Finite Group Databasebeta

← #16806705

Subgroups — #16806705

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130937C211yesmaximal, characteristic, complemented
2#13130936C211yesmaximal, characteristic, complemented
3#13130935C211yesmaximal, characteristic, complemented
4#13130912C211yesmaximal, characteristic
5#13130912C211yesmaximal, characteristic
6#13130908C211yesmaximal, characteristic
7#13130895C211yesmaximal, characteristic, complemented
8#13130894C211yesmaximal, characteristic, complemented
9#13130890C211yesmaximal, characteristic, complemented
10#13130784C211yesmaximal, characteristic
11#13130782C211yesmaximal, characteristic
12#13130782C211yesmaximal, characteristic
13#13130770C211yesmaximal, characteristic, complemented
14#13130765C211yesmaximal, characteristic, complemented
15#13118139C211yesmaximal, characteristic
16C22×#6118C2211yescharacteristic
17C2×#88112C2211yescharacteristic
18C2×#88112C2211yescharacteristic
19C2×#88112C2211yescharacteristic
20C2×#88112C2211yescharacteristic
21C2×#88111C2211yescharacteristic
22C2×#88111C2211yescharacteristic
23C2×#88111C2211yescharacteristic
24C2×#88110C2211yescharacteristic
25C2×#88110C2211yescharacteristic
26C2×C4⋊#1057C2211yescharacteristic
27C2×C4⋊#1057C2211yescharacteristic
28C2×C4⋊#1057C2211yescharacteristic
29C2×C4⋊#1057C2211yescharacteristic
30C2×C4⋊#1057C2211yescharacteristic
31C2×C4×#1057C2211yescharacteristic
32C13×#401C411yescharacteristic
33#11718337C411yescharacteristic
34#11718336C411yescharacteristic
35#11718336C411yescharacteristic
36#11718336C411yescharacteristic
37#11718327C2211yescharacteristic
38#11718327C2211yescharacteristic
39#11718327C2211yescharacteristic
40#11718319C411yescharacteristic
41#11718319C411yescharacteristic
42#11718319C411yescharacteristic
43#11718310C2211yescharacteristic
44#11718310C2211yescharacteristic
45#11718310C2211yescharacteristic
46#11718309C2211yescharacteristic
47#11718290C2211yescharacteristic
48#11718290C2211yescharacteristic
49#11718290C2211yescharacteristic
50#11718290C2211yescharacteristic
51#11718290C2211yescharacteristic
52#11718290C2211yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×#1057C2311yescharacteristic
61C22×#1057C2311yescharacteristic
62C22×#1057C2311yescharacteristic
63C22×#1057C2311yescharacteristic
64C22×#1057C2311yescharacteristic
65C22×#1057C2311yescharacteristic
66C22×#1057C2311yescharacteristic
67C22×#1057C2311yescharacteristic
68C2×#6118—41no—
69C2×#6118—41no—
70C2×#6118—41no—
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89#88112—41no—
90#88112—41no—
91#88112—41no—
92#88112—41no—
93#88111—41no—
94#88111—41no—
95#88111—41no—
96#88110—41no—
97#88110—41no—
98C4⋊#1057—41no—
99C4⋊#1057—41no—
100C4⋊#1057—41no—
101C4⋊#1057—41no—
102C4⋊#1057—41no—
103C4×#1057—41no—
104C13×#95C2×C411yescharacteristic
105C13×#95C2×C411yescharacteristic
106C13×#95C2×C411yescharacteristic
107C13×#95C2×C411yescharacteristic
108C13×#95C2×C411yescharacteristic
109C13×#95C2×C411yescharacteristic
110C13×#95C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#23382—131nomaximal, Sylow
121C23×D13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C2411yescharacteristic
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×#1057—21no—
143C2×#1057—21no—
144C2×#1057—21no—
145C2×#1057—21no—
146C2×#1057—21no—
147C2×#1057—21no—
148C2×#1057—21no—
149C2×#1057—21no—
150C2×#1057—21no—
151C2×#1057—21no—
152C2×#1057—21no—
153C2×#1057—21no—
154C2×#1057—21no—
155C2×#1057—21no—
156C2×#1057—21no—
157C2×#1057—21no—
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166#6118—44no—
167#6103—22no—
168#6103—41no—
169#6103—41no—
170#6103—41no—
171#6103—41no—
172#6103—41no—
173#6101—22no—
174#6101—22no—
175#6101—41no—
176#6101—41no—
177#6101—41no—
178#6101—41no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191#2401—131no—
192#1940—131no—
193#1940—131no—
194#1939—131no—
195#1924—131no—
196#1924—131no—
197#1923—131no—
198#1917—131no—
199#1917—131no—
200#1916—131no—
201#1851—131no—
202#1851—131no—
203#1851—131no—
204#1843—131no—
205#1840—131no—
206C23×C13C23×C411yescharacteristic
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
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—21no—
234C2×C4×C13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13#13112yes—
253C2×Dic13H(5,𝔽2)11yescharacteristic
254C2×Dic13H(5,𝔽2)11yescharacteristic
255C2×Dic13H(5,𝔽2)11yescharacteristic
256C2×Dic132−1+411yescharacteristic
257C2×Dic132−1+411yescharacteristic
258C2×Dic132−1+411yescharacteristic
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263#1057—41no—
264#1057—41no—
265#1057—41no—
266#1057—41no—
267#1057—41no—
268#1057—41no—
269#1057—41no—
270#1057—41no—
271C22×M16—131no—
272C2×C4⋊C8—131no—
273C2×C4⋊C8—131no—
274C2×C4⋊C8—131no—
275C2×C4⋊C8—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8—131no—
281C2×C22⋊C8—131no—
282C2×C22⋊C8—131no—
283C2×C22⋊C8—131no—
284C2×#97—131no—
285C2×#97—131no—
286C2×C4×C8—131no—
287#401#26111yescharacteristic
288#400—131no—
289#400—131no—
290#400—131no—
291#397—131no—
292#397—131no—
293#397—131no—
294#396—131no—
295C4×C4⋊C4—131no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C22⋊C4—131no—
299C4×C22⋊C4—131no—
300C4×C22⋊C4—131no—
301#376—131no—
302#336—131no—
303#336—131no—
304#336—131no—
305#336—131no—
306#336—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313#336—131no—
314C22×C13#52011yescharacteristic
315C22×C13#52011yescharacteristic
316C22×C13#52011yescharacteristic
317C22×C13C2×#13111yescharacteristic
318C22×C13#56811yescharacteristic
319C22×C13#56811yescharacteristic
320C22×C13#56811yescharacteristic
321C2×D13—41no—
322C2×D13—41no—
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335Dic13—22no—
336Dic13—41no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13#56011yescharacteristic
342Dic13#56311yescharacteristic
343Dic13#56311yescharacteristic
344Dic13#56311yescharacteristic
345C23×C4—131no—
346C2×M16—521no—
347C2×M16—521no—
348C2×M16—521no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C22⋊C4—131no—
364C2×C22⋊C4—131no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C4⋊C8—521no—
376C4⋊C8—521no—
377C4⋊C8—521no—
378C4⋊C8—521no—
379C4⋊C8—521no—
380C4⋊C8—521no—
381C4⋊C8—521no—
382C4⋊C8—521no—
383C4⋊C8—521no—
384C22⋊C8—521no—
385C22⋊C8—521no—
386C22⋊C8—521no—
387#97—521no—
388#97—521no—
389C4×C8—521no—
390#95—131no—
391#95—131no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—131no—
396#95—131no—
397#95—131no—
398#95—131no—
399#95C2×#26111yescharacteristic
400#95C2×#26111yescharacteristic
401#95C2×#26111yescharacteristic
402#95C2×#26111yescharacteristic
403#95C2×#26111yescharacteristic
404#95C2×#26111yescharacteristic
405#95C2×#26111yescharacteristic
406C2×C13#238311yescharacteristic
407C2×C13#299211yescharacteristic
408C2×C13#299311yescharacteristic
409C2×C13#299311yescharacteristic
410C2×C13#299511yescharacteristic
411C2×C13#299511yescharacteristic
412C2×C13#299511yescharacteristic
413D13—81no—
414C24—131no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4C22×#26111yescharacteristic
429C22×C4C22×#26111yescharacteristic
430C22×C4C22×#26111yescharacteristic
431C22×C4C22×#26111yescharacteristic
432C22×C4C22×#26111yescharacteristic
433C22×C4C22×#26111yescharacteristic
434C22×C4C22×#26111yescharacteristic
435M16—524no—
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—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C4⋊C4—521no—
463C4⋊C4—521no—
464C4⋊C4—521no—
465C4⋊C4—521no—
466C22⋊C4—262no—
467C22⋊C4—521no—
468C22⋊C4—521no—
469C22⋊C4—521no—
470C22⋊C4—521no—
471C22⋊C4—521no—
472C42—261no—
473C42—261no—
474C42—261no—
475C42—261no—
476C42—261no—
477C42—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C13#2338211yescharacteristic, complemented, Sylow
485C23—261no—
486C23—261no—
487C23—261no—
488C23—261no—
489C23—261no—
490C23—261no—
491C23—261no—
492C23C23×#26111yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
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—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—131no—
515C2×C4—131no—
516C2×C4—131no—
517C2×C4—131no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—132no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C8—521no—
543C8—521no—
544C8—521no—
545C8—521no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C22—521no—
551C22—521no—
552C22—521no—
553C22—521no—
554C22—521no—
555C22—521no—
556C22—521no—
557C22D13⋊#13111yescharacteristic
558C22#1171962911yescharacteristic
559C22#1171962911yescharacteristic
560C22#1171962911yescharacteristic
561C22#1171963111yescharacteristic
562C22#1171963111yescharacteristic
563C22#1171963111yescharacteristic
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—131no—
572C4—131no—
573C4—131no—
574C4—131no—
575C4—262no—
576C4—521no—
577C4—521no—
578C4—521no—
579C4—521no—
580C4—521no—
581C2—1041no—
582C2#1313138311yescharacteristic
583C2#1313177411yescharacteristic
584C2#1313178011yescharacteristic
585C2#1313178011yescharacteristic
586C2#1313179111yescharacteristic
587C2#1313179111yescharacteristic
588C2#1313179111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#401C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenter#401#261
hypocenterC13#23382
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. #13130937C2semidirect
2. #13130936C2semidirect
3. #13130935C2semidirect
7. #13130895C2semidirect
8. #13130894C2semidirect
9. #13130890C2semidirect
13. #13130770C2semidirect
14. #13130765C2semidirect
484. C13#23382semidirect

Maximal subgroups

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

subgroupindex
#131309372
#131309362
#131309352
#131309122
#131309082
#131308952
#131308942
#131308902
#131307842
#131307822
#131307702
#131307652
#131181392
#2338213