Finite Group Databasebeta

← #15873136

Subgroups — #15873136

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117329C211yesmaximal, characteristic
2#13115449C211yesmaximal, characteristic
3#13115448C211yesmaximal, characteristic
4#13115443C211yesmaximal, characteristic
5#13115440C211yesmaximal, characteristic
6#13115401C211yesmaximal, characteristic, complemented
7#13115395C211yesmaximal, characteristic, complemented
8#13115392C211yesmaximal, characteristic, complemented
9#13114987C211yesmaximal, characteristic, complemented
10#13114951C211yesmaximal, characteristic, complemented
11#13114819C211yesmaximal, characteristic
12#13114819C211yesmaximal, characteristic
13#13114696C211yesmaximal, characteristic, complemented
14#13114692C211yesmaximal, characteristic, complemented
15C13×#1917C211yesmaximal, characteristic, complemented
16C2×#88126C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#97C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88060C2211yescharacteristic
21C2×#88060C2211yescharacteristic
22C2×#88060C2211yescharacteristic
23C2×#88060C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25C2×#88054C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32#11718651C411yescharacteristic
33#11718651C411yescharacteristic
34#11718639C411yescharacteristic
35#11718639C411yescharacteristic
36C4×#6103C2211yescharacteristic
37C4×#6103C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718593C2211yescharacteristic
40C42×Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718331C411yescharacteristic
44#11718331C411yescharacteristic
45#11718316C411yescharacteristic
46#11718316C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C4⋊C4C2×C411yescharacteristic
65C2×C13×C4⋊C4C2×C411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×#6103C2×C411yescharacteristic
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90#88126—22no—
91#88126—22no—
92C13×C4⋊C8—41no—
93C13×#97—41no—
94C13×#95C2×C411yescharacteristic
95C13×#95C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×C411yescharacteristic
98#88071C2×C411yescharacteristic
99#88071C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88060—41no—
107#88060—41no—
108#88060—41no—
109#88060—41no—
110#88055—41no—
111#88054—22no—
112#88054—22no—
113#88054—22no—
114#88054—22no—
115#88054—41no—
116#88054—41no—
117C8×Dic13—41no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#21929—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×C13C2411yescharacteristic
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
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×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—41no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162#6103—22no—
163#6103—22no—
164#6103—22no—
165#6103—22no—
166#6103—41no—
167#6103—41no—
168C4⋊Dic13—22no—
169C4⋊Dic13—41no—
170#6101—22no—
171#6101—22no—
172C4×Dic13—22no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—22no—
178C4×Dic13—41no—
179C4×Dic13—41no—
180C4×Dic13#4112yes—
181C4×Dic13#4112yes—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194#2298—131no—
195#1924—131no—
196#1924—131no—
197#1923—131no—
198#1923—131no—
199#1917—131no—
200#1917D1311yescharacteristic, complemented
201#1916—131no—
202#1916—131no—
203#1842—131no—
204#1831—131no—
205#1798—131no—
206#1798—131no—
207#1768—131no—
208#1768—131no—
209C23×C13C23×C411yescharacteristic
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13—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#13112yes—
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13H(5,𝔽2)11yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
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—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13#11712yes—
260C2×Dic13#11712yes—
261C2×Dic13#13112yes—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269C8×C13—41no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274C2×#117—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×C4⋊C8—131no—
282C2×C4⋊C8C2×D1311yescharacteristic
283C2×C22⋊C8—131no—
284C2×C22⋊C8—131no—
285C2×C22⋊C8—131no—
286C2×C22⋊C8—131no—
287C2×#97—131no—
288C2×#97C2×D1311yescharacteristic
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291#388—131no—
292#388—131no—
293#388—131no—
294#388—131no—
295#387—131no—
296#387—131no—
297#387—131no—
298#387—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4C2×D1311yescharacteristic
301C4×C22⋊C4—131no—
302C4×C22⋊C4—131no—
303#376—131no—
304C43—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#336C2×D1311yescharacteristic
314#336C2×D1311yescharacteristic
315#336C2×D1311yescharacteristic
316#336C2×D1311yescharacteristic
317C22×C13C2×#11711yescharacteristic
318C22×C13#52011yescharacteristic
319C22×C13#52011yescharacteristic
320C22×C13C2×#13111yescharacteristic
321C22×C13C2×#13111yescharacteristic
322C22×C13#56811yescharacteristic
323C22×C13#56811yescharacteristic
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C2×D13—41no—
331C4×C13—22no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13#54011yescharacteristic
338C4×C13#54111yescharacteristic
339C4×C13#54211yescharacteristic
340C4×C13#54211yescharacteristic
341Dic13—22no—
342Dic13—22no—
343Dic13—22no—
344Dic13—41no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348C23×C4—131no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#117—262no—
358#117—262no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4C4×D1311yescharacteristic
364C2×C4⋊C4C4×D1311yescharacteristic
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C22⋊C4—131no—
370C2×C22⋊C4—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42C22×D1311yescharacteristic
379C2×C42C22×D1311yescharacteristic
380C2×C42C22×D1311yescharacteristic
381C4⋊C8—41no—
382C4⋊C8—262no—
383C4⋊C8—262no—
384C4⋊C8—262no—
385C4⋊C8—262no—
386C4⋊C8—521no—
387C4⋊C8—521no—
388C4⋊C8—521no—
389C22⋊C8—521no—
390C22⋊C8—521no—
391C22⋊C8—521no—
392C22⋊C8—521no—
393#97—41no—
394#97—521no—
395C4×C8—521no—
396C4×C8—521no—
397#95—131no—
398#95—131no—
399#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95—131no—
405#95—131no—
406#95—131no—
407#95C4×D1311yescharacteristic
408#95C4×D1311yescharacteristic
409C2×C13#231411yescharacteristic
410C2×C13#292511yescharacteristic
411C2×C13#292511yescharacteristic
412C2×C13#299211yescharacteristic
413C2×C13#299311yescharacteristic
414C2×C13#299411yescharacteristic
415C2×C13#299511yescharacteristic
416D13—81no—
417C24—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4C2×C4×D1311yescharacteristic
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C2×C4×D1311yescharacteristic
435C22×C4C2×C4×D1311yescharacteristic
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
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—
460C2×C8—261no—
461C2×C8—261no—
462C4⋊C4—22no—
463C4⋊C4—41no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C4⋊C4—262no—
467C4⋊C4—521no—
468C22⋊C4—262no—
469C22⋊C4—262no—
470C22⋊C4—262no—
471C22⋊C4—262no—
472C22⋊C4—521no—
473C22⋊C4—521no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—132no—
481C42—132no—
482C42—262no—
483C42—262no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—521no—
489C42—521no—
490C13#2192911yescharacteristic, complemented, Sylow
491C23—261no—
492C23—261no—
493C23—261no—
494C23—261no—
495C23—261no—
496C23—261no—
497C23—261no—
498C23C22×C4×D1311yescharacteristic
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—21no—
515C2×C4—21no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—261no—
520C2×C4—261no—
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—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4#8816112yes—
542C2×C4#8825111yescharacteristic
543C2×C4#8825411yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C2×C4#8825611yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8—521no—
556C22—521no—
557C22—521no—
558C22—521no—
559C22—521no—
560C22—521no—
561C22—521no—
562C22—521no—
563C22D13×#11711yescharacteristic
564C22#1171925111yescharacteristic
565C22#1171927911yescharacteristic
566C22C2×#8816111yescharacteristic
567C22#1171945011yescharacteristic
568C22D13×#13111yescharacteristic
569C22#1171945511yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—262no—
577C4—262no—
578C4—262no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4#1171934511yescharacteristic
584C4#1171936811yescharacteristic
585C4#1171940111yescharacteristic
586C4#1171941511yescharacteristic
587C2—1041no—
588C2#1311744211yescharacteristic
589C2#1312349911yescharacteristic
590C2#1312350311yescharacteristic
591C2#1312397611yescharacteristic
592C2#1312398211yescharacteristic
593C2#1312399911yescharacteristic
594C2#1312400511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1917C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1917D13
hypocenterC13#21929
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
6. #13115401C2semidirect
7. #13115395C2semidirect
8. #13115392C2semidirect
9. #13114987C2semidirect
10. #13114951C2semidirect
13. #13114696C2semidirect
14. #13114692C2semidirect
15. C13×#1917C2semidirect
200. #1917D13semidirect
490. C13#21929semidirect

Maximal subgroups

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

subgroupindex
#131173292
#131154492
#131154482
#131154432
#131154402
#131154012
#131153952
#131153922
#131149872
#131149512
#131148192
#131146962
#131146922
C13×#19172
#2192913