Finite Group Databasebeta

← #15921877

Subgroups — #15921877

Order 3328.

750 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#13119869C211yesmaximal, characteristic, complemented
2#13117781C211yesmaximal, characteristic
3#13116365C211yesmaximal, characteristic
4#13116361C211yesmaximal, characteristic
5#13116223C211yesmaximal, characteristic
6#13116219C211yesmaximal, characteristic
7#13115593C211yesmaximal, characteristic, complemented
8#13115591C211yesmaximal, characteristic, complemented
9#13115551C211yesmaximal, characteristic, complemented
10#13115410C211yesmaximal, characteristic, complemented
11#13115407C211yesmaximal, characteristic, complemented
12#13114994C211yesmaximal, characteristic, complemented
13#13114835C211yesmaximal, characteristic
14#13114650C211yesmaximal, characteristic
15C13×#1947C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88143—21no—
18C2×#88126—21no—
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C13×#384C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30#11718649C2211yescharacteristic
31#11718646C2211yescharacteristic
32#11718645—21no—
33#11718641—21no—
34#11718637C2211yescharacteristic
35#11718637C2211yescharacteristic
36#11718637C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C4⋊C4×Dic13C2211yescharacteristic
39#11718633—21no—
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718601—21no—
46#11718600C2211yescharacteristic
47C4×#6101C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718330—21no—
50#11718328—21no—
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
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×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×#6101—21no—
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101D411yescharacteristic
88C2×#6101D411yescharacteristic
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95#88147—22no—
96#88147Q814yes—
97#88143—44no—
98#88126—44no—
99C13×#107—41no—
100C13×#107—41no—
101C13×C4⋊C8—22no—
102C13×#95—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071D411yescharacteristic
108#88071D411yescharacteristic
109#88061—22no—
110#88061—41no—
111#88058—41no—
112#88054—22no—
113#88054—22no—
114C8×Dic13—22no—
115#88049—22no—
116#88049—41no—
117#88047—22no—
118#88047—22no—
119#88047—41no—
120#26086—131nomaximal, Sylow
121C23×D13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52C2×Q812yes—
142C2×C4×D13—24no—
143C2×C4×D13—42no—
144C2×C4×D13—42no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13#4112yes—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—81no—
160C13×C4⋊C4C2×Q812yes—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—42no—
164#6103—24no—
165#6103—42no—
166#6103—42no—
167#6103—81no—
168#6103—81no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—42no—
176#6101—22no—
177#6101—42no—
178#6101—42no—
179#6101—42no—
180#6101—42no—
181#6101—81no—
182#6101—81no—
183#6101—81no—
184#6101D814yes—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—42no—
188C4×Dic13—42no—
189C4×Dic13C2×Q812yes—
190C4×Dic13#4112yes—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055#4112yes—
197#2552—131no—
198#2354—131no—
199#2093—131no—
200#2093—131no—
201#2067—131no—
202#2067—131no—
203#1947—131no—
204#1947—131no—
205#1947D1311yescharacteristic, complemented
206#1939—131no—
207#1918—131no—
208#1918—131no—
209#1845—131no—
210#1802—131no—
211C4×#102—131no—
212C23×C13C22×D411yescharacteristic
213C22×D13—22no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13C2×D812yes—
238C2×C4×C13C22×Q811yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13H(5,𝔽2)11yescharacteristic
243C2×C4×C132−1+411yescharacteristic
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—41no—
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×Dic13C22⋊Q812yes—
261C2×Dic13C22⋊Q812yes—
262C2×Dic13C2×D812yes—
263C2×Dic13C2×D812yes—
264C2×Dic13#13712yes—
265D52—22no—
266D52—22no—
267D52—41no—
268D52—41no—
269C4×D13—48no—
270C8×C13—22no—
271C8×C13—41no—
272#1055—22no—
273#1055—41no—
274C2×#125—261no—
275C2×C4×D4—131no—
276C2×#117—261no—
277C2×#107—131no—
278C2×#107—131no—
279C2×#107—131no—
280C2×#107—131no—
281C2×#107C2×D1311yescharacteristic
282C2×#107C2×D1311yescharacteristic
283C2×C4⋊C8—131no—
284C2×C4⋊C8—131no—
285C2×C4⋊C8C2×D1311yescharacteristic
286C2×#102—131no—
287C2×#102—131no—
288C2×#102—131no—
289C2×#102—131no—
290C2×C4×C8—131no—
291#398—261no—
292#398—261no—
293#390—131no—
294#390—131no—
295#389—131no—
296#389—131no—
297#389—261no—
298#388—261no—
299#388—261no—
300#384—131no—
301#384—131no—
302#384—131no—
303#384C2×D1311yescharacteristic
304#380—261no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4C2×D1311yescharacteristic
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340C2×D1311yescharacteristic
314#340C2×D1311yescharacteristic
315#336—131no—
316#336—131no—
317C22×C13C2×C22⋊Q811yescharacteristic
318C22×C13#54711yescharacteristic
319C22×C13#55011yescharacteristic
320C22×C13C22×D811yescharacteristic
321C22×C13C2×#13711yescharacteristic
322C22×C13#57611yescharacteristic
323C22×C13#57811yescharacteristic
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—42no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—81no—
331C4×C13—22no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13#53311yescharacteristic
338C4×C13#54411yescharacteristic
339C4×C13#55211yescharacteristic
340C4×C13#55311yescharacteristic
341Dic13—22no—
342Dic13—22no—
343Dic13—41no—
344Dic13—81no—
345Dic13—81no—
346Dic13—81no—
347Dic13#47414yes—
348C22×D4—131no—
349C23×C4—261no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354#125—524no—
355C4×D4—134no—
356C4×D4—262no—
357#117—524no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—21no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—261no—
386C2×C42—261no—
387C2×C42C22×D1311yescharacteristic
388#107—41no—
389#107—41no—
390#107—262no—
391#107—262no—
392#107—521no—
393#107—521no—
394C4⋊C8—22no—
395C4⋊C8—262no—
396C4⋊C8—262no—
397#102—262no—
398#102—262no—
399#102—521no—
400#102—521no—
401C4×C8—262no—
402#95—21no—
403#95—131no—
404#95—131no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409C2×C13#244111yescharacteristic
410C2×C13C2×#47411yescharacteristic
411C2×C13#308311yescharacteristic
412C2×C13#333411yescharacteristic
413C2×C13#335711yescharacteristic
414C2×C13#339111yescharacteristic
415C2×C13#339811yescharacteristic
416D13—82no—
417C24—261no—
418C2×D4—132no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—264no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—522no—
437C22×C4—522no—
438C22×C4D4×D1311yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—132no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8#612712yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—134no—
463C4⋊C4—262no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—522no—
471C4⋊C4—522no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C4⋊C4—522no—
475C4⋊C4—1041no—
476C4⋊C4—1041no—
477C4⋊C4—1041no—
478C4⋊C4Q8×D1312yes—
479C22⋊C4—264no—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C22⋊C4—1041no—
483C22⋊C4—1041no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—132no—
488C42—132no—
489C42—261no—
490C42—261no—
491C42—522no—
492C42—522no—
493C13#2608611yescharacteristic, complemented, Sylow
494C23—262no—
495C23—521no—
496C23—521no—
497C23—521no—
498C23—521no—
499C23—521no—
500C23—521no—
501C23C2×D4×D1311yescharacteristic
502D4—262no—
503D4—262no—
504D4—521no—
505D4—521no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
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—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—132no—
524C2×C4—132no—
525C2×C4—132no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—528no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4D8×D1312yes—
546C2×C4C2×#612711yescharacteristic
547C2×C4#8825111yescharacteristic
548C2×C4C2×Q8×D1311yescharacteristic
549C2×C4#8825411yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4#41×D1311yescharacteristic
552C8—22no—
553C8—41no—
554C8—262no—
555C8—521no—
556C22—522no—
557C22—522no—
558C22—522no—
559C22—1041no—
560C22—1041no—
561C22—1041no—
562C22—1041no—
563C22#1171921211yescharacteristic
564C22#1171930411yescharacteristic
565C22D13×C22⋊Q811yescharacteristic
566C22C2×D8×D1311yescharacteristic
567C22#1171947111yescharacteristic
568C22#1171947911yescharacteristic
569C22D13×#13711yescharacteristic
570C4—22no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—134no—
577C4—262no—
578C4—262no—
579C4—521no—
580C4—1041no—
581C4—1041no—
582C4—1041no—
583C4#1171924511yescharacteristic
584C4#1171928311yescharacteristic
585C4#1171939811yescharacteristic
586C4#1171943411yescharacteristic
587C2—1042no—
588C2#1311854611yescharacteristic
589C2D13×#47411yescharacteristic
590C2#1312468411yescharacteristic
591C2#1312718111yescharacteristic
592C2#1312745811yescharacteristic
593C2#1312780711yescharacteristic
594C2#1312786211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1947C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#1947D13
hypocenterC13#26086
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. #13119869C2semidirect
7. #13115593C2semidirect
8. #13115591C2semidirect
9. #13115551C2semidirect
10. #13115410C2semidirect
11. #13115407C2semidirect
12. #13114994C2semidirect
15. C13×#1947C2semidirect
205. #1947D13semidirect
493. C13#26086semidirect

Maximal subgroups

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

subgroupindex
#131198692
#131177812
#131163652
#131163612
#131162232
#131162192
#131155932
#131155912
#131155512
#131154102
#131154072
#131149942
#131148352
#131146502
C13×#19472
#2608613