#131160362
#131152702
#131151342
#131151042
#131150292
#131149312
C2×C13×#5522
#2411113