Finite Group Databasebeta

← #15871175

Subgroups — #15871175

Order 3328.

702 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#13118137C211yesmaximal, characteristic
2#13115450C211yesmaximal, characteristic
3#13115449C211yesmaximal, characteristic
4#13115448C211yesmaximal, characteristic
5#13115403C211yesmaximal, characteristic, complemented
6#13115401C211yesmaximal, characteristic, complemented
7#13114980C211yesmaximal, characteristic, complemented
8#13114701C211yesmaximal, characteristic, complemented
9C4⋊C4×#1055C211yesmaximal, characteristic, complemented
10#13114697C211yesmaximal, characteristic, complemented
11#13114606C211yesmaximal, characteristic
12#13114606C211yesmaximal, characteristic
13#13114606C211yesmaximal, characteristic
14#13114524C211yesmaximal, characteristic, complemented
15C13×#1917C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#97C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88060C2211yescharacteristic
21C2×#88060C2211yescharacteristic
22C2×#88060C2211yescharacteristic
23C2×#88055C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25C2×#88054C2211yescharacteristic
26C2×C8×Dic13C2211yescharacteristic
27C2×C8×Dic13C2211yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29#11718655C411yescharacteristic
30#11718654C411yescharacteristic
31#11718647C411yescharacteristic
32#11718643C411yescharacteristic
33C4×#6103C2211yescharacteristic
34C4×#6103C2211yescharacteristic
35C4×#6103C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37#11718593C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40C2×C4×#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718336C411yescharacteristic
44#11718335C411yescharacteristic
45C13⋊#401C411yescharacteristic
46#11718321C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
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×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C2×C8×D13—22no—
87C2×C8×D13—22no—
88C2×C8×D13—22no—
89C13×C4⋊C8—22no—
90C13×#97—22no—
91C13×#95C2×C411yescharacteristic
92C13×#95C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×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#88071C2×C411yescharacteristic
107#88060—22no—
108#88060—22no—
109#88060—22no—
110#88055—22no—
111#88055—22no—
112#88054—22no—
113C8×Dic13—22no—
114C8×Dic13—22no—
115C8×Dic13—22no—
116C4⋊#1055—22no—
117C4×#1055—22no—
118C4×#1055—22no—
119C4×#1055—22no—
120#21668—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#4112yes—
153C2×C8×C13#4112yes—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
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—22no—
167#6103—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170#6101—22no—
171#6101—22no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
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#4112yes—
187C2×#1055#4112yes—
188C2×#1055#4112yes—
189C2×#1055#4112yes—
190C8×D13—44no—
191#2401—131no—
192#1924—131no—
193#1924—131no—
194#1924—131no—
195#1917—131no—
196#1917—131no—
197#1917D1311yescharacteristic, complemented
198#1840—131no—
199C8×C4⋊C4—131no—
200C8×C4⋊C4—131no—
201C8×C4⋊C4—131no—
202C8×C22⋊C4—131no—
203C8×C22⋊C4—131no—
204C8×C22⋊C4—131no—
205#1726—131no—
206C23×C13C23×C411yescharacteristic
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13#13112yes—
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#13112yes—
231C2×C4×C13#13112yes—
232C2×C4×C13C2×#4111yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
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—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13#13112yes—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C8×C13—22no—
264C8×C13—22no—
265C8×C13—41no—
266C8×C13—41no—
267#1055—22no—
268#1055—41no—
269#1055—41no—
270#1055#12614yes—
271C23×C8—131no—
272C2×C4⋊C8—131no—
273C2×C4⋊C8—131no—
274C2×C4⋊C8C2×D1311yescharacteristic
275C2×C22⋊C8—131no—
276C2×C22⋊C8—131no—
277C2×C22⋊C8—131no—
278C2×#97—131no—
279C2×#97—131no—
280C2×#97C2×D1311yescharacteristic
281C2×C4×C8—131no—
282C2×C4×C8—131no—
283C2×C4×C8—131no—
284C2×C4×C8—131no—
285C2×C4×C8—131no—
286C2×C4×C8—131no—
287#401—131no—
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⋊C4C2×D1311yescharacteristic
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#336C2×D1311yescharacteristic
311#336C2×D1311yescharacteristic
312#336C2×D1311yescharacteristic
313#336C2×D1311yescharacteristic
314C22×C13C4×#4111yescharacteristic
315C22×C13C4×#4111yescharacteristic
316C22×C13C4×#4111yescharacteristic
317C22×C13C2×#13111yescharacteristic
318C22×C13C2×#13111yescharacteristic
319C22×C13C2×#13111yescharacteristic
320C22×C13C2×#13111yescharacteristic
321C2×D13—22no—
322C2×D13—22no—
323C2×D13—22no—
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13C2×#12611yescharacteristic
335C4×C13#52911yescharacteristic
336C4×C13#52911yescharacteristic
337C4×C13#52911yescharacteristic
338Dic13—22no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C23×C4—131no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—262no—
351C22×C8—262no—
352C22×C8—262no—
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4C4×D1311yescharacteristic
362C2×C4⋊C4C4×D1311yescharacteristic
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×C42C22×D1311yescharacteristic
373C2×C42C22×D1311yescharacteristic
374C2×C42C22×D1311yescharacteristic
375C4⋊C8—22no—
376C4⋊C8—262no—
377C4⋊C8—262no—
378C22⋊C8—262no—
379C22⋊C8—262no—
380C22⋊C8—262no—
381#97—22no—
382#97—262no—
383#97—262no—
384C4×C8—262no—
385C4×C8—262no—
386C4×C8—262no—
387C4×C8—262no—
388C4×C8—262no—
389C4×C8—262no—
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#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95C4×D1311yescharacteristic
405#95C4×D1311yescharacteristic
406C2×C13C4×#12611yescharacteristic
407C2×C13#296611yescharacteristic
408C2×C13#296611yescharacteristic
409C2×C13#296611yescharacteristic
410C2×C13#296611yescharacteristic
411C2×C13#296611yescharacteristic
412C2×C13#296611yescharacteristic
413D13—42no—
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×C4C2×C4×D1311yescharacteristic
429C22×C4C2×C4×D1311yescharacteristic
430C22×C4C2×C4×D1311yescharacteristic
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4C2×C4×D1311yescharacteristic
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—132no—
446C2×C8—132no—
447C2×C8—132no—
448C2×C8—132no—
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—524no—
458C2×C8#612912yes—
459C2×C8#613112yes—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—262no—
463C4⋊C4—262no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C22⋊C4—262no—
467C22⋊C4—262no—
468C22⋊C4—262no—
469C22⋊C4—262no—
470C22⋊C4—262no—
471C22⋊C4—262no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C13#2166811yescharacteristic, complemented, Sylow
485C23—132no—
486C23—261no—
487C23—261no—
488C23—261no—
489C23—261no—
490C23—261no—
491C23—261no—
492C23C22×C4×D1311yescharacteristic
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—132no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
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—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4#8816112yes—
535C2×C4#8816112yes—
536C2×C4C2×#612911yescharacteristic
537C2×C4C2×#613111yescharacteristic
538C2×C4#41×D1311yescharacteristic
539C2×C4#41×D1311yescharacteristic
540C2×C4#41×D1311yescharacteristic
541C2×C4#41×D1311yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C8—134no—
547C8—262no—
548C8—521no—
549C8—521no—
550C22—262no—
551C22—262no—
552C22—262no—
553C22—521no—
554C22—521no—
555C22—521no—
556C22—521no—
557C22#1171922711yescharacteristic
558C22C4×#612911yescharacteristic
559C22C4×#613111yescharacteristic
560C22C2×#8816111yescharacteristic
561C22C2×#8816111yescharacteristic
562C22D13×#13111yescharacteristic
563C22D13×#13111yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—262no—
571C4—521no—
572C4—521no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4#1171932911yescharacteristic
578C4#1171935411yescharacteristic
579C4#1171939611yescharacteristic
580C4D13×#12611yescharacteristic
581C2—522no—
582C2#1311738611yescharacteristic
583C2#1312380511yescharacteristic
584C2#1312380611yescharacteristic
585C2#1312380911yescharacteristic
586C2#1312381011yescharacteristic
587C2#1312381011yescharacteristic
588C2#1312381411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1917C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1917D13
hypocenterC13#21668
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
5. #13115403C2semidirect
6. #13115401C2semidirect
7. #13114980C2semidirect
8. #13114701C2semidirect
9. C4⋊C4×#1055C2semidirect
10. #13114697C2semidirect
14. #13114524C2semidirect
15. C13×#1917C2semidirect
197. #1917D13semidirect
484. C13#21668semidirect

Maximal subgroups

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

subgroupindex
#131181372
#131154502
#131154492
#131154482
#131154032
#131154012
#131149802
#131147012
C4⋊C4×#10552
#131146972
#131146062
#131145242
C13×#19172
#2166813