Finite Group Databasebeta

← #15920531

Subgroups — #15920531

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic
2#13116404C211yesmaximal, characteristic, complemented
3#13116337C211yesmaximal, characteristic, complemented
4#13116332C211yesmaximal, characteristic, complemented
5#13116164C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115604C211yesmaximal, characteristic, complemented
8#13115428C211yesmaximal, characteristic, complemented
9#13115407C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114931C211yesmaximal, characteristic
13#13114863C211yesmaximal, characteristic
14#13114552C211yesmaximal, characteristic
15C13×#2347C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#388—21no—
23C13×#388—21no—
24C13×#383—21no—
25C13×#380C2211yescharacteristic
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88048C2211yescharacteristic
33C2×#88047C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36#11718609—21no—
37#11718608—21no—
38#11718597C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718316—21no—
44#11718307—21no—
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26—21no—
61C13×#117—22no—
62C13×#117Q814yescomplemented
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80#88180—22no—
81#88180—41no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C22×#1055—22no—
91C22×#1055—22no—
92C22×#1055—41no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88123—22no—
98#88123—41no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111C22⋊#1055—22no—
112#88048—41no—
113#88047—22no—
114#88047—22no—
115#88047—41no—
116C4⋊#1055—22no—
117C4⋊#1055—41no—
118#25989—131nomaximal, Sylow
119C24×C13C2×D411yescharacteristic
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×Q812yes—
134C22×C4×C13#4112yes—
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C2×Dic26—42no—
141C2×Dic26—42no—
142C2×Dic26—81no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—42no—
150C13×C4⋊C4—42no—
151C13×C4⋊C4C2×Q812yes—
152C13×C4⋊C4C2×Q812yes—
153C13×C22⋊C4—24no—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—81no—
157C42×C13—24no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—81no—
163C42×C13—81no—
164C22⋊Dic13—42no—
165C22⋊Dic13—81no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—42no—
174C4⋊Dic13#4112yes—
175#6101—42no—
176#6101—81no—
177C4×Dic13—42no—
178C2×#1055—21no—
179C2×#1055—21no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—44no—
190C2×#1055#4112yes—
191#2439—131no—
192#2347D1311yescharacteristic
193#2101—131no—
194#2088—131no—
195#2087—131no—
196#2057—131no—
197#1988—131no—
198#1949—131no—
199#1921—131no—
200#1918—131no—
201#1854—131no—
202#1850—131no—
203#1825—131no—
204#1808—131no—
205#1735—131no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13C22⋊Q812yes—
213C23×C13C22×D411yescharacteristic
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C22⋊Q812yes—
244C2×C4×C13#13512yes—
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C132−1+411yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263Dic26—84no—
264#1055—22no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268C23×C8—131no—
269C2×C4⋊Q8—131no—
270C2×#117—131no—
271C2×#117C2×D1311yescharacteristic
272C2×#107—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C22⋊C8—131no—
279#396—261no—
280#393—261no—
281#391—261no—
282#389—131no—
283#389—131no—
284#389C2×D1311yescharacteristic
285#389C2×D1311yescharacteristic
286#388—21no—
287#388—21no—
288#387—261no—
289#383—21no—
290#382—131no—
291#380—131no—
292#380C2×D1311yescharacteristic
293C4×C4⋊C4—21no—
294C4×C4⋊C4C2×D1311yescharacteristic
295C4×C4⋊C4C2×D1311yescharacteristic
296C4×C22⋊C4C2×D1311yescharacteristic
297#340—131no—
298#340—131no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#336—131no—
310#336—131no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13C2×C22⋊Q811yescharacteristic
319C22×C13#54611yescharacteristic
320C22×C13#54711yescharacteristic
321C22×C13C2×#13511yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57611yescharacteristic
324C22×C13#57811yescharacteristic
325C4×C13—22no—
326C4×C13—22no—
327C4×C13—42no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13#53311yescharacteristic
335C4×C13#54411yescharacteristic
336C4×C13#55111yescharacteristic
337C4×C13#55211yescharacteristic
338Dic13—42no—
339Dic13—81no—
340Dic13—81no—
341Dic13—81no—
342C22×Q8—261no—
343C23×C4C22×D1311yescharacteristic
344C22×C8—131no—
345C22×C8—131no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—262no—
349C22×C8—262no—
350C22×C8—521no—
351C4⋊Q8—262no—
352C4⋊Q8—521no—
353#117—22no—
354#117—262no—
355#117—521no—
356#117Dic2614yescomplemented
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4C22⋊D1311yescharacteristic
375C2×C22⋊C4C22⋊D1311yescharacteristic
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382#107—262no—
383#107—262no—
384#107—521no—
385#106—521no—
386C4⋊C8—262no—
387C4⋊C8—521no—
388C22⋊C8—262no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95C22⋊D1311yescharacteristic
400#95C22⋊D1311yescharacteristic
401C2×C13—42no—
402C2×C13#243811yescharacteristic
403C2×C13#307611yescharacteristic
404C2×C13#308311yescharacteristic
405C2×C13#329711yescharacteristic
406C2×C13#331311yescharacteristic
407C2×C13#334211yescharacteristic
408C2×C13#334711yescharacteristic
409C24C2×C22⋊D1311yescharacteristic
410C2×Q8—522no—
411C2×Q8—522no—
412C2×Q8—1041no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4C2×Dic2612yes—
426C22×C4#612712yes—
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C23×D1311yescharacteristic
433C2×C8—132no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—524no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—132no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—522no—
463C4⋊C4—522no—
464C4⋊C4—1041no—
465C4⋊C4C2×Dic2612yes—
466C4⋊C4C2×Dic2612yes—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—81no—
471C22⋊C4—522no—
472C22⋊C4—1041no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—81no—
479C42—81no—
480C42—522no—
481C13#2598911yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#8817812yes—
489C23C22×C22⋊D1311yescharacteristic
490Q8—1044no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—262no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4#8817812yes—
533C2×C4#8820412yes—
534C2×C4C22×Dic2611yescharacteristic
535C2×C4C2×#612711yescharacteristic
536C2×C4#41×D1311yescharacteristic
537C2×C4#41×D1311yescharacteristic
538C2×C4#8825611yescharacteristic
539C2×C4#8825711yescharacteristic
540C8—262no—
541C8—521no—
542C8—521no—
543C8—521no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#8817811yescharacteristic
552C22C2×#8820411yescharacteristic
553C22#1171952711yescharacteristic
554C22#1171952911yescharacteristic
555C22#1171953411yescharacteristic
556C22#1171954011yescharacteristic
557C22#1171954311yescharacteristic
558C4—22no—
559C4—22no—
560C4—42no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—522no—
568C4—1041no—
569C4—1041no—
570C4—1041no—
571C4#1171922211yescharacteristic
572C4#1171922411yescharacteristic
573C4#1171923211yescharacteristic
574C4#1171923611yescharacteristic
575C2—42no—
576C2#1311850611yescharacteristic
577C2#1312462411yescharacteristic
578C2#1312468711yescharacteristic
579C2#1312668011yescharacteristic
580C2#1312689611yescharacteristic
581C2#1312726211yescharacteristic
582C2#1312733011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2347C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2347D13
hypocenterC13#25989
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
3. #13116337C2semidirect
4. #13116332C2semidirect
5. #13116164C2semidirect
6. #13115788C2semidirect
7. #13115604C2semidirect
8. #13115428C2semidirect
9. #13115407C2semidirect
62. C13×#117Q8semidirect
356. #117Dic26semidirect
481. C13#25989semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131164042
#131163372
#131163322
#131161642
#131157882
#131156042
#131154282
#131154072
#131150332
#131150162
#131149312
#131148632
#131145522
C13×#23472
#2598913